Import sparskit_2.0.0.orig.tar.gz

[dgit import orig sparskit_2.0.0.orig.tar.gz]

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diff --git a/BLASSM/README b/BLASSM/README
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+++ b/BLASSM/README
@@ -0,0 +1,83 @@
+c----------------------------------------------------------------------c
+c                                                                      c
+c                BLASSM  and MATVEC MODULES                            c
+c                                                                      c
+c----------------------------------------------------------------------c
+c                                                                      c 
+c    This directory contains the BLASSM and MATVEC modules of SPARSKIT c
+c                                                                      c
+c----------------------------------------------------------------------c
+c                                                                      c
+c                Current contents                                      c 
+c----------------------------------------------------------------------c
+c                                                                      c 
+c    blassm.f : contains the latest version of the basc linear algerba c
+c               routines for sparse matrices.                          c
+c    								       c
+c    tester.f : is a main program to test the routines and the paths   c
+c                                                                      c
+c    matvec.f : contains the subroutines in the module matvec          c
+c                                                                      c
+c    rmatvec.f: a test program that runs all the routines in matvec    c
+c                                                                      c
+c----------------------------------------------------------------------c
+c                                                                      c
+c    makefile : make file for tester.ex (tests blassm.f) and mvec.ex   c
+c               (tests routines in matvec.f)                           c
+c                                                                      c
+c----------------------------------------------------------------------c
+c----------------------------------------------------------------------c   
+c----------------------------------------------------------------------c
+c              current status of blassm.f                              c
+c                                                                      c
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c        BASIC LINEAR ALGEBRA FOR SPARSE MATRICES. BLASSM MODULE       c
+c----------------------------------------------------------------------c
+c amub   :   computes     C = A*B                                      c
+c aplb   :   computes     C = A+B                                      c
+c aplsb  :   computes     C = A + s B                                  c
+c apmbt  :   Computes     C = A +/- transp(B)                          c
+c aplsbt :   Computes     C = A + s * transp(B)                        c
+c diamua :   Computes     C = Diag * A                                 c
+c amudia :   Computes     C = A* Diag                                  c
+c apldia :   Computes     C = A + Diag.                                c
+c aplsca :   Computes     A:= A + s I    (s = scalar)                  c 
+c----------------------------------------------------------------------c 
+c----------------------------------------------------------------------c
+c                                                                      c
+c              current status of matvec.f                              c
+c                                                                      c
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c          BASIC MATRIX-VECTOR OPERATIONS - MATVEC MODULE              c
+c         Matrix-vector Mulitiplications and Triang. Solves            c
+c----------------------------------------------------------------------c
+c contents:
+c----------                                                            c
+c 1) Matrix-vector products:                                           c
+c---------------------------                                           c
+c amux  : A times a vector. Compressed Sparse Row (CSR) format.        c
+c amuxms: A times a vector. Modified Compress Sparse Row format.       c
+c atmux : Transp(A) times a vector. CSR format.                        c
+c amuxe : A times a vector. Ellpack/Itpack (ELL) format.               c
+c amuxd : A times a vector. Diagonal (DIA) format.                     c
+c amuxj : A times a vector. Jagged Diagonal (JAD) format.              c
+c vbrmv : Sparse matrix-full vector product, in VBR format             c
+c                                                                      c
+c 2) Triangular system solutions:                                      c
+c-------------------------------                                       c
+c lsol  : Unit Lower Triang. solve. Compressed Sparse Row (CSR) format.c
+c ldsol : Lower Triang. solve.  Modified Sparse Row (MSR) format.      c
+c lsolc : Unit Lower Triang. solve. Comp. Sparse Column (CSC) format.  c
+c ldsolc: Lower Triang. solve. Modified Sparse Column (MSC) format.    c
+c ldsoll: Lower Triang. solve with level scheduling. MSR format.       c
+c usol  : Unit Upper Triang. solve. Compressed Sparse Row (CSR) format.c
+c udsol : Upper Triang. solve.  Modified Sparse Row (MSR) format.      c
+c usolc : Unit Upper Triang. solve. Comp. Sparse Column (CSC) format.  c
+c udsolc: Upper Triang. solve.  Modified Sparse Column (MSC) format.   c
+c----------------------------------------------------------------------c
+
+
diff --git a/BLASSM/blassm.f b/BLASSM/blassm.f
new file mode 100644
index 0000000..899deb3
--- /dev/null
+++ b/BLASSM/blassm.f
@@ -0,0 +1,1116 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c        BASIC LINEAR ALGEBRA FOR SPARSE MATRICES. BLASSM MODULE       c
+c----------------------------------------------------------------------c
+c amub   :   computes     C = A*B                                      c
+c aplb   :   computes     C = A+B                                      c
+c aplb1  :   computes     C = A+B  [Sorted version: A, B, C sorted]    c
+c aplsb  :   computes     C = A + s B                                  c
+c aplsb1 :   computes     C = A+sB  [Sorted version: A, B, C sorted]   c
+c apmbt  :   Computes     C = A +/- transp(B)                          c
+c aplsbt :   Computes     C = A + s * transp(B)                        c
+c diamua :   Computes     C = Diag * A                                 c
+c amudia :   Computes     C = A* Diag                                  c
+c aplsca :   Computes     A:= A + s I    (s = scalar)                  c 
+c apldia :   Computes     C = A + Diag.                                c
+c----------------------------------------------------------------------c 
+c Note: this module still incomplete.                                  c
+c----------------------------------------------------------------------c
+       subroutine amub (nrow,ncol,job,a,ja,ia,b,jb,ib,
+     *                  c,jc,ic,nzmax,iw,ierr) 
+      real*8 a(*), b(*), c(*) 
+      integer ja(*),jb(*),jc(*),ia(nrow+1),ib(*),ic(*),iw(ncol)
+c-----------------------------------------------------------------------
+c performs the matrix by matrix product C = A B 
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow  = integer. The row dimension of A = row dimension of C
+c ncol  = integer. The column dimension of B = column dimension of C
+c job   = integer. Job indicator. When job = 0, only the structure
+c                  (i.e. the arrays jc, ic) is computed and the
+c                  real values are ignored.
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format.
+c 
+c b, 
+c jb, 
+c ib    =  Matrix B in compressed sparse row format.
+c
+c nzmax = integer. The  length of the arrays c and jc.
+c         amub will stop if the result matrix C  has a number 
+c         of elements that exceeds exceeds nzmax. See ierr.
+c 
+c on return:
+c----------
+c c, 
+c jc, 
+c ic    = resulting matrix C in compressed sparse row sparse format.
+c           
+c ierr  = integer. serving as error message. 
+c         ierr = 0 means normal return,
+c         ierr .gt. 0 means that amub stopped while computing the
+c         i-th row  of C with i=ierr, because the number 
+c         of elements in C exceeds nzmax.
+c
+c work arrays:
+c------------
+c iw    = integer work array of length equal to the number of
+c         columns in A.
+c Note: 
+c-------
+c   The row dimension of B is not needed. However there is no checking 
+c   on the condition that ncol(A) = nrow(B). 
+c
+c----------------------------------------------------------------------- 
+      real*8 scal 
+      logical values
+      values = (job .ne. 0) 
+      len = 0
+      ic(1) = 1 
+      ierr = 0
+c     initialize array iw.
+      do 1 j=1, ncol
+         iw(j) = 0
+ 1    continue
+c
+      do 500 ii=1, nrow 
+c     row i 
+         do 200 ka=ia(ii), ia(ii+1)-1 
+	    if (values) scal = a(ka)
+	    jj   = ja(ka)
+	    do 100 kb=ib(jj),ib(jj+1)-1
+               jcol = jb(kb)
+               jpos = iw(jcol)
+               if (jpos .eq. 0) then
+                  len = len+1
+                  if (len .gt. nzmax) then
+                     ierr = ii
+                     return
+                  endif
+                  jc(len) = jcol
+                  iw(jcol)= len
+                  if (values) c(len)  = scal*b(kb)
+               else
+                  if (values) c(jpos) = c(jpos) + scal*b(kb)
+               endif
+ 100	    continue
+ 200     continue
+         do 201 k=ic(ii), len
+	    iw(jc(k)) = 0
+ 201     continue
+         ic(ii+1) = len+1
+ 500  continue
+      return
+c-------------end-of-amub-----------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine aplb (nrow,ncol,job,a,ja,ia,b,jb,ib,
+     *     c,jc,ic,nzmax,iw,ierr)
+      real*8 a(*), b(*), c(*) 
+      integer ja(*),jb(*),jc(*),ia(nrow+1),ib(nrow+1),ic(nrow+1),
+     *     iw(ncol)
+c-----------------------------------------------------------------------
+c performs the matrix sum  C = A+B. 
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A and B
+c ncol  = integer. The column dimension of A and B.
+c job   = integer. Job indicator. When job = 0, only the structure
+c                  (i.e. the arrays jc, ic) is computed and the
+c                  real values are ignored.
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format.
+c 
+c b, 
+c jb, 
+c ib	=  Matrix B in compressed sparse row format.
+c
+c nzmax	= integer. The  length of the arrays c and jc.
+c         amub will stop if the result matrix C  has a number 
+c         of elements that exceeds exceeds nzmax. See ierr.
+c 
+c on return:
+c----------
+c c, 
+c jc, 
+c ic	= resulting matrix C in compressed sparse row sparse format.
+c	    
+c ierr	= integer. serving as error message. 
+c         ierr = 0 means normal return,
+c         ierr .gt. 0 means that amub stopped while computing the
+c         i-th row  of C with i=ierr, because the number 
+c         of elements in C exceeds nzmax.
+c
+c work arrays:
+c------------
+c iw	= integer work array of length equal to the number of
+c         columns in A.
+c
+c-----------------------------------------------------------------------
+      logical values
+      values = (job .ne. 0) 
+      ierr = 0
+      len = 0
+      ic(1) = 1 
+      do 1 j=1, ncol
+         iw(j) = 0
+ 1    continue
+c     
+      do 500 ii=1, nrow
+c     row i 
+         do 200 ka=ia(ii), ia(ii+1)-1 
+            len = len+1
+            jcol    = ja(ka)
+            if (len .gt. nzmax) goto 999
+            jc(len) = jcol 
+            if (values) c(len)  = a(ka) 
+            iw(jcol)= len
+ 200     continue
+c     
+         do 300 kb=ib(ii),ib(ii+1)-1
+            jcol = jb(kb)
+            jpos = iw(jcol)
+            if (jpos .eq. 0) then
+               len = len+1
+               if (len .gt. nzmax) goto 999
+               jc(len) = jcol
+               if (values) c(len)  = b(kb)
+               iw(jcol)= len
+            else
+               if (values) c(jpos) = c(jpos) + b(kb)
+            endif
+ 300     continue
+         do 301 k=ic(ii), len
+	    iw(jc(k)) = 0
+ 301     continue
+         ic(ii+1) = len+1
+ 500  continue
+      return
+ 999  ierr = ii
+      return
+c------------end of aplb ----------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine aplb1(nrow,ncol,job,a,ja,ia,b,jb,ib,c,jc,ic,nzmax,ierr)
+      real*8 a(*), b(*), c(*) 
+      integer ja(*),jb(*),jc(*),ia(nrow+1),ib(nrow+1),ic(nrow+1)
+c-----------------------------------------------------------------------
+c performs the matrix sum  C = A+B for matrices in sorted CSR format.
+c the difference with aplb  is that the resulting matrix is such that
+c the elements of each row are sorted with increasing column indices in
+c each row, provided the original matrices are sorted in the same way. 
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A and B
+c ncol  = integer. The column dimension of A and B.
+c job   = integer. Job indicator. When job = 0, only the structure
+c                  (i.e. the arrays jc, ic) is computed and the
+c                  real values are ignored.
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format with entries sorted
+c 
+c b, 
+c jb, 
+c ib	=  Matrix B in compressed sparse row format with entries sorted
+c        ascendly in each row   
+c
+c nzmax	= integer. The  length of the arrays c and jc.
+c         amub will stop if the result matrix C  has a number 
+c         of elements that exceeds exceeds nzmax. See ierr.
+c 
+c on return:
+c----------
+c c, 
+c jc, 
+c ic	= resulting matrix C in compressed sparse row sparse format
+c         with entries sorted ascendly in each row. 
+c	    
+c ierr	= integer. serving as error message. 
+c         ierr = 0 means normal return,
+c         ierr .gt. 0 means that amub stopped while computing the
+c         i-th row  of C with i=ierr, because the number 
+c         of elements in C exceeds nzmax.
+c
+c Notes: 
+c-------
+c     this will not work if any of the two input matrices is not sorted
+c-----------------------------------------------------------------------
+      logical values
+      values = (job .ne. 0) 
+      ierr = 0
+      kc = 1
+      ic(1) = kc 
+c
+      do 6 i=1, nrow
+         ka = ia(i)
+         kb = ib(i)
+         kamax = ia(i+1)-1
+         kbmax = ib(i+1)-1 
+ 5       continue 
+         if (ka .le. kamax) then
+            j1 = ja(ka)
+         else
+            j1 = ncol+1
+         endif
+         if (kb .le. kbmax) then 
+            j2 = jb(kb)         
+         else 
+            j2 = ncol+1
+         endif
+c
+c     three cases
+c     
+         if (kc .gt. nzmax) goto 999
+         if (j1 .eq. j2) then 
+            if (values) c(kc) = a(ka)+b(kb)
+            jc(kc) = j1
+            ka = ka+1
+            kb = kb+1
+            kc = kc+1
+         else if (j1 .lt. j2) then
+            jc(kc) = j1
+            if (values) c(kc) = a(ka)
+            ka = ka+1
+            kc = kc+1
+         else if (j1 .gt. j2) then
+            jc(kc) = j2
+            if (values) c(kc) = b(kb)
+            kb = kb+1
+            kc = kc+1
+         endif
+         if (ka .le. kamax .or. kb .le. kbmax) goto 5
+         ic(i+1) = kc
+ 6    continue
+      return
+ 999  ierr = i 
+      return
+c------------end-of-aplb1----------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine aplsb (nrow,ncol,a,ja,ia,s,b,jb,ib,c,jc,ic,
+     *     nzmax,ierr)
+      real*8 a(*), b(*), c(*), s
+      integer ja(*),jb(*),jc(*),ia(nrow+1),ib(nrow+1),ic(nrow+1)
+c-----------------------------------------------------------------------
+c performs the operation C = A+s B for matrices in sorted CSR format.
+c the difference with aplsb is that the resulting matrix is such that
+c the elements of each row are sorted with increasing column indices in
+c each row, provided the original matrices are sorted in the same way. 
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A and B
+c ncol  = integer. The column dimension of A and B.
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format with entries sorted
+c
+c s	= real. scalar factor for B.
+c 
+c b, 
+c jb, 
+c ib	=  Matrix B in compressed sparse row format with entries sorted
+c        ascendly in each row   
+c
+c nzmax	= integer. The  length of the arrays c and jc.
+c         amub will stop if the result matrix C  has a number 
+c         of elements that exceeds exceeds nzmax. See ierr.
+c 
+c on return:
+c----------
+c c, 
+c jc, 
+c ic	= resulting matrix C in compressed sparse row sparse format
+c         with entries sorted ascendly in each row. 
+c	    
+c ierr	= integer. serving as error message. 
+c         ierr = 0 means normal return,
+c         ierr .gt. 0 means that amub stopped while computing the
+c         i-th row  of C with i=ierr, because the number 
+c         of elements in C exceeds nzmax.
+c
+c Notes: 
+c-------
+c     this will not work if any of the two input matrices is not sorted
+c-----------------------------------------------------------------------
+      ierr = 0
+      kc = 1
+      ic(1) = kc 
+c
+c     the following loop does a merge of two sparse rows + adds  them.
+c 
+      do 6 i=1, nrow
+         ka = ia(i)
+         kb = ib(i)
+         kamax = ia(i+1)-1
+         kbmax = ib(i+1)-1 
+ 5       continue 
+c
+c     this is a while  -- do loop -- 
+c 
+         if (ka .le. kamax .or. kb .le. kbmax) then 
+c     
+            if (ka .le. kamax) then
+               j1 = ja(ka)
+            else
+c     take j1 large enough  that always j2 .lt. j1
+               j1 = ncol+1
+            endif
+            if (kb .le. kbmax) then 
+               j2 = jb(kb)         
+            else 
+c     similarly take j2 large enough  that always j1 .lt. j2 
+               j2 = ncol+1
+            endif
+c     
+c     three cases
+c     
+            if (kc .gt. nzmax) goto 999
+            if (j1 .eq. j2) then 
+               c(kc) = a(ka)+s*b(kb)
+               jc(kc) = j1
+               ka = ka+1
+               kb = kb+1
+               kc = kc+1
+            else if (j1 .lt. j2) then
+               jc(kc) = j1
+               c(kc) = a(ka)
+               ka = ka+1
+               kc = kc+1
+            else if (j1 .gt. j2) then
+               jc(kc) = j2
+               c(kc) = s*b(kb)
+               kb = kb+1
+               kc = kc+1
+            endif
+            goto 5
+c
+c     end while loop
+c
+         endif
+         ic(i+1) = kc
+ 6    continue
+      return
+ 999  ierr = i 
+      return
+c------------end-of-aplsb --------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine aplsb1 (nrow,ncol,a,ja,ia,s,b,jb,ib,c,jc,ic,
+     *     nzmax,ierr)
+      real*8 a(*), b(*), c(*), s
+      integer ja(*),jb(*),jc(*),ia(nrow+1),ib(nrow+1),ic(nrow+1)
+c-----------------------------------------------------------------------
+c performs the operation C = A+s B for matrices in sorted CSR format.
+c the difference with aplsb is that the resulting matrix is such that
+c the elements of each row are sorted with increasing column indices in
+c each row, provided the original matrices are sorted in the same way. 
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A and B
+c ncol  = integer. The column dimension of A and B.
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format with entries sorted
+c
+c s	= real. scalar factor for B.
+c 
+c b, 
+c jb, 
+c ib	=  Matrix B in compressed sparse row format with entries sorted
+c        ascendly in each row   
+c
+c nzmax	= integer. The  length of the arrays c and jc.
+c         amub will stop if the result matrix C  has a number 
+c         of elements that exceeds exceeds nzmax. See ierr.
+c 
+c on return:
+c----------
+c c, 
+c jc, 
+c ic	= resulting matrix C in compressed sparse row sparse format
+c         with entries sorted ascendly in each row. 
+c	    
+c ierr	= integer. serving as error message. 
+c         ierr = 0 means normal return,
+c         ierr .gt. 0 means that amub stopped while computing the
+c         i-th row  of C with i=ierr, because the number 
+c         of elements in C exceeds nzmax.
+c
+c Notes: 
+c-------
+c     this will not work if any of the two input matrices is not sorted
+c-----------------------------------------------------------------------
+      ierr = 0
+      kc = 1
+      ic(1) = kc 
+c
+c     the following loop does a merge of two sparse rows + adds  them.
+c 
+      do 6 i=1, nrow
+         ka = ia(i)
+         kb = ib(i)
+         kamax = ia(i+1)-1
+         kbmax = ib(i+1)-1 
+ 5       continue 
+c
+c     this is a while  -- do loop -- 
+c 
+         if (ka .le. kamax .or. kb .le. kbmax) then 
+c     
+            if (ka .le. kamax) then
+               j1 = ja(ka)
+            else
+c     take j1 large enough  that always j2 .lt. j1
+               j1 = ncol+1
+            endif
+            if (kb .le. kbmax) then 
+               j2 = jb(kb)         
+            else 
+c     similarly take j2 large enough  that always j1 .lt. j2 
+               j2 = ncol+1
+            endif
+c     
+c     three cases
+c     
+            if (j1 .eq. j2) then 
+               c(kc) = a(ka)+s*b(kb)
+               jc(kc) = j1
+               ka = ka+1
+               kb = kb+1
+               kc = kc+1
+            else if (j1 .lt. j2) then
+               jc(kc) = j1
+               c(kc) = a(ka)
+               ka = ka+1
+               kc = kc+1
+            else if (j1 .gt. j2) then
+               jc(kc) = j2
+               c(kc) = s*b(kb)
+               kb = kb+1
+               kc = kc+1
+            endif
+            if (kc .gt. nzmax) goto 999
+            goto 5
+c
+c     end while loop
+c
+         endif
+         ic(i+1) = kc
+ 6    continue
+      return
+ 999  ierr = i 
+      return
+c------------end-of-aplsb1 --------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine apmbt (nrow,ncol,job,a,ja,ia,b,jb,ib,
+     *     c,jc,ic,nzmax,iw,ierr)
+      real*8 a(*), b(*), c(*) 
+      integer ja(*),jb(*),jc(*),ia(nrow+1),ib(ncol+1),ic(*),iw(*) 
+c-----------------------------------------------------------------------
+c performs the matrix sum  C = A + transp(B) or C = A - transp(B) 
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A and transp(B)
+c ncol  = integer. The column dimension of A. Also the row 
+c                  dimension of B. 
+c
+c job	= integer. if job = -1, apmbt will compute C= A - transp(B)
+c         (structure + values) 
+c         if (job .eq. 1)  it will compute C=A+transp(A) 
+c         (structure+ values) 
+c         if (job .eq. 0) it will compute the structure of
+c         C= A+/-transp(B) only (ignoring all real values).
+c         any other value of job will be treated as  job=1
+c a,
+c ja,
+c ia    = Matrix A in compressed sparse row format.
+c
+c b, 
+c jb, 
+c ib	=  Matrix B in compressed sparse row format.
+c
+c nzmax	= integer. The  length of the arrays c, jc, and ic.
+c         amub will stop if the result matrix C  has a number 
+c         of elements that exceeds exceeds nzmax. See ierr.
+c 
+c on return:
+c----------
+c c, 
+c jc, 
+c ic	= resulting matrix C in compressed sparse row format.
+c	    
+c ierr	= integer. serving as error message. 
+c         ierr = 0 means normal return.
+c         ierr = -1 means that nzmax was .lt. either the number of
+c         nonzero elements of A or the number of nonzero elements in B.
+c         ierr .gt. 0 means that amub stopped while computing the
+c         i-th row  of C with i=ierr, because the number 
+c         of elements in C exceeds nzmax.
+c
+c work arrays:
+c------------
+c iw	= integer work array of length at least max(ncol,nrow) 
+c
+c Notes:
+c------- It is important to note that here all of three arrays c, ic, 
+c        and jc are assumed to be of length nnz(c). This is because 
+c        the matrix is internally converted in coordinate format.
+c        
+c-----------------------------------------------------------------------
+      logical values
+      values = (job .ne. 0) 
+c
+      ierr = 0
+      do 1 j=1, ncol
+         iw(j) = 0
+ 1    continue
+c     
+      nnza = ia(nrow+1)-1
+      nnzb = ib(ncol+1)-1
+      len = nnzb
+      if (nzmax .lt. nnzb .or. nzmax .lt. nnza) then
+         ierr = -1
+         return
+      endif
+c     
+c trasnpose matrix b into c
+c
+      ljob = 0
+      if (values) ljob = 1
+      ipos = 1
+      call csrcsc (ncol,ljob,ipos,b,jb,ib,c,jc,ic) 
+c----------------------------------------------------------------------- 
+      if (job .eq. -1) then
+         do 2 k=1,len
+	    c(k) = -c(k)
+ 2       continue
+      endif
+c
+c--------------- main loop --------------------------------------------
+c
+      do 500 ii=1, nrow
+         do 200 k = ic(ii),ic(ii+1)-1
+            iw(jc(k)) = k
+ 200     continue
+c-----------------------------------------------------------------------     
+         do 300 ka = ia(ii), ia(ii+1)-1 
+            jcol = ja(ka)
+            jpos = iw(jcol)
+            if (jpos .eq. 0) then
+c
+c     if fill-in append in coordinate format to matrix.
+c 
+               len = len+1
+               if (len .gt. nzmax) goto 999
+               jc(len) = jcol
+               
+               ic(len) = ii
+               if (values) c(len)  = a(ka)
+            else
+c     else do addition.
+               if (values) c(jpos) = c(jpos) + a(ka)
+            endif
+ 300     continue
+         do 301 k=ic(ii), ic(ii+1)-1
+	    iw(jc(k)) = 0
+ 301     continue
+ 500  continue
+c     
+c     convert first part of matrix (without fill-ins) into coo format
+c     
+      ljob = 2
+      if (values) ljob = 3
+      do 501 i=1, nrow+1
+         iw(i) = ic(i) 
+ 501  continue
+      call csrcoo (nrow,ljob,nnzb,c,jc,iw,nnzb,c,ic,jc,ierr)
+c
+c     convert the whole thing back to csr format. 
+c 
+      ljob = 0
+      if (values) ljob = 1
+      call coicsr (nrow,len,ljob,c,jc,ic,iw)
+      return
+ 999  ierr = ii
+      return
+c--------end-of-apmbt---------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine aplsbt(nrow,ncol,a,ja,ia,s,b,jb,ib,
+     *     c,jc,ic,nzmax,iw,ierr)
+      real*8 a(*), b(*), c(*), s
+      integer ja(*),jb(*),jc(*),ia(nrow+1),ib(ncol+1),ic(*),iw(*)
+c-----------------------------------------------------------------------
+c performs the matrix sum  C = A + transp(B).
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A and transp(B)
+c ncol  = integer. The column dimension of A. Also the row 
+c                  dimension of B. 
+c
+c a,
+c ja,
+c ia    = Matrix A in compressed sparse row format.
+c
+c s	= real. scalar factor for B.
+c
+c 
+c b, 
+c jb, 
+c ib	=  Matrix B in compressed sparse row format.
+c
+c nzmax	= integer. The  length of the arrays c, jc, and ic.
+c         amub will stop if the result matrix C  has a number 
+c         of elements that exceeds exceeds nzmax. See ierr.
+c 
+c on return:
+c----------
+c c, 
+c jc, 
+c ic	= resulting matrix C in compressed sparse row format.
+c	    
+c ierr	= integer. serving as error message. 
+c         ierr = 0 means normal return.
+c         ierr = -1 means that nzmax was .lt. either the number of
+c         nonzero elements of A or the number of nonzero elements in B.
+c         ierr .gt. 0 means that amub stopped while computing the
+c         i-th row  of C with i=ierr, because the number 
+c         of elements in C exceeds nzmax.
+c
+c work arrays:
+c------------
+c iw	= integer work array of length at least max(nrow,ncol) 
+c
+c Notes:
+c------- It is important to note that here all of three arrays c, ic, 
+c        and jc are assumed to be of length nnz(c). This is because 
+c        the matrix is internally converted in coordinate format.
+c        
+c-----------------------------------------------------------------------
+      ierr = 0
+      do 1 j=1, ncol
+         iw(j) = 0
+ 1    continue
+c     
+      nnza = ia(nrow+1)-1
+      nnzb = ib(ncol+1)-1
+      len = nnzb
+      if (nzmax .lt. nnzb .or. nzmax .lt. nnza) then
+         ierr = -1
+         return
+      endif
+c     
+c     transpose matrix b into c
+c
+      ljob = 1
+      ipos = 1
+      call csrcsc (ncol,ljob,ipos,b,jb,ib,c,jc,ic) 
+      do 2 k=1,len
+ 2       c(k) = c(k)*s
+c     
+c     main loop. add rows from ii = 1 to nrow.
+c     
+         do 500 ii=1, nrow
+c     iw is used as a system to recognize whether there
+c     was a nonzero element in c. 
+            do 200 k = ic(ii),ic(ii+1)-1
+               iw(jc(k)) = k
+ 200        continue
+c     
+            do 300 ka = ia(ii), ia(ii+1)-1 
+               jcol = ja(ka)
+               jpos = iw(jcol)
+           if (jpos .eq. 0) then
+c     
+c     if fill-in append in coordinate format to matrix.
+c     
+              len = len+1
+              if (len .gt. nzmax) goto 999
+              jc(len) = jcol              
+              ic(len) = ii
+              c(len)  = a(ka)
+           else
+c     else do addition.
+              c(jpos) = c(jpos) + a(ka)
+           endif
+ 300    continue
+        do 301 k=ic(ii), ic(ii+1)-1
+           iw(jc(k)) = 0
+ 301    continue
+ 500  continue
+c     
+c     convert first part of matrix (without fill-ins) into coo format
+c     
+      ljob = 3
+      do 501 i=1, nrow+1
+         iw(i) = ic(i) 
+ 501  continue
+      call csrcoo (nrow,ljob,nnzb,c,jc,iw,nnzb,c,ic,jc,ierr)
+c
+c     convert the whole thing back to csr format. 
+c 
+      ljob = 1
+      call coicsr (nrow,len,ljob,c,jc,ic,iw)
+      return
+ 999  ierr = ii
+      return
+c--------end-of-aplsbt--------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine diamua (nrow,job, a, ja, ia, diag, b, jb, ib)
+      real*8 a(*), b(*), diag(nrow), scal
+      integer ja(*),jb(*), ia(nrow+1),ib(nrow+1) 
+c-----------------------------------------------------------------------
+c performs the matrix by matrix product B = Diag * A  (in place) 
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A
+c
+c job   = integer. job indicator. Job=0 means get array b only
+c         job = 1 means get b, and the integer arrays ib, jb.
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format.
+c 
+c diag = diagonal matrix stored as a vector dig(1:n)
+c
+c on return:
+c----------
+c
+c b, 
+c jb, 
+c ib	= resulting matrix B in compressed sparse row sparse format.
+c	    
+c Notes:
+c-------
+c 1)        The column dimension of A is not needed. 
+c 2)        algorithm in place (B can take the place of A).
+c           in this case use job=0.
+c-----------------------------------------------------------------
+      do 1 ii=1,nrow
+c     
+c     normalize each row 
+c     
+         k1 = ia(ii)
+         k2 = ia(ii+1)-1
+         scal = diag(ii) 
+         do 2 k=k1, k2
+            b(k) = a(k)*scal
+ 2       continue
+ 1    continue
+c     
+      if (job .eq. 0) return
+c     
+      do 3 ii=1, nrow+1
+         ib(ii) = ia(ii)
+ 3    continue
+      do 31 k=ia(1), ia(nrow+1) -1 
+         jb(k) = ja(k)
+ 31   continue
+      return
+c----------end-of-diamua------------------------------------------------
+c-----------------------------------------------------------------------
+      end 
+c----------------------------------------------------------------------- 
+      subroutine amudia (nrow,job, a, ja, ia, diag, b, jb, ib)
+      real*8 a(*), b(*), diag(nrow) 
+      integer ja(*),jb(*), ia(nrow+1),ib(nrow+1) 
+c-----------------------------------------------------------------------
+c performs the matrix by matrix product B = A * Diag  (in place) 
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A
+c
+c job   = integer. job indicator. Job=0 means get array b only
+c         job = 1 means get b, and the integer arrays ib, jb.
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format.
+c 
+c diag = diagonal matrix stored as a vector dig(1:n)
+c
+c on return:
+c----------
+c
+c b, 
+c jb, 
+c ib	= resulting matrix B in compressed sparse row sparse format.
+c	    
+c Notes:
+c-------
+c 1)        The column dimension of A is not needed. 
+c 2)        algorithm in place (B can take the place of A).
+c-----------------------------------------------------------------
+      do 1 ii=1,nrow
+c     
+c     scale each element 
+c     
+         k1 = ia(ii)
+         k2 = ia(ii+1)-1
+         do 2 k=k1, k2
+            b(k) = a(k)*diag(ja(k)) 
+ 2       continue
+ 1    continue
+c     
+      if (job .eq. 0) return
+c     
+      do 3 ii=1, nrow+1
+         ib(ii) = ia(ii)
+ 3    continue
+      do 31 k=ia(1), ia(nrow+1) -1 
+         jb(k) = ja(k)
+ 31   continue
+      return
+c-----------------------------------------------------------------------
+c-----------end-of-amudiag----------------------------------------------
+      end 
+c----------------------------------------------------------------------- 
+      subroutine aplsca (nrow, a, ja, ia, scal,iw) 
+      real*8 a(*), scal
+      integer ja(*), ia(nrow+1),iw(*)
+c-----------------------------------------------------------------------
+c Adds a scalar to the diagonal entries of a sparse matrix A :=A + s I 
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A
+c
+c a,
+c ja,
+c ia    = Matrix A in compressed sparse row format.
+c 
+c scal  = real. scalar to add to the diagonal entries. 
+c
+c on return:
+c----------
+c
+c a, 
+c ja, 
+c ia	= matrix A with diagonal elements shifted (or created).
+c	    
+c iw    = integer work array of length n. On return iw will
+c         contain  the positions of the diagonal entries in the 
+c         output matrix. (i.e., a(iw(k)), ja(iw(k)), k=1,...n,
+c         are the values/column indices of the diagonal elements 
+c         of the output matrix. ). 
+c
+c Notes:
+c-------
+c     The column dimension of A is not needed. 
+c     important: the matrix a may be expanded slightly to allow for
+c     additions of nonzero elements to previously nonexisting diagonals.
+c     The is no checking as to whether there is enough space appended
+c     to the arrays a and ja. if not sure allow for n additional 
+c     elemnts. 
+c     coded by Y. Saad. Latest version July, 19, 1990
+c-----------------------------------------------------------------------
+      logical test
+c
+      call diapos (nrow,ja,ia,iw)
+      icount = 0
+      do 1 j=1, nrow
+         if (iw(j) .eq. 0) then
+            icount = icount+1
+         else
+            a(iw(j)) = a(iw(j)) + scal 
+         endif
+ 1    continue
+c
+c     if no diagonal elements to insert in data structure return.
+c
+      if (icount .eq. 0) return
+c
+c shift the nonzero elements if needed, to allow for created 
+c diagonal elements. 
+c
+      ko = ia(nrow+1)+icount
+c
+c     copy rows backward
+c
+      do 5 ii=nrow, 1, -1 
+c     
+c     go through  row ii
+c     
+         k1 = ia(ii)
+         k2 = ia(ii+1)-1 
+         ia(ii+1) = ko
+         test = (iw(ii) .eq. 0) 
+         do 4 k = k2,k1,-1 
+            j = ja(k)
+            if (test .and. (j .lt. ii)) then 
+               test = .false. 
+               ko = ko - 1
+               a(ko) = scal 
+               ja(ko) = ii
+               iw(ii) = ko
+            endif
+            ko = ko-1
+            a(ko) = a(k) 
+            ja(ko) = j
+ 4       continue
+c     diagonal element has not been added yet.
+         if (test) then
+            ko = ko-1
+            a(ko) = scal 
+            ja(ko) = ii
+            iw(ii) = ko
+         endif
+ 5    continue
+      ia(1) = ko 
+      return
+c-----------------------------------------------------------------------
+c----------end-of-aplsca------------------------------------------------ 
+      end
+c-----------------------------------------------------------------------
+      subroutine apldia (nrow, job, a, ja, ia, diag, b, jb, ib, iw) 
+      real*8 a(*), b(*), diag(nrow) 
+      integer ja(*),jb(*), ia(nrow+1),ib(nrow+1), iw(*)
+c-----------------------------------------------------------------------
+c Adds a diagonal matrix to a general sparse matrix:  B = A + Diag 
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A
+c
+c job   = integer. job indicator. Job=0 means get array b only
+c         (i.e. assume that a has already been copied into array b,
+c         or that algorithm is used in place. ) For all practical 
+c         purposes enter job=0 for an in-place call and job=1 otherwise
+c 
+c         Note: in case there are missing diagonal elements in A, 
+c         then the option job =0 will be ignored, since the algorithm 
+c         must modify the data structure (i.e. jb, ib) in this 
+c         situation.
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format.
+c     
+c diag = diagonal matrix stored as a vector dig(1:n)
+c
+c on return:
+c----------
+c
+c b, 
+c jb, 
+c ib	= resulting matrix B in compressed sparse row sparse format.
+c
+c
+c iw    = integer work array of length n. On return iw will
+c         contain  the positions of the diagonal entries in the 
+c         output matrix. (i.e., a(iw(k)), ja(iw(k)), k=1,...n,
+c         are the values/column indices of the diagonal elements 
+c         of the output matrix. ). 
+c
+c Notes:
+c-------
+c 1)        The column dimension of A is not needed. 
+c 2)        algorithm in place (b, jb, ib, can be the same as
+c           a, ja, ia, on entry). See comments for parameter job.
+c
+c coded by Y. Saad. Latest version July, 19, 1990
+c-----------------------------------------------------------------
+      logical test
+c
+c     copy integer arrays into b's data structure if required
+c
+      if (job .ne. 0) then 
+         nnz = ia(nrow+1)-1
+         do 2  k=1, nnz
+            jb(k) = ja(k)
+            b(k)  = a(k) 
+ 2       continue
+         do 3 k=1, nrow+1
+            ib(k) = ia(k)
+ 3       continue
+      endif 
+c
+c     get positions of diagonal elements in data structure.
+c     
+      call diapos (nrow,ja,ia,iw)
+c     
+c     count number of holes in diagonal and add diag(*) elements to
+c     valid diagonal entries.
+c     
+      icount = 0
+      do 1 j=1, nrow
+         if (iw(j) .eq. 0) then
+            icount = icount+1
+         else
+            b(iw(j)) = a(iw(j)) + diag(j) 
+         endif
+ 1    continue
+c     
+c     if no diagonal elements to insert return
+c     
+      if (icount .eq. 0) return
+c     
+c     shift the nonzero elements if needed, to allow for created 
+c     diagonal elements. 
+c     
+      ko = ib(nrow+1)+icount
+c     
+c     copy rows backward
+c     
+      do 5 ii=nrow, 1, -1 
+c     
+c     go through  row ii
+c     
+         k1 = ib(ii)
+         k2 = ib(ii+1)-1 
+         ib(ii+1) = ko
+         test = (iw(ii) .eq. 0) 
+         do 4 k = k2,k1,-1 
+            j = jb(k)
+            if (test .and. (j .lt. ii)) then 
+               test = .false. 
+               ko = ko - 1
+               b(ko) = diag(ii) 
+               jb(ko) = ii
+               iw(ii) = ko
+            endif
+            ko = ko-1
+            b(ko) = a(k) 
+            jb(ko) = j
+ 4       continue
+c     diagonal element has not been added yet.
+         if (test) then
+            ko = ko-1
+            b(ko) =  diag(ii) 
+            jb(ko) = ii
+            iw(ii) = ko
+         endif
+ 5    continue
+      ib(1) = ko 
+      return
+c-----------------------------------------------------------------------
+c------------end-of-apldiag---------------------------------------------
+      end
diff --git a/BLASSM/makefile b/BLASSM/makefile
new file mode 100644
index 0000000..7fa9ff7
--- /dev/null
+++ b/BLASSM/makefile
@@ -0,0 +1,21 @@
+FFLAGS = 
+F77 = f77
+
+#F77 = cf77
+#FFLAGS = -Wf"-dp"
+
+mvec.ex: rmatvec.o ../MATGEN/FDIF/functns.o ../libskit.a
+	$(F77) $(FFLAGS) -o mvec.ex rmatvec.o ../MATGEN/FDIF/functns.o ../libskit.a
+
+tester.ex: tester.o ../MATGEN/FDIF/functns.o ../libskit.a
+	$(F77) $(FFLAGS) -o tester.ex tester.o ../MATGEN/FDIF/functns.o ../libskit.a
+
+clean:
+	rm -f *.o *.ex core *.trace fort.* ftn??
+
+../MATGEN/FDIF/functns.o:
+	(cd ../MATGEN/FDIF; $(F77) $(FFLAGS) -c functns.f)
+
+../libskit.a:
+	(cd ..; $(MAKE) $(MAKEFLAGS) libskit.a)
+
diff --git a/BLASSM/matvec.f b/BLASSM/matvec.f
new file mode 100644
index 0000000..60cbb9f
--- /dev/null
+++ b/BLASSM/matvec.f
@@ -0,0 +1,830 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c          BASIC MATRIX-VECTOR OPERATIONS - MATVEC MODULE              c
+c         Matrix-vector Mulitiplications and Triang. Solves            c
+c----------------------------------------------------------------------c
+c contents: (as of Nov 18, 1991)                                       c
+c----------                                                            c
+c 1) Matrix-vector products:                                           c
+c---------------------------                                           c
+c amux  : A times a vector. Compressed Sparse Row (CSR) format.        c
+c amuxms: A times a vector. Modified Compress Sparse Row format.       c
+c atmux : Transp(A) times a vector. CSR format.                        c
+c atmuxr: Transp(A) times a vector. CSR format. A rectangular.         c
+c amuxe : A times a vector. Ellpack/Itpack (ELL) format.               c
+c amuxd : A times a vector. Diagonal (DIA) format.                     c
+c amuxj : A times a vector. Jagged Diagonal (JAD) format.              c
+c vbrmv : Sparse matrix-full vector product, in VBR format             c
+c                                                                      c
+c 2) Triangular system solutions:                                      c
+c-------------------------------                                       c
+c lsol  : Unit Lower Triang. solve. Compressed Sparse Row (CSR) format.c
+c ldsol : Lower Triang. solve.  Modified Sparse Row (MSR) format.      c
+c lsolc : Unit Lower Triang. solve. Comp. Sparse Column (CSC) format.  c
+c ldsolc: Lower Triang. solve. Modified Sparse Column (MSC) format.    c
+c ldsoll: Lower Triang. solve with level scheduling. MSR format.       c
+c usol  : Unit Upper Triang. solve. Compressed Sparse Row (CSR) format.c
+c udsol : Upper Triang. solve.  Modified Sparse Row (MSR) format.      c
+c usolc : Unit Upper Triang. solve. Comp. Sparse Column (CSC) format.  c
+c udsolc: Upper Triang. solve.  Modified Sparse Column (MSC) format.   c
+c----------------------------------------------------------------------c
+c 1)     M A T R I X    B Y    V E C T O R     P R O D U C T S         c
+c----------------------------------------------------------------------c
+      subroutine amux (n, x, y, a,ja,ia) 
+      real*8  x(*), y(*), a(*) 
+      integer n, ja(*), ia(*)
+c-----------------------------------------------------------------------
+c         A times a vector
+c----------------------------------------------------------------------- 
+c multiplies a matrix by a vector using the dot product form
+c Matrix A is stored in compressed sparse row storage.
+c
+c on entry:
+c----------
+c n     = row dimension of A
+c x     = real array of length equal to the column dimension of
+c         the A matrix.
+c a, ja,
+c    ia = input matrix in compressed sparse row format.
+c
+c on return:
+c-----------
+c y     = real array of length n, containing the product y=Ax
+c
+c-----------------------------------------------------------------------
+c local variables
+c
+      real*8 t
+      integer i, k
+c-----------------------------------------------------------------------
+      do 100 i = 1,n
+c
+c     compute the inner product of row i with vector x
+c 
+         t = 0.0d0
+         do 99 k=ia(i), ia(i+1)-1 
+            t = t + a(k)*x(ja(k))
+ 99      continue
+c
+c     store result in y(i) 
+c
+         y(i) = t
+ 100  continue
+c
+      return
+c---------end-of-amux---------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine amuxms (n, x, y, a,ja)
+      real*8  x(*), y(*), a(*)
+      integer n, ja(*)
+c-----------------------------------------------------------------------
+c         A times a vector in MSR format
+c-----------------------------------------------------------------------
+c multiplies a matrix by a vector using the dot product form
+c Matrix A is stored in Modified Sparse Row storage.
+c
+c on entry:
+c----------
+c n     = row dimension of A
+c x     = real array of length equal to the column dimension of
+c         the A matrix.
+c a, ja,= input matrix in modified compressed sparse row format.
+c
+c on return:
+c-----------
+c y     = real array of length n, containing the product y=Ax
+c
+c-----------------------------------------------------------------------
+c local variables
+c
+      integer i, k
+c-----------------------------------------------------------------------
+        do 10 i=1, n
+        y(i) = a(i)*x(i)
+ 10     continue
+      do 100 i = 1,n
+c
+c     compute the inner product of row i with vector x
+c
+         do 99 k=ja(i), ja(i+1)-1
+            y(i) = y(i) + a(k) *x(ja(k))
+ 99      continue
+ 100  continue
+c
+      return
+c---------end-of-amuxm--------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine atmux (n, x, y, a, ja, ia)
+      real*8 x(*), y(*), a(*) 
+      integer n, ia(*), ja(*)
+c-----------------------------------------------------------------------
+c         transp( A ) times a vector
+c----------------------------------------------------------------------- 
+c multiplies the transpose of a matrix by a vector when the original
+c matrix is stored in compressed sparse row storage. Can also be
+c viewed as the product of a matrix by a vector when the original
+c matrix is stored in the compressed sparse column format.
+c-----------------------------------------------------------------------
+c
+c on entry:
+c----------
+c n     = row dimension of A
+c x     = real array of length equal to the column dimension of
+c         the A matrix.
+c a, ja,
+c    ia = input matrix in compressed sparse row format.
+c
+c on return:
+c-----------
+c y     = real array of length n, containing the product y=transp(A)*x
+c
+c-----------------------------------------------------------------------
+c     local variables 
+c
+      integer i, k 
+c-----------------------------------------------------------------------
+c
+c     zero out output vector
+c 
+      do 1 i=1,n
+         y(i) = 0.0
+ 1    continue
+c
+c loop over the rows
+c
+      do 100 i = 1,n
+         do 99 k=ia(i), ia(i+1)-1 
+            y(ja(k)) = y(ja(k)) + x(i)*a(k)
+ 99      continue
+ 100  continue
+c
+      return
+c-------------end-of-atmux---------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine atmuxr (m, n, x, y, a, ja, ia)
+      real*8 x(*), y(*), a(*) 
+      integer m, n, ia(*), ja(*)
+c-----------------------------------------------------------------------
+c         transp( A ) times a vector, A can be rectangular
+c----------------------------------------------------------------------- 
+c See also atmux.  The essential difference is how the solution vector
+c is initially zeroed.  If using this to multiply rectangular CSC 
+c matrices by a vector, m number of rows, n is number of columns.
+c-----------------------------------------------------------------------
+c
+c on entry:
+c----------
+c m     = column dimension of A
+c n     = row dimension of A
+c x     = real array of length equal to the column dimension of
+c         the A matrix.
+c a, ja,
+c    ia = input matrix in compressed sparse row format.
+c
+c on return:
+c-----------
+c y     = real array of length n, containing the product y=transp(A)*x
+c
+c-----------------------------------------------------------------------
+c     local variables 
+c
+      integer i, k 
+c-----------------------------------------------------------------------
+c
+c     zero out output vector
+c 
+      do 1 i=1,m
+         y(i) = 0.0
+ 1    continue
+c
+c loop over the rows
+c
+      do 100 i = 1,n
+         do 99 k=ia(i), ia(i+1)-1 
+            y(ja(k)) = y(ja(k)) + x(i)*a(k)
+ 99      continue
+ 100  continue
+c
+      return
+c-------------end-of-atmuxr--------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine amuxe (n,x,y,na,ncol,a,ja) 
+      real*8 x(n), y(n), a(na,*)  
+      integer  n, na, ncol, ja(na,*)
+c-----------------------------------------------------------------------
+c        A times a vector in Ellpack Itpack format (ELL)               
+c----------------------------------------------------------------------- 
+c multiplies a matrix by a vector when the original matrix is stored 
+c in the ellpack-itpack sparse format.
+c-----------------------------------------------------------------------
+c
+c on entry:
+c----------
+c n     = row dimension of A
+c x     = real array of length equal to the column dimension of
+c         the A matrix.
+c na    = integer. The first dimension of arrays a and ja
+c         as declared by the calling program.
+c ncol  = integer. The number of active columns in array a.
+c         (i.e., the number of generalized diagonals in matrix.)
+c a, ja = the real and integer arrays of the itpack format
+c         (a(i,k),k=1,ncol contains the elements of row i in matrix
+c          ja(i,k),k=1,ncol contains their column numbers) 
+c
+c on return:
+c-----------
+c y     = real array of length n, containing the product y=y=A*x
+c
+c-----------------------------------------------------------------------
+c local variables
+c
+      integer i, j 
+c-----------------------------------------------------------------------
+      do 1 i=1, n
+         y(i) = 0.0 
+ 1    continue
+      do 10 j=1,ncol
+         do 25 i = 1,n
+            y(i) = y(i)+a(i,j)*x(ja(i,j))
+ 25      continue
+ 10   continue
+c
+      return
+c--------end-of-amuxe--------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine amuxd (n,x,y,diag,ndiag,idiag,ioff) 
+      integer n, ndiag, idiag, ioff(idiag) 
+      real*8 x(n), y(n), diag(ndiag,idiag)
+c-----------------------------------------------------------------------
+c        A times a vector in Diagonal storage format (DIA) 
+c----------------------------------------------------------------------- 
+c multiplies a matrix by a vector when the original matrix is stored 
+c in the diagonal storage format.
+c-----------------------------------------------------------------------
+c
+c on entry:
+c----------
+c n     = row dimension of A
+c x     = real array of length equal to the column dimension of
+c         the A matrix.
+c ndiag  = integer. The first dimension of array adiag as declared in
+c         the calling program.
+c idiag  = integer. The number of diagonals in the matrix.
+c diag   = real array containing the diagonals stored of A.
+c idiag  = number of diagonals in matrix.
+c diag   = real array of size (ndiag x idiag) containing the diagonals
+c          
+c ioff   = integer array of length idiag, containing the offsets of the
+c   	   diagonals of the matrix:
+c          diag(i,k) contains the element a(i,i+ioff(k)) of the matrix.
+c
+c on return:
+c-----------
+c y     = real array of length n, containing the product y=A*x
+c
+c-----------------------------------------------------------------------
+c local variables 
+c
+      integer j, k, io, i1, i2 
+c-----------------------------------------------------------------------
+      do 1 j=1, n
+         y(j) = 0.0d0
+ 1    continue	
+      do 10 j=1, idiag
+         io = ioff(j)
+         i1 = max0(1,1-io)
+         i2 = min0(n,n-io)
+         do 9 k=i1, i2	
+            y(k) = y(k)+diag(k,j)*x(k+io)
+ 9       continue
+ 10   continue
+c 
+      return
+c----------end-of-amuxd-------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine amuxj (n, x, y, jdiag, a, ja, ia)
+      integer n, jdiag, ja(*), ia(*)
+      real*8 x(n), y(n), a(*)  
+c-----------------------------------------------------------------------
+c        A times a vector in Jagged-Diagonal storage format (JAD) 
+c----------------------------------------------------------------------- 
+c multiplies a matrix by a vector when the original matrix is stored 
+c in the jagged diagonal storage format.
+c-----------------------------------------------------------------------
+c
+c on entry:
+c----------
+c n      = row dimension of A
+c x      = real array of length equal to the column dimension of
+c         the A matrix.
+c jdiag  = integer. The number of jadded-diagonals in the data-structure.
+c a      = real array containing the jadded diagonals of A stored
+c          in succession (in decreasing lengths) 
+c j      = integer array containing the colum indices of the 
+c          corresponding elements in a.
+c ia     = integer array containing the lengths of the  jagged diagonals
+c
+c on return:
+c-----------
+c y      = real array of length n, containing the product y=A*x
+c
+c Note:
+c------- 
+c Permutation related to the JAD format is not performed.
+c this can be done by:
+c     call permvec (n,y,y,iperm) 
+c after the call to amuxj, where iperm is the permutation produced
+c by csrjad.
+c-----------------------------------------------------------------------
+c local variables 
+c
+      integer i, ii, k1, len, j 
+c-----------------------------------------------------------------------
+      do 1 i=1, n
+         y(i) = 0.0d0
+ 1    continue
+      do 70 ii=1, jdiag
+         k1 = ia(ii)-1
+         len = ia(ii+1)-k1-1
+         do 60 j=1,len
+            y(j)= y(j)+a(k1+j)*x(ja(k1+j)) 
+ 60      continue
+ 70   continue
+c
+      return
+c----------end-of-amuxj------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine vbrmv(nr, nc, ia, ja, ka, a, kvstr, kvstc, x, b)
+c-----------------------------------------------------------------------
+      integer nr, nc, ia(nr+1), ja(*), ka(*), kvstr(nr+1), kvstc(*)
+      real*8  a(*), x(*), b(*)
+c-----------------------------------------------------------------------
+c     Sparse matrix-full vector product, in VBR format.
+c-----------------------------------------------------------------------
+c     On entry:
+c--------------
+c     nr, nc  = number of block rows and columns in matrix A
+c     ia,ja,ka,a,kvstr,kvstc = matrix A in variable block row format
+c     x       = multiplier vector in full format
+c
+c     On return:
+c---------------
+c     b = product of matrix A times vector x in full format
+c
+c     Algorithm:
+c---------------
+c     Perform multiplication by traversing a in order.
+c
+c-----------------------------------------------------------------------
+c-----local variables
+      integer n, i, j, ii, jj, k, istart, istop
+      real*8  xjj
+c---------------------------------
+      n = kvstc(nc+1)-1
+      do i = 1, n
+         b(i) = 0.d0
+      enddo
+c---------------------------------
+      k = 1
+      do i = 1, nr
+         istart = kvstr(i)
+         istop  = kvstr(i+1)-1
+         do j = ia(i), ia(i+1)-1
+            do jj = kvstc(ja(j)), kvstc(ja(j)+1)-1
+               xjj = x(jj)
+               do ii = istart, istop
+                  b(ii) = b(ii) + xjj*a(k)
+                  k = k + 1
+               enddo
+            enddo
+         enddo
+      enddo
+c---------------------------------
+      return
+      end
+c-----------------------------------------------------------------------
+c----------------------end-of-vbrmv-------------------------------------
+c-----------------------------------------------------------------------
+c----------------------------------------------------------------------c
+c 2)     T R I A N G U L A R    S Y S T E M    S O L U T I O N S       c
+c----------------------------------------------------------------------c
+      subroutine lsol (n,x,y,al,jal,ial)
+      integer n, jal(*),ial(n+1) 
+      real*8  x(n), y(n), al(*) 
+c-----------------------------------------------------------------------
+c   solves    L x = y ; L = lower unit triang. /  CSR format
+c----------------------------------------------------------------------- 
+c solves a unit lower triangular system by standard (sequential )
+c forward elimination - matrix stored in CSR format. 
+c-----------------------------------------------------------------------
+c
+c On entry:
+c---------- 
+c n      = integer. dimension of problem.
+c y      = real array containg the right side.
+c
+c al,
+c jal,
+c ial,    = Lower triangular matrix stored in compressed sparse row
+c          format. 
+c
+c On return:
+c----------- 
+c	x  = The solution of  L x  = y.
+c--------------------------------------------------------------------
+c local variables 
+c
+      integer k, j 
+      real*8  t
+c-----------------------------------------------------------------------
+      x(1) = y(1) 
+      do 150 k = 2, n
+         t = y(k) 
+         do 100 j = ial(k), ial(k+1)-1
+            t = t-al(j)*x(jal(j))
+ 100     continue
+         x(k) = t 
+ 150  continue
+c
+      return
+c----------end-of-lsol-------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine ldsol (n,x,y,al,jal) 
+      integer n, jal(*) 
+      real*8 x(n), y(n), al(*) 
+c----------------------------------------------------------------------- 
+c     Solves L x = y    L = triangular. MSR format 
+c-----------------------------------------------------------------------
+c solves a (non-unit) lower triangular system by standard (sequential) 
+c forward elimination - matrix stored in MSR format 
+c with diagonal elements already inverted (otherwise do inversion,
+c al(1:n) = 1.0/al(1:n),  before calling ldsol).
+c-----------------------------------------------------------------------
+c
+c On entry:
+c---------- 
+c n      = integer. dimension of problem.
+c y      = real array containg the right hand side.
+c
+c al,
+c jal,   = Lower triangular matrix stored in Modified Sparse Row 
+c          format. 
+c
+c On return:
+c----------- 
+c	x = The solution of  L x = y .
+c--------------------------------------------------------------------
+c local variables 
+c
+      integer k, j 
+      real*8 t 
+c-----------------------------------------------------------------------
+      x(1) = y(1)*al(1) 
+      do 150 k = 2, n
+         t = y(k) 
+         do 100 j = jal(k), jal(k+1)-1
+            t = t - al(j)*x(jal(j))
+ 100     continue
+         x(k) = al(k)*t 
+ 150  continue
+      return
+c----------end-of-ldsol-------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine lsolc (n,x,y,al,jal,ial)
+      integer n, jal(*),ial(*) 
+      real*8  x(n), y(n), al(*) 
+c-----------------------------------------------------------------------
+c       SOLVES     L x = y ;    where L = unit lower trang. CSC format
+c-----------------------------------------------------------------------
+c solves a unit lower triangular system by standard (sequential )
+c forward elimination - matrix stored in CSC format. 
+c-----------------------------------------------------------------------
+c
+c On entry:
+c---------- 
+c n      = integer. dimension of problem.
+c y      = real*8 array containg the right side.
+c
+c al,
+c jal,
+c ial,    = Lower triangular matrix stored in compressed sparse column 
+c          format. 
+c
+c On return:
+c----------- 
+c	x  = The solution of  L x  = y.
+c-----------------------------------------------------------------------
+c local variables 
+c
+      integer k, j
+      real*8 t
+c-----------------------------------------------------------------------
+      do 140 k=1,n
+         x(k) = y(k) 
+ 140  continue
+      do 150 k = 1, n-1
+         t = x(k) 
+         do 100 j = ial(k), ial(k+1)-1
+            x(jal(j)) = x(jal(j)) - t*al(j) 
+ 100     continue
+ 150  continue
+c
+      return
+c----------end-of-lsolc------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine ldsolc (n,x,y,al,jal) 
+      integer n, jal(*)
+      real*8 x(n), y(n), al(*)
+c-----------------------------------------------------------------------
+c    Solves     L x = y ;    L = nonunit Low. Triang. MSC format 
+c----------------------------------------------------------------------- 
+c solves a (non-unit) lower triangular system by standard (sequential) 
+c forward elimination - matrix stored in Modified Sparse Column format 
+c with diagonal elements already inverted (otherwise do inversion,
+c al(1:n) = 1.0/al(1:n),  before calling ldsol).
+c-----------------------------------------------------------------------
+c
+c On entry:
+c---------- 
+c n      = integer. dimension of problem.
+c y      = real array containg the right hand side.
+c
+c al,
+c jal,
+c ial,    = Lower triangular matrix stored in Modified Sparse Column
+c           format.
+c
+c On return:
+c----------- 
+c	x = The solution of  L x = y .
+c--------------------------------------------------------------------
+c local variables
+c
+      integer k, j
+      real*8 t 
+c-----------------------------------------------------------------------
+      do 140 k=1,n
+         x(k) = y(k) 
+ 140  continue
+      do 150 k = 1, n 
+         x(k) = x(k)*al(k) 
+         t = x(k) 
+         do 100 j = jal(k), jal(k+1)-1
+            x(jal(j)) = x(jal(j)) - t*al(j) 
+ 100     continue
+ 150  continue
+c
+      return
+c----------end-of-lsolc------------------------------------------------ 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------  
+      subroutine ldsoll (n,x,y,al,jal,nlev,lev,ilev) 
+      integer n, nlev, jal(*), ilev(nlev+1), lev(n)
+      real*8 x(n), y(n), al(*)
+c-----------------------------------------------------------------------
+c    Solves L x = y    L = triangular. Uses LEVEL SCHEDULING/MSR format 
+c-----------------------------------------------------------------------
+c
+c On entry:
+c---------- 
+c n      = integer. dimension of problem.
+c y      = real array containg the right hand side.
+c
+c al,
+c jal,   = Lower triangular matrix stored in Modified Sparse Row 
+c          format. 
+c nlev   = number of levels in matrix
+c lev    = integer array of length n, containing the permutation
+c          that defines the levels in the level scheduling ordering.
+c ilev   = pointer to beginning of levels in lev.
+c          the numbers lev(i) to lev(i+1)-1 contain the row numbers
+c          that belong to level number i, in the level shcheduling
+c          ordering.
+c
+c On return:
+c----------- 
+c	x = The solution of  L x = y .
+c--------------------------------------------------------------------
+      integer ii, jrow, i 
+      real*8 t 
+c     
+c     outer loop goes through the levels. (SEQUENTIAL loop)
+c     
+      do 150 ii=1, nlev
+c     
+c     next loop executes within the same level. PARALLEL loop
+c     
+         do 100 i=ilev(ii), ilev(ii+1)-1 
+            jrow = lev(i)
+c
+c compute inner product of row jrow with x
+c 
+            t = y(jrow) 
+            do 130 k=jal(jrow), jal(jrow+1)-1 
+               t = t - al(k)*x(jal(k))
+ 130        continue
+            x(jrow) = t*al(jrow) 
+ 100     continue
+ 150  continue
+      return
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine usol (n,x,y,au,jau,iau)
+      integer n, jau(*),iau(n+1) 
+      real*8  x(n), y(n), au(*) 
+c----------------------------------------------------------------------- 
+c             Solves   U x = y    U = unit upper triangular. 
+c-----------------------------------------------------------------------
+c solves a unit upper triangular system by standard (sequential )
+c backward elimination - matrix stored in CSR format. 
+c-----------------------------------------------------------------------
+c
+c On entry:
+c---------- 
+c n      = integer. dimension of problem.
+c y      = real array containg the right side.
+c
+c au,
+c jau,
+c iau,    = Lower triangular matrix stored in compressed sparse row
+c          format. 
+c
+c On return:
+c----------- 
+c	x = The solution of  U x = y . 
+c-------------------------------------------------------------------- 
+c local variables 
+c
+      integer k, j 
+      real*8  t
+c-----------------------------------------------------------------------
+      x(n) = y(n) 
+      do 150 k = n-1,1,-1 
+         t = y(k) 
+         do 100 j = iau(k), iau(k+1)-1
+            t = t - au(j)*x(jau(j))
+ 100     continue
+         x(k) = t 
+ 150  continue
+c
+      return
+c----------end-of-usol-------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine udsol (n,x,y,au,jau) 
+      integer n, jau(*) 
+      real*8  x(n), y(n),au(*) 
+c----------------------------------------------------------------------- 
+c             Solves   U x = y  ;   U = upper triangular in MSR format
+c-----------------------------------------------------------------------
+c solves a non-unit upper triangular matrix by standard (sequential )
+c backward elimination - matrix stored in MSR format. 
+c with diagonal elements already inverted (otherwise do inversion,
+c au(1:n) = 1.0/au(1:n),  before calling).
+c-----------------------------------------------------------------------
+c
+c On entry:
+c---------- 
+c n      = integer. dimension of problem.
+c y      = real array containg the right side.
+c
+c au,
+c jau,    = Lower triangular matrix stored in modified sparse row
+c          format. 
+c
+c On return:
+c----------- 
+c	x = The solution of  U x = y .
+c--------------------------------------------------------------------
+c local variables 
+c
+      integer k, j
+      real*8 t
+c-----------------------------------------------------------------------
+      x(n) = y(n)*au(n)
+      do 150 k = n-1,1,-1
+         t = y(k) 
+         do 100 j = jau(k), jau(k+1)-1
+            t = t - au(j)*x(jau(j))
+ 100     continue
+         x(k) = au(k)*t 
+ 150  continue
+c
+      return
+c----------end-of-udsol-------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine usolc (n,x,y,au,jau,iau)
+      real*8  x(*), y(*), au(*) 
+      integer n, jau(*),iau(*)
+c-----------------------------------------------------------------------
+c       SOUVES     U x = y ;    where U = unit upper trang. CSC format
+c-----------------------------------------------------------------------
+c solves a unit upper triangular system by standard (sequential )
+c forward elimination - matrix stored in CSC format. 
+c-----------------------------------------------------------------------
+c
+c On entry:
+c---------- 
+c n      = integer. dimension of problem.
+c y      = real*8 array containg the right side.
+c
+c au,
+c jau,
+c iau,    = Uower triangular matrix stored in compressed sparse column 
+c          format. 
+c
+c On return:
+c----------- 
+c	x  = The solution of  U x  = y.
+c-----------------------------------------------------------------------
+c local variables 
+c     
+      integer k, j
+      real*8 t
+c-----------------------------------------------------------------------
+      do 140 k=1,n
+         x(k) = y(k) 
+ 140  continue
+      do 150 k = n,1,-1
+         t = x(k) 
+         do 100 j = iau(k), iau(k+1)-1
+            x(jau(j)) = x(jau(j)) - t*au(j) 
+ 100     continue
+ 150  continue
+c
+      return
+c----------end-of-usolc------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine udsolc (n,x,y,au,jau)   
+      integer n, jau(*) 
+      real*8 x(n), y(n), au(*)  
+c-----------------------------------------------------------------------
+c    Solves     U x = y ;    U = nonunit Up. Triang. MSC format 
+c----------------------------------------------------------------------- 
+c solves a (non-unit) upper triangular system by standard (sequential) 
+c forward elimination - matrix stored in Modified Sparse Column format 
+c with diagonal elements already inverted (otherwise do inversion,
+c auuuul(1:n) = 1.0/au(1:n),  before calling ldsol).
+c-----------------------------------------------------------------------
+c
+c On entry:
+c---------- 
+c n      = integer. dimension of problem.
+c y      = real*8 array containg the right hand side.
+c
+c au,
+c jau,   = Upper triangular matrix stored in Modified Sparse Column
+c          format.
+c
+c On return:
+c----------- 
+c	x = The solution of  U x = y .
+c--------------------------------------------------------------------
+c local variables 
+c 
+      integer k, j
+      real*8 t
+c----------------------------------------------------------------------- 
+      do 140 k=1,n
+         x(k) = y(k) 
+ 140  continue
+      do 150 k = n,1,-1
+         x(k) = x(k)*au(k) 
+         t = x(k) 
+         do 100 j = jau(k), jau(k+1)-1
+            x(jau(j)) = x(jau(j)) - t*au(j) 
+ 100     continue
+ 150  continue
+c
+      return
+c----------end-of-udsolc------------------------------------------------ 
+c-----------------------------------------------------------------------
+      end
diff --git a/BLASSM/rmatvec.f b/BLASSM/rmatvec.f
new file mode 100644
index 0000000..c34cbf9
--- /dev/null
+++ b/BLASSM/rmatvec.f
@@ -0,0 +1,202 @@
+      program rmatvec
+      parameter (nmax=10000, nzmax=80000) 
+      implicit real*8 (a-h,o-z)
+c-----------------------------------------------------------------------
+c This test program tests all the subroutines in matvec.
+c it generates matrices and transforms them in appropriate formats
+c and then call the appropriate routines. 
+c-----------------------------------------------------------------------
+      integer ia1(nmax), ia2(nmax), ja1(nzmax), ja2(nzmax), 
+     *     jad(nzmax), iwk1(nmax), iwk2(nmax), idim(11), ioff(10) 
+      real*8 a1(nzmax), a2(nzmax), 
+     *     x(nmax), y(nmax), y0(nmax), y1(nmax), stencil(100) 
+c common used only to generate nonsymmetric matrices      
+c      common /gam/ gamma, gamma1, cvar
+      data idim /4, 10, 15, 40, 50, 60, 70, 80, 90, 100, 200 /
+      data iout /6/
+c     
+c     initialize common gam 
+c     
+c      gamma = 0.5
+c      gamma1 = 1.0
+c      cvar = 1.0
+c-----------------------------------------------------------------------
+c     ii loop corresponds to size of problem 
+c-----------------------------------------------------------------------
+      do 100 ii = 1, 3 
+         write (iout,*) '---------------- ii ',ii,'--------------------' 
+         nfree = 1
+         nx = idim(ii) 
+         ny = nx
+c-----------------------------------------------------------------------
+c     jj loop corresponds to 2-D and 3-D problems.
+c-----------------------------------------------------------------------
+         do 150 jj=1, 2
+         write (iout,*) '     ----------- jj ',jj,' -------------' 
+            nz = 1
+            if (jj .eq. 2) nz = 10
+c     
+c     call matrix generation routine --
+c     (strange to use block version to generate 1 x 1 blocks...)
+c     
+            call gen57bl (nx,ny,nz,1,1,n,a1,ja1,ia1,ia2,stencil)
+c     
+c     initialize x
+c     
+            do 1 j=1, n
+               x(j) = real(j)
+ 1          continue
+c     
+c initial call to get `` exact '' answer in y0
+c
+            call amux(n,x,y0, a1, ja1, ia1) 
+c-----------------------------------------------------------------------
+c TESTING AMUXE
+c-----------------------------------------------------------------------
+c     
+c     convert to itpack format -----
+c     
+            call csrell (n,a1,ja1,ia1,7,a2,jad,n,ndiag,ierr)
+            call amuxe (n, x, y, n, ndiag, a2,jad)
+            call errpr (n, y, y0,iout,'amuxe ') 
+c-----------------------------------------------------------------------
+c TESTING AMUXD
+c-----------------------------------------------------------------------
+c     
+c     convert to diagonal format
+c
+            idiag = 7
+            call csrdia (n, idiag,10,a1, ja1, ia1, nmax, a2,
+     *           ioff, a2, ja2, ia2, jad) 
+            call amuxd (n,x,y,a2,nmax,idiag,ioff) 
+            call errpr (n, y, y0,iout,'amuxd ')
+c-----------------------------------------------------------------------
+c TESTING ATMUX
+c-----------------------------------------------------------------------
+c
+c    convert to csc format (transpose)
+c    
+            call csrcsc (n,1,1,a1,ja1,ia1,a2,ja2,ia2)
+            call atmux (n, x, y, a2, ja2, ia2)
+            call errpr (n, y, y0,iout,'atmux ')
+c-----------------------------------------------------------------------
+c TESTING AMUXJ
+c-----------------------------------------------------------------------
+c     
+c     convert to jagged diagonal format
+c     
+            call csrjad (n,a1,ja1,ia1, jdiag, jad, a2, ja2, ia2) 
+            call amuxj (n, x, y, jdiag, a2, ja2, ia2) 
+            call dvperm (n, y, jad) 
+            call errpr (n, y, y0,iout,'amuxj ') 
+c
+c convert back
+
+            call jadcsr (n, jdiag, a2, ja2, ia2, jad, a1, ja1, ia1)
+            call amux (n, x, y, a1, ja1, ia1)
+            call errpr (n, y, y0,iout,'jadcsr')
+c-----------------------------------------------------------------------
+c-----------------------------------------------------------------------
+c       triangular systems solutions
+c-----------------------------------------------------------------------
+c TESTING LDSOL
+c-----------------------------------------------------------------------
+            call getl (n, a1, ja1, ia1, a2, ja2, ia2)
+            call amux (n,x,y0, a2, ja2, ia2)
+            call atmux(n,x,y1, a2, ja2, ia2)
+            call csrmsr (n, a2, ja2, ia2, a2, ja2, y, iwk2) 
+           do 2 k=1,n
+               a2(k) = 1.0d0/ a2(k)
+ 2        continue
+            call ldsol (n, y, y0, a2, ja2)
+            call errpr (n, x, y, iout,'ldsol ') 
+c-----------------------------------------------------------------------
+c TESTING LDSOLL
+c----------------------------------------------------------------------- 
+            call levels (n, ja2, ja2, nlev, jad, iwk1, iwk2) 
+            call ldsoll (n, y, y0, a2, ja2, nlev, jad, iwk1) 
+            call errpr (n, x, y, iout,'ldsoll') 
+c-----------------------------------------------------------------------
+c TESTING UDSOLC
+c-----------------------------------------------------------------------
+c here we take advantage of the fact that the MSR format for U
+c is the MSC format for L
+c 
+            call udsolc (n, y, y1, a2, ja2)
+            call errpr (n, x, y, iout,'udsolc') 
+c-----------------------------------------------------------------------
+c TESTING LSOL 
+c-----------------------------------------------------------------------
+c here we exploit the fact that with MSR format a, ja, ja is actually
+c the correct data structure for the strict lower triangular part of
+c the CSR format. First rescale matrix. 
+c
+            scal = 0.1
+            do 3 k=ja2(1), ja2(n+1)-1
+               a2(k)=a2(k)*scal
+ 3          continue
+            call amux(n, x, y0, a2, ja2, ja2) 
+            do 4 j=1,n
+               y0(j) = x(j) + y0(j) 
+ 4          continue
+            call lsol (n, y, y0, a2, ja2, ja2) 
+            call errpr (n, x, y, iout,'lsol  ')             
+c-----------------------------------------------------------------------
+c TESTING UDSOL
+c-----------------------------------------------------------------------
+            call getu (n, a1, ja1, ia1, a2, ja2, ia2)
+            call amux (n,x,y0, a2, ja2, ia2)
+            call atmux(n,x,y1, a2, ja2, ia2)
+            call csrmsr (n, a2, ja2, ia2, a2, ja2, y, jad) 
+            do 5 k=1,n
+               a2(k) = 1.0d0/ a2(k)
+ 5          continue
+            call udsol (n, y, y0, a2, ja2)
+            call errpr (n, x, y, iout,'udsol ') 
+c-----------------------------------------------------------------------
+c TESTING LDSOLC
+c-----------------------------------------------------------------------
+c here we take advantage of the fact that the MSR format for L
+c is the MSC format for U 
+c 
+            call ldsolc (n, y, y1, a2, ja2)
+            call errpr (n, x, y, iout,'ldsolc') 
+c-----------------------------------------------------------------------
+c TESTING USOL 
+c-----------------------------------------------------------------------
+c here we exploit the fact that with MSR format a, ja, ja is actually
+c the correct data structure for the strict lower triangular part of
+c the CSR format. First rescale matrix. 
+c
+            scal = 0.1
+            do 6 k=ja2(1), ja2(n+1)-1
+               a2(k)=a2(k)*scal
+ 6          continue
+            call amux(n, x, y1, a2, ja2, ja2) 
+            do 7 j=1,n
+               y1(j) = x(j) + y1(j) 
+ 7          continue
+            call usol (n, y, y1, a2, ja2, ja2) 
+            call errpr (n, x, y, iout,'usol  ')             
+c-----------------------------------------------------------------------
+c   --  END --
+c----------------------------------------------------------------------- 
+ 150     continue
+ 100  continue
+      stop 
+c---------------end-of-main---------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+        subroutine errpr (n, y, y1,iout,msg) 
+        real*8 y(*), y1(*), t, sqrt
+        character*6 msg
+        t = 0.0d0
+        do 1 k=1,n
+           t = t+(y(k)-y1(k))**2
+ 1      continue
+        t = sqrt(t)
+        write (iout,*) ' 2-norm of difference in ',msg,' =', t
+        return
+        end
+       
diff --git a/BLASSM/tester.f b/BLASSM/tester.f
new file mode 100644
index 0000000..5b28fe7
--- /dev/null
+++ b/BLASSM/tester.f
@@ -0,0 +1,172 @@
+       program matprod
+c-----------------------------------------------------------------------
+c      test program for some routines in BLASSM.f
+c----------------------------------------------------------------------- 
+c      Last update: May 2, 1994
+c----------------------------------------------------------------------- 
+       implicit real*8 (a-h,o-z)
+       parameter (nxmax = 30,nmx = nxmax*nxmax,nzmax=7*nmx)	
+       integer ia(nmx+1),ib(nmx+1),ic(nzmax),
+     *	       ja(nzmax),jb(nzmax),jc(nzmax),iw(nmx)
+c-----------------------------------------------------------------------
+       real*8 a(nzmax),b(nzmax),c(nzmax),
+     *	      x(nmx),y(nmx),y1(nmx),rhs(nmx), al(6)
+       character title*71,key*8,type*3 
+
+       nx = 20
+       ny = 20
+       nz = 1
+       al(1) = 1.0D0
+       al(2) = 0.0D0
+       al(3) = 2.3D1
+       al(4) = 0.4D0
+       al(5) = 0.0D0
+       al(6) = 8.2D-2
+       iout = 8
+c-----------------------------------------------------------------------
+       call gen57pt (nx,ny,nz,al,0,n,a,ja,ia,iw,rhs)
+       call gen57pt (ny,nx,nz,al,0,n,b,jb,ib,iw,rhs)
+c
+       s = 3.812
+c        
+       call aplsb1(n,n,a,ja,ia,s,b,jb,ib,c,jc,ic,nzmax,ierr)
+       if (ierr .ne. 0) print *,' ierr = ',ierr
+c
+c       call dump (1,n,.true.,c,jc,ic,9) 
+c
+       do 1 k=1,n
+          x(k) = real(k)/real(n)
+ 1     continue
+c
+       call ope (n,x,y1,a,ja,ia)
+       call ope (n,x,y,b,jb,ib)
+       do 2 j=1, n
+          y1(j) = s*y(j) + y1(j)
+ 2     continue
+c     
+       call ope (n,x,y,c,jc,ic)
+c------------------------------------------------------
+       write (6,*) ' ------------ checking APLSB --------------'
+       call ydfnorm(n,y1,y,6)
+c------------------------------------------------------
+       
+       type = '--------'
+       title=' test matrix for blassm c = a+b '
+       key = 'rua'
+c     
+       ifmt = 103
+c     
+       job = -1
+c--------
+       do 121 jj=1,2
+	  write (9,*) 'DUMP A____________________________'
+          call dump (1,n,.true.,a,ja,ia,9) 
+	  write (9,*) 'DUMP B____________________________'
+          call dump (1,n,.true.,b,jb,ib,9) 
+          call apmbt(n,n,job,a,ja,ia,b,jb,ib,c,jc,ic,nzmax,iw,ierr)
+	  write (9,*) 'DUMP C____________________________'
+          call dump (1,n,.true.,c,jc,ic,9) 
+          if (ierr .ne. 0) print *,' ierr = ',ierr
+          call ope (n,x,y1,a,ja,ia)
+          call opet (n,x,y,b,jb,ib)
+          s = real(job) 
+          do 3 j=1, n
+ 3           y1(j) = y1(j) + s*y(j)
+c     
+             call ope (n,x,y,c,jc,ic)
+c------------xs------------------------------------------
+	 write (6,*) '  '
+	 write (6,*) ' ------------ checking APMBT---------------'
+	 write (6,*) ' ------------ with JOB = ',job,' -------------'
+	 call ydfnorm(n,y1,y,6)
+c------------------------------------------------------
+	 job = job + 2 
+ 121	 continue
+c
+	 type = '--------'
+	 title=' test matrix for blassm c = a+b^T '
+c 
+c
+c
+	s = 0.1232445
+	call aplsbt(n,n,a,ja,ia,s,b,jb,ib,c,jc,ic,nzmax,iw,ierr)
+c
+	if (ierr .ne. 0) print *,' ierr = ',ierr
+         call ope (n,x,y1,a,ja,ia)
+    	 call opet (n,x,y,b,jb,ib)
+	 do 4 j=1, n
+ 4	      y1(j) = y1(j) + s*y(j)
+c
+ 	 call ope (n,x,y,c,jc,ic)
+c------------------------------------------------------
+c------------------------------------------------------
+	 write (6,*) '  '
+	 write (6,*) ' ------------ checking APLSBT---------------'
+	 call ydfnorm(n,y1,y,6)
+c----------------------------------------------------------------------- 
+c testing products
+c-----------------------------------------------------------------------
+        job = 1 
+	call amub (n,n,job,a,ja,ia,b,jb,ib,c,jc,ic,nzmax,iw,ierr)
+c
+	if (ierr .ne. 0) print *,' ierr = ',ierr
+    	 call ope (n,x,y,b,jb,ib)
+    	 call ope (n,y,y1,a,ja,ia)
+c
+ 	 call ope (n,x,y,c,jc,ic)
+c----------------------------------------------------------------------- 
+	 write (6,*) '  '
+	 write (6,*) ' ------------ checking AMUB  ---------------'
+	 call ydfnorm(n,y1,y,6)
+c
+       stop
+       end
+c
+c
+    	subroutine ope (n,x,y,a,ja,ia) 
+	implicit real*8 (a-h,o-z)
+	real*8  x(1),y(1),a(1) 
+	integer ia(*),ja(*)
+c sparse matrix * vector multiplication
+c	
+	do 100 i=1,n
+		k1 = ia(i)
+		k2 = ia(i+1) -1
+	y(i) = 0.0
+	do 99 k=k1,k2
+		y(i) = y(i) + a(k)*x(ja(k)) 
+ 99	continue
+ 100	continue
+	return
+	end
+c
+    	subroutine opet (n,x,y,a,ja,ia) 
+	implicit real*8 (a-h,o-z)
+	real*8  x(1),y(1),a(1) 
+	integer ia(*),ja(*)
+c sparse matrix * vector multiplication
+c	
+	do 1 j=1, n
+ 1	y(j) = 0.0d0 
+c
+	do 100 i=1,n
+	do 99 k=ia(i), ia(i+1)-1 
+		y(ja(k)) = y(ja(k)) + x(i)*a(k)
+ 99	continue
+ 100	continue
+	return
+	end
+c
+	subroutine ydfnorm(n,y1,y,iout)
+	implicit real*8 (a-h,o-z)
+	real*8 y(*),y1(*)
+c
+	 t = 0.0d0
+	 do 21 k=1,n
+	 t = t+(y(k)-y1(k))**2
+ 21	 continue
+	 t = sqrt(t) 
+       write(iout,*) '2-norm of error (exact answer-tested answer)=',t
+c-----------------------------------------------------------------------
+	return
+	end
diff --git a/DOC/QUICK_REF b/DOC/QUICK_REF
new file mode 100644
index 0000000..20a30cf
--- /dev/null
+++ b/DOC/QUICK_REF
@@ -0,0 +1,200 @@
+c-------------------------------------------------------------------------------c
+c                                                                               c
+c                         QUICK REFERENCE                                       c
+c                                                                               c
+c-------------------------------------------------------------------------------c
+c  For convenience we list here the most important subroutines                  c
+c  in the various modules of SPARSKIT. More detailed information can be         c
+c  found either in the body of the paper or in the documentation of the package.c
+c                                                                               c
+c-------------------------------------------------------------------------------c
+c===============================================================================c
+c                         FORMATS Module                                        c
+c===============================================================================c
+c                                                                               c
+c   CSRDNS  : converts a row-stored sparse matrix into the dense format.        c
+c   DNSCSR  : converts a dense matrix to a sparse storage format.               c
+c   COOCSR  : converts coordinate to  to csr format				c
+c   COICSR  : in-place conversion of coordinate to csr format			c
+c   CSRCOO  : converts compressed sparse row to coordinate format.		c
+c   CSRSSR  : converts compressed sparse row to symmetric sparse row format.	c
+c   SSRCSR  : converts symmetric sparse row to compressed sparse row format.	c
+c   CSRELL  : converts compressed sparse row to Ellpack format			c
+c   ELLCSR  : converts Ellpack format to compressed sparse row format.		c
+c   CSRMSR  : converts compressed sparse row format to modified sparse		c
+c             row format.							c
+c   MSRCSR  : converts modified sparse row format to compressed sparse		c
+c             row format.							c
+c   CSRCSC  : converts compressed sparse row format to compressed sparse	c
+c             column format (transposition).					c
+c   CSRDIA  : converts the compressed sparse row format into the diagonal	c
+c             format.								c	
+c   DIACSR  : converts the diagonal format into the compressed sparse row	c
+c             format.								c
+c   BSRCSR  : converts the block-row sparse format into the compressed		c
+c             sparse row format.						c
+c   CSRBSR  : converts the compressed sparse row format into the block-row	c	
+c             sparse format.							c
+c   CSRBND  : converts the compressed sparse row format into the  banded	c
+c             format (Linpack style).						c
+c   BNDCSR  : converts the banded format (Linpack style) into the compressed	c
+c             sparse row storage.						c
+c   CSRSSK  : converts the compressed sparse row format to the symmetric	c
+c             skyline format							c
+c   SSKSSR  : converts symmetric skyline format to symmetric sparse row format.	c
+c   CSRJAD  : converts the csr format into the jagged diagonal format		c
+c   JADCSR  : converts the jagged-diagonal format into the csr format		c
+c   COOELL  : converts the coordinate format into the Ellpack/Itpack format.	c
+c   CSRVBR  : converts the compressed sparse row format into the		c
+c             variable block row format.					c
+c   VBRCSR  : converts the variable block row format into the		        c
+c             compressed sparse row format.					c
+c   CSORTED : Checks if matrix in CSR format is sorted by columns.              c
+c										c
+c-------------------------------------------------------------------------------c
+c===============================================================================c
+c                        UNARY Module						c
+c===============================================================================c
+c										c
+c   SUBMAT : extracts a submatrix from a sparse matrix.				c
+c   FILTER : filters elements from a matrix according to their magnitude.	c
+c   FILTERM: Same as above, but for the MSR format.				c
+c   TRANSP : in-place transposition routine (see also CSRCSC in formats)	c
+c   GETELM : returns a(i,j) for any (i,j)  from a CSR-stored matrix.		c
+c   COPMAT : copies a matrix into another matrix (both stored csr).		c
+c   MSRCOP : copies a matrix in MSR format into a matrix in MSR format.		c
+c   GETELM : returns a(i,j) for any (i,j) from a CSR-stored matrix.		c
+c   GETDIA : extracts a specified diagonal from a matrix.			c
+c   GETL   : extracts lower triangular part.					c
+c   GETU   : extracts upper triangular part.					c
+c   LEVELS : gets the level scheduling structure for lower triangular matrices.	c
+c   AMASK  : extracts  C = A * M 						c
+c   RPERM  : permutes the rows of a matrix (B = P A)				c
+c   CPERM  : permutes the columns of a matrix (B = A Q)				c
+c   DPERM  : permutes a matrix (B = P A Q) given two permutations P, Q		c
+c   DPERM2 : general submatrix permutation/extraction routine.			c
+c   DMPERM : symmetric permutation of row and column (B=PAP') in MSR fmt.	c
+c   DVPERM : permutes a vector (in-place).					c
+c   IVPERM : permutes an integer vector (in-place).				c
+c   RETMX  : returns the max absolute value in each row of the matrix.		c
+c   DIAPOS : returns the positions of the diagonal elements in A.		c
+c   EXTBDG : extracts the main diagonal blocks of a matrix.			c
+c   GETBWD : returns the bandwidth information on a matrix.			c
+c   BLKFND : finds the block-size of a matrix.					c
+c   BLKCHK : checks whether a given integer is the block size of A.		c
+c   INFDIA : obtains information on the diagonals of A.				c
+c   AMUBDG : computes the number of nonzero elements in each row of A*B.	c
+c   APLBDG : computes the number of nonzero elements in each row of  A+B.	c
+c   RNRMS  : computes the norms of the rows of A.				c
+c   CNRMS  : computes the norms of the columns of A.				c
+c   ROSCAL : scales the rows of a matrix by their norms.			c
+c   COSCAL : scales the columns of a matrix by their norms.			c
+c   ADDBLK : adds a matrix B into a block of A.					c
+c   GET1UP : collects the first elements of each row of the upper		c
+c            triangular portion of the matrix.					c
+c   XTROWS : extracts given rows from a matrix in CSR format.			c
+c   CSRKVSTR : Finds block row partitioning of matrix in CSR format             c
+c   CSRKVSTC : Finds block column partitioning of matrix in CSR format          c
+c   KVSTMERGE: Merges block partitionings, for conformal row/col pattern        c
+c										c
+c-------------------------------------------------------------------------------c
+c===============================================================================c
+c                     INOUT Module						c
+c===============================================================================c
+c										c
+c   READMT  : reads matrices in the boeing/Harewell format.			c
+c   PRTMT   : prints matrices in the boeing/Harewell format.			c
+c   DUMP    : prints rows of a matrix,  in a readable format.			c
+c   PLTMT   : produces a 'pic' file for plotting a sparse matrix.		c
+c   PSPLTM  : Generates a post-script plot of the non-zero pattern of A.	c
+c   SMMS    : Write the matrx in a format used in SMMS package.			c
+c   READSM  : Reads matrices in coordinate format (as in SMMS package).		c
+c   READSK  : Reads matrices in CSR format (simplified H/B formate).		c
+c   SKIT    : Writes matrices to a file, format same as above.			c
+c   PRTUNF  : Writes matrices (in CSR format) unformatted.			c
+c   READUNF : Reads unformatted data of matrices (in CSR format).		c
+c                                                                               c
+c-------------------------------------------------------------------------------c
+c===============================================================================c
+c                     INFO Module                                               c
+c===============================================================================c
+c										c
+c   DINFO1 :  obtains a number of statistics on a sparse matrix.		c
+c   VBRINFO:  Print info on matrix in variable block row format                 c
+c										c
+c-------------------------------------------------------------------------------c
+c===============================================================================c
+c                    MATGEN Module 						c
+c===============================================================================c
+c                                                                               c
+c   GEN57PT : generates 5-point and 7-point matrices.				c
+c   GEN57BL : generates block 5-point and 7-point matrices.			c
+c   GENFEA  : generates finite element matrices in assembled form.		c
+c   GENFEU  : generates finite element matrices in unassembled form.		c
+c   ASSMB1  : assembles an unassembled matrix (as produced by genfeu).		c
+c   MATRF2  : Routines for generating sparse matrices by Zlatev et al.		c
+c   DCN     : Routines for generating sparse matrices by Zlatev et al.		c
+c   ECN     : Routines for generating sparse matrices by Zlatev et al.		c
+c   MARKGEN : subroutine to produce a Markov chain matrix for a random walk.	c
+c                                                                               c
+c-------------------------------------------------------------------------------c
+c===============================================================================c
+c                    BLASSM Module						c
+c===============================================================================c
+c										c
+c   AMUB   :   computes      C = A*B						c
+c   APLB   :   computes      C = A+B 						c
+c   APLSB  :   computes      C = A + s B 					c
+c   APMBT  :   Computes      C = A +(-) B^T 					c
+c   APLSBT :   Computes      C = A + s * B^T 					c
+c   DIAMUA :   Computes      C = Diag * A   					c
+c   AMUDIA :   Computes      C = A* Diag  					c
+c   APLDIA :   Computes      C = A + Diag   					c
+c   APLSCA :   Computes      A:= A + s I   (s = scalar)				c
+c										c
+c-------------------------------------------------------------------------------c
+c===============================================================================c
+c                    MATVEC Module                                              c
+c===============================================================================c
+c										c
+c   AMUX  : A times a vector. Compressed Sparse Row (CSR) format.		c
+c   ATMUX : A^T  times a vector. CSR format.					c
+c   AMUXE : A times a vector. Ellpack/Itpack (ELL) format.			c
+c   AMUXD : A times a vector. Diagonal (DIA) format.				c
+c   AMUXJ : A times a vector. Jagged Diagonal (JAD) format.			c
+c   VBRMV : Sparse matrix-full vector product, in VBR format                    c
+c										c
+c   LSOL  : Unit lower triangular system solution. Compressed Sparse Row 	c
+c           (CSR) format.							c
+c   LDSOL : Lower triangular system solution. Modified Sparse Row (MSR) format.	c
+c   LSOL  : Unit lower triangular system solution. Compressed Sparse Column	c
+c           (CSC) format.							c
+c   LDSOLC: Lower triangular system solution. Modif. Sparse Column (MSC) format c
+c   LDSOLL: Lower triangular system solution with level scheduling. MSR format.	c
+c   USOL  : Unit upper triangular system solution. Compressed Sparse Row 	c
+c           (CSR) format.							c
+c   UDSOL : Upper triangular system solution. Modified Sparse Row (MSR) format.	c
+c   USOLC : Unit upper triangular system solution. Compressed Sparse 		c
+c           Column (CSC) format.						c
+c   UDSOLC: Upper triangular system solution. Modif. Sparse Column (MSC) format c
+c										c
+c-------------------------------------------------------------------------------c
+c===============================================================================c
+c                   ORDERINGS Module						c
+c===============================================================================c
+c										c
+c   LEVSET : The standard Cuthill-McKee ordering algorithm.			c
+c   COLOR  : A greedy algorithm for multicoloring ordering.			c
+c   CCN    : Strongly connected components.                                     c
+c										c
+c-------------------------------------------------------------------------------c
+c===============================================================================c
+c                    ITSOL Module						c
+c===============================================================================c
+c										c 
+c   ILUT    : ILUT(k) preconditioned GMRES mini package.			c
+c   ITERS   : Nine Krylov iterative solvers with reverse communication.         c
+c										c
+c-------------------------------------------------------------------------------c
+c===============================================================================c
+                   
diff --git a/DOC/README b/DOC/README
new file mode 100644
index 0000000..7f2f99a
--- /dev/null
+++ b/DOC/README
@@ -0,0 +1,14 @@
+
+ This directory contains some documentation on the package. 
+
+  paper.tex is the tex-file of the documentation. 
+  paper.ps is the post-script file
+  QUICK_REF is a quick-reference file that contains all existing routines
+            listed by module. * may need updating* 
+
+  all other files are pictures used by paper.tex.
+
+ *THANKS: to Daniel Heiserer (BMW, germany) for a the recent update to
+  the files (latex, figures..) in this directory
+
+-----------------------------------------------------------------------
diff --git a/DOC/dir.eps b/DOC/dir.eps
new file mode 100644
index 0000000..a3b7c1d
--- /dev/null
+++ b/DOC/dir.eps
@@ -0,0 +1,115 @@
+%!PS-Adobe-2.0 EPSF-2.0
+%%Title: /tmp/xfig-fig024490
+%%Creator: fig2dev
+%%CreationDate: Thu Aug 19 20:24:55 1993
+%%For: dsu@unity (Dongli Su,2-209 EECS,626-7512,378-3764)
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diff --git a/DOC/msh8.pdf b/DOC/msh8.pdf
new file mode 100644
index 0000000..ec0f6b2
--- /dev/null
+++ b/DOC/msh8.pdf
diff --git a/DOC/msh8.ps b/DOC/msh8.ps
new file mode 100644
index 0000000..2b15651
--- /dev/null
+++ b/DOC/msh8.ps
@@ -0,0 +1,10937 @@
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+%%BoundingBox:   80 0 530 450
+%%EndComments
+/cm {72 mul 2.54 div} def
+/mc {72 div 2.54 mul} def
+/pnum { 72 div 2.54 mul 20 string
+cvs print ( ) print} def
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+showpage
+%%EndDocument
+
+ endTexFig
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+showpage
+%%EndDocument
+ @endspecial 883 x Fi(7.3)70 b(Mark)n(o)n(v)25 b(Chains)60
+1223 y Fl(Mark)o(o)o(v)15 b(c)o(hain)g(matrices)f(arising)i(from)e(a)i
+(random)f(w)o(alk)h(on)g(a)g(triangular)g(grid.)21 b(This)16
+b(is)f(mainly)60 1283 y(useful)c(for)h(testing)g(nonsymmetric)c(eigen)o(v)m
+(alue)i(co)q(des.)20 b(It)12 b(has)g(b)q(een)f(suggested)i(b)o(y)e(G.W.)g
+(Stew)o(art)60 1343 y(in)16 b(one)h(of)g(his)g(pap)q(ers)h([10])e(and)i(w)o
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+(metho)q(ds,)g(see,)h(e.g.,)f([8].)60 1548 y Fi(7.4)70 b(Other)22
+b(Matrices)60 1640 y Fl(Curren)o(tly)d(w)o(e)h(ha)o(v)o(e)f(only)i(one)f
+(additional)g(set)g(of)h(matrices.)31 b(These)20 b(are)h(the)f(test)g
+(matrices)1900 1622 y Fd(2)60 1700 y Fl(from)f(Zlatev)g(et.)31
+b(al.)h([12])20 b(and)g(Osterb)o(y)f(and)h(Zlatev)f([7].)32
+b(The)19 b(\014rst)i(t)o(w)o(o)e(matrix)f(generators)60 1761
+y(describ)q(ed)f(in)g(the)g(ab)q(o)o(v)o(e)g(references)f(are)h(referred)f
+(to)i(as)g Fj(D)q Fl(\()p Fj(n;)8 b(c)p Fl(\))18 b(and)g Fj(E)s
+Fl(\()p Fj(n;)8 b(c)p Fl(\))17 b(resp)q(ectiv)o(ely)l(.)k(A)60
+1821 y(more)d(elab)q(orate)i(class)f(where)g(more)f(than)i(t)o(w)o(o)f
+(parameters)f(can)i(b)q(e)f(v)m(aried,)g(is)h(referred)e(to)h(as)60
+1881 y(the)c(class)h Fj(F)7 b Fl(\()p Fj(m;)h(n;)g(c;)g(r)o(;)g(\013)p
+Fl(\))13 b(in)i([7,)g(12)q(].)21 b(The)15 b(three)g(subroutines)g(to)h
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+Fl(\))17 b(\),)i(DCN)f(\(for)h(the)g(class)f Fj(D)q Fl(\()p
+Fj(c;)8 b(n)p Fl(\)\))20 b(and)f(ECN)60 2001 y(\(for)d(the)g(class)h
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diff --git a/DOC/paper.tex b/DOC/paper.tex
new file mode 100644
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--- /dev/null
+++ b/DOC/paper.tex
@@ -0,0 +1,1998 @@
+%\documentstyle[12pt]{article}  
+\documentclass[12pt]{article}
+\usepackage{graphicx}
+
+%% page lay-out  / RUNNING HEAD 
+\pagestyle{myheadings} 
+\markright{\underline{SPARSKIT \hskip 5.3in} \hskip -1.0in}
+\setlength{\headheight}{0.3in} 
+\setlength{\headsep}{0.3in}
+%% 
+\setlength{\textheight}{8.7in} 
+\setlength{\textwidth}{6.2in}     
+\setlength{\oddsidemargin}{0.2in}  % 
+\setlength{\evensidemargin}{0.2in} % 
+\setlength{\parindent}{0.2in} %
+\setlength{\topmargin}{-0.3in} %%
+%% abstract redefinition.
+\def\@abssec#1{\vspace{.5in}\footnotesize \parindent 0.2in 
+{\bf #1. }\ignorespaces}
+\def\abstract{\@abssec{Abstract}}
+%%
+\setcounter{secnumdepth}{5}
+\setcounter{tocdepth}{5}
+%%  a few macros 
+\def\half{{1\over2}}%
+\def\del{\partial} %
+\def\nref#1{(\ref{#1})} 
+%% more macros: for indented boxes. 
+\def\marg#1{\parbox[b]{1.3in}{\bf #1}} 
+\def\disp#1{\parbox[t]{4.62in}{#1} \vskip 0.2in } 
+%%
+%\input{psfig}
+
+\title{
+\parbox{4in}{SPARSKIT: a basic tool kit for sparse 
+matrix computations } }
+\author{\parbox{4in}{VERSION 2\\Youcef Saad\thanks{
+Work done partly at CSRD, university of Illinois and partly at RIACS
+(NASA Ames Research Center). Current address: Computer Science Dept.,
+University of Minnesota, Minneapolis, MN 55455.
+This work was supported in part by the NAS Systems 
+Division, via Cooperative Agreement NCC 2-387 between NASA and 
+the University Space Research Association (USRA)
+and in part  by the Department of Energy under grant 
+DE-FG02-85ER25001.}}}
+
+\date{ } 
+
+\begin{document}
+\bibliographystyle{plain}
+%\bibliographystyle{SIAM}
+
+\maketitle
+
+\vskip 1.5in
+
+\centerline{{\it June 6, 1994} } 
+%\centerline{{\it May 21, 1990} } 
+%\centerline{{\it Updated June 5, 1993 --- Version 2} }  
+
+\thispagestyle{empty}
+
+\begin{abstract} 
+This paper presents the main features of a tool package for 
+manipulating and working with sparse matrices.
+One of the  goals of the package is to provide 
+basic tools to facilitate exchange of software and data
+between researchers in sparse matrix computations.
+Our starting point is the Harwell/Boeing collection of matrices
+for which we provide a number of tools. 
+Among other things the package provides programs for converting
+data structures, printing simple statistics on a matrix, 
+plotting a matrix profile, performing  basic linear algebra 
+operations  with sparse matrices  and so on.
+\end{abstract}
+
+\newpage
+
+\section{Introduction} Research   on   sparse  matrix   techniques  has  become
+increasingly complex, and this trend is likely to accentuate if only
+because  of the growing need 
+to design efficient sparse matrix algorithms for modern supercomputers.   
+While there  are a  number of packages and `user
+friendly' tools, for  performing computations  with small dense
+matrices there is a lack of any similar tool or in fact of any 
+general-purpose libraries for 
+working with sparse  matrices.   Yet a  collection of  a few  basic programs to
+perform some elementary and  common tasks  may be  very useful  in reducing the
+typical time to implement and test sparse matrix algorithms.   That a common 
+set
+of routines  shared  among  researchers  does not  yet exist for sparse matrix
+computation is rather surprising.  Consider the contrasting  situation in dense
+matrix computations.  The Linpack  and Eispack  packages developed  in the 70's
+have been of tremendous  help in  various areas  of scientific  computing.  
+One might speculate on the number of hours of programming efforts 
+saved worldwide thanks to the widespread availability  of these  packages.
+In contrast,  it is  often the case that  researchers in  sparse  matrix 
+computation  
+code their own subroutine for  such  things as converting the storage mode
+of a matrix or for reordering a matrix
+according to a certain permutation.  One of the  reasons for this situation
+might be the absence of any standard for sparse
+matrix computations.  For instance, the number of different data
+structures used to store sparse matrices in various applications is
+staggering.  For the same basic data structure there often exist a
+large number of variations in use.  As sparse matrix computation
+technology is maturing there is a desperate need for some standard for
+the basic storage schemes and possibly, although this is more
+controversial, for the basic linear algebra operations.  
+
+An important example where a package such as SPARSKIT can be helpful is for
+exchanging matrices for research or other purposes.  In this
+situation, one must often translate the matrix from some initial data
+structure in which it is generated, into a different desired data
+structure.  One way around this difficulty is to restrict 
+the number of schemes that can be used and set  some standards.
+ However, this is not
+enough because often the data structures are chosen for their
+efficiency and convenience, and it is not reasonable to ask
+practitioners to abandon their favorite storage schemes.  What is
+needed is a large set of programs to translate one data structure into
+another. In the same vein, subroutines that generate test matrices
+would be extremely valuable since they would allow users to have
+access to a large number of matrices without the burden of actually
+passing large sets of data.
+
+A useful collection of sparse matrices known as the Harwell/Boeing
+collection, which is publically available \cite{Duff-HB}, has been
+widely used in recent years for testing and comparison purposes.
+Because of the importance of this collection many of the tools in
+SPARSKIT can be considered as companion tools to it. For
+example, SPARSKIT supplies simple routines to create a Harwell/Boeing (H/B)
+file from a matrix in any format, tools for creating pic files in
+order to plot a H/B matrix, a few routines that will deliver
+statistics for any H/B matrix, etc.. However, SPARSKIT is not limited
+to being a set of tools to 
+work with H/B matrices. Since one of our main motivations is
+research on iterative methods, we provide numerous subroutines that may help
+researchers in this specific area.  
+SPARSKIT will hopefully be an evolving package
+that will benefit from contributions from other researchers. This
+report is a succinct description of the  package in this release.
+
+\begin{figure}[h]
+%\special{psfile=dir.eps vscale = 75 hscale = 75 hoffset =0 voffset= -30}
+\includegraphics[width=15cm]{dir}
+\caption {General organization of SPARSKIT.}
+\label{organization}
+%\vskip 0.1cm
+\end{figure}
+
+\section{Data structures for sparse matrices and the conversion routines}
+
+One of the difficulties in sparse matrix computations is the variety
+of types of matrices that are encountered in practical applications.
+The purpose of each of these schemes is to gain efficiency both in
+terms of memory utilization and arithmetic operations.  As a result
+many different ways of storing sparse matrices have been devised to
+take advantage of the structure of the matrices or the specificity of
+the problem from which they arise.  For example if it is known that a
+matrix consists of a few diagonals one may simply store these
+diagonals as vectors and the offsets of each diagonal with respect to
+the main diagonal.  If the matrix is not regularly structured, then
+one of the most common storage schemes in use today is what we refer
+to in SPARSKIT as the Compressed Sparse Row (CSR) scheme. In this
+scheme all the nonzero entries are stored row by row  in a 
+one-dimensional real array $A$ together with an array $JA$ containing
+their column indices and a pointer array which contains the addresses
+in $A$ and $JA$ of the beginning of each row. The order of the elements 
+within each row does not matter. Also of importance
+because of its simplicity is the coordinate storage scheme in which
+the nonzero entries of $A$ are stored in any order together with their
+row and column indices.  Many of the other existing schemes are
+specialized to some extent. The reader is
+referred to the book by Duff et al. \cite{Duff-book} for more details.
+
+\subsection{Storage Formats} 	
+Currently, 
+the conversion routines of SPARSKIT can handle thirteen different storage
+formats. These include some of the most commonly used schemes but they
+are by no means exhaustive.  We found it particularly useful to have
+all these storage modes when trying to extract a matrix from someone
+else's application code in order, for example, to analyze it with the
+tools described in the next sections or, more commonly, to try a given
+solution method which requires a different data structure than the
+one originally used in the application.  Often the matrix is stored in
+one of these modes or a variant that is very close to it.  We hope to
+add many more conversion routines as SPARSKIT evolves.
+
+In this section we describe in detail the storage schemes that are
+handled in the FORMATS module.  For convenience we have decided to
+label by a three character name each format used.  We start by listing
+the formats and then describe them in detail  in separate subsections
+(except for the dense format which needs no detailed description).	
+
+\begin{description}
+\item{{\bf DNS}} Dense format
+\item{{\bf BND}} Linpack Banded format
+\item{{\bf CSR}} Compressed Sparse Row format 
+\item{{\bf CSC}} Compressed Sparse Column format 
+\item{{\bf COO}} Coordinate format
+\item{{\bf ELL}} Ellpack-Itpack generalized diagonal format
+\item{{\bf DIA}} Diagonal format
+\item{{\bf BSR}} Block Sparse Row format
+\item{{\bf MSR}} Modified Compressed Sparse Row format
+\item{{\bf SSK}} Symmetric Skyline format
+\item{{\bf NSK}} Nonsymmetric Skyline format
+\item{{\bf LNK}} Linked list storage format 
+\item{{\bf JAD}} The Jagged Diagonal format 
+\item{{\bf SSS}} The Symmetric Sparse Skyline format
+\item{{\bf USS}} The Unsymmetric Sparse Skyline format
+\item{{\bf VBR}} Variable Block Row format
+\end{description}
+
+In the following sections we denote by $A$ the matrix under
+consideration and by $N$ its row dimension and $NNZ$ the number of its
+nonzero elements.
+
+\subsubsection{Compressed Sparse Row and related formats
+ (CSR, CSC and MSR)} The Compressed Sparse Row format is the basic
+format used in SPARSKIT. Its  data structure consists of three arrays.
+
+\begin{itemize} 
+
+\item A real array $A$ containing the real values $a_{ij}$ stored row by row,
+from row 1 to $N$. The length of $A$ is NNZ.
+
+\item An integer array $JA$ containing the column indices
+of the elements $a_{ij}$ as stored in the array $A$.  The length of
+$JA$ is NNZ.
+
+\item An integer array $IA$ containing the pointers to the
+beginning of each row in the arrays $A$ and $JA$. Thus the content of
+$IA(i)$ is the position in arrays $A$ and $JA$ where the $i$-th row
+starts.  The length of $IA$ is $N+1$ with $IA(N+1)$ containing the
+number $IA(1)+NNZ$, i.e., the address in $A$ and $JA$ of the beginning
+of a fictitious row $N+1$.
+
+\end{itemize}
+The order of the nonzero elements within the same row are not important. 
+A variation to this scheme is to sort the elements in each row 
+in such a way that their column positions are in increasing order.
+When this sorting in enforced, it is often possible to 
+make substantial savings in the number of operations of 
+some well-known algorithms. 
+The Compressed Sparse Column format is identical with the Compressed
+Sparse Row format except that the columns of $A$ are stored instead of
+the rows. In other words the Compressed Sparse Column format is simply
+the Compressed Sparse Row format for the matrix $A^T$.
+
+The Modified Sparse Row (MSR) format is a rather common variation of
+the Compressed Sparse Row format which consists of keeping the main
+diagonal of $A$ separately. The corresponding data structure consists
+of a real array $A$ and an integer array $JA$. The first $N$ positions
+in $A$ contain the diagonal elements of the matrix, in order.  The position
+$N+1$ of the array $A$ is not used. Starting from position $N+2$, the
+nonzero elements of $A$, excluding its diagonal elements, are stored
+row-wise. Corresponding to each element $A(k)$ the integer $JA(k)$ is
+the column index of the element $A(k)$ in the matrix $A$. The $N+1$
+first positions of $JA$ contain the pointer to the beginning of each
+row in $A$ and $JA$. The advantage of this storage mode is that many
+matrices have a full main diagonal, i.e., $a_{ii} \ne 0, i=1,\ldots,
+N$, and this diagonal is best represented by an array of length $N$.
+This storage mode is particularly useful for triangular matrices with
+non-unit diagonals. Often the diagonal is then stored in inverted form
+(i.e. $1/a_{ii} $ is stored in place of $a_{ii} $) because triangular
+systems are often solved repeatedly with the same matrix many times,
+as is the case for example in preconditioned Conjugate Gradient
+methods.  The column oriented analogue of the MSR format, called MSC
+format, is also used in some of the other modules, but no
+transformation to/from it to the CSC format is necessary: for example
+to pass from CSC to MSC one can use the routine to pass from the CSR
+to the MSR formats, since the data structures are identical.  The 
+ above three storage modes are used in many well-known packages.
+
+\subsubsection{The banded Linpack format (BND)} 
+Banded matrices represent the simplest form of sparse matrices and
+they often convey the easiest way of exploiting sparsity.  There are
+many ways of storing a banded matrix. The one we adopted here follows
+the data structure used in the Linpack banded solution routines. Our
+motivation is that one can easily take advantage of this widely available 
+package if the matrices are banded.  For fairly small matrices (say,
+$N < 2000$ on supercomputers, $ N < 200 $ on fast workstations, and
+with a bandwidth of $O(N^{\half} )$), this may represent a viable and
+simple way of solving linear systems. One must first transform the
+initial data structure into the banded Linpack format and then call the
+appropriate band solver. For large problems it is clear that a better
+alternative would be to use a sparse solver such as MA28, which
+requires the input matrix to be in the coordinate format. 
+
+%%It is
+%%expected that these types of utilization of the conversion routines
+%% will in fact be among the most common ones.
+
+In the BND format the nonzero elements of $A$ are stored in a
+rectangular array $ABD$ with the nonzero elements of the $j$-th column
+being stored in the $j-th$ column of $ABD$. We also need to know the
+number $ML$ of diagonals below the main diagonals and the number $MU$
+of diagonals above the main diagonals. Thus the bandwidth of $A$ is
+$ML+MU+1$ which is the minimum number of rows required in the array
+$ABD$. An additional integer parameter is needed to indicate which row
+of $ABD$ contains the lowest diagonal.
+
+\subsubsection{The coordinate format (COO) } 
+
+The coordinate format is certainly the simplest storage scheme for
+sparse matrices. It consists of three arrays: a real array of size
+$NNZ$ containing the real values of nonzero elements of $A$ in any
+order, an integer array containing their row indices and a second
+integer array containing their column indices. Note that this scheme
+is as general as the CSR format, but from the point of view of memory
+requirement it is not as efficient.  On the other hand it is
+attractive because of its simplicity and the fact that it is very
+commonly used.  Incidentally, we should mention a variation to this
+mode which is perhaps the most economical in terms of memory usage.
+The modified version requires only a real array $A$ containing the
+real values $a_{ij}$ along with only one integer array that contains
+the integer values $ (i-1)N + j$ for each corresponding nonzero
+element $a_{ij}$.  It is clear that this is an unambiguous
+representation of all the nonzero elements of $A$.  There are two
+drawbacks to this scheme. First, it requires some integer arithmetic
+to extract the column and row indices of each element when they are
+needed. Second, for large matrices it may lead to integer overflow
+because of the need to deal with integers which may be very large (of
+the order of $N^2$).  Because of these two drawbacks this scheme has
+seldom been used in practice.
+
+\subsubsection{The diagonal format (DIA) }
+The matrices that arise in many applications often consist of a few
+diagonals. This structure has probably been the first one to be
+exploited for the purpose of improving performance of
+matrix by vector products on supercomputers, see references in
+\cite{Saad-Boeing}.  To store
+these matrices we may store the diagonals in a rectangular array
+$DIAG(1:N,1:NDIAG) $ where $NDIAG$ is the number of diagonals.  We
+also need to know the offsets of each of the diagonals with respect to
+the main diagonal. These will be stored in an array $IOFF(1:NDIAG)$.
+Thus, in position $(i,k)$ of the array $DIAG$ is located the element
+$a_{i,i+ioff(k)}$ of the original matrix.  The order in which the
+diagonals are stored in the columns of $DIAG$ is unimportant.  Note
+also that all the diagonals except the main diagonal have fewer than
+$N$ elements, so there are positions in $DIAG$ that will not be used.
+
+In many applications there is a small number of non-empty diagonals
+and this scheme is enough. In general however, it may be desirable to
+supplement this data structure, e.g., by a compressed sparse row
+format.  A general matrix is therefore represented as the sum of a
+diagonal-structured matrix and a general sparse matrix.  The
+conversion routine CSRDIA which converts from the compressed
+sparse row format to the diagonal format has an option	 to this
+effect.  If the user wants to convert a general sparse matrix to one
+with, say, 5 diagonals, and if the input matrix has more than 5
+diagonals, the rest of the matrix (after extraction of the 5 desired
+diagonals) will be put, if desired, into a matrix in the CSR format.
+In addition, the code may also compute the most important 5 diagonals
+if wanted, or it can get those indicated by the user through the array
+$IOFF$.
+
+\subsubsection{The Ellpack-Itpack format (ELL) }
+The Ellpack-Itpack format
+\cite{Oppe-Kincaid,Young-Oppe-al,Oppe-NSPCG} is a 
+generalization of the diagonal storage scheme which is intended for
+general sparse matrices with a limited maximum number of nonzeros per
+row. Two rectangular arrays of the same size are required, one real
+and one integer.  The first, $COEF$, is similar to $DIAG$ and contains
+the nonzero elements of $A$. Assuming that there are at most $NDIAG$
+nonzero elements in each row of $A$, we can store the nonzero elements
+of each row of the matrix in a row of the array $COEF(1:N,1:NDIAG)$
+completing the row by zeros if necessary.  Together with $COEF$ we
+need to store an integer array $JCOEF(1:N,1:NDIAG)$ which contains the
+column positions of each entry in $COEF$.
+
+\subsubsection{The Block Sparse Row format (BSR)} 
+Block matrices are common in all areas of scientific computing. The
+best way to describe block matrices is by viewing them as sparse
+matrices whose nonzero entries are square dense blocks. Block matrices
+arise from the discretization of partial differential equations when
+there are several degrees of freedom per grid point.  There are
+restrictions to this scheme. Each of the blocks is treated as a dense
+block. If there are zero elements within each block they must be
+treated as nonzero elements with the value zero.
+
+There are several variations to the method used for storing sparse
+matrices with block structure. The one considered here, the Block
+Sparse Row format, is a simple generalization of the Compressed Sparse
+Row format.
+
+We denote here by $NBLK$ the dimension of each block, by 
+$NNZR$ the number of nonzero blocks in $A$ (i.e., 
+$NNZR = NNZ/(NBLK^2) $) and by $NR$ the block dimension of $A$,
+(i.e., $NR = N/NBLK$), the letter $R$ standing for `reduced'. 
+Like the Compressed Sparse Row  format we need three arrays. A rectangular
+real array $A(1:NNZR,1:NBLK,1:NBLK) $ contains the nonzero
+blocks listed (block)-row-wise. Associated with this real array
+is an integer array 
+$JA(1:NNZR) $ which holds the actual column positions in the 
+original matrix of the $(1,1)$ elements of the nonzero blocks.
+Finally, the pointer array $IA(1:NR+1)$ points to the beginning
+of each block row in $A$ and $JA$. 
+
+The savings in memory and in the use of indirect addressing with  this
+scheme over Compressed Sparse Row   can be substantial for large
+values of $NBLK$.
+
+\subsubsection{The Symmetric Skyline format (SSK) }
+A skyline matrix is often referred to as a variable band
+matrix or a profile matrix \cite{Duff-book}.  The main 
+attraction of skyline matrices is that when pivoting is
+not necessary then the skyline structure of the matrix is preserved 
+during Gaussian elimination. If the matrix is symmetric
+we only need to store its lower triangular part. This is a
+collection of rows whose length varies. A simple method used to store
+a Symmetric Skyline matrix is to place all the rows in order from
+1 to $N$ in a  real array $A$ and then keep an integer array which holds 
+the pointers to the beginning of each row, see \cite{Duff-survey}.
+The column positions of the nonzero elements stored in $A$
+can easily be derived and are therefore not needed. However, there 
+are several variations to this scheme that are commonly used is
+commercial software packages. For example, we found that in many 
+instances the pointer is to the diagonal element rather than to the 
+first element in the row. In some cases (e.g., IBM's ISSL library)
+both are supported. Given that these variations are commonly used 
+it is a good idea to provide at least a few of them. 
+
+\subsubsection{The Non Symmetric Skyline format (NSK) }
+Conceptually, the  data structure of a nonsymmetric skyline 
+matrix consists of two substructures. 
+The first consists of the lower part of $A$ stored in skyline format
+and the second of its upper triangular part stored in a column
+oriented skyline format (i.e., the transpose is stored in
+standard row skyline mode). Several ways of putting these
+substructures together may be used and there are no compelling 
+reasons for preferring one strategy over another one. 
+One possibility is to use two separate arrays $AL$ and $AU$ for
+the lower part and upper part respectively, with the diagonal 
+element in the upper part. The data structures for each of 
+two parts is similar to that used for the SSK storage.
+
+%% NOT DONE YET --- 
+%%We chose to store contiguously each row of the lower part and column of 
+%%the upper part of the matrix.  The real array $A$ will contain 
+%%the 1-st row followed by the first column (empty), followed
+%%by the second row followed by the second column, etc..
+%%An additional pointer is needed to indicate where the
+%%diagonal elements, which separate the lower from the upper part,
+%%are located in this array. G
+
+\subsubsection{The linked list storage format (LNK) }  
+This is one of the oldest data structures used for sparse matrix computations.
+It consists of four arrays: $A$, $JCOL$, $LINK$ and $JSTART$. 
+The arrays $A$ and $JCOL$ contain the nonzero elements and their
+corresponding column indices respectively. The integer array $LINK$ is
+the usual link pointer array in linked list data structures: 
+$LINK(k)$ points to the position of the nonzero element next to 
+$A(k), JCOL(k)$ in the same row. Note that the order of the elements 
+within each row is unimportant.  If $LINK(k) =0$ then there is no
+next element, i.e., $A(k), JCOL(k)$ is the last element of the row.
+Finally, $ISTART$ points to the first element of each row in 
+in the previous arrays. Thus, $k=ISTART(1)$ points to the first element
+of the first row, in $A, ICOL$, 
+ $ISTART(2) $ to the second element, etc..
+As a convention $ISTART(i) = 0$, means that the $i$-th row is empty.
+
+\subsubsection{The Jagged Diagonal format (JAD)} 
+This storage mode is very useful for the efficient implementation
+of iterative methods on  parallel and vector processors
+\cite{Saad-Boeing}. Starting from the CSR format, the idea is to 
+first reorder the rows of the matrix decreasingly according to their 
+number of nonzeros entries. Then, a new data structure is built 
+by constructing what we call ``jagged diagonals" (j-diagonals).
+We store as a dense vector, the vector consisting of all
+the first elements in $A, JA$ from each row, together with an integer 
+vector containing the column positions of the corresponding 
+elements. This is followed by the second jagged  diagonal consisting of the
+elements in the second positions from the left. As we build more and
+more of these diagonals, their length decreases.  The number of
+j-diagonals is equal to the number of nonzero elements of the first
+row, i.e., to the largest number of nonzero elements per row.  The
+data structure to represent a general matrix in this form consists,
+before anything, of the permutation array which reorders the rows.
+Then the real array $A$ containing the jagged diagonals in succession
+and the array $JA$ of the corresponding column positions are stored,
+together with a pointer array $ IA $ which points to the beginning of
+each jagged diagonal in the arrays $A, JA$. The advantage of this
+scheme for matrix multiplications has been illustrated in
+\cite{Saad-Boeing} and in \cite{Anderson-Saad} in the 
+context of triangular system solutions.
+
+\subsubsection{The Symmetric and Unsymmetric Sparse Skyline format
+(SSS, USS)} 
+
+This is an extension of the CSR-type format described above.
+In the symmetric version, the following arrays are used:
+$DIAG$ stores the diagonal,
+$AL, JAL, IAL$ stores the strict lower part in CSR format, and
+$AU$ stores the values of the strict upper part in CSC format.
+In the unsymmetric version, instead of $AU$ alone, the strict upper part
+is stored in $AU, JAU, IAU$ in CSC format.
+
+%% THIS SECTION HAS BEEN MODIFIED
+%% \subsubsection{The Compressed Variable Block Format(CVB)}
+%% This is an extension of the Block Sparse Row format (BSR). In the BSR
+%% format, all the  blocks have the same size.
+%% A more general way of partitioning might allow the
+%% matrix to be split into different size blocks. In the CVB format, an
+%% arbitrary partitioning of the matrix is allowed. However, the columns and
+%% the rows must be split in the same way. 
+%%
+%% Figure 0 shows a 9x9 sparse matrix and its corresponding storage vectors.
+%% Let $h$ be the index of the leading elements of the $k^{th}$ block 
+%% stored in $AA$. Then $k^{th}$ block of size $m*p$ is stored in  
+%% $AA(h)$ to $AA(h+mp-1)$.
+%% For  example, the $3^{rd}$ block is stored in $AA(9)$ to $AA(17)$.
+%%
+%% The data structure consists of the integers \(N\), \(NB\), and the arrays 
+%% \(AA\), \(JA\), \(IA\), and
+%% \(KVST\), where \(N\) is the matrix size, i.e.~number of rows in the
+%% matrix, \(NB\) is the number of block rows, \(AA\) stores the non-zero
+%% values of the matrix, \(JA\) has the column indices of the first
+%% elements in the blocks, \(IA\) contains the pointers to the beginning
+%% of each block row (in \(AA\)), \(KVST\) contains the index of
+%% the first row in each block row.
+%%
+%% \begin{figure}[h]
+%% \vspace{3in}
+%% \special{psfile= fig1.eps vscale = 100 hscale = 100 hoffset =-50 voffset= -420}
+%%\caption {\bf Fig 1: An example of a 9x9 sparse matrix and its storage vectors.  }
+%%\label{conventional}
+%% \end{figure}
+
+\subsubsection{The Variable Block Row format (VBR)}
+In many applications, matrices are blocked, but the blocks are not all
+the same size.  These so-called variable block matrices arise from the
+discretization of systems of partial differential equations where there
+is a varying number of equations at each grid point.  Like in the Block
+Sparse Row (BSR) format, all entries of nonzero blocks (blocks which
+contain any nonzeros) are stored, even if their value is zero.  Also
+like the BSR format, there is significant savings in integer pointer
+overhead in the data structure.
+
+Variable block generalizations can be made to many matrix storage
+formats.  The Variable Block Row (VBR) format is a generalization of the
+Compressed Sparse Row (CSR) format, and is similar to the variable
+block format used at the University of Waterloo, and one currently
+proposed in the Sparse BLAS toolkit.
+
+In the VBR format, the $IA$ and $JA$ arrays of the CSR format store the
+sparsity structure of the blocks.  The entries in each block are stored
+in $A$ in column-major order so that each block may be passed as a small
+dense matrix to a Fortran subprogram.  The block row and block column
+partitionings are stored in the vectors {\em KVSTR} and {\em KVSTC},
+by storing the first row or column number of each block row or column
+respectively.  In most applications, the block row and column partitionings
+will be conformal, and the same array may be used in the programs.
+Finally, integer pointers to the beginning of each block in $A$ are stored
+in the array $KA$.
+
+$IA$ contains pointers to the beginning of each block row in $JA$ and $KA$.
+Thus $IA$ has length equal to the number of block rows (plus one to mark
+the end of the matrix), and $JA$ has length equal to the number of nonzero
+blocks.  $KA$ has the same length as $JA$ plus one to mark the end of
+the matrix.  {\em KVSTR} and {\em KVSTC} have length equal to the number
+of block rows and columns respectively, and $A$ has length equal to the
+number of nonzeros in the matrix.  The following
+figure shows the VBR format applied to a small matrix.
+
+This version of Sparskit has a number of routines to support the variable
+block matrix format.  CSRVBR and VBRCSR convert between the VBR and CSR
+formats; VBRINFO prints some elementary information about the block
+structure of a matrix in VBR format; AMUXV performs a matrix-vector product
+with a matrix in VBR format; CSRKVSTR and CSRKVSTC are used
+to determine row and column block partitionings of a matrix in CSR format,
+and KVSTMERGE is used to combine row and column partitionings to achieve
+a conformal partitioning.
+
+\begin{figure}[htb]
+%\vspace{4.8in}
+%\centerline{\psfig{figure=vbrpic.eps,width=6.2in}}
+\includegraphics[width=6.2in]{vbrpic}
+%\special{psfile=vbrpic.eps vscale = 100 hscale = 100}
+%\special{psfile=vbrpic.eps vscale = 100 hscale = 100 voffset= -420}
+\caption {A $6 \times 8$ sparse matrix and its storage vectors.}
+\end{figure}
+
+\subsection{The FORMATS conversion module}
+It is important to note that there is no need to have a subroutine for
+each pair of data structures, since all we need is to be able to
+convert any format to the standard row-compressed format and then back
+to any other format.  There are currently 32 different conversion
+routines in this module all of which are devoted to converting from
+one data structure into another.
+
+The naming mechanism adopted is to use a 6-character name for each of
+the subroutines, the first 3 for the input format and the last 3 for
+the output format.  Thus COOCSR performs the conversion from the
+coordinate format to the Compressed Sparse Row format.  However it was
+necessary to break the naming rule in one exception.  We needed a
+version of COOCSR that is in-place, i.e., which can take the input
+matrix, and convert it directly into a CSR format by using very little
+additional work space.  This routine is called COICSR.  Each of
+the formats has a routine to translate it to the CSR format and a routine
+to convert back to it from the CSR format.  The only exception is that
+a CSCCSR routine is not necessary since
+the conversion from Column Sparse format to Sparse Row format  can be
+performed with the same routine CSRCSC.  This is essentially a transposition
+operation.
+
+Considerable effort has been put at attempting to make the conversion
+routines in-place, i.e., in allowing some or all of 
+the output arrays to be the same as the input arrays. 
+The purpose is to save storage whenever possible without
+sacrificing performance. The added flexibility can be 
+very convenient in some situations. 
+When the additional coding complexity to  permit
+the routine to be in-place was not too high this was always done.
+If the subroutine is in-place this is clearly indicated in the
+documentation. As mentioned above, we found it necessary in one instance
+to provide both the in-place version as well as the regular version:
+ COICSR is an in-place version of the COOCSR routine.
+We would also like to add that other routines that avoid the
+CSR format for some of the more important data structures may
+eventually be included. For now, there is only one such routine
+\footnote{Contributed by E. Rothman from Cornell University.}
+namely, COOELL. 
+
+\subsection{Internal format used in SPARSKIT}
+Most of the routines in SPARSKIT  use internally the Compressed
+Sparse Row format. The selection of 
+the CSR mode has been motivated by several factors. Simplicity,
+generality, and widespread use are certainly the most 
+important ones. However, it has often been argued 
+that the column scheme may
+have been a better choice. One argument in this favor is that
+vector machines usually give a better performance for such 
+operations as matrix vector by multiplications for matrices
+stored in CSC format. In fact for parallel machines which
+have a low overhead in loop synchronization (e.g., the Alliants),
+the situation is reversed, see \cite{Saad-Boeing} for details.
+For almost any argument in favor of one scheme there seems
+to be an argument in favor of the other. Fortunately,
+the difference provided in functionality is rather minor.
+For example the subroutine APLB to add two matrices in CSR format,
+described in Section 5.1, can actually be also used to add 
+two matrices in CSC format, since the data structures
+are identical. Several such subroutines can be used for both
+schemes, by pretending that the input matrices
+are stored in CSR mode whereas in fact they are 
+stored in CSC mode. 
+
+\section{Manipulation routines} The module UNARY   
+of SPARSKIT consists of a  number of  utilities to  manipulate and perform
+basic operations with sparse matrices. The  following sections 
+give an overview of this part of the package.
+
+\subsection{Miscellaneous operations with sparse matrices}
+There are a large number of non-algebraic operations that
+are commonly used when working with sparse matrices. 
+A typical example is to transform $A$ into $B = P A Q $
+where $P$ and $Q$ are two permutation matrices. 
+Another example is to extract the lower triangular
+part of $A$ or a given diagonal from $A$. Several other 
+such `extraction' operations are supplied in SPARSKIT. 
+Also provided is the transposition function. This may seem
+as an unnecessary addition since the routine 
+CSRCSC already does perform this function economically. However,
+the new transposition provided is in-place, in that it may
+transpose the matrix and overwrite the result on the original matrix,
+thus saving memory usage. Since many of these manipulation routines
+involve one matrix (as opposed to two in the basic linear algebra routines)
+we created a module called  UNARY to include these subroutines.
+
+Another set of subroutines that are sometimes useful 
+are those involving  a `mask'. A mask
+defines a given nonzero pattern and for all practical
+purposes a mask matrix is a sparse matrix whose nonzero
+entries are all ones (therefore there is no need to store 
+its real values).  Sometimes it is useful
+to extract from a given matrix $A$ the `masked' matrix according
+to a mask $M$, i.e., to compute the matrix
+$A \odot M$ , where $\odot $ denotes the element-wise matrix
+product, and $M$ is some mask matrix.
+
+\subsection{The module UNARY}
+This module of SPARSKIT consists of a number of routines
+to  perform some basic non-algebraic operations on a matrix.
+The following is a list of the routines currently supported with
+a brief explanation. 
+%%There are many other routines which are not 
+%% listed their inclusion still being debated.
+
+\vskip .5in
+
+\marg{SUBMAT}\disp{Extracts a square or
+rectangular submatrix from a sparse matrix. Both the 
+input and output  matrices are in CSR format.
+The routine is in-place.} 
+
+\marg{FILTER}\disp{Filters out elements from a
+ matrix according to their magnitude. Both the input and
+the output matrices are in CSR format.
+The output matrix, is obtained from the
+input matrix by removing all the elements that are smaller than
+a  certain threshold. The threshold is computed for each row
+according to one of three provided options.
+The algorithm is in-place.}
+
+\marg{FILTERM}\disp{Same as above, but for the MSR format.}
+
+\marg{CSORT}\disp{Sorts the elements of a matrix stored in
+CSR format in increasing order of the column numbers. }
+
+\marg{ TRANSP  }\disp{ This is an in-place transposition routine,
+i.e., it can be viewed as an in-place version of the CSRCSC 
+routine in FORMATS.
+One notable disadvantage of  TRANSP is that unlike CSRCSC it 
+does not sort the
+nonzero elements in increasing number of the column positions.} 
+
+\marg{ COPMAT  }\disp{Copy of a matrix into another 
+matrix (both stored CSR).}
+
+\marg{MSRCOP}\disp{Copies a matrix in MSR format into a matrix in MSR format.}
+\marg{ GETELM }\disp{Function returning 
+the value of $a_{ij}$ for any pair $(i,j)$. Also returns address
+of the element in arrays $A, JA$. }
+
+\marg{ GETDIA  }\disp{ Extracts a specified diagonal from a matrix.
+An option is provided to transform the input matrix so that the 
+extracted diagonal is zeroed out in input matrix. Otherwise the diagonal 
+is extracted and the input matrix remains untouched.}
+
+\marg{ GETL    }\disp{This subroutine extracts the
+lower triangular part of a matrix, including the main diagonal.
+The algorithm is in-place.}
+
+\marg{ GETU    }\disp{Extracts the upper triangular part of
+a matrix. Similar to GETL.}
+
+\marg{ LEVELS  }\disp{ 
+Computes the level scheduling data structure for lower
+triangular matrices, see \cite{Anderson-Saad}.} 
+
+\marg{ AMASK   }\disp{ Extracts    $ C = A \odot M  $,
+i.e., performs the mask operation. 
+This routine computes a sparse matrix from an input matrix $A$ by 
+extracting only the elements in $A$, where the corresponding
+elements of $M$ are nonzero. The mask matrix $M$, is a
+sparse matrix in CSR format without the real values, i.e.,
+only the integer arrays of the CSR format are passed. }
+
+\marg{ CPERM   }\disp{ Permutes the columns of a matrix, i.e.,
+computes the matrix $B = A Q$ where $Q$ is a permutation matrix. }
+
+\marg{RPERM}\disp{ Permutes the rows of a matrix, i.e.,
+computes the matrix $B = P A$ where $P$ is a permutation matrix. }
+
+\marg{DPERM}\disp{Permutes the rows and columns of
+a matrix, i.e., computes $B = P A Q$
+given two permutation matrices  $ P$ and $ Q$. This routine gives a
+special treatment to the common case where $Q=P^T$.} 
+
+\marg{DPERM2}\disp{General submatrix permutation/extraction routine.}
+
+\marg{DMPERM}\disp{Symmetric permutation of row and column (B=PAP') in MSR format}
+
+\marg{DVPERM}\disp{ Performs an in-place permutation of a real vector, i.e.,
+performs $x := P x $, where $P$ is a permutation matrix. }
+
+\marg{IVPERM}\disp{ Performs an in-place permutation of an
+integer vector.} 
+
+\marg{RETMX}\disp{ Returns the maximum absolute value in each row  
+of an input matrix.  } 
+
+\marg{DIAPOS}\disp{ Returns the positions in the arrays $A$ and 
+$ JA$ of the  diagonal elements, for a matrix stored in CSR format. } 
+
+\marg{ EXTBDG  }\disp{ Extracts the main diagonal blocks of a matrix. 
+The output is a rectangular matrix of dimension $N \times NBLK$,
+containing the $N/NBLK$ blocks, 
+in which $NBLK$ is the block-size (input).}
+
+\marg{ GETBWD  }\disp{ Returns bandwidth information on a matrix. This
+subroutine returns the bandwidth of the lower part and the upper part
+of a given matrix. May be used to determine these two parameters
+for converting a matrix into the BND format.}
+
+\marg{ BLKFND  }\disp{ Attempts to find the block-size of a matrix
+stored in CSR format. One restriction is that the zero elements in 
+each block if there are any are assumed to be represented as nonzero 
+elements in the data structure for the $A$ matrix, with zero values. }
+
+\marg{ BLKCHK  }\disp{ Checks whether a given integer is the block 
+size of A.  This routine is called by BLKFND. Same restriction as
+above.} 
+
+\marg{ INFDIA  }\disp{ Computes the number of nonzero elements 
+of each of the $2n-1$ diagonals of a matrix. Note that the first diagonal 
+is the diagonal with offset $-n$ which consists of the entry
+$a_{n,1}$ and the last one is the diagonal with offset $n$ which consists
+of the element $a_{1,n}$.}
+
+\marg{ AMUBDG }\disp{ Computes the number of nonzero elements
+in each row of the product of two sparse matrices $A$ and $B$.
+Also returns the total number of nonzero elements.}
+
+\marg{ APLBDG }\disp{ Computes the number of nonzero elements
+in each row of the sum of two sparse matrices $A$ and $B$.
+Also returns the total number of nonzero elements.}
+
+\marg{ RNRMS }\disp{ Computes the norms of the rows of a matrix.
+The usual three norms $\|.\|_1, \|.\|_2, $ and $\|.\|_{\infty} $
+are supported. }
+
+\marg{ CNRMS }\disp{ Computes the norms of the columns of a matrix.
+Similar to RNRMS. }
+
+\marg{ ROSCAL }\disp{ Scales the rows of a matrix by their norms. 
+The same three norms as in RNRMS are available.  }
+
+\marg{ COSCAL }\disp{ Scales the columns of a matrix by their norms.
+The same three norms as in RNRMS are available. }
+
+\marg{ADDBLK}\disp{Adds a matrix B into a block of A. }
+
+\marg{GET1UP}\disp{Collects the first elements of each row of the upper
+triangular portion of the matrix. }
+ 
+\marg{XTROWS}\disp{Extracts given rows from a matrix in CSR format.}
+
+\marg{CSRKVSTR}\disp{Finds block partitioning of matrix in CSR format.}
+
+\marg{CSRKVSTC}\disp{Finds block column partitioning of matrix in CSR format.}
+
+\marg{KVSTMERGE}\disp{Merges block partitionings for conformal row/column pattern.}
+
+
+\section{Input/Output routines}
+The INOUT module of SPARSKIT  comprises a few routines for reading,
+writing, and for plotting and visualizing the structure 
+of sparse matrices. Many of these routines  are essentially geared towards 
+the utilization of the Harwell/Boeing collection of matrices.
+There are currently eleven subroutines in this module.
+
+\vskip .5in
+
+\marg{ READMT}\disp{ Reads a matrix in the Harwell/Boeing format.} 
+
+\marg{ PRTMT}\disp{ Creates a Harwell Boeing file from an arbitrary
+ matrix in CSR or CSC format.} 
+
+\marg{ DUMP }\disp{DUMP prints the rows of a 
+ matrix in a file, in a nice readable format.
+The best format is internally calculated depending on the number of
+nonzero elements. This is a simple routine which might be 
+helpful for debugging purposes.}  
+
+\marg{ PSPLTM }\disp{Generates a post-script plot of the non-zero 
+pattern of A.}
+
+\marg{ PLTMT }\disp{Creates a pic file for plotting the pattern of a 
+matrix.} 
+
+\marg{ SMMS }\disp{Write the matrx in a format used in SMMS package.}
+
+\marg{ READSM }\disp{Reads matrices in coordinate format (as in SMMS 
+package).}
+
+\marg{ READSK }\disp{Reads matrices in CSR format (simplified H/B format).}
+
+\marg{ SKIT }\disp{Writes matrices to a file, format same as above.}
+
+\marg{ PRTUNF }\disp{Writes matrices (in CSR format) in unformatted files.}
+
+\marg{ READUNF }\disp{Reads unformatted file containing matrices in CSR format.}
+
+ 
+\vskip 0.3in
+
+The routines readmt and prtmt allow to read and create files
+containing matrices stored in the H/B format. 
+For details concerning this format the reader is referred to
+\cite{Duff-HB} or the summary given in the documentation  of
+the subroutine READMT. While the purpose of
+readmt is clear, it is not obvious that one single 
+subroutine can write a matrix in H/B format and still satisfy
+the needs of all users. For example for some matrices all nonzero
+entries are actually integers and a format using say a 10 digit
+mantissa may entail an enormous waste of storage if the matrix
+is large. The solution provided is to compute internally the best
+formats for the integer arrays IA and JA. A little help is 
+required from the user for the real values in the arrays A and
+RHS. Specifically, the desired format is obtained from
+a parameter of the subroutine by using a simple notation, 
+which is explained in detail in the documentation of the routine. 
+
+Besides the pair of routines that can read/write matrices in H/B
+format, there are three other pairs which can be used to input and
+output matrices in different formats. The SMMS and READSM pair write
+and read matrices in the format used in the package SMMS.
+Specifically, READSM reads a matrix in SMMS format from a file and outputs
+it in CSR format. SMMS accepts a matrix in CSR format and
+writes it to a file in SMMS format. The SMMS format is
+essentially a COO format. 
+The size of the matrix appears in the first line of the file. Each other
+line of the file
+contains triplets in the form of ($i$, $j$, $a_{ij}$) which
+denote the non-zero elements of the matrix.
+Similarly, READSK and SKIT read and write matrices in CSR format. 
+This pair is very similar to READMT and PRTMT, only that the
+files read/written by READSK and SKIT do not have headers. The pair 
+READUNF and PRTUNF reads and writes the matrices (stored as $ia$, $ja$
+and $a$) in binary form,
+i.e.~the number in the file written by PRTUNF will be in machine
+representations. The primary motivation for this is that
+handling the arrays in binary form takes less space than in the
+usual ASCII form, and is usually  faster.
+If the matrices are large and they are only used on compatible computers,
+it might be desirable to use unformatted files.
+
+We found it extremely useful to be able to visualize a sparse matrix,
+notably for debugging purposes.  A simple look at the plot can
+sometimes reveal whether the matrix obtained from some reordering
+technique does indeed have the expected structure.  For now two simple
+plotting mechanisms are provided. First, a preprocessor called PLTMT
+to the Unix utility `Pic'  allows one to generate a pic file from a
+matrix that is in the Harwell/Boeing format or any other format. For
+example for a Harwell/Boeing matrix file, the command is of the form
+%%\[hb2pic.ex \; < \; HBfilename \] 
+\begin{center}
+{\tt hb2pic.ex < HB\_file.}
+\end{center}
+The output file is then printed by the usual troff or TeX commands. A
+translation of this routine into one that generates a post-script file
+is also available (called PSPLTM). We should point out that the
+plotting routines are very simple in nature and should not be used to
+plot large matrices. For example the pltmt routine outputs one pic
+command line for every nonzero element.  This constitutes a convenient
+tool for document preparation for example.  Matrices of size just up
+to a few thousands can be printed this way.  Several options
+concerning the size of the plot and caption generation are available.
+
+There is also a simple utility program called ``hb2ps'' which takes a
+matrix file with HB format and translates it into a post-script file.
+The usage of this program is as follows:
+\begin{center}
+{\tt hb2ps.ex < HB\_file > Postscript\_file.}
+\end{center}
+%%\[ hb2ps.ex   < HB\_file > Postscript\_file. \]
+The file can be previewed with ghostscript.
+The following graph shows a pattern of an unsymmetric matrix.
+
+\begin{figure}[htb]
+%\centerline{\psfig{figure=jpwh.ps,width=5in}}
+\includegraphics[width=5in]{jpwh}
+%\vskip 5.5in
+%\special{psfile=jpwh.ps vscale = 100 hscale = 100 hoffset = -85 voffset= -450}
+%\special{psfile=jpwh.ps hoffset = -85}
+\end{figure}
+
+\section{Basic algebraic operations}
+The usual algebraic operations involving two matrices,
+such as $C= A+ B$, $C= A+\beta B$, $C= A B $, etc..,
+are fairly common in sparse matrix computations.
+These basic matrix operations
+are included in the module called BLASSM.  In addition there is a
+large number of basic operations, involving a sparse matrix
+and a vector, such as matrix-vector products and
+triangular system solutions that are very commonly used. Some of
+these are included in the module MATVEC.
+Sometimes it is desirable to compute the 
+patterns of the matrices $A+B$ and $AB$, or in fact of any result 
+of the basic algebraic  operations. This can be implemented by
+way of job options which will determine whether to fill-in the real
+values or not during the computation.  
+We now briefly describe the contents of each of the 
+two modules BLASSM and MATVEC. 
+
+\subsection{The BLASSM module} 
+Currently, the module BLASSM (Basic Linear Algebra Subroutines for
+Sparse Matrices) contains the following nine subroutines:
+
+\vskip 0.3in
+
+\marg{ AMUB }\disp{ Performs the product of two matrices, i.e.,
+computes $C = A B $, where $A$ and $B$ are both in CSR format.}
+
+\marg{  APLB }\disp{ Performs the addition of two matrices, i.e.,
+computes $C = A + B $, where $A$ and $B$ are both in CSR format.}
+
+\marg{ APLSB }\disp{ Performs the operation $ C=A + \sigma B $, 
+where $\sigma$ is a scalar, and $A, B$ are two matrices in 
+CSR format. }
+
+\marg{ APMBT }\disp{ Performs either the addition $C = A + B^T$ or the 
+subtraction $C=A-B^T$.  }
+
+\marg{ APLSBT }\disp{ Performs the operation $C = A + s B^T$. }
+
+\marg{ DIAMUA }\disp{   Computes the product of diagonal 
+matrix (from the left) by a sparse matrix, i.e.,
+computes $C = D A$, where $D$ is a diagonal matrix and $A$
+is a general sparse matrix stored in CSR format. }
+
+\marg{ AMUDIA }\disp{ Computes the product of a sparse 
+matrix by a diagonal matrix from the right, i.e., 
+computes $C = A D $, where $D$ is a diagonal matrix and $A$
+is a general sparse matrix stored in CSR format. }
+
+\marg{ APLDIA }\disp{   Computes the sum of a sparse matrix and a 
+diagonal matrix, $ C = A + D $.  }
+
+\marg{ APLSCA }\disp{Performs an in-place
+addition of a scalar to the diagonal entries of 
+a sparse matrix, i.e., performs the operation
+ $A := A + \sigma I$.} 
+
+\vskip 0.3in 
+
+Missing from this list are the routines {\bf AMUBT} which multiplies $A$ by 
+the transpose of $B$, $C= AB^T$, and {\bf ATMUB } which multiplies the 
+transpose of $A$ by $B$,	$C= A^T B $.
+
+\vskip 0.3in
+
+These are very difficult to implement and we found it better to 
+perform it with two passes.
+Operations of the form $ t A + s B $ have been
+avoided as their occurrence does not warrant additional subroutines.
+Several other operations similar to those defined for
+vectors have not been included. For example the scaling
+of a matrix  in sparse format is simply a scaling of its
+real array $A$, which can be done with the usual BLAS1
+scaling routine, on the array $A$. 
+
+
+\subsection{The MATVEC module}
+In its current status, this module contains matrix
+by vector products and various sparse triangular 
+solution methods. The contents are as follows.
+
+\vskip 0.3in
+
+\marg{ AMUX   }\disp{ Performs the product of a  matrix by a vector.
+ Matrix stored in  Compressed Sparse Row (CSR) format.}
+
+\marg{  ATMUX  }\disp{  Performs the product of the transpose of
+a  matrix by a vector. Matrix $A$ stored in Compressed 
+Sparse Row format. Can also be
+viewed as the product of a matrix in the Compressed Sparse Column
+format by a vector.} 
+
+\marg{  AMUXE  }\disp{  Performs the product of a  matrix by a vector.
+Matrix stored in  Ellpack/Itpack (ELL) format.}
+
+\marg{ AMUXD  }\disp{  Performs the product of a  matrix by a vector.
+Matrix stored in  Diagonal (DIA) format.}
+
+\marg{ AMUXJ  }\disp{  Performs the product of a  matrix by a vector.
+Matrix stored in  Jagged Diagonal (JAD) format.} 
+
+\marg{ VBRMV }\disp{ Sparse matrix - full vector product in VBR format.} 
+
+\marg{ LSOL } 
+\disp{  Unit lower triangular system solution. Matrix stored in
+Compressed Sparse Row (CSR) format. }
+
+\marg{ LDSOL  }\disp{Lower triangular system solution. Matrix stored in
+Modified Sparse Row (MSR) format. Diagonal elements inverted. }
+
+\marg{ LSOLC  }\disp{ 
+Unit lower triangular system solution. Matrix stored in
+ Compressed Sparse Column (CSC) format.   }
+
+\marg{ LDSOLC }\disp{  
+Lower triangular system solution. Matrix stored in
+Modified Sparse Column (MSC) format with diagonal elements inverted. }
+
+\marg{ LDSOLL }\disp{ 
+Unit lower triangular system solution with the level scheduling
+approach.  Matrix 
+stored in Modified Sparse Row format, with diagonal elements inverted.}
+
+\marg{ USOL }\disp{  Unit upper triangular system solution. 
+Matrix stored in Compressed Sparse Row (CSR) format. }
+
+\marg{ UDSOL  }\disp{  Upper triangular system solution. 
+Matrix stored in Modified Sparse Row (MSR) format. Diagonal 
+elements inverted. }
+
+\marg{ USOLC  }\disp{ 
+Unit upper triangular system solution. Matrix stored in
+Compressed Sparse Column (CSC) format.   } 
+
+\marg{ UDSOLC }\disp{  
+Upper triangular system solution. Matrix stored in
+Modified Sparse Column (MSC) format with diagonal elements inverted. }
+
+\vskip 0.3in
+Most of the above routines are  short and rather straightforward.
+A long test program  is provided to run all of the subroutines
+on a large number of matrices that are dynamically generated
+using the MATGEN module. 
+
+\section{The basic statistics and information routines}
+It is sometimes very  informative when analyzing
+solution methods, to be able in a short amount of time to 
+obtain some statistical information about a sparse matrix.
+The purpose of the subroutine info1, is to print out such
+information. The first question we had to address 
+was to determine the type of information that
+is inexpensive to obtain and yet practical and useful.
+The simplest and most common statistics
+are: total number of nonzero elements, average number of nonzero
+elements per row (with standard deviation), band size.
+Our preliminary package Info1 contains the above and a 
+number of other features. For example it answers the following
+questions: Is the matrix lower triangular, upper triangular?
+does it have a symmetric structure? If not how close is it 
+from having this property? Is it weakly row-diagonally dominant?
+What percentage of the rows are weakly diagonally dominant?
+Same questions for column diagonal dominance.
+A sample output from  info1 is listed in 
+Figure\ref{Fig1}. This print-out was  generated by typing 
+\begin{center}
+{\tt info1.ex < pores\_2}
+\end{center}
+%\[ {\rm info1.ex}  < {\rm pores\_2} \]
+where {\tt pores\_2} is a file containing a matrix in H/B format.
+
+If the Harwell-Boeing matrix is symmetric then Info1 takes this
+information into account to obtain the correct information
+instead of the information on  the lower triangular part only.
+Moreover, in cases where only the pattern is provided (no real
+values), then info1 will print a message to this effect and 
+will then give information related only to the structure of 
+the matrix. The output for an example of this type is shown in 
+Figure~\ref{Fig2}. We should point out that the runs for these
+two tests were basically instantaneous on a Sun-4 workstation.
+
+Currently, this module contains the following subroutines:
+
+\vskip 0.3in
+ 
+\marg{ N\_IMP\_DIAG }\disp{ Computes the most important diagonals.}
+
+\marg{ DIAG\_DOMI }\disp{ Computes the percentage of weakly diagonally 
+dominant rows/columns.}
+
+\marg{ BANDWIDTH }\disp{ Computes the lower, upper, maximum, and 
+average bandwidths.}
+
+\marg{ NONZ }\disp{ Computes maximum numbers of nonzero elements
+per column/row, min numbers of nonzero elements per column/row,
+and numbers of zero columns/rows.}
+
+\marg{ FROBNORM }\disp{ Computes the Frobenius norm of A.}
+
+\marg{ ANSYM }\disp{ Computes the Frobenius norm of the symmetric and
+non-symmetric parts of A, computes the number of matching elements in symmetry 
+and the relative symmetry match.
+The routine ANSYM provides some information on the degree of symmetry of A.}
+
+\marg{ DISTAIJ }\disp{ Computes the average distance of a(i,j) from diag and
+standard deviation  for this average.}
+
+\marg{ SKYLINE }\disp{ Computes the number of nonzeros in the skyline storage.}
+
+\marg{ DISTDIAG }\disp{ Computes the numbers of elements in each diagonal.}
+
+\marg{ BANDPART }\disp{ Computes the bandwidth of the banded matrix,
+which contains 'nper' percent of the original matrix.}
+
+
+\marg{ NONZ\_LUD }\disp{ Computes the number of nonzero elements in strict
+lower part, strict upper part, and main diagonal.}
+
+\marg{ AVNZ\_COL }\disp{ Computes average number of nonzero elements/column
+and standard deviation for the average.}
+
+\marg{ VBRINFO }\disp{ Prints information about matrices in variable block row 
+format.}
+
+% This has been updated to match the new code. -- June 3, 1994.
+%* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+%* unsymmetric matrix from pores                                           *
+%*                    Key = pores_2  , Type = rua                          *
+%* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+%    *  Dimension N                                      =       1224  *
+%    *  Number of nonzero elements                       =       9613  *
+%    *  Average number of nonzero elements/Column        =     7.8538  *
+%    *  Standard deviation for above average             =     5.4337  *
+%    *  Nonzero elements in strict upper part            =       4384  *
+%    *  Nonzero elements in strict lower part            =       4005  *
+%    *  Nonzero elements in main diagonal                =       1224  *
+%    *  Weight of longest column                         =         30  *
+%    *  Weight of shortest column                        =          2  *
+%    *  Weight of longest row                            =         30  *
+%    *  Weight of shortest row                           =          2  *
+%    *  Matching elements in symmetry                    =       6358  *
+%    *  Relative Symmetry Match (symmetry=1)             =     0.6614  *
+%    *  Average distance of a(i,j)  from diag.           =  0.615E+02  *
+%    *  Standard deviation for above average             =  0.103E+03  *
+%    *-----------------------------------------------------------------*
+%    *  Frobenius norm of A                              =  0.150E+09  *
+%    *  Frobenius norm of symmetric part                 =  0.100E+09  *
+%    *  Frobenius norm of nonsymmetric part              =  0.951E+08  *
+%    *  Maximum element in A                             =  0.378E+08  *
+%    *  Percentage of weakly diagonally dominant rows    =  0.481E+00  *
+%    *  Percentage of weakly diagonally dominant columns =  0.490E-02  *
+%    *-----------------------------------------------------------------*
+%    *  Lower bandwidth  (max: i-j, a(i,j) .ne. 0)       =        470  *
+%    *  Upper bandwidth  (max: j-i, a(i,j) .ne. 0)       =        471  *
+%    *  Maximum Bandwidth                                =        736  *
+%    *  Average Bandwidth                                =  0.190E+03  *
+%    *  Number of nonzeros in skyline storage            =     340385  *
+%    *  90% of matrix is in the band of width            =        527  *
+%    *  80% of matrix is in the band of width            =        145  *
+%    *  The total number of nonvoid diagonals is         =        367  *
+%    *  The 10 most important diagonals are (offsets)    :             *
+%    *     0     1    -1    -2     2    -3   -32  -264   264    32     *
+%    *  The accumulated percentages they represent are   :             *   
+%    *  12.7  24.6  31.7  37.9  43.6  49.0  52.4  55.7  58.6  61.4     *
+%    *-----------------------------------------------------------------*
+%    *  The matrix does not have a block structure                     *
+%    *-----------------------------------------------------------------*
+\begin{figure}
+\begin{verbatim}
+* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+* UNSYMMETRIC MATRIX FROM PORES                                           *
+*                    Key = PORES 2  , Type = RUA                          *
+* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+    *  Dimension N                                      =       1224  *
+    *  Number of nonzero elements                       =       9613  *
+    *  Average number of nonzero elements/Column        =     7.8538  *
+    *  Standard deviation for above average             =     5.4337  *
+    *  Nonzero elements in strict lower part            =       4384  *
+    *  Nonzero elements in strict upper part            =       4005  *
+    *  Nonzero elements in main diagonal                =       1224  *
+    *  Weight of longest column                         =         30  *
+    *  Weight of shortest column                        =          2  *
+    *  Weight of longest row                            =         16  *
+    *  Weight of shortest row                           =          5  *
+    *  Matching elements in symmetry                    =       6358  *
+    *  Relative Symmetry Match (symmetry=1)             =     0.6614  *
+    *  Average distance of a(i,j)  from diag.           =  0.615E+02  *
+    *  Standard deviation for above average             =  0.103E+03  *
+    *-----------------------------------------------------------------*
+    *  Frobenius norm of A                              =  0.150E+09  *
+    *  Frobenius norm of symmetric part                 =  0.103E+09  *
+    *  Frobenius norm of nonsymmetric part              =  0.980E+08  *
+    *  Maximum element in A                             =  0.378E+08  *
+    *  Percentage of weakly diagonally dominant rows    =  0.490E-02  *
+    *  Percentage of weakly diagonally dominant columns =  0.481E+00  *
+    *-----------------------------------------------------------------*
+    *  Lower bandwidth  (max: i-j, a(i,j) .ne. 0)       =        470  *
+    *  Upper bandwidth  (max: j-i, a(i,j) .ne. 0)       =        471  *
+    *  Maximum Bandwidth                                =        736  *
+    *  Average Bandwidth                                =  0.190E+03  *
+    *  Number of nonzeros in skyline storage            =     342833  *
+    *  90% of matrix is in the band of width            =        527  *
+    *  80% of matrix is in the band of width            =        145  *
+    *  The total number of nonvoid diagonals is         =        367  *
+    *  The 10 most important diagonals are (offsets)    :             *
+    *     0    -1     1     2    -2     3    32   264  -264   -32     *
+    *  The accumulated percentages they represent are   :             *
+    *  12.7  24.6  31.7  37.9  43.6  49.0  52.4  55.7  58.6  61.4     *
+    *-----------------------------------------------------------------*
+    *  The matrix does not have a block structure                     *
+    *-----------------------------------------------------------------*
+\end{verbatim}
+\caption{Sample output from Info1.ex \label{Fig1} } 
+\end{figure}
+
+
+%* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+%* SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.                   *
+%*                    Key = CAN 1072 , Type = PSA                          *
+%* No values provided - Information on pattern only                        *
+%* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+%    *  Dimension N                                      =       1072  *
+%    *  Number of nonzero elements                       =       6758  *
+%    *  Average number of nonzero elements/Column        =    11.6082  *
+%    *  Standard deviation for above average             =     5.6474  *
+%    *  Nonzero elements in strict upper part            =       5686  *
+%    *  Nonzero elements in strict lower part            =       5686  *
+%    *  Nonzero elements in main diagonal                =       1072  *
+%    *  Weight of longest column                         =         35  *
+%    *  Weight of shortest column                        =          6  *
+%    *  Matching elements in symmetry                    =       6758  *
+%    *  Relative Symmetry Match (symmetry=1)             =     1.0000  *
+%    *  Average distance of a(i,j)  from diag.           =  0.110E+03  *
+%    *  Standard deviation for above average             =  0.174E+03  *
+%    *-----------------------------------------------------------------*
+%    *  Lower bandwidth  (max: i-j, a(i,j) .ne. 0)       =       1048  *
+%    *  Upper bandwidth  (max: j-i, a(i,j) .ne. 0)       =       1048  *
+%    *  Maximum Bandwidth                                =       1055  *
+%    *  Average Bandwidth                                =  0.376E+03  *
+%    *  Number of nonzeros in skyline storage            =     277248  *
+%    *  90% of matrix is in the band of width            =        639  *
+%    *  80% of matrix is in the band of width            =        343  *
+%    *  The total number of nonvoid diagonals is         =        627  *
+%    *  The  5 most important diagonals are (offsets)    :             *
+%    *     0    -1    -2    -3    -4                                   *
+%    *  The accumulated percentages they represent are   :             *
+%    *  15.9  24.7  29.7  33.9  36.3                                   *
+%    *-----------------------------------------------------------------*
+%    *  The matrix does not have a block structure                     *
+%    *-----------------------------------------------------------------*
+\begin{figure}
+\begin{verbatim}
+* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+* SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.                   *
+*                    Key = CAN 1072 , Type = PSA                          *
+* No values provided - Information on pattern only                        *
+* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+    *  Dimension N                                      =       1072  *
+    *  Number of nonzero elements                       =       6758  *
+    *  Average number of nonzero elements/Column        =     6.3041  *
+    *  Standard deviation for above average             =     6.2777  *
+    *  Nonzero elements in strict lower part            =       5686  *
+    *  Nonzero elements in strict upper part            =       5686  *
+    *  Nonzero elements in main diagonal                =       1072  *
+    *  Weight of longest column                         =         39  *
+    *  Weight of shortest column                        =          4  *
+    *  Matching elements in symmetry                    =       6758  *
+    *  Relative Symmetry Match (symmetry=1)             =     1.0000  *
+    *  Average distance of a(i,j)  from diag.           =  0.110E+03  *
+    *  Standard deviation for above average             =  0.174E+03  *
+    *-----------------------------------------------------------------*
+    *  Lower bandwidth  (max: i-j, a(i,j) .ne. 0)       =          0  *
+    *  Upper bandwidth  (max: j-i, a(i,j) .ne. 0)       =       1048  *
+    *  Maximum Bandwidth                                =       1049  *
+    *  Average Bandwidth                                =  0.117E+03  *
+    *  Number of nonzeros in skyline storage            =     278320  *
+    *  90% of matrix is in the band of width            =        639  *
+    *  80% of matrix is in the band of width            =        343  *
+    *  The total number of nonvoid diagonals is         =        627  *
+    *  The  5 most important diagonals are (offsets)    :             *
+    *     0     1     2     3     4                                   *
+    *  The accumulated percentages they represent are   :             *
+    *  15.9  24.7  29.7  33.9  36.3                                   *
+    *-----------------------------------------------------------------*
+    *  The matrix does not have a block structure                     *
+    *-----------------------------------------------------------------*
+\end{verbatim}
+\caption{Sample output from Info1.ex for matrix with pattern only \label{Fig2}}
+\end{figure}
+
+%% \vfill 
+
+\section{Matrix generation routines}
+One of the difficulties encountered when testing and comparing
+numerical methods, is that it is sometimes difficult to 
+guarantee that the matrices compared are indeed identical.
+Even though a paper may give full details on the test
+problems considered, programming errors or differences in coding
+may lead to the incorrect matrices and the incorrect conclusions.
+This has often happened in the past and is likely to be avoided  if 
+the matrices were generated with exactly the same code. 
+The module MATGEN of
+SPARSKIT includes several matrix generation routines.
+
+\subsection{Finite Difference Matrices}
+
+\begin{enumerate}
+\item Scalar 5-point and 7-point matrices arising 
+from discretization of the elliptic type equation:
+\begin{equation}
+L u = {\del \over \del x} ( a   {\del \over \del x } u ) 
++ {\del \over \del y } ( b   {\del \over \del y }  u) 
++ {\del \over \del z } ( c   {\del \over \del z } u ) 
++ {\del \over \del x } ( d   u ) + {\del \over \del y }  (e   u) 
++ {\del \over \del z } ( f   u ) + g   u  = h u
+\label{5-7pt}
+\end{equation} 
+on rectangular regions with general mixed type boundary conditions of
+the following form
+\[ \alpha {\del u \over \del n} + \beta u = \gamma \]
+The user provides the functions $a, b, c, ...,h$, $\beta, \gamma$ and
+$\alpha$ is a constant on each boundary surface. The resulting 
+matrix is in general sparse format, possibly printed in a file
+in the H/B format. 
+
+There is a switch in the subroutine which makes it possible to choose
+between a strict centered difference type of discretization, or an
+upwind scheme for the first order derivatives.
+
+\item
+Block 5-point and 7-point matrices arising 
+from discretization of the elliptic type equation \nref{5-7pt}
+in which $u$ is now a vector of $nfree$ components, and
+$a,b,c, ..., g$ are $nfree \times  nfree $ matrices provided by the
+user.
+
+\end{enumerate}
+
+\subsection{Finite Element Matrices}
+
+Finite element matrices created from the convection-diffusion type problem 
+\begin{equation} - \nabla . ({ K \nabla u }) + {C \nabla u} = f \label{kikuchi} 
+\end{equation}
+on a domain $D$ with Dirichlet boundary conditions.  A coarse initial domain
+is described by the user and the code does an arbitrary user-specified number
+of refinements of the grid and assembles the matrix, in CSR format.
+Linear triangular elements are used.  If only the matrix is desired the heat
+source $f$ can be zero. Arbitrary grids can be input, but the user may 
+also take advantage of nine initial grids
+supplied by the package for simple test problems. 
+
+Two examples of meshes and the corresponding assemble matrices are shown
+in the following two pairs of figures: the first pair of figures are the mesh 
+and assembled matrix with mesh number 8 and refinement 1; the second pair of
+figures are the mesh and assembled matrix with mesh number 9 and refinement 1.
+
+\begin{figure}[b]
+\begin{minipage}[h]{6.5cm}
+\includegraphics[height=5cm]{msh8} 
+\end{minipage}
+\hfill
+\begin{minipage}[h]{6.5cm}
+\includegraphics[height=5cm]{mat8}
+\end{minipage}
+\hfill
+\end{figure}
+
+\newpage
+
+\begin{figure}
+\begin{minipage}[h]{6.5cm}
+\includegraphics[width=8cm]{msh9} 
+\end{minipage}
+\hfill
+\begin{minipage}[h]{6.5cm}
+\includegraphics[height=7cm]{mat9}
+\end{minipage}
+\hfill
+\end{figure}
+
+\vskip 2.5in
+\subsection{Markov Chains}
+
+Markov chain matrices arising from a random walk on a
+triangular grid. This is mainly useful for testing nonsymmetric 
+eigenvalue codes. It has been suggested by G.W. Stewart in one of his
+papers \cite{Stewart-SRRIT} and was used by Y. Saad in a few
+subsequent papers as a test problem for nonsymmetric eigenvalue methods,
+see,  e.g., \cite{Saad-cheb}. 
+
+\subsection{Other Matrices}
+
+Currently we have only one additional set of matrices. These are
+the test matrices
+\footnote{These subroutines have been contributed 
+to the author by E. Rothman from Cornell University.} from 
+Zlatev et. al. \cite{Zlatev-tests} and Osterby and Zlatev
+\cite{OsterbyZlatev-book}. The first two matrix generators
+described in the above references 
+are referred to as $D(n,c) $ and $E(n,c)$ respectively.
+A more elaborate class where more than two parameters can be varied,
+is referred to as the class $F(m,n,c,r,\alpha) $ in
+\cite{OsterbyZlatev-book,Zlatev-tests}. The three subroutines to generate
+these matrices are called MATRF2 (for the class $F(m,n,c,r,\alpha)$ ),
+DCN (for the class $D(c,n)$) and ECN (for the class $E(c,n) $).
+These codes can generate rectangular as well as square 
+matrices and allow a good flexibility in making the matrices 
+more or less dense and more or less well conditioned.
+
+\section{The ORDERING Routines}
+The following subroutines are available in the directory ORDERINGS.
+
+\vskip 0.3in
+
+\marg{ levset.f }\disp{Reordering based on level sets, including
+Cuthill-McKee implemented with breadth first search.}
+
+\marg{ color.f }\disp{Reordering based on coloring, including a greedy 
+algorithm for multicolor ordering.}
+
+\marg{ ccn.f }\disp{Reordering routines based on strongly connected
+components.  Contributed by Laura C. Dutto (CERCA and Concordia
+University.}
+
+
+\section{The ITSOL routines}
+
+\marg{ILUT}\disp{This file contains a preconditioned GMRES algorithm 
+  with four preconditioners:}
+\marg{pgmres}\disp{Preconditioned GMRES solver.  This solver may be used
+  with all four of the precondioners below.  Supports right preconditioning 
+  only.}
+\marg{ilut}\disp{ A robust preconditioner called ILUT 
+ which uses a dual thresholding strategy for dropping elements.
+ Arbitrary accuracy is allowed in ILUT.}
+\marg{ilutp}\disp{ ILUT with partial pivoting}
+\marg{ilu0}\disp{ simple ILU(0) preconditioner}
+\marg{milu0}\disp{ MILU(0) preconditioner}
+
+\marg{ITERS}\disp{This file currently has several basic iterative linear 
+ system solvers which use reverse communication. They are:}
+\marg{cg}\disp{Conjugate Gradient Method}
+\marg{cgnr}\disp{Conjugate Gradient Method\-- for Normal Residual equation}
+\marg{bcg}\disp{Bi\-Conjugate Gradient Method}
+\marg{bcgstab}\disp{BCG stablized}
+\marg{tfqmr}\disp{Transpose\-Free Quasi\-Minimum Residual method}
+\marg{gmres}\disp{Generalized Minimum Residual method}
+\marg{fgmres}\disp{Flexible version of Generalized Minimum Residual method}
+\marg{dqgmres}\disp{Direct versions of Quasi Generalized Minimum Residual
+                       method}
+\marg{dbcg}\disp{BCG with partial pivoting}
+
+
+\section{The UNSUPP directory}
+In addition to the basic tools described in the previous 
+sections, SPARSKIT includes a directory 
+called UNSUPP includes software that is not necessarily 
+portable or that does not fit in all previous modules.
+For example software for viewing matrix patterns on 
+some particular workstation
+may be found here. Another example is 
+routines related to matrix exponentials.
+%all the different
+%reordering schemes, such as minimum degree ordering, or
+%nested dissection etc.. 
+Many of these are available from
+NETLIB but others may be contributed by researchers for
+comparison purposes.
+
+%The  two basic programs for viewing matrix patterns on
+%a sun screen will eventually be replaced by 
+%programs for the X-windows environment which is fast becoming
+%a standard. 
+
+%There are three subdirecitories in this directory.
+%\subsection{Blas1}
+%The following items are available in Blas1.
+%
+%\vskip 0.3in
+%
+%\marg{dcopy} \disp{copies a vector, x, to a vector, y.}
+%\marg{ddot}  \disp{dot product of two vectors.}
+%\marg{csscal}\disp{scales a complex vector by a real constant.}
+%\marg{cswap} \disp{interchanges two vectors.}
+%\marg{csrot} \disp{applies a plane rotation.}
+%\marg{cscal} \disp{scales a vector by a constant.}
+%\marg{ccopy} \disp{copies a vector, x, to a vector, y.}
+%\marg{drotg} \disp{construct givens plane rotation.}
+%\marg{drot}  \disp{applies a plane rotation.}
+%\marg{dswap} \disp{interchanges two vectors.}
+%\marg{dscal} \disp{scales a vector by a constant.}
+%\marg{daxpy} \disp{constant times a vector plus a vector.}
+
+
+\subsection{Plots}
+The following items are available in PLOTS. 
+
+\vskip 0.3in
+
+%\marg{ PLTMTPS}\disp{ a translation of the pltmt subroutine 
+%  in INOUT/inout.f
+%  to produce a post-script file rather than a pic file. 
+%  Does not yet offer the same functionality as pltmt. } 
+%
+%\marg{ HB2PIC}\disp{ reads a Harwell-Boeing 
+%  matrix and creates a picture file for pattern.}
+%
+%\marg{ HB2PS}\disp{translates a Harwell-Boeing file into a 
+%Post-Script file.}
+
+\marg{ PSGRD}\disp{ contains subroutine "psgrid" which plots 
+  a symmetric graph.}
+
+%\marg{ RUNPS}\disp{ contains subroutine "rpltps" which reads 
+%  a Harwell-Boeing file from standard input and creates a  
+%  Post-Script file for it}
+
+\marg{ TEXPLT1}\disp{ contains subroutine "texplt" allows 
+  several matrices in the same picture by calling texplt several 
+  times and exploiting job and different shifts.}
+
+\marg{ TEXGRID1}\disp{ contains subroutine "texgrd" which  
+  generates tex commands for plotting a symmetric graph associated
+  with a mesh. Allows several grids in the same picture by 
+  calling texgrd several times and exploiting job and different 
+  shifts.}  
+
+
+\subsection{Matrix Exponentials}
+Two subroutines are available in this directory.
+\vskip 0.3in
+\marg{ EXPPRO}\disp{ A subroutine for computing the product of a matrix 
+  exponential times a vector, i.e. $w = exp(t\ A)\ v$.}
+\marg{ PHIPRO}\disp{ computes $w = \phi(A\ t)\ v$,
+  where $\phi(x) = (1-exp(x))/x$; Also can solve the 
+  system of ODE's $ y'= A y + b$.}
+
+\section{Distribution}
+The SPARSKIT package 
+follows the Linpack-Eispack approach in that it  aims at providing
+efficient and well tested subroutines written in portable FORTRAN.
+Similarly to the Linpack and Eispack packages, the goal is to
+make available a common base of useful codes for a specific 
+area of computation, in this case sparse linear algebra.
+The package is in the public domain and will be made 
+accessible through the internet.
+
+See Figure \ref{organization} for an illustration of the organization
+of SPARSKIT.  Read the README file in the main directory for more
+information.
+
+%Currently, the package is organized in six distinct subdirectories,
+%each containing one or more modules. The six directories 
+%and the modules they contain are the following:
+%INOUT (inout.f), FORMATS (formats.f, unary.f), BLASSM (blassm.f,
+%matvec.f), MATGEN (genmat.f, zlatev.f), INFO (dinfo1.f), 
+%UNSUPP (various routines).   Test programs with unix makefiles
+%are provided in each
+%subdirectory to test a large number of the subroutines.
+%Each directory contains a README file listing contents,
+%and giving additional information. 
+
+For information concerning distribution contact the author at
+%%saad@riacs.edu.
+saad@cs.umn.edu.
+
+\section{Conclusion and Future Plans}
+It is hoped that SPARSKIT will be useful in many 
+ways to researchers in different areas of scientific computing.
+In this version of SPARSKIT, there are few sparse
+problem solvers, such as direct solution methods, or 
+eigenvalue solvers. Some of these are available from different
+sources and we felt that it was not appropriate to provide
+additional ones. The original 
+motivation for SPARSKIT is  that there is 
+a gap to fill in the manipulation and basic computations
+with sparse matrices. Once this gap is filled with some
+satisfaction, then additional functionality may be added.
+
+We briefly mentioned in the introduction the possibility of using 
+SPARSKIT to develop an interactive package.
+Large matrices of dimension tens of of thousands can 
+easily be manipulated with the current supercomputers, 
+in real time. One of the difficulties
+with such an interactive package is that we do not yet
+have reliable routines for computing eigenvalues/eigenvectors of
+large sparse matrices. The state of the art in solving linear 
+systems is in a much better situation. However, one must not 
+contemplate performing the same type of computations as with 
+small dense matrices. As an example,
+getting all the eigenvalues of a sparse matrix is not likely
+to be too useful when the matrix is very large.
+
+Beyond interactive software for sparse linear algebra, one can
+envision the integration of SPARSKIT in a larger package 
+devoted to solving certain types of Partial Differential Equations, 
+possibly interactively. 
+
+\vskip 1.3in
+\noindent
+{\bf Acknowledgements.} The idea of creating a tool package for
+sparse matrices germinated while the author was at the Center for 
+Supercomputing Research and Development of the University of Illinois
+(1986-1987) and part of this work was performed there. 
+Initially the author has benefited from helpful comments from Iain Duff
+(then visiting CSRD) and a number of colleagues at CSRD.  
+Billy Stewart and his students at NCSU used a preliminary version of 
+SPARSKIT in a class project and made some
+valuable comments. Ernie Rothman (Cornell) and
+Laura Dutto (Montreal) contributed some software.
+The author has also benefited from helpful discussions
+from a number of other colleagues, including 
+Mike Heroux, Giuseppe Radicatti, Ahmed Sameh, Horst Simon, 
+Phuong Vu, and Harry Wijshoff.  Students who contributed to
+version 2 of SPARSKIT include Kesheng Wu, Edmond Chow, and Dongli Su.
+
+\newpage
+\begin{thebibliography}{10}
+
+\bibitem{Anderson-Saad}
+E.~C. Anderson and Y.~Saad.
+\newblock Solving sparse triangular systems on parallel computers.
+\newblock Technical Report 794, University of Illinois, CSRD, Urbana, IL, 1988.
+
+\bibitem{Duff-survey}
+I.~S. Duff.
+\newblock A survey of sparse matrix research.
+\newblock In {\em Proceedings of the IEEE, 65}, pages 500--535, New York, 1977.
+  Prentice Hall.
+
+\bibitem{Duff-book}
+I.~S. Duff, {A. M. Erisman}, and {J. K. Reid}.
+\newblock {\em Direct Methods for Sparse Matrices}.
+\newblock Clarendon Press, Oxford, 1986.
+
+\bibitem{Duff-HB}
+I.~S. Duff, R.~G. Grimes, and J.~G. Lewis.
+\newblock Sparse matrix test problems.
+\newblock {\em ACM trans. Math. Soft.}, 15:1--14, 1989.
+
+\bibitem{Oppe-NSPCG}
+T.~C. Oppe~Wayne Joubert and D.~R. Kincaid.
+\newblock Nspcg user's guide. a package for solving large linear systems by
+  various iterative methods.
+\newblock Technical report, The University of Texas at Austin, 1988.
+
+\bibitem{Oppe-Kincaid}
+T.~C. Oppe and D.~R. Kincaid.
+\newblock The performance of {ITPACK} on vector computers for solving large
+  sparse linear systems arising in sample oil reservoir simulation problems.
+\newblock {\em Communications in applied numerical methods}, 2:1--7, 1986.
+
+\bibitem{OsterbyZlatev-book}
+O.~Osterby and Z.~Zlatev.
+\newblock {\em Direct methods for sparse matrices}.
+\newblock Springer Verlag, New York, 1983.
+
+\bibitem{Saad-cheb}
+Y.~Saad.
+\newblock {Chebyshev} acceleration techniques for solving nonsymmetric
+  eigenvalue problems.
+\newblock {\em Mathematics of Computation}, 42:567--588, 1984.
+
+\bibitem{Saad-Boeing}
+Y.~Saad.
+\newblock {Krylov} subspace methods on supercomputers.
+\newblock {\em SIAM J. Scient. Stat. Comput.}, 10:1200--1232, 1989.
+
+\bibitem{Stewart-SRRIT}
+G.W. Stewart.
+\newblock {SRRIT} - a FORTRAN subroutine to calculate the dominant invariant
+  subspaces of a real matrix.
+\newblock Technical Report TR-514, University of Maryland, College Park, MD,
+  1978.
+
+\bibitem{Young-Oppe-al}
+D.~M. Young, T.C. Oppe, D.~R. Kincaid, and L.~J. Hayes.
+\newblock On the use of vector computers for solving large sparse linear
+  systems.
+\newblock Technical Report CNA-199, Center for Numerical Analysis, University
+  of Texas at Austin, Austin, Texas, 1985.
+
+\bibitem{Zlatev-tests}
+Z.~Zlatev, K.~Schaumburg, and J.~Wasniewski.
+\newblock A testing scheme for subroutines solving large linear problems.
+\newblock {\em Computers and Chemistry}, 5:91--100, 1981.
+
+\end{thebibliography}
+%%
+
+\newpage
+
+\appendix
+\centerline{\bf APPENDIX: QUICK REFERENCE}
+\vskip 0.3in
+
+For convenience we list in this 
+appendix the most important subroutines in the various
+modules of SPARSKIT. More detailed information can be found either
+in the body of the paper or in the documentation of the package.
+
+\vskip 0.3in
+\centerline{\bf FORMATS Module} 
+
+\begin{itemize} 
+
+\item CSRDNS  : converts a row-stored sparse matrix into the dense format. 
+\item DNSCSR  : converts a dense matrix to a sparse storage format.        
+\item COOCSR  : converts coordinate to  to csr format                      
+\item COICSR  : in-place conversion of coordinate to csr format            
+\item CSRCOO  : converts compressed sparse row to coordinate format.
+\item CSRSSR  : converts compressed sparse row to symmetric sparse row format.
+\item SSRCSR  : converts symmetric sparse row to compressed sparse row format.
+\item CSRELL  : converts compressed sparse row to Ellpack format           
+\item ELLCSR  : converts Ellpack format to compressed sparse row format.
+\item CSRMSR  : converts compressed sparse row format to modified sparse   
+           row format.
+\item MSRCSR  : converts modified sparse row format to compressed sparse   
+           row format.
+\item CSRCSC  : converts compressed sparse row format to compressed sparse 
+           column format (transposition).
+\item CSRLNK  : converts compressed sparse row to linked list format.
+\item LNKCSR  : converts linked list format to compressed sparse row fmt.
+\item CSRDIA  : converts the compressed sparse row format into the diagonal    
+           format.                                                    
+\item DIACSR  : converts the diagonal format into the compressed sparse row    
+           format.                                                    
+\item BSRCSR  : converts the block-row sparse format into the compressed       
+           sparse row format.                                         
+\item CSRBSR  : converts the compressed sparse row format into the block-row   
+           sparse format.                                             
+\item CSRBND  : converts the compressed sparse row format into the  banded   
+           format (Linpack style).                                    
+\item BNDCSR  : converts the banded format (Linpack style) into the compressed 
+           sparse row storage.                                        
+\item CSRSSK  : converts the compressed sparse row format to the symmetric
+           skyline format                                           
+\item SSKSSR  : converts symmetric skyline format to symmetric
+sparse row           format.                             
+\item CSRJAD  : converts the csr format into the jagged diagonal format.
+\item JADCSR  : converts the jagged-diagonal format into the csr format.
+\item CSRUSS  : converts the csr format to unsymmetric sparse skyline format.
+\item USSCSR  : converts unsymmetric sparse skyline format to the csr format.
+\item CSRSSS  : converts the csr format to symmetric sparse skyline format.
+\item SSSCSR  : converts symmetric sparse skyline format to the csr format.
+\item CSRVBR  : converts compressed sparse row into variable block row format.
+\item VBRCSR  : converts the variable block row format into the
+\item COOELL  : converts the coordinate format into the Ellpack/Itpack format.
+compressed sparse row format.
+\end{itemize}
+
+\vskip 0.3in
+\centerline{\bf UNARY Module}
+
+\begin{itemize} 
+
+\item SUBMAT : extracts a submatrix from a sparse matrix.                  
+\item FILTER : filters elements from a matrix according to their magnitude.
+\item FILTERM: Same as above, but for the MSR format.
+\item TRANSP : in-place transposition routine (see also CSRCSC in formats) 
+\item GETELM : returns $a(i,j)$ for any $(i,j)$	 from a CSR-stored matrix.
+\item COPMAT : copies a matrix into another matrix (both stored csr).
+\item MSRCOP : copies a matrix in MSR format into a matrix in MSR format.
+\item GETELM : returns a(i,j) for any (i,j) from a CSR-stored matrix.
+\item GETDIA : extracts a specified diagonal from a matrix.                
+\item GETL   : extracts lower triangular part.
+\item GETU   : extracts upper triangular part.                             
+\item LEVELS : gets the level scheduling structure for lower triangular    
+ matrices.                                                   
+\item AMASK  : extracts  $C = A \odot  M $
+\item RPERM  : permutes the rows of a matrix ($B = P A$)                     
+\item CPERM  : permutes the columns of a matrix ($B = A Q$)                  
+\item DPERM  : permutes a matrix ($B = P A Q$) given two permutations P, Q   
+\item DPERM2 : general submatrix permutation/extraction routine.
+\item DMPERM : symmetric permutation of row and column (B=PAP') in MSR fmt.
+\item DVPERM : permutes a vector (in-place).                                
+\item IVPERM : permutes an integer vector (in-place).
+\item RETMX  : returns the max absolute value in each row of the matrix.
+\item DIAPOS : returns the positions of the diagonal elements in A.
+\item EXTBDG : extracts the main diagonal blocks of a matrix.   
+\item GETBWD : returns the bandwidth information on a matrix.              
+\item BLKFND : finds the block-size of a matrix.        
+\item BLKCHK : checks whether a given integer is the block size of $A$.
+\item INFDIA : obtains information on the diagonals of $A$.    
+\item AMUBDG : computes the number of nonzero elements in each 
+	row of $A*B$.
+\item APLBDG : computes the number of nonzero elements in each 
+	row of $ A+B$. 
+\item RNRMS  : computes the norms of the rows of $A$.                
+\item CNRMS  : computes the norms of the columns of $A$.                      
+\item ROSCAL : scales the rows of a matrix by their norms.                 
+\item COSCAL : scales the columns of a matrix by their norms.              
+\item ADDBLK : adds a matrix B into a block of A. 
+\item GET1UP : collects the first elements of each row of the upper
+               triangular portion of the matrix.
+\item XTROWS : extracts given rows from a matrix in CSR format.
+
+\end{itemize}
+
+\vskip 0.3in
+\centerline{\bf INOUT Module} 
+
+\begin{itemize} 
+
+\item  READMT : reads matrices in the boeing/Harwell format.               
+\item  PRTMT  : prints matrices in the boeing/Harwell format.   
+\item  DUMP   : prints rows of a matrix,  in a readable format.
+\item  PLTMT  : produces a 'pic' file for plotting a sparse matrix.
+\item PSPLTM  : Generates a post-script plot of the non-zero 
+pattern of A.
+\item SMMS    : Write the matrix in a format used in SMMS package.
+\item READSM  : Reads matrices in coordinate format (as in SMMS 
+package).
+\item READSK  : Reads matrices in CSR format (simplified H/B formate).
+\item SKIT    : Writes matrices to a file, format same as above.
+\item PRTUNF  : Writes matrices (in CSR format) unformatted.
+\item READUNF : Reads unformatted data of matrices (in CSR format).
+\end{itemize}
+
+\vskip 0.3in
+\centerline{\bf INFO Module}
+
+\begin{itemize} 
+\item INFOFUN :  routines for statistics on a sparse matrix.
+\end{itemize}
+
+\vskip 0.3in
+\centerline{\bf MATGEN Module}
+
+\begin{itemize} 
+
+\item GEN57PT : generates 5-point and 7-point matrices.                   
+\item GEN57BL  : generates block 5-point and 7-point matrices.             
+\item GENFEA   : generates finite element matrices in assembled form.
+\item GENFEU   : generates finite element matrices in unassembled form.     
+\item ASSMB1   : assembles an unassembled matrix (as produced by genfeu).
+\item MATRF2 :  Routines for generating sparse matrices by Zlatev et al.
+\item  DCN:  Routines for generating sparse matrices by Zlatev et al.
+\item  ECN:  Routines for generating sparse matrices by Zlatev et al.
+\item MARKGEN: subroutine to produce a Markov chain matrix for 	
+	a random walk.
+\end{itemize}
+
+\vskip 0.3in
+\centerline{\bf BLASSM Module} 
+\begin{itemize} 
+\item AMUB   :   computes     $ C = A*B $ .
+\item APLB   :   computes     $ C = A+B $  .                                
+\item APLSB  :   computes     $ C = A + s B $.   
+\item APMBT  :   Computes     $ C = A \pm  B^T $.   
+\item APLSBT :   Computes     $ C = A + s * B^T $  .                     
+\item DIAMUA :   Computes     $ C = Diag * A $  .                      
+\item AMUDIA :   Computes     $ C = A* Diag $ .  
+\item APLDIA :   Computes     $ C = A + Diag $  .
+\item APLSCA :   Computes     $ A:= A + s I  $ ($s$ = scalar).
+\end{itemize}
+
+\vskip 0.3in
+\centerline{\bf MATVEC Module}
+
+\begin{itemize} 
+
+\item AMUX  : $A$ times a vector. Compressed Sparse Row (CSR) format.        
+\item ATMUX : $A^T $ times a vector. CSR format.                        
+\item AMUXE : $A$ times a vector. Ellpack/Itpack (ELL) format.               
+\item AMUXD : $A$ times a vector. Diagonal (DIA) format.                     
+\item AMUXJ : $A$ times a vector. Jagged Diagonal (JAD) format.              
+\item VBRMV : $A$ times a vector. Variable Block Row (VBR) format.              
+\item LSOL  : Unit lower triangular system solution.
+Compressed Sparse Row (CSR) format.
+\item LDSOL : Lower triangular system solution.
+  Modified Sparse Row (MSR) format.      
+\item LSOL  : Unit lower triangular system solution.
+ Compressed Sparse Column (CSC) format.  
+\item LDSOLC: Lower triangular system solution.
+ Modified Sparse Column (MSC) format.    
+\item LDSOLL: Lower triangular system solution 
+with level scheduling. MSR format.       
+\item USOL  : Unit upper triangular system solution.
+ Compressed Sparse Row (CSR) format.
+\item UDSOL : Upper triangular system solution.
+  Modified Sparse Row (MSR) format.      
+\item USOLC : Unit upper triangular system solution.
+ Compressed Sparse Column (CSC) format.  
+\item UDSOLC: Upper triangular system solution.
+  Modified Sparse Column (MSC) format.   
+
+\end{itemize} 
+
+\vskip 0.3in
+\vbox{ 
+\centerline{\bf ORDERINGS Module}
+\begin{itemize} 
+\item levset.f : level set based reordering, including RCM
+\item color.f  : coloring based reordering 
+\item ccn.f    : reordering based on strongly connected components
+\end{itemize}
+}
+
+\vskip 0.3in
+\vbox{
+\centerline{\bf ITSOL Module}
+\begin{itemize}
+\item ILUT: ILUT(k) preconditioned GMRES mini package.
+\item ITERS: nine basic iterative linear system solvers. 
+\end{itemize}
+}
+
+\vskip 0.3in
+\vbox{ 
+\centerline{\bf PLOTS Module}
+\begin{itemize} 
+%\item PLTMTPS : creates a Post Script file to plot a sparse matrix.
+%\item HB2PIC: reads a Harwell-Boeing matrix and creates a pic file 
+%             for pattern.
+%\item HB2PS: translates a Harwell - Boeing file into a Post-Script file.
+\item PSGRD: plots a symmetric graph.
+%\item RUNPS: reads a Harwell - Boeing file from standard input and 
+%             creates a Post-Script file for it.
+\item TEXPLT1: allows several matrices in the same picture.
+\item TEXGRID1: allows several grids in the same picture.
+\end{itemize}
+  } 
+
+\vskip 0.3in
+\vbox{
+\centerline{\bf MATEXP Module}
+\begin{itemize}
+\item EXPPRO: computes $w = exp(t\ A)\ v$.
+\item PHIPRO: computes $w = \phi(A\ t)\ v$, 
+              where $ \phi(x) = (1-exp(x))/x$.
+              Also solves the P.D.E. system $y' = Ay+b$.
+\end{itemize}
+  }
+
+\end{document} 
+
+\begin{thebibliography}{1}
+
diff --git a/DOC/vbrpic.eps b/DOC/vbrpic.eps
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+%!PS-Adobe-2.0 EPSF-2.0
+%%Title: /tmp/xfig-fig009549
+%%Creator: fig2dev
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diff --git a/DOC/vbrpic.pdf b/DOC/vbrpic.pdf
new file mode 100644
index 0000000..02ab7ae
--- /dev/null
+++ b/DOC/vbrpic.pdf
diff --git a/FORMATS/README b/FORMATS/README
new file mode 100644
index 0000000..dbe5d9e
--- /dev/null
+++ b/FORMATS/README
@@ -0,0 +1,143 @@
+c----------------------------------------------------------------------c
+c                                                                      c
+c            SPARSKIT  Modules  FORMATS and UNARY                      c
+c                                                                      c
+c----------------------------------------------------------------------c
+c                                                                      c    
+c    This directory contains both the module FORMATS and UNARY         c
+c    of SPARSKIT.                                                      c
+c                                                                      c
+c----------------------------------------------------------------------c    
+c                     CONTENTS:                                        c
+c======================================================================c 
+c                                                                      c
+c    formats.f : mostly format conversion routines.                    c
+c                                                                      c
+c    unary.f   : elementary manipulation routines.                     c
+c                                                                      c
+c    chkfmt1   : a long test-suite for the conversion routines.        c
+c                                                                      c
+c    chkun.f   : a test-suite for *some* of the routines in unary.f    c
+c                                                                      c
+c    rvbr.f    : Test program for Variable Block Matrix support        c
+c                                                                      c
+c                                                                      c
+c    makefile  : makefile for the sample programs chkfmt1.f, chkun.f   c
+c                and rvbr.f produces the executables fmt.ex for format c
+c                (usage: make fmt.ex), un.ex for unary.f (usage:       c
+c                make un.ex) and vbr.ex for VBR functions (usage:      c
+c                make vbr.ex).                                         c
+c                                                                      c
+c----------------------------------------------------------------------c
+c                                                                      c
+c       Here are the contents of formats.f and unary.f                 c
+c                                                                      c
+c----------------------------------------------------------------------c
+c======================================================================c
+c                  formats.f:        				       c
+c======================================================================c 
+c                                                                      c
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c                    FORMAT CONVERSION MODULE                          c
+c----------------------------------------------------------------------c
+c contents:                                                            c
+c----------                                                            c
+c csrdns  : converts a row-stored sparse matrix into the dense format. c
+c dnscsr  : converts a dense matrix to a sparse storage format.        c
+c coocsr  : converts coordinate to  to csr format                      c
+c coicsr  : in-place conversion of coordinate to csr format            c
+c csrcoo  : converts compressed sparse row to coordinate.              c
+c csrssr  : converts compressed sparse row to symmetric sparse row     c
+c ssrcsr  : converts symmetric sparse row to compressed sparse row     c
+c csrell  : converts compressed sparse row to ellpack format           c
+c ellcsr  : converts ellpack format to compressed sparse row format    c
+c csrmsr  : converts compressed sparse row format to modified sparse   c
+c           row format                                                 c
+c msrcsr  : converts modified sparse row format to compressed sparse   c
+c           row format.                                                c
+c csrcsc  : converts compressed sparse row format to compressed sparse c
+c           column format (transposition)                              c
+c csrlnk  : converts compressed sparse row to linked list format       c
+c lnkcsr  : converts linked list format to compressed sparse row fmt   c
+c csrdia  : converts a compressed sparse row format into a diagonal    c
+c           format.                                                    c
+c diacsr  : converts a diagonal format into a compressed sparse row    c
+c           format.                                                    c
+c bsrcsr  : converts a block-row sparse format into a compressed       c
+c           sparse row format.                                         c
+c csrbsr  : converts a compressed sparse row format into a block-row   c
+c           sparse format.                                             c
+c csrbnd  : converts a compressed sparse row format into a banded      c
+c           format (linpack style).                                    c
+c bndcsr  : converts a banded format (linpack style) into a compressed c
+c           sparse row storage.                                        c
+c csrssk  : converts the compressed sparse row format to the symmetric c
+c           skyline format                                             c
+c sskssr  : converts symmetric skyline format to symmetric  sparse row c
+c           format.                                                    c
+c csrjad  : converts the csr format into the jagged diagonal format    c
+c jadcsr  : converts the jagged-diagonal format into the csr format    c
+c csruss  : Compressed Sparse Row to Unsymmetric Sparse Skyline format c
+c usscsr  : Unsymmetric Sparse Skyline format to Compressed Sparse Row c
+c csrsss  : Compressed Sparse Row to Symmetric Sparse Skyline format   c
+c ssscsr  : Symmetric Sparse Skyline format to Compressed Sparse Row   c
+c csrvbr  : Converts compressed sparse row to var block row format     c
+c vbrcsr  : Converts var block row to compressed sparse row format     c
+c--------- miscalleneous additions not involving the csr format--------c
+c cooell  : converts coordinate to Ellpack/Itpack format               c
+c dcsort  : sorting routine used by crsjad                             c
+c csorted :  Checks if matrix in CSR format is sorted by columns       c
+c----------------------------------------------------------------------c
+c======================================================================c
+c                        unary.f:  				       c  
+c======================================================================c
+c                                                                      c
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c                     UNARY SUBROUTINES MODULE                         c
+c----------------------------------------------------------------------c
+c contents:                                                            c
+c----------                                                            c
+c submat : extracts a submatrix from a sparse matrix.                  c
+c filter : filters elements from a matrix according to their magnitude.c
+c filterm: same as above, but for the MSR format                       c
+c csort  : sorts the elements in increasing order of columns           c
+c transp : in-place transposition routine (see also csrcsc in formats) c
+c copmat : copy of a matrix into another matrix (both stored csr)      c
+c getelm : returns a(i,j) for any (i,j) from a CSR-stored matrix.      c
+c getdia : extracts a specified diagonal from a matrix.                c
+c getl   : extracts lower triangular part                              c
+c getu   : extracts upper triangular part                              c
+c levels : gets the level scheduling structure for lower triangular    c
+c          matrices.                                                   c
+c amask  : extracts     C = A mask M                                   c
+c rperm  : permutes the rows of a matrix (B = P A)                     c
+c cperm  : permutes the columns of a matrix (B = A Q)                  c
+c dperm  : permutes both the rows and columns of a matrix (B = P A Q ) c
+c dmperm : symmetric permutation of row and column (B = P A P')        c
+c dvperm : permutes a real vector (in-place)                           c
+c ivperm : permutes an integer vector (in-place)                       c
+c retmx  : returns the max absolute value in each row of the matrix    c
+c diapos : returns the positions of the diagonal elements in A.        c
+c extbdg : extracts the main diagonal blocks of a matrix.              c
+c getbwd : returns the bandwidth information on a matrix.              c
+c blkfnd : finds the block-size of a matrix.                           c
+c blkchk : checks whether a given integer is the block size of A.      c
+c infdia : obtains information on the diagonals of A.                  c
+c amubdg : gets number of nonzeros in each row of A*B (as well as NNZ) c 
+c aplbdg : gets number of nonzeros in each row of A+B (as well as NNZ) c
+c rnrms  : computes the norms of the rows of A                         c
+c cnrms  : computes the norms of the columns of A                      c
+c rscal  : scales the rows of a matrix by their norms.                 c
+c cscal  : scales the columns of a matrix by their norms.              c
+c addblk : Adds a matrix B into a block of A.                          c
+c get1up : Collects the first elements of each row of the upper        c
+c          triangular portion of the matrix.                           c
+c xtrows : extracts given rows from a matrix in CSR format.            c
+c csrkvstr:  Finds block row partitioning of matrix in CSR format      c
+c csrkvstc:  Finds block column partitioning of matrix in CSR format   c
+c kvstmerge: Merges block partitionings, for conformal row/col pattern c
+c----------------------------------------------------------------------c
diff --git a/FORMATS/chkfmt1.f b/FORMATS/chkfmt1.f
new file mode 100644
index 0000000..846a220
--- /dev/null
+++ b/FORMATS/chkfmt1.f
@@ -0,0 +1,424 @@
+        program chkfmt 
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c test suite for the Formats routines.                                 c
+c tests all of the routines in the module formats.                     c
+c----------------------------------------------------------------------c 
+c Note: the comments may not have been updated. 
+c
+c Here is the sequence of what is done by this program.            
+c 1) call gen57bl togenerate a block matrix associated with a simple
+c     5-point matrix on a 4 x 2 grid (2-D) with 2 degrees of freedom
+c     per grid point.  Thus N = 16. This is produced in BSR format.
+c    the pattern of the reduced  matrix is written in csr.mat. 
+c
+c 2) the block format is translated into a compressed sparse row
+c    format by bsrcsr. The result is dumped in file csr.mat
+c    matrix is converted back to bsr format. block pattern shown again
+c
+c 3) the matrix is translated in dense format by csrdns.
+c    result a 16 x 16 matrix is written in unit dns.mat.
+c    This is a good file to look at to see what the matrix is
+c    and to compare results of other formats with.
+c 4) the dense matrix obtained in 3) is reconverted back to
+c    csr format using dnscsr. Result appended to file csr.mat
+c 5) The matrix obtained in 4) is converted in coordinate format
+c    and the resulting matrix is written in file coo.mat
+c 6) the result is converted back to csr format. matrix 
+c    appended to csr.mat.
+c 7) result of 6) is converted to symmetric sparse row storage
+c    (ssr) and the result is appended to csr.mat
+c 8) result of 7) converted back to csr format and result is
+c    appended to csr.mat
+c 9) matrix resulting from 8) is converted to modified sparse
+c    row format using csrmsr and result is written in msr.mat.
+c10) the resulting matrix is converted back to csrformat and
+c    result is appended to csr.mat
+c11) result is converted to ellpack-itpack format with 
+c    csrell and result is printed in itp.mat
+c12) result is converted back to csr format and appended to csr.mat 
+c12) result converted to csc format (transposition) using csrcsc
+c    which should produce the same matrix here. result appended 
+c    to csr.mat. A second call to csrcsc is made on resulting
+c    matrix.
+c13) the subroutine csrdia is used to extract two diagonals
+c    (offsets -1 and 0) and then all the diagonals of matrix.
+c    results in dia.mat
+c14) diacsr is then called to convert the diagonally stored matrix
+c    back to csr format. result appended to csr.mat
+c15) result is converted to band format (bnd) by calling
+c    csrbnd. result dumped to bnd.mat
+c16) result is converted back to csr format and appended to csr.mat
+c17) result sorted by a call to csrcsc and then converted to
+c    block format (csrbsr) and then back to csr format again.
+c    result appedned to csr.mat. 
+c18) matrix converted to symmetric skyline format. result appended
+c    to file band.mat 
+c19) matrix converted back to csr format and result appended to
+c    csr.mat.
+c20) result converted to jad format. result output in jad.mat
+c21) result concverted back to csr fromat. appended to csr.mat
+c------------------------------------------------------------------
+      implicit none 
+      integer ndns, nxmax, nmx, nnzmax
+      parameter (nxmax = 10, nmx = nxmax*nxmax, nnzmax=10*nmx)
+      integer ia(nmx+1),ja(nnzmax),ia1(nnzmax),ja1(nnzmax),
+     *         iwk(nmx*2+1),ioff(20),iwk2(nmx+1)
+      real*8 stencil(7,100),a(nnzmax),a1(nnzmax),dns(20,20),wk(nmx)
+c
+      integer k,nx,ny,nz,nfree,na,nr,n,iout,nnz,i,ierr,
+     *     maxcol, ndiag,job,lowd,len,imod,j,kend,k1,k2,
+     *     kstart,mu,ml,idiag,idiag0,kdiag 
+c-----------------------------------------------------------------------
+      data ndns/20/
+c----- open statements ---------------- 
+      open (unit=7,file='csr.mat')
+      open (unit=8,file='dns.mat')
+      open (unit=9,file='coo.mat')
+      open (unit=10,file='msr.mat')
+      open (unit=11,file='itp.mat')
+      open (unit=12,file='dia.mat')
+      open (unit=13,file='bnd.mat')
+      open (unit=14,file='jad.mat')
+c
+c---- dimension of grid 
+c
+      nx = 4
+      ny = 2
+      nz = 1
+      nfree = 2
+c
+c---- generate grid problem.
+c
+c      na = nx*ny*nz*5
+      na = nfree*nfree 
+      call gen57bl (nx,ny,nz,nfree,na,nr,a1,ja1,ia1,iwk,stencil)
+c      nr = n / nfree 
+      n = nr*nfree 
+c
+c---- dump the reduced matrix 
+c 
+      iout = 7
+      nnz = ia(n+1)-1
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '  +++ Pattern of block matrix  (CSR) +++ '
+      write (iout,*) '-----------------------------------------'
+c
+      call dump(1,nr,.false.,a1,ja1,ia1,7)
+c
+c---- convert to CSR format and dump result 
+c
+      call bsrcsr (1,nr,nfree,na,a1,ja1,ia1,a,ja,ia)
+      iout = 7
+      nnz = ia(n+1)-1
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '  +++  initial matrix in CSR format +++ '
+      write (iout,*) '-----------------------------------------'
+      call dump(1,n,.true.,a,ja,ia,7)
+c
+c---- convert back to BSR format and dump pattern again.
+c
+      call csrbsr (1,n,nfree,na,a,ja,ia,a1,ja1,ia1,iwk2,ierr) 
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '  +++ Pattern of block matrix  (CSR) +++ '
+      write (iout,*) '-----------------------------------------'
+      call dump(1,nr,.false.,a1,ja1,ia1,7)
+c
+c----- convert to BSR format. 
+c
+      call bsrcsr (1,nr,nfree,na,a1,ja1,ia1,a,ja,ia)
+      iout = 7
+      nnz = ia(n+1)-1
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) ' +++  matrix after BSRCSR conversion +++ '
+      write (iout,*) '-----------------------------------------'
+      call dump(1,n,.true.,a,ja,ia,7)
+c
+c----- convert to dense format. 
+c
+      call csrdns(n,n,a,ja,ia,dns,ndns,ierr)
+c
+      iout = iout+1 
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '  +++  initial matrix in DENSE format+++ '
+      write (iout,*) '-----------------------------------------'
+      write (iout,'(4x,16i4)') (j,j=1,n)
+      write (iout,'(3x,65(1h-))') 
+      do 3  i=1,n
+         write (8,102) i,(dns(i,j), j=1,n)
+ 102     format(1h ,i2,1h|,16f4.1)
+ 3    continue
+c     
+c----- convert back to sparse format.
+c
+      call dnscsr(n,n,nnzmax,dns,ndns,a1,ja1,ia1,ierr)
+      write (7,*) '-----------------------------------------'
+      write (7,*) '  +++ matrix after conversion from dnscsr +++ '
+      write (7,*) '-----------------------------------------'
+      if (ierr .ne. 0) write (7,*) ' ***** ERROR FROM DNSCSR'
+      if (ierr .ne. 0) write (7,*)  '     IERR = ', ierr
+      call dump(1,n,.true.,a1,ja1,ia1,7)
+c     
+c     convert it to coordinate format.
+c     
+      call csrcoo(n,3,nnzmax,a,ja,ia,nnz,a1,ia1,ja1,ierr)
+      iout = iout+ 1
+      if (ierr .ne. 0) write (iout,*) ' ***** ERROR IN CSRCOO'
+      if (ierr .ne. 0) write (iout,*)   '     IERR = ', ierr
+      write (iout,*) '-----------------------------------------'
+      write(iout,*) ' +++ Matrix in coordinate format +++ '
+      write (iout,*) '-----------------------------------------'
+      write(iout,103) (ia1(j),ja1(j),a1(j),j=1,nnz) 
+ 103  format (' i =', i3,'    j = ',i3,'     a(i,j) = ',f4.1) 
+c     
+c     convert it back again to csr format 
+c     
+      call coocsr(n,nnz,a1,ia1,ja1,a,ja,ia)
+      
+      write (7,*) '-----------------------------------------'
+      write (7,*) '  +++ matrix after conversion from coocsr +++ '
+      write (7,*) '-----------------------------------------'
+      call dump(1,n,.true.,a,ja,ia,7)
+c     
+c     going to srs format
+c     
+      call csrssr(n,a,ja,ia,nnzmax,a1,ja1,ia1,ierr)
+      write (7,*) '-----------------------------------------'
+      write (7,*) '  +++ matrix after conversion to ssr format +++ '
+      write (7,*) '      (lower part only stored in csr format)    '
+      write (7,*) '-----------------------------------------'
+      call dump(1,n,.true.,a1,ja1,ia1,7)
+c     back to csr
+      call ssrcsr (3,1,n,a1,ja1,ia1,nnzmax,a,ja,ia,iwk,iwk2,ierr)
+      if (ierr .ne. 0) write(7,*) ' error in ssrcsr-IERR=',ierr
+      write (7,*) '-----------------------------------------'
+      write (7,*) '  +++ matrix after conversion from ssrcsr +++ '
+      write (7,*) '-----------------------------------------'
+      call dump(1,n,.true.,a,ja,ia,7)
+c---- msr format
+      iout = iout+1
+      call csrmsr (n,a,ja,ia,a1,ja1,a1,ja1)
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '  +++ matrix in modified sparse row format +++'
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) ' ** MAIN DIAGONAL '
+      write (iout,'(16f4.1)') (a1(k),k=1,n)
+      write (iout,*) ' ** POINTERS: '
+      write (iout,'(17i4)') (ja1(k),k=1,n+1)
+      write (iout,*) ' ** REMAINDER :'
+      call dump(1,n,.true.,a1,ja1,ja1,iout)
+c-------
+      call msrcsr (n,a1,ja1,a,ja,ia,wk,iwk2)
+      write (7,*) '-----------------------------------------'
+      write (7,*) ' +++ matrix after conversion from msrcsr +++'
+      write (7,*) '-----------------------------------------'
+c     
+      call dump(1,n,.true.,a,ja,ia,7)
+c     
+      maxcol = 13 
+c     
+      call csrell (n,a,ja,ia,maxcol,a1,ja1,n,ndiag,ierr)
+      iout = iout+1 
+      if (ierr .ne. 0) write (iout,*) ' ***** ERROR IN CSRELL'
+      if (ierr .ne. 0) write (iout,*)   '     IERR = ', ierr
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '  +++ matrix in ELLPACK-ITPACK format +++ '
+      write (iout,*) '-----------------------------------------'
+      do 12 i=1,ndiag
+         write (iout,*) ' Column number: ', i
+         write (iout,104) (a1(n*(i-1)+k),k=1,n)
+ 104     format(9h COEF  = ,16f4.0)
+         write (iout,105) (ja1(n*(i-1)+k),k=1,n)
+ 105     format (9h JCOEF = ,16i4) 
+ 12   continue
+      call ellcsr (n,a1,ja1,n,ndiag,a,ja,ia,nnzmax,ierr)
+      if (ierr .ne. 0) write (7,*) ' ***** ERROR IN ELLCSR'
+      if (ierr .ne. 0) write (7,*)   '     IERR = ', ierr
+      write (7,*) '-----------------------------------------'
+      write (7,*) '  +++ matrix after conversion from ellcsr +++'
+      write (7,*) '-----------------------------------------'
+      call dump(1,n,.true.,a,ja,ia,7)
+c     
+      call csrcsc(n,1,1,a,ja,ia, a1,ja1,ia1)
+      write (7,*) '-----------------------------------------'
+      write (7,*) '  +++ matrix after conversion from csrcsc  +++ '
+      write (7,*) '-----------------------------------------'
+      call dump(1,n,.true.,a1,ja1,ia1,7)
+      call csrcsc(n,1,1,a1,ja1,ia1, a,ja,ia)	
+c     
+c--------test 1 : get main diagonal and subdiagonal
+c     get some info on diagonals
+      call infdia(n,ja,ia,iwk,idiag0)
+      job = 0
+      ioff(1) = 0
+      ioff(2) = -1
+      idiag = 2
+      call csrdia (n,idiag,job,a,ja,ia,ndns,dns,ioff,a1,ja1,ia1,iwk)
+      iout = iout+1
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '  +++  diagonal format +++ '
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '  diagonals ioff = 0 and ioff = -1 '
+      write (iout,*) ' number of diag.s returned from csrdia=',idiag
+      do 13 kdiag = 1, idiag
+	 write (iout,*) ' diagonal offset = ', ioff(kdiag)
+         write (iout,'(16f4.1)') (dns(k,kdiag),k=1,n)
+ 13   continue
+c     reverse conversion
+      ndiag = ndns
+      idiag = idiag0 
+      job = 10
+      call csrdia (n,idiag,job,a,ja,ia,ndns,dns,ioff,a1,ja1,ia1,iwk)
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '  +++  second test diagonal format +++ '
+      write (iout,*) '         ** all diagonals of A  ** '
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) ' number of diagonals on return from csrdia=',
+     *     idiag
+      do 131 kdiag = 1, idiag
+	 write (iout,*) ' diagonal offset = ', ioff(kdiag)
+         write (iout,'(16f4.1)') (dns(k,kdiag),k=1,n)
+ 131  continue
+c     
+c     reverse conversion
+c     
+      job = 0
+      call diacsr (n,job,idiag,dns,ndns,ioff,a,ja,ia)
+c--------
+      write (7,*) '-----------------------------------------'
+      write (7,*) '  +++ matrix after conversion from diacsr  +++ '
+      write (7,*) '-----------------------------------------'
+      call dump(1,n,.true.,a,ja,ia,7)
+c     
+c     checking the banded format
+c     
+      lowd = 0
+      job = 1
+      call csrbnd(n,a,ja,ia,job,dns,ndns,lowd,ml,mu,ierr)
+      iout = iout+1
+      if (ierr .ne. 0) write (iout,*) ' ***** ERROR IN CSRBND'
+      if (ierr .ne. 0) write (iout,*)   '     IERR = ', ierr
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '       +++  banded  format +++ '
+      write (iout,*) ' bandwidth values found ml=',ml,'  mu=',mu
+      write (iout,*) '-----------------------------------------' 
+      write (iout,'(4x,16i4)') (j,j=1,n)
+      write (iout,'(3x,65(1h-))') 
+      do 14  i=1, lowd
+         write (iout,102) i, (dns(i,j), j=1,n)
+ 14   continue
+c     
+c     convert back to a, ja, ia format.
+c
+      len = nnzmax 
+c--------
+      call bndcsr(n,dns,ndns,lowd,ml,mu,a,ja,ia,len,ierr)
+      write (7,*) ' IERR IN BNDCSR = ', ierr
+      write (7,*) '-----------------------------------------'
+      write (7,*) '  +++ matrix after conversion from bndcsr +++'
+      write (7,*) '-----------------------------------------'
+      call dump(1,n,.true.,a,ja,ia,7)
+c     
+c     make sure it is sorted
+c     
+      call csrcsc(n,1,1,a,ja,ia, a1,ja1,ia1)	
+c     
+c     checking skyline format.
+c     
+      imod = 1
+      call csrssk (n,imod,a1,ja1,ia1,a,ia,nnzmax,ierr)
+c     
+      if (ierr .ne. 0) write (iout,*)   '     IERR = ', ierr
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '    +++ Sym. Skyline format +++ '
+      write (iout,*) '-----------------------------------------' 
+      write (iout,'(3x,65(1h-))') 
+c---------------------
+c     create column values.
+c---------------------
+      do 15  i=1, n
+         kend = ia(i+1)-1 
+         kstart = ia(i)  
+         do k=kstart,kend             
+            ja(k) =  i-(kend-k)
+         enddo
+ 15   continue
+c     
+      call dump(1,n,.true.,a,ja,ia,iout)
+c     
+c     back to ssr format..
+c     
+      call sskssr (n,imod,a,ia,a1,ja1,ia1,nnzmax,ierr)
+      write (7,*) '-----------------------------------------'
+      write (7,*) '  +++ matrix after conversion from sskcsr +++'
+      write (7,*) '-----------------------------------------'
+      call dump(1,n,.true.,a1,ja1,ia1,7)
+c     
+c     checking jad format -----
+c     
+c     first go back to the csr format ----
+c     
+      call ssrcsr (3,1,n,a1,ja1,ia1,nnzmax,a,ja,ia,iwk,iwk2,ierr)
+c     
+      call csrjad (n, a, ja, ia, ndiag, iwk, a1, ja1, ia1) 
+c     
+      iout = iout+1 
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '   +++   matrix in JAD format +++ '
+      write (iout,*) '-----------------------------------------'
+c     
+c     permutation array
+c     
+      write (iout,*) ' ** PERMUTATION ARRAY '
+      write (iout,'(17i4)') (iwk(k),k=1,n)
+c     ------ diagonals 
+      do 16 i=1,ndiag
+         write (iout,*) ' J-diagonal number: ', i
+         k1 = ia1(i)
+         k2 = ia1(i+1)-1 
+         write (iout,104) (a1(k),k=k1,k2) 
+         write (iout,105) (ja1(k),k=k1,k2) 
+ 16   continue
+c     
+c     back to csr format..
+c     
+      call jadcsr (n, ndiag, a1, ja1, ia1, iwk, a, ja, ia) 
+c     
+      write (7,*) '-----------------------------------------'
+      write (7,*) '  +++ matrix after conversion from jadcsr +++'
+      write (7,*) '-----------------------------------------'
+      call dump(1,n,.true.,a,ja,ia,7)
+c-----------------------------------------------------------------------
+c     checking the linked list format 
+c-----------------------------------------------------------------------
+c     
+      nnz = ia(n+1) - ia(1) 
+      call csrlnk (n, a, ja, ia, iwk) 
+c     
+c     print links in file 7 (no need for another file) 
+c     
+      iout = 7 
+      write (iout,*) '-----------------------------------------'
+      write (iout,*) '   +++   matrix in LNK format +++ '
+      write (iout,*) '-----------------------------------------'
+c     
+c     permutation array
+c     
+      write (iout,*) ' LINK ARRAY '
+      write (iout,*) ' ---------- ' 
+      write (iout,'(17i4)') (iwk(k),k=1,nnz) 
+c     
+c     back to csr format..
+c     
+      call lnkcsr (n, a, ja, ia, iwk, a1, ja1, ia1) 
+c     
+      write (7,*) '-----------------------------------------'
+      write (7,*) '  +++ matrix after conversion from lnkcsr +++'
+      write (7,*) '-----------------------------------------'
+      call dump(1,n,.true.,a,ja,ia,7)
+c------------------------------------------------------------
+      stop
+c-----------------------------------------------------------------------
+c-----------end-of-chkfmt1---------------------------------------------- 
+      end
diff --git a/FORMATS/chkun.f b/FORMATS/chkun.f
new file mode 100644
index 0000000..1778637
--- /dev/null
+++ b/FORMATS/chkun.f
@@ -0,0 +1,168 @@
+        program chkfmt 
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c test suite for the unary routines.                                   c
+c tests some of the routines in the module unary. Still needs to tests c
+c many other routines.                                                 c
+c Last update: May 2, 1994.
+c----------------------------------------------------------------------c 
+      parameter (nxmax = 10, nmx = nxmax*nxmax, nnzmax=10*nmx)
+      implicit real*8 (a-h,o-z)
+      integer ia(nmx+1),ja(nnzmax),ia1(nnzmax),ja1(nnzmax),
+     *         iwk(nmx*2+1), perm(16), qperm(16) ,
+     *         iwork(nnzmax*2) 
+      real*8 a(nnzmax),a1(nnzmax),dns(20,20),rhs(nnzmax),al(6)
+      data ndns/20/
+      data qperm /1, 3, 6, 8, 9, 11, 14, 16, 2, 4, 5, 7, 10, 12, 13, 15/
+c
+c define correct permutation
+c 
+      do 1 i=1, 16
+         perm(qperm(i)) = i
+ 1    continue
+c----- open statements ---------------- 
+      open (unit=7,file='unary.mat') 
+c
+c---- dimension of grid 
+c
+c     generate a 16 by 16 matrix (after eliminating boundary)
+      nx = 6
+      ny = 6
+      nz = 1
+      al(1) = 0.D0
+      al(2) = 0.D0
+      al(3) = 0.D0
+      al(4) = 0.D0
+      al(5) = 0.D0
+      al(6) = 0.D0
+c
+c---- generate grid problem.
+c
+      call gen57pt (nx,ny,nz,al,0,n,a,ja,ia,iwk,rhs)
+c
+c---- write out the matrix
+c
+	iout = 7
+	nnz = ia(n+1)-1
+	write (iout,*) '-----------------------------------------'
+        write (iout,*) '  +++  initial matrix in CSR format +++ '
+	write (iout,*) '-----------------------------------------'
+        call dump(1,n,.true.,a,ja,ia,iout)
+c
+c call csrdns
+c
+	 call csrdns(n,n,a,ja,ia,dns,ndns,ierr)
+c
+c write it out as a dense matrix. 
+c
+	 write (iout,*) '-----------------------------------------'
+         write (iout,*) '  +++ initial matrix in DENSE format+++ '
+	 write (iout,*) '-----------------------------------------'
+         call dmpdns(n, n, ndns, dns, iout)
+c
+c red black ordering 
+c
+         job = 1
+c
+        call dperm (n,a,ja,ia,a1,ja1,ia1,perm,perm,job)
+c
+	nnz = ia(n+1)-1
+	write (iout,*) '-----------------------------------------'
+        write (iout,*) '  +++ red-black matrix in CSR format +++ '
+	write (iout,*) '-----------------------------------------'
+        call dump(1,n,.true.,a1,ja1,ia1,iout)
+c
+c sort matrix
+c 
+        call csort (n,a1,ja1,ia1,iwork,.true.) 
+	nnz = ia(n+1)-1
+	write (iout,*) '-----------------------------------------'
+        write (iout,*) '  +++     matrix after sorting    +++ '
+	write (iout,*) '-----------------------------------------'
+        call dump(1,n,.true.,a1,ja1,ia1,iout)
+c
+c
+c convert into dense format
+c
+         call csrdns(n, n, a1,ja1,ia1,dns,ndns,ierr) 
+	 write (iout,*) '-----------------------------------------'
+         write (iout,*) '  +++ red-black matrix in DENSE format+++ '
+	 write (iout,*) '-----------------------------------------'
+         call dmpdns(n,n, ndns, dns, iout)
+         stop
+         end
+c----------------------------------------------------------------------- 
+         subroutine dmpdns(nrow, ncol, ndns, dns, iout) 
+         integer nrow, ncol, ndns, iout
+         real*8 dns(ndns,*) 
+c-----------------------------------------------------------------------
+c this subroutine prints out a dense matrix in a simple format.
+c the zero elements of the matrix are omitted. The format for the
+c nonzero elements is f4.1, i.e., very little precision is provided.
+c-----------------------------------------------------------------------
+c on entry
+c --------
+c nrow = row dimension of matrix
+c ncol = column dimension of matrix
+c ndns = first dimension of array dns.
+c dns  = double dimensional array of size n x n containing the matrix 
+c iout = logical unit where to write matrix
+c
+c on return
+c ---------
+c matrix will be printed out on unit output iout.
+c------------------------------------------------------------------------ 
+c         local variables
+         integer j, j1, j2, last, i
+         character*80 fmt 
+c
+c prints out a dense matrix -- without the zeros. 
+c
+	 write (iout,'(4x,16i4)') (j,j=1,ncol) 
+         fmt(1:5) = '    |'
+         j1 = 6
+         do 1 j=1, ncol
+            j2 = j1+4
+            fmt(j1:j2) = '----'
+            j1 = j2
+ 1       continue 
+         last = j1 
+         fmt(last:last) = '|'
+            write (iout,*) fmt
+c
+c undo loop 1 --- 
+c
+         j1 = 6
+         do 2 j=1,ncol
+            j2 = j1+4
+            fmt(j1:j2) = '   '
+            j1 = j2
+ 2          continue            
+c           
+         do 4  i=1, nrow 
+         j1 = 6 
+         write (fmt,101) i
+ 101     format(1h ,i2,2h |)
+         do 3 j=1, ncol 
+            j2= j1+4
+            if (dns(i,j) .ne. 0.0) then
+               write (fmt(j1:j2),102) dns(i,j)
+ 102           format(f4.1) 
+            endif
+           j1 = j2
+ 3       continue
+           fmt(last:last) = '|'
+           write (iout,*) fmt
+ 4       continue
+         fmt(1:5) = '    |'
+         j1 = 6
+         do 5 j=1, ncol 
+            j2 = j1+4
+            fmt(j1:j2) = '----'
+            j1 = j2
+ 5       continue 
+         fmt(last:last) = '|'
+            write (iout,*) fmt
+         return
+         end
diff --git a/FORMATS/formats.f b/FORMATS/formats.f
new file mode 100644
index 0000000..fde8f92
--- /dev/null
+++ b/FORMATS/formats.f
@@ -0,0 +1,3716 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c                    FORMAT CONVERSION MODULE                          c
+c----------------------------------------------------------------------c
+c contents:                                                            c
+c----------                                                            c
+c csrdns  : converts a row-stored sparse matrix into the dense format. c
+c dnscsr  : converts a dense matrix to a sparse storage format.        c
+c coocsr  : converts coordinate to  to csr format                      c
+c coicsr  : in-place conversion of coordinate to csr format            c
+c csrcoo  : converts compressed sparse row to coordinate.              c
+c csrssr  : converts compressed sparse row to symmetric sparse row     c
+c ssrcsr  : converts symmetric sparse row to compressed sparse row     c
+c csrell  : converts compressed sparse row to ellpack format           c
+c ellcsr  : converts ellpack format to compressed sparse row format    c
+c csrmsr  : converts compressed sparse row format to modified sparse   c
+c           row format                                                 c
+c msrcsr  : converts modified sparse row format to compressed sparse   c
+c           row format.                                                c
+c csrcsc  : converts compressed sparse row format to compressed sparse c
+c           column format (transposition)                              c
+c csrcsc2 : rectangular version of csrcsc                              c
+c csrlnk  : converts compressed sparse row to linked list format       c
+c lnkcsr  : converts linked list format to compressed sparse row fmt   c
+c csrdia  : converts a compressed sparse row format into a diagonal    c
+c           format.                                                    c
+c diacsr  : converts a diagonal format into a compressed sparse row    c
+c           format.                                                    c
+c bsrcsr  : converts a block-row sparse format into a compressed       c
+c           sparse row format.                                         c
+c csrbsr  : converts a compressed sparse row format into a block-row   c
+c           sparse format.                                             c
+c csrbnd  : converts a compressed sparse row format into a banded      c
+c           format (linpack style).                                    c
+c bndcsr  : converts a banded format (linpack style) into a compressed c
+c           sparse row storage.                                        c
+c csrssk  : converts the compressed sparse row format to the symmetric c
+c           skyline format                                             c
+c sskssr  : converts symmetric skyline format to symmetric  sparse row c
+c           format.                                                    c
+c csrjad  : converts the csr format into the jagged diagonal format    c
+c jadcsr  : converts the jagged-diagonal format into the csr format    c
+c csruss  : Compressed Sparse Row to Unsymmetric Sparse Skyline        c
+c           format                                                     c
+c usscsr  : Unsymmetric Sparse Skyline format to Compressed Sparse Row c
+c csrsss  : Compressed Sparse Row to Symmetric Sparse Skyline format   c
+c ssscsr  : Symmetric Sparse Skyline format to Compressed Sparse Row   c
+c csrvbr  : Converts compressed sparse row to var block row format     c
+c vbrcsr  : Converts var block row to compressed sparse row format     c
+c csorted : Checks if matrix in CSR format is sorted by columns        c
+c--------- miscalleneous additions not involving the csr format--------c
+c cooell  : converts coordinate to Ellpack/Itpack format               c
+c dcsort  : sorting routine used by crsjad                             c
+c----------------------------------------------------------------------c
+      subroutine csrdns(nrow,ncol,a,ja,ia,dns,ndns,ierr) 
+      real*8 dns(ndns,*),a(*)
+      integer ja(*),ia(*)
+c-----------------------------------------------------------------------
+c Compressed Sparse Row    to    Dense 
+c-----------------------------------------------------------------------
+c
+c converts a row-stored sparse matrix into a densely stored one
+c
+c On entry:
+c---------- 
+c
+c nrow	= row-dimension of a
+c ncol	= column dimension of a
+c a, 
+c ja, 
+c ia    = input matrix in compressed sparse row format. 
+c         (a=value array, ja=column array, ia=pointer array)
+c dns   = array where to store dense matrix
+c ndns	= first dimension of array dns 
+c
+c on return: 
+c----------- 
+c dns   = the sparse matrix a, ja, ia has been stored in dns(ndns,*)
+c 
+c ierr  = integer error indicator. 
+c         ierr .eq. 0  means normal return
+c         ierr .eq. i  means that the code has stopped when processing
+c         row number i, because it found a column number .gt. ncol.
+c 
+c----------------------------------------------------------------------- 
+      ierr = 0
+      do 1 i=1, nrow
+         do 2 j=1,ncol
+	    dns(i,j) = 0.0d0
+ 2       continue
+ 1    continue
+c     
+      do 4 i=1,nrow
+         do 3 k=ia(i),ia(i+1)-1
+            j = ja(k) 
+	    if (j .gt. ncol) then
+               ierr = i
+               return
+	    endif
+	    dns(i,j) = a(k)
+ 3       continue	   
+ 4    continue
+      return
+c---- end of csrdns ----------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine dnscsr(nrow,ncol,nzmax,dns,ndns,a,ja,ia,ierr)
+      real*8 dns(ndns,*),a(*)
+      integer ia(*),ja(*)
+c-----------------------------------------------------------------------
+c Dense		to    Compressed Row Sparse 
+c----------------------------------------------------------------------- 
+c
+c converts a densely stored matrix into a row orientied
+c compactly sparse matrix. ( reverse of csrdns )
+c Note: this routine does not check whether an element 
+c is small. It considers that a(i,j) is zero if it is exactly
+c equal to zero: see test below.
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c
+c nrow	= row-dimension of a
+c ncol	= column dimension of a
+c nzmax = maximum number of nonzero elements allowed. This
+c         should be set to be the lengths of the arrays a and ja.
+c dns   = input nrow x ncol (dense) matrix.
+c ndns	= first dimension of dns. 
+c
+c on return:
+c---------- 
+c 
+c a, ja, ia = value, column, pointer  arrays for output matrix 
+c
+c ierr	= integer error indicator: 
+c         ierr .eq. 0 means normal retur
+c         ierr .eq. i means that the the code stopped while
+c         processing row number i, because there was no space left in
+c         a, and ja (as defined by parameter nzmax).
+c----------------------------------------------------------------------- 
+      ierr = 0
+      next = 1
+      ia(1) = 1
+      do 4 i=1,nrow
+         do 3 j=1, ncol 
+            if (dns(i,j) .eq. 0.0d0) goto 3
+            if (next .gt. nzmax) then
+               ierr = i
+               return
+            endif
+            ja(next) = j
+            a(next) = dns(i,j)
+            next = next+1
+ 3       continue	   
+         ia(i+1) = next
+ 4    continue
+      return
+c---- end of dnscsr ---------------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c----------------------------------------------------------------------- 
+      subroutine coocsr(nrow,nnz,a,ir,jc,ao,jao,iao)
+c----------------------------------------------------------------------- 
+      real*8 a(*),ao(*),x
+      integer ir(*),jc(*),jao(*),iao(*)
+c-----------------------------------------------------------------------
+c  Coordinate     to   Compressed Sparse Row 
+c----------------------------------------------------------------------- 
+c converts a matrix that is stored in coordinate format
+c  a, ir, jc into a row general sparse ao, jao, iao format.
+c
+c on entry:
+c--------- 
+c nrow	= dimension of the matrix 
+c nnz	= number of nonzero elements in matrix
+c a,
+c ir, 
+c jc    = matrix in coordinate format. a(k), ir(k), jc(k) store the nnz
+c         nonzero elements of the matrix with a(k) = actual real value of
+c 	  the elements, ir(k) = its row number and jc(k) = its column 
+c	  number. The order of the elements is arbitrary. 
+c
+c on return:
+c----------- 
+c ir 	is destroyed
+c
+c ao, jao, iao = matrix in general sparse matrix format with ao 
+c 	continung the real values, jao containing the column indices, 
+c	and iao being the pointer to the beginning of the row, 
+c	in arrays ao, jao.
+c
+c Notes:
+c------ This routine is NOT in place.  See coicsr
+c
+c------------------------------------------------------------------------
+      do 1 k=1,nrow+1
+         iao(k) = 0
+ 1    continue
+c determine row-lengths.
+      do 2 k=1, nnz
+         iao(ir(k)) = iao(ir(k))+1
+ 2    continue
+c starting position of each row..
+      k = 1
+      do 3 j=1,nrow+1
+         k0 = iao(j)
+         iao(j) = k
+         k = k+k0
+ 3    continue
+c go through the structure  once more. Fill in output matrix.
+      do 4 k=1, nnz
+         i = ir(k)
+         j = jc(k)
+         x = a(k)
+         iad = iao(i)
+         ao(iad) =  x
+         jao(iad) = j
+         iao(i) = iad+1
+ 4    continue
+c shift back iao
+      do 5 j=nrow,1,-1
+         iao(j+1) = iao(j)
+ 5    continue
+      iao(1) = 1
+      return
+c------------- end of coocsr ------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c----------------------------------------------------------------------- 
+      subroutine coicsr (n,nnz,job,a,ja,ia,iwk)
+      integer ia(nnz),ja(nnz),iwk(n+1) 
+      real*8 a(*)
+c------------------------------------------------------------------------
+c IN-PLACE coo-csr conversion routine.
+c------------------------------------------------------------------------
+c this subroutine converts a matrix stored in coordinate format into 
+c the csr format. The conversion is done in place in that the arrays 
+c a,ja,ia of the result are overwritten onto the original arrays.
+c------------------------------------------------------------------------
+c on entry:
+c--------- 
+c n	= integer. row dimension of A.
+c nnz	= integer. number of nonzero elements in A.
+c job   = integer. Job indicator. when job=1, the real values in a are
+c         filled. Otherwise a is not touched and the structure of the
+c         array only (i.e. ja, ia)  is obtained.
+c a	= real array of size nnz (number of nonzero elements in A)
+c         containing the nonzero elements 
+c ja	= integer array of length nnz containing the column positions
+c 	  of the corresponding elements in a.
+c ia	= integer array of length nnz containing the row positions
+c 	  of the corresponding elements in a.
+c iwk	= integer work array of length n+1 
+c on return:
+c----------
+c a
+c ja 
+c ia	= contains the compressed sparse row data structure for the 
+c         resulting matrix.
+c Note: 
+c-------
+c         the entries of the output matrix are not sorted (the column
+c         indices in each are not in increasing order) use coocsr
+c         if you want them sorted.
+c----------------------------------------------------------------------c
+c  Coded by Y. Saad, Sep. 26 1989                                      c
+c----------------------------------------------------------------------c
+      real*8 t,tnext
+      logical values
+c----------------------------------------------------------------------- 
+      values = (job .eq. 1) 
+c find pointer array for resulting matrix. 
+      do 35 i=1,n+1
+         iwk(i) = 0
+ 35   continue
+      do 4 k=1,nnz
+         i = ia(k)
+         iwk(i+1) = iwk(i+1)+1
+ 4    continue 
+c------------------------------------------------------------------------
+      iwk(1) = 1 
+      do 44 i=2,n
+         iwk(i) = iwk(i-1) + iwk(i)
+ 44   continue 
+c
+c     loop for a cycle in chasing process. 
+c
+      init = 1
+      k = 0
+ 5    if (values) t = a(init)
+      i = ia(init)
+      j = ja(init)
+      ia(init) = -1
+c------------------------------------------------------------------------
+ 6    k = k+1 		
+c     current row number is i.  determine  where to go. 
+      ipos = iwk(i)
+c     save the chased element. 
+      if (values) tnext = a(ipos)
+      inext = ia(ipos)
+      jnext = ja(ipos)
+c     then occupy its location.
+      if (values) a(ipos)  = t
+      ja(ipos) = j
+c     update pointer information for next element to come in row i. 
+      iwk(i) = ipos+1
+c     determine  next element to be chased,
+      if (ia(ipos) .lt. 0) goto 65
+      t = tnext
+      i = inext
+      j = jnext 
+      ia(ipos) = -1
+      if (k .lt. nnz) goto 6
+      goto 70
+ 65   init = init+1
+      if (init .gt. nnz) goto 70
+      if (ia(init) .lt. 0) goto 65
+c     restart chasing --	
+      goto 5
+ 70   do 80 i=1,n 
+         ia(i+1) = iwk(i)
+ 80   continue
+      ia(1) = 1
+      return
+c----------------- end of coicsr ----------------------------------------
+c------------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine csrcoo (nrow,job,nzmax,a,ja,ia,nnz,ao,ir,jc,ierr)
+c-----------------------------------------------------------------------
+      real*8 a(*),ao(*) 
+      integer ir(*),jc(*),ja(*),ia(nrow+1) 
+c----------------------------------------------------------------------- 
+c  Compressed Sparse Row      to      Coordinate 
+c----------------------------------------------------------------------- 
+c converts a matrix that is stored in coordinate format
+c  a, ir, jc into a row general sparse ao, jao, iao format.
+c
+c on entry: 
+c---------
+c nrow	= dimension of the matrix.
+c job   = integer serving as a job indicator. 
+c         if job = 1 fill in only the array ir, ignore jc, and ao.
+c         if job = 2 fill in ir, and jc but not ao 
+c         if job = 3 fill in everything.
+c         The reason why these options are provided is that on return 
+c         ao and jc are the same as a, ja. So when job = 3, a and ja are
+c         simply copied into ao, jc.  When job=2, only jc and ir are
+c         returned. With job=1 only the array ir is returned. Moreover,
+c         the algorithm is in place:
+c	     call csrcoo (nrow,1,nzmax,a,ja,ia,nnz,a,ia,ja,ierr) 
+c         will write the output matrix in coordinate format on a, ja,ia.
+c
+c a,
+c ja,
+c ia    = matrix in compressed sparse row format.
+c nzmax = length of space available in ao, ir, jc.
+c         the code will stop immediatly if the number of
+c         nonzero elements found in input matrix exceeds nzmax.
+c 
+c on return:
+c----------- 
+c ao, ir, jc = matrix in coordinate format.
+c
+c nnz        = number of nonzero elements in matrix.
+c ierr       = integer error indicator.
+c         ierr .eq. 0 means normal retur
+c         ierr .eq. 1 means that the the code stopped 
+c         because there was no space in ao, ir, jc 
+c         (according to the value of  nzmax).
+c 
+c NOTES: 1)This routine is PARTIALLY in place: csrcoo can be called with 
+c         ao being the same array as as a, and jc the same array as ja. 
+c         but ir CANNOT be the same as ia. 
+c         2) note the order in the output arrays, 
+c------------------------------------------------------------------------
+      ierr = 0
+      nnz = ia(nrow+1)-1
+      if (nnz .gt. nzmax) then
+         ierr = 1
+         return
+      endif
+c------------------------------------------------------------------------
+      goto (3,2,1) job
+ 1    do 10 k=1,nnz
+         ao(k) = a(k)
+ 10   continue
+ 2    do 11 k=1,nnz
+         jc(k) = ja(k)
+ 11   continue
+c
+c     copy backward to allow for in-place processing. 
+c
+ 3    do 13 i=nrow,1,-1
+         k1 = ia(i+1)-1
+         k2 = ia(i)
+         do 12 k=k1,k2,-1
+            ir(k) = i
+ 12      continue
+ 13   continue
+      return
+c------------- end-of-csrcoo ------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c----------------------------------------------------------------------- 
+      subroutine csrssr (nrow,a,ja,ia,nzmax,ao,jao,iao,ierr)
+      real*8 a(*), ao(*), t
+      integer ia(*), ja(*), iao(*), jao(*)
+c-----------------------------------------------------------------------
+c Compressed Sparse Row     to     Symmetric Sparse Row
+c----------------------------------------------------------------------- 
+c this subroutine extracts the lower triangular part of a matrix.
+c It can used as a means for converting a symmetric matrix for 
+c which all the entries are stored in sparse format into one
+c in which only the lower part is stored. The routine is in place in 
+c that the output matrix ao, jao, iao can be overwritten on 
+c the  input matrix  a, ja, ia if desired. Csrssr has been coded to
+c put the diagonal elements of the matrix in the last position in
+c each row (i.e. in position  ao(ia(i+1)-1   of ao and jao) 
+c----------------------------------------------------------------------- 
+c On entry
+c-----------
+c nrow  = dimension of the matrix a.
+c a, ja, 
+c    ia = matrix stored in compressed row sparse format
+c
+c nzmax = length of arrays ao,  and jao. 
+c
+c On return:
+c----------- 
+c ao, jao, 
+c     iao = lower part of input matrix (a,ja,ia) stored in compressed sparse 
+c          row format format.
+c  
+c ierr   = integer error indicator. 
+c          ierr .eq. 0  means normal return
+c          ierr .eq. i  means that the code has stopped when processing
+c          row number i, because there is not enough space in ao, jao
+c          (according to the value of nzmax) 
+c
+c----------------------------------------------------------------------- 
+      ierr = 0
+      ko = 0
+c-----------------------------------------------------------------------
+      do  7 i=1, nrow
+         kold = ko
+         kdiag = 0
+         do 71 k = ia(i), ia(i+1) -1
+            if (ja(k)  .gt. i) goto 71
+            ko = ko+1
+            if (ko .gt. nzmax) then
+               ierr = i
+               return
+            endif
+            ao(ko) = a(k)
+            jao(ko) = ja(k)
+            if (ja(k)  .eq. i) kdiag = ko
+ 71      continue
+         if (kdiag .eq. 0 .or. kdiag .eq. ko) goto 72
+c     
+c     exchange
+c     
+         t = ao(kdiag)
+         ao(kdiag) = ao(ko)
+         ao(ko) = t
+c     
+         k = jao(kdiag)
+         jao(kdiag) = jao(ko)
+         jao(ko) = k
+ 72      iao(i) = kold+1
+ 7    continue
+c     redefine iao(n+1)
+      iao(nrow+1) = ko+1
+      return
+c--------- end of csrssr ----------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c----------------------------------------------------------------------- 
+      subroutine ssrcsr(job, value2, nrow, a, ja, ia, nzmax,
+     &                  ao, jao, iao, indu, iwk, ierr)
+c     .. Scalar Arguments ..
+      integer            ierr, job, nrow, nzmax, value2
+c     ..
+c     .. Array Arguments ..
+      integer            ia(nrow+1), iao(nrow+1), indu(nrow),
+     &                   iwk(nrow+1), ja(*), jao(nzmax)
+      real*8             a(*), ao(nzmax)
+c     ..
+c-----------------------------------------------------------------------
+c     Symmetric Sparse Row to Compressed Sparse Row format
+c-----------------------------------------------------------------------
+c     This subroutine converts a given matrix in SSR format to regular
+c     CSR format by computing Ao = A + A' - diag(A), where A' is A
+c     transpose.
+c
+c     Typically this routine is used to expand the SSR matrix of
+c     Harwell Boeing matrices, or to obtain a symmetrized graph of
+c     unsymmetric matrices.
+c
+c     This routine is inplace, i.e., (Ao,jao,iao) may be same as
+c     (a,ja,ia).
+c
+c     It is possible to input an arbitrary CSR matrix to this routine,
+c     since there is no syntactical difference between CSR and SSR
+c     format. It also removes duplicate entries and perform a partial
+c     ordering. The output matrix has an order of lower half, main
+c     diagonal and upper half after the partial ordering.
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c
+c job   = options
+c         0 -- duplicate entries are not removed. If the input matrix is
+c              SSR (not an arbitary CSR) matrix, no duplicate entry should
+c              arise from this routine.
+c         1 -- eliminate duplicate entries, zero entries.
+c         2 -- eliminate duplicate entries and perform partial ordering.
+c         3 -- eliminate duplicate entries, sort the entries in the
+c              increasing order of clumn indices.
+c              
+c value2= will the values of A be copied?
+c         0 -- only expand the graph (a, ao are not touched)
+c         1 -- expand the matrix with the values.
+c
+c nrow  = column dimension of inout matrix
+c a,
+c ia,
+c ja    = matrix in compressed sparse row format.
+c
+c nzmax = size of arrays ao and jao. SSRCSR will abort if the storage
+c          provided in ao, jao is not sufficient to store A. See ierr.
+c
+c on return:
+c----------
+c ao, jao, iao
+c       = output matrix in compressed sparse row format. The resulting
+c         matrix is symmetric and is equal to A+A'-D. ao, jao, iao,
+c         can be the same as a, ja, ia in the calling sequence.
+c
+c indu  = integer array of length nrow. INDU will contain pointers
+c         to the beginning of upper traigular part if job > 1.
+c         Otherwise it is also used as a work array (size nrow).
+c
+c iwk   = integer work space (size nrow+1).
+c
+c ierr  = integer. Serving as error message. If the length of the arrays
+c         ao, jao exceeds nzmax, ierr returns the minimum value
+c         needed for nzmax. otherwise ierr=0 (normal return).
+c
+c-----------------------------------------------------------------------
+c     .. Local Scalars ..
+      integer            i, ipos, j, k, kfirst, klast, ko, kosav, nnz
+      real*8             tmp
+c     ..
+c     .. Executable Statements ..
+      ierr = 0
+      do 10 i = 1, nrow
+         indu(i) = 0
+         iwk(i) = 0
+ 10   continue
+      iwk(nrow+1) = 0
+c
+c     .. compute number of elements in each row of (A'-D)
+c     put result in iwk(i+1)  for row i.
+c
+      do 30 i = 1, nrow
+         do 20 k = ia(i), ia(i+1) - 1
+            j = ja(k)
+            if (j.ne.i)
+     &         iwk(j+1) = iwk(j+1) + 1
+ 20      continue
+ 30   continue
+c
+c     .. find addresses of first elements of ouput matrix. result in iwk
+c
+      iwk(1) = 1
+      do 40 i = 1, nrow
+         indu(i) = iwk(i) + ia(i+1) - ia(i)
+         iwk(i+1) = iwk(i+1) + indu(i)
+         indu(i) = indu(i) - 1
+ 40   continue
+c.....Have we been given enough storage in ao, jao ?
+      nnz = iwk(nrow+1) - 1
+      if (nnz.gt.nzmax) then
+         ierr = nnz
+         return
+      endif
+c
+c     .. copy the existing matrix (backwards).
+c
+      kosav = iwk(nrow+1)
+      do 60 i = nrow, 1, -1
+         klast = ia(i+1) - 1
+         kfirst = ia(i)
+         iao(i+1) = kosav
+         kosav = iwk(i)
+         ko = iwk(i) - kfirst
+         iwk(i) = ko + klast + 1
+         do 50 k = klast, kfirst, -1
+            if (value2.ne.0)
+     &         ao(k+ko) = a(k)
+            jao(k+ko) = ja(k)
+ 50      continue
+ 60   continue
+      iao(1) = 1
+c
+c     now copy (A'-D). Go through the structure of ao, jao, iao
+c     that has already been copied. iwk(i) is the address
+c     of the next free location in row i for ao, jao.
+c
+      do 80 i = 1, nrow
+         do 70 k = iao(i), indu(i)
+            j = jao(k)
+            if (j.ne.i) then
+               ipos = iwk(j)
+               if (value2.ne.0)
+     &            ao(ipos) = ao(k)
+               jao(ipos) = i
+               iwk(j) = ipos + 1
+            endif
+ 70      continue
+ 80   continue
+      if (job.le.0) return
+c
+c     .. eliminate duplicate entries --
+c     array INDU is used as marker for existing indices, it is also the
+c     location of the entry.
+c     IWK is used to stored the old IAO array.
+c     matrix is copied to squeeze out the space taken by the duplicated
+c     entries.
+c
+      do 90 i = 1, nrow
+         indu(i) = 0
+         iwk(i) = iao(i)
+ 90   continue
+      iwk(nrow+1) = iao(nrow+1)
+      k = 1
+      do 120 i = 1, nrow
+         iao(i) = k
+         ipos = iwk(i)
+         klast = iwk(i+1)
+ 100     if (ipos.lt.klast) then
+            j = jao(ipos)
+            if (indu(j).eq.0) then
+c     .. new entry ..
+               if (value2.ne.0) then
+                  if (ao(ipos) .ne. 0.0D0) then
+                     indu(j) = k
+                     jao(k) = jao(ipos)
+                     ao(k) = ao(ipos)
+                     k = k + 1
+                  endif
+               else
+                  indu(j) = k
+                  jao(k) = jao(ipos)
+                  k = k + 1
+               endif
+            else if (value2.ne.0) then
+c     .. duplicate entry ..
+               ao(indu(j)) = ao(indu(j)) + ao(ipos)
+            endif
+            ipos = ipos + 1
+            go to 100
+         endif
+c     .. remove marks before working on the next row ..
+         do 110 ipos = iao(i), k - 1
+            indu(jao(ipos)) = 0
+ 110     continue
+ 120  continue
+      iao(nrow+1) = k
+      if (job.le.1) return
+c
+c     .. partial ordering ..
+c     split the matrix into strict upper/lower triangular
+c     parts, INDU points to the the beginning of the strict upper part.
+c
+      do 140 i = 1, nrow
+         klast = iao(i+1) - 1
+         kfirst = iao(i)
+ 130     if (klast.gt.kfirst) then
+            if (jao(klast).lt.i .and. jao(kfirst).ge.i) then
+c     .. swap klast with kfirst ..
+               j = jao(klast)
+               jao(klast) = jao(kfirst)
+               jao(kfirst) = j
+               if (value2.ne.0) then
+                  tmp = ao(klast)
+                  ao(klast) = ao(kfirst)
+                  ao(kfirst) = tmp
+               endif
+            endif
+            if (jao(klast).ge.i)
+     &         klast = klast - 1
+            if (jao(kfirst).lt.i)
+     &         kfirst = kfirst + 1
+            go to 130
+         endif
+c
+         if (jao(klast).lt.i) then
+            indu(i) = klast + 1
+         else
+            indu(i) = klast
+         endif
+ 140  continue
+      if (job.le.2) return
+c
+c     .. order the entries according to column indices
+c     bubble-sort is used
+c
+      do 190 i = 1, nrow
+         do 160 ipos = iao(i), indu(i)-1
+            do 150 j = indu(i)-1, ipos+1, -1
+               k = j - 1
+               if (jao(k).gt.jao(j)) then
+                  ko = jao(k)
+                  jao(k) = jao(j)
+                  jao(j) = ko
+                  if (value2.ne.0) then
+                     tmp = ao(k)
+                     ao(k) = ao(j)
+                     ao(j) = tmp
+                  endif
+               endif
+ 150        continue
+ 160     continue
+         do 180 ipos = indu(i), iao(i+1)-1
+            do 170 j = iao(i+1)-1, ipos+1, -1
+               k = j - 1
+               if (jao(k).gt.jao(j)) then
+                  ko = jao(k)
+                  jao(k) = jao(j)
+                  jao(j) = ko
+                  if (value2.ne.0) then
+                     tmp = ao(k)
+                     ao(k) = ao(j)
+                     ao(j) = tmp
+                  endif
+               endif
+ 170        continue
+ 180     continue
+ 190  continue
+c
+      return
+c---- end of ssrcsr ----------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine xssrcsr (nrow,a,ja,ia,nzmax,ao,jao,iao,indu,ierr)
+      integer ia(nrow+1),iao(nrow+1),ja(*),jao(nzmax),indu(nrow+1)
+      real*8 a(*),ao(nzmax)
+c-----------------------------------------------------------------------
+c Symmetric Sparse Row   to    (regular) Compressed Sparse Row
+c----------------------------------------------------------------------- 
+c this subroutine converts  a symmetric  matrix in which only the lower 
+c part is  stored in compressed sparse row format, i.e.,
+c a matrix stored in symmetric sparse format, into a fully stored matrix
+c i.e., a matrix where both the lower and upper parts are stored in 
+c compressed sparse row format. the algorithm is in place (i.e. result 
+c may be overwritten onto the input matrix a, ja, ia ----- ). 
+c the output matrix delivered by ssrcsr is such that each row starts with
+c the elements of the lower part followed by those of the upper part.
+c----------------------------------------------------------------------- 
+c on entry:
+c--------- 
+c	
+c nrow  = row dimension of inout matrix
+c a, 
+c ia, 
+c ja    = matrix in compressed sparse row format. This is assumed to be
+c         a lower triangular matrix. 
+c
+c nzmax	= size of arrays ao and jao. ssrcsr will abort if the storage 
+c	   provided in a, ja is not sufficient to store A. See ierr. 
+c	
+c on return:
+c----------
+c ao, iao, 
+c   jao = output matrix in compressed sparse row format. The resulting 
+c         matrix is symmetric and is equal to A+A**T - D, if
+c         A is the original lower triangular matrix. ao, jao, iao,
+c         can be the same as a, ja, ia in the calling sequence.
+c      
+c indu  = integer array of length nrow+1. If the input matrix is such 
+c         that the last element in each row is its diagonal element then
+c         on return, indu will contain the pointers to the diagonal 
+c         element in each row of the output matrix. Otherwise used as
+c         work array.
+c ierr  = integer. Serving as error message. If the length of the arrays
+c         ao, jao exceeds nzmax, ierr returns the minimum value
+c         needed for nzmax. otherwise ierr=0 (normal return).
+c 
+c----------------------------------------------------------------------- 
+      ierr = 0
+      do 1 i=1,nrow+1
+         indu(i) = 0     
+ 1    continue
+c     
+c     compute  number of elements in each row of strict upper part. 
+c     put result in indu(i+1)  for row i. 
+c     
+      do 3 i=1, nrow
+         do 2 k=ia(i),ia(i+1)-1 
+            j = ja(k)
+            if (j .lt. i) indu(j+1) = indu(j+1)+1
+ 2       continue 
+ 3    continue
+c-----------
+c     find addresses of first elements of ouput matrix. result in indu
+c-----------
+      indu(1) = 1 
+      do 4 i=1,nrow
+         lenrow = ia(i+1)-ia(i)
+         indu(i+1) = indu(i) + indu(i+1) + lenrow
+ 4    continue
+c--------------------- enough storage in a, ja ? --------
+      nnz = indu(nrow+1)-1 
+      if (nnz .gt. nzmax) then
+         ierr = nnz
+         return
+      endif
+c
+c     now copy lower part (backwards).
+c     
+      kosav = indu(nrow+1)
+      do 6 i=nrow,1,-1
+         klast = ia(i+1)-1
+         kfirst = ia(i)
+         iao(i+1) = kosav
+         ko = indu(i) 
+         kosav = ko
+         do 5 k = kfirst, klast
+            ao(ko) = a(k)
+            jao(ko) = ja(k)
+	    ko = ko+1
+ 5       continue
+         indu(i) = ko 
+ 6    continue
+      iao(1) = 1
+c
+c     now copy upper part. Go through the structure of ao, jao, iao
+c     that has already been copied (lower part). indu(i) is the address
+c     of the next free location in row i for ao, jao.
+c     
+      do 8 i=1,nrow
+c     i-th row is now in ao, jao, iao structure -- lower half part
+         do 9 k=iao(i), iao(i+1)-1 
+            j = jao(k)
+            if (j .ge. i)  goto 8
+            ipos = indu(j)
+            ao(ipos) = ao(k)
+            jao(ipos) = i
+            indu(j) = indu(j) + 1 
+ 9       continue
+ 8    continue
+      return
+c----- end of xssrcsr -------------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c-----------------------------------------------------------------------
+      subroutine csrell (nrow,a,ja,ia,maxcol,coef,jcoef,ncoef,
+     *                   ndiag,ierr)
+      integer ia(nrow+1), ja(*), jcoef(ncoef,1)  
+      real*8 a(*), coef(ncoef,1)
+c----------------------------------------------------------------------- 
+c Compressed Sparse Row	    to    Ellpack - Itpack format 
+c----------------------------------------------------------------------- 
+c this subroutine converts  matrix stored in the general a, ja, ia 
+c format into the coef, jcoef itpack format.
+c
+c----------------------------------------------------------------------- 
+c on entry:
+c---------- 
+c nrow 	  = row dimension of the matrix A.
+c
+c a, 
+c ia, 
+c ja      = input matrix in compressed sparse row format. 
+c
+c ncoef  = first dimension of arrays coef, and jcoef.
+c 
+c maxcol = integer equal to the number of columns available in coef.
+c
+c on return: 
+c----------
+c coef	= real array containing the values of the matrix A in 
+c         itpack-ellpack format.
+c jcoef = integer array containing the column indices of coef(i,j) 
+c         in A.
+c ndiag = number of active 'diagonals' found. 
+c
+c ierr 	= error message. 0 = correct return. If ierr .ne. 0 on
+c	  return this means that the number of diagonals found
+c         (ndiag) exceeds maxcol.
+c
+c----------------------------------------------------------------------- 
+c first determine the length of each row of lower-part-of(A)
+      ierr = 0
+      ndiag = 0
+      do 3 i=1, nrow
+         k = ia(i+1)-ia(i)
+         ndiag = max0(ndiag,k) 
+ 3    continue
+c----- check whether sufficient columns are available. ----------------- 
+      if (ndiag .gt. maxcol) then
+         ierr = 1 
+         return
+      endif
+c
+c fill coef with zero elements and jcoef with row numbers.------------ 
+c
+      do 4 j=1,ndiag 
+         do 41 i=1,nrow
+            coef(i,j) = 0.0d0
+            jcoef(i,j) = i
+ 41      continue
+ 4    continue
+c     
+c------- copy elements row by row.-------------------------------------- 
+c     
+      do 6 i=1, nrow
+         k1 = ia(i)
+         k2 = ia(i+1)-1
+         do 5 k=k1,k2
+            coef(i,k-k1+1) = a(k)
+            jcoef(i,k-k1+1) = ja(k)
+ 5       continue
+ 6    continue
+      return
+c--- end of csrell------------------------------------------------------ 
+c----------------------------------------------------------------------- 
+      end
+c-----------------------------------------------------------------------
+      subroutine ellcsr(nrow,coef,jcoef,ncoef,ndiag,a,ja,ia,nzmax,ierr)
+      integer ia(nrow+1), ja(*), jcoef(ncoef,1) 
+      real*8 a(*), coef(ncoef,1)
+c----------------------------------------------------------------------- 
+c  Ellpack - Itpack format  to  Compressed Sparse Row
+c----------------------------------------------------------------------- 
+c this subroutine converts a matrix stored in ellpack-itpack format 
+c coef-jcoef into the compressed sparse row format. It actually checks
+c whether an entry in the input matrix is a nonzero element before
+c putting it in the output matrix. The test does not account for small
+c values but only for exact zeros. 
+c----------------------------------------------------------------------- 
+c on entry:
+c---------- 
+c
+c nrow 	= row dimension of the matrix A.
+c coef	= array containing the values of the matrix A in ellpack format.
+c jcoef = integer arraycontains the column indices of coef(i,j) in A.
+c ncoef = first dimension of arrays coef, and jcoef.
+c ndiag = number of active columns in coef, jcoef.
+c 
+c ndiag = on entry the number of columns made available in coef.
+c
+c on return: 
+c----------
+c a, ia, 
+c    ja = matrix in a, ia, ja format where. 
+c 
+c nzmax	= size of arrays a and ja. ellcsr will abort if the storage 
+c	   provided in a, ja is not sufficient to store A. See ierr. 
+c
+c ierr 	= integer. serves are output error message. 
+c         ierr = 0 means normal return. 
+c         ierr = 1 means that there is not enough space in
+c         a and ja to store output matrix.
+c----------------------------------------------------------------------- 
+c first determine the length of each row of lower-part-of(A)
+      ierr = 0
+c-----check whether sufficient columns are available. ----------------- 
+c
+c------- copy elements row by row.-------------------------------------- 
+      kpos = 1
+      ia(1) = kpos
+      do 6 i=1, nrow
+         do 5 k=1,ndiag
+            if (coef(i,k) .ne. 0.0d0) then
+               if (kpos .gt. nzmax) then
+                  ierr = kpos
+                  return
+               endif
+               a(kpos) = coef(i,k)
+               ja(kpos) = jcoef(i,k)
+               kpos = kpos+1
+	    endif
+ 5       continue
+         ia(i+1) = kpos
+ 6    continue	
+      return
+c--- end of ellcsr ----------------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c-----------------------------------------------------------------------
+      subroutine csrmsr (n,a,ja,ia,ao,jao,wk,iwk)
+      real*8 a(*),ao(*),wk(n)
+      integer ia(n+1),ja(*),jao(*),iwk(n+1)
+c----------------------------------------------------------------------- 
+c Compressed Sparse Row   to      Modified - Sparse Row 
+c                                 Sparse row with separate main diagonal
+c----------------------------------------------------------------------- 
+c converts a general sparse matrix a, ja, ia into 
+c a compressed matrix using a separated diagonal (referred to as
+c the bell-labs format as it is used by bell labs semi conductor
+c group. We refer to it here as the modified sparse row format.
+c Note: this has been coded in such a way that one can overwrite
+c the output matrix onto the input matrix if desired by a call of
+c the form 
+c
+c     call csrmsr (n, a, ja, ia, a, ja, wk,iwk)
+c
+c In case ao, jao, are different from a, ja, then one can
+c use ao, jao as the work arrays in the calling sequence:
+c
+c     call csrmsr (n, a, ja, ia, ao, jao, ao,jao)
+c
+c----------------------------------------------------------------------- 
+c
+c on entry :
+c---------
+c a, ja, ia = matrix in csr format. note that the 
+c	     algorithm is in place: ao, jao can be the same
+c            as a, ja, in which case it will be overwritten on it
+c            upon return.
+c	 
+c on return :
+c-----------
+c
+c ao, jao  = sparse matrix in modified sparse row storage format:
+c	   +  ao(1:n) contains the diagonal of the matrix. 
+c	   +  ao(n+2:nnz) contains the nondiagonal elements of the
+c             matrix, stored rowwise.
+c	   +  jao(n+2:nnz) : their column indices
+c	   +  jao(1:n+1) contains the pointer array for the nondiagonal
+c             elements in ao(n+1:nnz) and jao(n+2:nnz).
+c             i.e., for i .le. n+1 jao(i) points to beginning of row i 
+c	      in arrays ao, jao.
+c	       here nnz = number of nonzero elements+1 
+c work arrays:
+c------------
+c wk	= real work array of length n
+c iwk   = integer work array of length n+1
+c
+c notes: 
+c------- 
+c        Algorithm is in place.  i.e. both:
+c
+c          call csrmsr (n, a, ja, ia, ao, jao, ao,jao)
+c          (in which  ao, jao, are different from a, ja)
+c           and
+c          call csrmsr (n, a, ja, ia, a, ja, wk,iwk) 
+c          (in which  wk, jwk, are different from a, ja)
+c        are OK.
+c--------
+c coded by Y. Saad Sep. 1989. Rechecked Feb 27, 1990.
+c-----------------------------------------------------------------------
+      icount = 0
+c
+c store away diagonal elements and count nonzero diagonal elements.
+c
+      do 1 i=1,n
+         wk(i) = 0.0d0
+         iwk(i+1) = ia(i+1)-ia(i)
+         do 2 k=ia(i),ia(i+1)-1
+            if (ja(k) .eq. i) then
+               wk(i) = a(k)
+               icount = icount + 1 
+               iwk(i+1) = iwk(i+1)-1
+            endif
+ 2       continue
+ 1    continue
+c     
+c compute total length
+c     
+      iptr = n + ia(n+1) - icount
+c     
+c     copy backwards (to avoid collisions)
+c     
+      do 500 ii=n,1,-1
+         do 100 k=ia(ii+1)-1,ia(ii),-1
+            j = ja(k)
+            if (j .ne. ii) then
+               ao(iptr) = a(k)
+               jao(iptr) = j 
+               iptr = iptr-1
+            endif
+ 100     continue
+ 500  continue
+c
+c compute pointer values and copy wk(*)
+c
+      jao(1) = n+2
+      do 600 i=1,n
+         ao(i) = wk(i) 
+         jao(i+1) = jao(i)+iwk(i+1)
+ 600  continue
+      return	
+c------------ end of subroutine csrmsr ---------------------------------
+c----------------------------------------------------------------------- 
+      end
+c-----------------------------------------------------------------------
+      subroutine msrcsr (n,a,ja,ao,jao,iao,wk,iwk)
+      real*8 a(*),ao(*),wk(n)
+      integer ja(*),jao(*),iao(n+1),iwk(n+1)
+c----------------------------------------------------------------------- 
+c       Modified - Sparse Row  to   Compressed Sparse Row   
+c
+c----------------------------------------------------------------------- 
+c converts a compressed matrix using a separated diagonal 
+c (modified sparse row format) in the Compressed Sparse Row   
+c format.
+c does not check for zero elements in the diagonal.
+c
+c
+c on entry :
+c---------
+c n          = row dimension of matrix
+c a, ja      = sparse matrix in msr sparse storage format
+c              see routine csrmsr for details on data structure 
+c        
+c on return :
+c-----------
+c
+c ao,jao,iao = output matrix in csr format.  
+c
+c work arrays:
+c------------
+c wk       = real work array of length n
+c iwk      = integer work array of length n+1
+c
+c notes:
+c   The original version of this was NOT in place, but has
+c   been modified by adding the vector iwk to be in place.
+c   The original version had ja instead of iwk everywhere in
+c   loop 500.  Modified  Sun 29 May 1994 by R. Bramley (Indiana).
+c   
+c----------------------------------------------------------------------- 
+      logical added
+      do 1 i=1,n
+         wk(i) = a(i)
+         iwk(i) = ja(i)
+ 1    continue
+      iwk(n+1) = ja(n+1)
+      iao(1) = 1
+      iptr = 1
+c---------
+      do 500 ii=1,n 
+         added = .false.
+         idiag = iptr + (iwk(ii+1)-iwk(ii)) 
+         do 100 k=iwk(ii),iwk(ii+1)-1
+            j = ja(k)
+            if (j .lt. ii) then
+               ao(iptr) = a(k)
+               jao(iptr) = j 
+               iptr = iptr+1
+            elseif (added) then
+               ao(iptr) = a(k)
+               jao(iptr) = j 
+               iptr = iptr+1
+            else 
+c add diag element - only reserve a position for it. 
+               idiag = iptr
+               iptr = iptr+1
+               added = .true.
+c     then other element
+               ao(iptr) = a(k)
+               jao(iptr) = j 
+               iptr = iptr+1
+            endif
+ 100     continue
+         ao(idiag) = wk(ii)
+         jao(idiag) = ii
+         if (.not. added) iptr = iptr+1
+         iao(ii+1) = iptr 
+ 500  continue
+      return    
+c------------ end of subroutine msrcsr --------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine csrcsc (n,job,ipos,a,ja,ia,ao,jao,iao)
+      integer ia(n+1),iao(n+1),ja(*),jao(*)
+      real*8  a(*),ao(*)
+c-----------------------------------------------------------------------
+c Compressed Sparse Row     to      Compressed Sparse Column
+c
+c (transposition operation)   Not in place. 
+c----------------------------------------------------------------------- 
+c -- not in place --
+c this subroutine transposes a matrix stored in a, ja, ia format.
+c ---------------
+c on entry:
+c----------
+c n	= dimension of A.
+c job	= integer to indicate whether to fill the values (job.eq.1) of the
+c         matrix ao or only the pattern., i.e.,ia, and ja (job .ne.1)
+c
+c ipos  = starting position in ao, jao of the transposed matrix.
+c         the iao array takes this into account (thus iao(1) is set to ipos.)
+c         Note: this may be useful if one needs to append the data structure
+c         of the transpose to that of A. In this case use for example
+c                call csrcsc (n,1,ia(n+1),a,ja,ia,a,ja,ia(n+2)) 
+c	  for any other normal usage, enter ipos=1.
+c a	= real array of length nnz (nnz=number of nonzero elements in input 
+c         matrix) containing the nonzero elements.
+c ja	= integer array of length nnz containing the column positions
+c 	  of the corresponding elements in a.
+c ia	= integer of size n+1. ia(k) contains the position in a, ja of
+c	  the beginning of the k-th row.
+c
+c on return:
+c ---------- 
+c output arguments:
+c ao	= real array of size nzz containing the "a" part of the transpose
+c jao	= integer array of size nnz containing the column indices.
+c iao	= integer array of size n+1 containing the "ia" index array of
+c	  the transpose. 
+c
+c----------------------------------------------------------------------- 
+      call csrcsc2 (n,n,job,ipos,a,ja,ia,ao,jao,iao)
+      end
+c-----------------------------------------------------------------------
+      subroutine csrcsc2 (n,n2,job,ipos,a,ja,ia,ao,jao,iao)
+      integer ia(n+1),iao(n2+1),ja(*),jao(*)
+      real*8  a(*),ao(*)
+c-----------------------------------------------------------------------
+c Compressed Sparse Row     to      Compressed Sparse Column
+c
+c (transposition operation)   Not in place. 
+c----------------------------------------------------------------------- 
+c Rectangular version.  n is number of rows of CSR matrix,
+c                       n2 (input) is number of columns of CSC matrix.
+c----------------------------------------------------------------------- 
+c -- not in place --
+c this subroutine transposes a matrix stored in a, ja, ia format.
+c ---------------
+c on entry:
+c----------
+c n	= number of rows of CSR matrix.
+c n2    = number of columns of CSC matrix.
+c job	= integer to indicate whether to fill the values (job.eq.1) of the
+c         matrix ao or only the pattern., i.e.,ia, and ja (job .ne.1)
+c
+c ipos  = starting position in ao, jao of the transposed matrix.
+c         the iao array takes this into account (thus iao(1) is set to ipos.)
+c         Note: this may be useful if one needs to append the data structure
+c         of the transpose to that of A. In this case use for example
+c                call csrcsc2 (n,n,1,ia(n+1),a,ja,ia,a,ja,ia(n+2)) 
+c	  for any other normal usage, enter ipos=1.
+c a	= real array of length nnz (nnz=number of nonzero elements in input 
+c         matrix) containing the nonzero elements.
+c ja	= integer array of length nnz containing the column positions
+c 	  of the corresponding elements in a.
+c ia	= integer of size n+1. ia(k) contains the position in a, ja of
+c	  the beginning of the k-th row.
+c
+c on return:
+c ---------- 
+c output arguments:
+c ao	= real array of size nzz containing the "a" part of the transpose
+c jao	= integer array of size nnz containing the column indices.
+c iao	= integer array of size n+1 containing the "ia" index array of
+c	  the transpose. 
+c
+c----------------------------------------------------------------------- 
+c----------------- compute lengths of rows of transp(A) ----------------
+      do 1 i=1,n2+1
+         iao(i) = 0
+ 1    continue
+      do 3 i=1, n
+         do 2 k=ia(i), ia(i+1)-1 
+            j = ja(k)+1
+            iao(j) = iao(j)+1
+ 2       continue 
+ 3    continue
+c---------- compute pointers from lengths ------------------------------
+      iao(1) = ipos 
+      do 4 i=1,n2
+         iao(i+1) = iao(i) + iao(i+1)
+ 4    continue
+c--------------- now do the actual copying ----------------------------- 
+      do 6 i=1,n
+         do 62 k=ia(i),ia(i+1)-1 
+            j = ja(k) 
+            next = iao(j)
+            if (job .eq. 1)  ao(next) = a(k)
+            jao(next) = i
+            iao(j) = next+1
+ 62      continue
+ 6    continue
+c-------------------------- reshift iao and leave ---------------------- 
+      do 7 i=n2,1,-1
+         iao(i+1) = iao(i)
+ 7    continue
+      iao(1) = ipos
+c--------------- end of csrcsc2 ---------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine csrlnk (n,a,ja,ia,link) 
+      real*8 a(*) 
+      integer n, ja(*), ia(n+1), link(*)
+c----------------------------------------------------------------------- 
+c      Compressed Sparse Row         to    Linked storage format. 
+c----------------------------------------------------------------------- 
+c this subroutine translates a matrix stored in compressed sparse
+c row into one with a linked list storage format. Only the link
+c array needs to be obtained since the arrays a, ja, and ia may
+c be unchanged and  carry the same meaning for the output matrix.
+c in  other words a, ja, ia, link   is the output linked list data
+c structure with a, ja, unchanged from input, and ia possibly 
+c altered (in case therea re null rows in matrix). Details on
+c the output array link are given below.
+c----------------------------------------------------------------------- 
+c Coded by Y. Saad, Feb 21, 1991.
+c----------------------------------------------------------------------- 
+c
+c on entry:
+c----------
+c n	= integer equal to the dimension of A.	
+c         
+c a	= real array of size nna containing the nonzero elements
+c ja	= integer array of size	nnz containing the column positions
+c 	  of the corresponding elements in a.
+c ia	= integer of size n+1 containing the pointers to the beginning 
+c         of each row. ia(k) contains the position in a, ja of the 
+c         beginning of the k-th row.
+c
+c on return:
+c---------- 
+c a, ja, are not changed.
+c ia    may be changed if there are null rows.
+c 
+c a     = nonzero elements.
+c ja    = column positions. 
+c ia    = ia(i) points to the first element of row i in linked structure.
+c link	= integer array of size containing the linked list information.
+c         link(k) points to the next element of the row after element 
+c         a(k), ja(k). if link(k) = 0, then there is no next element,
+c         i.e., a(k), jcol(k) is the last element of the current row.
+c
+c  Thus row number i can be accessed as follows:
+c     next = ia(i) 
+c     while(next .ne. 0) do 
+c          value = a(next)      ! value a(i,j) 
+c          jcol  = ja(next)     ! column index j
+c          next  = link(next)   ! address of next element in row
+c     endwhile
+c notes:
+c ------ ia may be altered on return.
+c----------------------------------------------------------------------- 
+c local variables
+      integer i, k
+c
+c loop through all rows
+c
+      do 100 i =1, n
+         istart = ia(i) 
+         iend = ia(i+1)-1
+         if (iend .gt. istart) then
+            do 99  k=istart, iend-1 
+               link(k) = k+1
+ 99         continue
+            link(iend) = 0
+         else
+            ia(i) = 0
+         endif
+ 100  continue
+c     
+      return
+c-------------end-of-csrlnk --------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine lnkcsr (n, a, jcol, istart, link, ao, jao, iao) 
+      real*8 a(*), ao(*) 
+      integer n, jcol(*), istart(n), link(*), jao(*), iao(*) 
+c----------------------------------------------------------------------- 
+c     Linked list storage format   to      Compressed Sparse Row  format
+c----------------------------------------------------------------------- 
+c this subroutine translates a matrix stored in linked list storage 
+c format into the compressed sparse row format. 
+c----------------------------------------------------------------------- 
+c Coded by Y. Saad, Feb 21, 1991.
+c----------------------------------------------------------------------- 
+c
+c on entry:
+c----------
+c n	= integer equal to the dimension of A.	
+c         
+c a	= real array of size nna containing the nonzero elements
+c jcol	= integer array of size	nnz containing the column positions
+c 	  of the corresponding elements in a.
+c istart= integer array of size n poiting to the beginning of the rows.
+c         istart(i) contains the position of the first element of 
+c         row i in data structure. (a, jcol, link).
+c         if a row is empty istart(i) must be zero.
+c link	= integer array of size nnz containing the links in the linked 
+c         list data structure. link(k) points to the next element 
+c         of the row after element ao(k), jcol(k). if link(k) = 0, 
+c         then there is no next element, i.e., ao(k), jcol(k) is 
+c         the last element of the current row.
+c
+c on return:
+c-----------
+c ao, jao, iao = matrix stored in csr format:
+c
+c ao    = real array containing the values of the nonzero elements of 
+c         the matrix stored row-wise. 
+c jao	= integer array of size nnz containing the column indices.
+c iao	= integer array of size n+1 containing the pointers array to the 
+c         beginning of each row. iao(i) is the address in ao,jao of
+c         first element of row i.
+c
+c----------------------------------------------------------------------- 
+c first determine individial bandwidths and pointers.
+c----------------------------------------------------------------------- 
+c local variables
+      integer irow, ipos, next
+c-----------------------------------------------------------------------
+      ipos = 1
+      iao(1) = ipos
+c     
+c     loop through all rows
+c     
+      do 100 irow =1, n
+c     
+c     unroll i-th row.
+c     
+         next = istart(irow)
+ 10      if (next .eq. 0) goto 99
+         jao(ipos) = jcol(next)
+         ao(ipos)  = a(next)
+         ipos = ipos+1
+         next = link(next) 
+         goto 10
+ 99      iao(irow+1) = ipos 
+ 100  continue
+c     
+      return
+c-------------end-of-lnkcsr ------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine csrdia (n,idiag,job,a,ja,ia,ndiag,
+     *                   diag,ioff,ao,jao,iao,ind)
+      real*8 diag(ndiag,idiag), a(*), ao(*)
+      integer ia(*), ind(*), ja(*), jao(*), iao(*), ioff(*)
+c----------------------------------------------------------------------- 
+c Compressed sparse row     to    diagonal format
+c----------------------------------------------------------------------- 
+c this subroutine extracts  idiag diagonals  from the  input matrix a,
+c a, ia, and puts the rest of  the matrix  in the  output matrix ao,
+c jao, iao.  The diagonals to be extracted depend  on the  value of job
+c (see below for details.)  In  the first  case, the  diagonals to be
+c extracted are simply identified by  their offsets  provided in ioff
+c by the caller.  In the second case, the  code internally determines
+c the idiag most significant diagonals, i.e., those  diagonals of the
+c matrix which  have  the  largest  number  of  nonzero elements, and
+c extracts them.
+c----------------------------------------------------------------------- 
+c on entry:
+c---------- 
+c n	= dimension of the matrix a.
+c idiag = integer equal to the number of diagonals to be extracted. 
+c         Note: on return idiag may be modified.
+c a, ja, 			
+c    ia = matrix stored in a, ja, ia, format
+c job	= integer. serves as a job indicator.  Job is better thought 
+c         of as a two-digit number job=xy. If the first (x) digit
+c         is one on entry then the diagonals to be extracted are 
+c         internally determined. In this case csrdia exctracts the
+c         idiag most important diagonals, i.e. those having the largest
+c         number on nonzero elements. If the first digit is zero
+c         then csrdia assumes that ioff(*) contains the offsets 
+c         of the diagonals to be extracted. there is no verification 
+c         that ioff(*) contains valid entries.
+c         The second (y) digit of job determines whether or not
+c         the remainder of the matrix is to be written on ao,jao,iao.
+c         If it is zero  then ao, jao, iao is not filled, i.e., 
+c         the diagonals are found  and put in array diag and the rest is
+c         is discarded. if it is one, ao, jao, iao contains matrix
+c         of the remaining elements.
+c         Thus:
+c         job= 0 means do not select diagonals internally (pick those
+c                defined by ioff) and do not fill ao,jao,iao
+c         job= 1 means do not select diagonals internally 
+c                      and fill ao,jao,iao
+c         job=10 means  select diagonals internally 
+c                      and do not fill ao,jao,iao
+c         job=11 means select diagonals internally 
+c                      and fill ao,jao,iao
+c 
+c ndiag = integer equal to the first dimension of array diag.
+c
+c on return:
+c----------- 
+c
+c idiag = number of diagonals found. This may be smaller than its value 
+c         on entry. 
+c diag  = real array of size (ndiag x idiag) containing the diagonals
+c         of A on return
+c          
+c ioff  = integer array of length idiag, containing the offsets of the
+c   	  diagonals to be extracted.
+c ao, jao
+c  iao  = remainder of the matrix in a, ja, ia format.
+c work arrays:
+c------------ 
+c ind   = integer array of length 2*n-1 used as integer work space.
+c         needed only when job.ge.10 i.e., in case the diagonals are to
+c         be selected internally.
+c
+c Notes:
+c-------
+c    1) The algorithm is in place: ao, jao, iao can be overwritten on 
+c       a, ja, ia if desired 
+c    2) When the code is required to select the diagonals (job .ge. 10) 
+c       the selection of the diagonals is done from left to right 
+c       as a result if several diagonals have the same weight (number 
+c       of nonzero elemnts) the leftmost one is selected first.
+c-----------------------------------------------------------------------
+      job1 = job/10
+      job2 = job-job1*10
+      if (job1 .eq. 0) goto 50
+      n2 = n+n-1
+      call infdia(n,ja,ia,ind,idum)
+c----------- determine diagonals to  accept.---------------------------- 
+c----------------------------------------------------------------------- 
+      ii = 0
+ 4    ii=ii+1
+      jmax = 0
+      do 41 k=1, n2
+         j = ind(k)
+         if (j .le. jmax) goto 41
+         i = k
+         jmax = j
+ 41   continue
+      if (jmax .le. 0) then
+         ii = ii-1
+         goto 42
+      endif
+      ioff(ii) = i-n
+      ind(i) = - jmax
+      if (ii .lt.  idiag) goto 4
+ 42   idiag = ii
+c---------------- initialize diago to zero ----------------------------- 
+ 50   continue
+      do 55 j=1,idiag
+         do 54 i=1,n
+            diag(i,j) = 0.0d0
+ 54      continue
+ 55   continue
+c----------------------------------------------------------------------- 
+      ko = 1
+c----------------------------------------------------------------------- 
+c extract diagonals and accumulate remaining matrix.
+c----------------------------------------------------------------------- 
+      do 6 i=1, n
+         do 51 k=ia(i),ia(i+1)-1 
+            j = ja(k)
+            do 52 l=1,idiag
+               if (j-i .ne. ioff(l)) goto 52
+               diag(i,l) = a(k)
+               goto 51
+ 52         continue
+c--------------- append element not in any diagonal to ao,jao,iao ----- 
+            if (job2 .eq. 0) goto 51
+            ao(ko) = a(k)
+            jao(ko) = j
+            ko = ko+1
+ 51      continue
+         if (job2 .ne. 0 ) ind(i+1) = ko
+ 6    continue
+      if (job2 .eq. 0) return
+c     finish with iao
+      iao(1) = 1
+      do 7 i=2,n+1
+         iao(i) = ind(i)
+ 7    continue
+      return
+c----------- end of csrdia ---------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine diacsr (n,job,idiag,diag,ndiag,ioff,a,ja,ia)
+      real*8 diag(ndiag,idiag), a(*), t
+      integer ia(*), ja(*), ioff(*)
+c----------------------------------------------------------------------- 
+c    diagonal format     to     compressed sparse row     
+c----------------------------------------------------------------------- 
+c this subroutine extract the idiag most important diagonals from the 
+c input matrix a, ja, ia, i.e, those diagonals of the matrix which have
+c the largest number of nonzero elements. If requested (see job),
+c the rest of the matrix is put in a the output matrix ao, jao, iao
+c----------------------------------------------------------------------- 
+c on entry:
+c---------- 
+c n	= integer. dimension of the matrix a.
+c job	= integer. job indicator with the following meaning.
+c         if (job .eq. 0) then check for each entry in diag
+c         whether this entry is zero. If it is then do not include
+c         in the output matrix. Note that the test is a test for
+c         an exact arithmetic zero. Be sure that the zeros are
+c         actual zeros in double precision otherwise this would not
+c         work.
+c         
+c idiag = integer equal to the number of diagonals to be extracted. 
+c         Note: on return idiag may be modified.
+c
+c diag  = real array of size (ndiag x idiag) containing the diagonals
+c         of A on return. 
+c 
+c ndiag = integer equal to the first dimension of array diag.
+c
+c ioff  = integer array of length idiag, containing the offsets of the
+c   	  diagonals to be extracted.
+c
+c on return:
+c----------- 
+c a, 
+c ja, 			
+c ia    = matrix stored in a, ja, ia, format
+c
+c Note:
+c ----- the arrays a and ja should be of length n*idiag.
+c
+c----------------------------------------------------------------------- 
+      ia(1) = 1
+      ko = 1
+      do 80 i=1, n
+         do 70 jj = 1, idiag
+            j = i+ioff(jj) 
+            if (j .lt. 1 .or. j .gt. n) goto 70
+            t = diag(i,jj) 
+            if (job .eq. 0 .and. t .eq. 0.0d0) goto 70
+            a(ko) = t
+            ja(ko) = j
+            ko = ko+1
+ 70      continue
+         ia(i+1) = ko
+ 80   continue
+      return
+c----------- end of diacsr ---------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine bsrcsr (job, n, m, na, a, ja, ia, ao, jao, iao)
+      implicit none
+      integer job, n, m, na, ia(*), ja(*), jao(*), iao(n+1)
+      real*8 a(na,*), ao(*)
+c-----------------------------------------------------------------------
+c             Block Sparse Row  to Compressed Sparse Row.
+c----------------------------------------------------------------------- 
+c NOTE: ** meanings of parameters may have changed wrt earlier versions
+c FORMAT DEFINITION HAS CHANGED WRT TO EARLIER VERSIONS... 
+c-----------------------------------------------------------------------
+c
+c converts a  matrix stored in block-reduced   a, ja, ia  format to the
+c general  sparse row a,  ja, ia  format.  A matrix   that has  a block
+c structure is a matrix whose entries are blocks  of the same size m
+c (e.g.  3 x 3).   Then it is often preferred  to work with the reduced
+c graph of the matrix. Instead of storing one element at a time one can
+c store a whole block at a time.  In this storage scheme  an entry is a
+c square array holding the m**2 elements of a block.
+c 
+c-----------------------------------------------------------------------
+c on entry:
+c----------
+c job   = if job.eq.0 on entry, values are not copied (pattern only)
+c
+c n	= the block row dimension of the matrix.
+c
+c m     = the dimension of each block. Thus, the actual row dimension 
+c         of A is n x m.  
+c
+c na	= first dimension of array a as declared in calling program.
+c         This should be .ge. m**2.
+c
+c a	= real array containing the real entries of the matrix. Recall
+c         that each entry is in fact an m x m block. These entries 
+c         are stored column-wise in locations a(1:m*m,k) for each k-th
+c         entry. See details below.
+c 
+c ja	= integer array of length n. ja(k) contains the column index 
+c         of the leading element, i.e., the element (1,1) of the block
+c         that is held in the column a(*,k) of the value array. 
+c
+c ia    = integer array of length n+1. ia(i) points to the beginning
+c         of block row number i in the arrays a and ja. 
+c 
+c on return:
+c-----------
+c ao, jao, 
+c iao   = matrix stored in compressed sparse row format. The number of
+c         rows in the new matrix is n x m. 
+c 
+c Notes: THIS CODE IS NOT IN PLACE.
+c 
+c-----------------------------------------------------------------------
+c BSR FORMAT.
+c---------- 
+c Each row of A contains the m x m block matrix unpacked column-
+c wise (this allows the user to declare the array a as a(m,m,*) on entry 
+c if desired). The block rows are stored in sequence just as for the
+c compressed sparse row format. 
+c
+c-----------------------------------------------------------------------
+c     example  with m = 2:
+c                                                       1  2 3   
+c    +-------|--------|--------+                       +-------+
+c    | 1   2 |  0   0 |  3   4 |     Block             | x 0 x | 1
+c    | 5   6 |  0   0 |  7   8 |     Representation:   | 0 x x | 2 
+c    +-------+--------+--------+                       | x 0 0 | 3 
+c    | 0   0 |  9  10 | 11  12 |                       +-------+ 
+c    | 0   0 | 13  14 | 15  16 |  
+c    +-------+--------+--------+   
+c    | 17 18 |  0   0 |  0   0 |
+c    | 22 23 |  0   0 |  0   0 |
+c    +-------+--------+--------+
+c
+c    For this matrix:     n    = 3
+c                         m    = 2
+c                         nnz  = 5 
+c-----------------------------------------------------------------------
+c Data structure in Block Sparse Row format:      
+c-------------------------------------------
+c Array A:
+c------------------------- 
+c     1   3   9   11   17   <<--each m x m block is stored column-wise 
+c     5   7   13  15   22       in a  column of the array A.
+c     2   4   10  12   18      
+c     6   8   14  16   23
+c------------------------- 
+c JA  1   3   2    3    1   <<-- column indices for each block. Note that
+c-------------------------       these indices are wrt block matrix.
+c IA  1   3   5    6        <<-- pointers to beginning of each block row 
+c-------------------------       in arrays A and JA. 
+c-----------------------------------------------------------------------
+c locals 
+c 
+      integer i, i1, i2, ij, ii, irow, j, jstart, k, krow, no
+      logical val
+c     
+      val = (job.ne.0)
+      no = n * m 
+      irow = 1	
+      krow = 1
+      iao(irow) = 1      
+c-----------------------------------------------------------------------
+      do 2 ii=1, n
+c
+c     recall: n is the block-row dimension
+c
+         i1 = ia(ii)
+         i2 = ia(ii+1)-1
+c
+c     create m rows for each block row -- i.e., each k. 
+c     
+         do 23 i=1,m
+            do 21 k=i1, i2
+               jstart = m*(ja(k)-1)
+               do 22  j=1,m
+                  ij = (j-1)*m + i
+                  if (val) ao(krow) = a(ij,k) 
+                  jao(krow) = jstart+j
+                  krow = krow+1
+ 22            continue	    
+ 21         continue
+            irow = irow+1 
+            iao(irow) = krow
+ 23      continue
+ 2    continue
+      return
+c-------------end-of-bsrcsr -------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine csrbsr (job,nrow,m,na,a,ja,ia,ao,jao,iao,iw,ierr)
+      implicit none
+      integer job,ierr,nrow,m,na,ia(nrow+1),ja(*),jao(na),iao(*),iw(*)
+      real*8 a(*),ao(na,*)
+c-----------------------------------------------------------------------
+c     Compressed Sparse Row  to    Block Sparse Row
+c-----------------------------------------------------------------------
+c
+c This  subroutine converts a matrix stored  in a general compressed a,
+c ja, ia format into a a block  sparse row format a(m,m,*),ja(*),ia(*).
+c See routine  bsrcsr  for more  details on  data   structure for block
+c matrices. 
+c
+c NOTES: 1) the initial matrix does not have to have a block structure. 
+c zero padding is done for general sparse matrices. 
+c        2) For most practical purposes, na should be the same as m*m.
+c 
+c-----------------------------------------------------------------------
+c 
+c In what follows nr=1+(nrow-1)/m = block-row dimension of output matrix 
+c 
+c on entry:
+c----------
+c 
+c job   =  job indicator.
+c          job =  0 -> only the pattern of output matrix is generated 
+c          job >  0 -> both pattern and values are generated. 
+c          job = -1 -> iao(1) will return the number of nonzero blocks,
+c            in the output matrix. In this case jao(1:nr) is used as 
+c            workspace, ao is untouched, iao is untouched except iao(1)
+c
+c nrow	= integer, the actual row dimension of the matrix.
+c 
+c m     = integer equal to the dimension of each block. m should be > 0. 
+c 
+c na	= first dimension of array ao as declared in calling program.
+c         na should be .ge. m*m. 
+c
+c a, ja, 
+c    ia = input matrix stored in compressed sparse row format.
+c
+c on return:
+c-----------
+c 
+c ao    = real  array containing the  values of the matrix. For details
+c         on the format  see below. Each  row of  a contains the  m x m
+c         block matrix  unpacked column-wise (this  allows the  user to
+c         declare the  array a as ao(m,m,*) on  entry if desired).  The
+c         block rows are stored in sequence  just as for the compressed
+c         sparse row format. The block  dimension  of the output matrix
+c         is  nr = 1 + (nrow-1) / m.
+c         
+c jao   = integer array. containing the block-column indices of the 
+c         block-matrix. Each jao(k) is an integer between 1 and nr
+c         containing the block column index of the block ao(*,k).  
+c
+c iao   = integer array of length nr+1. iao(i) points to the beginning
+c         of block row number i in the arrays ao and jao. When job=-1
+c         iao(1) contains the number of nonzero blocks of the output
+c         matrix and the rest of iao is unused. This is useful for
+c         determining the lengths of ao and jao. 
+c
+c ierr  = integer, error code. 
+c              0 -- normal termination
+c              1 -- m is equal to zero 
+c              2 -- NA too small to hold the blocks (should be .ge. m**2)
+c
+c Work arrays:
+c------------- 
+c iw    = integer work array of dimension  nr = 1 + (nrow-1) / m
+c
+c NOTES: 
+c-------
+c     1) this code is not in place.
+c     2) see routine bsrcsr for details on data sctructure for block 
+c        sparse row format.
+c     
+c-----------------------------------------------------------------------
+c     nr is the block-dimension of the output matrix.
+c     
+      integer nr, m2, io, ko, ii, len, k, jpos, j, i, ij, jr, irow   
+      logical vals  
+c----- 
+      ierr = 0 
+      if (m*m .gt. na) ierr = 2 
+      if (m .eq. 0) ierr = 1 
+      if (ierr .ne. 0) return
+c----------------------------------------------------------------------- 
+      vals = (job .gt. 0) 
+      nr = 1 + (nrow-1) / m
+      m2 = m*m 
+      ko = 1 
+      io = 1 
+      iao(io) = 1 
+      len = 0 
+c     
+c     iw determines structure of block-row (nonzero indicator) 
+c 
+         do j=1, nr
+            iw(j) = 0
+         enddo
+c     
+c     big loop -- leap by m rows each time.
+c     
+      do ii=1, nrow, m
+         irow = 0
+c
+c     go through next m rows -- make sure not to go beyond nrow. 
+c
+         do while (ii+irow .le. nrow .and. irow .le. m-1) 
+            do k=ia(ii+irow),ia(ii+irow+1)-1
+c     
+c     block column index = (scalar column index -1) / m + 1 
+c
+               j = ja(k)-1 
+               jr = j/m + 1                
+               j = j - (jr-1)*m 
+               jpos = iw(jr) 
+               if (jpos .eq. 0) then
+c
+c     create a new block
+c     
+                  iw(jr) = ko 
+                  jao(ko) = jr 
+                  if (vals) then
+c     
+c     initialize new block to zero -- then copy nonzero element
+c     
+                     do i=1, m2
+                        ao(i,ko) = 0.0d0
+                     enddo
+                     ij = j*m + irow + 1 
+                     ao(ij,ko) = a(k) 
+                  endif
+                  ko = ko+1
+               else
+c
+c     copy column index and nonzero element 
+c     
+                  jao(jpos) = jr 
+                  ij = j*m + irow + 1 
+                  if (vals) ao(ij,jpos) = a(k) 
+               endif 
+            enddo  
+            irow = irow+1
+         enddo
+c     
+c     refresh iw
+c                      
+         do j = iao(io),ko-1 
+            iw(jao(j)) = 0
+         enddo
+         if (job .eq. -1) then
+            len = len + ko-1
+            ko = 1
+         else
+            io = io+1 
+            iao(io) = ko
+         endif
+      enddo
+      if (job .eq. -1) iao(1) = len
+c
+      return
+c--------------end-of-csrbsr-------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c-----------------------------------------------------------------------
+      subroutine csrbnd (n,a,ja,ia,job,abd,nabd,lowd,ml,mu,ierr)
+      real*8 a(*),abd(nabd,n)
+      integer ia(n+1),ja(*)
+c----------------------------------------------------------------------- 
+c   Compressed Sparse Row  to  Banded (Linpack ) format.
+c----------------------------------------------------------------------- 
+c this subroutine converts a general sparse matrix stored in
+c compressed sparse row format into the banded format. for the
+c banded format,the Linpack conventions are assumed (see below).
+c----------------------------------------------------------------------- 
+c on entry:
+c----------
+c n	= integer,the actual row dimension of the matrix.
+c
+c a,
+c ja,
+c ia    = input matrix stored in compressed sparse row format.
+c
+c job	= integer. if job=1 then the values of the lower bandwith ml 
+c         and the upper bandwidth mu are determined internally. 
+c         otherwise it is assumed that the values of ml and mu 
+c         are the correct bandwidths on input. See ml and mu below.
+c
+c nabd  = integer. first dimension of array abd.
+c
+c lowd  = integer. this should be set to the row number in abd where
+c         the lowest diagonal (leftmost) of A is located. 
+c         lowd should be  ( 1  .le.  lowd  .le. nabd).
+c         if it is not known in advance what lowd should be
+c         enter lowd = 0 and the default value lowd = ml+mu+1
+c         will be chosen. Alternative: call routine getbwd from unary
+c         first to detrermione ml and mu then define lowd accordingly.
+c         (Note: the banded solvers in linpack use lowd=2*ml+mu+1. )
+c
+c ml	= integer. equal to the bandwidth of the strict lower part of A
+c mu	= integer. equal to the bandwidth of the strict upper part of A
+c         thus the total bandwidth of A is ml+mu+1.
+c         if ml+mu+1 is found to be larger than lowd then an error 
+c         flag is raised (unless lowd = 0). see ierr.
+c
+c note:   ml and mu are assumed to have	 the correct bandwidth values
+c         as defined above if job is set to zero on entry.
+c
+c on return:
+c-----------
+c
+c abd   = real array of dimension abd(nabd,n).
+c         on return contains the values of the matrix stored in
+c         banded form. The j-th column of abd contains the elements
+c         of the j-th column of  the original matrix comprised in the
+c         band ( i in (j-ml,j+mu) ) with the lowest diagonal at
+c         the bottom row (row lowd). See details below for this format.
+c
+c ml	= integer. equal to the bandwidth of the strict lower part of A
+c mu	= integer. equal to the bandwidth of the strict upper part of A
+c         if job=1 on entry then these two values are internally computed.
+c
+c lowd  = integer. row number in abd where the lowest diagonal 
+c         (leftmost) of A is located on return. In case lowd = 0
+c         on return, then it is defined to ml+mu+1 on return and the
+c         lowd will contain this value on return. `
+c
+c ierr  = integer. used for error messages. On return:
+c         ierr .eq. 0  :means normal return
+c         ierr .eq. -1 : means invalid value for lowd. (either .lt. 0
+c         or larger than nabd).
+c         ierr .eq. -2 : means that lowd is not large enough and as 
+c         result the matrix cannot be stored in array abd. 
+c         lowd should be at least ml+mu+1, where ml and mu are as
+c         provided on output.
+c
+c----------------------------------------------------------------------* 
+c Additional details on banded format.  (this closely follows the      *
+c format used in linpack. may be useful for converting a matrix into   *
+c this storage format in order to use the linpack  banded solvers).    * 
+c----------------------------------------------------------------------*
+c             ---  band storage format  for matrix abd ---             * 
+c uses ml+mu+1 rows of abd(nabd,*) to store the diagonals of           *
+c a in rows of abd starting from the lowest (sub)-diagonal  which  is  *
+c stored in row number lowd of abd. the minimum number of rows needed  *
+c in abd is ml+mu+1, i.e., the minimum value for lowd is ml+mu+1. the  *
+c j-th  column  of  abd contains the elements of the j-th column of a, *
+c from bottom to top: the element a(j+ml,j) is stored in  position     *
+c abd(lowd,j), then a(j+ml-1,j) in position abd(lowd-1,j) and so on.   *
+c Generally, the element a(j+k,j) of original matrix a is stored in    *
+c position abd(lowd+k-ml,j), for k=ml,ml-1,..,0,-1, -mu.               *
+c The first dimension nabd of abd must be .ge. lowd                    *
+c                                                                      *
+c     example [from linpack ]:   if the original matrix is             *
+c                                                                      *
+c              11 12 13  0  0  0                                       *
+c              21 22 23 24  0  0                                       *
+c               0 32 33 34 35  0     original banded matrix            *
+c               0  0 43 44 45 46                                       *
+c               0  0  0 54 55 56                                       *
+c               0  0  0  0 65 66                                       *
+c                                                                      *
+c then  n = 6, ml = 1, mu = 2. lowd should be .ge. 4 (=ml+mu+1)  and   *
+c if lowd = 5 for example, abd  should be:                             *
+c                                                                      *
+c untouched --> x  x  x  x  x  x                                       *
+c               *  * 13 24 35 46                                       *
+c               * 12 23 34 45 56    resulting abd matrix in banded     *
+c              11 22 33 44 55 66    format                             *
+c  row lowd--> 21 32 43 54 65  *                                       *
+c                                                                      *
+c * = not used                                                         *
+c                                                                      
+*
+c----------------------------------------------------------------------*
+c first determine ml and mu.
+c----------------------------------------------------------------------- 
+      ierr = 0
+c-----------
+      if (job .eq. 1) call getbwd(n,a,ja,ia,ml,mu)
+      m = ml+mu+1
+      if (lowd .eq. 0) lowd = m
+      if (m .gt. lowd)  ierr = -2
+      if (lowd .gt. nabd .or. lowd .lt. 0) ierr = -1
+      if (ierr .lt. 0) return
+c------------
+      do 15  i=1,m
+         ii = lowd -i+1
+         do 10 j=1,n
+	    abd(ii,j) = 0.0d0
+ 10      continue
+ 15   continue
+c---------------------------------------------------------------------	   
+      mdiag = lowd-ml
+      do 30 i=1,n
+         do 20 k=ia(i),ia(i+1)-1
+            j = ja(k)
+            abd(i-j+mdiag,j) = a(k) 
+ 20      continue
+ 30   continue
+      return
+c------------- end of csrbnd ------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c-----------------------------------------------------------------------
+      subroutine bndcsr (n,abd,nabd,lowd,ml,mu,a,ja,ia,len,ierr)
+      real*8 a(*),abd(nabd,*), t
+      integer ia(n+1),ja(*)
+c----------------------------------------------------------------------- 
+c Banded (Linpack ) format   to    Compressed Sparse Row  format.
+c----------------------------------------------------------------------- 
+c on entry:
+c----------
+c n	= integer,the actual row dimension of the matrix.
+c
+c nabd  = first dimension of array abd.
+c
+c abd   = real array containing the values of the matrix stored in
+c         banded form. The j-th column of abd contains the elements
+c         of the j-th column of  the original matrix,comprised in the
+c         band ( i in (j-ml,j+mu) ) with the lowest diagonal located
+c         in row lowd (see below). 
+c    
+c lowd  = integer. this should be set to the row number in abd where
+c         the lowest diagonal (leftmost) of A is located. 
+c         lowd should be s.t.  ( 1  .le.  lowd  .le. nabd).
+c         The subroutines dgbco, ... of linpack use lowd=2*ml+mu+1.
+c
+c ml	= integer. equal to the bandwidth of the strict lower part of A
+c mu	= integer. equal to the bandwidth of the strict upper part of A
+c         thus the total bandwidth of A is ml+mu+1.
+c         if ml+mu+1 is found to be larger than nabd then an error 
+c         message is set. see ierr.
+c
+c len   = integer. length of arrays a and ja. bndcsr will stop if the
+c         length of the arrays a and ja is insufficient to store the 
+c         matrix. see ierr.
+c
+c on return:
+c-----------
+c a,
+c ja,
+c ia    = input matrix stored in compressed sparse row format.
+c
+c lowd  = if on entry lowd was zero then lowd is reset to the default
+c         value ml+mu+l. 
+c
+c ierr  = integer. used for error message output. 
+c         ierr .eq. 0 :means normal return
+c         ierr .eq. -1 : means invalid value for lowd. 
+c	  ierr .gt. 0 : means that there was not enough storage in a and ja
+c         for storing the ourput matrix. The process ran out of space 
+c         (as indicated by len) while trying to fill row number ierr. 
+c         This should give an idea of much more storage might be required. 
+c         Moreover, the first irow-1 rows are correctly filled. 
+c
+c notes:  the values in abd found to be equal to zero
+c -----   (actual test: if (abd(...) .eq. 0.0d0) are removed.
+c         The resulting may not be identical to a csr matrix
+c         originally transformed to a bnd format.
+c          
+c----------------------------------------------------------------------- 
+      ierr = 0
+c-----------
+      if (lowd .gt. nabd .or. lowd .le. 0) then 
+         ierr = -1
+         return
+      endif
+c-----------
+      ko = 1
+      ia(1) = 1
+      do 30 irow=1,n
+c-----------------------------------------------------------------------
+         i = lowd 
+          do  20 j=irow-ml,irow+mu
+             if (j .le. 0 ) goto 19
+             if (j .gt. n) goto 21
+             t = abd(i,j) 
+             if (t .eq. 0.0d0) goto 19
+             if (ko .gt. len) then 
+               ierr = irow 
+               return
+            endif
+            a(ko) = t
+            ja(ko) = j
+            ko = ko+1
+ 19         i = i-1
+ 20      continue
+c     end for row irow
+ 21      ia(irow+1) = ko
+ 30   continue
+      return
+c------------- end of bndcsr ------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c----------------------------------------------------------------------- 
+      subroutine csrssk (n,imod,a,ja,ia,asky,isky,nzmax,ierr)
+      real*8 a(*),asky(nzmax) 
+      integer n, imod, nzmax, ierr, ia(n+1), isky(n+1), ja(*)
+c----------------------------------------------------------------------- 
+c      Compressed Sparse Row         to     Symmetric Skyline Format 
+c  or  Symmetric Sparse Row        
+c----------------------------------------------------------------------- 
+c this subroutine translates a compressed sparse row or a symmetric
+c sparse row format into a symmetric skyline format.
+c the input matrix can be in either compressed sparse row or the 
+c symmetric sparse row format. The output matrix is in a symmetric
+c skyline format: a real array containing the (active portions) of the
+c rows in  sequence and a pointer to the beginning of each row.
+c
+c This module is NOT  in place.
+c----------------------------------------------------------------------- 
+c Coded by Y. Saad, Oct 5, 1989. Revised Feb. 18, 1991.
+c----------------------------------------------------------------------- 
+c
+c on entry:
+c----------
+c n	= integer equal to the dimension of A.	
+c imod  = integer indicating the variant of skyline format wanted:
+c         imod = 0 means the pointer isky points to the `zeroth' 
+c         element of the row, i.e., to the position of the diagonal
+c         element of previous row (for i=1, isky(1)= 0)
+c         imod = 1 means that itpr points to the beginning of the row. 
+c         imod = 2 means that isky points to the end of the row (diagonal
+c                  element) 
+c         
+c a	= real array of size nna containing the nonzero elements
+c ja	= integer array of size	nnz containing the column positions
+c 	  of the corresponding elements in a.
+c ia	= integer of size n+1. ia(k) contains the position in a, ja of
+c	  the beginning of the k-th row.
+c nzmax = integer. must be set to the number of available locations
+c         in the output array asky. 
+c
+c on return:
+c---------- 
+c
+c asky    = real array containing the values of the matrix stored in skyline
+c         format. asky contains the sequence of active rows from 
+c         i=1, to n, an active row being the row of elemnts of 
+c         the matrix contained between the leftmost nonzero element 
+c         and the diagonal element. 
+c isky	= integer array of size n+1 containing the pointer array to 
+c         each row. The meaning of isky depends on the input value of
+c         imod (see above). 
+c ierr  =  integer.  Error message. If the length of the 
+c         output array asky exceeds nzmax. ierr returns the minimum value
+c         needed for nzmax. otherwise ierr=0 (normal return).
+c 
+c Notes:
+c         1) This module is NOT  in place.
+c         2) even when imod = 2, length of  isky is  n+1, not n.
+c
+c----------------------------------------------------------------------- 
+c first determine individial bandwidths and pointers.
+c----------------------------------------------------------------------- 
+      ierr = 0
+      isky(1) = 0
+      do 3 i=1,n
+         ml = 0
+         do 31 k=ia(i),ia(i+1)-1 
+            ml = max(ml,i-ja(k)+1) 
+ 31      continue
+         isky(i+1) = isky(i)+ml
+ 3    continue
+c
+c     test if there is enough space  asky to do the copying.  
+c
+      nnz = isky(n+1) 
+      if (nnz .gt. nzmax) then
+         ierr = nnz
+         return
+      endif
+c    
+c   fill asky with zeros.
+c     
+      do 1 k=1, nnz 
+         asky(k) = 0.0d0
+ 1    continue
+c     
+c     copy nonzero elements.
+c     
+      do 4 i=1,n
+         kend = isky(i+1) 
+         do 41 k=ia(i),ia(i+1)-1 
+            j = ja(k)
+            if (j .le. i) asky(kend+j-i) = a(k)
+ 41      continue
+ 4    continue
+c 
+c modify pointer according to imod if necessary.
+c
+      if (imod .eq. 0) return
+      if (imod .eq. 1) then 
+         do 50 k=1, n+1
+            isky(k) = isky(k)+1
+ 50      continue
+      endif
+      if (imod .eq. 2) then
+         do 60 k=1, n
+            isky(k) = isky(k+1) 
+ 60      continue
+      endif
+c
+      return
+c------------- end of csrssk ------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c-----------------------------------------------------------------------
+      subroutine sskssr (n,imod,asky,isky,ao,jao,iao,nzmax,ierr)
+      real*8 asky(*),ao(nzmax) 
+      integer n, imod,nzmax,ierr, isky(n+1),iao(n+1),jao(nzmax) 
+c----------------------------------------------------------------------- 
+c     Symmetric Skyline Format  to  Symmetric Sparse Row format.
+c----------------------------------------------------------------------- 
+c  tests for exact zeros in skyline matrix (and ignores them in
+c  output matrix).  In place routine (a, isky :: ao, iao)
+c----------------------------------------------------------------------- 
+c this subroutine translates a  symmetric skyline format into a 
+c symmetric sparse row format. Each element is tested to see if it is
+c a zero element. Only the actual nonzero elements are retained. Note 
+c that the test used is simple and does take into account the smallness 
+c of a value. the subroutine filter (see unary module) can be used
+c for this purpose. 
+c----------------------------------------------------------------------- 
+c Coded by Y. Saad, Oct 5, 1989. Revised Feb 18, 1991./
+c----------------------------------------------------------------------- 
+c
+c on entry:
+c----------
+c n	= integer equal to the dimension of A.	
+c imod  = integer indicating the variant of skyline format used:
+c         imod = 0 means the pointer iao points to the `zeroth' 
+c         element of the row, i.e., to the position of the diagonal
+c         element of previous row (for i=1, iao(1)= 0)
+c         imod = 1 means that itpr points to the beginning of the row. 
+c         imod = 2 means that iao points to the end of the row 
+c                  (diagonal element) 
+c asky  = real array containing the values of the matrix. asky contains 
+c         the sequence of active rows from i=1, to n, an active row 
+c         being the row of elemnts of the matrix contained between the 
+c         leftmost nonzero element and the diagonal element. 
+c isky 	= integer array of size n+1 containing the pointer array to 
+c         each row. isky (k) contains the address of the beginning of the
+c         k-th active row in the array asky. 
+c nzmax = integer. equal to the number of available locations in the 
+c         output array ao.  
+c
+c on return:
+c ---------- 
+c ao	= real array of size nna containing the nonzero elements
+c jao	= integer array of size	nnz containing the column positions
+c 	  of the corresponding elements in a.
+c iao	= integer of size n+1. iao(k) contains the position in a, ja of
+c	  the beginning of the k-th row.
+c ierr  = integer. Serving as error message. If the length of the 
+c         output arrays ao, jao exceeds nzmax then ierr returns 
+c         the row number where the algorithm stopped: rows
+c         i, to ierr-1 have been processed succesfully.
+c         ierr = 0 means normal return.
+c         ierr = -1  : illegal value for imod
+c Notes:
+c------- 
+c This module is in place: ao and iao can be the same as asky, and isky.
+c-----------------------------------------------------------------------
+c local variables
+      integer next, kend, kstart, i, j 
+      ierr = 0
+c
+c check for validity of imod
+c 
+      if (imod.ne.0 .and. imod.ne.1 .and. imod .ne. 2) then
+         ierr =-1
+         return
+      endif 
+c
+c next  = pointer to next available position in output matrix
+c kend  = pointer to end of current row in skyline matrix. 
+c
+      next = 1
+c
+c set kend = start position -1 in  skyline matrix.
+c 
+      kend = 0 
+      if (imod .eq. 1) kend = isky(1)-1
+      if (imod .eq. 0) kend = isky(1) 
+c
+c loop through all rows
+c     
+      do 50 i=1,n
+c
+c save value of pointer to ith row in output matrix
+c
+         iao(i) = next
+c
+c get beginnning and end of skyline  row 
+c
+         kstart = kend+1
+         if (imod .eq. 0) kend = isky(i+1)
+         if (imod .eq. 1) kend = isky(i+1)-1
+         if (imod .eq. 2) kend = isky(i) 
+c 
+c copy element into output matrix unless it is a zero element.
+c 
+         do 40 k=kstart,kend
+            if (asky(k) .eq. 0.0d0) goto 40
+            j = i-(kend-k) 
+            jao(next) = j
+            ao(next)  = asky(k)
+            next=next+1
+            if (next .gt. nzmax+1) then
+               ierr = i
+               return
+            endif 
+ 40      continue
+ 50    continue
+      iao(n+1) = next
+      return
+c-------------end-of-sskssr -------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine csrjad (nrow, a, ja, ia, idiag, iperm, ao, jao, iao) 
+      integer ja(*), jao(*), ia(nrow+1), iperm(nrow), iao(nrow) 
+      real*8 a(*), ao(*)
+c-----------------------------------------------------------------------
+c    Compressed Sparse Row  to   JAgged Diagonal storage. 
+c----------------------------------------------------------------------- 
+c this subroutine converts  matrix stored in the compressed sparse
+c row format to the jagged diagonal format. The data structure
+c for the JAD (Jagged Diagonal storage) is as follows. The rows of 
+c the matrix are (implicitly) permuted so that their lengths are in
+c decreasing order. The real entries ao(*) and their column indices 
+c jao(*) are stored in succession. The number of such diagonals is idiag.
+c the lengths of each of these diagonals is stored in iao(*).
+c For more details see [E. Anderson and Y. Saad,
+c ``Solving sparse triangular systems on parallel computers'' in
+c Inter. J. of High Speed Computing, Vol 1, pp. 73-96 (1989).]
+c or  [Y. Saad, ``Krylov Subspace Methods on Supercomputers''
+c SIAM J. on  Stat. Scient. Comput., volume 10, pp. 1200-1232 (1989).]
+c----------------------------------------------------------------------- 
+c on entry:
+c---------- 
+c nrow 	  = row dimension of the matrix A.
+c
+c a, 
+c ia, 
+c ja      = input matrix in compressed sparse row format. 
+c
+c on return: 
+c----------
+c 
+c idiag = integer. The number of jagged diagonals in the matrix.
+c
+c iperm = integer array of length nrow containing the permutation
+c         of the rows that leads to a decreasing order of the
+c         number of nonzero elements.
+c
+c ao    = real array containing the values of the matrix A in 
+c         jagged diagonal storage. The j-diagonals are stored
+c         in ao in sequence. 
+c
+c jao   = integer array containing the column indices of the 
+c         entries in ao.
+c
+c iao   = integer array containing pointers to the beginning 
+c         of each j-diagonal in ao, jao. iao is also used as 
+c         a work array and it should be of length n at least.
+c
+c----------------------------------------------------------------------- 
+c     ---- define initial iperm and get lengths of each row
+c     ---- jao is used a work vector to store tehse lengths
+c     
+      idiag = 0
+      ilo = nrow 
+      do 10 j=1, nrow
+         iperm(j) = j 
+         len = ia(j+1) - ia(j)
+         ilo = min(ilo,len) 
+         idiag = max(idiag,len) 
+         jao(j) = len
+ 10   continue 
+c     
+c     call sorter to get permutation. use iao as work array.
+c    
+      call dcsort (jao, nrow, iao, iperm, ilo, idiag) 
+c     
+c     define output data structure. first lengths of j-diagonals
+c     
+      do 20 j=1, nrow
+         iao(j) = 0
+ 20   continue
+      do 40 k=1, nrow
+         len = jao(iperm(k)) 
+         do 30 i=1,len
+            iao(i) = iao(i)+1
+ 30      continue
+ 40   continue
+c     
+c     get the output matrix itself
+c     
+      k1 = 1
+      k0 = k1
+      do 60 jj=1, idiag
+         len = iao(jj)
+         do 50 k=1,len
+            i = ia(iperm(k))+jj-1
+            ao(k1) = a(i)
+            jao(k1) = ja(i) 
+            k1 = k1+1
+ 50      continue
+         iao(jj) = k0
+         k0 = k1
+ 60   continue
+      iao(idiag+1) = k1
+      return
+c----------end-of-csrjad------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine jadcsr (nrow, idiag, a, ja, ia, iperm, ao, jao, iao) 
+      integer ja(*), jao(*), ia(idiag+1), iperm(nrow), iao(nrow+1) 
+      real*8 a(*), ao(*)
+c-----------------------------------------------------------------------
+c     Jagged Diagonal Storage   to     Compressed Sparse Row  
+c----------------------------------------------------------------------- 
+c this subroutine converts a matrix stored in the jagged diagonal format
+c to the compressed sparse row format.
+c----------------------------------------------------------------------- 
+c on entry:
+c---------- 
+c nrow 	  = integer. the row dimension of the matrix A.
+c 
+c idiag   = integer. The  number of jagged diagonals in the data
+c           structure a, ja, ia.
+c 
+c a, 
+c ja,
+c ia      = input matrix in jagged diagonal format. 
+c
+c iperm   = permutation of the rows used to obtain the JAD ordering. 
+c        
+c on return: 
+c----------
+c 
+c ao, jao,
+c iao     = matrix in CSR format.
+c-----------------------------------------------------------------------
+c determine first the pointers for output matrix. Go through the
+c structure once:
+c
+      do 137 j=1,nrow
+         jao(j) = 0
+ 137  continue
+c     
+c     compute the lengths of each row of output matrix - 
+c     
+      do 140 i=1, idiag
+         len = ia(i+1)-ia(i) 
+         do 138 k=1,len
+            jao(iperm(k)) = jao(iperm(k))+1
+ 138     continue
+ 140  continue
+c     
+c     remember to permute
+c     
+      kpos = 1
+      iao(1) = 1
+      do 141 i=1, nrow 
+         kpos = kpos+jao(i) 
+         iao(i+1) = kpos
+ 141  continue
+c     
+c     copy elemnts one at a time.
+c     
+      do 200 jj = 1, idiag
+         k1 = ia(jj)-1
+         len = ia(jj+1)-k1-1 
+         do 160 k=1,len
+            kpos = iao(iperm(k))
+            ao(kpos) = a(k1+k) 
+            jao(kpos) = ja(k1+k) 
+            iao(iperm(k)) = kpos+1
+ 160     continue
+ 200  continue
+c     
+c     rewind pointers
+c     
+      do 5 j=nrow,1,-1
+         iao(j+1) = iao(j)
+ 5    continue
+      iao(1) = 1
+      return
+c----------end-of-jadcsr------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+      subroutine dcsort(ival, n, icnt, index, ilo, ihi)
+c-----------------------------------------------------------------------
+c     Specifications for arguments:
+c     ----------------------------
+      integer n, ilo, ihi, ival(n), icnt(ilo:ihi), index(n)
+c-----------------------------------------------------------------------
+c    This routine computes a permutation which, when applied to the
+c    input vector ival, sorts the integers in ival in descending
+c    order.  The permutation is represented by the vector index.  The
+c    permuted ival can be interpreted as follows:
+c      ival(index(i-1)) .ge. ival(index(i)) .ge. ival(index(i+1))
+c
+c    A specialized sort, the distribution counting sort, is used 
+c    which takes advantage of the knowledge that
+c        1)  The values are in the (small) range [ ilo, ihi ]
+c        2)  Values are likely to be repeated often
+c
+c    contributed to SPARSKIT by Mike Heroux. (Cray Research) 
+c    --------------------------------------- 
+c----------------------------------------------------------------------- 
+c Usage:
+c------ 
+c     call dcsort( ival, n, icnt, index, ilo, ihi )
+c
+c Arguments:
+c----------- 
+c    ival  integer array (input)
+c          On entry, ia is an n dimensional array that contains
+c          the values to be sorted.  ival is unchanged on exit.
+c
+c    n     integer (input)
+c          On entry, n is the number of elements in ival and index.
+c
+c    icnt  integer (work)
+c          On entry, is an integer work vector of length 
+c          (ihi - ilo + 1).
+c
+c    index integer array (output)
+c          On exit, index is an n-length integer vector containing
+c          the permutation which sorts the vector ival.
+c
+c    ilo   integer (input)
+c          On entry, ilo is .le. to the minimum value in ival.
+c
+c    ihi   integer (input)
+c          On entry, ihi is .ge. to the maximum value in ival.
+c
+c Remarks:
+c--------- 
+c         The permutation is NOT applied to the vector ival.
+c
+c----------------------------------------------------------------
+c
+c Local variables:
+c    Other integer values are temporary indices.
+c
+c Author: 
+c-------- 
+c    Michael Heroux
+c    Sandra Carney
+c       Mathematical Software Research Group
+c       Cray Research, Inc.
+c
+c References:
+c    Knuth, Donald E., "The Art of Computer Programming, Volume 3:
+c    Sorting and Searching," Addison-Wesley, Reading, Massachusetts,
+c    1973, pp. 78-79.
+c
+c Revision history:
+c    05/09/90: Original implementation.  A variation of the 
+c              Distribution Counting Sort recommended by
+c              Sandra Carney. (Mike Heroux)
+c
+c-----------------------------------------------------------------
+c     ----------------------------------
+c     Specifications for local variables
+c     ----------------------------------
+      integer i, j, ivalj
+c
+c     --------------------------
+c     First executable statement
+c     --------------------------
+      do 10 i = ilo, ihi
+        icnt(i) = 0
+ 10   continue
+c
+      do 20 i = 1, n
+        icnt(ival(i)) = icnt(ival(i)) + 1
+ 20   continue
+c
+      do 30 i = ihi-1,ilo,-1
+        icnt(i) = icnt(i) + icnt(i+1)
+ 30   continue
+c
+      do 40 j = n, 1, -1
+        ivalj = ival(j)
+        index(icnt(ivalj)) = j
+        icnt(ivalj) = icnt(ivalj) - 1
+ 40   continue
+      return
+      end
+c-------end-of-dcsort---------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine cooell(job,n,nnz,a,ja,ia,ao,jao,lda,ncmax,nc,ierr)
+      implicit none
+      integer job,n,nnz,lda,ncmax,nc,ierr
+      integer ja(nnz),ia(nnz),jao(lda,ncmax)
+      real*8  a(nnz),ao(lda,ncmax)
+c-----------------------------------------------------------------------
+c     COOrdinate format to ELLpack format
+c-----------------------------------------------------------------------
+c     On entry:
+c     job     -- 0 if only pattern is to be processed(AO is not touched)
+c     n       -- number of rows in the matrix
+c     a,ja,ia -- input matix in COO format
+c     lda     -- leading dimension of array AO and JAO
+c     ncmax   -- size of the second dimension of array AO and JAO
+c
+c     On exit:
+c     ao,jao  -- the matrix in ELL format
+c     nc      -- maximum number of nonzeros per row
+c     ierr    -- 0 if convertion succeeded
+c                -1 if LDA < N
+c                nc if NC > ncmax
+c
+c     NOTE: the last column of JAO is used as work space!!
+c-----------------------------------------------------------------------
+      integer i,j,k,ip
+      real*8  zero
+      logical copyval
+      parameter (zero=0.0D0)
+c     .. first executable statement ..
+      copyval = (job.ne.0)
+      if (lda .lt. n) then
+         ierr = -1
+         return
+      endif
+c     .. use the last column of JAO as workspace
+c     .. initialize the work space
+      do i = 1, n
+         jao(i,ncmax) = 0
+      enddo
+      nc = 0
+c     .. go through ia and ja to find out number nonzero per row
+      do k = 1, nnz
+         i = ia(k)
+         jao(i,ncmax) = jao(i,ncmax) + 1
+      enddo
+c     .. maximum number of nonzero per row
+      nc = 0
+      do i = 1, n
+         if (nc.lt.jao(i,ncmax)) nc = jao(i,ncmax)
+         jao(i,ncmax) = 0
+      enddo
+c     .. if nc > ncmax retrun now
+      if (nc.gt.ncmax) then
+         ierr = nc
+         return
+      endif
+c     .. go through ia and ja to copy the matrix to AO and JAO
+      do k = 1, nnz
+         i = ia(k)
+         j = ja(k)
+         jao(i,ncmax) = jao(i,ncmax) + 1
+         ip = jao(i,ncmax)
+         if (ip.gt.nc) nc = ip
+         if (copyval) ao(i,ip) = a(k)
+         jao(i,ip) = j
+      enddo
+c     .. fill the unspecified elements of AO and JAO with zero diagonals
+      do i = 1, n
+         do j = ia(i+1)-ia(i)+1, nc
+            jao(i,j)=i
+            if(copyval) ao(i,j) = zero
+         enddo
+      enddo
+      ierr = 0
+c
+      return
+      end
+c-----end-of-cooell-----------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine xcooell(n,nnz,a,ja,ia,ac,jac,nac,ner,ncmax,ierr)
+C-----------------------------------------------------------------------
+C   coordinate format to ellpack format.
+C-----------------------------------------------------------------------
+C
+C   DATE WRITTEN: June 4, 1989. 
+C
+C   PURPOSE
+C   -------
+C  This subroutine takes a sparse matrix in coordinate format and
+C  converts it into the Ellpack-Itpack storage.
+C
+C  Example:
+C  -------
+C       (   11   0   13    0     0     0  )
+C       |   21  22    0   24     0     0  |
+C       |    0  32   33    0    35     0  |
+C   A = |    0   0   43   44     0    46  |
+C       |   51   0    0   54    55     0  |
+C       (   61  62    0    0    65    66  )
+C
+C   Coordinate storage scheme:
+C
+C    A  = (11,22,33,44,55,66,13,21,24,32,35,43,46,51,54,61,62,65)
+C    IA = (1, 2, 3, 4, 5, 6, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6 )
+C    JA = ( 1, 2, 3, 4, 5, 6, 3, 1, 4, 2, 5, 3, 6, 1, 4, 1, 2, 5)
+C
+C   Ellpack-Itpack storage scheme:
+C
+C       (   11  13    0    0   )          (   1   3   *    *  )
+C       |   22  21   24    0   |          |   2   1   4    *  |
+C  AC = |   33  32   35    0   |    JAC = |   3   2   5    *  |
+C       |   44  43   46    0   |          |   4   3   6    *  |
+C       |   55  51   54    0   |          |   5   1   4    *  |
+C       (   66  61   62   65   )          (   6   1   2    5  )
+C
+C   Note: * means that you can store values from 1 to 6 (1 to n, where
+C         n is the order of the matrix) in that position in the array.
+C
+C   Contributed by:
+C   --------------- 
+C   Ernest E. Rothman
+C   Cornell Thoery Center/Cornell National Supercomputer Facility
+C   e-mail address: BITNET:   EER@CORNELLF.BITNET
+C                   INTERNET: eer@cornellf.tn.cornell.edu
+C   
+C   checked and modified  04/13/90 Y.Saad.
+C
+C   REFERENCES
+C   ----------
+C   Kincaid, D. R.; Oppe, T. C.; Respess, J. R.; Young, D. M. 1984.
+C   ITPACKV 2C User's Guide, CNA-191. Center for Numerical Analysis,
+C   University of Texas at Austin.
+C
+C   "Engineering and Scientific Subroutine Library; Guide and
+C   Reference; Release 3 (SC23-0184-3). Pp. 79-86.
+C
+C-----------------------------------------------------------------------
+C
+C   INPUT PARAMETERS
+C   ----------------
+C  N       - Integer. The size of the square matrix.
+C
+C  NNZ     - Integer. Must be greater than or equal to the number of
+C            nonzero elements in the sparse matrix. Dimension of A, IA 
+C            and JA.
+C
+C  NCA     - Integer. First dimension of output arrays ca and jac.
+C
+C  A(NNZ)  - Real array. (Double precision)
+C            Stored entries of the sparse matrix A.
+C            NNZ is the number of nonzeros.
+C
+C  IA(NNZ) - Integer array.
+C            Pointers to specify rows for the stored nonzero entries
+C            in A.
+C
+C  JA(NNZ) - Integer array.
+C            Pointers to specify columns for the stored nonzero
+C            entries in A.
+C
+C  NER     - Integer. Must be set greater than or equal to the maximum
+C            number of nonzeros in any row of the sparse matrix.
+C
+C  OUTPUT PARAMETERS
+C  -----------------
+C  AC(NAC,*)  - Real array. (Double precision)
+C               Stored entries of the sparse matrix A in compressed
+C               storage mode.
+C
+C  JAC(NAC,*) - Integer array.
+C               Contains the column numbers of the sparse matrix
+C               elements stored in the corresponding positions in
+C               array AC.
+C
+C  NCMAX   -  Integer. Equals the maximum number of nonzeros in any
+C             row of the sparse matrix.
+C
+C  IERR    - Error parameter is returned as zero on successful
+C             execution of the subroutin<e.
+C             Error diagnostics are given by means of positive values
+C             of this parameter as follows:
+C
+C             IERR = -1   -  NER is too small and should be set equal
+C                            to NCMAX. The array AC may not be large
+C                            enough to accomodate all the non-zeros of
+C                            of the sparse matrix.
+C             IERR =  1   -  The array AC has a zero column. (Warning) 
+C             IERR =  2   -  The array AC has a zero row.    (Warning)
+C
+C---------------------------------------------------------------------
+      real*8 a(nnz), ac(nac,ner)
+      integer ja(nnz), ia(nnz), jac(nac,ner), ierr, ncmax, icount
+c
+c- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+c   Initial error parameter to zero:
+c
+      ierr = 0
+c
+c- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+c   Initial output arrays to zero:
+c
+      do 4 in = 1,ner
+         do 4 innz =1,n
+            jac(innz,in) = n
+            ac(innz,in) = 0.0d0
+ 4    continue
+c     
+c- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+c
+c   Assign nonzero elements of the sparse matrix (stored in the one
+c   dimensional array A to the two dimensional array AC.
+c   Also, assign the correct values with information about their
+c   column indices to the two dimensional array KA. And at the same
+c   time count the number of nonzeros in each row so that the
+c   parameter NCMAX equals the maximum number of nonzeros in any row
+c   of the sparse matrix.
+c
+      ncmax = 1
+      do 10 is = 1,n
+         k = 0
+         do 30 ii = 1,nnz
+            if(ia(ii).eq.is)then
+               k = k + 1
+               if (k .le. ner) then
+                  ac(is,k) = a(ii)
+                  jac(is,k) = ja(ii)
+               endif 
+            endif
+ 30      continue
+         if (k.ge.ncmax) ncmax = k
+ 10   continue
+c- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+c     
+c     Perform some simple error checks:
+c     
+check maximum number of nonzeros in each row:
+      if (ncmax.eq.ner) ierr = 0
+      if (ncmax.gt.ner) then
+         ierr = -1
+         return
+      endif
+c     
+check if there are any zero columns in AC:
+c     
+      do 45 in = 1,ncmax
+         icount = 0
+         do 44 inn =1,n
+            if (ac(inn,in).ne.0.0d0) icount = 1
+ 44      continue
+         if (icount.eq.0) then
+            ierr = 1
+            return
+         endif
+ 45   continue
+c     
+check if there are any zero rows in AC:
+c     
+      do 55 inn = 1,n
+         icount = 0
+         do 54 in =1,ncmax
+            if (ac(inn,in).ne.0.0d0) icount = 1
+ 54      continue
+         if (icount.eq.0) then
+            ierr = 2
+            return
+         endif
+ 55   continue
+      return
+c------------- end of xcooell ------------------------------------------- 
+      end
+c----------------------------------------------------------------------- 
+      subroutine csruss (nrow,a,ja,ia,diag,al,jal,ial,au,jau,iau) 
+      real*8 a(*),al(*),diag(*),au(*) 
+      integer nrow,ja(*),ia(nrow+1),jal(*),ial(nrow+1),jau(*),
+     *     iau(nrow+1)
+c-----------------------------------------------------------------------
+c Compressed Sparse Row     to     Unsymmetric Sparse Skyline format
+c----------------------------------------------------------------------- 
+c this subroutine converts a matrix stored in csr format into a nonsym. 
+c sparse skyline format. This latter format does not assume
+c that the matrix has a symmetric pattern and consists of the following 
+c * the diagonal of A stored separately in diag(*);
+c * The strict lower part of A is stored  in CSR format in al,jal,ial 
+c * The strict upper part is stored in CSC format in au,jau,iau.
+c----------------------------------------------------------------------- 
+c On entry
+c---------
+c nrow  = dimension of the matrix a.
+c a     = real array containing the nonzero values of the matrix 
+c         stored rowwise.
+c ja    = column indices of the values in array a
+c ia    = integer array of length n+1 containing the pointers to
+c         beginning of each row in arrays a, ja.
+c 
+c On return
+c----------
+c diag  = array containing the diagonal entries of A
+c al,jal,ial = matrix in CSR format storing the strict lower 
+c              trangular part of A.
+c au,jau,iau = matrix in CSC format storing the strict upper
+c              triangular part of A. 
+c----------------------------------------------------------------------- 
+      integer i, j, k, kl, ku 
+c
+c determine U's data structure first
+c 
+      do 1 i=1,nrow+1
+         iau(i) = 0
+ 1    continue
+      do 3 i=1, nrow
+         do 2 k=ia(i), ia(i+1)-1 
+            j = ja(k)
+            if (j .gt. i) iau(j+1) = iau(j+1)+1
+ 2       continue 
+ 3    continue
+c
+c     compute pointers from lengths
+c
+      iau(1) = 1
+      do 4 i=1,nrow
+         iau(i+1) = iau(i)+iau(i+1)
+         ial(i+1) = ial(i)+ial(i+1)
+ 4    continue
+c
+c     now do the extractions. scan all rows.
+c
+      kl = 1
+      ial(1) = kl
+      do  7 i=1, nrow
+c
+c     scan all elements in a row
+c 
+         do 71 k = ia(i), ia(i+1)-1
+            j = ja(k) 
+c
+c     if in upper part, store in row j (of transp(U) )
+c     
+            if (j  .gt. i) then
+               ku = iau(j) 
+               au(ku) = a(k)
+               jau(ku) = i
+               iau(j) = ku+1
+            elseif (j  .eq. i) then
+               diag(i) = a(k) 
+            elseif (j .lt. i) then
+               al(kl) = a(k)
+               jal(kl) = j
+               kl = kl+1
+            endif
+ 71      continue
+         ial(i+1) = kl 
+ 7    continue
+c
+c readjust iau
+c
+      do 8 i=nrow,1,-1
+         iau(i+1) = iau(i)
+ 8    continue
+      iau(1) = 1
+c--------------- end-of-csruss ----------------------------------------- 
+c-----------------------------------------------------------------------
+      end 
+c-----------------------------------------------------------------------
+      subroutine usscsr (nrow,a,ja,ia,diag,al,jal,ial,au,jau,iau) 
+      real*8 a(*),al(*),diag(*),au(*) 
+      integer ja(*),ia(nrow+1),jal(*),ial(nrow+1),jau(*),iau(nrow+1)
+c-----------------------------------------------------------------------
+c Unsymmetric Sparse Skyline   format   to Compressed Sparse Row 
+c----------------------------------------------------------------------- 
+c this subroutine converts a matrix stored in nonsymmetric sparse
+c skyline format into csr format. The sparse skyline format is 
+c described in routine csruss. 
+c----------------------------------------------------------------------- 
+c----------------------------------------------------------------------- 
+c On entry
+c-----------------------------------------------------------------------
+c nrow  = dimension of the matrix a.
+c diag  = array containing the diagonal entries of A
+c al,jal,ial = matrix in CSR format storing the strict lower 
+c              trangular part of A.
+c au,jau,iau = matrix in CSC format storing the strict upper
+c              trangular part of A.
+c On return
+c --------- 
+c a     = real array containing the nonzero values of the matrix 
+c         stored rowwise.
+c ja    = column indices of the values in array a
+c ia    = integer array of length n+1 containing the pointers to
+c         beginning of each row in arrays a, ja.
+c 
+c-----------------------------------------------------------------------
+c
+c count elements in lower part + diagonal 
+c 
+      do 1 i=1, nrow
+         ia(i+1) = ial(i+1)-ial(i)+1
+ 1    continue
+c
+c count elements in upper part
+c 
+      do 3 i=1, nrow
+         do 2 k=iau(i), iau(i+1)-1 
+            j = jau(k)
+            ia(j+1) = ia(j+1)+1
+ 2       continue 
+ 3    continue
+c---------- compute pointers from lengths ------------------------------
+      ia(1) = 1
+      do 4 i=1,nrow
+         ia(i+1) = ia(i)+ia(i+1)
+ 4    continue
+c
+c copy lower part + diagonal 
+c 
+      do 6 i=1, nrow
+         ka = ia(i) 
+         do 5 k=ial(i), ial(i+1)-1
+            a(ka) = al(k) 
+            ja(ka) = jal(k) 
+            ka = ka+1
+ 5       continue
+         a(ka) = diag(i) 
+         ja(ka) = i
+         ia(i) = ka+1
+ 6    continue
+c     
+c     copy upper part
+c     
+      do 8 i=1, nrow
+         do 7 k=iau(i), iau(i+1)-1
+c
+c row number
+c
+            jak = jau(k) 
+c
+c where element goes
+c
+            ka = ia(jak) 
+            a(ka) = au(k) 
+            ja(ka) = i
+            ia(jak) = ka+1
+ 7       continue
+ 8    continue
+c
+c readjust ia
+c
+      do 9 i=nrow,1,-1
+         ia(i+1) = ia(i)
+ 9    continue
+      ia(1) = 1
+c----------end-of-usscsr------------------------------------------------
+      end 
+c----------------------------------------------------------------------- 
+      subroutine csrsss (nrow,a,ja,ia,sorted,diag,al,jal,ial,au)
+      real*8 a(*),al(*),diag(*),au(*) 
+      integer ja(*),ia(nrow+1),jal(*),ial(nrow+1)
+      logical sorted 
+c-----------------------------------------------------------------------
+c Compressed Sparse Row     to     Symmetric Sparse Skyline   format 
+c----------------------------------------------------------------------- 
+c this subroutine converts a matrix stored in csr format into the 
+c Symmetric sparse skyline   format. This latter format assumes that 
+c that the matrix has a symmetric pattern. It consists of the following 
+c * the diagonal of A stored separately in diag(*);
+c * The strict lower part of A is stored  in csr format in al,jal,ial 
+c * The values only of strict upper part as stored in csc format in au. 
+c----------------------------------------------------------------------- 
+c On entry
+c-----------
+c nrow  = dimension of the matrix a.
+c a     = real array containing the nonzero values of the matrix 
+c         stored rowwise.
+c ja    = column indices of the values in array a
+c ia    = integer array of length n+1 containing the pointers to
+c         beginning of each row in arrays a, ja.
+c sorted= a logical indicating whether or not the elements in a,ja,ia
+c         are sorted. 
+c 
+c On return
+c --------- 
+c diag  = array containing the diagonal entries of A
+c al,jal,ial = matrix in csr format storing the strict lower 
+c              trangular part of A.
+c au    = values of the strict upper trangular part of A, column wise.
+c----------------------------------------------------------------------- 
+c 
+c     extract lower part and diagonal.
+c
+      kl = 1
+      ial(1) = kl
+      do  7 i=1, nrow
+c
+c scan all elements in a row
+c 
+         do 71 k = ia(i), ia(i+1)-1
+            jak = ja(k) 
+            if (jak  .eq. i) then
+               diag(i) = a(k) 
+            elseif (jak .lt. i) then
+               al(kl) = a(k)
+               jal(kl) = jak
+               kl = kl+1
+            endif
+ 71      continue
+         ial(i+1) = kl 
+ 7    continue
+c
+c sort if not sorted
+c 
+      if (.not. sorted) then
+c%%%%%---- incompatible arg list! 
+         call csort (nrow, al, jal, ial, au, .true.) 
+      endif
+c
+c copy u
+c 
+      do  8 i=1, nrow
+c
+c scan all elements in a row
+c 
+         do 81 k = ia(i), ia(i+1)-1
+            jak = ja(k) 
+            if (jak  .gt. i) then
+               ku = ial(jak) 
+               au(ku) = a(k)
+               ial(jak) = ku+1
+            endif
+ 81      continue
+ 8    continue
+c   
+c readjust ial
+c
+      do 9 i=nrow,1,-1
+         ial(i+1) = ial(i)
+ 9    continue
+      ial(1) = 1
+c--------------- end-of-csrsss ----------------------------------------- 
+c-----------------------------------------------------------------------
+      end 
+c
+      subroutine ssscsr (nrow,a,ja,ia,diag,al,jal,ial,au) 
+      real*8 a(*),al(*),diag(*),au(*) 
+      integer ja(*),ia(nrow+1),jal(*),ial(nrow+1) 
+c-----------------------------------------------------------------------
+c Unsymmetric Sparse Skyline   format   to Compressed Sparse Row 
+c----------------------------------------------------------------------- 
+c this subroutine converts a matrix stored in nonsymmetric sparse 
+c skyline format into csr format. The sparse skyline format is 
+c described in routine csruss. 
+c----------------------------------------------------------------------- 
+c On entry
+c--------- 
+c diag  = array containing the diagonal entries of A
+c al,jal,ial = matrix in csr format storing the strict lower 
+c              trangular part of A.
+c au    = values of strict upper part. 
+c
+c On return
+c --------- 
+c nrow  = dimension of the matrix a.
+c a     = real array containing the nonzero values of the matrix 
+c         stored rowwise.
+c ja    = column indices of the values in array a
+c ia    = integer array of length n+1 containing the pointers to
+c         beginning of each row in arrays a, ja.
+c 
+c-----------------------------------------------------------------------
+c
+c count elements in lower part + diagonal 
+c 
+      do 1 i=1, nrow
+         ia(i+1) = ial(i+1)-ial(i)+1
+ 1    continue
+c
+c count elements in upper part
+c 
+      do 3 i=1, nrow
+         do 2 k=ial(i), ial(i+1)-1 
+            j = jal(k)
+            ia(j+1) = ia(j+1)+1
+ 2       continue 
+ 3    continue
+c---------- compute pointers from lengths ------------------------------
+      ia(1) = 1
+      do 4 i=1,nrow
+         ia(i+1) = ia(i)+ia(i+1)
+ 4    continue
+c
+c copy lower part + diagonal 
+c 
+      do 6 i=1, nrow
+         ka = ia(i) 
+         do 5 k=ial(i), ial(i+1)-1
+            a(ka) = al(k) 
+            ja(ka) = jal(k) 
+            ka = ka+1
+ 5       continue
+         a(ka) = diag(i) 
+         ia(i) = ka+1
+ 6    continue
+c     
+c     copy upper part
+c     
+      do 8 i=1, nrow
+         do 7 k=ial(i), ial(i+1)-1
+c
+c row number
+c
+            jak = jal(k) 
+c
+c where element goes
+c
+            ka = ia(jak) 
+            a(ka) = au(k) 
+            ja(ka) = i
+            ia(jak) = ka+1
+ 7       continue
+ 8    continue
+c
+c readjust ia
+c
+      do 9 i=nrow,1,-1
+         ia(i+1) = ia(i)
+ 9    continue
+      ia(1) = 1
+c----------end-of-ssscsr------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine csrvbr(n,ia,ja,a,nr,nc,kvstr,kvstc,ib,jb,kb,
+     &     b, job, iwk, nkmax, nzmax, ierr )
+c-----------------------------------------------------------------------
+      integer n, ia(n+1), ja(*), nr, nc, ib(*), jb(nkmax-1), kb(nkmax)
+      integer kvstr(*), kvstc(*), job, iwk(*), nkmax, nzmax, ierr
+      real*8  a(*), b(nzmax)
+c-----------------------------------------------------------------------
+c     Converts compressed sparse row to variable block row format.
+c-----------------------------------------------------------------------
+c     On entry:
+c--------------
+c     n       = number of matrix rows
+c     ia,ja,a = input matrix in CSR format
+c
+c     job     = job indicator.
+c               If job=0, kvstr and kvstc are used as supplied.
+c               If job=1, kvstr and kvstc are determined by the code.
+c               If job=2, a conformal row/col partitioning is found and
+c               returned in both kvstr and kvstc.  In the latter two cases,
+c               an optimized algorithm can be used to perform the
+c               conversion because all blocks are full.
+c
+c     nkmax   = size of supplied jb and kb arrays
+c     nzmax   = size of supplied b array
+c
+c     If job=0 then the following are input:
+c     nr,nc   = matrix block row and block column dimension
+c     kvstr   = first row number for each block row
+c     kvstc   = first column number for each block column.
+c               (kvstr and kvstc may be the same array)
+c
+c     On return:
+c---------------
+c
+c     ib,jb,kb,b = output matrix in VBR format
+c
+c     ierr    = error message
+c               ierr = 0 means normal return
+c               ierr = 1 out of space in jb and/or kb arrays
+c               ierr = 2 out of space in b array
+c               ierr = 3 nonsquare matrix used with job=2
+c
+c     If job=1,2 then the following are output:
+c     nr,nc   = matrix block row and block column dimension
+c     kvstr   = first row number for each block row
+c     kvstc   = first column number for each block column
+c               If job=2, then kvstr and kvstc contain the same info.
+c
+c     Work space:
+c----------------
+c     iwk(1:ncol) = inverse kvstc array.  If job=1,2 then we also need:
+c     iwk(ncol+1:ncol+nr) = used to help determine sparsity of each block row.
+c     The workspace is not assumed to be initialized to zero, nor is it
+c     left that way.
+c
+c     Algorithms:
+c----------------
+c     There are two conversion codes in this routine.  The first assumes
+c     that all blocks are full (there is a nonzero in the CSR data
+c     structure for each entry in the block), and is used if the routine
+c     determines the block partitioning itself.  The second code makes
+c     no assumptions about the block partitioning, and is used if the
+c     caller provides the partitioning.  The second code is much less
+c     efficient than the first code.
+c
+c     In the first code, the CSR data structure is traversed sequentially
+c     and entries are placed into the VBR data structure with stride
+c     equal to the row dimension of the block row.  The columns of the
+c     CSR data structure are sorted first if necessary.
+c
+c     In the second code, the block sparsity pattern is first determined.
+c     This is done by traversing the CSR data structure and using an
+c     implied linked list to determine which blocks are nonzero.  Then
+c     the VBR data structure is filled by mapping each individual entry
+c     in the CSR data structure into the VBR data structure.  The columns
+c     of the CSR data structure are sorted first if necessary.
+c
+c-----------------------------------------------------------------------
+c     Local variables:
+c---------------------
+      integer ncol, nb, neqr, numc, a0, b0, b1, k0, i, ii, j, jj, jnew
+      logical sorted
+c
+c     ncol = number of scalar columns in matrix
+c     nb = number of blocks in conformal row/col partitioning
+c     neqr = number of rows in block row
+c     numc = number of nonzero columns in row
+c     a0 = index for entries in CSR a array
+c     b0 = index for entries in VBR b array
+c     b1 = temp
+c     k0 = index for entries in VBR kb array
+c     i  = loop index for block rows
+c     ii = loop index for scalar rows in block row
+c     j  = loop index for block columns
+c     jj = loop index for scalar columns in block column
+c     jnew = block column number
+c     sorted = used to indicate if matrix already sorted by columns
+c
+c-----------------------------------------------------------------------
+      ierr = 0
+c-----sort matrix by column indices
+      call csorted(n, ia, ja, sorted)
+      if (.not. sorted) then
+         call csort (n, a, ja, ia, b, .true.)
+      endif
+      if (job .eq. 1 .or. job .eq. 2) then
+c--------need to zero workspace; first find ncol
+         ncol = 0
+         do i = 2, n
+            ncol = max0(ncol, ja(ia(i)-1))
+         enddo
+         do i = 1, ncol
+            iwk(i) = 0
+         enddo
+         call csrkvstr(n, ia, ja, nr, kvstr)
+         call csrkvstc(n, ia, ja, nc, kvstc, iwk)
+      endif
+c-----check if want conformal partitioning
+      if (job .eq. 2) then
+         if (kvstr(nr+1) .ne. kvstc(nc+1)) then
+            ierr = 3
+            return
+         endif
+c        use iwk temporarily
+         call kvstmerge(nr, kvstr, nc, kvstc, nb, iwk)
+         nr = nb
+         nc = nb
+         do i = 1, nb+1
+            kvstr(i) = iwk(i)
+            kvstc(i) = iwk(i)
+         enddo
+      endif
+c-----------------------------------------------------------------------
+c     inverse kvst (scalar col number) = block col number
+c     stored in iwk(1:n)
+c-----------------------------------------------------------------------
+      do i = 1, nc
+         do j = kvstc(i), kvstc(i+1)-1
+            iwk(j) = i
+         enddo
+      enddo
+      ncol = kvstc(nc+1)-1
+c-----jump to conversion routine
+      if (job .eq. 0) goto 400
+c-----------------------------------------------------------------------
+c     Fast conversion for computed block partitioning
+c-----------------------------------------------------------------------
+      a0 = 1
+      b0 = 1
+      k0 = 1
+      kb(1) = 1
+c-----loop on block rows
+      do i = 1, nr
+         neqr = kvstr(i+1) - kvstr(i)
+         numc = ia(kvstr(i)+1) - ia(kvstr(i))
+         ib(i) = k0
+c--------loop on first row in block row to determine block sparsity
+         j = 0
+         do jj = ia(kvstr(i)), ia(kvstr(i)+1)-1
+            jnew = iwk(ja(jj))
+            if (jnew .ne. j) then
+c--------------check there is enough space in kb and jb arrays
+               if (k0+1 .gt. nkmax) then
+                  ierr = 1
+                  write (*,*) 'csrvbr: no space in kb for block row ', i
+                  return
+               endif
+c--------------set entries for this block
+               j = jnew
+               b0 = b0 + neqr * (kvstc(j+1) - kvstc(j))
+               kb(k0+1) = b0
+               jb(k0) = j
+               k0 = k0 + 1
+            endif
+         enddo
+c--------loop on scalar rows in block row
+         do ii = 0, neqr-1
+            b1 = kb(ib(i))+ii
+c-----------loop on elements in a scalar row
+            do jj = 1, numc
+c--------------check there is enough space in b array
+               if (b1 .gt. nzmax) then
+                  ierr = 2
+                  write (*,*) 'csrvbr: no space in b for block row ', i
+                  return
+               endif
+               b(b1) = a(a0)
+               b1 = b1 + neqr
+               a0 = a0 + 1
+            enddo
+         enddo
+      enddo
+      ib(nr+1) = k0
+      return
+c-----------------------------------------------------------------------
+c     Conversion for user supplied block partitioning
+c-----------------------------------------------------------------------
+ 400  continue
+c-----initialize workspace for sparsity indicator
+      do i = ncol+1, ncol+nc
+         iwk(i) = 0
+      enddo
+      k0 = 1
+      kb(1) = 1
+c-----find sparsity of block rows
+      do i = 1, nr
+         neqr = kvstr(i+1) - kvstr(i)
+         numc = ia(kvstr(i)+1) - ia(kvstr(i))
+         ib(i) = k0
+c--------loop on all the elements in the block row to determine block sparsity
+         do jj = ia(kvstr(i)), ia(kvstr(i+1))-1
+            iwk(iwk(ja(jj))+ncol) = 1
+         enddo
+c--------use sparsity to set jb and kb arrays
+         do j = 1, nc
+            if (iwk(j+ncol) .ne. 0) then
+c--------------check there is enough space in kb and jb arrays
+               if (k0+1 .gt. nkmax) then
+                  ierr = 1
+                  write (*,*) 'csrvbr: no space in kb for block row ', i
+                  return
+               endif
+               kb(k0+1) = kb(k0) + neqr * (kvstc(j+1) - kvstc(j))
+               jb(k0) = j
+               k0 = k0 + 1
+               iwk(j+ncol) = 0
+            endif
+         enddo
+      enddo
+      ib(nr+1) = k0
+c-----Fill b with entries from a by traversing VBR data structure.
+      a0 = 1
+c-----loop on block rows
+      do i = 1, nr
+         neqr = kvstr(i+1) - kvstr(i)
+c--------loop on scalar rows in block row
+         do ii = 0, neqr-1
+            b0 = kb(ib(i)) + ii
+c-----------loop on block columns
+            do j = ib(i), ib(i+1)-1
+c--------------loop on scalar columns within block column
+               do jj = kvstc(jb(j)), kvstc(jb(j)+1)-1
+c-----------------check there is enough space in b array
+                  if (b0 .gt. nzmax) then
+                     ierr = 2
+                     write (*,*)'csrvbr: no space in b for blk row',i
+                     return
+                  endif
+                  if (a0 .ge. ia(kvstr(i)+ii+1)) then
+                     b(b0) = 0.d0
+                  else
+                     if (jj .eq. ja(a0)) then
+                        b(b0) = a(a0)
+                        a0 = a0 + 1
+                     else
+                        b(b0) = 0.d0
+                     endif
+                  endif
+                  b0 = b0 + neqr
+c--------------endloop on scalar columns
+               enddo
+c-----------endloop on block columns
+            enddo
+ 2020       continue
+         enddo
+      enddo
+      return
+      end
+c-----------------------------------------------------------------------
+c----------------------------end-of-csrvbr------------------------------
+c----------------------------------------------------------------------c
+      subroutine vbrcsr(ia, ja, a, nr, kvstr, kvstc, ib, jb, kb,
+     &   b, nzmax, ierr)
+c-----------------------------------------------------------------------
+      integer ia(*), ja(*), nr, ib(nr+1), jb(*), kb(*)
+      integer kvstr(nr+1), kvstc(*), nzmax, ierr
+      real*8  a(*), b(nzmax)
+c-----------------------------------------------------------------------
+c     Converts variable block row to compressed sparse row format.
+c-----------------------------------------------------------------------
+c     On entry:
+c--------------
+c     nr      = number of block rows
+c     kvstr   = first row number for each block row
+c     kvstc   = first column number for each block column
+c     ib,jb,kb,b = input matrix in VBR format
+c     nzmax   = size of supplied ja and a arrays
+c
+c     On return:
+c---------------
+c     ia,ja,a = output matrix in CSR format
+c
+c     ierr    = error message
+c               ierr = 0 means normal return
+c               ierr = negative row number when out of space in
+c                      ja and a arrays
+c
+c     Work space:
+c----------------
+c     None
+c
+c     Algorithm:
+c---------------
+c     The VBR data structure is traversed in the order that is required
+c     to fill the CSR data structure.  In a given block row, consecutive
+c     entries in the CSR data structure are entries in the VBR data
+c     structure with stride equal to the row dimension of the block.
+c     The VBR data structure is assumed to be sorted by block columns.
+c
+c-----------------------------------------------------------------------
+c     Local variables:
+c---------------------
+      integer neqr, numc, a0, b0, i, ii, j, jj
+c
+c     neqr = number of rows in block row
+c     numc = number of nonzero columns in row
+c     a0 = index for entries in CSR a array
+c     b0 = index for entries in VBR b array
+c     i  = loop index for block rows
+c     ii = loop index for scalar rows in block row
+c     j  = loop index for block columns
+c     jj = loop index for scalar columns in block column
+c
+c-----------------------------------------------------------------------
+      ierr = 0
+      a0 = 1
+      b0 = 1
+c-----loop on block rows
+      do i = 1, nr
+c--------set num of rows in block row, and num of nonzero cols in row
+         neqr = kvstr(i+1) - kvstr(i)
+         numc = ( kb(ib(i+1)) - kb(ib(i)) ) / neqr
+c--------construct ja for a scalar row
+         do j = ib(i), ib(i+1)-1
+            do jj = kvstc(jb(j)), kvstc(jb(j)+1)-1
+               ja(a0) = jj
+               a0 = a0 + 1
+            enddo
+         enddo
+c--------construct neqr-1 additional copies of ja for the block row
+         do ii = 1, neqr-1
+            do j = 1, numc
+               ja(a0) = ja(a0-numc)
+               a0 = a0 + 1
+            enddo
+         enddo
+c--------reset a0 back to beginning of block row
+         a0 = kb(ib(i))
+c--------loop on scalar rows in block row
+         do ii = 0, neqr-1
+            ia(kvstr(i)+ii) = a0
+            b0 = kb(ib(i)) + ii
+c-----------loop on elements in a scalar row
+            do jj = 1, numc
+c--------------check there is enough space in a array
+               if (a0 .gt. nzmax) then
+                  ierr = -(kvstr(i)+ii)
+                  write (*,*) 'vbrcsr: no space for row ', -ierr
+                  return
+               endif
+               a(a0) = b(b0)
+               a0 = a0 + 1
+               b0 = b0 + neqr
+            enddo
+         enddo
+c-----endloop on block rows
+      enddo
+      ia(kvstr(nr+1)) = a0
+      return
+      end
+c-----------------------------------------------------------------------
+c---------------------------end-of-vbrcsr-------------------------------
+c-----------------------------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine csorted(n, ia, ja, sorted)
+c-----------------------------------------------------------------------
+      integer n, ia(n+1), ja(*)
+      logical sorted
+c-----------------------------------------------------------------------
+c     Checks if matrix in CSR format is sorted by columns.
+c-----------------------------------------------------------------------
+c     On entry:
+c--------------
+c     n       = number of rows in matrix
+c     ia, ja  = sparsity structure of matrix in CSR format
+c
+c     On return:
+c---------------
+c     sorted  = indicates if matrix is sorted by columns
+c
+c-----------------------------------------------------------------------
+c-----local variables
+      integer i,j
+c---------------------------------
+      do i = 1, n
+         do j = ia(i)+1, ia(i+1)-1
+            if (ja(j-1) .ge. ja(j)) then
+               sorted = .false.
+               return
+            endif
+         enddo
+      enddo
+      sorted = .true.
+      return
+      end
+c-----------------------------------------------------------------------
+c------------------------end-of-csorted---------------------------------
diff --git a/FORMATS/makefile b/FORMATS/makefile
new file mode 100644
index 0000000..69ba330
--- /dev/null
+++ b/FORMATS/makefile
@@ -0,0 +1,28 @@
+FFLAGS =
+F77 = f77
+
+#F77 = cf77
+#FFLAGS = -Wf"-dp"
+
+FILES1 = chkun.o 
+FILES2 = chkfmt1.o 
+FILES3 = rvbr.o
+
+un.ex:	$(FILES1) ../MATGEN/FDIF/functns.o ../libskit.a 
+	$(F77) $(FFLAGS) -o un.ex $(FILES1) ../MATGEN/FDIF/functns.o ../libskit.a 
+
+fmt.ex:	$(FILES2) ../MATGEN/FDIF/functns.o ../libskit.a 
+	$(F77) $(FFLAGS) -o fmt.ex $(FILES2) ../MATGEN/FDIF/functns.o ../libskit.a 
+
+rvbr.ex: $(FILES3) ../MATGEN/FDIF/functns.o ../libskit.a 
+	$(F77) $(FFLAGS) -o rvbr.ex $(FILES3) ../MATGEN/FDIF/functns.o ../libskit.a
+
+clean:
+	rm -f *.o *.ex core *.trace
+
+../MATGEN/FDIF/functns.o:
+	(cd ../MATGEN/FDIF; $(F77) $(FFLAGS) -c functns.f)
+
+../libskit.a:
+	(cd ..; $(MAKE) $(MAKEFLAGS) libskit.a)
+
diff --git a/FORMATS/rvbr.f b/FORMATS/rvbr.f
new file mode 100644
index 0000000..3ce9823
--- /dev/null
+++ b/FORMATS/rvbr.f
@@ -0,0 +1,142 @@
+      program rvbr
+c-----------------------------------------------------------------------
+c     SPARSKIT test program for Variable Block Matrix Support
+c-----------------------------------------------------------------------
+c     This program tests all three conversion routines of csrvbr.
+c     For each conversion to VBR, the format is converted back to CSR
+c     with vbrcsr.  The subroutines csrkvstr, csrkvstc, and kvstmerge
+c     become tested in the process.  The subroutines vbrinfo and vbrmv 
+c     are also tested.
+c-----------------------------------------------------------------------
+      integer nxmax, nmx, nnzmax
+      parameter (nxmax = 10, nmx = nxmax*nxmax, nnzmax=10*nmx)
+      integer ia(nmx+1),ja(nnzmax),ia1(nnzmax),ja1(nnzmax), iwk(nmx*2+1)
+      real*8 stencil(7,100),a(nnzmax),a1(nnzmax)
+      integer ib(nmx+1),kvstr(nmx+1),kvstc(nmx+1),jb(nmx*10),kb(nmx*10)
+      real*8 b(nnzmax)
+      real*8 x(nmx),rhs(nmx),ans(nmx)
+      integer n, na, nx, ny, nz, nfree
+      integer nr, nc, i, job, maxblock, ierr
+      real*8 rnd
+c-----dimension of grid
+      nx = 4
+      ny = 2
+      nz = 1
+      nfree = 2
+c-----generate grid problem.
+      na = nfree*nfree
+      call gen57bl (nx,ny,nz,nfree,na,n,a1,ja1,ia1,iwk,stencil)
+c-----convert matrix to CSR
+      call bsrcsr (1,n,nfree,na,a1,ja1,ia1,a,ja,ia)
+      n = n * nfree 
+c     call dump(1, n, .true., a, ja, ia, 6)
+c-----generate random x vector for testing matrix-vector product
+      do i = 1, n
+         x(i) = rnd()
+      enddo
+c-----generate correct solution for matrix-vector product
+      call amux(n, x, ans, a, ja, ia)
+      do job = 0, 2
+         write (*,*) 'Testing job = ', job
+         if (job .eq. 0) then
+c-----------maximum blocksize for random block partitioning
+            maxblock = n/4
+c-----------generate random block partitioning for rows
+            nr = 1
+            kvstr(1) = 1
+ 2000       continue
+               nr = nr + 1
+               kvstr(nr) = kvstr(nr-1) + int(rnd()*maxblock)+1
+            if (kvstr(nr) .lt. n+1) goto 2000
+            kvstr(nr) = n+1
+            nr = nr - 1
+c-----------generate random block partitioning for columns
+            nc = 1
+            kvstc(1) = 1
+ 2010       continue
+               nc = nc + 1
+               kvstc(nc) = kvstc(nc-1) + int(rnd()*maxblock)+1
+            if (kvstc(nc) .lt. n+1) goto 2010
+            kvstc(nc) = n+1
+            nc = nc - 1
+         endif
+c--------convert to VBR format------------------------------------------
+         call csrvbr(n, ia, ja, a, nr, nc, kvstr, kvstc, ib, jb, kb,
+     &      b, job, iwk, nmx*10, nnzmax, ierr)
+c--------convert back to CSR format-------------------------------------
+         call vbrcsr(ia1, ja1, a1, nr, kvstr, kvstc, ib, jb, kb,
+     &      b, nnzmax, ierr)
+c--------compare original and converted CSR structures if job not 0
+         write (*,*) 'Checking conversions....'
+         if (job .ne. 0) then
+            do i = 1, n
+               if (ia(i) .ne. ia1(i)) then
+                  write (*,*) 'csrvbr or vbrcsr conversion mismatch'
+                  stop
+               endif
+            enddo
+            do i = 1, ia(n+1)-1
+               if ((ja(i) .ne. ja1(i)) .or. (a(i) .ne. a1(i))) then
+                  write (*,*) 'csrvbr or vbrcsr conversion mismatch'
+                  stop
+               endif
+            enddo
+         endif
+c--------test vbrinfo---------------------------------------------------
+         call vbrinfo(nr, nc, kvstr, kvstc, ib, jb, kb, iwk, 6)
+c--------test vbrmv-----------------------------------------------------
+         call vbrmv(nr, nc, ib, jb, kb, b, kvstr, kvstc, x, rhs)
+c--------compare answer with answer computed with CSR format
+         do i = 1, n
+            if (abs(ans(i) - rhs(i)) .gt. abs(0.001d0*ans(i))) then
+               write (*,*) 'VBR matrix-vector product is erroneous ',i
+               stop
+            endif
+         enddo
+c--------fill CSR structure with garbage
+         do i = 1, ia1(n+1)-1
+            ja1(i) = -1
+            a1(i) = -1.d0
+         enddo
+         do i = 1, n+1
+            ia1(i) = -1
+         enddo
+c--------fill VBR structure with garbage
+         do i = 1, kb(ib(nr+1))-1
+            b(i) = -1.d0
+         enddo
+         do i = 1, ib(nr+1)
+            jb(i) = -1
+            kb(i) = -1
+         enddo
+         do i = 1, nr+1
+            ib(i) = -1
+         enddo
+c--------fill kvstr and kvstc with garbage
+         do i = 1, nr+1
+            kvstr(i) = -1
+         enddo
+         do i = 1, nc+1
+            kvstc(i) = -1
+         enddo
+c--------fill rhs with garbage
+         do i = 1, n
+            rhs(i) = -1.d0
+         enddo
+c-----endloop on job
+      enddo
+      stop
+      end
+c-----------------------------------------------------------------------
+      function rnd()
+      real*8 rnd
+      integer im, ia, ic, jran
+      save jran
+      data im /6075/, ia /106/, ic /1283/, jran/1/
+      jran = mod(jran*ia+ic, im)
+      rnd = dble(jran)/dble(im)
+      return
+      end
+c-----------------------------------------------------------------------
+c     Coded by Edmond Chow, chow@cs.umn.edu
+c-----------------------------------------------------------------------
diff --git a/FORMATS/unary.f b/FORMATS/unary.f
new file mode 100644
index 0000000..00860c7
--- /dev/null
+++ b/FORMATS/unary.f
@@ -0,0 +1,3141 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c                     UNARY SUBROUTINES MODULE                         c
+c----------------------------------------------------------------------c
+c contents:                                                            c
+c----------                                                            c
+c submat : extracts a submatrix from a sparse matrix.                  c
+c filter : filters elements from a matrix according to their magnitude.c
+c filterm: same as above, but for the MSR format                       c
+c csort  : sorts the elements in increasing order of columns           c
+c clncsr : clean up the CSR format matrix, remove duplicate entry, etc c
+c transp : in-place transposition routine (see also csrcsc in formats) c
+c copmat : copy of a matrix into another matrix (both stored csr)      c
+c msrcop : copies a matrix in MSR format into a matrix in MSR format   c
+c getelm : returns a(i,j) for any (i,j) from a CSR-stored matrix.      c
+c getdia : extracts a specified diagonal from a matrix.                c
+c getl   : extracts lower triangular part                              c
+c getu   : extracts upper triangular part                              c
+c levels : gets the level scheduling structure for lower triangular    c
+c          matrices.                                                   c
+c amask  : extracts     C = A mask M                                   c
+c rperm  : permutes the rows of a matrix (B = P A)                     c
+c cperm  : permutes the columns of a matrix (B = A Q)                  c
+c dperm  : permutes both the rows and columns of a matrix (B = P A Q ) c
+c dperm1 : general extractiob routine (extracts arbitrary rows)        c
+c dperm2 : general submatrix permutation/extraction routine            c
+c dmperm : symmetric permutation of row and column (B=PAP') in MSR fmt c
+c dvperm : permutes a real vector (in-place)                           c
+c ivperm : permutes an integer vector (in-place)                       c
+c retmx  : returns the max absolute value in each row of the matrix    c
+c diapos : returns the positions of the diagonal elements in A.        c
+c extbdg : extracts the main diagonal blocks of a matrix.              c
+c getbwd : returns the bandwidth information on a matrix.              c
+c blkfnd : finds the block-size of a matrix.                           c
+c blkchk : checks whether a given integer is the block size of A.      c
+c infdia : obtains information on the diagonals of A.                  c
+c amubdg : gets number of nonzeros in each row of A*B (as well as NNZ) c 
+c aplbdg : gets number of nonzeros in each row of A+B (as well as NNZ) c
+c rnrms  : computes the norms of the rows of A                         c
+c cnrms  : computes the norms of the columns of A                      c
+c roscal : scales the rows of a matrix by their norms.                 c
+c coscal : scales the columns of a matrix by their norms.              c
+c addblk : Adds a matrix B into a block of A.                          c
+c get1up : Collects the first elements of each row of the upper        c
+c          triangular portion of the matrix.                           c
+c xtrows : extracts given rows from a matrix in CSR format.            c
+c csrkvstr:  Finds block row partitioning of matrix in CSR format      c
+c csrkvstc:  Finds block column partitioning of matrix in CSR format   c
+c kvstmerge: Merges block partitionings, for conformal row/col pattern c
+c----------------------------------------------------------------------c
+      subroutine submat (n,job,i1,i2,j1,j2,a,ja,ia,nr,nc,ao,jao,iao)
+      integer n,job,i1,i2,j1,j2,nr,nc,ia(*),ja(*),jao(*),iao(*)
+      real*8 a(*),ao(*) 
+c-----------------------------------------------------------------------
+c extracts the submatrix A(i1:i2,j1:j2) and puts the result in 
+c matrix ao,iao,jao
+c---- In place: ao,jao,iao may be the same as a,ja,ia.
+c-------------- 
+c on input
+c---------
+c n	= row dimension of the matrix 
+c i1,i2 = two integers with i2 .ge. i1 indicating the range of rows to be
+c          extracted. 
+c j1,j2 = two integers with j2 .ge. j1 indicating the range of columns 
+c         to be extracted.
+c         * There is no checking whether the input values for i1, i2, j1,
+c           j2 are between 1 and n. 
+c a,
+c ja,
+c ia    = matrix in compressed sparse row format. 
+c
+c job	= job indicator: if job .ne. 1 then the real values in a are NOT
+c         extracted, only the column indices (i.e. data structure) are.
+c         otherwise values as well as column indices are extracted...
+c         
+c on output
+c-------------- 
+c nr	= number of rows of submatrix 
+c nc	= number of columns of submatrix 
+c	  * if either of nr or nc is nonpositive the code will quit.
+c
+c ao,
+c jao,iao = extracted matrix in general sparse format with jao containing
+c	the column indices,and iao being the pointer to the beginning 
+c	of the row,in arrays a,ja.
+c----------------------------------------------------------------------c
+c           Y. Saad, Sep. 21 1989                                      c
+c----------------------------------------------------------------------c
+      nr = i2-i1+1
+      nc = j2-j1+1
+c     
+      if ( nr .le. 0 .or. nc .le. 0) return
+c     
+      klen = 0
+c     
+c     simple procedure. proceeds row-wise...
+c     
+      do 100 i = 1,nr
+         ii = i1+i-1
+         k1 = ia(ii)
+         k2 = ia(ii+1)-1
+         iao(i) = klen+1
+c-----------------------------------------------------------------------
+         do 60 k=k1,k2
+            j = ja(k)
+            if (j .ge. j1 .and. j .le. j2) then
+               klen = klen+1
+               if (job .eq. 1) ao(klen) = a(k)
+               jao(klen) = j - j1+1
+            endif
+ 60      continue
+ 100  continue
+      iao(nr+1) = klen+1
+      return
+c------------end-of submat---------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c-----------------------------------------------------------------------
+      subroutine filter(n,job,drptol,a,ja,ia,b,jb,ib,len,ierr)
+      real*8 a(*),b(*),drptol
+      integer ja(*),jb(*),ia(*),ib(*),n,job,len,ierr
+c-----------------------------------------------------------------------
+c     This module removes any elements whose absolute value
+c     is small from an input matrix A and puts the resulting
+c     matrix in B.  The input parameter job selects a definition
+c     of small.
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c  n	 = integer. row dimension of matrix
+c  job   = integer. used to determine strategy chosen by caller to
+c         drop elements from matrix A. 
+c          job = 1  
+c              Elements whose absolute value is less than the
+c              drop tolerance are removed.
+c          job = 2
+c              Elements whose absolute value is less than the 
+c              product of the drop tolerance and the Euclidean
+c              norm of the row are removed. 
+c          job = 3
+c              Elements whose absolute value is less that the
+c              product of the drop tolerance and the largest
+c              element in the row are removed.
+c 
+c drptol = real. drop tolerance used for dropping strategy.
+c a	
+c ja
+c ia     = input matrix in compressed sparse format
+c len	 = integer. the amount of space available in arrays b and jb.
+c
+c on return:
+c---------- 
+c b	
+c jb
+c ib    = resulting matrix in compressed sparse format. 
+c 
+c ierr	= integer. containing error message.
+c         ierr .eq. 0 indicates normal return
+c         ierr .gt. 0 indicates that there is'nt enough
+c         space is a and ja to store the resulting matrix.
+c         ierr then contains the row number where filter stopped.
+c note:
+c------ This module is in place. (b,jb,ib can ne the same as 
+c       a, ja, ia in which case the result will be overwritten).
+c----------------------------------------------------------------------c
+c           contributed by David Day,  Sep 19, 1989.                   c
+c----------------------------------------------------------------------c
+c local variables
+      real*8 norm,loctol
+      integer index,row,k,k1,k2 
+c
+      index = 1
+      do 10 row= 1,n
+         k1 = ia(row)
+         k2 = ia(row+1) - 1
+         ib(row) = index
+	 goto (100,200,300) job
+ 100     norm = 1.0d0
+         goto 400
+ 200     norm = 0.0d0
+         do 22 k = k1,k2
+            norm = norm + a(k) * a(k)
+ 22      continue
+         norm = sqrt(norm)
+         goto 400
+ 300     norm = 0.0d0
+         do 23 k = k1,k2
+            if( abs(a(k))  .gt. norm) then
+               norm = abs(a(k))
+            endif
+ 23      continue
+ 400     loctol = drptol * norm
+	 do 30 k = k1,k2
+	    if( abs(a(k)) .gt. loctol)then 
+               if (index .gt. len) then
+               ierr = row 
+               return
+            endif
+            b(index) =  a(k)
+            jb(index) = ja(k)
+            index = index + 1
+         endif
+ 30   continue
+ 10   continue
+      ib(n+1) = index
+      return
+c--------------------end-of-filter -------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine filterm (n,job,drop,a,ja,b,jb,len,ierr)
+      real*8 a(*),b(*),drop
+      integer ja(*),jb(*),n,job,len,ierr
+c-----------------------------------------------------------------------
+c     This subroutine removes any elements whose absolute value
+c     is small from an input matrix A. Same as filter but
+c     uses the MSR format.
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c  n	 = integer. row dimension of matrix
+c  job   = integer. used to determine strategy chosen by caller to
+c         drop elements from matrix A. 
+c          job = 1  
+c              Elements whose absolute value is less than the
+c              drop tolerance are removed.
+c          job = 2
+c              Elements whose absolute value is less than the 
+c              product of the drop tolerance and the Euclidean
+c              norm of the row are removed. 
+c          job = 3
+c              Elements whose absolute value is less that the
+c              product of the drop tolerance and the largest
+c              element in the row are removed.
+c 
+c drop = real. drop tolerance used for dropping strategy.
+c a	
+c ja     = input matrix in Modifief Sparse Row format
+c len	 = integer. the amount of space in arrays b and jb.
+c
+c on return:
+c---------- 
+c
+c b, jb = resulting matrix in Modifief Sparse Row format
+c 
+c ierr	= integer. containing error message.
+c         ierr .eq. 0 indicates normal return
+c         ierr .gt. 0 indicates that there is'nt enough
+c         space is a and ja to store the resulting matrix.
+c         ierr then contains the row number where filter stopped.
+c note:
+c------ This module is in place. (b,jb can ne the same as 
+c       a, ja in which case the result will be overwritten).
+c----------------------------------------------------------------------c
+c           contributed by David Day,  Sep 19, 1989.                   c
+c----------------------------------------------------------------------c
+c local variables
+c
+      real*8 norm,loctol
+      integer index,row,k,k1,k2 
+c
+      index = n+2
+      do 10 row= 1,n
+         k1 = ja(row)
+         k2 = ja(row+1) - 1
+         jb(row) = index
+	 goto (100,200,300) job
+ 100     norm = 1.0d0
+         goto 400
+ 200     norm = a(row)**2 
+         do 22 k = k1,k2
+            norm = norm + a(k) * a(k)
+ 22      continue
+         norm = sqrt(norm)
+         goto 400
+ 300     norm = abs(a(row)) 
+         do 23 k = k1,k2
+            norm = max(abs(a(k)),norm) 
+ 23      continue
+ 400     loctol = drop * norm
+	 do 30 k = k1,k2
+	    if( abs(a(k)) .gt. loctol)then 
+               if (index .gt. len) then
+                  ierr = row 
+                  return
+               endif
+               b(index) =  a(k)
+               jb(index) = ja(k)
+               index = index + 1
+            endif
+ 30      continue
+ 10   continue
+      jb(n+1) = index
+      return
+c--------------------end-of-filterm-------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine csort (n,a,ja,ia,iwork,values) 
+      logical values
+      integer n, ja(*), ia(n+1), iwork(*) 
+      real*8 a(*) 
+c-----------------------------------------------------------------------
+c This routine sorts the elements of  a matrix (stored in Compressed
+c Sparse Row Format) in increasing order of their column indices within 
+c each row. It uses a form of bucket sort with a cost of O(nnz) where
+c nnz = number of nonzero elements. 
+c requires an integer work array of length 2*nnz.  
+c-----------------------------------------------------------------------
+c on entry:
+c--------- 
+c n     = the row dimension of the matrix
+c a     = the matrix A in compressed sparse row format.
+c ja    = the array of column indices of the elements in array a.
+c ia    = the array of pointers to the rows. 
+c iwork = integer work array of length max ( m+1, 2*nnz ) 
+c         where m   = column dimension of the matrix
+c               nnz = (ia(n+1)-ia(1))
+c values= logical indicating whether or not the real values a(*) must 
+c         also be permuted. if (.not. values) then the array a is not
+c         touched by csort and can be a dummy array. 
+c 
+c on return:
+c----------
+c the matrix stored in the structure a, ja, ia is permuted in such a
+c way that the column indices are in increasing order within each row.
+c iwork(1:nnz) contains the permutation used  to rearrange the elements.
+c----------------------------------------------------------------------- 
+c Y. Saad - Feb. 1, 1991.
+c L. M. Baker - Oct. 15, 2009.  Correct computation of column pointers
+c                               for rectangular matrices 
+c-----------------------------------------------------------------------
+c local variables
+      integer i, k, j, m, ifirst, nnz, next  
+c
+c count the number of elements in each column
+c
+      m = 0
+      do 11 i=1, n
+         do 1 k=ia(i), ia(i+1)-1 
+            m = max( m, ja(k) )
+ 1       continue 
+ 11   continue
+      do 2 j=1,m
+         iwork(j+1) = 0
+ 2    continue
+      do 33 i=1, n
+         do 3 k=ia(i), ia(i+1)-1 
+            j = ja(k)
+            iwork(j+1) = iwork(j+1)+1
+ 3       continue 
+ 33   continue
+c
+c compute pointers from lengths. 
+c
+      iwork(1) = 1
+      do 4 i=1,m
+         iwork(i+1) = iwork(i) + iwork(i+1)
+ 4    continue
+c 
+c get the positions of the nonzero elements in order of columns.
+c
+      ifirst = ia(1) 
+      nnz = ia(n+1)-ifirst
+      do 5 i=1,n
+         do 51 k=ia(i),ia(i+1)-1 
+            j = ja(k) 
+            next = iwork(j)
+            iwork(nnz+next) = k
+            iwork(j) = next+1
+ 51      continue
+ 5    continue
+c
+c convert to coordinate format
+c 
+      do 6 i=1, n
+         do 61 k=ia(i), ia(i+1)-1 
+            iwork(k) = i
+ 61      continue
+ 6    continue
+c
+c loop to find permutation: for each element find the correct 
+c position in (sorted) arrays a, ja. Record this in iwork. 
+c 
+      do 7 k=1, nnz
+         ko = iwork(nnz+k) 
+         irow = iwork(ko)
+         next = ia(irow)
+c
+c the current element should go in next position in row. iwork
+c records this position. 
+c 
+         iwork(ko) = next
+         ia(irow)  = next+1
+ 7       continue
+c
+c perform an in-place permutation of the  arrays.
+c 
+         call ivperm (nnz, ja(ifirst), iwork) 
+         if (values) call dvperm (nnz, a(ifirst), iwork) 
+c
+c reshift the pointers of the original matrix back.
+c 
+      do 8 i=n,1,-1
+         ia(i+1) = ia(i)
+ 8    continue
+      ia(1) = ifirst 
+c
+      return 
+c---------------end-of-csort-------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+
+
+c-----------------------------------------------------------------------
+      subroutine clncsr(job,value2,nrow,a,ja,ia,indu,iwk)
+c     .. Scalar Arguments ..
+      integer job, nrow, value2
+c     ..
+c     .. Array Arguments ..
+      integer ia(nrow+1),indu(nrow),iwk(nrow+1),ja(*)
+      real*8  a(*)
+c     ..
+c
+c     This routine performs two tasks to clean up a CSR matrix
+c     -- remove duplicate/zero entries,
+c     -- perform a partial ordering, new order lower triangular part,
+c        main diagonal, upper triangular part.
+c
+c     On entry:
+c
+c     job   = options
+c         0 -- nothing is done
+c         1 -- eliminate duplicate entries, zero entries.
+c         2 -- eliminate duplicate entries and perform partial ordering.
+c         3 -- eliminate duplicate entries, sort the entries in the
+c              increasing order of clumn indices.
+c
+c     value2  -- 0 the matrix is pattern only (a is not touched)
+c                1 matrix has values too.
+c     nrow    -- row dimension of the matrix
+c     a,ja,ia -- input matrix in CSR format
+c
+c     On return:
+c     a,ja,ia -- cleaned matrix
+c     indu    -- pointers to the beginning of the upper triangular
+c                portion if job > 1
+c
+c     Work space:
+c     iwk     -- integer work space of size nrow+1
+c
+c     .. Local Scalars ..
+      integer i,j,k,ko,ipos,kfirst,klast
+      real*8  tmp
+c     ..
+c
+      if (job.le.0) return
+c
+c     .. eliminate duplicate entries --
+c     array INDU is used as marker for existing indices, it is also the
+c     location of the entry.
+c     IWK is used to stored the old IA array.
+c     matrix is copied to squeeze out the space taken by the duplicated
+c     entries.
+c
+      do 90 i = 1, nrow
+         indu(i) = 0
+         iwk(i) = ia(i)
+ 90   continue
+      iwk(nrow+1) = ia(nrow+1)
+      k = 1
+      do 120 i = 1, nrow
+         ia(i) = k
+         ipos = iwk(i)
+         klast = iwk(i+1)
+ 100     if (ipos.lt.klast) then
+            j = ja(ipos)
+            if (indu(j).eq.0) then
+c     .. new entry ..
+               if (value2.ne.0) then
+                  if (a(ipos) .ne. 0.0D0) then
+                     indu(j) = k
+                     ja(k) = ja(ipos)
+                     a(k) = a(ipos)
+                     k = k + 1
+                  endif
+               else
+                  indu(j) = k
+                  ja(k) = ja(ipos)
+                  k = k + 1
+               endif
+            else if (value2.ne.0) then
+c     .. duplicate entry ..
+               a(indu(j)) = a(indu(j)) + a(ipos)
+            endif
+            ipos = ipos + 1
+            go to 100
+         endif
+c     .. remove marks before working on the next row ..
+         do 110 ipos = ia(i), k - 1
+            indu(ja(ipos)) = 0
+ 110     continue
+ 120  continue
+      ia(nrow+1) = k
+      if (job.le.1) return
+c
+c     .. partial ordering ..
+c     split the matrix into strict upper/lower triangular
+c     parts, INDU points to the the beginning of the upper part.
+c
+      do 140 i = 1, nrow
+         klast = ia(i+1) - 1
+         kfirst = ia(i)
+ 130     if (klast.gt.kfirst) then
+            if (ja(klast).lt.i .and. ja(kfirst).ge.i) then
+c     .. swap klast with kfirst ..
+               j = ja(klast)
+               ja(klast) = ja(kfirst)
+               ja(kfirst) = j
+               if (value2.ne.0) then
+                  tmp = a(klast)
+                  a(klast) = a(kfirst)
+                  a(kfirst) = tmp
+               endif
+            endif
+            if (ja(klast).ge.i)
+     &         klast = klast - 1
+            if (ja(kfirst).lt.i)
+     &         kfirst = kfirst + 1
+            go to 130
+         endif
+c
+         if (ja(klast).lt.i) then
+            indu(i) = klast + 1
+         else
+            indu(i) = klast
+         endif
+ 140  continue
+      if (job.le.2) return
+c
+c     .. order the entries according to column indices
+c     burble-sort is used
+c
+      do 190 i = 1, nrow
+         do 160 ipos = ia(i), indu(i)-1
+            do 150 j = indu(i)-1, ipos+1, -1
+               k = j - 1
+               if (ja(k).gt.ja(j)) then
+                  ko = ja(k)
+                  ja(k) = ja(j)
+                  ja(j) = ko
+                  if (value2.ne.0) then
+                     tmp = a(k)
+                     a(k) = a(j)
+                     a(j) = tmp
+                  endif
+               endif
+ 150        continue
+ 160     continue
+         do 180 ipos = indu(i), ia(i+1)-1
+            do 170 j = ia(i+1)-1, ipos+1, -1
+               k = j - 1
+               if (ja(k).gt.ja(j)) then
+                  ko = ja(k)
+                  ja(k) = ja(j)
+                  ja(j) = ko
+                  if (value2.ne.0) then
+                     tmp = a(k)
+                     a(k) = a(j)
+                     a(j) = tmp
+                  endif
+               endif
+ 170        continue
+ 180     continue
+ 190  continue
+      return
+c---- end of clncsr ----------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine copmat (nrow,a,ja,ia,ao,jao,iao,ipos,job) 
+      real*8 a(*),ao(*) 
+      integer nrow, ia(*),ja(*),jao(*),iao(*), ipos, job 
+c----------------------------------------------------------------------
+c copies the matrix a, ja, ia, into the matrix ao, jao, iao. 
+c----------------------------------------------------------------------
+c on entry:
+c---------
+c nrow	= row dimension of the matrix 
+c a,
+c ja,
+c ia    = input matrix in compressed sparse row format. 
+c ipos  = integer. indicates the position in the array ao, jao
+c         where the first element should be copied. Thus 
+c         iao(1) = ipos on return. 
+c job   = job indicator. if (job .ne. 1) the values are not copies 
+c         (i.e., pattern only is copied in the form of arrays ja, ia).
+c
+c on return:
+c----------
+c ao,
+c jao,
+c iao   = output matrix containing the same data as a, ja, ia.
+c-----------------------------------------------------------------------
+c           Y. Saad, March 1990. 
+c-----------------------------------------------------------------------
+c local variables
+      integer kst, i, k 
+c
+      kst    = ipos -ia(1) 
+      do 100 i = 1, nrow+1
+         iao(i) = ia(i) + kst
+ 100  continue
+c     
+      do 200 k=ia(1), ia(nrow+1)-1
+         jao(kst+k)= ja(k)
+ 200  continue
+c
+      if (job .ne. 1) return
+      do 201 k=ia(1), ia(nrow+1)-1
+         ao(kst+k) = a(k)
+ 201  continue
+c
+      return
+c--------end-of-copmat -------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine msrcop (nrow,a,ja,ao,jao,job) 
+      real*8 a(*),ao(*) 
+      integer nrow, ja(*),jao(*), job 
+c----------------------------------------------------------------------
+c copies the MSR matrix a, ja, into the MSR matrix ao, jao 
+c----------------------------------------------------------------------
+c on entry:
+c---------
+c nrow	= row dimension of the matrix 
+c a,ja  = input matrix in Modified compressed sparse row format. 
+c job   = job indicator. Values are not copied if job .ne. 1 
+c       
+c on return:
+c----------
+c ao, jao   = output matrix containing the same data as a, ja.
+c-----------------------------------------------------------------------
+c           Y. Saad, 
+c-----------------------------------------------------------------------
+c local variables
+      integer i, k 
+c
+      do 100 i = 1, nrow+1
+         jao(i) = ja(i) 
+ 100  continue
+c     
+      do 200 k=ja(1), ja(nrow+1)-1
+         jao(k)= ja(k)
+ 200  continue
+c
+      if (job .ne. 1) return
+      do 201 k=ja(1), ja(nrow+1)-1
+         ao(k) = a(k)
+ 201  continue
+      do 202 k=1,nrow
+         ao(k) = a(k)
+ 202  continue
+c
+      return
+c--------end-of-msrcop -------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      double precision function getelm (i,j,a,ja,ia,iadd,sorted) 
+c-----------------------------------------------------------------------
+c     purpose:
+c     -------- 
+c     this function returns the element a(i,j) of a matrix a, 
+c     for any pair (i,j).  the matrix is assumed to be stored 
+c     in compressed sparse row (csr) format. getelm performs a
+c     binary search in the case where it is known that the elements 
+c     are sorted so that the column indices are in increasing order. 
+c     also returns (in iadd) the address of the element a(i,j) in 
+c     arrays a and ja when the search is successsful (zero if not).
+c----- 
+c     first contributed by noel nachtigal (mit). 
+c     recoded jan. 20, 1991, by y. saad [in particular
+c     added handling of the non-sorted case + the iadd output] 
+c-----------------------------------------------------------------------
+c     parameters:
+c     ----------- 
+c on entry: 
+c---------- 
+c     i      = the row index of the element sought (input).
+c     j      = the column index of the element sought (input).
+c     a      = the matrix a in compressed sparse row format (input).
+c     ja     = the array of column indices (input).
+c     ia     = the array of pointers to the rows' data (input).
+c     sorted = logical indicating whether the matrix is knonw to 
+c              have its column indices sorted in increasing order 
+c              (sorted=.true.) or not (sorted=.false.).
+c              (input). 
+c on return:
+c----------- 
+c     getelm = value of a(i,j). 
+c     iadd   = address of element a(i,j) in arrays a, ja if found,
+c              zero if not found. (output) 
+c
+c     note: the inputs i and j are not checked for validity. 
+c-----------------------------------------------------------------------
+c     noel m. nachtigal october 28, 1990 -- youcef saad jan 20, 1991.
+c----------------------------------------------------------------------- 
+      integer i, ia(*), iadd, j, ja(*)
+      double precision a(*)
+      logical sorted 
+c
+c     local variables.
+c
+      integer ibeg, iend, imid, k
+c
+c     initialization 
+c
+      iadd = 0 
+      getelm = 0.0
+      ibeg = ia(i)
+      iend = ia(i+1)-1
+c
+c     case where matrix is not necessarily sorted
+c     
+      if (.not. sorted) then 
+c
+c scan the row - exit as soon as a(i,j) is found
+c
+         do 5  k=ibeg, iend
+            if (ja(k) .eq.  j) then
+               iadd = k 
+               goto 20 
+            endif
+ 5       continue
+c     
+c     end unsorted case. begin sorted case
+c     
+      else
+c     
+c     begin binary search.   compute the middle index.
+c     
+ 10      imid = ( ibeg + iend ) / 2
+c     
+c     test if  found
+c     
+         if (ja(imid).eq.j) then
+            iadd = imid 
+            goto 20
+         endif
+         if (ibeg .ge. iend) goto 20
+c     
+c     else     update the interval bounds. 
+c     
+         if (ja(imid).gt.j) then
+            iend = imid -1
+         else 
+            ibeg = imid +1
+         endif
+         goto 10  
+c     
+c     end both cases
+c     
+      endif
+c     
+ 20   if (iadd .ne. 0) getelm = a(iadd) 
+c
+      return
+c--------end-of-getelm--------------------------------------------------
+c-----------------------------------------------------------------------
+      end 
+c-----------------------------------------------------------------------
+      subroutine getdia (nrow,ncol,job,a,ja,ia,len,diag,idiag,ioff)
+      real*8 diag(*),a(*)
+      integer nrow, ncol, job, len, ioff, ia(*), ja(*), idiag(*)
+c-----------------------------------------------------------------------
+c this subroutine extracts a given diagonal from a matrix stored in csr 
+c format. the output matrix may be transformed with the diagonal removed
+c from it if desired (as indicated by job.) 
+c----------------------------------------------------------------------- 
+c our definition of a diagonal of matrix is a vector of length nrow
+c (always) which contains the elements in rows 1 to nrow of
+c the matrix that are contained in the diagonal offset by ioff
+c with respect to the main diagonal. if the diagonal element
+c falls outside the matrix then it is defined as a zero entry.
+c thus the proper definition of diag(*) with offset ioff is 
+c
+c     diag(i) = a(i,ioff+i) i=1,2,...,nrow
+c     with elements falling outside the matrix being defined as zero.
+c 
+c----------------------------------------------------------------------- 
+c 
+c on entry:
+c---------- 
+c
+c nrow	= integer. the row dimension of the matrix a.
+c ncol	= integer. the column dimension of the matrix a.
+c job   = integer. job indicator.  if job = 0 then
+c         the matrix a, ja, ia, is not altered on return.
+c         if job.ne.0  then getdia will remove the entries
+c         collected in diag from the original matrix.
+c         this is done in place.
+c
+c a,ja,
+c    ia = matrix stored in compressed sparse row a,ja,ia,format
+c ioff  = integer,containing the offset of the wanted diagonal
+c	  the diagonal extracted is the one corresponding to the
+c	  entries a(i,j) with j-i = ioff.
+c	  thus ioff = 0 means the main diagonal
+c
+c on return:
+c----------- 
+c len   = number of nonzero elements found in diag.
+c         (len .le. min(nrow,ncol-ioff)-max(1,1-ioff) + 1 )
+c
+c diag  = real*8 array of length nrow containing the wanted diagonal.
+c	  diag contains the diagonal (a(i,j),j-i = ioff ) as defined 
+c         above. 
+c
+c idiag = integer array of  length len, containing the poisitions 
+c         in the original arrays a and ja of the diagonal elements
+c         collected in diag. a zero entry in idiag(i) means that 
+c         there was no entry found in row i belonging to the diagonal.
+c         
+c a, ja,
+c    ia = if job .ne. 0 the matrix is unchanged. otherwise the nonzero
+c         diagonal entries collected in diag are removed from the 
+c         matrix and therefore the arrays a, ja, ia will change.
+c	  (the matrix a, ja, ia will contain len fewer elements) 
+c 
+c----------------------------------------------------------------------c
+c     Y. Saad, sep. 21 1989 - modified and retested Feb 17, 1996.      c 
+c----------------------------------------------------------------------c
+c     local variables
+      integer istart, max, iend, i, kold, k, kdiag, ko
+c     
+      istart = max(0,-ioff)
+      iend = min(nrow,ncol-ioff)
+      len = 0
+      do 1 i=1,nrow
+         idiag(i) = 0
+	 diag(i) = 0.0d0 
+ 1    continue
+c     
+c     extract  diagonal elements
+c     
+      do 6 i=istart+1, iend
+         do 51 k= ia(i),ia(i+1) -1
+            if (ja(k)-i .eq. ioff) then
+               diag(i)= a(k)
+               idiag(i) = k
+               len = len+1
+               goto 6
+            endif
+ 51      continue
+ 6    continue
+      if (job .eq. 0 .or. len .eq.0) return
+c
+c     remove diagonal elements and rewind structure
+c 
+      ko = 0
+      do  7 i=1, nrow 
+         kold = ko
+         kdiag = idiag(i) 
+         do 71 k= ia(i), ia(i+1)-1 
+            if (k .ne. kdiag) then
+               ko = ko+1
+               a(ko) = a(k)
+               ja(ko) = ja(k)
+            endif
+ 71      continue
+         ia(i) = kold+1
+ 7    continue
+c
+c     redefine ia(nrow+1)
+c
+      ia(nrow+1) = ko+1
+      return
+c------------end-of-getdia----------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine transp (nrow,ncol,a,ja,ia,iwk,ierr)
+      integer nrow, ncol, ia(*), ja(*), iwk(*), ierr
+      real*8 a(*) 
+c------------------------------------------------------------------------
+c In-place transposition routine.
+c------------------------------------------------------------------------
+c this subroutine transposes a matrix stored in compressed sparse row 
+c format. the transposition is done in place in that the arrays a,ja,ia
+c of the transpose are overwritten onto the original arrays.
+c------------------------------------------------------------------------
+c on entry:
+c--------- 
+c nrow	= integer. The row dimension of A.
+c ncol	= integer. The column dimension of A.
+c a	= real array of size nnz (number of nonzero elements in A).
+c         containing the nonzero elements 
+c ja	= integer array of length nnz containing the column positions
+c 	  of the corresponding elements in a.
+c ia	= integer of size n+1, where n = max(nrow,ncol). On entry
+c         ia(k) contains the position in a,ja of  the beginning of 
+c         the k-th row.
+c
+c iwk	= integer work array of same length as ja.
+c
+c on return:
+c----------
+c
+c ncol	= actual row dimension of the transpose of the input matrix.
+c         Note that this may be .le. the input value for ncol, in
+c         case some of the last columns of the input matrix are zero
+c         columns. In the case where the actual number of rows found
+c         in transp(A) exceeds the input value of ncol, transp will
+c         return without completing the transposition. see ierr.
+c a,
+c ja,
+c ia	= contains the transposed matrix in compressed sparse
+c         row format. The row dimension of a, ja, ia is now ncol.
+c
+c ierr	= integer. error message. If the number of rows for the
+c         transposed matrix exceeds the input value of ncol,
+c         then ierr is  set to that number and transp quits.
+c         Otherwise ierr is set to 0 (normal return).
+c
+c Note: 
+c----- 1) If you do not need the transposition to be done in place
+c         it is preferrable to use the conversion routine csrcsc 
+c         (see conversion routines in formats).
+c      2) the entries of the output matrix are not sorted (the column
+c         indices in each are not in increasing order) use csrcsc
+c         if you want them sorted.
+c----------------------------------------------------------------------c
+c           Y. Saad, Sep. 21 1989                                      c
+c  modified Oct. 11, 1989.                                             c
+c----------------------------------------------------------------------c
+c local variables
+      real*8 t, t1
+      ierr = 0
+      nnz = ia(nrow+1)-1
+c
+c     determine column dimension
+c
+      jcol = 0
+      do 1 k=1, nnz
+         jcol = max(jcol,ja(k))
+ 1    continue
+      if (jcol .gt. ncol) then
+         ierr = jcol
+         return
+      endif
+c     
+c     convert to coordinate format. use iwk for row indices.
+c     
+      ncol = jcol
+c     
+      do 3 i=1,nrow
+         do 2 k=ia(i),ia(i+1)-1
+            iwk(k) = i
+ 2       continue 
+ 3    continue
+c     find pointer array for transpose. 
+      do 35 i=1,ncol+1
+         ia(i) = 0
+ 35   continue
+      do 4 k=1,nnz
+         i = ja(k)
+         ia(i+1) = ia(i+1)+1
+ 4    continue 
+      ia(1) = 1 
+c------------------------------------------------------------------------
+      do 44 i=1,ncol
+         ia(i+1) = ia(i) + ia(i+1)
+ 44   continue 
+c     
+c     loop for a cycle in chasing process. 
+c     
+      init = 1
+      k = 0
+ 5    t = a(init)
+      i = ja(init)
+      j = iwk(init)
+      iwk(init) = -1
+c------------------------------------------------------------------------
+ 6    k = k+1 		
+c     current row number is i.  determine  where to go. 
+      l = ia(i)
+c     save the chased element. 
+      t1 = a(l)
+      inext = ja(l)
+c     then occupy its location.
+      a(l)  = t
+      ja(l) = j
+c     update pointer information for next element to be put in row i. 
+      ia(i) = l+1
+c     determine  next element to be chased
+      if (iwk(l) .lt. 0) goto 65
+      t = t1
+      i = inext
+      j = iwk(l)
+      iwk(l) = -1
+      if (k .lt. nnz) goto 6
+      goto 70
+ 65   init = init+1
+      if (init .gt. nnz) goto 70
+      if (iwk(init) .lt. 0) goto 65
+c     restart chasing --	
+      goto 5
+ 70   continue
+      do 80 i=ncol,1,-1 
+         ia(i+1) = ia(i)
+ 80   continue
+      ia(1) = 1
+c
+      return
+c------------------end-of-transp ----------------------------------------
+c------------------------------------------------------------------------
+      end 
+c------------------------------------------------------------------------ 
+      subroutine getl (n,a,ja,ia,ao,jao,iao)
+      integer n, ia(*), ja(*), iao(*), jao(*)
+      real*8 a(*), ao(*)
+c------------------------------------------------------------------------
+c this subroutine extracts the lower triangular part of a matrix 
+c and writes the result ao, jao, iao. The routine is in place in
+c that ao, jao, iao can be the same as a, ja, ia if desired.
+c-----------
+c on input:
+c
+c n     = dimension of the matrix a.
+c a, ja, 
+c    ia = matrix stored in compressed sparse row format.
+c On return:
+c ao, jao, 
+c    iao = lower triangular matrix (lower part of a) 
+c	stored in a, ja, ia, format
+c note: the diagonal element is the last element in each row.
+c i.e. in  a(ia(i+1)-1 ) 
+c ao, jao, iao may be the same as a, ja, ia on entry -- in which case
+c getl will overwrite the result on a, ja, ia.
+c
+c------------------------------------------------------------------------
+c local variables
+      real*8 t
+      integer ko, kold, kdiag, k, i
+c
+c inititialize ko (pointer for output matrix)
+c
+      ko = 0
+      do  7 i=1, n
+         kold = ko
+         kdiag = 0
+         do 71 k = ia(i), ia(i+1) -1
+            if (ja(k)  .gt. i) goto 71
+            ko = ko+1
+            ao(ko) = a(k)
+            jao(ko) = ja(k)
+            if (ja(k)  .eq. i) kdiag = ko
+ 71      continue
+         if (kdiag .eq. 0 .or. kdiag .eq. ko) goto 72
+c
+c     exchange
+c
+         t = ao(kdiag)
+         ao(kdiag) = ao(ko)
+         ao(ko) = t
+c     
+         k = jao(kdiag)
+         jao(kdiag) = jao(ko)
+         jao(ko) = k
+ 72      iao(i) = kold+1
+ 7    continue
+c     redefine iao(n+1)
+      iao(n+1) = ko+1
+      return
+c----------end-of-getl ------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine getu (n,a,ja,ia,ao,jao,iao)
+      integer n, ia(*), ja(*), iao(*), jao(*)
+      real*8 a(*), ao(*)
+c------------------------------------------------------------------------
+c this subroutine extracts the upper triangular part of a matrix 
+c and writes the result ao, jao, iao. The routine is in place in
+c that ao, jao, iao can be the same as a, ja, ia if desired.
+c-----------
+c on input:
+c
+c n     = dimension of the matrix a.
+c a, ja, 
+c    ia = matrix stored in a, ja, ia, format
+c On return:
+c ao, jao, 
+c    iao = upper triangular matrix (upper part of a) 
+c	stored in compressed sparse row format
+c note: the diagonal element is the last element in each row.
+c i.e. in  a(ia(i+1)-1 ) 
+c ao, jao, iao may be the same as a, ja, ia on entry -- in which case
+c getu will overwrite the result on a, ja, ia.
+c
+c------------------------------------------------------------------------
+c local variables
+      real*8 t 
+      integer ko, k, i, kdiag, kfirst 
+      ko = 0
+      do  7 i=1, n
+         kfirst = ko+1
+         kdiag = 0
+         do 71 k = ia(i), ia(i+1) -1
+            if (ja(k)  .lt. i) goto 71
+            ko = ko+1
+            ao(ko) = a(k)
+            jao(ko) = ja(k)
+            if (ja(k)  .eq. i) kdiag = ko
+ 71      continue
+         if (kdiag .eq. 0 .or. kdiag .eq. kfirst) goto 72
+c     exchange
+         t = ao(kdiag)
+         ao(kdiag) = ao(kfirst)
+         ao(kfirst) = t
+c     
+         k = jao(kdiag)
+         jao(kdiag) = jao(kfirst)
+         jao(kfirst) = k
+ 72      iao(i) = kfirst
+ 7    continue
+c     redefine iao(n+1)
+      iao(n+1) = ko+1
+      return
+c----------end-of-getu ------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine levels (n, jal, ial, nlev, lev, ilev, levnum)
+      integer jal(*),ial(*), levnum(*), ilev(*), lev(*) 
+c-----------------------------------------------------------------------
+c levels gets the level structure of a lower triangular matrix 
+c for level scheduling in the parallel solution of triangular systems
+c strict lower matrices (e.g. unit) as well matrices with their main 
+c diagonal are accepted. 
+c-----------------------------------------------------------------------
+c on entry:
+c----------
+c n        = integer. The row dimension of the matrix
+c jal, ial = 
+c 
+c on return:
+c-----------
+c nlev     = integer. number of levels found
+c lev      = integer array of length n containing the level
+c            scheduling permutation.
+c ilev     = integer array. pointer to beginning of levels in lev.
+c            the numbers lev(i) to lev(i+1)-1 contain the row numbers
+c            that belong to level number i, in the level scheduling
+c            ordering. The equations of the same level can be solved
+c            in parallel, once those of all the previous levels have
+c            been solved.
+c work arrays:
+c-------------
+c levnum   = integer array of length n (containing the level numbers
+c            of each unknown on return)
+c-----------------------------------------------------------------------
+      do 10 i = 1, n
+         levnum(i) = 0
+ 10   continue
+c
+c     compute level of each node --
+c
+      nlev = 0
+      do 20 i = 1, n
+         levi = 0
+         do 15 j = ial(i), ial(i+1) - 1
+            levi = max (levi, levnum(jal(j)))
+ 15      continue
+         levi = levi+1 
+         levnum(i) = levi 
+         nlev = max(nlev,levi) 
+ 20   continue
+c-------------set data structure  --------------------------------------
+      do 21 j=1, nlev+1
+         ilev(j) = 0
+ 21   continue
+c------count  number   of elements in each level ----------------------- 
+      do 22 j=1, n
+         i = levnum(j)+1
+         ilev(i) = ilev(i)+1
+ 22   continue
+c---- set up pointer for  each  level ---------------------------------- 
+      ilev(1) = 1
+      do 23 j=1, nlev
+         ilev(j+1) = ilev(j)+ilev(j+1)
+ 23   continue
+c-----determine elements of each level -------------------------------- 
+      do 30 j=1,n
+         i = levnum(j)
+         lev(ilev(i)) = j
+         ilev(i) = ilev(i)+1
+ 30   continue
+c     reset pointers backwards
+      do 35 j=nlev, 1, -1
+         ilev(j+1) = ilev(j) 
+ 35   continue
+      ilev(1) = 1
+      return
+c----------end-of-levels------------------------------------------------ 
+C-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine amask (nrow,ncol,a,ja,ia,jmask,imask,
+     *                  c,jc,ic,iw,nzmax,ierr)
+c---------------------------------------------------------------------
+      real*8 a(*),c(*) 
+      integer ia(nrow+1),ja(*),jc(*),ic(nrow+1),jmask(*),imask(nrow+1) 
+      logical iw(ncol)
+c-----------------------------------------------------------------------
+c This subroutine builds a sparse matrix from an input matrix by 
+c extracting only elements in positions defined by the mask jmask, imask
+c-----------------------------------------------------------------------
+c On entry:
+c---------
+c nrow  = integer. row dimension of input matrix 
+c ncol	= integer. Column dimension of input matrix.
+c
+c a,
+c ja,
+c ia	= matrix in Compressed Sparse Row format
+c
+c jmask,
+c imask = matrix defining mask (pattern only) stored in compressed
+c         sparse row format.
+c
+c nzmax = length of arrays c and jc. see ierr.
+c 
+c On return:
+c-----------
+c
+c a, ja, ia and jmask, imask are unchanged.
+c
+c c
+c jc, 
+c ic	= the output matrix in Compressed Sparse Row format.
+c 
+c ierr  = integer. serving as error message.c
+c         ierr = 1  means normal return
+c         ierr .gt. 1 means that amask stopped when processing
+c         row number ierr, because there was not enough space in
+c         c, jc according to the value of nzmax.
+c
+c work arrays:
+c------------- 
+c iw	= logical work array of length ncol.
+c
+c note: 
+c------ the  algorithm is in place: c, jc, ic can be the same as 
+c a, ja, ia in which cas the code will overwrite the matrix c
+c on a, ja, ia
+c
+c-----------------------------------------------------------------------
+      ierr = 0
+      len = 0
+      do 1 j=1, ncol
+         iw(j) = .false.
+ 1    continue
+c     unpack the mask for row ii in iw
+      do 100 ii=1, nrow
+c     save pointer in order to be able to do things in place
+         do 2 k=imask(ii), imask(ii+1)-1
+            iw(jmask(k)) = .true.
+ 2       continue
+c     add umasked elemnts of row ii
+         k1 = ia(ii)
+         k2 = ia(ii+1)-1
+         ic(ii) = len+1
+         do 200 k=k1,k2 
+            j = ja(k)
+            if (iw(j)) then
+               len = len+1
+               if (len .gt. nzmax) then
+                  ierr = ii
+                  return
+               endif
+               jc(len) = j
+               c(len) = a(k)
+            endif
+ 200     continue	      
+c     
+         do 3 k=imask(ii), imask(ii+1)-1
+            iw(jmask(k)) = .false.
+ 3       continue
+ 100  continue	  
+      ic(nrow+1)=len+1
+c
+      return
+c-----end-of-amask -----------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine rperm (nrow,a,ja,ia,ao,jao,iao,perm,job)
+      integer nrow,ja(*),ia(nrow+1),jao(*),iao(nrow+1),perm(nrow),job
+      real*8 a(*),ao(*) 
+c-----------------------------------------------------------------------
+c this subroutine permutes the rows of a matrix in CSR format. 
+c rperm  computes B = P A  where P is a permutation matrix.  
+c the permutation P is defined through the array perm: for each j, 
+c perm(j) represents the destination row number of row number j. 
+c Youcef Saad -- recoded Jan 28, 1991.
+c-----------------------------------------------------------------------
+c on entry:
+c----------
+c n 	= dimension of the matrix
+c a, ja, ia = input matrix in csr format
+c perm 	= integer array of length nrow containing the permutation arrays
+c	  for the rows: perm(i) is the destination of row i in the
+c         permuted matrix. 
+c         ---> a(i,j) in the original matrix becomes a(perm(i),j) 
+c         in the output  matrix.
+c
+c job	= integer indicating the work to be done:
+c 		job = 1	permute a, ja, ia into ao, jao, iao 
+c                       (including the copying of real values ao and
+c                       the array iao).
+c 		job .ne. 1 :  ignore real values.
+c                     (in which case arrays a and ao are not needed nor
+c                      used).
+c
+c------------
+c on return: 
+c------------ 
+c ao, jao, iao = input matrix in a, ja, ia format
+c note : 
+c        if (job.ne.1)  then the arrays a and ao are not used.
+c----------------------------------------------------------------------c
+c           Y. Saad, May  2, 1990                                      c
+c----------------------------------------------------------------------c
+      logical values
+      values = (job .eq. 1) 
+c     
+c     determine pointers for output matix. 
+c     
+      do 50 j=1,nrow
+         i = perm(j)
+         iao(i+1) = ia(j+1) - ia(j)
+ 50   continue
+c
+c get pointers from lengths
+c
+      iao(1) = 1
+      do 51 j=1,nrow
+         iao(j+1)=iao(j+1)+iao(j)
+ 51   continue
+c
+c copying 
+c
+      do 100 ii=1,nrow
+c
+c old row = ii  -- new row = iperm(ii) -- ko = new pointer
+c        
+         ko = iao(perm(ii)) 
+         do 60 k=ia(ii), ia(ii+1)-1 
+            jao(ko) = ja(k) 
+            if (values) ao(ko) = a(k)
+            ko = ko+1
+ 60      continue
+ 100  continue
+c
+      return
+c---------end-of-rperm ------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine cperm (nrow,a,ja,ia,ao,jao,iao,perm,job) 
+      integer nrow,ja(*),ia(nrow+1),jao(*),iao(nrow+1),perm(*), job
+      real*8 a(*), ao(*) 
+c-----------------------------------------------------------------------
+c this subroutine permutes the columns of a matrix a, ja, ia.
+c the result is written in the output matrix  ao, jao, iao.
+c cperm computes B = A P, where  P is a permutation matrix
+c that maps column j into column perm(j), i.e., on return 
+c      a(i,j) becomes a(i,perm(j)) in new matrix 
+c Y. Saad, May 2, 1990 / modified Jan. 28, 1991. 
+c-----------------------------------------------------------------------
+c on entry:
+c----------
+c nrow 	= row dimension of the matrix
+c
+c a, ja, ia = input matrix in csr format. 
+c
+c perm	= integer array of length ncol (number of columns of A
+c         containing the permutation array  the columns: 
+c         a(i,j) in the original matrix becomes a(i,perm(j))
+c         in the output matrix.
+c
+c job	= integer indicating the work to be done:
+c 		job = 1	permute a, ja, ia into ao, jao, iao 
+c                       (including the copying of real values ao and
+c                       the array iao).
+c 		job .ne. 1 :  ignore real values ao and ignore iao.
+c
+c------------
+c on return: 
+c------------ 
+c ao, jao, iao = input matrix in a, ja, ia format (array ao not needed)
+c
+c Notes:
+c------- 
+c 1. if job=1 then ao, iao are not used.
+c 2. This routine is in place: ja, jao can be the same. 
+c 3. If the matrix is initially sorted (by increasing column number) 
+c    then ao,jao,iao  may not be on return. 
+c 
+c----------------------------------------------------------------------c
+c local parameters:
+      integer k, i, nnz
+c
+      nnz = ia(nrow+1)-1
+      do 100 k=1,nnz
+         jao(k) = perm(ja(k)) 
+ 100  continue
+c
+c     done with ja array. return if no need to touch values.
+c
+      if (job .ne. 1) return
+c
+c else get new pointers -- and copy values too.
+c 
+      do 1 i=1, nrow+1
+         iao(i) = ia(i)
+ 1    continue
+c
+      do 2 k=1, nnz
+         ao(k) = a(k)
+ 2    continue
+c
+      return
+c---------end-of-cperm-------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine dperm (nrow,a,ja,ia,ao,jao,iao,perm,qperm,job)
+      integer nrow,ja(*),ia(nrow+1),jao(*),iao(nrow+1),perm(nrow),
+     +        qperm(*),job
+      real*8 a(*),ao(*) 
+c-----------------------------------------------------------------------
+c This routine permutes the rows and columns of a matrix stored in CSR
+c format. i.e., it computes P A Q, where P, Q are permutation matrices. 
+c P maps row i into row perm(i) and Q maps column j into column qperm(j): 
+c      a(i,j)    becomes   a(perm(i),qperm(j)) in new matrix
+c In the particular case where Q is the transpose of P (symmetric 
+c permutation of A) then qperm is not needed. 
+c note that qperm should be of length ncol (number of columns) but this
+c is not checked. 
+c-----------------------------------------------------------------------
+c Y. Saad, Sep. 21 1989 / recoded Jan. 28 1991. 
+c-----------------------------------------------------------------------
+c on entry: 
+c---------- 
+c n 	= dimension of the matrix
+c a, ja, 
+c    ia = input matrix in a, ja, ia format
+c perm 	= integer array of length n containing the permutation arrays
+c	  for the rows: perm(i) is the destination of row i in the
+c         permuted matrix -- also the destination of column i in case
+c         permutation is symmetric (job .le. 2) 
+c
+c qperm	= same thing for the columns. This should be provided only
+c         if job=3 or job=4, i.e., only in the case of a nonsymmetric
+c	  permutation of rows and columns. Otherwise qperm is a dummy
+c
+c job	= integer indicating the work to be done:
+c * job = 1,2 permutation is symmetric  Ao :== P * A * transp(P)
+c 		job = 1	permute a, ja, ia into ao, jao, iao 
+c 		job = 2 permute matrix ignoring real values.
+c * job = 3,4 permutation is non-symmetric  Ao :== P * A * Q 
+c 		job = 3	permute a, ja, ia into ao, jao, iao 
+c 		job = 4 permute matrix ignoring real values.
+c		
+c on return: 
+c-----------
+c ao, jao, iao = input matrix in a, ja, ia format
+c
+c in case job .eq. 2 or job .eq. 4, a and ao are never referred to 
+c and can be dummy arguments. 
+c Notes:
+c------- 
+c  1) algorithm is in place 
+c  2) column indices may not be sorted on return even  though they may be 
+c     on entry.
+c----------------------------------------------------------------------c
+c local variables 
+      integer locjob, mod
+c
+c     locjob indicates whether or not real values must be copied. 
+c     
+      locjob = mod(job,2) 
+c
+c permute rows first 
+c 
+      call rperm (nrow,a,ja,ia,ao,jao,iao,perm,locjob)
+c
+c then permute columns
+c
+      locjob = 0
+c
+      if (job .le. 2) then
+         call cperm (nrow,ao,jao,iao,ao,jao,iao,perm,locjob) 
+      else 
+         call cperm (nrow,ao,jao,iao,ao,jao,iao,qperm,locjob) 
+      endif 
+c     
+      return
+c-------end-of-dperm----------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine dperm1 (i1,i2,a,ja,ia,b,jb,ib,perm,ipos,job)
+      integer i1,i2,job,ja(*),ia(*),jb(*),ib(*),perm(*)
+      real*8 a(*),b(*)
+c----------------------------------------------------------------------- 
+c     general submatrix extraction routine.
+c----------------------------------------------------------------------- 
+c     extracts rows perm(i1), perm(i1+1), ..., perm(i2) (in this order) 
+c     from a matrix (doing nothing in the column indices.) The resulting 
+c     submatrix is constructed in b, jb, ib. A pointer ipos to the
+c     beginning of arrays b,jb,is also allowed (i.e., nonzero elements
+c     are accumulated starting in position ipos of b, jb). 
+c-----------------------------------------------------------------------
+c Y. Saad,Sep. 21 1989 / recoded Jan. 28 1991 / modified for PSPARSLIB 
+c Sept. 1997.. 
+c-----------------------------------------------------------------------
+c on entry: 
+c---------- 
+c n 	= dimension of the matrix
+c a,ja,
+c   ia  = input matrix in CSR format
+c perm 	= integer array of length n containing the indices of the rows
+c         to be extracted. 
+c
+c job   = job indicator. if (job .ne.1) values are not copied (i.e.,
+c         only pattern is copied).
+c
+c on return: 
+c-----------
+c b,ja,
+c ib   = matrix in csr format. b(ipos:ipos+nnz-1),jb(ipos:ipos+nnz-1) 
+c     contain the value and column indices respectively of the nnz
+c     nonzero elements of the permuted matrix. thus ib(1)=ipos.
+c
+c Notes:
+c------- 
+c  algorithm is NOT in place 
+c----------------------------------------------------------------------- 
+c local variables
+c
+      integer ko,irow,k 
+      logical values
+c-----------------------------------------------------------------------
+      values = (job .eq. 1) 
+      ko = ipos 
+      ib(1) = ko
+      do 900 i=i1,i2
+         irow = perm(i) 
+         do 800 k=ia(irow),ia(irow+1)-1
+            if (values) b(ko) = a(k)
+            jb(ko) = ja(k)
+            ko=ko+1
+ 800     continue
+         ib(i-i1+2) = ko
+ 900  continue
+      return
+c--------end-of-dperm1--------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine dperm2 (i1,i2,a,ja,ia,b,jb,ib,cperm,rperm,istart,
+     *        ipos,job)
+      integer i1,i2,job,istart,ja(*),ia(*),jb(*),ib(*),cperm(*),rperm(*) 
+      real*8 a(*),b(*)
+c----------------------------------------------------------------------- 
+c     general submatrix permutation/ extraction routine.
+c----------------------------------------------------------------------- 
+c     extracts rows rperm(i1), rperm(i1+1), ..., rperm(i2) and does an
+c     associated column permutation (using array cperm). The resulting
+c     submatrix is constructed in b, jb, ib. For added flexibility, the
+c     extracted elements are put in sequence starting from row 'istart' 
+c     of B. In addition a pointer ipos to the beginning of arrays b,jb,
+c     is also allowed (i.e., nonzero elements are accumulated starting in
+c     position ipos of b, jb). In most applications istart and ipos are 
+c     equal to one. However, the generality adds substantial flexiblity.
+c     EXPLE: (1) to permute msr to msr (excluding diagonals) 
+c     call dperm2 (1,n,a,ja,ja,b,jb,jb,rperm,rperm,1,n+2) 
+c            (2) To extract rows 1 to 10: define rperm and cperm to be
+c     identity permutations (rperm(i)=i, i=1,n) and then
+c            call dperm2 (1,10,a,ja,ia,b,jb,ib,rperm,rperm,1,1) 
+c            (3) to achieve a symmetric permutation as defined by perm: 
+c            call dperm2 (1,10,a,ja,ia,b,jb,ib,perm,perm,1,1) 
+c            (4) to get a symmetric permutation of A and append the
+c            resulting data structure to A's data structure (useful!) 
+c            call dperm2 (1,10,a,ja,ia,a,ja,ia(n+1),perm,perm,1,ia(n+1))
+c-----------------------------------------------------------------------
+c Y. Saad,Sep. 21 1989 / recoded Jan. 28 1991. 
+c-----------------------------------------------------------------------
+c on entry: 
+c---------- 
+c n 	= dimension of the matrix
+c i1,i2 = extract rows rperm(i1) to rperm(i2) of A, with i1<i2.
+c
+c a,ja,
+c   ia  = input matrix in CSR format
+c cperm = integer array of length n containing the permutation arrays
+c	  for the columns: cperm(i) is the destination of column j, 
+c         i.e., any column index ja(k) is transformed into cperm(ja(k)) 
+c
+c rperm	=  permutation array for the rows. rperm(i) = origin (in A) of
+c          row i in B. This is the reverse permutation relative to the
+c          ones used in routines cperm, dperm,.... 
+c          rows rperm(i1), rperm(i1)+1, ... rperm(i2) are 
+c          extracted from A and stacked into B, starting in row istart
+c          of B. 
+c istart= starting row for B where extracted matrix is to be added.
+c         this is also only a pointer of the be beginning address for
+c         ib , on return. 
+c ipos  = beginning position in arrays b and jb where to start copying 
+c         elements. Thus, ib(istart) = ipos. 
+c
+c job   = job indicator. if (job .ne.1) values are not copied (i.e.,
+c         only pattern is copied).
+c
+c on return: 
+c-----------
+c b,ja,
+c ib   = matrix in csr format. positions 1,2,...,istart-1 of ib 
+c     are not touched. b(ipos:ipos+nnz-1),jb(ipos:ipos+nnz-1) 
+c     contain the value and column indices respectively of the nnz
+c     nonzero elements of the permuted matrix. thus ib(istart)=ipos.
+c
+c Notes:
+c------- 
+c  1) algorithm is NOT in place 
+c  2) column indices may not be sorted on return even  though they 
+c     may be on entry.
+c----------------------------------------------------------------------- 
+c local variables
+c
+      integer ko,irow,k 
+      logical values
+c-----------------------------------------------------------------------
+      values = (job .eq. 1) 
+      ko = ipos 
+      ib(istart) = ko
+      do 900 i=i1,i2
+         irow = rperm(i) 
+         do 800 k=ia(irow),ia(irow+1)-1
+            if (values) b(ko) = a(k)
+            jb(ko) = cperm(ja(k))
+            ko=ko+1
+ 800     continue
+         ib(istart+i-i1+1) = ko
+ 900  continue
+      return
+c--------end-of-dperm2--------------------------------------------------
+c-----------------------------------------------------------------------
+      end 
+c-----------------------------------------------------------------------
+      subroutine dmperm (nrow,a,ja,ao,jao,perm,job)
+      integer nrow,ja(*),jao(*),perm(nrow),job
+      real*8 a(*),ao(*) 
+c-----------------------------------------------------------------------
+c This routine performs a symmetric permutation of the rows and 
+c columns of a matrix stored in MSR format. i.e., it computes 
+c B = P A transp(P), where P, is  a permutation matrix. 
+c P maps row i into row perm(i) and column j into column perm(j): 
+c      a(i,j)    becomes   a(perm(i),perm(j)) in new matrix
+c (i.e.  ao(perm(i),perm(j)) = a(i,j) ) 
+c calls dperm. 
+c-----------------------------------------------------------------------
+c Y. Saad, Nov 15, 1991. 
+c-----------------------------------------------------------------------
+c on entry: 
+c---------- 
+c n 	= dimension of the matrix
+c a, ja = input matrix in MSR format. 
+c perm 	= integer array of length n containing the permutation arrays
+c	  for the rows: perm(i) is the destination of row i in the
+c         permuted matrix -- also the destination of column i in case
+c         permutation is symmetric (job .le. 2) 
+c
+c job	= integer indicating the work to be done:
+c 		job = 1	permute a, ja, ia into ao, jao, iao 
+c 		job = 2 permute matrix ignoring real values.
+c		
+c on return: 
+c-----------
+c ao, jao = output matrix in MSR. 
+c
+c in case job .eq. 2 a and ao are never referred to and can be dummy 
+c arguments. 
+c
+c Notes:
+c------- 
+c  1) algorithm is NOT in place 
+c  2) column indices may not be sorted on return even  though they may be 
+c     on entry.
+c----------------------------------------------------------------------c
+c     local variables
+c     
+      integer n1, n2
+      n1 = nrow+1
+      n2 = n1+1
+c      
+      call dperm (nrow,a,ja,ja,ao(n2),jao(n2),jao,perm,perm,job) 
+c     
+      jao(1) = n2
+      do 101 j=1, nrow 
+         ao(perm(j)) = a(j) 
+         jao(j+1) = jao(j+1)+n1
+ 101  continue
+c
+c done
+c     
+      return
+c-----------------------------------------------------------------------
+c--------end-of-dmperm--------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine dvperm (n, x, perm) 
+      integer n, perm(n) 
+      real*8 x(n)
+c-----------------------------------------------------------------------
+c this subroutine performs an in-place permutation of a real vector x 
+c according to the permutation array perm(*), i.e., on return, 
+c the vector x satisfies,
+c
+c	x(perm(j)) :== x(j), j=1,2,.., n
+c
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c n 	= length of vector x.
+c perm 	= integer array of length n containing the permutation  array.
+c x	= input vector
+c
+c on return:
+c---------- 
+c x	= vector x permuted according to x(perm(*)) :=  x(*)
+c
+c----------------------------------------------------------------------c
+c           Y. Saad, Sep. 21 1989                                      c
+c----------------------------------------------------------------------c
+c local variables 
+      real*8 tmp, tmp1
+c
+      init      = 1
+      tmp	= x(init)	
+      ii        = perm(init)
+      perm(init)= -perm(init)
+      k         = 0
+c     
+c loop
+c 
+ 6    k = k+1
+c
+c save the chased element --
+c 
+      tmp1	  = x(ii) 
+      x(ii)     = tmp
+      next	  = perm(ii) 
+      if (next .lt. 0 ) goto 65
+c     
+c test for end 
+c
+      if (k .gt. n) goto 101
+      tmp       = tmp1
+      perm(ii)  = - perm(ii)
+      ii        = next 
+c
+c end loop 
+c
+      goto 6
+c
+c reinitilaize cycle --
+c
+ 65   init      = init+1
+      if (init .gt. n) goto 101
+      if (perm(init) .lt. 0) goto 65
+      tmp	= x(init)
+      ii	= perm(init)
+      perm(init)=-perm(init)
+      goto 6
+c     
+ 101  continue
+      do 200 j=1, n
+         perm(j) = -perm(j)
+ 200  continue 
+c     
+      return
+c-------------------end-of-dvperm--------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine ivperm (n, ix, perm) 
+      integer n, perm(n), ix(n)
+c-----------------------------------------------------------------------
+c this subroutine performs an in-place permutation of an integer vector 
+c ix according to the permutation array perm(*), i.e., on return, 
+c the vector x satisfies,
+c
+c	ix(perm(j)) :== ix(j), j=1,2,.., n
+c
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c n 	= length of vector x.
+c perm 	= integer array of length n containing the permutation  array.
+c ix	= input vector
+c
+c on return:
+c---------- 
+c ix	= vector x permuted according to ix(perm(*)) :=  ix(*)
+c
+c----------------------------------------------------------------------c
+c           Y. Saad, Sep. 21 1989                                      c
+c----------------------------------------------------------------------c
+c local variables
+      integer tmp, tmp1
+c
+      init      = 1
+      tmp	= ix(init)	
+      ii        = perm(init)
+      perm(init)= -perm(init)
+      k         = 0
+c     
+c loop
+c 
+ 6    k = k+1
+c
+c save the chased element --
+c 
+      tmp1	  = ix(ii) 
+      ix(ii)     = tmp
+      next	  = perm(ii) 
+      if (next .lt. 0 ) goto 65
+c     
+c test for end 
+c
+      if (k .gt. n) goto 101
+      tmp       = tmp1
+      perm(ii)  = - perm(ii)
+      ii        = next 
+c
+c end loop 
+c
+      goto 6
+c
+c reinitilaize cycle --
+c
+ 65   init      = init+1
+      if (init .gt. n) goto 101
+      if (perm(init) .lt. 0) goto 65
+      tmp	= ix(init)
+      ii	= perm(init)
+      perm(init)=-perm(init)
+      goto 6
+c     
+ 101  continue
+      do 200 j=1, n
+         perm(j) = -perm(j)
+ 200  continue 
+c     
+      return
+c-------------------end-of-ivperm--------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------  
+      subroutine retmx (n,a,ja,ia,dd)
+      real*8 a(*),dd(*)
+      integer n,ia(*),ja(*)
+c-----------------------------------------------------------------------
+c returns in dd(*) the max absolute value of elements in row *.
+c used for scaling purposes. superseded by rnrms  .
+c
+c on entry:
+c n	= dimension of A
+c a,ja,ia
+c	= matrix stored in compressed sparse row format
+c dd	= real*8 array of length n. On output,entry dd(i) contains
+c	  the element of row i that has the largest absolute value.
+c	  Moreover the sign of dd is modified such that it is the
+c	  same as that of the diagonal element in row i.
+c----------------------------------------------------------------------c
+c           Y. Saad, Sep. 21 1989                                      c
+c----------------------------------------------------------------------c
+c local variables
+      integer k2, i, k1, k
+      real*8 t, t1, t2
+c
+c initialize 
+c
+      k2 = 1
+      do 11 i=1,n
+         k1 = k2
+         k2 = ia(i+1) - 1
+         t = 0.0d0
+         do 101  k=k1,k2
+            t1 = abs(a(k))
+            if (t1 .gt. t) t = t1
+            if (ja(k) .eq. i) then 
+               if (a(k) .ge. 0.0) then 
+                  t2 = a(k) 
+               else 
+                  t2 = - a(k)
+               endif
+            endif
+ 101     continue		
+         dd(i) =  t2*t
+c     we do not invert diag
+ 11   continue
+      return
+c---------end of retmx -------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine diapos  (n,ja,ia,idiag) 
+      integer ia(n+1), ja(*), idiag(n) 
+c-----------------------------------------------------------------------
+c this subroutine returns the positions of the diagonal elements of a
+c sparse matrix a, ja, ia, in the array idiag.
+c-----------------------------------------------------------------------
+c on entry:
+c---------- 
+c
+c n	= integer. row dimension of the matrix a.
+c a,ja,
+c    ia = matrix stored compressed sparse row format. a array skipped.
+c
+c on return:
+c-----------
+c idiag  = integer array of length n. The i-th entry of idiag 
+c          points to the diagonal element a(i,i) in the arrays
+c          a, ja. (i.e., a(idiag(i)) = element A(i,i) of matrix A)
+c          if no diagonal element is found the entry is set to 0.
+c----------------------------------------------------------------------c
+c           Y. Saad, March, 1990
+c----------------------------------------------------------------------c
+      do 1 i=1, n 
+         idiag(i) = 0
+ 1    continue
+c     
+c     sweep through data structure. 
+c     
+      do  6 i=1,n
+         do 51 k= ia(i),ia(i+1) -1
+            if (ja(k) .eq. i) idiag(i) = k
+ 51      continue
+ 6    continue
+c----------- -end-of-diapos---------------------------------------------
+c-----------------------------------------------------------------------
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine dscaldg (n,a,ja,ia,diag,job)
+      real*8 a(*), diag(*),t
+      integer ia(*),ja(*)
+c----------------------------------------------------------------------- 
+c scales rows by diag where diag is either given (job=0)
+c or to be computed:
+c  job = 1 ,scale row i by  by  +/- max |a(i,j) | and put inverse of 
+c       scaling factor in diag(i),where +/- is the sign of a(i,i).
+c  job = 2 scale by 2-norm of each row..
+c if diag(i) = 0,then diag(i) is replaced by one
+c (no scaling)..
+c----------------------------------------------------------------------c
+c           Y. Saad, Sep. 21 1989                                      c
+c----------------------------------------------------------------------c
+      goto (12,11,10) job+1
+ 10   do 110 j=1,n
+         k1= ia(j)
+         k2 = ia(j+1)-1
+         t = 0.0d0
+         do 111 k = k1,k2
+ 111        t = t+a(k)*a(k)
+ 110        diag(j) = sqrt(t)
+            goto 12
+ 11   continue
+      call retmx (n,a,ja,ia,diag)
+c------
+ 12   do 1 j=1,n
+         if (diag(j) .ne. 0.0d0) then 
+            diag(j) = 1.0d0/diag(j)
+         else 
+            diag(j) = 1.0d0
+         endif
+ 1    continue
+      do 2 i=1,n
+         t = diag(i)
+         do 21 k=ia(i),ia(i+1) -1
+            a(k) = a(k)*t
+ 21      continue
+ 2    continue
+      return 
+c--------end of dscaldg -----------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine extbdg (n,a,ja,ia,bdiag,nblk,ao,jao,iao)
+      implicit real*8 (a-h,o-z)
+      real*8 bdiag(*),a(*),ao(*)
+      integer ia(*),ja(*),jao(*),iao(*) 
+c-----------------------------------------------------------------------
+c this subroutine extracts the main diagonal blocks of a 
+c matrix stored in compressed sparse row format and puts the result
+c into the array bdiag and the remainder in ao,jao,iao.
+c-----------------------------------------------------------------------
+c on entry:
+c----------
+c n	= integer. The row dimension of the matrix a.
+c a,
+c ja,
+c ia    = matrix stored in csr format
+c nblk  = dimension of each diagonal block. The diagonal blocks are
+c         stored in compressed format rowwise,i.e.,we store in 
+c	  succession the i nonzeros of the i-th row after those of
+c	  row number i-1..
+c
+c on return:
+c----------
+c bdiag = real*8 array of size (n x nblk) containing the diagonal
+c	  blocks of A on return
+c ao,
+c jao,
+C iao   = remainder of the matrix stored in csr format.
+c----------------------------------------------------------------------c
+c           Y. Saad, Sep. 21 1989                                      c
+c----------------------------------------------------------------------c
+      m = 1 + (n-1)/nblk
+c this version is sequential -- there is a more parallel version
+c that goes through the structure twice ....
+      ltr =  ((nblk-1)*nblk)/2 
+      l = m * ltr
+      do 1 i=1,l
+         bdiag(i) = 0.0d0
+ 1    continue
+      ko = 0
+      kb = 1
+      iao(1) = 1
+c-------------------------
+      do 11 jj = 1,m
+         j1 = (jj-1)*nblk+1
+         j2 =  min0 (n,j1+nblk-1)
+         do 12 j=j1,j2
+            do 13 i=ia(j),ia(j+1) -1
+               k = ja(i)
+               if (k .lt. j1) then
+                  ko = ko+1
+                  ao(ko) = a(i)
+                  jao(ko) = k
+               else if (k .lt. j) then
+c     kb = (jj-1)*ltr+((j-j1)*(j-j1-1))/2+k-j1+1
+c     bdiag(kb) = a(i)
+                  bdiag(kb+k-j1) = a(i)
+               endif
+ 13         continue 	
+            kb = kb + j-j1
+            iao(j+1) = ko+1
+ 12      continue
+ 11   continue
+      return
+c---------end-of-extbdg------------------------------------------------- 
+c----------------------------------------------------------------------- 
+      end
+c----------------------------------------------------------------------- 
+      subroutine getbwd(n,a,ja,ia,ml,mu)
+c-----------------------------------------------------------------------
+c gets the bandwidth of lower part and upper part of A.
+c does not assume that A is sorted.
+c-----------------------------------------------------------------------
+c on entry:
+c----------
+c n	= integer = the row dimension of the matrix
+c a, ja,
+c    ia = matrix in compressed sparse row format.
+c 
+c on return:
+c----------- 
+c ml	= integer. The bandwidth of the strict lower part of A
+c mu	= integer. The bandwidth of the strict upper part of A 
+c
+c Notes:
+c ===== ml and mu are allowed to be negative or return. This may be 
+c       useful since it will tell us whether a band is confined 
+c       in the strict  upper/lower triangular part. 
+c       indeed the definitions of ml and mu are
+c
+c       ml = max ( (i-j)  s.t. a(i,j) .ne. 0  )
+c       mu = max ( (j-i)  s.t. a(i,j) .ne. 0  )
+c----------------------------------------------------------------------c
+c Y. Saad, Sep. 21 1989                                                c
+c----------------------------------------------------------------------c
+      real*8 a(*) 
+      integer ja(*),ia(n+1),ml,mu,ldist,i,k 
+      ml = - n
+      mu = - n
+      do 3 i=1,n
+         do 31 k=ia(i),ia(i+1)-1 
+            ldist = i-ja(k)
+            ml = max(ml,ldist)
+            mu = max(mu,-ldist)
+ 31      continue
+ 3    continue
+      return
+c---------------end-of-getbwd ------------------------------------------ 
+c----------------------------------------------------------------------- 
+      end
+c----------------------------------------------------------------------- 
+      subroutine blkfnd (nrow,ja,ia,nblk)
+c-----------------------------------------------------------------------
+c This routine attemptps to determine whether or not  the input
+c matrix has a block structure and finds the blocks size
+c if it does. A block matrix is one which is
+c comprised of small square dense blocks. If there are zero
+c elements within the square blocks and the original data structure
+c takes these zeros into account then blkchk may fail to find the
+c correct block size. 
+c----------------------------------------------------------------------- 
+c on entry
+c---------
+c nrow	= integer equal to the row dimension of the matrix.  
+c ja    = integer array containing the column indices of the entries 
+c         nonzero entries of the matrix stored by row.
+c ia    = integer array of length nrow + 1 containing the pointers 
+c         beginning of each row in array ja.
+c		
+c nblk  = integer containing the assumed value of nblk if job = 0
+c         
+c on return
+c---------- 
+c nblk  = integer containing the value found for nblk when job = 1.
+c         if imsg .ne. 0 this value is meaningless however.
+c
+c----------------------------------------------------------------------c
+c           Y. Saad, Sep. 21 1989                                      c
+c----------------------------------------------------------------------c
+      integer ia(nrow+1),ja(*) 
+c----------------------------------------------------------------------- 
+c first part of code will find candidate block sizes.
+c criterion used here is a simple one: scan rows and  determine groups 
+c of rows that have the same length and such that the first column 
+c number and the last column number are identical. 
+c----------------------------------------------------------------------- 
+      minlen = ia(2)-ia(1)
+      irow   = 1
+      do 1 i=2,nrow
+         len = ia(i+1)-ia(i)
+         if (len .lt. minlen) then
+            minlen = len 
+            irow = i
+         endif
+ 1    continue
+c     
+c     ---- candidates are all dividers of minlen
+c
+      nblk = 1
+      if (minlen .le. 1) return
+c     
+      do 99 iblk = minlen, 1, -1
+         if (mod(minlen,iblk) .ne. 0) goto 99
+         len = ia(2) - ia(1)
+         len0 = len
+         jfirst = ja(1) 
+         jlast = ja(ia(2)-1)
+         do 10 jrow = irow+1,irow+nblk-1
+            i1 = ia(jrow)
+            i2 = ia(jrow+1)-1
+            len = i2+1-i1
+            jf = ja(i1)
+            jl = ja(i2) 
+            if (len .ne. len0 .or. jf .ne. jfirst .or. 
+     *           jl .ne. jlast) goto 99
+ 10      continue
+c     
+c     check for this candidate ----
+c     
+         call blkchk (nrow,ja,ia,iblk,imsg)	       
+         if (imsg .eq. 0) then 
+c     
+c     block size found
+c     
+            nblk = iblk
+            return
+         endif 
+ 99   continue	       
+c--------end-of-blkfnd ------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine blkchk (nrow,ja,ia,nblk,imsg)
+c----------------------------------------------------------------------- 
+c This routine checks whether the input matrix is a block
+c matrix with block size of nblk. A block matrix is one which is
+c comprised of small square dense blocks. If there are zero
+c elements within the square blocks and the data structure
+c takes them into account then blkchk may fail to find the
+c correct block size. 
+c----------------------------------------------------------------------- 
+c on entry
+c---------
+c nrow	= integer equal to the row dimension of the matrix.  
+c ja    = integer array containing the column indices of the entries 
+c         nonzero entries of the matrix stored by row.
+c ia    = integer array of length nrow + 1 containing the pointers 
+c         beginning of each row in array ja.
+c
+c nblk  = integer containing the value of nblk to be checked. 
+c         
+c on return
+c---------- 
+c
+c imsg  = integer containing a message  with the following meaning.
+c          imsg = 0 means that the output value of nblk is a correct
+c                   block size. nblk .lt. 0 means nblk not correct 
+c                   block size.
+c          imsg = -1 : nblk does not divide nrow 
+c          imsg = -2 : a starting element in a row is at wrong position
+c             (j .ne. mult*nblk +1 )
+c          imsg = -3 : nblk does divide a row length - 
+c          imsg = -4 : an element is isolated outside a block or
+c             two rows in same group have different lengths
+c----------------------------------------------------------------------c
+c           Y. Saad, Sep. 21 1989                                      c
+c----------------------------------------------------------------------c
+      integer ia(nrow+1),ja(*) 
+c---------------------------------------------------------------------- 
+c first part of code will find candidate block sizes.
+c this is not guaranteed to work . so a check is done at the end
+c the criterion used here is a simple one:
+c scan rows and determine groups of rows that have the same length
+c and such that the first column number and the last column number 
+c are identical. 
+c---------------------------------------------------------------------- 
+      imsg = 0
+      if (nblk .le. 1) return
+      nr = nrow/nblk
+      if (nr*nblk .ne. nrow) goto 101
+c--   main loop --------------------------------------------------------- 
+      irow = 1
+      do 20 ii=1, nr
+c     i1= starting position for group of nblk rows in original matrix
+         i1 = ia(irow)
+         j2 = i1
+c     lena = length of each row in that group  in the original matrix
+         lena = ia(irow+1)-i1
+c     len = length of each block-row in that group in the output matrix
+         len = lena/nblk
+         if (len* nblk .ne. lena) goto 103
+c     
+c     for each row
+c     
+         do 6 i = 1, nblk
+            irow = irow + 1
+            if (ia(irow)-ia(irow-1) .ne. lena ) goto 104
+c     
+c     for each block
+c     
+            do 7 k=0, len-1
+               jstart = ja(i1+nblk*k)-1
+               if ( (jstart/nblk)*nblk .ne. jstart) goto 102
+c     
+c     for each column
+c     
+               do 5 j=1, nblk
+                  if (jstart+j .ne. ja(j2) )  goto 104
+                  j2 = j2+1 
+ 5             continue
+ 7          continue
+ 6       continue
+ 20   continue
+c     went through all loops successfully:
+      return
+ 101  imsg = -1
+      return
+ 102  imsg = -2
+      return
+ 103  imsg = -3
+      return
+ 104  imsg = -4
+c----------------end of chkblk ----------------------------------------- 
+c-----------------------------------------------------------------------
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine infdia (n,ja,ia,ind,idiag) 
+      integer ia(*), ind(*), ja(*)
+c-----------------------------------------------------------------------
+c     obtains information on the diagonals of A. 
+c----------------------------------------------------------------------- 
+c this subroutine finds the lengths of each of the 2*n-1 diagonals of A
+c it also outputs the number of nonzero diagonals found. 
+c----------------------------------------------------------------------- 
+c on entry:
+c---------- 
+c n	= dimension of the matrix a.
+c
+c a,    ..... not needed here.
+c ja, 			
+c ia    = matrix stored in csr format
+c
+c on return:
+c----------- 
+c
+c idiag = integer. number of nonzero diagonals found. 
+c 
+c ind   = integer array of length at least 2*n-1. The k-th entry in
+c         ind contains the number of nonzero elements in the diagonal
+c         number k, the numbering beeing from the lowermost diagonal
+c         (bottom-left). In other words ind(k) = length of diagonal
+c         whose offset wrt the main diagonal is = - n + k.
+c----------------------------------------------------------------------c
+c           Y. Saad, Sep. 21 1989                                      c
+c----------------------------------------------------------------------c
+      n2= n+n-1
+      do 1 i=1,n2
+         ind(i) = 0
+ 1    continue
+      do 3 i=1, n
+         do 2 k=ia(i),ia(i+1)-1
+            j = ja(k)
+            ind(n+j-i) = ind(n+j-i) +1
+ 2       continue 
+ 3    continue
+c     count the nonzero ones.
+      idiag = 0 
+      do 41 k=1, n2
+         if (ind(k) .ne. 0) idiag = idiag+1
+ 41   continue
+      return
+c done
+c------end-of-infdia ---------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine amubdg (nrow,ncol,ncolb,ja,ia,jb,ib,ndegr,nnz,iw) 
+      integer ja(*),jb(*),ia(nrow+1),ib(ncol+1),ndegr(nrow),iw(ncolb) 
+c-----------------------------------------------------------------------
+c gets the number of nonzero elements in each row of A*B and the total 
+c number of nonzero elements in A*B. 
+c-----------------------------------------------------------------------
+c on entry:
+c -------- 
+c
+c nrow  = integer.  row dimension of matrix A
+c ncol  = integer.  column dimension of matrix A = row dimension of 
+c                   matrix B.
+c ncolb = integer. the colum dimension of the matrix B.
+c
+c ja, ia= row structure of input matrix A: ja = column indices of
+c         the nonzero elements of A stored by rows.
+c         ia = pointer to beginning of each row  in ja.
+c 
+c jb, ib= row structure of input matrix B: jb = column indices of
+c         the nonzero elements of A stored by rows.
+c         ib = pointer to beginning of each row  in jb.
+c 
+c on return:
+c ---------
+c ndegr	= integer array of length nrow containing the degrees (i.e., 
+c         the number of nonzeros in  each row of the matrix A * B 
+c				
+c nnz   = total number of nonzero elements found in A * B
+c
+c work arrays:
+c-------------
+c iw	= integer work array of length ncolb. 
+c-----------------------------------------------------------------------
+      do 1 k=1, ncolb 
+         iw(k) = 0 
+ 1    continue
+      
+      do 2 k=1, nrow
+         ndegr(k) = 0 
+ 2    continue
+c     
+c     method used: Transp(A) * A = sum [over i=1, nrow]  a(i)^T a(i)
+c     where a(i) = i-th row of  A. We must be careful not to add  the
+c     elements already accounted for.
+c     
+c     
+      do 7 ii=1,nrow 
+c     
+c     for each row of A
+c     
+         ldg = 0 
+c     
+c    end-of-linked list
+c     
+         last = -1 
+         do 6 j = ia(ii),ia(ii+1)-1 
+c     
+c     row number to be added:
+c     
+            jr = ja(j) 
+            do 5 k=ib(jr),ib(jr+1)-1
+               jc = jb(k) 
+               if (iw(jc) .eq. 0) then 
+c     
+c     add one element to the linked list 
+c     
+                  ldg = ldg + 1
+                  iw(jc) = last 
+                  last = jc
+               endif
+ 5          continue
+ 6       continue
+         ndegr(ii) = ldg
+c     
+c     reset iw to zero
+c     
+         do 61 k=1,ldg 
+            j = iw(last) 
+            iw(last) = 0
+            last = j
+ 61      continue
+c-----------------------------------------------------------------------
+ 7    continue
+c     
+      nnz = 0
+      do 8 ii=1, nrow 
+         nnz = nnz+ndegr(ii) 
+ 8    continue
+c     
+      return
+c---------------end-of-amubdg ------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine aplbdg (nrow,ncol,ja,ia,jb,ib,ndegr,nnz,iw) 
+      integer ja(*),jb(*),ia(nrow+1),ib(nrow+1),iw(ncol),ndegr(nrow) 
+c-----------------------------------------------------------------------
+c gets the number of nonzero elements in each row of A+B and the total 
+c number of nonzero elements in A+B. 
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A and B
+c ncol  = integer. The column dimension of A and B.
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format.
+c 
+c b, 
+c jb, 
+c ib	=  Matrix B in compressed sparse row format.
+c
+c on return:
+c----------
+c ndegr	= integer array of length nrow containing the degrees (i.e., 
+c         the number of nonzeros in  each row of the matrix A + B.
+c				
+c nnz   = total number of nonzero elements found in A * B
+c
+c work arrays:
+c------------
+c iw	= integer work array of length equal to ncol. 
+c
+c-----------------------------------------------------------------------
+      do 1 k=1, ncol 
+         iw(k) = 0 
+ 1    continue
+c
+      do 2 k=1, nrow
+         ndegr(k) = 0 
+ 2    continue
+c
+      do 7 ii=1,nrow 
+         ldg = 0 
+c     
+c    end-of-linked list
+c     
+         last = -1 
+c     
+c     row of A
+c     
+         do 5 j = ia(ii),ia(ii+1)-1 
+            jr = ja(j) 
+c     
+c     add element to the linked list 
+c     
+            ldg = ldg + 1
+            iw(jr) = last 
+            last = jr
+ 5       continue
+c     
+c     row of B
+c     
+         do 6 j=ib(ii),ib(ii+1)-1
+            jc = jb(j)
+            if (iw(jc) .eq. 0) then 
+c     
+c     add one element to the linked list 
+c     
+               ldg = ldg + 1
+               iw(jc) = last 
+               last = jc
+            endif
+ 6       continue
+c     done with row ii. 
+         ndegr(ii) = ldg
+c     
+c     reset iw to zero
+c     
+         do 61 k=1,ldg 
+            j = iw(last) 
+            iw(last) = 0
+            last = j
+ 61      continue
+c-----------------------------------------------------------------------
+ 7    continue
+c     
+      nnz = 0
+      do 8 ii=1, nrow 
+         nnz = nnz+ndegr(ii) 
+ 8    continue
+      return
+c----------------end-of-aplbdg -----------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine rnrms   (nrow, nrm, a, ja, ia, diag) 
+      real*8 a(*), diag(nrow), scal 
+      integer ja(*), ia(nrow+1) 
+c-----------------------------------------------------------------------
+c gets the norms of each row of A. (choice of three norms)
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A
+c
+c nrm   = integer. norm indicator. nrm = 1, means 1-norm, nrm =2
+c                  means the 2-nrm, nrm = 0 means max norm
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format.
+c 
+c on return:
+c----------
+c
+c diag = real vector of length nrow containing the norms
+c
+c-----------------------------------------------------------------
+      do 1 ii=1,nrow
+c
+c     compute the norm if each element.
+c     
+         scal = 0.0d0
+         k1 = ia(ii)
+         k2 = ia(ii+1)-1
+         if (nrm .eq. 0) then
+            do 2 k=k1, k2
+               scal = max(scal,abs(a(k) ) ) 
+ 2          continue
+         elseif (nrm .eq. 1) then
+            do 3 k=k1, k2
+               scal = scal + abs(a(k) ) 
+ 3          continue
+         else
+            do 4 k=k1, k2
+               scal = scal+a(k)**2
+ 4          continue
+         endif 
+         if (nrm .eq. 2) scal = sqrt(scal) 
+         diag(ii) = scal
+ 1    continue
+      return
+c-----------------------------------------------------------------------
+c-------------end-of-rnrms----------------------------------------------
+      end 
+c----------------------------------------------------------------------- 
+      subroutine cnrms   (nrow, nrm, a, ja, ia, diag) 
+      real*8 a(*), diag(nrow) 
+      integer ja(*), ia(nrow+1) 
+c-----------------------------------------------------------------------
+c gets the norms of each column of A. (choice of three norms)
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A
+c
+c nrm   = integer. norm indicator. nrm = 1, means 1-norm, nrm =2
+c                  means the 2-nrm, nrm = 0 means max norm
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format.
+c 
+c on return:
+c----------
+c
+c diag = real vector of length nrow containing the norms
+c NOTE: this is designed for square matrices. For the case 
+c nrow .ne. ncol -- diag must be of size max(nrow,ncol) even
+c though only the ncol first entries will be filled.. 
+c [report E. Canot 10/20/05 ] 
+c-----------------------------------------------------------------
+      do 10 k=1, nrow 
+         diag(k) = 0.0d0
+ 10   continue
+      do 1 ii=1,nrow
+         k1 = ia(ii)
+         k2 = ia(ii+1)-1
+         do 2 k=k1, k2
+            j = ja(k) 
+c     update the norm of each column
+            if (nrm .eq. 0) then
+               diag(j) = max(diag(j),abs(a(k) ) ) 
+            elseif (nrm .eq. 1) then
+               diag(j) = diag(j) + abs(a(k) ) 
+            else
+               diag(j) = diag(j)+a(k)**2
+            endif 
+ 2       continue
+ 1    continue
+      if (nrm .ne. 2) return
+      do 3 k=1, nrow
+         diag(k) = sqrt(diag(k))
+ 3    continue
+      return
+c-----------------------------------------------------------------------
+c------------end-of-cnrms-----------------------------------------------
+      end 
+c----------------------------------------------------------------------- 
+      subroutine roscal(nrow,job,nrm,a,ja,ia,diag,b,jb,ib,ierr) 
+      real*8 a(*), b(*), diag(nrow) 
+      integer nrow,job,nrm,ja(*),jb(*),ia(nrow+1),ib(nrow+1),ierr 
+c-----------------------------------------------------------------------
+c scales the rows of A such that their norms are one on return
+c 3 choices of norms: 1-norm, 2-norm, max-norm.
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A
+c
+c job   = integer. job indicator. Job=0 means get array b only
+c         job = 1 means get b, and the integer arrays ib, jb.
+c
+c nrm   = integer. norm indicator. nrm = 1, means 1-norm, nrm =2
+c                  means the 2-nrm, nrm = 0 means max norm
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format.
+c 
+c on return:
+c----------
+c
+c diag = diagonal matrix stored as a vector containing the matrix
+c        by which the rows have been scaled, i.e., on return 
+c        we have B = Diag*A.
+c
+c b, 
+c jb, 
+c ib	= resulting matrix B in compressed sparse row sparse format.
+c	    
+c ierr  = error message. ierr=0     : Normal return 
+c                        ierr=i > 0 : Row number i is a zero row.
+c Notes:
+c-------
+c 1)        The column dimension of A is not needed. 
+c 2)        algorithm in place (B can take the place of A).
+c-----------------------------------------------------------------
+      call rnrms (nrow,nrm,a,ja,ia,diag)
+      ierr = 0
+      do 1 j=1, nrow
+         if (diag(j) .eq. 0.0d0) then
+            ierr = j 
+            return
+         else
+            diag(j) = 1.0d0/diag(j)
+         endif
+ 1    continue
+      call diamua(nrow,job,a,ja,ia,diag,b,jb,ib)
+      return
+c-------end-of-roscal---------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine coscal(nrow,job,nrm,a,ja,ia,diag,b,jb,ib,ierr) 
+c----------------------------------------------------------------------- 
+      real*8 a(*),b(*),diag(nrow) 
+      integer nrow,job,ja(*),jb(*),ia(nrow+1),ib(nrow+1),ierr 
+c-----------------------------------------------------------------------
+c scales the columns of A such that their norms are one on return
+c result matrix written on b, or overwritten on A.
+c 3 choices of norms: 1-norm, 2-norm, max-norm. in place.
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrow	= integer. The row dimension of A
+c
+c job   = integer. job indicator. Job=0 means get array b only
+c         job = 1 means get b, and the integer arrays ib, jb.
+c
+c nrm   = integer. norm indicator. nrm = 1, means 1-norm, nrm =2
+c                  means the 2-nrm, nrm = 0 means max norm
+c
+c a,
+c ja,
+c ia   = Matrix A in compressed sparse row format.
+c 
+c on return:
+c----------
+c
+c diag = diagonal matrix stored as a vector containing the matrix
+c        by which the columns have been scaled, i.e., on return 
+c        we have B = A * Diag
+c
+c b, 
+c jb, 
+c ib	= resulting matrix B in compressed sparse row sparse format.
+c
+c ierr  = error message. ierr=0     : Normal return 
+c                        ierr=i > 0 : Column number i is a zero row.
+c Notes:
+c-------
+c 1)     The column dimension of A is not needed. 
+c 2)     algorithm in place (B can take the place of A).
+c-----------------------------------------------------------------
+      call cnrms (nrow,nrm,a,ja,ia,diag)
+      ierr = 0
+      do 1 j=1, nrow
+         if (diag(j) .eq. 0.0) then
+            ierr = j 
+            return
+         else
+            diag(j) = 1.0d0/diag(j)
+         endif
+ 1    continue
+      call amudia (nrow,job,a,ja,ia,diag,b,jb,ib)
+      return
+c--------end-of-coscal-------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine addblk(nrowa, ncola, a, ja, ia, ipos, jpos, job,
+     & nrowb, ncolb, b, jb, ib, nrowc, ncolc, c, jc, ic, nzmx, ierr)
+c      implicit none
+      integer nrowa, nrowb, nrowc, ncola, ncolb, ncolc, ipos, jpos
+      integer nzmx, ierr, job
+      integer ja(1:*), ia(1:*), jb(1:*), ib(1:*), jc(1:*), ic(1:*)
+      real*8 a(1:*), b(1:*), c(1:*)
+c-----------------------------------------------------------------------
+c     This subroutine adds a matrix B into a submatrix of A whose 
+c     (1,1) element is located in the starting position (ipos, jpos). 
+c     The resulting matrix is allowed to be larger than A (and B), 
+c     and the resulting dimensions nrowc, ncolc will be redefined 
+c     accordingly upon return.  
+c     The input matrices are assumed to be sorted, i.e. in each row
+c     the column indices appear in ascending order in the CSR format.
+c-----------------------------------------------------------------------
+c on entry:
+c ---------
+c nrowa    = number of rows in A.
+c bcola    = number of columns in A.
+c a,ja,ia  = Matrix A in compressed sparse row format with entries sorted
+c nrowb    = number of rows in B.
+c ncolb    = number of columns in B.
+c b,jb,ib  = Matrix B in compressed sparse row format with entries sorted
+c
+c nzmax	   = integer. The  length of the arrays c and jc. addblk will 
+c            stop if the number of nonzero elements in the matrix C
+c            exceeds nzmax. See ierr.
+c 
+c on return:
+c----------
+c nrowc    = number of rows in C.
+c ncolc    = number of columns in C.
+c c,jc,ic  = resulting matrix C in compressed sparse row sparse format
+c            with entries sorted ascendly in each row. 
+c	    
+c ierr	   = integer. serving as error message. 
+c         ierr = 0 means normal return,
+c         ierr .gt. 0 means that addblk stopped while computing the
+c         i-th row  of C with i=ierr, because the number 
+c         of elements in C exceeds nzmax.
+c
+c Notes: 
+c-------
+c     this will not work if any of the two input matrices is not sorted
+c-----------------------------------------------------------------------
+      logical values
+      integer i,j1,j2,ka,kb,kc,kamax,kbmax
+      values = (job .ne. 0) 
+      ierr = 0
+      nrowc = max(nrowa, nrowb+ipos-1)
+      ncolc = max(ncola, ncolb+jpos-1)
+      kc = 1
+      kbmax = 0
+      ic(1) = kc
+c
+      do 10 i=1, nrowc
+         if (i.le.nrowa) then
+            ka = ia(i)
+            kamax = ia(i+1)-1
+         else
+            ka = ia(nrowa+1)
+         end if
+         if ((i.ge.ipos).and.((i-ipos).le.nrowb)) then
+            kb = ib(i-ipos+1)
+            kbmax = ib(i-ipos+2)-1 
+         else
+            kb = ib(nrowb+1)
+         end if
+c
+c     a do-while type loop -- goes through all the elements in a row.
+c
+ 20      continue 
+         if (ka .le. kamax) then
+            j1 = ja(ka)
+         else
+            j1 = ncolc+1
+         endif
+         if (kb .le. kbmax) then 
+            j2 = jb(kb) + jpos - 1
+         else 
+            j2 = ncolc+1
+         endif
+c
+c     if there are more elements to be added.
+c
+         if ((ka .le. kamax .or. kb .le. kbmax) .and.
+     &        (j1 .le. ncolc .or. j2 .le. ncolc)) then
+c
+c     three cases
+c
+            if (j1 .eq. j2) then 
+               if (values) c(kc) = a(ka)+b(kb)
+               jc(kc) = j1
+               ka = ka+1
+               kb = kb+1
+               kc = kc+1
+            else if (j1 .lt. j2) then
+               jc(kc) = j1
+               if (values) c(kc) = a(ka)
+               ka = ka+1
+               kc = kc+1
+            else if (j1 .gt. j2) then
+               jc(kc) = j2
+               if (values) c(kc) = b(kb)
+               kb = kb+1
+               kc = kc+1
+            endif
+            if (kc .gt. nzmx) goto 999
+            goto 20
+         end if
+         ic(i+1) = kc
+ 10   continue
+      return
+ 999  ierr = i 
+      return
+c---------end-of-addblk------------------------------------------------- 
+      end
+c----------------------------------------------------------------------- 
+      subroutine get1up (n,ja,ia,ju)
+      integer  n, ja(*),ia(*),ju(*)
+c----------------------------------------------------------------------
+c obtains the first element of each row of the upper triangular part
+c of a matrix. Assumes that the matrix is already sorted.
+c-----------------------------------------------------------------------
+c parameters
+c input
+c ----- 
+c ja      = integer array containing the column indices of aij
+c ia      = pointer array. ia(j) contains the position of the 
+c           beginning of row j in ja
+c 
+c output 
+c ------ 
+c ju      = integer array of length n. ju(i) is the address in ja 
+c           of the first element of the uper triangular part of
+c           of A (including rthe diagonal. Thus if row i does have
+c           a nonzero diagonal element then ju(i) will point to it.
+c           This is a more general version of diapos.
+c-----------------------------------------------------------------------
+c local vAriables
+      integer i, k 
+c     
+      do 5 i=1, n
+         ju(i) = 0
+         k = ia(i) 
+c
+ 1       continue
+         if (ja(k) .ge. i) then
+            ju(i) = k
+            goto 5
+         elseif (k .lt. ia(i+1) -1) then
+            k=k+1
+c 
+c go try next element in row 
+c 
+            goto 1
+         endif 
+ 5    continue
+      return
+c-----end-of-get1up-----------------------------------------------------
+      end 
+c----------------------------------------------------------------------
+      subroutine xtrows (i1,i2,a,ja,ia,ao,jao,iao,iperm,job)
+      integer i1,i2,ja(*),ia(*),jao(*),iao(*),iperm(*),job
+      real*8 a(*),ao(*) 
+c-----------------------------------------------------------------------
+c this subroutine extracts given rows from a matrix in CSR format. 
+c Specifically, rows number iperm(i1), iperm(i1+1), ...., iperm(i2)
+c are extracted and put in the output matrix ao, jao, iao, in CSR
+c format.  NOT in place. 
+c Youcef Saad -- coded Feb 15, 1992. 
+c-----------------------------------------------------------------------
+c on entry:
+c----------
+c i1,i2   = two integers indicating the rows to be extracted.
+c           xtrows will extract rows iperm(i1), iperm(i1+1),..,iperm(i2),
+c           from original matrix and stack them in output matrix 
+c           ao, jao, iao in csr format
+c
+c a, ja, ia = input matrix in csr format
+c
+c iperm	= integer array of length nrow containing the reverse permutation 
+c         array for the rows. row number iperm(j) in permuted matrix PA
+c         used to be row number j in unpermuted matrix.
+c         ---> a(i,j) in the permuted matrix was a(iperm(i),j) 
+c         in the inout matrix.
+c
+c job	= integer indicating the work to be done:
+c 		job .ne. 1 : get structure only of output matrix,,
+c               i.e., ignore real values. (in which case arrays a 
+c               and ao are not used nor accessed).
+c 		job = 1	get complete data structure of output matrix. 
+c               (i.e., including arrays ao and iao).
+c------------
+c on return: 
+c------------ 
+c ao, jao, iao = input matrix in a, ja, ia format
+c note : 
+c        if (job.ne.1)  then the arrays a and ao are not used.
+c----------------------------------------------------------------------c
+c           Y. Saad, revised May  2, 1990                              c
+c----------------------------------------------------------------------c
+      logical values
+      values = (job .eq. 1) 
+c
+c copying 
+c
+      ko = 1
+      iao(1) = ko
+      do 100 j=i1,i2 
+c
+c ii=iperm(j) is the index of old row to be copied.
+c        
+         ii = iperm(j) 
+         do 60 k=ia(ii), ia(ii+1)-1 
+            jao(ko) = ja(k) 
+            if (values) ao(ko) = a(k)
+            ko = ko+1
+ 60      continue
+         iao(j-i1+2) = ko
+ 100  continue
+c
+      return
+c---------end-of-xtrows------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine csrkvstr(n, ia, ja, nr, kvstr)
+c-----------------------------------------------------------------------
+      integer n, ia(n+1), ja(*), nr, kvstr(*)
+c-----------------------------------------------------------------------
+c     Finds block row partitioning of matrix in CSR format.
+c-----------------------------------------------------------------------
+c     On entry:
+c--------------
+c     n       = number of matrix scalar rows
+c     ia,ja   = input matrix sparsity structure in CSR format
+c
+c     On return:
+c---------------
+c     nr      = number of block rows
+c     kvstr   = first row number for each block row
+c
+c     Notes:
+c-----------
+c     Assumes that the matrix is sorted by columns.
+c     This routine does not need any workspace.
+c
+c-----------------------------------------------------------------------
+c     local variables
+      integer i, j, jdiff
+c-----------------------------------------------------------------------
+      nr = 1
+      kvstr(1) = 1
+c---------------------------------
+      do i = 2, n
+         jdiff = ia(i+1)-ia(i)
+         if (jdiff .eq. ia(i)-ia(i-1)) then
+            do j = ia(i), ia(i+1)-1
+               if (ja(j) .ne. ja(j-jdiff)) then
+                  nr = nr + 1
+                  kvstr(nr) = i
+                  goto 299
+               endif
+            enddo
+ 299        continue
+         else
+ 300        nr = nr + 1
+            kvstr(nr) = i
+         endif
+      enddo
+      kvstr(nr+1) = n+1
+c---------------------------------
+      return
+      end
+c-----------------------------------------------------------------------
+c------------------------end-of-csrkvstr--------------------------------
+      subroutine csrkvstc(n, ia, ja, nc, kvstc, iwk)
+c-----------------------------------------------------------------------
+      integer n, ia(n+1), ja(*), nc, kvstc(*), iwk(*)
+c-----------------------------------------------------------------------
+c     Finds block column partitioning of matrix in CSR format.
+c-----------------------------------------------------------------------
+c     On entry:
+c--------------
+c     n       = number of matrix scalar rows
+c     ia,ja   = input matrix sparsity structure in CSR format
+c
+c     On return:
+c---------------
+c     nc      = number of block columns
+c     kvstc   = first column number for each block column
+c
+c     Work space:
+c----------------
+c     iwk(*) of size equal to the number of scalar columns plus one.
+c        Assumed initialized to 0, and left initialized on return.
+c
+c     Notes:
+c-----------
+c     Assumes that the matrix is sorted by columns.
+c
+c-----------------------------------------------------------------------
+c     local variables
+      integer i, j, k, ncol
+c
+c-----------------------------------------------------------------------
+c-----use ncol to find maximum scalar column number
+      ncol = 0
+c-----mark the beginning position of the blocks in iwk
+      do i = 1, n
+         if (ia(i) .lt. ia(i+1)) then
+            j = ja(ia(i))
+            iwk(j) = 1
+            do k = ia(i)+1, ia(i+1)-1
+               j = ja(k)
+               if (ja(k-1).ne.j-1) then
+                  iwk(j) = 1
+                  iwk(ja(k-1)+1) = 1
+               endif
+            enddo
+            iwk(j+1) = 1
+            ncol = max0(ncol, j)
+         endif
+      enddo
+c---------------------------------
+      nc = 1
+      kvstc(1) = 1
+      do i = 2, ncol+1
+         if (iwk(i).ne.0) then
+            nc = nc + 1
+            kvstc(nc) = i
+            iwk(i) = 0
+         endif
+      enddo
+      nc = nc - 1
+c---------------------------------
+      return
+      end
+c-----------------------------------------------------------------------
+c------------------------end-of-csrkvstc--------------------------------
+c-----------------------------------------------------------------------
+      subroutine kvstmerge(nr, kvstr, nc, kvstc, n, kvst)
+c-----------------------------------------------------------------------
+      integer nr, kvstr(nr+1), nc, kvstc(nc+1), n, kvst(*)
+c-----------------------------------------------------------------------
+c     Merges block partitionings, for conformal row/col pattern.
+c-----------------------------------------------------------------------
+c     On entry:
+c--------------
+c     nr,nc   = matrix block row and block column dimension
+c     kvstr   = first row number for each block row
+c     kvstc   = first column number for each block column
+c
+c     On return:
+c---------------
+c     n       = conformal row/col matrix block dimension
+c     kvst    = conformal row/col block partitioning
+c
+c     Notes:
+c-----------
+c     If matrix is not square, this routine returns without warning.
+c
+c-----------------------------------------------------------------------
+c-----local variables
+      integer i,j
+c---------------------------------
+      if (kvstr(nr+1) .ne. kvstc(nc+1)) return
+      i = 1
+      j = 1
+      n = 1
+  200 if (i .gt. nr+1) then
+         kvst(n) = kvstc(j)
+         j = j + 1
+      elseif (j .gt. nc+1) then
+         kvst(n) = kvstr(i)
+         i = i + 1
+      elseif (kvstc(j) .eq. kvstr(i)) then
+         kvst(n) = kvstc(j)
+         j = j + 1
+         i = i + 1
+      elseif (kvstc(j) .lt. kvstr(i)) then
+         kvst(n) = kvstc(j)
+         j = j + 1
+      else
+         kvst(n) = kvstr(i)
+         i = i + 1
+      endif
+      n = n + 1
+      if (i.le.nr+1 .or. j.le.nc+1) goto 200
+      n = n - 2
+c---------------------------------
+      return
+c------------------------end-of-kvstmerge-------------------------------
+      end
diff --git a/INFO/README b/INFO/README
new file mode 100644
index 0000000..05dff92
--- /dev/null
+++ b/INFO/README
@@ -0,0 +1,66 @@
+c------------------------------------------------------------------------------c
+c                          INFO MODULE                                         c
+c------------------------------------------------------------------------------c
+c  The INFO module provides some elementary information on a sparse            c
+c  matrix. Geared towards a matrix in Harwell-Boeing format.                   c
+c  There is also a short main program that will read a Harwell-Boeing          c
+c  matrix and produce the information on the standard output. See below.       c
+c                                                                              c
+c------------------------------------------------------------------------------c
+c  infofun.f contains subroutines:                                             c
+c------------------------------------------------------------------------------c
+c    bandwidth :  computes the lower, upper, maximum, and average bandwidths.  c
+c    nonz      :  computes maximum numbers of nonzero elements per column/row, c
+c                minimum numbers of nonzero elements per column/row, and       c
+c                numbers of zero columns/rows.                                 c
+c    diag_domi : computes the percentage of weakly diagonally dominant         c
+c                rows/columns.                                                 c
+c    frobnorm  : computes the Frobenius norm of A.                             c
+c    ansym     : computes the Frobenius norm of the symmetric and non-symmetricc
+c                parts of A, computes number of matching elements in symmetry  c
+c                and relative symmetry match.                                  c
+c    distaij   : computes the average distance of a(i,j) from diag and standardc
+c                deviation  for this average.                                  c
+c    skyline   : computes the number of nonzeros in the skyline storage.       c
+c    distdiag  : computes the numbers of elements in each diagonal.            c
+c    bandpart  : computes the bandwidth of the banded matrix, which contains   c
+c                'nper' percent of the original matrix.                        c
+c    n_imp_diag: computes the most important diagonals.                        c
+c    nonz_lud  : computes the number of nonzero elements in strict lower part, c
+c                strict upper part, and main diagonal.                         c
+c    avnz_col  : computes average number of nonzero elements/column and std    c
+c                deviation for this average.                                   c
+c    vbrinfo   : Print info on matrix in variable block row format             c
+c------------------------------------------------------------------------------c
+c  rinfo1.f  : contains the main program to produce an executable              c
+c  rinfoC.f  : same thing in C -- info1.ex is made by makeC  makefile          c
+c------------------------------------------------------------------------------c
+c  dinfo13.f : contains the main subroutine called by rinfo1.f                 c
+c------------------------------------------------------------------------------c
+c  makefile: contains the make file to produce info1.ex                        c
+c  makeC: contains the make file to produce info1.ex from rinfoC.c             c
+c------------------------------------------------------------------------------c
+c  saylr1 :  contains the Harwell-Boeing matrix saylr1 for testing purposes.   c
+c------------------------------------------------------------------------------c
+c  info.saylr1 : contains a sample output (see below) for the matrix saylr1.   c
+c------------------------------------------------------------------------------c
+c------------------------------------------------------------------------------c
+c                          Notes:                                              c
+c------------------------------------------------------------------------------c
+c  The makefile will actually create an executable tool called info1.ex        c
+c  which will provide some information on a Harwell/Boeing matrix.             c
+c                                                                              c
+c  Once you have made the executable info1 using the makefile,                 c
+c  you can execute for a matrix stored in the Harwell-Boeing                   c
+c  format. You will need to have a matrix in the harwell/boeing                c
+c  format and type                                                             c
+c                                                                              c
+c  info1.ex < HB_file                                                          c
+c                                                                              c
+c  This will dump the info on the standard output/                             c
+c                                                                              c
+c    for example typing info1.ex < saylr1 > info.saylr1                        c
+c                                                                              c
+c  produces the file info.saylr1.  [info.saylr1 is included in this directory  c
+c  to check whether you get the same answers].                                 c
+c------------------------------------------------------------------------------c
diff --git a/INFO/dinfo13.f b/INFO/dinfo13.f
new file mode 100644
index 0000000..156c052
--- /dev/null
+++ b/INFO/dinfo13.f
@@ -0,0 +1,394 @@
+       subroutine dinfo1(n,iout,a,ja,ia,valued,
+     *		          title,key,type,ao,jao,iao)
+	implicit real*8 (a-h,o-z)
+        real*8 a(*),ao(*)
+        integer ja(*),ia(n+1),jao(*),iao(n+1),nzdiag 
+        character title*72,key*8,type*3 
+        logical valued 
+c----------------------------------------------------------------------c
+c  SPARSKIT:  ELEMENTARY INFORMATION ROUTINE.                          c
+c----------------------------------------------------------------------c
+c info1 obtains a number of statistics on a sparse matrix and writes   c
+c it into the output unit iout. The matrix is assumed                  c
+c to be stored in the compressed sparse COLUMN format sparse a, ja, ia c
+c----------------------------------------------------------------------c
+c Modified Nov 1, 1989. 1) Assumes A is stored in column               
+c format. 2) Takes symmetry into account, i.e., handles Harwell-Boeing
+c            matrices correctly. 
+c          ***  (Because of the recent modification the words row and 
+c            column may be mixed-up at occasions... to be checked...
+c
+c bug-fix July 25: 'upper' 'lower' mixed up in formats 108-107.
+c
+c On entry :
+c-----------
+c n	= integer. column dimension of matrix	
+c iout  = integer. unit number where the information it to be output.	
+c a	= real array containing the nonzero elements of the matrix
+c	  the elements are stored by columns in order 
+c	  (i.e. column i comes before column i+1, but the elements
+c         within each column can be disordered).
+c ja	= integer array containing the row indices of elements in a
+c ia	= integer array containing of length n+1 containing the 
+c         pointers to the beginning of the columns in arrays a and ja.
+c	  It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
+c 
+c valued= logical equal to .true. if values are provided and .false.
+c         if only the pattern of the matrix is provided. (in that
+c         case a(*) and ao(*) are dummy arrays.
+c
+c title = a 72-character title describing the matrix
+c         NOTE: The first character in title is ignored (it is often
+c         a one).
+c
+c key   = an 8-character key for the matrix
+c type  = a 3-character string to describe the type of the matrix.
+c         see harwell/Boeing documentation for more details on the 
+c         above three parameters.
+c 
+c on return
+c---------- 
+c 1) elementary statistics on the matrix is written on output unit 
+c    iout. See below for detailed explanation of typical output. 
+c 2) the entries of a, ja, ia are sorted.
+c
+c---------- 
+c 
+c ao	= real*8 array of length nnz used as work array.
+c jao	= integer work array of length max(2*n+1,nnz) 
+c iao   = integer work array of length n+1
+c
+c Note  : title, key, type are the same paramaters as those
+c         used for Harwell-Bowing matrices.
+c 
+c-----------------------------------------------------------------------
+c Output description:
+c--------------------
+c *** The following info needs to be updated.
+c
+c + A header containing the Title, key, type of the matrix and, if values
+c   are not provided a message to that effect.
+c    * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+c    * SYMMETRIC STRUCTURE MEDIEVAL RUSSIAN TOWNS                       
+c    *                    Key = RUSSIANT , Type = SSA                   
+c    * No values provided - Information of pattern only                 
+c    * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+c
+c +  dimension n, number of nonzero elements nnz, average number of
+c    nonzero elements per column, standard deviation for this average.
+c +  if the matrix is upper or lower triangular a message to that effect
+c    is printed. Also the number of nonzeros in the strict upper 
+c    (lower) parts and the main diagonal are printed.
+c +  weight of longest column. This is the largest number of nonzero 
+c    elements in a column encountered. Similarly for weight of 
+c    largest/smallest row.
+c +  lower dandwidth as defined by
+c          ml = max ( i-j, / all  a(i,j).ne. 0 ) 
+c +  upper bandwidth as defined by
+c          mu = max ( j-i, / all  a(i,j).ne. 0 ) 
+c    NOTE that ml or mu can be negative. ml .lt. 0 would mean
+c    that A is confined to the strict upper part above the diagonal 
+c    number -ml. Similarly for mu.
+c
+c +  maximun bandwidth as defined by
+c    Max (  Max [ j ; a(i,j) .ne. 0 ] - Min [ j ; a(i,j) .ne. 0 ] )
+c     i  
+c +  average bandwidth = average over all columns of the widths each column.
+c
+c +  If there are zero columns /or rows a message is printed
+c    giving the number of such columns/rows.
+c    
+c +  matching elements in A and transp(A) :this counts the number of
+c    positions (i,j) such that if a(i,j) .ne. 0 then a(j,i) .ne. 0.
+c    if this number is equal to nnz then the matrix is symmetric.
+c +  Relative symmetry match : this is the ratio of the previous integer
+c    over nnz. If this ratio is equal to one then the matrix has a
+c    symmetric structure. 
+c
+c +  average distance of a given element from the diagonal, standard dev.
+c    the distance of a(i,j) is defined as iabs(j-i). 
+c
+c +  Frobenius norm of A
+c    Frobenius norm of 0.5*(A + transp(A))
+c    Frobenius norm of 0.5*(A - transp(A))
+c    these numbers provide information on the degree of symmetry
+c    of the matrix. If the norm of the nonsymmetric part is
+c    zero then the matrix is symmetric.
+c
+c + 90% of matrix is in the band of width k, means that
+c   by moving away and in a symmetric manner from the main
+c   diagonal you would have to include exactly k diagonals 
+c   (k is always odd), in order to include 90% of the nonzero 
+c   elements of A.  The same thing is then for 80%.
+c 
+c + The total number of nonvoid diagonals, i.e., among the
+c   2n-1 diagonals of the matrix which have at least one nonxero
+c   element.
+c
+c +  Most important diagonals. The code selects a number of k
+c    (k .le. 10) diagonals that are the most important ones, i.e.
+c    that have the largest number of nonzero elements. Any diagonal
+c    that has fewer than 1% of the nonzero elements of A is dropped.
+c    the numbers printed are the offsets with respect to the 
+c    main diagonal, going from left tp right. 
+c    Thus 0 means the main diagonal -1 means the subdiagonal, and 
+c    +10 means the 10th upper diagonal.
+c +  The accumulated percentages in the next line represent the 
+c    percentage of the nonzero elements represented by the diagonals
+c    up the current one put together. 
+c    Thus:
+c    *  The 10 most important diagonals are (offsets)    :             *
+c    *     0     1     2    24    21     4    23    22    20    19     *
+c    *  The accumulated percentages they represent are   :             *
+c    *  40.4  68.1  77.7  80.9  84.0  86.2  87.2  88.3  89.4  90.4     *
+c    *-----------------------------------------------------------------*
+c    shows the offsets of the most important  diagonals and
+c    40.4 represent ratio of the number of nonzero elements in the
+c    diagonal zero (main diagonal) over the total number of nonzero
+c    elements. the second number indicates that the diagonal 0 and the 
+c    diagonal 1 together hold 68.1% of the matrix, etc..
+c
+c +  Block structure:
+c    if the matrix has a block structure then the block size is found
+c    and printed. Otherwise the info1 will say that the matrix
+c    does not have a block structure. Note that block struture has
+c    a very specific meaning here. the matrix has a block structure
+c    if it consists of square blocks that are dense. even if there
+c    are zero elements in the blocks  they should be represented 
+c    otherwise it would be possible to determine the block size.
+c
+c-----------------------------------------------------------------------
+	real*8 dcount(20),amx
+	integer ioff(20)
+	character*61 tmpst
+	logical sym
+c-----------------------------------------------------------------------
+	data ipar1 /1/
+	write (iout,99) 
+        write (iout,97) title(2:72), key, type
+ 97     format(2x,' * ',a71,' *'/,
+     *         2x,' *',20x,'Key = ',a8,' , Type = ',a3,25x,' *')
+	if (.not. valued) write (iout,98)
+ 98    format(2x,' * No values provided - Information on pattern only',
+     *   23x,' *')
+c---------------------------------------------------------------------
+	nnz = ia(n+1)-ia(1)
+	sym = ((type(2:2) .eq. 'S') .or. (type(2:2) .eq. 'Z')
+     *    .or. (type(2:2) .eq. 's') .or. (type(2:2) .eq. 'z')) 
+c
+        write (iout, 99)
+        write(iout, 100) n, nnz
+	job = 0
+	if (valued) job = 1
+	ipos = 1
+        call csrcsc(n, job, ipos, a, ja, ia, ao, jao, iao)
+        call csrcsc(n, job, ipos, ao, jao, iao, a, ja, ia)
+c-------------------------------------------------------------------
+c computing max bandwith, max number of nonzero elements per column
+c min nonzero elements per column/row, row/column diagonal dominance 
+c occurences, average distance of an element from diagonal, number of 
+c elemnts in lower and upper parts, ...
+c------------------------------------------------------------------
+c    jao will be modified later, so we call skyline here
+          call skyline(n,sym,ja,ia,jao,iao,nsky)
+          call nonz_lud(n,ja,ia,nlower, nupper, ndiag) 
+          call avnz_col(n,ja,ia,iao, ndiag, av, st)
+c------ write out info ----------------------------------------------
+	  if (sym)  nupper = nlower 
+          write(iout, 101) av, st
+          if (nlower .eq. 0 ) write(iout, 105)
+ 1        if (nupper .eq. 0) write(iout, 106)
+          write(iout, 107) nlower
+          write(iout, 108) nupper
+          write(iout, 109) ndiag
+c
+          call nonz(n,sym, ja, ia, iao, nzmaxc, nzminc,
+     *                  nzmaxr, nzminr, nzcol, nzrow)
+          write(iout, 1020) nzmaxc, nzminc
+c
+	  if (.not. sym) write(iout, 1021) nzmaxr, nzminr
+c
+	  if (nzcol .ne. 0) write(iout,116) nzcol
+	  if (nzrow .ne. 0) write(iout,115) nzrow
+c     
+          call diag_domi(n,sym,valued,a, ja,ia,ao, jao, iao,
+     *                           ddomc, ddomr)
+c----------------------------------------------------------------------- 
+c symmetry and near symmetry - Frobenius  norms
+c-----------------------------------------------------------------------
+          call frobnorm(n,sym,a,ja,ia,Fnorm)   
+          call ansym(n,sym,a,ja,ia,ao,jao,iao,imatch,av,fas,fan)
+          call distaij(n,nnz,sym,ja,ia,dist, std)
+          amx = 0.0d0
+          do 40 k=1, nnz
+            amx = max(amx, abs(a(k)) )
+ 40       continue
+          write (iout,103) imatch, av, dist, std
+          write(iout,96) 
+          if (valued) then
+             write(iout,104) Fnorm, fas, fan, amx, ddomr, ddomc
+             write (iout,96)
+          endif
+c-----------------------------------------------------------------------
+c--------------------bandedness- main diagonals ----------------------- -
+c-----------------------------------------------------------------------
+	n2 = n+n-1
+	do 8 i=1, n2
+             jao(i) = 0
+ 8        continue
+          do 9 i=1, n
+             k1 = ia(i)
+             k2 = ia(i+1) -1
+             do 91 k=k1, k2
+                j = ja(k)
+                jao(n+i-j) = jao(n+i-j) +1
+ 91          continue 
+ 9        continue
+c
+          call bandwidth(n,ja, ia, ml, mu, iband, bndav)
+c
+c     write bandwidth information .
+c     
+          write(iout,117)  ml, mu, iband, bndav
+c     
+          write(iout,1175) nsky
+c     
+c         call percentage_matrix(n,nnz,ja,ia,jao,90,jb2)
+c         call percentage_matrix(n,nnz,ja,ia,jao,80,jb1)
+          nrow = n
+          ncol = n
+          call distdiag(nrow,ncol,ja,ia,jao)
+          call bandpart(n,ja,ia,jao,90,jb2)
+          call bandpart(n,ja,ia,jao,80,jb1)
+          write (iout,112) 2*jb2+1, 2*jb1+1
+c-----------------------------------------------------------------
+          nzdiag = 0
+          n2 = n+n-1
+          do 42 i=1, n2
+             if (jao(i) .ne. 0) nzdiag=nzdiag+1
+ 42       continue
+          call n_imp_diag(n,nnz,jao,ipar1, ndiag,ioff,dcount)
+          write (iout,118) nzdiag
+          write (tmpst,'(10i6)') (ioff(j),j=1,ndiag)
+          write (iout,110) ndiag,tmpst
+          write (tmpst,'(10f6.1)')(dcount(j), j=1,ndiag)
+          write (iout,111) tmpst
+          write (iout, 96)
+c     jump to next page -- optional //
+c     write (iout,'(1h1)') 
+c-----------------------------------------------------------------------
+c     determine block size if matrix is a block matrix..
+c-----------------------------------------------------------------------
+          call blkfnd(n, ja, ia, nblk)
+          if (nblk .le. 1) then 
+             write(iout,113)  
+          else 
+             write(iout,114) nblk
+          endif 
+          write (iout,96)
+c     
+c---------- done. Next define all the formats -------------------------- 
+c
+ 99    format (2x,38(2h *))
+ 96    format (6x,' *',65(1h-),'*')
+c-----------------------------------------------------------------------
+ 100   format(
+     * 6x,' *  Dimension N                                      = ',
+     * i10,'  *'/
+     * 6x,' *  Number of nonzero elements                       = ',
+     * i10,'  *')
+ 101   format(
+     * 6x,' *  Average number of nonzero elements/Column        = ',
+     * f10.4,'  *'/
+     * 6x,' *  Standard deviation for above average             = ',
+     * f10.4,'  *')
+c-----------------------------------------------------------------------
+ 1020       format(
+     * 6x,' *  Weight of longest column                         = ',
+     * i10,'  *'/
+     * 6x,' *  Weight of shortest column                        = ',
+     * i10,'  *')
+ 1021       format(
+     * 6x,' *  Weight of longest row                            = ',
+     * i10,'  *'/
+     * 6x,' *  Weight of shortest row                           = ',
+     * i10,'  *')
+ 117        format(
+     * 6x,' *  Lower bandwidth  (max: i-j, a(i,j) .ne. 0)       = ',
+     * i10,'  *'/
+     * 6x,' *  Upper bandwidth  (max: j-i, a(i,j) .ne. 0)       = ',
+     * i10,'  *'/
+     * 6x,' *  Maximum Bandwidth                                = ',
+     * i10,'  *'/
+     * 6x,' *  Average Bandwidth                                = ',
+     * e10.3,'  *')
+ 1175       format(
+     * 6x,' *  Number of nonzeros in skyline storage            = ',
+     * i10,'  *')
+ 103   format(
+     * 6x,' *  Matching elements in symmetry                    = ',
+     * i10,'  *'/
+     * 6x,' *  Relative Symmetry Match (symmetry=1)             = ',
+     * f10.4,'  *'/
+     * 6x,' *  Average distance of a(i,j)  from diag.           = ',
+     * e10.3,'  *'/
+     * 6x,' *  Standard deviation for above average             = ',
+     * e10.3,'  *') 
+ 104   format(
+     * 6x,' *  Frobenius norm of A                              = ',
+     * e10.3,'  *'/
+     * 6x,' *  Frobenius norm of symmetric part                 = ',
+     * e10.3,'  *'/
+     * 6x,' *  Frobenius norm of nonsymmetric part              = ',
+     * e10.3,'  *'/
+     * 6x,' *  Maximum element in A                             = ',
+     * e10.3,'  *'/
+     * 6x,' *  Percentage of weakly diagonally dominant rows    = ',
+     * e10.3,'  *'/
+     * 6x,' *  Percentage of weakly diagonally dominant columns = ',
+     * e10.3,'  *')
+ 105        format(
+     * 6x,' *  The matrix is lower triangular ...       ',21x,' *')
+ 106        format(
+     * 6x,' *  The matrix is upper triangular ...       ',21x,' *')
+ 107        format(
+     * 6x,' *  Nonzero elements in strict lower part            = ',
+     * i10,'  *')
+ 108       format(
+     * 6x,' *  Nonzero elements in strict upper part            = ',
+     * i10,'  *')
+ 109       format(
+     * 6x,' *  Nonzero elements in main diagonal                = ',
+     * i10,'  *')
+ 110   format(6x,' *  The ', i2, ' most important',
+     *	   ' diagonals are (offsets)    : ',10x,'  *',/,  
+     * 6x,' *',a61,3x,' *')
+ 111   format(6x,' *  The accumulated percentages they represent are ',
+     * '  : ', 10x,'  *',/,
+     * 6x,' *',a61,3x,' *')
+c 111	format( 
+c     * 6x,' *  They constitute the following % of A             = ',
+c     * f8.1,' %  *') 
+ 112	format( 
+     * 6x,' *  90% of matrix is in the band of width            = ',
+     * i10,'  *',/,
+     * 6x,' *  80% of matrix is in the band of width            = ',
+     * i10,'  *')
+ 113 	format( 
+     * 6x,' *  The matrix does not have a block structure ',19x,
+     *    ' *')
+ 114 	format( 
+     * 6x,' *  Block structure found with block size            = ',
+     * i10,'  *')
+ 115 	format( 
+     * 6x,' *  There are zero rows. Number of such rows         = ', 
+     * i10,'  *')
+ 116 	format( 
+     * 6x,' *  There are zero columns. Number of such columns   = ', 
+     * i10,'  *')
+ 118 	format( 
+     * 6x,' *  The total number of nonvoid diagonals is         = ', 
+     * i10,'  *')
+c-------------------------- end of dinfo --------------------------
+        return
+        end
diff --git a/INFO/info.saylr1 b/INFO/info.saylr1
new file mode 100644
index 0000000..5f301b0
--- /dev/null
+++ b/INFO/info.saylr1
@@ -0,0 +1,42 @@
+   * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+   * unsymmetric matrix of paul saylor - 14 by 17 2d grid   may, 1983        *
+   *                    Key = saylr1   , Type = rua                          *
+   * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+       *  Dimension N                                      =        238  *
+       *  Number of nonzero elements                       =       1128  *
+       *  Average number of nonzero elements/Column        =     4.7395  *
+       *  Standard deviation for above average             =     0.4757  *
+       *  Nonzero elements in strict lower part            =        445  *
+       *  Nonzero elements in strict upper part            =        445  *
+       *  Nonzero elements in main diagonal                =        238  *
+       *  Weight of longest column                         =          5  *
+       *  Weight of shortest column                        =          3  *
+       *  Weight of longest row                            =          5  *
+       *  Weight of shortest row                           =          3  *
+       *  Matching elements in symmetry                    =       1128  *
+       *  Relative Symmetry Match (symmetry=1)             =     1.0000  *
+       *  Average distance of a(i,j)  from diag.           =  0.595E+01  *
+       *  Standard deviation for above average             =  0.654E+01  *
+       *-----------------------------------------------------------------*
+       *  Frobenius norm of A                              =  0.886E+09  *
+       *  Frobenius norm of symmetric part                 =  0.991E+09  *
+       *  Frobenius norm of nonsymmetric part              =  0.443E+09  *
+       *  Maximum element in A                             =  0.306E+09  *
+       *  Percentage of weakly diagonally dominant rows    =  0.761E+00  *
+       *  Percentage of weakly diagonally dominant columns =  0.744E+00  *
+       *-----------------------------------------------------------------*
+       *  Lower bandwidth  (max: i-j, a(i,j) .ne. 0)       =         14  *
+       *  Upper bandwidth  (max: j-i, a(i,j) .ne. 0)       =         14  *
+       *  Maximum Bandwidth                                =         29  *
+       *  Average Bandwidth                                =  0.275E+02  *
+       *  Number of nonzeros in skyline storage            =       6536  *
+       *  90% of matrix is in the band of width            =         27  *
+       *  80% of matrix is in the band of width            =         27  *
+       *  The total number of nonvoid diagonals is         =          5  *
+       *  The  5 most important diagonals are (offsets)    :             *
+       *     0    14   -14     1    -1                                   *
+       *  The accumulated percentages they represent are   :             *
+       *  21.1  41.0  60.8  80.4 100.0                                   *
+       *-----------------------------------------------------------------*
+       *  The matrix does not have a block structure                     *
+       *-----------------------------------------------------------------*
diff --git a/INFO/infofun.f b/INFO/infofun.f
new file mode 100644
index 0000000..85b4c7f
--- /dev/null
+++ b/INFO/infofun.f
@@ -0,0 +1,800 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c                  INFORMATION ROUTINES. INFO MODULE                   c
+c----------------------------------------------------------------------c
+c bandwidth :  Computes  ml     = lower_bandwidth(A)                   c
+c                        mu     = upper_bandwidth(A)                   c
+c                        iband  = max_bandwidth(A)                     c
+c                        bndav  = average_bandwidth(A)                 c
+c nonz      :  Computes  nzmaxc = max_column_length(A)                 c
+c                        nzminc = min_column_length(A)                 c
+c                        nzmaxr = max_row_length(A)                    c
+c                        nzminr = min_row_length(A)                    c
+c                        nzcol  = zero_column_number(A)                c
+c                        nzrow  = zero_row_number(A)                   c
+c diag_domi :  Computes  ddomc  = diag_domi_column_percentage(A)       c
+c                        ddomr  = diag_domi_row_percentage(A)          c
+c frobnorm  :  Computes  Fnorm  = Frobenius_norm(A)                    c
+c ansym     :  Computes  fas    = sym_part_Frobenius_norm(A)           c
+c                        fan    = nonsym_part_Frobenius_norm(A)        c
+c                        imatch = matching_elements_number(A)          c
+c                        av     = relative_sym_match(A)                c
+c distaij   :  Computes  dist   = average_dist_of_a(i,j)(A)            c
+c                        std    = standard_deviation(A)                c
+c skyline   :  Computes  nsky   = nonzero_number_in_skyline(A)         c
+c distdiag  :  Computes  dist   = element_number_in_eachdiag(A)        c
+c bandpart  :  Computes  band   = bandwidth_width(A)                   c
+c n_imp_diag:  Computes  ndiag  = important_diag_number(A)             c
+c nonz_lud  :  Computes  nlower = nonzero_number_of_lower_part(A)      c
+c                        nupper = nonzero_number_of_upper_part(A)      c
+c                        ndiag  = nonzero_number_of_maindiag(A)        c
+c avnz_col  :  Computes  av     = average_nonzero_number_in_column(A)  c
+c                        st     = standard_deviation(A)                c
+c vbrinfo   :  Print info on matrix in variable block row format       c
+c----------------------------------------------------------------------c
+      subroutine bandwidth(n,ja, ia, ml, mu, iband, bndav)
+      implicit none 
+      integer n, ml, mu, iband
+      integer ja(*), ia(n+1)
+      real*8 bndav
+c-----------------------------------------------------------------------
+c this routine computes the lower, upper, maximum, and average 
+c bandwidths.     revised -- July 12, 2001  -- bug fix -- YS. 
+c-----------------------------------------------------------------------
+c On Entry:
+c----------
+c n     = integer. column dimension of matrix
+c a     = real array containing the nonzero elements of the matrix
+c         the elements are stored by columns in order
+c         (i.e. column i comes before column i+1, but the elements
+c         within each column can be disordered).
+c ja    = integer array containing the row indices of elements in a
+c ia    = integer array containing of length n+1 containing the
+c         pointers to the beginning of the columns in arrays a and ja.
+c         It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
+c
+c on return
+c----------
+c ml    = lower bandwidth as defined by
+c        ml = max(i-j | all  a(i,j).ne. 0)
+c mu    = upper bandwidth as defined by
+c        mu = max ( j-i | all  a(i,j).ne. 0 )
+c iband =  maximum bandwidth as defined by
+c         iband = Max (  Max [ j | a(i,j) .ne. 0 ] - 
+c                        Min [ j | a(i,j) .ne. 0 ] )
+c bndav = Average Bandwidth          
+c-----------------------------------------------------------------------
+c     locals
+      integer max 
+      integer j0, j1, jminc, jmaxc, i
+c-----------------------------------------------------------------------
+      ml = -n
+      mu = -n
+      bndav = 0.0d0
+      iband = 0 
+      do 10 i=1,n
+         j0 = ia(i)
+         j1 = ia(i+1) - 1
+         jminc = ja(j0)
+         jmaxc = ja(j1)
+         ml = max(ml,i-jminc)
+         mu = max(mu,jmaxc-i)
+         iband = max(iband,jmaxc-jminc+1)
+         bndav = bndav+real( jmaxc-jminc+1)
+ 10   continue
+      bndav = bndav/real(n)
+      return
+c-----end-of-bandwidth--------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine nonz(n,sym, ja, ia, iao, nzmaxc, nzminc, 
+     *     nzmaxr, nzminr, nzcol, nzrow)
+      implicit none 
+      integer n , nzmaxc, nzminc, nzmaxr, nzminr, nzcol, nzrow
+      integer ja(*), ia(n+1), iao(n+1)
+      logical sym
+c----------------------------------------------------------------------
+c     this routine computes maximum numbers of nonzero elements 
+c     per column/row, minimum numbers of nonzero elements per column/row, 
+c     and  numbers of zero columns/rows.
+c----------------------------------------------------------------------
+c     On Entry:
+c----------
+c     n     = integer column dimension of matrix
+c     ja    = integer array containing the row indices of elements in a
+c     ia    = integer array containing of length n+1 containing the
+c     pointers to the beginning of the columns in arrays a and ja.
+c     It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
+c     iao   = similar array for the transpose of the matrix. 
+c     sym   = logical variable indicating whether or not the matrix is 
+c     stored in symmetric mode.
+c     on return
+c----------
+c     nzmaxc = max length of columns
+c     nzminc = min length of columns 
+c     nzmaxr = max length of rows
+c nzminr = min length of rows
+c     nzcol  = number of zero columns
+c     nzrow = number of zero rows
+c-----------------------------------------------------------------------
+      integer  i, j0, j0r, j1r, indiag, k, j1, lenc, lenr 
+c
+      nzmaxc = 0
+      nzminc = n
+      nzmaxr = 0
+      nzminr = n
+      nzcol  = 0
+      nzrow  = 0
+c-----------------------------------------------------------------------
+      do 10 i = 1, n
+         j0 = ia(i)
+         j1 = ia(i+1) 
+         j0r = iao(i)
+         j1r = iao(i+1)
+         indiag = 0
+         do 20 k=j0, j1-1 
+            if (ja(k) .eq. i) indiag = 1
+ 20      continue
+c         
+         lenc = j1-j0
+         lenr = j1r-j0r
+c         
+         if (sym) lenc = lenc + lenr - indiag
+         if (lenc .le. 0) nzcol = nzcol +1
+         nzmaxc = max0(nzmaxc,lenc)
+         nzminc = min0(nzminc,lenc)
+         if (lenr .le. 0) nzrow = nzrow+1
+         nzmaxr = max0(nzmaxr,lenr)
+         nzminr = min0(nzminr,lenr)
+ 10   continue
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine diag_domi(n,sym,valued,a, ja,ia,ao,jao, iao, 
+     *     ddomc, ddomr)
+      implicit none 
+      real*8 a(*), ao(*), ddomc, ddomr
+      integer n, ja(*), ia(n+1), jao(*), iao(n+1)
+      logical sym, valued
+c-----------------------------------------------------------------
+c     this routine computes the percentage of weakly diagonally 
+c     dominant rows/columns
+c-----------------------------------------------------------------
+c     on entry:
+c     ---------
+c     n     = integer column dimension of matrix
+c a     = real array containing the nonzero elements of the matrix
+c     the elements are stored by columns in order
+c     (i.e. column i comes before column i+1, but the elements
+c     within each column can be disordered).
+c     ja    = integer array containing the row indices of elements in a
+c ia    = integer array containing of length n+1 containing the
+c     pointers to the beginning of the columns in arrays a and ja.
+c     It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
+c     ao    = real array containing the nonzero elements of the matrix
+c     the elements are stored by rows in order
+c     (i.e. row i comes before row i+1, but the elements
+c     within each row can be disordered).
+c ao,jao, iao, 
+c     structure for transpose of a 
+c     sym   = logical variable indicating whether or not the matrix is
+c     symmetric.
+c     valued= logical equal to .true. if values are provided and .false.
+c         if only the pattern of the matrix is provided. (in that
+c     case a(*) and ao(*) are dummy arrays.
+c     
+c     ON RETURN
+c----------
+c     ddomc = percentage of weakly diagonally dominant columns
+c     ddomr = percentage of weakly diagonally dominant rows
+c-------------------------------------------------------------------
+c     locals
+      integer i, j0, j1, k, j 
+      real*8 aii, dsumr, dsumc 
+c     number of diagonally dominant columns
+c     real arithmetic used to avoid problems.. YS. 03/27/01 
+      ddomc = 0.0  
+c     number of diagonally dominant rows
+      ddomr = 0.0 
+      do 10 i = 1, n
+         j0 = ia(i)
+         j1 = ia(i+1) - 1
+         if (valued) then
+            aii = 0.0d0
+            dsumc = 0.0d0
+            do 20 k=j0,j1
+               j = ja(k) 
+               if (j .eq. i) then
+                  aii = abs(a(k))
+               else
+                  dsumc = dsumc + abs(a(k))
+               endif
+ 20         continue
+            dsumr = 0.0d0
+            if (.not. sym) then
+               do 30 k=iao(i), iao(i+1)-1
+                  if (jao(k) .ne. i) dsumr = dsumr+abs(ao(k))
+ 30            continue 
+            else
+               dsumr = dsumc
+            endif
+            if (dsumc .le. aii) ddomc = ddomc + 1.0
+            if (dsumr .le. aii) ddomr = ddomr + 1.0
+         endif
+ 10   continue
+      ddomr = ddomr / real(n)
+      ddomc = ddomc / real(n)
+      return
+c-----------------------------------------------------------------------
+c--------end-of-diag_moni-----------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine frobnorm(n,sym,a,ja,ia,Fnorm)
+      implicit none 
+      integer n 
+      real*8 a(*),Fnorm
+      integer ja(*),ia(n+1)
+      logical sym
+c--------------------------------------------------------------------------
+c     this routine computes the Frobenius norm of A.
+c--------------------------------------------------------------------------
+c     on entry:
+c-----------
+c n      = integer colum dimension of matrix
+c a      = real array containing the nonzero elements of the matrix
+c          the elements are stored by columns in order
+c          (i.e. column i comes before column i+1, but the elements
+c          within each column can be disordered).
+c ja     = integer array containing the row indices of elements in a.
+c ia     = integer array containing of length n+1 containing the
+c          pointers to the beginning of the columns in arrays a and 
+c          ja. It is assumed that ia(*)= 1 and ia(n+1)  = nnz +1.
+c sym    = logical variable indicating whether or not the matrix is
+c          symmetric.
+c
+c on return
+c-----------
+c Fnorm  = Frobenius norm of A.
+c--------------------------------------------------------------------------
+      real*8 Fdiag
+      integer i, k 
+      Fdiag = 0.0
+      Fnorm = 0.0
+      do i =1,n
+         do k = ia(i), ia(i+1)-1
+            if (ja(k) .eq. i) then
+               Fdiag = Fdiag + a(k)**2
+            else
+               Fnorm = Fnorm + a(k)**2
+            endif
+         enddo 
+      enddo 
+      if (sym) then
+         Fnorm = 2*Fnorm +Fdiag
+      else
+        Fnorm = Fnorm + Fdiag
+      endif
+      Fnorm = sqrt(Fnorm)
+      return
+      end
+c----------------------------------------------------------------------
+      subroutine ansym(n,sym,a,ja,ia,ao,jao,iao,imatch,
+     *     av,fas,fan)
+c---------------------------------------------------------------------
+c     this routine computes the Frobenius norm of the symmetric and
+c     non-symmetric parts of A, computes number of matching elements
+c     in symmetry and relative symmetry match. 
+c---------------------------------------------------------------------
+c on entry:
+c----------
+c n   = integer column dimension of matrix
+c a   = real array containing the nonzero elements of the matrix
+c       the elements are stored by columns in order
+c       (i.e. column i comes before column i+1, but the elements
+c       within each column can be disordered).
+c ja  = integer array containing the row indices of elements in a
+c ia  = integer array containing of length n+1 containing the
+c       pointers to the beginning of the columns in arrays a and ja.
+c       It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
+c sym = logical variable indicating whether or not the matrix is
+c       symmetric.
+c on return
+c----------
+c fas   = Frobenius norm of symmetric part
+c fan   = Frobenius norm of non-symmetric part
+c imatch = number of matching elements in symmetry
+c av     = relative symmetry match (symmetry = 1)
+c ao,jao,iao = transpose of A just as a, ja, ia contains 
+c              information of A.
+c-----------------------------------------------------------------------
+      implicit real*8 (a-h, o-z)
+      real*8 a(*),ao(*),fas,fan,av, Fnorm, st
+      integer n, ja(*), ia(n+1), jao(*), iao(n+1),imatch
+      logical sym
+c-----------------------------------------------------------------------
+      nnz    = ia(n+1)-ia(1)
+      call csrcsc(n,1,1,a,ja,ia,ao,jao,iao)
+      if (sym) goto 7
+      st     = 0.0d0
+      fas    = 0.0d0
+      fan    = 0.0d0
+      imatch = 0
+      do 6 i=1,n
+         k1 = ia(i)
+         k2 = iao(i)
+         k1max = ia(i+1) - 1
+         k2max = iao(i+1) - 1
+c     
+ 5       if (k1 .gt. k1max .or. k2 .gt. k2max) goto 6
+c     
+         j1 = ja(k1)
+         j2 = jao(k2)
+         if (j1 .ne. j2 ) goto 51
+         fas = fas + (a(k1)+ao(k2))**2
+         fan = fan + (a(k1)-ao(k2))**2
+         st  = st + a(k1)**2
+         imatch = imatch + 1
+ 51      k1 = k1+1
+         k2 = k2+1
+         if (j1 .lt. j2)  k2 = k2 - 1
+         if (j1 .gt. j2)  k1 = k1 - 1
+         goto 5
+ 6    continue
+      fas = 0.25D0 * fas
+      fan = 0.25D0 * fan
+ 7    call frobnorm(n,sym,ao,jao,iao,Fnorm)
+      if (sym) then
+         imatch = nnz
+         fas = Fnorm
+         fan = 0.0d0
+      else
+         if (imatch.eq.nnz) then
+            st = 0.0D0
+         else
+            st = 0.5D0 * (Fnorm**2 - st)
+            if (st.lt.0.0D0) st = 0.0D0
+         endif
+         fas = sqrt(fas + st)
+         fan = sqrt(fan + st)
+      endif
+      av = real(imatch)/real(nnz)
+      return
+      end
+c------end-of-ansym-----------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine distaij(n,nnz,sym,ja,ia,dist, std)
+      implicit real*8 (a-h, o-z)
+      real*8  dist, std
+      integer ja(*), ia(n+1)
+c-----------------------------------------------------------------------
+c     this routine computes the average distance of a(i,j) from diag and
+c     standard deviation  for this average.
+c-----------------------------------------------------------------------
+c On entry :
+c-----------
+c n     = integer. column dimension of matrix
+c nnz   = number of nonzero elements of matrix
+c ja    = integer array containing the row indices of elements in a
+c ia    = integer array containing of length n+1 containing the
+c         pointers to the beginning of the columns in arrays a and ja.
+c         It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
+c sym   = logical variable indicating whether or not the matrix is
+c         symmetric.
+c on return
+c----------
+c dist  = average distance of a(i,j) from diag.
+c std   = standard deviation for above average.
+c-----------------------------------------------------------------------
+c
+c distance of an element from diagonal.
+c
+      dist   = 0.0
+      std = 0.0
+      do 3 i=1,n
+         j0 = ia(i)
+         j1 = ia(i+1) - 1
+         do 31 k=j0, j1
+            j=ja(k)
+            dist = dist + real(iabs(j-i) )
+ 31      continue
+ 3    continue
+      dist = dist/real(nnz)
+      do 6 i = 1, n 
+         do 61 k=ia(i), ia(i+1) - 1
+            std=std+(dist-real(iabs(ja(k)-i)))**2
+ 61      continue
+ 6    continue
+      std = sqrt(std/ real(nnz))
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine skyline(n,sym,ja,ia,jao,iao,nsky)
+      implicit real*8 (a-h, o-z)
+      integer n, ja(*), ia(n+1), jao(*), iao(n+1)
+      integer nskyl, nskyu, nsky
+      logical sym
+c-------------------------------------------------------------------
+c this routine computes the number of nonzeros in the skyline storage.
+c-------------------------------------------------------------------
+c
+c On entry :
+c-----------
+c n     = integer. column dimension of matrix
+c ja    = integer array containing the row indices of elements in a
+c ia    = integer array containing of length n+1 containing the
+c         pointers to the beginning of the columns in arrays a and ja.
+c         It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
+c iao   = integer array containing of length n+1 containing the
+c         pointers to the beginning of the rows in arrays ao and jao.
+c         It is assumed that iao(*) = 1 and iao(n+1) = nzz+1.
+c jao   = integer array containing the column indices of elements in ao.
+c sym   = logical variable indicating whether or not the matrix is
+c         symmetric.
+c on return
+c----------
+c nsky  = number of nonzeros in skyline storage
+c-------------------------------------------------------------------
+c
+c nskyu = skyline storage for upper part
+      nskyu = 0
+c nskyl = skyline storage for lower part
+      nskyl = 0
+      do 10 i=1,n
+         j0 = ia(i)
+         j0r = iao(i)
+         
+         jminc = ja(j0)
+         jminr = jao(j0r)
+         if (sym) jminc = jminr
+         
+         nskyl = nskyl + i-jminr + 1
+         nskyu = nskyu + i-jminc + 1
+         
+ 10   continue
+      nsky = nskyl+nskyu-n
+      if (sym)  nsky = nskyl
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine distdiag(nrow,ncol,ja,ia,dist)
+      implicit real*8 (a-h, o-z)
+      integer nrow,ncol,ja(*), ia(nrow+1),dist(*)
+c----------------------------------------------------------------------
+c this routine computes the numbers of elements in each diagonal. 
+c----------------------------------------------------------------------
+c On entry :
+c-----------
+c nrow  = integer. row dimension of matrix
+c ncol  = integer. column dimension of matrix
+c ja    = integer array containing the row indices of elements in a
+c ia    = integer array containing of length n+1 containing the
+c         pointers to the beginning of the columns in arrays a and ja.
+c         It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
+c on return
+c----------
+c dist  = integer array containing the numbers of elements in each of 
+c         the nrow+ncol-1 diagonals of A. dist(k) contains the 
+c         number of elements in diagonal '-nrow+k'.  k ranges from 
+c         1 to (nrow+ncol-1).
+c----------------------------------------------------------------------
+      nnz  = ia(nrow+1)-ia(1)
+      n2   = nrow+ncol-1
+      do 8 i=1, n2
+         dist(i) = 0
+ 8    continue
+      do 9 i=1, nrow
+         k1 = ia(i)
+         k2 = ia(i+1) -1
+         do 91 k=k1, k2
+            j = ja(k)
+            dist(nrow+j-i) = dist(nrow+j-i) +1
+ 91      continue
+ 9    continue
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine bandpart(n,ja,ia,dist,nper,band)
+      implicit real*8 (a-h, o-z)
+      integer n,ja(*), ia(n+1),dist(*)
+      integer nper,band
+c-------------------------------------------------------------------------
+c this routine computes the bandwidth of the banded matrix, which contains
+c 'nper' percent of the original matrix.
+c-------------------------------------------------------------------------
+c On entry :
+c-----------
+c n     = integer. column dimension of matrix
+c ja    = integer array containing the row indices of elements in a
+c ia    = integer array containing of length n+1 containing the
+c         pointers to the beginning of the columns in arrays a and ja.
+c         It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
+c dist  = integer array containing the numbers of elements in the 
+c         matrix with different distance of row indices and column 
+c         indices.
+c nper  = percentage of matrix  within the bandwidth
+c on return
+c----------
+c band  = the width of the bandwidth
+c----------------------------------------------------------------------
+      nnz  = ia(n+1)-ia(1)
+      iacc  = dist(n)
+      band  = 0
+      j     = 0
+ 10   j     = j+1
+      iacc  = iacc + dist(n+j) +dist(n-j) 
+      if (iacc*100 .le. nnz*nper) then 
+         band = band +1 
+         goto 10         
+      endif 
+      return 
+      end 
+c-----------------------------------------------------------------------      
+      subroutine  n_imp_diag(n,nnz,dist, ipar1,ndiag,ioff,dcount)
+      implicit real*8 (a-h, o-z)
+      real*8  dcount(*)
+      integer n,nnz, dist(*), ndiag, ioff(*), ipar1
+c-----------------------------------------------------------------------
+c     this routine computes the most important diagonals.
+c-----------------------------------------------------------------------
+c
+c On entry :
+c-----------
+c n     = integer. column dimension of matrix
+c nnz   = number of nonzero elements of matrix
+c dist  = integer array containing the numbers of elements in the 
+c         matrix with different distance of row indices and column 
+c         indices. ipar1 = percentage of nonzero  elements of A that 
+c         a diagonal should have in order to be an important diagonal 
+c on return
+c----------
+c ndiag = number of the most important diagonals
+c ioff  = the offsets with respect to the main diagonal
+c dcount= the accumulated percentages
+c-----------------------------------------------------------------------
+      n2 = n+n-1
+      ndiag = 10
+      ndiag = min0(n2,ndiag)
+      itot  = 0
+      ii = 0
+      idiag = 0
+c     sort diagonals by decreasing order of weights.
+ 40   jmax = 0
+      i    = 1
+      do 41 k=1, n2
+         j = dist(k)
+         if (j .lt. jmax) goto 41
+         i = k
+         jmax = j
+ 41   continue
+c     permute ----
+c     save offsets and accumulated count if diagonal is acceptable
+c     (if it has at least ipar1*nnz/100 nonzero elements)
+c     quite if no more acceptable diagonals --
+c     
+      if (jmax*100 .lt. ipar1*nnz) goto 4
+      ii = ii+1
+      ioff(ii) = i-n
+      dist(i)   = - jmax
+      itot = itot + jmax
+      dcount(ii) = real(100*itot)/real(nnz)
+      if (ii .lt. ndiag) goto 40
+ 4    continue
+      ndiag = ii
+      return
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine nonz_lud(n,ja,ia,nlower, nupper, ndiag)
+      implicit real*8 (a-h, o-z)
+      integer n,  ja(*), ia(n+1)
+      integer nlower, nupper, ndiag
+c-----------------------------------------------------------------------
+c this routine computes the number of nonzero elements in strict lower
+c part, strict upper part, and main diagonal.
+c-----------------------------------------------------------------------
+c
+c On entry :
+c-----------
+c n     = integer. column dimension of matrix
+c ja    = integer array containing the row indices of elements in a
+c ia    = integer array containing of length n+1 containing the
+c         pointers to the beginning of the columns in arrays a and ja.
+c         It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
+c on return
+c----------
+c nlower= number of nonzero elements in strict lower part
+c nupper= number of nonzero elements in strict upper part
+c ndiag = number of nonzero elements in main diagonal
+c------------------------------------------------------------------- 
+c
+c number of nonzero elements in upper part
+c
+      nupper = 0
+      ndiag = 0
+      
+      do 3 i=1,n
+c     indiag = nonzero diagonal element indicator
+         do 31 k=ia(i), ia(i+1)-1
+            j=ja(k)
+            if (j .lt. i) nupper = nupper+1
+            if (j .eq. i) ndiag = ndiag + 1 
+ 31      continue
+ 3    continue
+      nlower = ia(n+1)-1-nupper-ndiag
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine avnz_col(n,ja,ia,iao, ndiag, av, st)
+      implicit real*8 (a-h, o-z)
+      real*8 av, st
+      integer n,  ja(*), ia(n+1), iao(n+1)
+c---------------------------------------------------------------------
+c     this routine computes average number of nonzero elements/column and
+c     standard deviation for this average
+c---------------------------------------------------------------------
+c
+c On entry :
+c-----------
+c n     = integer. column dimension of matrix
+c ja    = integer array containing the row indices of elements in a
+c ia    = integer array containing of length n+1 containing the
+c         pointers to the beginning of the columns in arrays a and ja.
+c         It is assumed that ia(*) = 1 and ia(n+1) = nzz+1.
+c ndiag = number of the most important diagonals
+c On return
+c----------
+c av    = average number of nonzero elements/column
+c st    = standard deviation for this average
+c Notes
+c---------
+c standard deviation will not be correct for symmetric storage. 
+c----------------------------------------------------------------------
+c     standard deviatioan for the average
+      st = 0.0d0
+c     average and standard deviation
+c     
+      av = real(ia(n+1)-1)/real(n)
+c     
+c     will be corrected later.
+c     
+      do 3 i=1,n
+         j0 = ia(i)
+         j1 = ia(i+1) - 1
+c     indiag = nonzero diagonal element indicator
+         do 31 k=j0, j1
+            j=ja(k)
+ 31      continue
+         lenc = j1+1-j0
+         st = st + (real(lenc) - av)**2
+ 3    continue
+c     
+      st = sqrt( st / real(n) )
+      return
+      end
+c-----------------------------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine vbrinfo(nr, nc, kvstr, kvstc, ia, ja, ka, iwk, iout)
+c-----------------------------------------------------------------------
+      integer nr, nc, kvstr(nr+1), kvstc(nc+1), ia(nr+1), ja(*), ka(*)
+      integer iwk(nr+nc+2+nr), iout
+c-----------------------------------------------------------------------
+c     Print info on matrix in variable block row format.
+c-----------------------------------------------------------------------
+c     On entry:
+c--------------
+c     nr,nc   = matrix block row and block column dimension
+c     kvstr   = first row number for each block row
+c     kvstc   = first column number for each block column
+c     ia,ja,ka,a = input matrix in VBR format
+c     iout    = unit number for printed output
+c
+c     On return:
+c---------------
+c     Printed output to unit number specified in iout.  If a non-square
+c     matrix is provided, the analysis will be performed on the block
+c     rows, otherwise a row/column conformal partitioning will be used.
+c
+c     Work space:
+c----------------
+c     iwk(1:nb+1) = conformal block partitioning
+c        (nb is unknown at start but is no more than nr+nc)
+c     iwk(nb+2:nb+2+nr) = frequency of each blocksize
+c     The workspace is not assumed to be initialized to zero, nor is it
+c     left that way.
+c
+c-----------------------------------------------------------------------
+c-----local variables
+      integer n, nb, nnz, nnzb, i, j, neq, max, num
+      character*101 tmpst
+      integer bsiz(10), freq(10)
+c-----------------------------------------------------------------------
+      n = kvstr(nr+1)-1
+      nnz = ka(ia(nr+1)) - ka(1)
+      nnzb = ia(nr+1) - ia(1)
+      write (iout, 96)
+      write (iout, 100) n, nnz, real(nnz)/real(n)
+      write (iout, 101) nr, nnzb, real(nnzb)/real(nr)
+c-----if non-square matrix, do analysis on block rows,
+c     else do analysis on conformal partitioning
+      if (kvstr(nr+1) .ne. kvstc(nc+1)) then
+         write (iout, 103)
+         do i = 1, nr+1
+            iwk(i) = kvstr(i)
+         enddo
+         nb = nr
+      else
+         call kvstmerge(nr, kvstr, nc, kvstc, nb, iwk)
+         if ((nr .ne. nc) .or. (nc .ne. nb)) write (iout, 104) nb
+      endif
+c-----accumulate frequencies of each blocksize
+      max = 1
+      iwk(1+nb+2) = 0
+      do i = 1, nb
+         neq = iwk(i+1) - iwk(i)
+         if (neq .gt. max) then
+            do j = max+1, neq
+               iwk(j+nb+2) = 0
+            enddo
+            max = neq
+         endif
+         iwk(neq+nb+2) = iwk(neq+nb+2) + 1
+      enddo
+c-----store largest 10 of these blocksizes
+      num = 0
+      do i = max, 1, -1
+         if ((iwk(i+nb+2) .ne. 0) .and. (num .lt. 10)) then
+            num = num + 1
+            bsiz(num) = i
+            freq(num) = iwk(i+nb+2)
+         endif
+      enddo
+c-----print information about blocksizes
+      write (iout, 109) num
+      write (tmpst,'(10i6)') (bsiz(j),j=1,num)
+      write (iout,110) num,tmpst
+      write (tmpst,'(10i6)') (freq(j),j=1,num)
+      write (iout,111) tmpst
+      write (iout, 96)
+c-----------------------------------------------------------------------
+ 99    format (2x,38(2h *))
+ 96    format (6x,' *',65(1h-),'*')
+ 100   format(
+     * 6x,' *  Number of rows                                   = ',
+     * i10,'  *'/
+     * 6x,' *  Number of nonzero elements                       = ',
+     * i10,'  *'/
+     * 6x,' *  Average number of nonzero elements/Row           = ',
+     * f10.4,'  *')
+ 101   format(
+     * 6x,' *  Number of block rows                             = ',
+     * i10,'  *'/
+     * 6x,' *  Number of nonzero blocks                         = ',
+     * i10,'  *'/
+     * 6x,' *  Average number of nonzero blocks/Block row       = ',
+     * f10.4,'  *')
+ 103   format(
+     * 6x,' *  Non-square matrix.                                 ',
+     *     '            *'/
+     * 6x,' *  Performing analysis on block rows.                 ',
+     *     '            *')
+ 104   format(
+     * 6x,' *  Non row-column conformal partitioning supplied.    ',
+     *     '            *'/
+     * 6x,' *  Using conformal partitioning.  Number of bl rows = ',
+     * i10,'  *')
+ 109   format(
+     * 6x,' *  Number of different blocksizes                   = ',
+     * i10,'  *')
+ 110   format(6x,' *  The ', i2, ' largest dimension nodes',
+     *     ' have dimension    : ',10x,'  *',/,
+     * 6x,' *',a61,3x,' *')
+ 111   format(6x,' *  The frequency of nodes these ',
+     *     'dimensions are      : ',10x,'  *',/,
+     * 6x,' *',a61,3x,' *')
+c---------------------------------
+      return
+      end
+c-----------------------------------------------------------------------
+c-----------------------end-of-vbrinfo----------------------------------
diff --git a/INFO/makefile b/INFO/makefile
new file mode 100644
index 0000000..8e1acac
--- /dev/null
+++ b/INFO/makefile
@@ -0,0 +1,18 @@
+# 
+F77 = f77
+#F77 = cf77
+FFLAGS = -g -Wall 
+
+FILES = rinfo1.o dinfo13.o
+## needs library libskit.a in whatever machine version -- 
+
+LIB   = -L/project/darpa/lib/PC -lskit
+##LIB   = -L/project/darpa/lib/solaris -lskit
+
+info1.ex: $(FILES) 
+	$(F77) -o info1.ex $(FILES) $(LIB) 
+
+clean:
+	rm -f *.o *.ex core *.trace *~ 
+
+.f.o  : ;       $(F77) $(FFLAGS) -c $*.f -o $*.o
\ No newline at end of file
diff --git a/INFO/rinfo1.f b/INFO/rinfo1.f
new file mode 100644
index 0000000..9ebbc82
--- /dev/null
+++ b/INFO/rinfo1.f
@@ -0,0 +1,39 @@
+      program info1
+c---------------------------------------------------------------------- 
+c usage    info1.ex < HB_file 
+c 
+c where info1 is the executable generated by makefile, HB_file is a 
+c file containing a matrix stored in Harwell-Boeing matrices.
+c Info1 will then dump the information into the standard output.
+c
+c To use with larger matrices, increase nmax and nzmax.
+c---------------------------------------------------------------------- 
+      implicit none 
+      integer nmax, nzmax
+      parameter (nmax = 30000, nzmax = 800000)
+      integer ia(nmax+1),ia1(nmax+1),ja(nzmax),ja1(nzmax) 
+      real*8  a(nzmax),a1(nzmax),rhs(1)
+      character title*72, type*3, key*8, guesol*2 
+      logical valued
+c
+      integer job, iin, nrow,ncol,nnz,ierr, nrhs, iout
+c--------------
+      data iin /5/, iout/6/
+c--------------
+      job = 2
+      nrhs = 0
+      call readmt (nmax,nzmax,job,iin,a,ja,ia, rhs, nrhs,
+     *     guesol,nrow,ncol,nnz,title,key,type,ierr)
+c---- if not readable return 
+      if (ierr .ne. 0) then
+         write (iout,100) ierr
+ 100     format(' **ERROR: Unable to read matrix',/,
+     *        ' Message returned fom readmt was ierr =',i3)
+         stop
+      endif
+      valued = (job .ge. 2)
+c-------
+      call dinfo1(ncol,iout,a,ja,ia,valued,title,key,type,a1,ja1,ia1)
+c--------------------end------------------------------------------------ 
+c-----------------------------------------------------------------------
+      end
diff --git a/INFO/rinfoC.c b/INFO/rinfoC.c
new file mode 100644
index 0000000..65253a4
--- /dev/null
+++ b/INFO/rinfoC.c
@@ -0,0 +1,104 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdarg.h>
+
+#define readmtc readmtc_
+#define dinfo1  dinfo1_
+
+#define max(a,b) (((a)>(b))?(a):(b))
+
+void errexit( char *f_str, ... )
+{
+  va_list argp;
+  char out1[256], out2[256];
+
+  va_start(argp, f_str);
+  vsprintf(out1, f_str, argp);
+  va_end(argp);
+
+  sprintf(out2, "Error! %s\n", out1);
+
+  fprintf(stdout, out2);
+  fflush(stdout);
+
+  exit( -1 );
+}
+
+void *Malloc( int nbytes, char *msg )
+{
+  void *ptr;
+
+  if (nbytes == 0)
+    return NULL;
+
+  ptr = (void *)malloc(nbytes);
+  if (ptr == NULL)
+    errexit( "Not enough mem for %s. Requested size: %d bytes", msg, nbytes );
+
+  return ptr;
+}
+
+int main( int argc, char **argv )
+{
+/*---------------------------------------------------------------------- 
+ * usage    info1.ex HB_file 
+ *
+ * where info1 is the executable generated by makefile, HB_file is a 
+ * file containing a matrix stored in Harwell-Boeing matrices.
+ * Info1 will then dump the information into the standard output.
+ *--------------------------------------------------------------------*/
+    int job, ncol, nrow, nnz, nrhs, ierr, valued = 0;
+    char guesol[3], title[73], key[9], type[4];
+    int *ia = NULL, *ja = NULL, *ia1 = NULL, *ja1 = NULL;
+    double *a = NULL, *a1 = NULL, *rhs = NULL;
+    int tmp1, tmp2, maxnnz;
+    int iout = 6;
+
+    if( argc < 2 ) {
+        printf( "usage: info1.ex HB_file\n" );
+        return 0;
+    }
+
+/* find out size of Harwell-Boeing matrix ---------------------------*/
+    job = 0;
+    tmp1 = tmp2 = 1;
+    readmtc( &tmp1, &tmp2, &job, argv[1], a, ja, ia, rhs, &nrhs,
+             guesol, &nrow, &ncol, &nnz, title, key, type, &ierr );
+    if( ierr != 0 ) {
+        fprintf( stderr, "readhb: err in read matrix header = %d\n", ierr );
+        exit(-1);
+    }
+/* allocate space ---------------------------------------------------*/
+    maxnnz = max( nnz, 2*ncol+1 );
+    ia     = (int *)Malloc( sizeof(int)*(ncol+1), "readhb" );
+    ja     = (int *)Malloc( sizeof(int)*nnz, "readhb" );
+    a      = (double *)Malloc( sizeof(double)*nnz, "readhb" );
+    ia1    = (int *)Malloc( sizeof(int)*(ncol+1), "readhb" );
+    ja1    = (int *)Malloc( sizeof(int)*maxnnz, "readhb" );
+    a1     = (double *)Malloc( sizeof(double)*nnz, "readhb" );
+/* read matrix ------------------------------------------------------*/
+    job = 2;
+    nrhs = 0;
+    tmp1 = ncol+1;
+    tmp2 = nnz;
+    readmtc( &tmp1, &tmp2, &job, argv[1], a, ja, ia, rhs, &nrhs,
+             guesol, &nrow, &ncol, &nnz, title, key, type, &ierr );
+    if( ierr != 0 ) {
+        fprintf( stderr, "readhb: err in read matrix data = %d\n", ierr );
+        exit(-1);
+    }
+
+    if( job >= 2 ) valued = 1;
+
+    dinfo1( &ncol, &iout, a, ja, ia, &valued, title, key, type,
+            a1, ja1, ia1 );
+
+    free( ia );
+    free( ja );
+    free( a );
+    free( ia1 );
+    free( ja1 );
+    free( a1 );
+
+    return 0;
+}
diff --git a/INFO/saylr1 b/INFO/saylr1
new file mode 100644
index 0000000..0ed933c
--- /dev/null
+++ b/INFO/saylr1
@@ -0,0 +1,368 @@
+1unsymmetric matrix of paul saylor - 14 by 17 2d grid   may, 1983       saylr1  
+           363            24           113           226             0
+rua                      238           238          1128             0
+(10i8)          (10i8)          (5e16.8)                                
+       1       4       8      12      16      20      24      28      32      36
+      40      44      48      52      55      59      64      69      74      79
+      84      89      94      99     104     109     114     119     123     127
+     132     137     142     147     152     157     162     167     172     177
+     182     187     191     195     200     205     210     215     220     225
+     230     235     240     245     250     255     259     263     268     273
+     278     283     288     293     298     303     308     313     318     323
+     327     331     336     341     346     351     356     361     366     371
+     376     381     386     391     395     399     404     409     414     419
+     424     429     434     439     444     449     454     459     463     467
+     472     477     482     487     492     497     502     507     512     517
+     522     527     531     535     540     545     550     555     560     565
+     570     575     580     585     590     595     599     603     608     613
+     618     623     628     633     638     643     648     653     658     663
+     667     671     676     681     686     691     696     701     706     711
+     716     721     726     731     735     739     744     749     754     759
+     764     769     774     779     784     789     794     799     803     807
+     812     817     822     827     832     837     842     847     852     857
+     862     867     871     875     880     885     890     895     900     905
+     910     915     920     925     930     935     939     943     948     953
+     958     963     968     973     978     983     988     993     998    1003
+    1007    1011    1016    1021    1026    1031    1036    1041    1046    1051
+    1056    1061    1066    1071    1075    1078    1082    1086    1090    1094
+    1098    1102    1106    1110    1114    1118    1122    1126    1129
+       1       2      15       1       2       3      16       2       3       4
+      17       3       4       5      18       4       5       6      19       5
+       6       7      20       6       7       8      21       7       8       9
+      22       8       9      10      23       9      10      11      24      10
+      11      12      25      11      12      13      26      12      13      14
+      27      13      14      28       1      15      16      29       2      15
+      16      17      30       3      16      17      18      31       4      17
+      18      19      32       5      18      19      20      33       6      19
+      20      21      34       7      20      21      22      35       8      21
+      22      23      36       9      22      23      24      37      10      23
+      24      25      38      11      24      25      26      39      12      25
+      26      27      40      13      26      27      28      41      14      27
+      28      42      15      29      30      43      16      29      30      31
+      44      17      30      31      32      45      18      31      32      33
+      46      19      32      33      34      47      20      33      34      35
+      48      21      34      35      36      49      22      35      36      37
+      50      23      36      37      38      51      24      37      38      39
+      52      25      38      39      40      53      26      39      40      41
+      54      27      40      41      42      55      28      41      42      56
+      29      43      44      57      30      43      44      45      58      31
+      44      45      46      59      32      45      46      47      60      33
+      46      47      48      61      34      47      48      49      62      35
+      48      49      50      63      36      49      50      51      64      37
+      50      51      52      65      38      51      52      53      66      39
+      52      53      54      67      40      53      54      55      68      41
+      54      55      56      69      42      55      56      70      43      57
+      58      71      44      57      58      59      72      45      58      59
+      60      73      46      59      60      61      74      47      60      61
+      62      75      48      61      62      63      76      49      62      63
+      64      77      50      63      64      65      78      51      64      65
+      66      79      52      65      66      67      80      53      66      67
+      68      81      54      67      68      69      82      55      68      69
+      70      83      56      69      70      84      57      71      72      85
+      58      71      72      73      86      59      72      73      74      87
+      60      73      74      75      88      61      74      75      76      89
+      62      75      76      77      90      63      76      77      78      91
+      64      77      78      79      92      65      78      79      80      93
+      66      79      80      81      94      67      80      81      82      95
+      68      81      82      83      96      69      82      83      84      97
+      70      83      84      98      71      85      86      99      72      85
+      86      87     100      73      86      87      88     101      74      87
+      88      89     102      75      88      89      90     103      76      89
+      90      91     104      77      90      91      92     105      78      91
+      92      93     106      79      92      93      94     107      80      93
+      94      95     108      81      94      95      96     109      82      95
+      96      97     110      83      96      97      98     111      84      97
+      98     112      85      99     100     113      86      99     100     101
+     114      87     100     101     102     115      88     101     102     103
+     116      89     102     103     104     117      90     103     104     105
+     118      91     104     105     106     119      92     105     106     107
+     120      93     106     107     108     121      94     107     108     109
+     122      95     108     109     110     123      96     109     110     111
+     124      97     110     111     112     125      98     111     112     126
+      99     113     114     127     100     113     114     115     128     101
+     114     115     116     129     102     115     116     117     130     103
+     116     117     118     131     104     117     118     119     132     105
+     118     119     120     133     106     119     120     121     134     107
+     120     121     122     135     108     121     122     123     136     109
+     122     123     124     137     110     123     124     125     138     111
+     124     125     126     139     112     125     126     140     113     127
+     128     141     114     127     128     129     142     115     128     129
+     130     143     116     129     130     131     144     117     130     131
+     132     145     118     131     132     133     146     119     132     133
+     134     147     120     133     134     135     148     121     134     135
+     136     149     122     135     136     137     150     123     136     137
+     138     151     124     137     138     139     152     125     138     139
+     140     153     126     139     140     154     127     141     142     155
+     128     141     142     143     156     129     142     143     144     157
+     130     143     144     145     158     131     144     145     146     159
+     132     145     146     147     160     133     146     147     148     161
+     134     147     148     149     162     135     148     149     150     163
+     136     149     150     151     164     137     150     151     152     165
+     138     151     152     153     166     139     152     153     154     167
+     140     153     154     168     141     155     156     169     142     155
+     156     157     170     143     156     157     158     171     144     157
+     158     159     172     145     158     159     160     173     146     159
+     160     161     174     147     160     161     162     175     148     161
+     162     163     176     149     162     163     164     177     150     163
+     164     165     178     151     164     165     166     179     152     165
+     166     167     180     153     166     167     168     181     154     167
+     168     182     155     169     170     183     156     169     170     171
+     184     157     170     171     172     185     158     171     172     173
+     186     159     172     173     174     187     160     173     174     175
+     188     161     174     175     176     189     162     175     176     177
+     190     163     176     177     178     191     164     177     178     179
+     192     165     178     179     180     193     166     179     180     181
+     194     167     180     181     182     195     168     181     182     196
+     169     183     184     197     170     183     184     185     198     171
+     184     185     186     199     172     185     186     187     200     173
+     186     187     188     201     174     187     188     189     202     175
+     188     189     190     203     176     189     190     191     204     177
+     190     191     192     205     178     191     192     193     206     179
+     192     193     194     207     180     193     194     195     208     181
+     194     195     196     209     182     195     196     210     183     197
+     198     211     184     197     198     199     212     185     198     199
+     200     213     186     199     200     201     214     187     200     201
+     202     215     188     201     202     203     216     189     202     203
+     204     217     190     203     204     205     218     191     204     205
+     206     219     192     205     206     207     220     193     206     207
+     208     221     194     207     208     209     222     195     208     209
+     210     223     196     209     210     224     197     211     212     225
+     198     211     212     213     226     199     212     213     214     227
+     200     213     214     215     228     201     214     215     216     229
+     202     215     216     217     230     203     216     217     218     231
+     204     217     218     219     232     205     218     219     220     233
+     206     219     220     221     234     207     220     221     222     235
+     208     221     222     223     236     209     222     223     224     237
+     210     223     224     238     211     225     226     212     225     226
+     227     213     226     227     228     214     227     228     229     215
+     228     229     230     216     229     230     231     217     230     231
+     232     218     231     232     233     219     232     233     234     220
+     233     234     235     221     234     235     236     222     235     236
+     237     223     236     237     238     224     237     238
+ -0.19315001E+02  0.19311001E+02  0.44227000E-02  0.19311001E+02 -0.38639999E+02
+  0.19311001E+02  0.17690999E-01  0.19311001E+02 -0.38693001E+02  0.19311001E+02
+  0.70762999E-01  0.19311001E+02 -0.38904999E+02  0.19311001E+02  0.28305000E+00
+  0.19311001E+02 -0.39755001E+02  0.19311001E+02  0.11322000E+01  0.19311001E+02
+ -0.43155998E+02  0.19311001E+02  0.45289001E+01  0.19311001E+02 -0.56756001E+02
+  0.19311001E+02  0.18115000E+02  0.19311001E+02 -0.11116000E+03  0.19311001E+02
+  0.72461998E+02  0.19311001E+02 -0.32876999E+03  0.19311001E+02  0.28985001E+03
+  0.19311001E+02 -0.11992000E+04  0.19309999E+02  0.11593000E+04  0.19309999E+02
+ -0.46805000E+04  0.19309000E+02  0.46370000E+04  0.19309000E+02 -0.18586000E+05
+  0.11061000E+02  0.18536000E+05  0.11060000E+02 -0.75788000E+05  0.19722000E+02
+  0.75689000E+05  0.19698999E+02 -0.41574000E+08  0.41579000E+08  0.44227000E-02
+ -0.10241000E+04  0.10230000E+04  0.11876000E+01  0.17690999E-01  0.10230000E+04
+ -0.20507000E+04  0.10230000E+04  0.47505999E+01  0.70762999E-01  0.10230000E+04
+ -0.20650000E+04  0.10230000E+04  0.19002001E+02  0.28305000E+00  0.10230000E+04
+ -0.21222000E+04  0.10230000E+04  0.76009003E+02  0.11322000E+01  0.10230000E+04
+ -0.23511001E+04  0.10230000E+04  0.30404001E+03  0.45288000E+01  0.10230000E+04
+ -0.32666001E+04  0.10230000E+04  0.12161000E+04  0.18115000E+02  0.10230000E+04
+ -0.69286001E+04  0.10229000E+04  0.48646001E+04  0.72460999E+02  0.10229000E+04
+ -0.21577000E+05  0.10230000E+04  0.19458000E+05  0.28984000E+03  0.10230000E+04
+ -0.80170000E+05  0.10229000E+04  0.77833000E+05  0.11593000E+04  0.10229000E+04
+ -0.31474000E+06  0.10229000E+04  0.31153000E+06  0.46368999E+04  0.10229000E+04
+ -0.12527000E+07  0.10229000E+04  0.12460000E+07  0.18536000E+05  0.10229000E+04
+ -0.50005000E+07  0.34723999E+03  0.49805000E+07  0.75682000E+05  0.34710001E+03
+ -0.27150000E+08  0.13908000E+04  0.27075000E+08  0.41574000E+08  0.13891000E+04
+ -0.90850000E+08  0.49273000E+08  0.11876000E+01 -0.19842000E+03  0.19612000E+03
+  0.11083000E+01  0.47505002E+01  0.19612000E+03 -0.40142999E+03  0.19612000E+03
+  0.44330001E+01  0.19002001E+02  0.19612000E+03 -0.42898001E+03  0.19612000E+03
+  0.17732000E+02  0.76008003E+02  0.19612000E+03 -0.53917999E+03  0.19612000E+03
+  0.70928001E+02  0.30403000E+03  0.19612000E+03 -0.97998999E+03  0.19612000E+03
+  0.28370999E+03  0.12161000E+04  0.19612000E+03 -0.27432000E+04  0.19612000E+03
+  0.11348000E+04  0.48645000E+04  0.19612000E+03 -0.97962002E+04  0.19612000E+03
+  0.45393999E+04  0.19458000E+05  0.19612000E+03 -0.38008000E+05  0.19612000E+03
+  0.18158000E+05  0.77832000E+05  0.19612000E+03 -0.15086000E+06  0.19612000E+03
+  0.72630000E+05  0.31152000E+06  0.19612000E+03 -0.60243000E+06  0.19612000E+03
+  0.29051000E+06  0.12460000E+07  0.19612000E+03 -0.24083000E+07  0.19611000E+03
+  0.11619000E+07  0.49805000E+07  0.19610001E+03 -0.96025000E+07  0.19986000E+03
+  0.46215000E+07  0.27072000E+08  0.19977000E+03 -0.52340000E+08  0.26682999E+03
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+  0.31485999E+00  0.11816000E+02 -0.24131001E+02  0.11816000E+02  0.18426000E+00
+  0.12594000E+01  0.11816000E+02 -0.25629999E+02  0.11816000E+02  0.73703998E+00
+  0.50377002E+01  0.11816000E+02 -0.31624001E+02  0.11816000E+02  0.29482000E+01
+  0.20150999E+02  0.11816000E+02 -0.55603001E+02  0.11816000E+02  0.11793000E+02
+  0.80603996E+02  0.11816000E+02 -0.15152000E+03  0.11816000E+02  0.47171001E+02
+  0.32242001E+03  0.11816000E+02 -0.53519000E+03  0.11816000E+02  0.18867999E+03
+  0.12897000E+04  0.11816000E+02 -0.20698999E+04  0.11817000E+02  0.75475000E+03
+  0.51593999E+04  0.11816000E+02 -0.82095996E+04  0.11825000E+02  0.30193000E+04
+  0.20652000E+05  0.11818000E+02 -0.32791000E+05  0.11841000E+02  0.12086000E+05
+  0.51064000E+08  0.11827000E+02 -0.80948000E+08  0.29884000E+08  0.71965001E-03
+ -0.55196999E+02  0.55195999E+02  0.28786000E-02  0.55195999E+02 -0.11039000E+03
+  0.55195999E+02  0.11514000E-01  0.55195999E+02 -0.11040000E+03  0.55195999E+02
+  0.46057999E-01  0.55195999E+02 -0.11044000E+03  0.55195999E+02  0.18423000E+00
+  0.55195999E+02 -0.11058000E+03  0.55195999E+02  0.73693001E+00  0.55195999E+02
+ -0.11114000E+03  0.55195999E+02  0.29477000E+01  0.55195999E+02 -0.11337000E+03
+  0.55195000E+02  0.11791000E+02  0.55195000E+02 -0.12232000E+03  0.55195999E+02
+  0.47162998E+02  0.55195999E+02 -0.15809000E+03  0.55195999E+02  0.18864999E+03
+  0.55195000E+02 -0.30120001E+03  0.55196999E+02  0.75463000E+03  0.55195999E+02
+ -0.87365002E+03  0.55202999E+02  0.30188999E+04  0.55196999E+02 -0.31638000E+04
+  0.55240002E+02  0.12084000E+05  0.55206001E+02 -0.12333000E+05  0.55314999E+02
+  0.29879000E+08  0.55248001E+02 -0.29912000E+08
+
diff --git a/INOUT/README b/INOUT/README
new file mode 100644
index 0000000..e104ff3
--- /dev/null
+++ b/INOUT/README
@@ -0,0 +1,23 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+C                        INPUT-OUTPUT MODULE                           c
+c----------------------------------------------------------------------c
+c contents:                                                            c
+c----------                                                            c
+c  readmt : reads matrices in the Boeing/Harwell format.               c
+c  prtmt  : prints matrices in the Boeing/Harwell format.              c
+c  dump   : outputs matrix rows in a simple format (debugging purposes)c 
+c  pspltm : generates a post-script plot of the non-zero pattern of A  c
+c  pltmt  : produces a 'pic' file for plotting a sparse matrix         c
+c  smms   : write the matrx in a format used in SMMS package           c
+c  readsm : reads matrics in coordinate format (as in SMMS package)    c
+c  readsk : reads matrices in CSR format (simplified H/B formate).     c
+c  skit   : writes matrics to a file, format same as above.            c
+c  prtunf : writes matrics (in CSR format) unformatted                 c
+c  readunf: reads unformatted data of matrics (in CSR format)          c
+c----------------------------------------------------------------------c
+
+To visualize a Harwell-Boeing matrix on a Unix workstation, it is easiest
+to convert it to a postscript file and then view it with ghostview or gs.
+The program hb2ps.ex may be used for the former purpose.
diff --git a/INOUT/chkio.f b/INOUT/chkio.f
new file mode 100644
index 0000000..0d66deb
--- /dev/null
+++ b/INOUT/chkio.f
@@ -0,0 +1,100 @@
+        program chkio                                               
+c------------------------------------------------------------------c
+c test suite for Part I : I/O routines.                            c
+c tests the following : gen5pt.f, prtmt, readmt, amd pltmt.        c
+c 1) generates a 100 x 100 5pt matrix,                             c 
+c 2) prints it with a given format in file 'first.mat'             c
+c 3) reads the matrix from 'first.mat' using readmat               c 
+c 4) prints it again in file 'second.mat' in  a different format   c 
+c 5) makes 4 pic files to show the different options of pltmt.     c
+c    these are in job0.pic, job01.pic, job10.pic, job11.pic        c
+c                          coded by Y. Saad, RIACS, 08/31/1989.    c
+c------------------------------------------------------------------c
+      parameter (nxmax = 20, nmx = nxmax*nxmax)
+      implicit real*8 (a-h,o-z)
+      integer ia(nmx),ja(7*nmx),iau(nmx) 
+      real*8 a(7*nmx),rhs(3*nmx),al(6)
+      character title*72, key*8, type*3, guesol*2 
+c----- open statements ---------------- 
+      open (unit=7,file='first.mat')
+      open (unit=8,file='second.mat')
+      open (unit=20,file='job00.pic')
+      open (unit=21,file='job01.pic')
+      open (unit=22,file='job10.pic')
+      open (unit=23,file='job11.pic')
+c
+c---- dimension of grid 
+c
+      nx = 10
+      ny = 10
+      nz = 1
+      al(1) = 1.0D0
+      al(2) = 0.0D0
+      al(3) = 2.3D1
+      al(4) = 0.4D0
+      al(5) = 0.0D0
+      al(6) = 8.2D-2
+c
+c---- generate grid problem.
+c
+      call gen57pt (nx,ny,nz,al,0,n,a,ja,ia,iau,rhs)
+c
+c---- create the Harwell-Boeing matrix. Start by defining title, 
+c     and type. them define format and print it.
+c
+      write (title,9) nx, ny
+ 9    format('Five-point matrix on a square region',
+     *  ' using a ',I2,' by ',I2,' grid *SPARSKIT*')
+      key = 'Fivept10'
+      type= 'RSA'
+      ifmt = 5
+      job = 3
+      guesol = 'GX'
+c
+c define a right hand side of ones, an initial guess of two's
+c and an exact solution of three's.
+c 
+      do 2 k=1, 3*n
+	 rhs(k) = real( 1 +  (k-1)/n ) 
+ 2    continue
+c
+      call prtmt (n,n,a,ja,ia,rhs,guesol,title,key,type,
+     1	                  ifmt,job,7)
+c---- read it again in same matrix a, ja, ia  
+       nmax = nmx
+       nzmax = 7*nmx
+      do 3 k=1, 3*n
+	 rhs(k) = 0.0
+ 3    continue
+       job = 3
+c
+       rewind 7
+c
+       nrhs = 3*n   
+c
+       call readmt (nmax,nzmax,job,7,a,ja,ia,rhs,nrhs,guesol,
+     1             nrow,ncol,nnz,title,key,type,ierr)
+	 print *,  ' ierr = ', ierr, ' nrhs ' , nrhs
+c
+c matrix read.  print it again in a different format
+c
+      ifmt = 102
+      ncol = nrow
+      job = 3 
+c
+      call prtmt (nrow,ncol,a,ja,ia,rhs,guesol,title,key,type,
+     1	                  ifmt,job,8)
+c
+c---- print four pic files 
+c
+      mode = 0
+      do 10 i=1, 2
+	 do 11 j=1, 2
+	 job = (i-1)*10 +j-1
+	 iout = 20+(i-1)*2+j-1
+      call pltmt (nrow,ncol,mode,ja,ia,title,key,type,job,iout)
+ 11   continue
+ 10   continue
+c-------- 
+      stop
+      end
diff --git a/INOUT/hb2pic.f b/INOUT/hb2pic.f
new file mode 100644
index 0000000..358ff5c
--- /dev/null
+++ b/INOUT/hb2pic.f
@@ -0,0 +1,35 @@
+        program hb2pic                                               
+c------------------------------------------------------------------c
+c
+c reads a harwell-Boeing matrix and creates a pic file for pattern.
+c 
+c------------------------------------------------------------------c
+        implicit real*8 (a-h,o-z)
+        parameter (nmax = 5000, nzmax = 70000)
+        integer ia(nmax+1), ja(nzmax)
+	real*8  a(nzmax), rhs(1)
+        character title*72, key*8, guesol*2 
+        logical valued
+c--------------
+      data iin /5/, iout/6/
+c--------------
+      job = 2
+      nrhs = 0
+      call readmt (nmax,nzmax,job,iin,a,ja,ia, rhs, nrhs,
+     *     guesol,nrow,ncol,nnz,title,key,type,ierr)
+c---- if not readable return 
+      if (ierr .ne. 0) then
+         write (iout,100) ierr
+ 100     format(' **ERROR: Unable to read matrix',/,
+     *        ' Message returned fom readmt was ierr =',i3)
+         stop
+      endif
+      valued = (job .ge. 2)
+c-------
+      mode = 1
+      iounit = 6
+      job = 11
+      call pltmt (nrow,ncol,mode,ja,ia,title,key,type,job,iout)
+c----------------------------------------------------------------------- 
+      stop
+      end
diff --git a/INOUT/hb2ps.f b/INOUT/hb2ps.f
new file mode 100644
index 0000000..83d0b1f
--- /dev/null
+++ b/INOUT/hb2ps.f
@@ -0,0 +1,42 @@
+      program hb2ps 
+c----------------------------------------------------------------------
+c translates a harwell - boeing file into a post-script file. Usage:   
+c                   hb2ps < HB_file > Postscript_file 
+c where hb2ps is the executable generated from this program,
+c HB_file is a file containing a matrix stored in Harwell-Boeing
+c format and Postscript_file is a file to contain the post-script file. 
+c---------------------------------------------------------------------- 
+      parameter (nmax = 10000, nzmax = 100000)
+      integer ia(nmax+1),ja(nzmax), idummy(1), ptitle
+      real*8  a(1),rhs(1)
+      real size
+      character title*72, key*8, guesol*2, munt*2 
+      data iin /5/, iout/6/, size/5.0/, nlines/0/, ptitle/0/,mode/0/
+      data munt/'in'/
+c-----------------------------------------------------------------------
+      job = 1 
+      nrhs = 0
+c
+c     read matrix in Harwell-Boeing format 
+c
+      call readmt (nmax,nzmax,job,iin,a,ja,ia, rhs, nrhs,
+     *     guesol,nrow,ncol,nnz,title,key,type,ierr)
+c
+c     if   not readable return 
+c
+      if (ierr .ne. 0) then 
+         write (iout,100) ierr
+         stop
+      endif
+c
+c     call post script generator
+c     
+      call pspltm(nrow,ncol,mode,ja,ia,title,ptitle,size,munt,
+     *     nlines,idummy,iout) 
+c
+ 100     format(' **ERROR: Unable to read matrix',/,
+     *        ' Message returned fom readmt was ierr =',i3)
+c-----------------------------------------------------------------------  
+      stop
+      end
+
diff --git a/INOUT/inout.f b/INOUT/inout.f
new file mode 100644
index 0000000..820c548
--- /dev/null
+++ b/INOUT/inout.f
@@ -0,0 +1,1504 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+C                        INPUT-OUTPUT MODULE                           c
+c----------------------------------------------------------------------c
+c contents:                                                            c
+c----------                                                            c
+c  readmt : reads matrices in the Boeing/Harwell format.               c
+c  prtmt  : prints matrices in the Boeing/Harwell format.              c
+c  dump   : outputs matrix rows in a simple format (debugging purposes)c 
+c  pspltm : generates a post-script plot of the non-zero pattern of A  c
+c  pltmt  : produces a 'pic' file for plotting a sparse matrix         c
+c  smms   : write the matrx in a format used in SMMS package           c
+c  readsm : reads matrics in coordinate format (as in SMMS package)    c
+c  readsk : reads matrices in CSR format (simplified H/B formate).     c
+c  skit   : writes matrics to a file, format same as above.            c
+c  prtunf : writes matrics (in CSR format) unformatted                 c
+c  readunf: reads unformatted data of matrics (in CSR format)          c
+c----------------------------------------------------------------------c
+	subroutine readmt (nmax,nzmax,job,iounit,a,ja,ia,rhs,nrhs,
+     *                     guesol,nrow,ncol,nnz,title,key,type,ierr)
+c-----------------------------------------------------------------------
+c this subroutine reads  a boeing/harwell matrix. handles right hand 
+c sides in full format only (no sparse right hand sides).
+c Also the matrix must be in assembled forms.
+c Author: Youcef Saad - Date: Sept., 1989
+c         updated Oct 31, 1989.
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c nmax 	 =  max column dimension  allowed for matrix. The array ia should 
+c	    be of length at least ncol+1 (see below) if job.gt.0
+c nzmax	 = max number of nonzeros elements allowed. the arrays a, 
+c          and ja should be of length equal to nnz (see below) if these
+c          arrays are to be read (see job).
+c          
+c job	 = integer to indicate what is to be read. (note: job is an
+c          input and output parameter, it can be modified on return)
+c          job = 0    read the values of ncol, nrow, nnz, title, key,
+c                     type and return. matrix is not read and arrays
+c                     a, ja, ia, rhs are not touched.
+c          job = 1    read srtucture only, i.e., the arrays ja and ia.
+c          job = 2    read matrix including values, i.e., a, ja, ia
+c          job = 3    read matrix and right hand sides: a,ja,ia,rhs.
+c		      rhs may contain initial guesses and exact 
+c                     solutions appended to the actual right hand sides.
+c		      this will be indicated by the output parameter
+c                     guesol [see below]. 
+c                     
+c nrhs   = integer. nrhs is an input as well as ouput parameter.
+c          at input nrhs contains the total length of the array rhs.
+c          See also ierr and nrhs in output parameters.
+c
+c iounit = logical unit number where to read the matrix from.
+c
+c on return:
+c---------- 
+c job    = on return job may be modified to the highest job it could
+c          do: if job=2 on entry but no matrix values are available it
+c          is reset to job=1 on return. Similarly of job=3 but no rhs 
+c          is provided then it is rest to job=2 or job=1 depending on 
+c          whether or not matrix values are provided.
+c          Note that no error message is triggered (i.e. ierr = 0 
+c          on return in these cases. It is therefore important to
+c          compare the values of job on entry and return ).
+c
+c a	 = the a matrix in the a, ia, ja (column) storage format
+c ja 	 = row number of element a(i,j) in array a.
+c ia     = pointer  array. ia(i) points to the beginning of column i.
+c
+c rhs    = real array of size nrow + 1 if available (see job)
+c
+c nrhs   = integer containing the number of right-hand sides found
+c          each right hand side may be accompanied with an intial guess
+c          and also the exact solution.
+c
+c guesol = a 2-character string indicating whether an initial guess 
+c          (1-st character) and / or the exact solution (2-nd
+c          character) is provided with the right hand side.
+c	   if the first character of guesol is 'G' it means that an
+c          an intial guess is provided for each right-hand side.
+c          These are appended to the right hand-sides in the array rhs.
+c	   if the second character of guesol is 'X' it means that an
+c          exact solution is provided for each right-hand side.
+c          These are  appended to the right hand-sides 
+c          and the initial guesses (if any) in the array rhs.
+c
+c nrow   = number of rows in matrix
+c ncol	 = number of columns in matrix 
+c nnz	 = number of nonzero elements in A. This info is returned
+c          even if there is not enough space in a, ja, ia, in order
+c          to determine the minimum storage needed. 
+c
+c title  = character*72 = title of matrix test ( character a*72). 
+c key    = character*8  = key of matrix 
+c type   = charatcer*3  = type of matrix.
+c          for meaning of title, key and type refer to documentation 
+c          Harwell/Boeing matrices.
+c
+c ierr   = integer used for error messages 
+c         * ierr  =  0 means that  the matrix has been read normally. 
+c         * ierr  =  1 means that  the array matrix could not be read 
+c         because ncol+1 .gt. nmax
+c         * ierr  =  2 means that  the array matrix could not be read 
+c         because nnz .gt. nzmax 
+c         * ierr  =  3 means that  the array matrix could not be read 
+c         because both (ncol+1 .gt. nmax) and  (nnz .gt. nzmax )
+c         * ierr  =  4 means that  the right hand side (s) initial 
+c         guesse (s) and exact solution (s)   could  not be
+c         read because they are stored in sparse format (not handled
+c         by this routine ...) 
+c         * ierr  =  5 means that the right-hand-sides, initial guesses
+c         and exact solutions could not be read because the length of 
+c         rhs as specified by the input value of nrhs is not 
+c         sufficient to store them. The rest of the matrix may have
+c         been read normally.
+c 
+c Notes:
+c-------
+c 1) The file inout must be open (and possibly rewound if necessary)
+c    prior to calling readmt.
+c 2) Refer to the documentation on the Harwell-Boeing formats
+c    for details on the format assumed by readmt.
+c    We summarize the format here for convenience.
+c  
+c    a) all lines in inout are assumed to be 80 character long.
+c    b) the file consists of a header followed by the block of the 
+c       column start pointers followed by the block of the
+c       row indices, followed by the block of the real values and
+c       finally the numerical values of the right-hand-side if a 
+c       right hand side is supplied. 
+c    c) the file starts by a header which contains four lines if no
+c       right hand side is supplied and five lines otherwise.
+c       * first line contains the title (72 characters long) followed by
+c         the 8-character identifier (name of the matrix, called key)
+c        [ A72,A8 ]
+c       * second line contains the number of lines for each
+c         of the following data blocks (4 of them) and the total number 
+c         of lines excluding the header.
+c        [5i4]
+c       * the third line contains a three character string identifying
+c         the type of matrices as they are referenced in the Harwell
+c         Boeing documentation [e.g., rua, rsa,..] and the number of
+c         rows, columns, nonzero entries.
+c         [A3,11X,4I14]
+c       * The fourth line contains the variable fortran format
+c         for the following data blocks.
+c         [2A16,2A20] 
+c       * The fifth line is only present if right-hand-sides are 
+c         supplied. It consists of three one character-strings containing
+c         the storage format for the right-hand-sides 
+c         ('F'= full,'M'=sparse=same as matrix), an initial guess 
+c         indicator ('G' for yes), an exact solution indicator 
+c         ('X' for yes), followed by the number of right-hand-sides
+c         and then the number of row indices. 
+c         [A3,11X,2I14] 
+c     d) The three following blocks follow the header as described 
+c        above.
+c     e) In case the right hand-side are in sparse formats then 
+c        the fourth block uses the same storage format as for the matrix
+c        to describe the NRHS right hand sides provided, with a column
+c        being replaced by a right hand side.
+c-----------------------------------------------------------------------
+      character title*72, key*8, type*3, ptrfmt*16, indfmt*16,
+     1       valfmt*20, rhsfmt*20, rhstyp*3, guesol*2
+      integer totcrd, ptrcrd, indcrd, valcrd, rhscrd, nrow, ncol,
+     1     nnz, neltvl, nrhs, nmax, nzmax, nrwindx
+      integer ia (nmax+1), ja (nzmax) 
+      real*8 a(nzmax), rhs(*) 
+c-----------------------------------------------------------------------
+      ierr = 0
+      lenrhs = nrhs
+c
+      read (iounit,10) title, key, totcrd, ptrcrd, indcrd, valcrd, 
+     1     rhscrd, type, nrow, ncol, nnz, neltvl, ptrfmt, indfmt, 
+     2     valfmt, rhsfmt
+ 10   format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20)
+c
+      if (rhscrd .gt. 0) read (iounit,11) rhstyp, nrhs, nrwindx
+ 11   format (a3,11x,i14,i14)
+c
+c anything else to read ?
+c
+      if (job .le. 0) return
+c     ---- check whether matrix is readable ------ 
+      n = ncol
+      if (ncol .gt. nmax) ierr = 1
+      if (nnz .gt. nzmax) ierr = ierr + 2
+      if (ierr .ne. 0) return
+c     ---- read pointer and row numbers ---------- 
+      read (iounit,ptrfmt) (ia (i), i = 1, n+1)
+      read (iounit,indfmt) (ja (i), i = 1, nnz)
+c     --- reading values of matrix if required....
+      if (job .le. 1)  return
+c     --- and if available ----------------------- 
+      if (valcrd .le. 0) then
+	 job = 1
+	 return
+      endif
+      read (iounit,valfmt) (a(i), i = 1, nnz)
+c     --- reading rhs if required ---------------- 
+      if (job .le. 2)  return
+c     --- and if available ----------------------- 
+      if ( rhscrd .le. 0) then
+	 job = 2
+	 nrhs = 0
+	 return
+      endif
+c     
+c     --- read right-hand-side.-------------------- 
+c     
+      if (rhstyp(1:1) .eq. 'M') then 
+         ierr = 4
+         return
+      endif
+c
+      guesol = rhstyp(2:3) 
+c     
+      nvec = 1 
+      if (guesol(1:1) .eq. 'G' .or. guesol(1:1) .eq. 'g') nvec=nvec+1
+      if (guesol(2:2) .eq. 'X' .or. guesol(2:2) .eq. 'x') nvec=nvec+1
+c     
+      len = nrhs*nrow 
+c     
+      if (len*nvec .gt. lenrhs) then
+         ierr = 5
+         return
+      endif
+c
+c read right-hand-sides
+c
+      next = 1
+      iend = len
+      read(iounit,rhsfmt) (rhs(i), i = next, iend)
+c
+c read initial guesses if available
+c
+      if (guesol(1:1) .eq. 'G' .or. guesol(1:1) .eq. 'g') then
+         next = next+len
+         iend = iend+ len
+         read(iounit,valfmt) (rhs(i), i = next, iend)
+      endif
+c     
+c read exact solutions if available
+c
+      if (guesol(2:2) .eq. 'X' .or. guesol(2:2) .eq. 'x') then
+         next = next+len
+         iend = iend+ len
+         read(iounit,valfmt) (rhs(i), i = next, iend)
+      endif
+c     
+      return
+c--------- end of readmt -----------------------------------------------
+c----------------------------------------------------------------------- 
+      end
+c-----------------------------------------------------------------------
+      subroutine prtmt (nrow,ncol,a,ja,ia,rhs,guesol,title,key,type,
+     1     ifmt,job,iounit)
+c-----------------------------------------------------------------------
+c writes a matrix in Harwell-Boeing format into a file.
+c assumes that the matrix is stored in COMPRESSED SPARSE COLUMN FORMAT.
+c some limited functionality for right hand sides. 
+c Author: Youcef Saad - Date: Sept., 1989 - updated Oct. 31, 1989 to
+c cope with new format. 
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c nrow   = number of rows in matrix
+c ncol	 = number of columns in matrix 
+c a	 = real*8 array containing the values of the matrix stored 
+c          columnwise
+c ja 	 = integer array of the same length as a containing the column
+c          indices of the corresponding matrix elements of array a.
+c ia     = integer array of containing the pointers to the beginning of 
+c	   the row in arrays a and ja.
+c rhs    = real array  containing the right-hand-side (s) and optionally
+c          the associated initial guesses and/or exact solutions
+c          in this order. See also guesol for details. the vector rhs will
+c          be used only if job .gt. 2 (see below). Only full storage for
+c          the right hand sides is supported. 
+c
+c guesol = a 2-character string indicating whether an initial guess 
+c          (1-st character) and / or the exact solution (2-nd)
+c          character) is provided with the right hand side.
+c	   if the first character of guesol is 'G' it means that an
+c          an intial guess is provided for each right-hand sides. 
+c          These are assumed to be appended to the right hand-sides in 
+c          the array rhs.
+c	   if the second character of guesol is 'X' it means that an
+c          exact solution is provided for each right-hand side.
+c          These are assumed to be appended to the right hand-sides 
+c          and the initial guesses (if any) in the array rhs.
+c
+c title  = character*72 = title of matrix test ( character a*72 ).
+c key    = character*8  = key of matrix 
+c type   = charatcer*3  = type of matrix.
+c
+c ifmt	 = integer specifying the format chosen for the real values
+c	   to be output (i.e., for a, and for rhs-guess-sol if 
+c          applicable). The meaning of ifmt is as follows.
+c	  * if (ifmt .lt. 100) then the D descriptor is used,
+c           format Dd.m, in which the length (m) of the mantissa is 
+c           precisely the integer ifmt (and d = ifmt+6)
+c	  * if (ifmt .gt. 100) then prtmt will use the 
+c           F- descriptor (format Fd.m) in which the length of the 
+c           mantissa (m) is the integer mod(ifmt,100) and the length 
+c           of the integer part is k=ifmt/100 (and d = k+m+2)
+c	    Thus  ifmt= 4   means  D10.4  +.xxxxD+ee    while
+c	          ifmt=104  means  F7.4   +x.xxxx
+c	          ifmt=205  means  F9.5   +xx.xxxxx
+c	    Note: formats for ja, and ia are internally computed.
+c
+c job	 = integer to indicate whether matrix values and
+c	   a right-hand-side is available to be written
+c          job = 1   write srtucture only, i.e., the arrays ja and ia.
+c          job = 2   write matrix including values, i.e., a, ja, ia
+c          job = 3   write matrix and one right hand side: a,ja,ia,rhs.
+c	   job = nrhs+2 write matrix and nrhs successive right hand sides
+c	   Note that there cannot be any right-hand-side if the matrix
+c	   has no values. Also the initial guess and exact solutions when 
+c          provided are for each right hand side. For example if nrhs=2 
+c          and guesol='GX' there are 6 vectors to write.
+c          
+c
+c iounit = logical unit number where to write the matrix into.
+c
+c on return:
+c---------- 
+c the matrix a, ja, ia will be written in output unit iounit
+c in the Harwell-Boeing format. None of the inputs is modofied.
+c  
+c Notes: 1) This code attempts to pack as many elements as possible per
+c        80-character line. 
+c        2) this code attempts to avoid as much as possible to put
+c        blanks in the formats that are written in the 4-line header
+c	 (This is done for purely esthetical reasons since blanks
+c        are ignored in format descriptors.)
+c        3) sparse formats for right hand sides and guesses are not
+c        supported.
+c-----------------------------------------------------------------------
+      character title*72,key*8,type*3,ptrfmt*16,indfmt*16,valfmt*20,
+     1     guesol*2, rhstyp*3
+      integer totcrd, ptrcrd, indcrd, valcrd, rhscrd, nrow, ncol,
+     1     nnz, nrhs, len, nperli, nrwindx
+      integer ja(*), ia(*) 	
+      real*8 a(*),rhs(*)
+c--------------
+c     compute pointer format
+c--------------
+       nnz    = ia(ncol+1) -1
+       if (nnz .eq. 0) then
+	   return
+	endif
+      len    = int ( alog10(0.1+real(nnz+1))) + 1
+      nperli = 80/len
+      ptrcrd = ncol/nperli + 1
+      if (len .gt. 9) then
+         assign 101 to ix
+      else
+         assign 100 to ix
+      endif
+      write (ptrfmt,ix) nperli,len
+ 100  format(1h(,i2,1HI,i1,1h) )
+ 101  format(1h(,i2,1HI,i2,1h) )
+c----------------------------
+c compute ROW index format
+c----------------------------
+      len    = int ( alog10(0.1+real(nrow) )) + 1
+      nperli = min0(80/len,nnz)
+      indcrd = (nnz-1)/nperli+1
+      write (indfmt,100) nperli,len
+c---------------
+c compute values and rhs format (using the same for both)
+c--------------- 
+      valcrd	= 0
+      rhscrd  = 0
+c quit this part if no values provided.
+      if (job .le. 1) goto 20
+c     
+      if (ifmt .ge. 100) then
+         ihead = ifmt/100
+         ifmt = ifmt-100*ihead
+         len = ihead+ifmt+2
+         nperli = 80/len
+c     
+         if (len .le. 9 ) then
+            assign 102 to ix
+         elseif (ifmt .le. 9) then
+            assign 103 to ix
+         else 
+            assign 104 to ix
+         endif
+c     
+         write(valfmt,ix) nperli,len,ifmt
+ 102     format(1h(,i2,1hF,i1,1h.,i1,1h) )
+ 103     format(1h(,i2,1hF,i2,1h.,i1,1h) )
+ 104     format(1h(,i2,1hF,i2,1h.,i2,1h) )
+C
+      else
+         len = ifmt + 6
+         nperli = 80/len
+c     try to minimize the blanks in the format strings.
+         if (nperli .le. 9) then
+	    if (len .le. 9 ) then
+	       assign 105 to ix
+	    elseif (ifmt .le. 9) then
+	       assign 106 to ix
+	    else 
+	       assign 107 to ix
+	    endif
+	 else 
+	    if (len .le. 9 ) then
+	       assign 108 to ix
+	    elseif (ifmt .le. 9) then
+	       assign 109 to ix
+	    else 
+               assign 110 to ix
+            endif
+         endif
+c-----------
+         write(valfmt,ix) nperli,len,ifmt
+ 105     format(1h(,i1,1hD,i1,1h.,i1,1h) )
+ 106     format(1h(,i1,1hD,i2,1h.,i1,1h) )
+ 107     format(1h(,i1,1hD,i2,1h.,i2,1h) )
+ 108     format(1h(,i2,1hD,i1,1h.,i1,1h) )
+ 109     format(1h(,i2,1hD,i2,1h.,i1,1h) )
+ 110     format(1h(,i2,1hD,i2,1h.,i2,1h) )
+c     
+      endif 	    
+      valcrd = (nnz-1)/nperli+1
+      nrhs   = job -2
+      if (nrhs .ge. 1) then
+         i = (nrhs*nrow-1)/nperli+1
+         rhscrd = i
+         if (guesol(1:1) .eq. 'G' .or. guesol(1:1) .eq. 'g')
+     +      rhscrd = rhscrd+i
+         if (guesol(2:2) .eq. 'X' .or. guesol(2:2) .eq. 'x')
+     +      rhscrd = rhscrd+i
+         rhstyp = 'F'//guesol
+      endif 
+ 20   continue
+c     
+      totcrd = ptrcrd+indcrd+valcrd+rhscrd
+c     write 4-line or five line header
+      write(iounit,10) title,key,totcrd,ptrcrd,indcrd,valcrd,
+     1     rhscrd,type,nrow,ncol,nnz,nrhs,ptrfmt,indfmt,valfmt,valfmt
+c-----------------------------------------------------------------------
+      nrwindx = 0
+      if (nrhs .ge. 1) write (iounit,11) rhstyp, nrhs, nrwindx
+ 10   format (a72, a8 / 5i14 / a3, 11x, 4i14 / 2a16, 2a20)
+ 11   format(A3,11x,i14,i14)
+c     
+      write(iounit,ptrfmt) (ia (i), i = 1, ncol+1)
+      write(iounit,indfmt) (ja (i), i = 1, nnz)
+      if (job .le. 1) return
+      write(iounit,valfmt) (a(i), i = 1, nnz)
+      if (job .le. 2) return 
+      len = nrow*nrhs 
+      next = 1
+      iend = len
+      write(iounit,valfmt) (rhs(i), i = next, iend)
+c     
+c     write initial guesses if available
+c     
+      if (guesol(1:1) .eq. 'G' .or. guesol(1:1) .eq. 'g') then
+         next = next+len
+         iend = iend+ len
+         write(iounit,valfmt) (rhs(i), i = next, iend)
+      endif
+c     
+c     write exact solutions if available
+c     
+      if (guesol(2:2) .eq. 'X' .or. guesol(2:2) .eq. 'x') then
+         next = next+len
+         iend = iend+ len
+         write(iounit,valfmt) (rhs(i), i = next, iend)
+      endif
+c     
+      return
+c----------end of prtmt ------------------------------------------------ 
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine dump (i1,i2,values,a,ja,ia,iout)
+      integer i1, i2, ia(*), ja(*), iout
+      real*8 a(*) 
+      logical values 
+c-----------------------------------------------------------------------
+c outputs rows i1 through i2 of a sparse matrix stored in CSR format 
+c (or columns i1 through i2 of a matrix stored in CSC format) in a file, 
+c one (column) row at a time in a nice readable format. 
+c This is a simple routine which is useful for debugging. 
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c i1    = first row (column) to print out
+c i2    = last row (column) to print out 
+c values= logical. indicates whether or not to print real values.
+c         if value = .false. only the pattern will be output.
+c a,
+c ja, 
+c ia    =  matrix in CSR format (or CSC format) 
+c iout  = logical unit number for output.
+c---------- 
+c the output file iout will have written in it the rows or columns 
+c of the matrix in one of two possible formats (depending on the max 
+c number of elements per row. The values are output with only 
+c two digits of accuracy (D9.2). )
+c-----------------------------------------------------------------------
+c     local variables
+      integer maxr, i, k1, k2 
+c
+c select mode horizontal or vertical 
+c
+        maxr = 0
+        do 1 i=i1, i2
+           maxr = max0(maxr,ia(i+1)-ia(i))
+ 1      continue
+        
+        if (maxr .le. 8) then
+c
+c able to do one row acros line
+c
+        do 2 i=i1, i2
+           write(iout,100) i
+	   k1=ia(i)
+	   k2 = ia(i+1)-1
+	   write (iout,101) (ja(k),k=k1,k2)
+	   if (values) write (iout,102) (a(k),k=k1,k2)
+ 2      continue
+      else 
+c
+c unable to one row acros line. do three items at a time
+c across a line 
+         do 3 i=i1, i2
+            if (values) then
+               write(iout,200) i
+            else
+               write(iout,203) i               
+            endif
+            k1=ia(i)
+            k2 = ia(i+1)-1
+            if (values) then
+               write (iout,201) (ja(k),a(k),k=k1,k2)
+            else
+                write (iout,202) (ja(k),k=k1,k2)
+             endif
+ 3       continue
+      endif 
+c
+c formats :
+c
+ 100  format (1h ,34(1h-),' row',i6,1x,34(1h-) )
+ 101  format(' col:',8(i5,6h     : ))
+ 102  format(' val:',8(D9.2,2h :) )
+ 200  format (1h ,30(1h-),' row',i3,1x,30(1h-),/
+     *     3('  columns :    values  * ') )
+c-------------xiiiiiihhhhhhddddddddd-*-
+ 201  format(3(1h ,i6,6h   :  ,D9.2,3h * ) )
+ 202  format(6(1h ,i5,6h  *    ) ) 
+ 203  format (1h ,30(1h-),' row',i3,1x,30(1h-),/
+     *     3('  column  :  column   *') )
+      return
+c----end-of-dump--------------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine pspltm(nrow,ncol,mode,ja,ia,title,ptitle,size,munt,
+     *     nlines,lines,iunt)
+c-----------------------------------------------------------------------
+      integer nrow,ncol,ptitle,mode,iunt, ja(*), ia(*), lines(nlines) 
+      real size
+      character title*(*), munt*2 
+c----------------------------------------------------------------------- 
+c PSPLTM - PostScript PLoTer of a (sparse) Matrix
+c This version by loris renggli (renggli@masg1.epfl.ch), Dec 1991
+c and Youcef Saad 
+c------
+c Loris RENGGLI, Swiss Federal Institute of Technology, Math. Dept
+c CH-1015 Lausanne (Switzerland)  -- e-mail:  renggli@masg1.epfl.ch
+c Modified by Youcef Saad -- June 24, 1992 to add a few features:
+c separation lines + acceptance of MSR format.
+c-----------------------------------------------------------------------
+c input arguments description :
+c
+c nrow   = number of rows in matrix
+c
+c ncol   = number of columns in matrix 
+c
+c mode   = integer indicating whether the matrix is stored in 
+c           CSR mode (mode=0) or CSC mode (mode=1) or MSR mode (mode=2) 
+c
+c ja     = column indices of nonzero elements when matrix is
+c          stored rowise. Row indices if stores column-wise.
+c ia     = integer array of containing the pointers to the 
+c          beginning of the columns in arrays a, ja.
+c
+c title  = character*(*). a title of arbitrary length to be printed 
+c          as a caption to the figure. Can be a blank character if no
+c          caption is desired.
+c
+c ptitle = position of title; 0 under the drawing, else above
+c
+c size   = size of the drawing  
+c
+c munt   = units used for size : 'cm' or 'in'
+c
+c nlines = number of separation lines to draw for showing a partionning
+c          of the matrix. enter zero if no partition lines are wanted.
+c
+c lines  = integer array of length nlines containing the coordinates of 
+c          the desired partition lines . The partitioning is symmetric: 
+c          a horizontal line across the matrix will be drawn in 
+c          between rows lines(i) and lines(i)+1 for i=1, 2, ..., nlines
+c          an a vertical line will be similarly drawn between columns
+c          lines(i) and lines(i)+1 for i=1,2,...,nlines 
+c
+c iunt   = logical unit number where to write the matrix into.
+c----------------------------------------------------------------------- 
+c additional note: use of 'cm' assumes european format for paper size
+c (21cm wide) and use of 'in' assumes american format (8.5in wide).
+c The correct centering of the figure depends on the proper choice. Y.S.
+c-----------------------------------------------------------------------
+c external 
+      integer LENSTR
+      external LENSTR
+c local variables ---------------------------------------------------
+      integer n,nr,nc,maxdim,istart,ilast,ii,k,ltit
+      real lrmrgn,botmrgn,xtit,ytit,ytitof,fnstit,siz
+      real xl,xr, yb,yt, scfct,u2dot,frlw,delt,paperx,conv,xx,yy
+      logical square 
+c change square to .true. if you prefer a square frame around
+c a rectangular matrix
+      data haf /0.5/, zero/0.0/, conv/2.54/,square/.false./
+c-----------------------------------------------------------------------
+      siz = size
+      nr = nrow
+      nc = ncol
+      n = nc
+      if (mode .eq. 0) n = nr
+c      nnz = ia(n+1) - ia(1) 
+      maxdim = max(nrow, ncol)
+      m = 1 + maxdim
+      nc = nc+1
+      nr = nr+1
+c
+c units (cm or in) to dot conversion factor and paper size
+c 
+      if (munt.eq.'cm' .or. munt.eq.'CM') then
+         u2dot = 72.0/conv
+        paperx = 21.0
+      else
+        u2dot = 72.0
+        paperx = 8.5*conv
+        siz = siz*conv
+      end if
+c
+c left and right margins (drawing is centered)
+c 
+      lrmrgn = (paperx-siz)/2.0
+c
+c bottom margin : 2 cm
+c
+      botmrgn = 2.0
+c scaling factor
+      scfct = siz*u2dot/m
+c matrix frame line witdh
+      frlw = 0.25
+c font size for title (cm)
+      fnstit = 0.5
+      ltit = LENSTR(title)
+c position of title : centered horizontally
+c                     at 1.0 cm vertically over the drawing
+      ytitof = 1.0
+      xtit = paperx/2.0
+      ytit = botmrgn+siz*nr/m + ytitof
+c almost exact bounding box
+      xl = lrmrgn*u2dot - scfct*frlw/2
+      xr = (lrmrgn+siz)*u2dot + scfct*frlw/2
+      yb = botmrgn*u2dot - scfct*frlw/2
+      yt = (botmrgn+siz*nr/m)*u2dot + scfct*frlw/2
+      if (ltit.gt.0) then
+        yt = yt + (ytitof+fnstit*0.70)*u2dot
+      end if
+c add some room to bounding box
+      delt = 10.0
+      xl = xl-delt
+      xr = xr+delt
+      yb = yb-delt
+      yt = yt+delt
+c
+c correction for title under the drawing
+      if (ptitle.eq.0 .and. ltit.gt.0) then
+      ytit = botmrgn + fnstit*0.3
+      botmrgn = botmrgn + ytitof + fnstit*0.7
+      end if
+c begin of output
+c
+      write(iunt,10) '%!'
+      write(iunt,10) '%%Creator: PSPLTM routine'
+      write(iunt,12) '%%BoundingBox:',xl,yb,xr,yt
+      write(iunt,10) '%%EndComments'
+      write(iunt,10) '/cm {72 mul 2.54 div} def'
+      write(iunt,10) '/mc {72 div 2.54 mul} def'
+      write(iunt,10) '/pnum { 72 div 2.54 mul 20 string'
+      write(iunt,10) 'cvs print ( ) print} def'
+      write(iunt,10)
+     1  '/Cshow {dup stringwidth pop -2 div 0 rmoveto show} def'
+c
+c we leave margins etc. in cm so it is easy to modify them if
+c needed by editing the output file
+      write(iunt,10) 'gsave'
+      if (ltit.gt.0) then
+      write(iunt,*) '/Helvetica findfont ',fnstit,
+     &             ' cm scalefont setfont '
+      write(iunt,*) xtit,' cm ',ytit,' cm moveto '
+      write(iunt,'(3A)') '(',title(1:ltit),') Cshow'
+      end if
+      write(iunt,*) lrmrgn,' cm ',botmrgn,' cm translate'
+      write(iunt,*) siz,' cm ',m,' div dup scale '
+c------- 
+c draw a frame around the matrix
+      write(iunt,*) frlw,' setlinewidth'
+      write(iunt,10) 'newpath'
+      write(iunt,11) 0, 0, ' moveto'
+      if (square) then
+      write(iunt,11) m,0,' lineto'
+      write(iunt,11) m, m, ' lineto'
+      write(iunt,11) 0,m,' lineto'
+      else
+      write(iunt,11) nc,0,' lineto'
+      write(iunt,11) nc,nr,' lineto'
+      write(iunt,11) 0,nr,' lineto'
+      end if
+      write(iunt,10) 'closepath stroke'
+c
+c     drawing the separation lines 
+c 
+      write(iunt,*)  ' 0.2 setlinewidth'
+      do 22 kol=1, nlines 
+         isep = lines(kol) 
+c
+c     horizontal lines 
+c
+         yy =  real(nrow-isep) + haf 
+         xx = real(ncol+1) 
+         write(iunt,13) zero, yy, ' moveto '
+         write(iunt,13)  xx, yy, ' lineto stroke '
+c
+c vertical lines 
+c
+         xx = real(isep) + haf 
+         yy = real(nrow+1)  
+         write(iunt,13) xx, zero,' moveto '
+         write(iunt,13) xx, yy, ' lineto stroke '             
+ 22     continue
+c 
+c----------- plotting loop ---------------------------------------------
+c
+      write(iunt,10) '1 1 translate'
+      write(iunt,10) '0.8 setlinewidth'
+      write(iunt,10) '/p {moveto 0 -.40 rmoveto '
+      write(iunt,10) '           0  .80 rlineto stroke} def'
+c     
+      do 1 ii=1, n
+        istart = ia(ii)
+        ilast  = ia(ii+1)-1 
+        if (mode .eq. 1) then
+          do 2 k=istart, ilast
+            write(iunt,11) ii-1, nrow-ja(k), ' p'
+ 2        continue 
+        else
+          do 3 k=istart, ilast
+            write(iunt,11) ja(k)-1, nrow-ii, ' p'
+ 3        continue          
+c add diagonal element if MSR mode.
+          if (mode .eq. 2) 
+     *         write(iunt,11) ii-1, nrow-ii, ' p' 
+c
+        endif
+ 1    continue
+c-----------------------------------------------------------------------
+      write(iunt,10) 'showpage'
+      return
+c
+ 10   format (A)
+ 11   format (2(I6,1x),A)
+ 12   format (A,4(1x,F9.2))
+ 13   format (2(F9.2,1x),A)
+c-----------------------------------------------------------------------
+      end
+c
+      integer function lenstr(s)
+c-----------------------------------------------------------------------
+c return length of the string S
+c-----------------------------------------------------------------------
+      character*(*) s
+      integer len
+      intrinsic len
+      integer n
+c----------------------------------------------------------------------- 
+      n = len(s)
+10    continue
+        if (s(n:n).eq.' ') then
+          n = n-1
+          if (n.gt.0) go to 10
+        end if
+      lenstr = n
+c
+      return
+c--------end-of-pspltm--------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine pltmt (nrow,ncol,mode,ja,ia,title,key,type,
+     1     job, iounit)
+c-----------------------------------------------------------------------
+c this subroutine creates a 'pic' file for plotting the pattern of 
+c a sparse matrix stored in general sparse format. it is not intended
+c to be a means of plotting large matrices (it is very inefficient).
+c It is however useful for small matrices and can be used for example
+c for inserting matrix plots in a text. The size of the plot can be
+c 7in x 7in or 5 in x 5in .. There is also an option for writing a 
+c 3-line header in troff (see description of parameter job).
+c Author: Youcef Saad - Date: Sept., 1989
+c See SPARSKIT/UNSUPP/ for a version of this to produce a post-script
+c file. 
+c-----------------------------------------------------------------------
+c nrow   = number of rows in matrix
+c
+c ncol	 = number of columns in matrix 
+c
+c mode   = integer indicating whether the matrix is stored
+c          row-wise (mode = 0) or column-wise (mode=1)
+c
+c ja     = column indices of nonzero elements when matrix is
+c	   stored rowise. Row indices if stores column-wise.
+c ia     = integer array of containing the pointers to the 
+c	   beginning of the columns in arrays a, ja.
+c
+c title  = character*71 = title of matrix test ( character a*71 ).
+c key    = character*8  = key of matrix 
+c type   = character*3  = type of matrix. 
+c
+c job    = this integer parameter allows to set a few minor 
+c          options. First it tells pltmt whether or not to
+c          reduce the plot. The standard size of 7in is then
+c          replaced by a 5in plot. It also tells pltmt whether or
+c          not to append to the pic file a few 'troff' lines that 
+c          produce a centered caption includingg the title, key and 
+c          types as well as the size and number of nonzero elements.
+c          job =  0 : do not reduce and do not make caption.
+c          job =  1 : reduce and do not make caption.
+c          job = 10 : do not reduce and make caption
+c          job = 11 : reduce and make caption.
+c          (i.e. trailing digit for reduction, leading digit for caption)
+c
+c iounit = logical unit number where to write the matrix into.
+c
+c-----------------------------------------------------------------------
+c example of usage . 
+c-----------------
+c In the fortran code:
+c  a) read a Harwell/Boeing matrix
+c          call readmt (.....)
+c	   iout = 13
+c  b) generate pic file:
+c          call  pltmt (nrow,ncol,mode,ja,ia,title,key,type,iout)
+c	   stop
+c ---------
+c Then in a unix environment plot the matrix by the command
+c
+c	pic FOR013.DAT | troff -me | lpr -Ppsx
+c
+c-----------------------------------------------------------------------
+c notes: 1) Plots square as well as rectangular matrices.
+c            (however not as much tested with rectangular matrices.)
+c	  2) the dot-size is adapted according to the size of the
+c            matrix.
+c	  3) This is not meant at all as a way of plotting large
+c            matrices. The pic file generaled will have one line for
+c            each nonzero element. It is  only meant for use in
+c	     such things as document poreparations etc..
+c         4) The caption written will print the 71 character long
+c            title. This may not be centered correctly if the
+c            title has trailing blanks (a problem with Troff).
+c            if you want the title centered then you can center
+c            the string in title before calling pltmt. 
+c       
+c-----------------------------------------------------------------------
+      integer ja(*), ia(*)
+      character key*8,title*72,type*3
+      real x, y
+c-------
+      n = ncol
+      if (mode .eq. 0) n = nrow
+      nnz = ia(n+1) - ia(1) 
+      maxdim = max0 (nrow, ncol)
+      xnrow = real(nrow)
+      ptsize = 0.08
+      hscale = (7.0 -2.0*ptsize)/real(maxdim-1) 
+      vscale = hscale 
+      xwid  = ptsize + real(ncol-1)*hscale + ptsize
+      xht   = ptsize + real(nrow-1)*vscale + ptsize
+      xshift = (7.0-xwid)/2.0
+      yshift = (7.0-xht)/2.0 
+c------
+      if (mod(job,10) .eq. 1) then
+         write (iounit,88)
+      else
+         write (iounit,89)
+      endif
+ 88   format('.PS 5in',/,'.po 1.8i')
+ 89   format('.PS',/,'.po 0.7i')
+      write(iounit,90) 
+ 90   format('box invisible wid 7.0 ht 7.0 with .sw at (0.0,0.0) ') 
+      write(iounit,91) xwid, xht, xshift, yshift
+ 91   format('box wid ',f5.2,' ht ',f5.2,
+     *     ' with .sw at (',f5.2,',',f5.2,')' )
+c     
+c     shift points slightly to account for size of dot , etc..
+c     
+      tiny = 0.03
+      if (mod(job,10) .eq. 1) tiny = 0.05
+      xshift = xshift + ptsize - tiny
+      yshift = yshift + ptsize + tiny
+c     
+c-----------------------------------------------------------------------
+c     
+      ips = 8
+      if (maxdim .le. 500) ips = 10
+      if (maxdim .le. 300) ips = 12
+      if (maxdim .le. 100) ips = 16
+      if (maxdim .lt. 50) ips = 24
+      write(iounit,92) ips
+ 92   format ('.ps ',i2)
+c     
+c-----------plottingloop --------------------------------------------- 
+c     
+      do 1 ii=1, n
+         istart = ia(ii)
+         ilast  = ia(ii+1)-1 
+         if (mode .ne. 0) then
+            x = real(ii-1)
+            do 2 k=istart, ilast
+               y = xnrow-real(ja(k))
+               write(iounit,128) xshift+x*hscale, yshift+y*vscale
+ 2          continue 
+         else
+            y = xnrow - real(ii)
+            do 3 k=istart, ilast
+               x = real(ja(k)-1)
+               write(iounit,128) xshift+x*hscale, yshift+y*vscale
+ 3          continue	    
+         endif
+ 1    continue
+c-----------------------------------------------------------------------
+ 128  format(7h"." at ,f6.3,1h,,f6.3,8h ljust  )
+      write (iounit, 129)
+ 129  format('.PE')
+c     quit if caption not desired. 
+      if ( (job/10) .ne. 1)  return
+c     
+      write(iounit,127) key, type, title
+      write(iounit,130) nrow,ncol,nnz
+ 127  format('.sp 4'/'.ll 7i'/'.ps 12'/'.po 0.7i'/'.ce 3'/,
+     *     'Matrix:  ',a8,',  Type:  ',a3,/,a72)
+ 130  format('Dimension: ',i4,' x ',i4,',  Nonzero elements: ',i5)
+      return
+c----------------end-of-pltmt ------------------------------------------
+c----------------------------------------------------------------------- 
+      end
+c-----------------------------------------------------------------------
+      subroutine smms (n,first,last,mode,a,ja,ia,iout)
+      integer ia(*), ja(*), n, first, last, mode, iout
+      real*8 a(*)
+c-----------------------------------------------------------------------
+c writes a matrix in Coordinate (SMMS) format -- 
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c n     = integer = size of matrix -- number of rows (columns if matrix
+c         is stored columnwise) 
+c first  = first row (column) to be output. This routine will output 
+c          rows (colums) first to last. 
+c last   = last row (column) to be output. 
+c mode   = integer giving some information about the storage of the 
+c          matrix. A 3-digit decimal number. 'htu' 
+c         * u = 0 means that matrix is stored row-wise 
+c         * u = 1 means that matrix is stored column-wise 
+c         * t = 0 indicates that the matrix is stored in CSR format 
+c         * t = 1 indicates that the matrix is stored in MSR format. 
+c         * h = ... to be added. 
+c a,
+c ja,
+c ia    =  matrix in CSR or MSR format (see mode) 
+c iout  = output unit number.
+c
+c on return:
+c----------
+c the output file iout will have written in it the matrix in smms
+c (coordinate format)
+c
+c-----------------------------------------------------------------------
+        logical msr, csc 
+c
+c determine mode ( msr or csr )
+c
+        msr = .false.
+        csc = .false. 
+	if (mod(mode,10) .eq. 1) csc = .true.
+        if ( (mode/10) .eq. 1) msr = .true. 
+        
+        write (iout,*) n
+      do 2 i=first, last 
+         k1=ia(i)
+         k2 = ia(i+1)-1
+c     write (iout,*) ' row ', i 
+         if (msr) write(iout,'(2i6,e22.14)')  i, i, a(i) 
+         do 10 k=k1, k2
+            if (csc) then
+               write(iout,'(2i6,e22.14)')  ja(k), i, a(k)
+            else
+               write(iout,'(2i6,e22.14)')  i, ja(k), a(k)
+            endif 
+ 10      continue
+ 2    continue
+c----end-of-smms--------------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine readsm (nmax,nzmax,n,nnz,ia,ja,a,iout,ierr)
+      integer nmax, nzmax, row, n, iout, i, j, k, ierr
+      integer ia(nmax+1), ja(nzmax)
+      real*8  a(nzmax), x
+c-----------------------------------------------------------------------
+c     read a matrix in coordinate format as is used in the SMMS
+c     package (F. Alvarado), i.e. the row is in ascending order.
+c     Outputs the matrix in CSR format.
+c-----------------------------------------------------------------------
+c coded by Kesheng Wu on Oct 21, 1991 with the supervision of Y. Saad
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c nmax  = the maximum size of array
+c nzmax = the maximum number of nonzeros
+c iout  = the I/O unit that has the data file
+c
+c on return:
+c---------- 
+c n     = integer = size of matrix
+c nnz   = number of non-zero entries in the matrix
+c a,
+c ja, 
+c ia    = matrix in CSR format
+c ierr  = error code,
+c         0 -- subroutine end with intended job done
+c         1 -- error in I/O unit iout
+c         2 -- end-of-file reached while reading n, i.e. a empty data file
+c         3 -- n non-positive or too large
+c         4 -- nnz is zero or larger than nzmax
+c         5 -- data file is not orgnized in the order of ascending
+c              row indices
+c
+c in case of errors:
+c   n will be set to zero (0). In case the data file has more than nzmax
+c   number of entries, the first nzmax entries will be read, and are not 
+c   cleared on return. The total number of entry is determined.
+c   Ierr is set.
+c-----------------------------------------------------------------------
+c
+      rewind(iout)
+      nnz = 0
+      ia(1) = 1
+      row = 1
+c
+      read (iout,*, err=1000, end=1010) n
+      if ((n.le.0) .or. (n.gt.nmax)) goto 1020
+c
+ 10   nnz = nnz + 1
+      read (iout, *, err=1000, end=100) i, j, x
+
+c     set the pointers when needed
+      if (i.gt.row) then
+         do 20 k = row+1, i
+            ia(k) = nnz
+ 20      continue
+         row = i
+      else if (i.lt.row) then
+         goto 1040
+      endif
+
+      ja(nnz) = j
+      a (nnz) = x
+
+      if (nnz.lt.nzmax) then
+         goto 10
+      else
+         goto 1030
+      endif
+
+c     normal return -- end of file reached
+ 100  ia(row+1) = nnz
+      nnz = nnz - 1
+      if (nnz.eq.0) goto 1030
+c
+c     everything seems to be OK.
+c
+      ierr = 0
+      return
+c
+c     error handling code
+c
+c     error in reading data entries
+c
+ 1000 ierr = 1
+      goto 2000
+c
+c     empty file
+c
+ 1010 ierr  = 2
+      goto 2000
+c
+c     problem with n
+c
+ 1020 ierr = 3
+      goto 2000
+c
+c     problem with nnz
+c
+ 1030 ierr = 4
+c
+c     try to determine the real number of entries, in case needed
+c
+      if (nnz.ge.nzmax) then
+ 200     read(iout, *, err=210, end=210) i, j, x
+         nnz = nnz + 1
+         goto 200
+ 210     continue
+      endif
+      goto 2000
+c
+c     data entries not ordered
+c
+ 1040 ierr = 5
+ 2000 n = 0
+      return
+c----end-of-readsm------------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine readsk (nmax,nzmax,n,nnz,a,ja,ia,iounit,ierr)
+      integer nmax, nzmax, iounit, n, nnz, i, ierr
+      integer ia(nmax+1), ja(nzmax) 
+      real*8 a(nzmax)
+c-----------------------------------------------------------------------
+c Reads matrix in Compressed Saprse Row format. The data is supposed to
+c appear in the following order -- n, ia, ja, a
+c Only square matrices accepted. Format has following features
+c (1) each number is separated by at least one space (or end-of-line), 
+c (2) each array starts with a new line.
+c-----------------------------------------------------------------------
+c coded by Kesheng Wu on Oct 21, 1991 with supervision of Y. Saad
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c nmax 	 = max column dimension  allowed for matrix.
+c nzmax	 = max number of nonzeros elements allowed. the arrays a, 
+c          and ja should be of length equal to nnz (see below).
+c iounit = logical unit number where to read the matrix from.
+c
+c on return:
+c---------- 
+c ia,
+c ja,
+c a      = matrx in CSR format
+c n      = number of rows(columns) in matrix
+c nnz	 = number of nonzero elements in A. This info is returned
+c          even if there is not enough space in a, ja, ia, in order
+c          to determine the minimum storage needed.
+c ierr   = error code,
+c          0 : OK;
+c          1 : error when try to read the specified I/O unit.
+c          2 : end-of-file reached during reading of data file.
+c          3 : array size in data file is negtive or larger than nmax;
+c          4 : nunmer of nonzeros in data file is negtive or larger than nzmax
+c in case of errors:
+c---------
+c     n is set to 0 (zero), at the same time ierr is set.
+c-----------------------------------------------------------------------
+c     
+c     read the size of the matrix
+c
+      rewind(iounit)
+      read (iounit, *, err=1000, end=1010) n
+      if ((n.le.0).or.(n.gt.nmax)) goto 1020
+c     
+c     read the pointer array ia(*)
+c     
+      read (iounit, *, err=1000, end=1010) (ia(i), i=1, n+1)
+c     
+c     Number of None-Zeros
+c     
+      nnz = ia(n+1) - 1
+      if ((nnz.le.0).or.(nnz.gt.nzmax)) goto 1030
+c     
+c     read the column indices array
+c     
+      read (iounit, *, err=1000, end=1010) (ja(i), i=1, nnz)
+c     
+c     read the matrix elements
+c     
+      read (iounit, *, err=1000, end=1010) (a(i), i=1, nnz)
+c     
+c     normal return
+c
+      ierr = 0
+      return
+c     
+c     error handling code
+c     
+c     error in reading I/O unit
+ 1000 ierr = 1
+      goto 2000
+c
+c     EOF reached in reading
+ 1010 ierr =2
+      goto 2000
+c
+c     n non-positive or too large
+ 1020 ierr = 3
+      n = 0
+      goto 2000
+c
+c     NNZ non-positive or too large
+ 1030 ierr = 4
+c     
+c     the real return statement
+c     
+ 2000 n = 0
+      return
+c---------end of readsk ------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine skit (n, a, ja, ia, ifmt, iounit, ierr)
+c-----------------------------------------------------------------------
+c     Writes a matrix in Compressed Sparse Row format to an I/O unit.
+c     It tryes to pack as many number as possible into lines of less than
+c     80 characters. Space is inserted in between numbers for separation
+c     to avoid carrying a header in the data file. This can be viewed
+c     as a simplified Harwell-Boeing format. 
+c-----------------------------------------------------------------------
+c Modified from subroutine prtmt written by Y. Saad
+c-----------------------------------------------------------------------
+c on entry:
+c---------
+c n      = number of rows(columns) in matrix
+c a      = real*8 array containing the values of the matrix stored 
+c          columnwise
+c ja     = integer array of the same length as a containing the column
+c          indices of the corresponding matrix elements of array a.
+c ia     = integer array of containing the pointers to the beginning of 
+c          the row in arrays a and ja.
+c ifmt   = integer specifying the format chosen for the real values
+c          to be output (i.e., for a, and for rhs-guess-sol if 
+c          applicable). The meaning of ifmt is as follows.
+c          * if (ifmt .lt. 100) then the D descriptor is used,
+c          format Dd.m, in which the length (m) of the mantissa is 
+c          precisely the integer ifmt (and d = ifmt+6)
+c          * if (ifmt .gt. 100) then prtmt will use the 
+c          F- descriptor (format Fd.m) in which the length of the 
+c          mantissa (m) is the integer mod(ifmt,100) and the length 
+c          of the integer part is k=ifmt/100 (and d = k+m+2)
+c          Thus  ifmt= 4   means  D10.4  +.xxxxD+ee    while
+c          ifmt=104  means  F7.4   +x.xxxx
+c          ifmt=205  means  F9.5   +xx.xxxxx
+c          Note: formats for ja, and ia are internally computed.
+c     
+c iounit = logical unit number where to write the matrix into.
+c     
+c on return:
+c----------
+c ierr   = error code, 0 for normal 1 for error in writing to iounit.
+c
+c on error:
+c--------
+c     If error is encontacted when writing the matrix, the whole matrix
+c     is written to the standard output.
+c     ierr is set to 1.
+c-----------------------------------------------------------------------
+      character ptrfmt*16,indfmt*16,valfmt*20
+      integer iounit, n, ifmt, len, nperli, nnz, i, ihead
+      integer ja(*), ia(*), ierr
+      real*8 a(*)
+c--------------
+c     compute pointer format
+c--------------
+      nnz    = ia(n+1)
+      len    = int ( alog10(0.1+real(nnz))) + 2
+      nnz    = nnz - 1
+      nperli = 80/len
+      
+      print *, ' skit entries:', n, nnz, len, nperli
+
+      if (len .gt. 9) then
+         assign 101 to ix
+      else
+         assign 100 to ix
+      endif
+      write (ptrfmt,ix) nperli,len
+ 100  format(1h(,i2,1HI,i1,1h) )
+ 101  format(1h(,i2,1HI,i2,1h) )
+c----------------------------
+c     compute ROW index format
+c----------------------------
+      len    = int ( alog10(0.1+real(n) )) + 2
+      nperli = min0(80/len,nnz)
+      write (indfmt,100) nperli,len
+c---------------------------
+c     compute value format
+c---------------------------
+      if (ifmt .ge. 100) then
+         ihead = ifmt/100
+         ifmt = ifmt-100*ihead
+         len = ihead+ifmt+3
+         nperli = 80/len
+c     
+         if (len .le. 9 ) then
+            assign 102 to ix
+         elseif (ifmt .le. 9) then
+            assign 103 to ix
+         else 
+            assign 104 to ix
+         endif
+c     
+         write(valfmt,ix) nperli,len,ifmt
+ 102     format(1h(,i2,1hF,i1,1h.,i1,1h) )
+ 103     format(1h(,i2,1hF,i2,1h.,i1,1h) )
+ 104     format(1h(,i2,1hF,i2,1h.,i2,1h) )
+C     
+      else
+         len = ifmt + 7
+         nperli = 80/len
+c     try to minimize the blanks in the format strings.
+         if (nperli .le. 9) then
+	    if (len .le. 9 ) then
+	       assign 105 to ix
+	    elseif (ifmt .le. 9) then
+	       assign 106 to ix
+	    else 
+	       assign 107 to ix
+	    endif
+	 else 
+	    if (len .le. 9 ) then
+	       assign 108 to ix
+	    elseif (ifmt .le. 9) then
+	       assign 109 to ix
+	    else 
+               assign 110 to ix
+            endif
+         endif
+c-----------
+         write(valfmt,ix) nperli,len,ifmt
+ 105     format(1h(,i1,1hD,i1,1h.,i1,1h) )
+ 106     format(1h(,i1,1hD,i2,1h.,i1,1h) )
+ 107     format(1h(,i1,1hD,i2,1h.,i2,1h) )
+ 108     format(1h(,i2,1hD,i1,1h.,i1,1h) )
+ 109     format(1h(,i2,1hD,i2,1h.,i1,1h) )
+ 110     format(1h(,i2,1hD,i2,1h.,i2,1h) )
+c     
+      endif 	    
+c     
+c     output the data
+c     
+      write(iounit, *) n
+      write(iounit,ptrfmt,err=1000) (ia(i), i = 1, n+1)
+      write(iounit,indfmt,err=1000) (ja(i), i = 1, nnz)
+      write(iounit,valfmt,err=1000) ( a(i), i = 1, nnz)
+c
+c     done, if no trouble is encounted in writing data
+c
+      ierr = 0
+      return
+c     
+c     if can't write the data to the I/O unit specified, should be able to
+c     write everything to standard output (unit 6)
+c     
+ 1000 write(0, *) 'Error, Can''t write data to sepcified unit',iounit
+      write(0, *) 'Write the matrix into standard output instead!'
+      ierr = 1
+      write(6,*) n
+      write(6,ptrfmt) (ia(i), i=1, n+1)
+      write(6,indfmt) (ja(i), i=1, nnz)
+      write(6,valfmt) ( a(i), i=1, nnz)
+      return
+c----------end of skit ------------------------------------------------- 
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine prtunf(n, a, ja, ia, iout, ierr)
+c-----------------------------------------------------------------------
+c This subroutine dumps the arrays used for storing sparse compressed row
+c format in machine code, i.e. unformatted using standard FORTRAN term.
+c-----------------------------------------------------------------------
+c First coded by Kesheng Wu on Oct 21, 1991 under the instruction of
+c Prof. Y. Saad
+c-----------------------------------------------------------------------
+c On entry:
+c     n: the size of the matrix (matrix is n X n)
+c    ia: integer array stores the stariting position of each row.
+c    ja: integer array stores the column indices of each entry.
+c     a: the non-zero entries of the matrix.
+c  iout: the unit number opened for storing the matrix.
+c On return:
+c  ierr: a error, 0 if everything's OK, else 1 if error in writing data.
+c On error:
+c  set ierr to 1.
+c  No redirection is made, since direct the machine code to the standard
+c output may cause unpridictable consequences.
+c-----------------------------------------------------------------------
+      integer iout, n, nnz, ierr, ia(*), ja(*)
+      real*8  a(*)
+      nnz = ia(n+1)-ia(1) 
+c
+      write(unit=iout, err=1000)  n
+      write(unit=iout, err=1000) (ia(k),k=1,n+1) 
+      if (nnz .gt. 0) then
+         write(unit=iout, err=1000) (ja(k),k=1,nnz)
+         write(unit=iout, err=1000) ( a(k),k=1,nnz)
+      endif 
+c
+      ierr = 0
+      return
+c
+ 1000 ierr = 1
+      return
+      end
+c---------end of prtunf ------------------------------------------------
+c
+c-----------------------------------------------------------------------
+      subroutine readunf(nmax,nzmax,n,nnz,a,ja,ia,iounit,ierr)
+c-----------------------------------------------------------------------
+c This subroutine reads a matix store in machine code (FORTRAN
+c unformatted form). The matrix is in CSR format.
+c-----------------------------------------------------------------------
+c First coded by Kesheng Wu on Oct 21, 1991 under the instruction of
+c Prof. Y. Saad
+c-----------------------------------------------------------------------
+c On entry:
+c    nmax: the maximum value of matrix size.
+c   nzmax: the maximum number of non-zero entries.
+c  iounit: the I/O unit that opened for reading.
+c On return:
+c       n: the actual size of array.
+c     nnz: the actual number of non-zero entries.
+c ia,ja,a: the matrix in CSR format.
+c    ierr: a error code, it's same as that used in reaadsk
+c          0 -- OK
+c          1 -- error in reading iounit
+c          2 -- end-of-file reached while reading data file
+c          3 -- n is non-positive or too large
+c          4 -- nnz is non-positive or too large
+c On error:
+c     return with n set to 0 (zero). nnz is kept if it's set already,
+c     in case one want to use it to determine the size of array needed
+c     to hold the data.
+c-----------------------------------------------------------------------
+c
+      integer nmax, nzmax, n, iounit, nnz, k
+      integer ia(nmax+1), ja(nzmax)
+      real*8  a(nzmax)
+c
+      rewind iounit
+c      
+      read (unit=iounit, err=1000, end=1010) n
+      if ((n.le.0) .or. (n.gt.nmax)) goto 1020
+c
+      read(unit=iounit, err=1000, end=1010) (ia(k),k=1,n+1)
+c
+      nnz = ia(n+1) - 1
+      if ((nnz.le.0) .or. (nnz.gt.nzmax)) goto 1030
+c
+      read(unit=iounit, err=1000, end=1010) (ja(k),k=1,nnz)
+      read(unit=iounit, err=1000, end=1010) (a(k),k=1,nnz)
+c
+c     everything seems to be OK.
+c
+      ierr = 0
+      return
+c
+c     error handling
+c
+ 1000 ierr = 1
+      goto 2000
+ 1010 ierr = 2
+      goto 2000
+ 1020 ierr = 3
+      goto 2000
+ 1030 ierr = 4
+ 2000 n = 0
+      return
+      end
+c---------end of readunf ----------------------------------------------
diff --git a/INOUT/makefile b/INOUT/makefile
new file mode 100644
index 0000000..993582c
--- /dev/null
+++ b/INOUT/makefile
@@ -0,0 +1,28 @@
+FFLAGS = 
+F77 = f77
+
+#F77 = cf77
+#FFLAGS = -Wf"-dp"
+
+FILES1 = chkio.o
+FILES2 = hb2ps.o 
+FILES3 = hb2pic.o 
+
+chk.ex: $(FILES1) ../MATGEN/FDIF/functns.o ../libskit.a
+	$(F77) $(FFLAGS) -o chk.ex $(FILES1) ../MATGEN/FDIF/functns.o ../libskit.a
+
+hb2ps.ex: $(FILES2) ../libskit32.a
+	$(F77) $(FFLAGS) -o hb2ps.ex $(FILES2) ../libskit32.a
+
+hb2pic.ex: $(FILES3) ../libskit.a
+	$(F77) $(FFLAGS) -o hb2pic.ex $(FILES3) ../libskit.a
+
+clean:
+	rm -f *.o *.ex core *.trace *.pic *.mat *.ps
+
+../MATGEN/FDIF/functns.o:
+	(cd ../MATGEN/FDIF; $(F77) $(FFLAGS) -c functns.f)
+
+../libskit.a:
+	(cd ..; $(MAKE) $(MAKEFLAGS) libskit.a)
+
diff --git a/INOUT/semantic.cache b/INOUT/semantic.cache
new file mode 100644
index 0000000..5676fe7
--- /dev/null
+++ b/INOUT/semantic.cache
@@ -0,0 +1,15 @@
+;; Object INOUT/
+;; SEMANTICDB Tags save file
+(semanticdb-project-database-file "INOUT/"
+  :tables (list 
+   (semanticdb-table "makefile"
+    :major-mode 'makefile-mode
+    :tags '(("FFLAGS" variable nil nil [1 11]) ("F77" variable (:default-value ("f77")) nil [11 21]) ("FILES1" variable (:default-value ("chkio.o")) nil [54 71]) ("FILES2" variable (:default-value ("hb2ps.o")) nil [71 89]) ("FILES3" variable (:default-value ("hb2pic.o")) nil [89 108]) ("chk.ex" function (:arguments ("$(FILES1)" "../MATGEN/FDIF/functns.o" "../libskit.a")) nil [109 242]) ("hb2ps.ex" function (:arguments ("$(FILES2)" "../libskit32.a")) nil [242 333]) ("hb2pic.ex" function (:arguments ("$(FILES3)" "../libskit.a")) nil [333 422]) ("clean" function nil nil [422 476]) ("../MATGEN/FDIF/functns.o" function nil nil [476 555]) ("../libskit.a" function nil nil [555 611]))
+    :file "makefile"
+    :pointmax 611
+    )
+   )
+  :file "semantic.cache"
+  :semantic-tag-version "2.0pre3"
+  :semanticdb-version "2.0pre3"
+  )
diff --git a/ITSOL/README b/ITSOL/README
new file mode 100644
index 0000000..e362ada
--- /dev/null
+++ b/ITSOL/README
@@ -0,0 +1,63 @@
+
+		             ----------------- 
+		             Current contents:
+			     -----------------
+
+ Solvers
+ -------
+
+ iters.f : This file currently has several basic iterative linear system
+           solvers. They are:
+           CG       -- Conjugate Gradient Method
+           CGNR     -- Conjugate Gradient Method on Normal Residual equation
+           BCG      -- Bi-Conjugate Gradient Method
+           BCGSTAB  -- BCG stablized
+           TFQMR    -- Transpose-Free Quasi-Minimum Residual method
+           GMRES    -- Generalized Minimum RESidual method
+           FGMRES   -- Flexible version of Generalized Minimum RESidual method
+           DQGMRES  -- Direct verions of Quasi Generalized Minimum Residual 
+                       method
+           DBCG     -- BCG with partial pivoting
+
+ Preconditioners
+ ---------------
+	
+ ilut.f :  ILUT + GMRES: a combination of a robust preconditioner
+	   using dual thresholding for dropping strategy and
+	   the GMRES algorithm. ILU0 and MILU0 are also provided
+	   for comparison purposes.
+	   large number of updates on Feb 10, 1992 Y.S. 
+	   ILUTP, or ILUT with partial pivoting is also provided.
+
+ Drivers
+ -------
+
+ rilut.f : test program for GMRES/ILU*.
+           It tests three preconditioners ilu0, milu0 and ilut using
+           GMRES as the solver.
+
+riters.f : test program for ITERS -- the basic iterative solvers
+           with reverse communication.
+           The test matrix is generated with GEN57PT.
+
+riter2.f : test program for ITERS. It reads a Harwell/Boeing matrix
+           from the standard input.
+
+ Other
+ -----
+
+ itaux.f : The file contains some of the auxiliary functions that is
+           required to run the test prgram rilut.f and riters.f It
+           includes the routine that drive the reverse-communincation
+           routines and the definitions of the partial differential
+           equations used to generate the matrix in rilut.f and
+	   riters.f.
+
+ executables
+ ----------- 
+
+ rilut.ex : generated by "make rilut.ex" from the driver rilut.f
+riters.ex : generated by "make riters.ex" from the driver riters.f
+riter2.ex : generated by "make riter2.ex" from the driver riter2.f
+
+	    see makefile for the details of the dependencies.
diff --git a/ITSOL/ilut.f b/ITSOL/ilut.f
new file mode 100644
index 0000000..5136347
--- /dev/null
+++ b/ITSOL/ilut.f
@@ -0,0 +1,2430 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c                   ITERATIVE SOLVERS MODULE                           c
+c----------------------------------------------------------------------c
+c This Version Dated: August 13, 1996. Warning: meaning of some        c
+c ============ arguments have changed w.r.t. earlier versions. Some    c
+c              Calling sequences may also have changed                 c
+c----------------------------------------------------------------------c 
+c Contents:                                                            c
+c-------------------------preconditioners------------------------------c 
+c                                                                      c
+c ILUT    : Incomplete LU factorization with dual truncation strategy  c
+c ILUTP   : ILUT with column  pivoting                                 c
+c ILUD    : ILU with single dropping + diagonal compensation (~MILUT)  c
+c ILUDP   : ILUD with column pivoting                                  c
+c ILUK    : level-k ILU                                                c
+c ILU0    : simple ILU(0) preconditioning                              c
+c MILU0   : MILU(0) preconditioning                                    c
+c                                                                      c
+c----------sample-accelerator-and-LU-solvers---------------------------c 
+c                                                                      c
+c PGMRES  : preconditioned GMRES solver                                c
+c LUSOL   : forward followed by backward triangular solve (Precond.)   c
+c LUTSOL  : solving v = (LU)^{-T} u (used for preconditioning)         c
+c                                                                      c
+c-------------------------utility-routine------------------------------c
+c                                                                      c 
+c QSPLIT  : quick split routine used by ilut to sort out the k largest c
+c           elements in absolute value                                 c
+c                                                                      c
+c----------------------------------------------------------------------c
+c                                                                      c 
+c Note: all preconditioners are preprocessors to pgmres.               c
+c usage: call preconditioner then call pgmres                          c
+c                                                                      c
+c----------------------------------------------------------------------c
+      subroutine ilut(n,a,ja,ia,lfil,droptol,alu,jlu,ju,iwk,w,jw,ierr)
+c-----------------------------------------------------------------------
+      implicit none 
+      integer n 
+      real*8 a(*),alu(*),w(n+1),droptol
+      integer ja(*),ia(n+1),jlu(*),ju(n),jw(2*n),lfil,iwk,ierr
+c----------------------------------------------------------------------*
+c                      *** ILUT preconditioner ***                     *
+c      incomplete LU factorization with dual truncation mechanism      *
+c----------------------------------------------------------------------*
+c     Author: Yousef Saad *May, 5, 1990, Latest revision, August 1996  *
+c----------------------------------------------------------------------*
+c PARAMETERS                                                           
+c-----------                                                           
+c
+c on entry:
+c========== 
+c n       = integer. The row dimension of the matrix A. The matrix 
+c
+c a,ja,ia = matrix stored in Compressed Sparse Row format.              
+c
+c lfil    = integer. The fill-in parameter. Each row of L and each row
+c           of U will have a maximum of lfil elements (excluding the 
+c           diagonal element). lfil must be .ge. 0.
+c           ** WARNING: THE MEANING OF LFIL HAS CHANGED WITH RESPECT TO
+c           EARLIER VERSIONS. 
+c
+c droptol = real*8. Sets the threshold for dropping small terms in the
+c           factorization. See below for details on dropping strategy.
+c
+c  
+c iwk     = integer. The lengths of arrays alu and jlu. If the arrays
+c           are not big enough to store the ILU factorizations, ilut
+c           will stop with an error message. 
+c
+c On return:
+c===========
+c
+c alu,jlu = matrix stored in Modified Sparse Row (MSR) format containing
+c           the L and U factors together. The diagonal (stored in
+c           alu(1:n) ) is inverted. Each i-th row of the alu,jlu matrix
+c           contains the i-th row of L (excluding the diagonal entry=1)
+c           followed by the i-th row of U.
+c
+c ju      = integer array of length n containing the pointers to
+c           the beginning of each row of U in the matrix alu,jlu.
+c
+c ierr    = integer. Error message with the following meaning.
+c           ierr  = 0    --> successful return.
+c           ierr .gt. 0  --> zero pivot encountered at step number ierr.
+c           ierr  = -1   --> Error. input matrix may be wrong.
+c                            (The elimination process has generated a
+c                            row in L or U whose length is .gt.  n.)
+c           ierr  = -2   --> The matrix L overflows the array al.
+c           ierr  = -3   --> The matrix U overflows the array alu.
+c           ierr  = -4   --> Illegal value for lfil.
+c           ierr  = -5   --> zero row encountered.
+c
+c work arrays:
+c=============
+c jw      = integer work array of length 2*n.
+c w       = real work array of length n+1.
+c  
+c----------------------------------------------------------------------
+c w, ju (1:n) store the working array [1:ii-1 = L-part, ii:n = u] 
+c jw(n+1:2n)  stores nonzero indicators
+c 
+c Notes:
+c ------
+c The diagonal elements of the input matrix must be  nonzero (at least
+c 'structurally'). 
+c
+c----------------------------------------------------------------------* 
+c---- Dual drop strategy works as follows.                             *
+c                                                                      *
+c     1) Theresholding in L and U as set by droptol. Any element whose *
+c        magnitude is less than some tolerance (relative to the abs    *
+c        value of diagonal element in u) is dropped.                   *
+c                                                                      *
+c     2) Keeping only the largest lfil elements in the i-th row of L   * 
+c        and the largest lfil elements in the i-th row of U (excluding *
+c        diagonal elements).                                           *
+c                                                                      *
+c Flexibility: one  can use  droptol=0  to get  a strategy  based on   *
+c keeping  the largest  elements in  each row  of L  and U.   Taking   *
+c droptol .ne.  0 but lfil=n will give  the usual threshold strategy   *
+c (however, fill-in is then mpredictible).                             *
+c----------------------------------------------------------------------*
+c     locals
+      integer ju0,k,j1,j2,j,ii,i,lenl,lenu,jj,jrow,jpos,len 
+      real*8 tnorm, t, abs, s, fact 
+      if (lfil .lt. 0) goto 998
+c-----------------------------------------------------------------------
+c     initialize ju0 (points to next element to be added to alu,jlu)
+c     and pointer array.
+c-----------------------------------------------------------------------
+      ju0 = n+2
+      jlu(1) = ju0
+c
+c     initialize nonzero indicator array. 
+c
+      do 1 j=1,n
+         jw(n+j)  = 0
+ 1    continue
+c-----------------------------------------------------------------------
+c     beginning of main loop.
+c-----------------------------------------------------------------------
+      do 500 ii = 1, n
+         j1 = ia(ii)
+         j2 = ia(ii+1) - 1
+         tnorm = 0.0d0
+         do 501 k=j1,j2
+            tnorm = tnorm+abs(a(k))
+ 501     continue
+         if (tnorm .eq. 0.0) goto 999
+         tnorm = tnorm/real(j2-j1+1)
+c     
+c     unpack L-part and U-part of row of A in arrays w 
+c     
+         lenu = 1
+         lenl = 0
+         jw(ii) = ii
+         w(ii) = 0.0
+         jw(n+ii) = ii
+c
+         do 170  j = j1, j2
+            k = ja(j)
+            t = a(j)
+            if (k .lt. ii) then
+               lenl = lenl+1
+               jw(lenl) = k
+               w(lenl) = t
+               jw(n+k) = lenl
+            else if (k .eq. ii) then
+               w(ii) = t
+            else
+               lenu = lenu+1
+               jpos = ii+lenu-1 
+               jw(jpos) = k
+               w(jpos) = t
+               jw(n+k) = jpos
+            endif
+ 170     continue
+         jj = 0
+         len = 0 
+c     
+c     eliminate previous rows
+c     
+ 150     jj = jj+1
+         if (jj .gt. lenl) goto 160
+c-----------------------------------------------------------------------
+c     in order to do the elimination in the correct order we must select
+c     the smallest column index among jw(k), k=jj+1, ..., lenl.
+c-----------------------------------------------------------------------
+         jrow = jw(jj)
+         k = jj
+c     
+c     determine smallest column index
+c     
+         do 151 j=jj+1,lenl
+            if (jw(j) .lt. jrow) then
+               jrow = jw(j)
+               k = j
+            endif
+ 151     continue
+c
+         if (k .ne. jj) then
+c     exchange in jw
+            j = jw(jj)
+            jw(jj) = jw(k)
+            jw(k) = j
+c     exchange in jr
+            jw(n+jrow) = jj
+            jw(n+j) = k
+c     exchange in w
+            s = w(jj)
+            w(jj) = w(k)
+            w(k) = s
+         endif
+c
+c     zero out element in row by setting jw(n+jrow) to zero.
+c     
+         jw(n+jrow) = 0
+c
+c     get the multiplier for row to be eliminated (jrow).
+c     
+         fact = w(jj)*alu(jrow)
+         if (abs(fact) .le. droptol) goto 150
+c     
+c     combine current row and row jrow
+c
+         do 203 k = ju(jrow), jlu(jrow+1)-1
+            s = fact*alu(k)
+            j = jlu(k)
+            jpos = jw(n+j)
+            if (j .ge. ii) then
+c     
+c     dealing with upper part.
+c     
+               if (jpos .eq. 0) then
+c
+c     this is a fill-in element
+c     
+                  lenu = lenu+1
+                  if (lenu .gt. n) goto 995
+                  i = ii+lenu-1
+                  jw(i) = j
+                  jw(n+j) = i
+                  w(i) = - s
+               else
+c
+c     this is not a fill-in element 
+c
+                  w(jpos) = w(jpos) - s
+
+               endif
+            else
+c     
+c     dealing  with lower part.
+c     
+               if (jpos .eq. 0) then
+c
+c     this is a fill-in element
+c     
+                  lenl = lenl+1
+                  if (lenl .gt. n) goto 995
+                  jw(lenl) = j
+                  jw(n+j) = lenl
+                  w(lenl) = - s
+               else
+c     
+c     this is not a fill-in element 
+c     
+                  w(jpos) = w(jpos) - s
+               endif
+            endif
+ 203     continue
+c     
+c     store this pivot element -- (from left to right -- no danger of
+c     overlap with the working elements in L (pivots). 
+c     
+         len = len+1 
+         w(len) = fact
+         jw(len)  = jrow
+         goto 150
+ 160     continue
+c     
+c     reset double-pointer to zero (U-part)
+c     
+         do 308 k=1, lenu
+            jw(n+jw(ii+k-1)) = 0
+ 308     continue
+c     
+c     update L-matrix
+c     
+         lenl = len 
+         len = min0(lenl,lfil)
+c     
+c     sort by quick-split
+c
+         call qsplit (w,jw,lenl,len)
+c
+c     store L-part
+c 
+         do 204 k=1, len 
+            if (ju0 .gt. iwk) goto 996
+            alu(ju0) =  w(k)
+            jlu(ju0) =  jw(k)
+            ju0 = ju0+1
+ 204     continue
+c     
+c     save pointer to beginning of row ii of U
+c     
+         ju(ii) = ju0
+c
+c     update U-matrix -- first apply dropping strategy 
+c
+         len = 0
+         do k=1, lenu-1
+            if (abs(w(ii+k)) .gt. droptol*tnorm) then 
+               len = len+1
+               w(ii+len) = w(ii+k) 
+               jw(ii+len) = jw(ii+k) 
+            endif
+         enddo
+         lenu = len+1
+         len = min0(lenu,lfil)
+c
+         call qsplit (w(ii+1), jw(ii+1), lenu-1,len)
+c
+c     copy
+c 
+         t = abs(w(ii))
+         if (len + ju0 .gt. iwk) goto 997
+         do 302 k=ii+1,ii+len-1 
+            jlu(ju0) = jw(k)
+            alu(ju0) = w(k)
+            t = t + abs(w(k) )
+            ju0 = ju0+1
+ 302     continue
+c     
+c     store inverse of diagonal element of u
+c     
+         if (w(ii) .eq. 0.0) w(ii) = (0.0001 + droptol)*tnorm
+c     
+         alu(ii) = 1.0d0/ w(ii) 
+c     
+c     update pointer to beginning of next row of U.
+c     
+         jlu(ii+1) = ju0
+c-----------------------------------------------------------------------
+c     end main loop
+c-----------------------------------------------------------------------
+ 500  continue
+      ierr = 0
+      return
+c
+c     incomprehensible error. Matrix must be wrong.
+c     
+ 995  ierr = -1
+      return
+c     
+c     insufficient storage in L.
+c     
+ 996  ierr = -2
+      return
+c     
+c     insufficient storage in U.
+c     
+ 997  ierr = -3
+      return
+c     
+c     illegal lfil entered.
+c     
+ 998  ierr = -4
+      return
+c     
+c     zero row encountered
+c     
+ 999  ierr = -5
+      return
+c----------------end-of-ilut--------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------
+      subroutine ilutp(n,a,ja,ia,lfil,droptol,permtol,mbloc,alu,
+     *     jlu,ju,iwk,w,jw,iperm,ierr)
+c-----------------------------------------------------------------------
+c     implicit none
+      integer n,ja(*),ia(n+1),lfil,jlu(*),ju(n),jw(2*n),iwk,
+     *     iperm(2*n),ierr
+      real*8 a(*), alu(*), w(n+1), droptol
+c----------------------------------------------------------------------*
+c       *** ILUTP preconditioner -- ILUT with pivoting  ***            *
+c      incomplete LU factorization with dual truncation mechanism      *
+c----------------------------------------------------------------------*
+c author Yousef Saad *Sep 8, 1993 -- Latest revision, August 1996.     *
+c----------------------------------------------------------------------*
+c on entry:
+c==========
+c n       = integer. The dimension of the matrix A.
+c
+c a,ja,ia = matrix stored in Compressed Sparse Row format.
+c           ON RETURN THE COLUMNS OF A ARE PERMUTED. SEE BELOW FOR 
+c           DETAILS. 
+c
+c lfil    = integer. The fill-in parameter. Each row of L and each row
+c           of U will have a maximum of lfil elements (excluding the 
+c           diagonal element). lfil must be .ge. 0.
+c           ** WARNING: THE MEANING OF LFIL HAS CHANGED WITH RESPECT TO
+c           EARLIER VERSIONS. 
+c
+c droptol = real*8. Sets the threshold for dropping small terms in the
+c           factorization. See below for details on dropping strategy.
+c
+c lfil    = integer. The fill-in parameter. Each row of L and
+c           each row of U will have a maximum of lfil elements.
+c           WARNING: THE MEANING OF LFIL HAS CHANGED WITH RESPECT TO
+c           EARLIER VERSIONS. 
+c           lfil must be .ge. 0.
+c
+c permtol = tolerance ratio used to  determne whether or not to permute
+c           two columns.  At step i columns i and j are permuted when 
+c
+c                     abs(a(i,j))*permtol .gt. abs(a(i,i))
+c
+c           [0 --> never permute; good values 0.1 to 0.01]
+c
+c mbloc   = if desired, permuting can be done only within the diagonal
+c           blocks of size mbloc. Useful for PDE problems with several
+c           degrees of freedom.. If feature not wanted take mbloc=n.
+c
+c  
+c iwk     = integer. The lengths of arrays alu and jlu. If the arrays
+c           are not big enough to store the ILU factorizations, ilut
+c           will stop with an error message. 
+c
+c On return:
+c===========
+c
+c alu,jlu = matrix stored in Modified Sparse Row (MSR) format containing
+c           the L and U factors together. The diagonal (stored in
+c           alu(1:n) ) is inverted. Each i-th row of the alu,jlu matrix
+c           contains the i-th row of L (excluding the diagonal entry=1)
+c           followed by the i-th row of U.
+c
+c ju      = integer array of length n containing the pointers to
+c           the beginning of each row of U in the matrix alu,jlu.
+c
+c iperm   = contains the permutation arrays. 
+c           iperm(1:n) = old numbers of unknowns
+c           iperm(n+1:2*n) = reverse permutation = new unknowns.
+c
+c ierr    = integer. Error message with the following meaning.
+c           ierr  = 0    --> successful return.
+c           ierr .gt. 0  --> zero pivot encountered at step number ierr.
+c           ierr  = -1   --> Error. input matrix may be wrong.
+c                            (The elimination process has generated a
+c                            row in L or U whose length is .gt.  n.)
+c           ierr  = -2   --> The matrix L overflows the array al.
+c           ierr  = -3   --> The matrix U overflows the array alu.
+c           ierr  = -4   --> Illegal value for lfil.
+c           ierr  = -5   --> zero row encountered.
+c
+c work arrays:
+c=============
+c jw      = integer work array of length 2*n.
+c w       = real work array of length n 
+c
+c IMPORTANR NOTE:
+c --------------
+c TO AVOID PERMUTING THE SOLUTION VECTORS ARRAYS FOR EACH LU-SOLVE, 
+C THE MATRIX A IS PERMUTED ON RETURN. [all column indices are
+c changed]. SIMILARLY FOR THE U MATRIX. 
+c To permute the matrix back to its original state use the loop:
+c
+c      do k=ia(1), ia(n+1)-1
+c         ja(k) = iperm(ja(k)) 
+c      enddo
+c 
+c-----------------------------------------------------------------------
+c     local variables
+c
+      integer k,i,j,jrow,ju0,ii,j1,j2,jpos,len,imax,lenu,lenl,jj,mbloc,
+     *     icut
+      real*8 s, tmp, tnorm,xmax,xmax0, fact, abs, t, permtol
+c     
+      if (lfil .lt. 0) goto 998
+c----------------------------------------------------------------------- 
+c     initialize ju0 (points to next element to be added to alu,jlu)
+c     and pointer array.
+c-----------------------------------------------------------------------
+      ju0 = n+2
+      jlu(1) = ju0
+c
+c  integer double pointer array.
+c
+      do 1 j=1, n
+         jw(n+j)  = 0
+         iperm(j) = j
+         iperm(n+j) = j
+ 1    continue
+c-----------------------------------------------------------------------
+c     beginning of main loop.
+c-----------------------------------------------------------------------
+      do 500 ii = 1, n
+         j1 = ia(ii)
+         j2 = ia(ii+1) - 1
+         tnorm = 0.0d0
+         do 501 k=j1,j2
+            tnorm = tnorm+abs(a(k))
+ 501     continue
+         if (tnorm .eq. 0.0) goto 999
+         tnorm = tnorm/(j2-j1+1)
+c
+c     unpack L-part and U-part of row of A in arrays  w  --
+c
+         lenu = 1
+         lenl = 0
+         jw(ii) = ii
+         w(ii) = 0.0
+         jw(n+ii) = ii
+c
+         do 170  j = j1, j2
+            k = iperm(n+ja(j))
+            t = a(j)
+            if (k .lt. ii) then
+               lenl = lenl+1
+               jw(lenl) = k
+               w(lenl) = t
+               jw(n+k) = lenl
+            else if (k .eq. ii) then
+               w(ii) = t
+            else
+               lenu = lenu+1
+               jpos = ii+lenu-1 
+               jw(jpos) = k
+               w(jpos) = t
+               jw(n+k) = jpos
+            endif
+ 170     continue
+         jj = 0
+         len = 0 
+c
+c     eliminate previous rows
+c
+ 150     jj = jj+1
+         if (jj .gt. lenl) goto 160
+c-----------------------------------------------------------------------
+c     in order to do the elimination in the correct order we must select
+c     the smallest column index among jw(k), k=jj+1, ..., lenl.
+c-----------------------------------------------------------------------
+         jrow = jw(jj)
+         k = jj
+c
+c     determine smallest column index
+c
+         do 151 j=jj+1,lenl
+            if (jw(j) .lt. jrow) then
+               jrow = jw(j)
+               k = j
+            endif
+ 151     continue
+c
+         if (k .ne. jj) then
+c     exchange in jw
+            j = jw(jj)
+            jw(jj) = jw(k)
+            jw(k) = j
+c     exchange in jr
+            jw(n+jrow) = jj
+            jw(n+j) = k
+c     exchange in w
+            s = w(jj)
+            w(jj) = w(k)
+            w(k) = s
+         endif
+c
+c     zero out element in row by resetting jw(n+jrow) to zero.
+c     
+         jw(n+jrow) = 0
+c
+c     get the multiplier for row to be eliminated: jrow
+c
+         fact = w(jj)*alu(jrow)
+c
+c     drop term if small
+c     
+         if (abs(fact) .le. droptol) goto 150
+c
+c     combine current row and row jrow
+c
+         do 203 k = ju(jrow), jlu(jrow+1)-1
+            s = fact*alu(k)
+c     new column number
+            j = iperm(n+jlu(k))
+            jpos = jw(n+j)
+            if (j .ge. ii) then
+c
+c     dealing with upper part.
+c
+               if (jpos .eq. 0) then
+c
+c     this is a fill-in element
+c
+                  lenu = lenu+1
+                  i = ii+lenu-1 
+                  if (lenu .gt. n) goto 995
+                  jw(i) = j
+                  jw(n+j) = i 
+                  w(i) = - s
+               else
+c     no fill-in element --
+                  w(jpos) = w(jpos) - s
+               endif
+            else
+c
+c     dealing with lower part.
+c
+               if (jpos .eq. 0) then
+c
+c     this is a fill-in element
+c
+                 lenl = lenl+1
+                 if (lenl .gt. n) goto 995
+                 jw(lenl) = j
+                 jw(n+j) = lenl
+                 w(lenl) = - s
+              else
+c
+c     this is not a fill-in element
+c
+                 w(jpos) = w(jpos) - s
+              endif
+           endif
+ 203	continue
+c     
+c     store this pivot element -- (from left to right -- no danger of
+c     overlap with the working elements in L (pivots). 
+c     
+        len = len+1 
+        w(len) = fact
+        jw(len)  = jrow
+	goto 150
+ 160    continue
+c
+c     reset double-pointer to zero (U-part)
+c     
+        do 308 k=1, lenu
+           jw(n+jw(ii+k-1)) = 0
+ 308	continue
+c
+c     update L-matrix
+c
+        lenl = len 
+        len = min0(lenl,lfil)
+c     
+c     sort by quick-split
+c
+        call qsplit (w,jw,lenl,len)
+c
+c     store L-part -- in original coordinates ..
+c
+        do 204 k=1, len
+           if (ju0 .gt. iwk) goto 996
+           alu(ju0) =  w(k)  
+           jlu(ju0) = iperm(jw(k))
+           ju0 = ju0+1
+ 204    continue
+c
+c     save pointer to beginning of row ii of U
+c
+        ju(ii) = ju0
+c
+c     update U-matrix -- first apply dropping strategy 
+c
+         len = 0
+         do k=1, lenu-1
+            if (abs(w(ii+k)) .gt. droptol*tnorm) then 
+               len = len+1
+               w(ii+len) = w(ii+k) 
+               jw(ii+len) = jw(ii+k) 
+            endif
+         enddo
+         lenu = len+1
+         len = min0(lenu,lfil)
+         call qsplit (w(ii+1), jw(ii+1), lenu-1,len)
+c
+c     determine next pivot -- 
+c
+        imax = ii
+        xmax = abs(w(imax))
+        xmax0 = xmax
+        icut = ii - 1 + mbloc - mod(ii-1,mbloc)
+        do k=ii+1,ii+len-1
+           t = abs(w(k))
+           if (t .gt. xmax .and. t*permtol .gt. xmax0 .and.
+     *          jw(k) .le. icut) then
+              imax = k
+              xmax = t
+           endif
+        enddo
+c
+c     exchange w's
+c
+        tmp = w(ii)
+        w(ii) = w(imax)
+        w(imax) = tmp
+c
+c     update iperm and reverse iperm
+c
+        j = jw(imax)
+        i = iperm(ii)
+        iperm(ii) = iperm(j)
+        iperm(j) = i
+c
+c     reverse iperm
+c
+        iperm(n+iperm(ii)) = ii
+        iperm(n+iperm(j)) = j
+c----------------------------------------------------------------------- 
+c
+        if (len + ju0 .gt. iwk) goto 997
+c
+c     copy U-part in original coordinates
+c     
+        do 302 k=ii+1,ii+len-1 
+           jlu(ju0) = iperm(jw(k))
+           alu(ju0) = w(k)
+           ju0 = ju0+1
+ 302	continue
+c
+c     store inverse of diagonal element of u
+c
+        if (w(ii) .eq. 0.0) w(ii) = (1.0D-4 + droptol)*tnorm
+        alu(ii) = 1.0d0/ w(ii) 
+c
+c     update pointer to beginning of next row of U.
+c
+	jlu(ii+1) = ju0
+c-----------------------------------------------------------------------
+c     end main loop
+c-----------------------------------------------------------------------
+ 500  continue
+c
+c     permute all column indices of LU ...
+c
+      do k = jlu(1),jlu(n+1)-1
+         jlu(k) = iperm(n+jlu(k))
+      enddo
+c
+c     ...and of A
+c
+      do k=ia(1), ia(n+1)-1
+         ja(k) = iperm(n+ja(k))
+      enddo
+c
+      ierr = 0
+      return
+c
+c     incomprehensible error. Matrix must be wrong.
+c
+ 995  ierr = -1
+      return
+c
+c     insufficient storage in L.
+c
+ 996  ierr = -2
+      return
+c
+c     insufficient storage in U.
+c
+ 997  ierr = -3
+      return
+c
+c     illegal lfil entered.
+c
+ 998  ierr = -4
+      return
+c
+c     zero row encountered
+c
+ 999  ierr = -5
+      return
+c----------------end-of-ilutp-------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine ilud(n,a,ja,ia,alph,tol,alu,jlu,ju,iwk,w,jw,ierr)
+c-----------------------------------------------------------------------
+      implicit none 
+      integer n
+      real*8 a(*),alu(*),w(2*n),tol, alph 
+      integer ja(*),ia(n+1),jlu(*),ju(n),jw(2*n),iwk,ierr
+c----------------------------------------------------------------------*
+c                     *** ILUD preconditioner ***                      *
+c    incomplete LU factorization with standard droppoing strategy      *
+c----------------------------------------------------------------------*
+c Author: Yousef Saad * Aug. 1995 --                                   * 
+c----------------------------------------------------------------------*
+c This routine computes the ILU factorization with standard threshold  *
+c dropping: at i-th step of elimination, an element a(i,j) in row i is *
+c dropped  if it satisfies the criterion:                              *
+c                                                                      *
+c  abs(a(i,j)) < tol * [average magnitude of elements in row i of A]   *
+c                                                                      *
+c There is no control on memory size required for the factors as is    *
+c done in ILUT. This routines computes also various diagonal compensa- * 
+c tion ILU's such MILU. These are defined through the parameter alph   *
+c----------------------------------------------------------------------* 
+c on entry:
+c========== 
+c n       = integer. The row dimension of the matrix A. The matrix 
+c
+c a,ja,ia = matrix stored in Compressed Sparse Row format              
+c
+c alph    = diagonal compensation parameter -- the term: 
+c
+c           alph*(sum of all dropped out elements in a given row) 
+c
+c           is added to the diagonal element of U of the factorization 
+c           Thus: alph = 0 ---> ~ ILU with threshold,
+c                 alph = 1 ---> ~ MILU with threshold. 
+c 
+c tol     = Threshold parameter for dropping small terms in the
+c           factorization. During the elimination, a term a(i,j) is 
+c           dropped whenever abs(a(i,j)) .lt. tol * [weighted norm of
+c           row i]. Here weighted norm = 1-norm / number of nnz 
+c           elements in the row. 
+c  
+c iwk     = The length of arrays alu and jlu -- this routine will stop
+c           if storage for the factors L and U is not sufficient 
+c
+c On return:
+c=========== 
+c
+c alu,jlu = matrix stored in Modified Sparse Row (MSR) format containing
+c           the L and U factors together. The diagonal (stored in
+c           alu(1:n) ) is inverted. Each i-th row of the alu,jlu matrix
+c           contains the i-th row of L (excluding the diagonal entry=1)
+c           followed by the i-th row of U.
+c
+c ju      = integer array of length n containing the pointers to
+c           the beginning of each row of U in the matrix alu,jlu.
+c
+c ierr    = integer. Error message with the following meaning.
+c           ierr  = 0    --> successful return.
+c           ierr .gt. 0  --> zero pivot encountered at step number ierr.
+c           ierr  = -1   --> Error. input matrix may be wrong.
+c                            (The elimination process has generated a
+c                            row in L or U whose length is .gt.  n.)
+c           ierr  = -2   --> Insufficient storage for the LU factors --
+c                            arrays alu/ jalu are  overflowed. 
+c           ierr  = -3   --> Zero row encountered.
+c
+c Work Arrays:
+c=============
+c jw      = integer work array of length 2*n.
+c w       = real work array of length n 
+c  
+c----------------------------------------------------------------------
+c
+c w, ju (1:n) store the working array [1:ii-1 = L-part, ii:n = u] 
+c jw(n+1:2n)  stores the nonzero indicator. 
+c 
+c Notes:
+c ------
+c All diagonal elements of the input matrix must be  nonzero.
+c
+c----------------------------------------------------------------------- 
+c     locals
+      integer ju0,k,j1,j2,j,ii,i,lenl,lenu,jj,jrow,jpos,len 
+      real*8 tnorm, t, abs, s, fact, dropsum  
+c-----------------------------------------------------------------------
+c     initialize ju0 (points to next element to be added to alu,jlu)
+c     and pointer array.
+c-----------------------------------------------------------------------
+      ju0 = n+2
+      jlu(1) = ju0
+c
+c     initialize nonzero indicator array. 
+c
+      do 1 j=1,n
+         jw(n+j)  = 0
+ 1    continue
+c-----------------------------------------------------------------------
+c     beginning of main loop.
+c-----------------------------------------------------------------------
+      do 500 ii = 1, n
+         j1 = ia(ii)
+         j2 = ia(ii+1) - 1
+         dropsum = 0.0d0 
+         tnorm = 0.0d0
+         do 501 k=j1,j2
+            tnorm = tnorm + abs(a(k)) 
+ 501     continue
+         if (tnorm .eq. 0.0) goto 997
+         tnorm = tnorm / real(j2-j1+1) 
+c     
+c     unpack L-part and U-part of row of A in arrays w 
+c     
+         lenu = 1
+         lenl = 0
+         jw(ii) = ii
+         w(ii) = 0.0
+         jw(n+ii) = ii
+c
+         do 170  j = j1, j2
+            k = ja(j)
+            t = a(j)
+            if (k .lt. ii) then
+               lenl = lenl+1
+               jw(lenl) = k
+               w(lenl) = t
+               jw(n+k) = lenl
+            else if (k .eq. ii) then
+               w(ii) = t
+            else
+               lenu = lenu+1
+               jpos = ii+lenu-1 
+               jw(jpos) = k
+               w(jpos) = t
+               jw(n+k) = jpos
+            endif
+ 170     continue
+         jj = 0
+         len = 0 
+c     
+c     eliminate previous rows
+c     
+ 150     jj = jj+1
+         if (jj .gt. lenl) goto 160
+c-----------------------------------------------------------------------
+c     in order to do the elimination in the correct order we must select
+c     the smallest column index among jw(k), k=jj+1, ..., lenl.
+c-----------------------------------------------------------------------
+         jrow = jw(jj)
+         k = jj
+c     
+c     determine smallest column index
+c     
+         do 151 j=jj+1,lenl
+            if (jw(j) .lt. jrow) then
+               jrow = jw(j)
+               k = j
+            endif
+ 151     continue
+c
+         if (k .ne. jj) then
+c     exchange in jw
+            j = jw(jj)
+            jw(jj) = jw(k)
+            jw(k) = j
+c     exchange in jr
+            jw(n+jrow) = jj
+            jw(n+j) = k
+c     exchange in w
+            s = w(jj)
+            w(jj) = w(k)
+            w(k) = s
+         endif
+c
+c     zero out element in row by setting resetting jw(n+jrow) to zero.
+c     
+         jw(n+jrow) = 0
+c
+c     drop term if small
+c     
+c         if (abs(w(jj)) .le. tol*tnorm) then
+c            dropsum = dropsum + w(jj) 
+c            goto 150
+c         endif
+c     
+c     get the multiplier for row to be eliminated (jrow).
+c     
+         fact = w(jj)*alu(jrow)
+c
+c     drop term if small
+c     
+         if (abs(fact) .le. tol) then
+            dropsum = dropsum + w(jj) 
+            goto 150
+         endif
+c     
+c     combine current row and row jrow
+c
+         do 203 k = ju(jrow), jlu(jrow+1)-1
+            s = fact*alu(k)
+            j = jlu(k)
+            jpos = jw(n+j)
+            if (j .ge. ii) then
+c     
+c     dealing with upper part.
+c     
+               if (jpos .eq. 0) then
+c
+c     this is a fill-in element
+c     
+                  lenu = lenu+1
+                  if (lenu .gt. n) goto 995
+                  i = ii+lenu-1
+                  jw(i) = j
+                  jw(n+j) = i
+                  w(i) = - s
+               else
+c
+c     this is not a fill-in element 
+c
+                  w(jpos) = w(jpos) - s
+               endif
+            else
+c     
+c     dealing with lower part.
+c     
+               if (jpos .eq. 0) then
+c
+c     this is a fill-in element
+c
+                  lenl = lenl+1
+                  if (lenl .gt. n) goto 995
+                  jw(lenl) = j
+                  jw(n+j) = lenl
+                  w(lenl) = - s
+               else
+c
+c     this is not a fill-in element 
+c
+                  w(jpos) = w(jpos) - s
+               endif
+            endif
+ 203     continue
+         len = len+1 
+         w(len) = fact
+         jw(len)  = jrow
+         goto 150
+ 160     continue
+c     
+c     reset double-pointer to zero (For U-part only)
+c     
+         do 308 k=1, lenu
+            jw(n+jw(ii+k-1)) = 0
+ 308     continue
+c
+c     update l-matrix
+c
+         do 204 k=1, len
+            if (ju0 .gt. iwk) goto 996
+            alu(ju0) =  w(k) 
+            jlu(ju0) =  jw(k)
+            ju0 = ju0+1
+ 204     continue
+c     
+c     save pointer to beginning of row ii of U
+c     
+         ju(ii) = ju0
+c
+c     go through elements in U-part of w to determine elements to keep
+c
+         len = 0
+         do k=1, lenu-1
+c            if (abs(w(ii+k)) .gt. tnorm*tol) then 
+            if (abs(w(ii+k)) .gt. abs(w(ii))*tol) then 
+               len = len+1
+               w(ii+len) = w(ii+k) 
+               jw(ii+len) = jw(ii+k)
+            else
+               dropsum = dropsum + w(ii+k) 
+            endif
+         enddo
+c
+c     now update u-matrix
+c
+         if (ju0 + len-1 .gt. iwk) goto 996
+         do 302 k=ii+1,ii+len
+            jlu(ju0) = jw(k)
+            alu(ju0) = w(k)
+            ju0 = ju0+1
+ 302     continue
+c
+c     define diagonal element 
+c 
+         w(ii) = w(ii) + alph*dropsum 
+c
+c     store inverse of diagonal element of u
+c              
+         if (w(ii) .eq. 0.0) w(ii) = (0.0001 + tol)*tnorm
+c     
+         alu(ii) = 1.0d0/ w(ii) 
+c     
+c     update pointer to beginning of next row of U.
+c     
+         jlu(ii+1) = ju0
+c-----------------------------------------------------------------------
+c     end main loop
+c-----------------------------------------------------------------------
+ 500  continue
+      ierr = 0
+      return
+c
+c     incomprehensible error. Matrix must be wrong.
+c     
+ 995  ierr = -1
+      return
+c     
+c     insufficient storage in alu/ jlu arrays for  L / U factors 
+c     
+ 996  ierr = -2
+      return
+c     
+c     zero row encountered
+c     
+ 997  ierr = -3 
+      return
+c----------------end-of-ilud  ------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------
+      subroutine iludp(n,a,ja,ia,alph,droptol,permtol,mbloc,alu,
+     *     jlu,ju,iwk,w,jw,iperm,ierr)
+c-----------------------------------------------------------------------
+      implicit none
+      integer n,ja(*),ia(n+1),mbloc,jlu(*),ju(n),jw(2*n),iwk,
+     *     iperm(2*n),ierr
+      real*8 a(*), alu(*), w(2*n), alph, droptol, permtol 
+c----------------------------------------------------------------------*
+c                     *** ILUDP preconditioner ***                     *
+c    incomplete LU factorization with standard droppoing strategy      *
+c    and column pivoting                                               * 
+c----------------------------------------------------------------------*
+c author Yousef Saad -- Aug 1995.                                      *
+c----------------------------------------------------------------------*
+c on entry:
+c==========
+c n       = integer. The dimension of the matrix A.
+c
+c a,ja,ia = matrix stored in Compressed Sparse Row format.
+c           ON RETURN THE COLUMNS OF A ARE PERMUTED.
+c
+c alph    = diagonal compensation parameter -- the term: 
+c
+c           alph*(sum of all dropped out elements in a given row) 
+c
+c           is added to the diagonal element of U of the factorization 
+c           Thus: alph = 0 ---> ~ ILU with threshold,
+c                 alph = 1 ---> ~ MILU with threshold. 
+c 
+c droptol = tolerance used for dropping elements in L and U.
+c           elements are dropped if they are .lt. norm(row) x droptol
+c           row = row being eliminated
+c
+c permtol = tolerance ratio used for determning whether to permute
+c           two columns.  Two columns are permuted only when 
+c           abs(a(i,j))*permtol .gt. abs(a(i,i))
+c           [0 --> never permute; good values 0.1 to 0.01]
+c
+c mbloc   = if desired, permuting can be done only within the diagonal
+c           blocks of size mbloc. Useful for PDE problems with several
+c           degrees of freedom.. If feature not wanted take mbloc=n.
+c
+c iwk     = integer. The declared lengths of arrays alu and jlu
+c           if iwk is not large enough the code will stop prematurely
+c           with ierr = -2 or ierr = -3 (see below).
+c
+c On return:
+c===========
+c
+c alu,jlu = matrix stored in Modified Sparse Row (MSR) format containing
+c           the L and U factors together. The diagonal (stored in
+c           alu(1:n) ) is inverted. Each i-th row of the alu,jlu matrix
+c           contains the i-th row of L (excluding the diagonal entry=1)
+c           followed by the i-th row of U.
+c
+c ju      = integer array of length n containing the pointers to
+c           the beginning of each row of U in the matrix alu,jlu.
+c iperm   = contains the permutation arrays ..
+c           iperm(1:n) = old numbers of unknowns
+c           iperm(n+1:2*n) = reverse permutation = new unknowns.
+c
+c ierr    = integer. Error message with the following meaning.
+c           ierr  = 0    --> successful return.
+c           ierr .gt. 0  --> zero pivot encountered at step number ierr.
+c           ierr  = -1   --> Error. input matrix may be wrong.
+c                            (The elimination process has generated a
+c                            row in L or U whose length is .gt.  n.)
+c           ierr  = -2   --> The L/U matrix overflows the arrays alu,jlu
+c           ierr  = -3   --> zero row encountered.
+c
+c work arrays:
+c=============
+c jw      = integer work array of length 2*n.
+c w       = real work array of length 2*n 
+c
+c Notes:
+c ------
+c IMPORTANT: TO AVOID PERMUTING THE SOLUTION VECTORS ARRAYS FOR EACH 
+c LU-SOLVE, THE MATRIX A IS PERMUTED ON RETURN. [all column indices are
+c changed]. SIMILARLY FOR THE U MATRIX. 
+c To permute the matrix back to its original state use the loop:
+c
+c      do k=ia(1), ia(n+1)-1
+c         ja(k) = perm(ja(k)) 
+c      enddo
+c 
+c-----------------------------------------------------------------------
+c     local variables
+c
+      integer k,i,j,jrow,ju0,ii,j1,j2,jpos,len,imax,lenu,lenl,jj,icut
+      real*8 s,tmp,tnorm,xmax,xmax0,fact,abs,t,dropsum 
+c----------------------------------------------------------------------- 
+c     initialize ju0 (points to next element to be added to alu,jlu)
+c     and pointer array.
+c-----------------------------------------------------------------------
+      ju0 = n+2
+      jlu(1) = ju0
+c
+c  integer double pointer array.
+c
+      do 1 j=1,n
+         jw(n+j)  = 0
+         iperm(j) = j
+         iperm(n+j) = j
+ 1    continue
+c-----------------------------------------------------------------------
+c     beginning of main loop.
+c-----------------------------------------------------------------------
+      do 500 ii = 1, n
+         j1 = ia(ii)
+         j2 = ia(ii+1) - 1
+         dropsum = 0.0d0 
+         tnorm = 0.0d0
+         do 501 k=j1,j2
+            tnorm = tnorm+abs(a(k))
+ 501     continue
+         if (tnorm .eq. 0.0) goto 997
+         tnorm = tnorm/(j2-j1+1)
+c
+c     unpack L-part and U-part of row of A in arrays  w  --
+c
+         lenu = 1
+         lenl = 0
+         jw(ii) = ii
+         w(ii) = 0.0
+         jw(n+ii) = ii
+c
+         do 170  j = j1, j2
+            k = iperm(n+ja(j))
+            t = a(j)
+            if (k .lt. ii) then
+               lenl = lenl+1
+               jw(lenl) = k
+               w(lenl) = t
+               jw(n+k) = lenl
+            else if (k .eq. ii) then
+               w(ii) = t
+            else
+               lenu = lenu+1
+               jpos = ii+lenu-1 
+               jw(jpos) = k
+               w(jpos) = t
+               jw(n+k) = jpos
+            endif
+ 170     continue
+         jj = 0
+         len = 0 
+c
+c     eliminate previous rows
+c
+ 150     jj = jj+1
+         if (jj .gt. lenl) goto 160
+c-----------------------------------------------------------------------
+c     in order to do the elimination in the correct order we must select
+c     the smallest column index among jw(k), k=jj+1, ..., lenl.
+c-----------------------------------------------------------------------
+         jrow = jw(jj)
+         k = jj
+c
+c     determine smallest column index
+c
+         do 151 j=jj+1,lenl
+            if (jw(j) .lt. jrow) then
+               jrow = jw(j)
+               k = j
+            endif
+ 151     continue
+c
+         if (k .ne. jj) then
+c     exchange in jw
+            j = jw(jj)
+            jw(jj) = jw(k)
+            jw(k) = j
+c     exchange in jr
+            jw(n+jrow) = jj
+            jw(n+j) = k
+c     exchange in w
+            s = w(jj)
+            w(jj) = w(k)
+            w(k) = s
+         endif
+c
+c     zero out element in row by resetting jw(n+jrow) to zero.
+c     
+         jw(n+jrow) = 0
+c
+c     drop term if small
+c     
+         if (abs(w(jj)) .le. droptol*tnorm) then
+            dropsum = dropsum + w(jj) 
+            goto 150
+         endif      
+c
+c     get the multiplier for row to be eliminated: jrow
+c
+         fact = w(jj)*alu(jrow)
+c
+c     combine current row and row jrow
+c
+         do 203 k = ju(jrow), jlu(jrow+1)-1
+            s = fact*alu(k)
+c     new column number
+            j = iperm(n+jlu(k))
+            jpos = jw(n+j)
+c
+c     if fill-in element is small then disregard:
+c     
+            if (j .ge. ii) then
+c
+c     dealing with upper part.
+c
+               if (jpos .eq. 0) then
+c     this is a fill-in element
+                  lenu = lenu+1
+                  i = ii+lenu-1 
+                  if (lenu .gt. n) goto 995
+                  jw(i) = j
+                  jw(n+j) = i 
+                  w(i) = - s
+               else
+c     no fill-in element --
+                  w(jpos) = w(jpos) - s
+               endif
+            else
+c
+c     dealing with lower part.
+c
+               if (jpos .eq. 0) then
+c     this is a fill-in element
+                 lenl = lenl+1
+                 if (lenl .gt. n) goto 995
+                 jw(lenl) = j
+                 jw(n+j) = lenl
+                 w(lenl) = - s
+              else
+c     no fill-in element --
+                 w(jpos) = w(jpos) - s
+              endif
+           endif
+ 203	continue
+        len = len+1 
+        w(len) = fact
+        jw(len)  = jrow
+	goto 150
+ 160    continue
+c
+c     reset double-pointer to zero (U-part)
+c     
+        do 308 k=1, lenu
+           jw(n+jw(ii+k-1)) = 0
+ 308	continue
+c
+c     update L-matrix
+c
+        do 204 k=1, len
+           if (ju0 .gt. iwk) goto 996
+           alu(ju0) =  w(k)
+           jlu(ju0) = iperm(jw(k))
+           ju0 = ju0+1
+ 204    continue
+c
+c     save pointer to beginning of row ii of U
+c
+        ju(ii) = ju0
+c
+c     update u-matrix -- first apply dropping strategy 
+c
+         len = 0
+         do k=1, lenu-1
+            if (abs(w(ii+k)) .gt. tnorm*droptol) then 
+               len = len+1
+               w(ii+len) = w(ii+k) 
+               jw(ii+len) = jw(ii+k) 
+            else
+               dropsum = dropsum + w(ii+k) 
+            endif
+         enddo
+c
+        imax = ii
+        xmax = abs(w(imax))
+        xmax0 = xmax
+        icut = ii - 1 + mbloc - mod(ii-1,mbloc)
+c
+c     determine next pivot -- 
+c 
+        do k=ii+1,ii+len 
+           t = abs(w(k))
+           if (t .gt. xmax .and. t*permtol .gt. xmax0 .and.
+     *          jw(k) .le. icut) then
+              imax = k
+              xmax = t
+           endif
+        enddo
+c
+c     exchange w's
+c
+        tmp = w(ii)
+        w(ii) = w(imax)
+        w(imax) = tmp
+c
+c     update iperm and reverse iperm
+c
+        j = jw(imax)
+        i = iperm(ii)
+        iperm(ii) = iperm(j)
+        iperm(j) = i
+c     reverse iperm
+        iperm(n+iperm(ii)) = ii
+        iperm(n+iperm(j)) = j
+c----------------------------------------------------------------------- 
+        if (len + ju0-1 .gt. iwk) goto 996
+c
+c     copy U-part in original coordinates
+c     
+        do 302 k=ii+1,ii+len
+           jlu(ju0) = iperm(jw(k))
+           alu(ju0) = w(k)
+           ju0 = ju0+1
+ 302	continue
+c
+c     define diagonal element 
+c 
+         w(ii) = w(ii) + alph*dropsum 
+c
+c     store inverse of diagonal element of u
+c
+        if (w(ii) .eq. 0.0) w(ii) = (1.0D-4 + droptol)*tnorm
+c
+        alu(ii) = 1.0d0/ w(ii) 
+c
+c     update pointer to beginning of next row of U.
+c
+	jlu(ii+1) = ju0
+c-----------------------------------------------------------------------
+c     end main loop
+c-----------------------------------------------------------------------
+ 500  continue
+c
+c     permute all column indices of LU ...
+c
+      do k = jlu(1),jlu(n+1)-1
+         jlu(k) = iperm(n+jlu(k))
+      enddo
+c
+c     ...and of A
+c
+      do k=ia(1), ia(n+1)-1
+         ja(k) = iperm(n+ja(k))
+      enddo
+c
+      ierr = 0
+      return
+c
+c     incomprehensible error. Matrix must be wrong.
+c
+ 995  ierr = -1
+      return
+c
+c     insufficient storage in arrays alu, jlu to store factors
+c
+ 996  ierr = -2
+      return
+c
+c     zero row encountered
+c
+ 997  ierr = -3 
+      return
+c----------------end-of-iludp---------------------------!----------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine iluk(n,a,ja,ia,lfil,alu,jlu,ju,levs,iwk,w,jw,ierr)
+      implicit none 
+      integer n
+      real*8 a(*),alu(*),w(n)
+      integer ja(*),ia(n+1),jlu(*),ju(n),levs(*),jw(3*n),lfil,iwk,ierr
+c----------------------------------------------------------------------* 
+c     SPARSKIT ROUTINE ILUK -- ILU WITH LEVEL OF FILL-IN OF K (ILU(k)) *
+c----------------------------------------------------------------------*
+c
+c on entry:
+c========== 
+c n       = integer. The row dimension of the matrix A. The matrix 
+c
+c a,ja,ia = matrix stored in Compressed Sparse Row format.              
+c
+c lfil    = integer. The fill-in parameter. Each element whose
+c           leve-of-fill exceeds lfil during the ILU process is dropped.
+c           lfil must be .ge. 0 
+c
+c tol     = real*8. Sets the threshold for dropping small terms in the
+c           factorization. See below for details on dropping strategy.
+c  
+c iwk     = integer. The minimum length of arrays alu, jlu, and levs.
+c
+c On return:
+c===========
+c
+c alu,jlu = matrix stored in Modified Sparse Row (MSR) format containing
+c           the L and U factors together. The diagonal (stored in
+c           alu(1:n) ) is inverted. Each i-th row of the alu,jlu matrix
+c           contains the i-th row of L (excluding the diagonal entry=1)
+c           followed by the i-th row of U.
+c
+c ju      = integer array of length n containing the pointers to
+c           the beginning of each row of U in the matrix alu,jlu.
+c
+c levs    = integer (work) array of size iwk -- which contains the 
+c           levels of each element in alu, jlu.
+c
+c ierr    = integer. Error message with the following meaning.
+c           ierr  = 0    --> successful return.
+c           ierr .gt. 0  --> zero pivot encountered at step number ierr.
+c           ierr  = -1   --> Error. input matrix may be wrong.
+c                            (The elimination process has generated a
+c                            row in L or U whose length is .gt.  n.)
+c           ierr  = -2   --> The matrix L overflows the array al.
+c           ierr  = -3   --> The matrix U overflows the array alu.
+c           ierr  = -4   --> Illegal value for lfil.
+c           ierr  = -5   --> zero row encountered in A or U.
+c
+c work arrays:
+c=============
+c jw      = integer work array of length 3*n.
+c w       = real work array of length n 
+c
+c Notes/known bugs: This is not implemented efficiently storage-wise.
+c       For example: Only the part of the array levs(*) associated with
+c       the U-matrix is needed in the routine.. So some storage can 
+c       be saved if needed. The levels of fills in the LU matrix are
+c       output for information only -- they are not needed by LU-solve. 
+c        
+c----------------------------------------------------------------------
+c w, ju (1:n) store the working array [1:ii-1 = L-part, ii:n = u] 
+c jw(n+1:2n)  stores the nonzero indicator. 
+c 
+c Notes:
+c ------
+c All the diagonal elements of the input matrix must be  nonzero.
+c
+c----------------------------------------------------------------------* 
+c     locals
+      integer ju0,k,j1,j2,j,ii,i,lenl,lenu,jj,jrow,jpos,n2,
+     *     jlev, min 
+      real*8 t, s, fact 
+      if (lfil .lt. 0) goto 998
+c-----------------------------------------------------------------------
+c     initialize ju0 (points to next element to be added to alu,jlu)
+c     and pointer array.
+c-----------------------------------------------------------------------
+      n2 = n+n 
+      ju0 = n+2
+      jlu(1) = ju0
+c
+c     initialize nonzero indicator array + levs array -- 
+c
+      do 1 j=1,2*n 
+         jw(j)  = 0
+ 1    continue
+c-----------------------------------------------------------------------
+c     beginning of main loop.
+c-----------------------------------------------------------------------
+      do 500 ii = 1, n
+         j1 = ia(ii)
+         j2 = ia(ii+1) - 1
+c     
+c     unpack L-part and U-part of row of A in arrays w 
+c     
+         lenu = 1
+         lenl = 0
+         jw(ii) = ii
+         w(ii) = 0.0
+         jw(n+ii) = ii
+c
+         do 170  j = j1, j2
+            k = ja(j)
+            t = a(j)
+            if (t .eq. 0.0) goto 170 
+            if (k .lt. ii) then
+               lenl = lenl+1
+               jw(lenl) = k
+               w(lenl) = t
+               jw(n2+lenl) = 0 
+               jw(n+k) = lenl
+            else if (k .eq. ii) then
+               w(ii) = t
+               jw(n2+ii) = 0 
+            else
+               lenu = lenu+1
+               jpos = ii+lenu-1 
+               jw(jpos) = k
+               w(jpos) = t
+               jw(n2+jpos) = 0 
+               jw(n+k) = jpos
+            endif
+ 170     continue
+c
+         jj = 0
+c
+c     eliminate previous rows
+c     
+ 150     jj = jj+1
+         if (jj .gt. lenl) goto 160
+c-----------------------------------------------------------------------
+c     in order to do the elimination in the correct order we must select
+c     the smallest column index among jw(k), k=jj+1, ..., lenl.
+c-----------------------------------------------------------------------
+         jrow = jw(jj)
+         k = jj
+c     
+c     determine smallest column index
+c     
+         do 151 j=jj+1,lenl
+            if (jw(j) .lt. jrow) then
+               jrow = jw(j)
+               k = j
+            endif
+ 151     continue
+c
+         if (k .ne. jj) then
+c     exchange in jw
+            j = jw(jj)
+            jw(jj) = jw(k)
+            jw(k) = j
+c     exchange in jw(n+  (pointers/ nonzero indicator).
+            jw(n+jrow) = jj
+            jw(n+j) = k
+c     exchange in jw(n2+  (levels) 
+            j = jw(n2+jj) 
+            jw(n2+jj)  = jw(n2+k) 
+            jw(n2+k) = j
+c     exchange in w
+            s = w(jj)
+            w(jj) = w(k)
+            w(k) = s
+         endif
+c
+c     zero out element in row by resetting jw(n+jrow) to zero.
+c     
+         jw(n+jrow) = 0
+c     
+c     get the multiplier for row to be eliminated (jrow) + its level
+c     
+         fact = w(jj)*alu(jrow)
+         jlev = jw(n2+jj) 
+         if (jlev .gt. lfil) goto 150
+c
+c     combine current row and row jrow
+c
+         do 203 k = ju(jrow), jlu(jrow+1)-1
+            s = fact*alu(k)
+            j = jlu(k)
+            jpos = jw(n+j)
+            if (j .ge. ii) then
+c     
+c     dealing with upper part.
+c     
+               if (jpos .eq. 0) then
+c
+c     this is a fill-in element
+c     
+                  lenu = lenu+1
+                  if (lenu .gt. n) goto 995
+                  i = ii+lenu-1
+                  jw(i) = j
+                  jw(n+j) = i
+                  w(i) = - s
+                  jw(n2+i) = jlev+levs(k)+1 
+               else
+c
+c     this is not a fill-in element 
+c
+                  w(jpos) = w(jpos) - s
+                  jw(n2+jpos) = min(jw(n2+jpos),jlev+levs(k)+1)
+               endif
+            else
+c     
+c     dealing with lower part.
+c     
+               if (jpos .eq. 0) then
+c
+c     this is a fill-in element
+c
+                  lenl = lenl+1
+                  if (lenl .gt. n) goto 995
+                  jw(lenl) = j
+                  jw(n+j) = lenl
+                  w(lenl) = - s
+                  jw(n2+lenl) = jlev+levs(k)+1 
+               else
+c
+c     this is not a fill-in element 
+c
+                  w(jpos) = w(jpos) - s
+                  jw(n2+jpos) = min(jw(n2+jpos),jlev+levs(k)+1)
+               endif
+            endif
+ 203     continue
+         w(jj) = fact
+         jw(jj)  = jrow
+         goto 150 
+ 160     continue 
+c     
+c     reset double-pointer to zero (U-part) 
+c     
+         do 308 k=1, lenu
+            jw(n+jw(ii+k-1)) = 0
+ 308     continue
+c
+c     update l-matrix
+c         
+         do 204 k=1, lenl 
+            if (ju0 .gt. iwk) goto 996
+            if (jw(n2+k) .le. lfil) then
+               alu(ju0) =  w(k)
+               jlu(ju0) =  jw(k)
+               ju0 = ju0+1
+            endif
+ 204     continue
+c     
+c     save pointer to beginning of row ii of U
+c     
+         ju(ii) = ju0
+c
+c     update u-matrix
+c
+         do 302 k=ii+1,ii+lenu-1 
+            if (jw(n2+k) .le. lfil) then
+               jlu(ju0) = jw(k)
+               alu(ju0) = w(k)
+               levs(ju0) = jw(n2+k) 
+               ju0 = ju0+1
+            endif
+ 302     continue
+
+         if (w(ii) .eq. 0.0) goto 999 
+c     
+         alu(ii) = 1.0d0/ w(ii) 
+c     
+c     update pointer to beginning of next row of U.
+c     
+         jlu(ii+1) = ju0
+c-----------------------------------------------------------------------
+c     end main loop
+c-----------------------------------------------------------------------
+ 500  continue
+      ierr = 0
+      return
+c
+c     incomprehensible error. Matrix must be wrong.
+c     
+ 995  ierr = -1
+      return
+c     
+c     insufficient storage in L.
+c     
+ 996  ierr = -2
+      return
+c     
+c     insufficient storage in U.
+c     
+ 997  ierr = -3
+      return
+c     
+c     illegal lfil entered.
+c     
+ 998  ierr = -4
+      return
+c     
+c     zero row encountered in A or U. 
+c     
+ 999  ierr = -5
+      return
+c----------------end-of-iluk--------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------
+	subroutine ilu0(n, a, ja, ia, alu, jlu, ju, iw, ierr)
+	implicit real*8 (a-h,o-z)
+	real*8 a(*), alu(*)
+        integer ja(*), ia(*), ju(*), jlu(*), iw(*)
+c------------------ right preconditioner ------------------------------*
+c                    ***   ilu(0) preconditioner.   ***                *
+c----------------------------------------------------------------------*
+c Note that this has been coded in such a way that it can be used
+c with pgmres. Normally, since the data structure of the L+U matrix is
+c the same as that the A matrix, savings can be made. In fact with
+c some definitions (not correct for general sparse matrices) all we
+c need in addition to a, ja, ia is an additional diagonal.
+c ILU0 is not recommended for serious problems. It is only provided
+c here for comparison purposes.
+c-----------------------------------------------------------------------
+c
+c on entry:
+c---------
+c n       = dimension of matrix
+c a, ja,
+c ia      = original matrix in compressed sparse row storage.
+c
+c on return:
+c-----------
+c alu,jlu = matrix stored in Modified Sparse Row (MSR) format containing
+c           the L and U factors together. The diagonal (stored in
+c           alu(1:n) ) is inverted. Each i-th row of the alu,jlu matrix
+c           contains the i-th row of L (excluding the diagonal entry=1)
+c           followed by the i-th row of U.
+c
+c ju	  = pointer to the diagonal elements in alu, jlu.
+c
+c ierr	  = integer indicating error code on return
+c	     ierr = 0 --> normal return
+c	     ierr = k --> code encountered a zero pivot at step k.
+c work arrays:
+c-------------
+c iw	    = integer work array of length n.
+c------------
+c IMPORTANT
+c-----------
+c it is assumed that the the elements in the input matrix are stored
+c    in such a way that in each row the lower part comes first and
+c    then the upper part. To get the correct ILU factorization, it is
+c    also necessary to have the elements of L sorted by increasing
+c    column number. It may therefore be necessary to sort the
+c    elements of a, ja, ia prior to calling ilu0. This can be
+c    achieved by transposing the matrix twice using csrcsc.
+c
+c-----------------------------------------------------------------------
+        ju0 = n+2
+        jlu(1) = ju0
+c
+c initialize work vector to zero's
+c
+	do 31 i=1, n
+           iw(i) = 0
+ 31     continue
+c
+c main loop
+c
+	do 500 ii = 1, n
+           js = ju0
+c
+c generating row number ii of L and U.
+c
+           do 100 j=ia(ii),ia(ii+1)-1
+c
+c     copy row ii of a, ja, ia into row ii of alu, jlu (L/U) matrix.
+c
+              jcol = ja(j)
+              if (jcol .eq. ii) then
+                 alu(ii) = a(j)
+                 iw(jcol) = ii
+                 ju(ii)  = ju0
+              else
+                 alu(ju0) = a(j)
+                 jlu(ju0) = ja(j)
+                 iw(jcol) = ju0
+                 ju0 = ju0+1
+              endif
+ 100       continue
+           jlu(ii+1) = ju0
+           jf = ju0-1
+           jm = ju(ii)-1
+c
+c     exit if diagonal element is reached.
+c
+           do 150 j=js, jm
+              jrow = jlu(j)
+              tl = alu(j)*alu(jrow)
+              alu(j) = tl
+c
+c     perform  linear combination
+c
+              do 140 jj = ju(jrow), jlu(jrow+1)-1
+                 jw = iw(jlu(jj))
+                 if (jw .ne. 0) alu(jw) = alu(jw) - tl*alu(jj)
+ 140          continue
+ 150       continue
+c
+c     invert  and store diagonal element.
+c
+           if (alu(ii) .eq. 0.0d0) goto 600
+           alu(ii) = 1.0d0/alu(ii)
+c
+c     reset pointer iw to zero
+c
+           iw(ii) = 0
+           do 201 i = js, jf
+ 201          iw(jlu(i)) = 0
+ 500       continue
+           ierr = 0
+           return
+c
+c     zero pivot :
+c
+ 600       ierr = ii
+c
+           return
+c------- end-of-ilu0 ---------------------------------------------------
+c-----------------------------------------------------------------------
+           end
+c----------------------------------------------------------------------
+	subroutine milu0(n, a, ja, ia, alu, jlu, ju, iw, ierr)
+	implicit real*8 (a-h,o-z)
+	real*8 a(*), alu(*)
+	integer ja(*), ia(*), ju(*), jlu(*), iw(*)
+c----------------------------------------------------------------------*
+c                *** simple milu(0) preconditioner. ***                *
+c----------------------------------------------------------------------*
+c Note that this has been coded in such a way that it can be used
+c with pgmres. Normally, since the data structure of a, ja, ia is
+c the same as that of a, ja, ia, savings can be made. In fact with
+c some definitions (not correct for general sparse matrices) all we
+c need in addition to a, ja, ia is an additional diagonal.
+c Ilu0 is not recommended for serious problems. It is only provided
+c here for comparison purposes.
+c-----------------------------------------------------------------------
+c
+c on entry:
+c----------
+c n       = dimension of matrix
+c a, ja,
+c ia      = original matrix in compressed sparse row storage.
+c
+c on return:
+c----------
+c alu,jlu = matrix stored in Modified Sparse Row (MSR) format containing
+c           the L and U factors together. The diagonal (stored in
+c           alu(1:n) ) is inverted. Each i-th row of the alu,jlu matrix
+c           contains the i-th row of L (excluding the diagonal entry=1)
+c           followed by the i-th row of U.
+c
+c ju	  = pointer to the diagonal elements in alu, jlu.
+c
+c ierr	  = integer indicating error code on return
+c	     ierr = 0 --> normal return
+c	     ierr = k --> code encountered a zero pivot at step k.
+c work arrays:
+c-------------
+c iw	    = integer work array of length n.
+c------------
+c Note (IMPORTANT):
+c-----------
+C it is assumed that the the elements in the input matrix are ordered
+c    in such a way that in each row the lower part comes first and
+c    then the upper part. To get the correct ILU factorization, it is
+c    also necessary to have the elements of L ordered by increasing
+c    column number. It may therefore be necessary to sort the
+c    elements of a, ja, ia prior to calling milu0. This can be
+c    achieved by transposing the matrix twice using csrcsc.
+c-----------------------------------------------------------
+          ju0 = n+2
+          jlu(1) = ju0
+c initialize work vector to zero's
+	do 31 i=1, n
+ 31           iw(i) = 0
+c
+c-------------- MAIN LOOP ----------------------------------
+c
+	do 500 ii = 1, n
+           js = ju0
+c
+c generating row number ii or L and U.
+c
+           do 100 j=ia(ii),ia(ii+1)-1
+c
+c     copy row ii of a, ja, ia into row ii of alu, jlu (L/U) matrix.
+c     
+              jcol = ja(j)
+              if (jcol .eq. ii) then
+                 alu(ii) = a(j)
+                 iw(jcol) = ii
+                 ju(ii)  = ju0
+              else
+                 alu(ju0) = a(j)
+                 jlu(ju0) = ja(j)
+                 iw(jcol) = ju0
+                 ju0 = ju0+1
+              endif
+ 100       continue
+           jlu(ii+1) = ju0
+           jf = ju0-1
+           jm = ju(ii)-1
+c     s accumulates fill-in values
+           s = 0.0d0
+           do 150 j=js, jm
+              jrow = jlu(j)
+              tl = alu(j)*alu(jrow)
+              alu(j) = tl
+c-----------------------perform linear combination --------
+              do 140 jj = ju(jrow), jlu(jrow+1)-1
+                 jw = iw(jlu(jj))
+                 if (jw .ne. 0) then
+                       alu(jw) = alu(jw) - tl*alu(jj)
+                    else
+                       s = s + tl*alu(jj)
+                    endif
+ 140          continue
+ 150       continue
+c----------------------- invert and store diagonal element.
+           alu(ii) = alu(ii)-s
+           if (alu(ii) .eq. 0.0d0) goto 600
+           alu(ii) = 1.0d0/alu(ii)
+c----------------------- reset pointer iw to zero
+           iw(ii) = 0
+           do 201 i = js, jf
+ 201          iw(jlu(i)) = 0
+ 500       continue
+           ierr = 0
+           return
+c     zero pivot :
+ 600       ierr = ii
+           return
+c------- end-of-milu0 --------------------------------------------------
+c-----------------------------------------------------------------------
+           end
+c-----------------------------------------------------------------------
+       subroutine pgmres(n, im, rhs, sol, vv, eps, maxits, iout,
+     *                    aa, ja, ia, alu, jlu, ju, ierr)
+c-----------------------------------------------------------------------
+       implicit real*8 (a-h,o-z)
+       integer n, im, maxits, iout, ierr, ja(*), ia(n+1), jlu(*), ju(n)
+       real*8 vv(n,*), rhs(n), sol(n), aa(*), alu(*), eps
+c----------------------------------------------------------------------*
+c                                                                      *
+c                 *** ILUT - Preconditioned GMRES ***                  *
+c                                                                      *
+c----------------------------------------------------------------------*
+c This is a simple version of the ILUT preconditioned GMRES algorithm. *
+c The ILUT preconditioner uses a dual strategy for dropping elements   *
+c instead  of the usual level of-fill-in approach. See details in ILUT *
+c subroutine documentation. PGMRES uses the L and U matrices generated *
+c from the subroutine ILUT to precondition the GMRES algorithm.        *
+c The preconditioning is applied to the right. The stopping criterion  *
+c utilized is based simply on reducing the residual norm by epsilon.   *
+c This preconditioning is more reliable than ilu0 but requires more    *
+c storage. It seems to be much less prone to difficulties related to   *
+c strong nonsymmetries in the matrix. We recommend using a nonzero tol *
+c (tol=.005 or .001 usually give good results) in ILUT. Use a large    *
+c lfil whenever possible (e.g. lfil = 5 to 10). The higher lfil the    *
+c more reliable the code is. Efficiency may also be much improved.     *
+c Note that lfil=n and tol=0.0 in ILUT  will yield the same factors as *
+c Gaussian elimination without pivoting.                               *
+c                                                                      *
+c ILU(0) and MILU(0) are also provided for comparison purposes         *
+c USAGE: first call ILUT or ILU0 or MILU0 to set up preconditioner and *
+c then call pgmres.                                                    *
+c----------------------------------------------------------------------*
+c Coded by Y. Saad - This version dated May, 7, 1990.                  *
+c----------------------------------------------------------------------*
+c parameters                                                           *
+c-----------                                                           *
+c on entry:                                                            *
+c==========                                                            *
+c                                                                      *
+c n     == integer. The dimension of the matrix.                       *
+c im    == size of krylov subspace:  should not exceed 50 in this      *
+c          version (can be reset by changing parameter command for     *
+c          kmax below)                                                 *
+c rhs   == real vector of length n containing the right hand side.     *
+c          Destroyed on return.                                        *
+c sol   == real vector of length n containing an initial guess to the  *
+c          solution on input. approximate solution on output           *
+c eps   == tolerance for stopping criterion. process is stopped        *
+c          as soon as ( ||.|| is the euclidean norm):                  *
+c          || current residual||/||initial residual|| <= eps           *
+c maxits== maximum number of iterations allowed                        *
+c iout  == output unit number number for printing intermediate results *
+c          if (iout .le. 0) nothing is printed out.                    *
+c                                                                      *
+c aa, ja,                                                              *
+c ia    == the input matrix in compressed sparse row format:           *
+c          aa(1:nnz)  = nonzero elements of A stored row-wise in order *
+c          ja(1:nnz) = corresponding column indices.                   *
+c          ia(1:n+1) = pointer to beginning of each row in aa and ja.  *
+c          here nnz = number of nonzero elements in A = ia(n+1)-ia(1)  *
+c                                                                      *
+c alu,jlu== A matrix stored in Modified Sparse Row format containing   *
+c           the L and U factors, as computed by subroutine ilut.       *
+c                                                                      *
+c ju     == integer array of length n containing the pointers to       *
+c           the beginning of each row of U in alu, jlu as computed     *
+c           by subroutine ILUT.                                        *
+c                                                                      *
+c on return:                                                           *
+c==========                                                            *
+c sol   == contains an approximate solution (upon successful return).  *
+c ierr  == integer. Error message with the following meaning.          *
+c          ierr = 0 --> successful return.                             *
+c          ierr = 1 --> convergence not achieved in itmax iterations.  *
+c          ierr =-1 --> the initial guess seems to be the exact        *
+c                       solution (initial residual computed was zero)  *
+c                                                                      *
+c----------------------------------------------------------------------*
+c                                                                      *
+c work arrays:                                                         *
+c=============                                                         *
+c vv    == work array of length  n x (im+1) (used to store the Arnoli  *
+c          basis)                                                      *
+c----------------------------------------------------------------------*
+c subroutines called :                                                 *
+c amux   : SPARSKIT routine to do the matrix by vector multiplication  *
+c          delivers y=Ax, given x  -- see SPARSKIT/BLASSM/amux         *
+c lusol : combined forward and backward solves (Preconditioning ope.) *
+c BLAS1  routines.                                                     *
+c----------------------------------------------------------------------*
+       parameter (kmax=50)
+       real*8 hh(kmax+1,kmax), c(kmax), s(kmax), rs(kmax+1),t
+c-------------------------------------------------------------
+c arnoldi size should not exceed kmax=50 in this version..
+c to reset modify paramter kmax accordingly.
+c-------------------------------------------------------------
+       data epsmac/1.d-16/
+       n1 = n + 1
+       its = 0
+c-------------------------------------------------------------
+c outer loop starts here..
+c-------------- compute initial residual vector --------------
+       call amux (n, sol, vv, aa, ja, ia)
+       do 21 j=1,n
+          vv(j,1) = rhs(j) - vv(j,1)
+ 21    continue
+c-------------------------------------------------------------
+ 20    ro = dnrm2(n, vv, 1)
+       if (iout .gt. 0 .and. its .eq. 0)
+     *      write(iout, 199) its, ro
+       if (ro .eq. 0.0d0) goto 999
+       t = 1.0d0/ ro
+       do 210 j=1, n
+          vv(j,1) = vv(j,1)*t
+ 210   continue
+       if (its .eq. 0) eps1=eps*ro
+c     ** initialize 1-st term  of rhs of hessenberg system..
+       rs(1) = ro
+       i = 0
+ 4     i=i+1
+       its = its + 1
+       i1 = i + 1
+       call lusol (n, vv(1,i), rhs, alu, jlu, ju)
+       call amux (n, rhs, vv(1,i1), aa, ja, ia)
+c-----------------------------------------
+c     modified gram - schmidt...
+c-----------------------------------------
+       do 55 j=1, i
+          t = ddot(n, vv(1,j),1,vv(1,i1),1)
+          hh(j,i) = t
+          call daxpy(n, -t, vv(1,j), 1, vv(1,i1), 1)
+ 55    continue
+       t = dnrm2(n, vv(1,i1), 1)
+       hh(i1,i) = t
+       if ( t .eq. 0.0d0) goto 58
+       t = 1.0d0/t
+       do 57  k=1,n
+          vv(k,i1) = vv(k,i1)*t
+ 57    continue
+c
+c     done with modified gram schimd and arnoldi step..
+c     now  update factorization of hh
+c
+ 58    if (i .eq. 1) goto 121
+c--------perfrom previous transformations  on i-th column of h
+       do 66 k=2,i
+          k1 = k-1
+          t = hh(k1,i)
+          hh(k1,i) = c(k1)*t + s(k1)*hh(k,i)
+          hh(k,i) = -s(k1)*t + c(k1)*hh(k,i)
+ 66    continue
+ 121   gam = sqrt(hh(i,i)**2 + hh(i1,i)**2)
+c
+c     if gamma is zero then any small value will do...
+c     will affect only residual estimate
+c
+       if (gam .eq. 0.0d0) gam = epsmac
+c
+c     get  next plane rotation
+c
+       c(i) = hh(i,i)/gam
+       s(i) = hh(i1,i)/gam
+       rs(i1) = -s(i)*rs(i)
+       rs(i) =  c(i)*rs(i)
+c
+c     detrermine residual norm and test for convergence-
+c
+       hh(i,i) = c(i)*hh(i,i) + s(i)*hh(i1,i)
+       ro = abs(rs(i1))
+ 131   format(1h ,2e14.4)
+       if (iout .gt. 0)
+     *      write(iout, 199) its, ro
+       if (i .lt. im .and. (ro .gt. eps1))  goto 4
+c
+c     now compute solution. first solve upper triangular system.
+c
+       rs(i) = rs(i)/hh(i,i)
+       do 30 ii=2,i
+          k=i-ii+1
+          k1 = k+1
+          t=rs(k)
+          do 40 j=k1,i
+             t = t-hh(k,j)*rs(j)
+ 40       continue
+          rs(k) = t/hh(k,k)
+ 30    continue
+c
+c     form linear combination of v(*,i)'s to get solution
+c
+       t = rs(1)
+       do 15 k=1, n
+          rhs(k) = vv(k,1)*t
+ 15    continue
+       do 16 j=2, i
+          t = rs(j)
+          do 161 k=1, n
+             rhs(k) = rhs(k)+t*vv(k,j)
+ 161      continue
+ 16    continue
+c
+c     call preconditioner.
+c
+       call lusol (n, rhs, rhs, alu, jlu, ju)
+       do 17 k=1, n
+          sol(k) = sol(k) + rhs(k)
+ 17    continue
+c
+c     restart outer loop  when necessary
+c
+       if (ro .le. eps1) goto 990
+       if (its .ge. maxits) goto 991
+c
+c     else compute residual vector and continue..
+c
+       do 24 j=1,i
+          jj = i1-j+1
+          rs(jj-1) = -s(jj-1)*rs(jj)
+          rs(jj) = c(jj-1)*rs(jj)
+ 24    continue
+       do 25  j=1,i1
+          t = rs(j)
+          if (j .eq. 1)  t = t-1.0d0
+          call daxpy (n, t, vv(1,j), 1,  vv, 1)
+ 25    continue
+ 199   format('   its =', i4, ' res. norm =', d20.6)
+c     restart outer loop.
+       goto 20
+ 990   ierr = 0
+       return
+ 991   ierr = 1
+       return
+ 999   continue
+       ierr = -1
+       return
+c-----------------end of pgmres ---------------------------------------
+c-----------------------------------------------------------------------
+       end
+c-----------------------------------------------------------------------
+	subroutine lusol(n, y, x, alu, jlu, ju)
+        real*8 x(n), y(n), alu(*)
+	integer n, jlu(*), ju(*)
+c-----------------------------------------------------------------------
+c
+c This routine solves the system (LU) x = y, 
+c given an LU decomposition of a matrix stored in (alu, jlu, ju) 
+c modified sparse row format 
+c
+c-----------------------------------------------------------------------
+c on entry:
+c n   = dimension of system 
+c y   = the right-hand-side vector
+c alu, jlu, ju 
+c     = the LU matrix as provided from the ILU routines. 
+c
+c on return
+c x   = solution of LU x = y.     
+c-----------------------------------------------------------------------
+c 
+c Note: routine is in place: call lusol (n, x, x, alu, jlu, ju) 
+c       will solve the system with rhs x and overwrite the result on x . 
+c
+c-----------------------------------------------------------------------
+c local variables
+c
+        integer i,k
+c
+c forward solve
+c
+        do 40 i = 1, n
+           x(i) = y(i)
+           do 41 k=jlu(i),ju(i)-1
+              x(i) = x(i) - alu(k)* x(jlu(k))
+ 41        continue
+ 40     continue
+c
+c     backward solve.
+c
+	do 90 i = n, 1, -1
+	   do 91 k=ju(i),jlu(i+1)-1
+              x(i) = x(i) - alu(k)*x(jlu(k))
+ 91	   continue
+           x(i) = alu(i)*x(i)
+ 90     continue
+c
+  	return
+c----------------end of lusol ------------------------------------------
+c-----------------------------------------------------------------------
+	end
+c-----------------------------------------------------------------------
+	subroutine lutsol(n, y, x, alu, jlu, ju) 
+        real*8 x(n), y(n), alu(*)
+	integer n, jlu(*), ju(*)
+c-----------------------------------------------------------------------
+c
+c This routine solves the system  Transp(LU) x = y,
+c given an LU decomposition of a matrix stored in (alu, jlu, ju) 
+c modified sparse row format. Transp(M) is the transpose of M. 
+c----------------------------------------------------------------------- 
+c on entry:
+c n   = dimension of system 
+c y   = the right-hand-side vector
+c alu, jlu, ju 
+c     = the LU matrix as provided from the ILU routines. 
+c
+c on return
+c x   = solution of transp(LU) x = y.   
+c-----------------------------------------------------------------------
+c
+c Note: routine is in place: call lutsol (n, x, x, alu, jlu, ju) 
+c       will solve the system with rhs x and overwrite the result on x . 
+c 
+c-----------------------------------------------------------------------
+c local variables
+c
+        integer i,k
+c
+        do 10 i = 1, n
+           x(i) = y(i)
+ 10     continue
+c
+c forward solve (with U^T)
+c
+        do 20 i = 1, n
+           x(i) = x(i) * alu(i)
+           do 30 k=ju(i),jlu(i+1)-1
+              x(jlu(k)) = x(jlu(k)) - alu(k)* x(i)
+ 30        continue
+ 20     continue
+c     
+c     backward solve (with L^T)
+c     
+	do 40 i = n, 1, -1 
+	   do 50 k=jlu(i),ju(i)-1
+              x(jlu(k)) = x(jlu(k)) - alu(k)*x(i)
+ 50        continue
+ 40     continue
+c
+  	return
+c----------------end of lutsol -----------------------------------------
+c-----------------------------------------------------------------------
+	end
+c----------------------------------------------------------------------- 
+        subroutine qsplit(a,ind,n,ncut)
+        real*8 a(n)
+        integer ind(n), n, ncut
+c-----------------------------------------------------------------------
+c     does a quick-sort split of a real array.
+c     on input a(1:n). is a real array
+c     on output a(1:n) is permuted such that its elements satisfy:
+c
+c     abs(a(i)) .ge. abs(a(ncut)) for i .lt. ncut and
+c     abs(a(i)) .le. abs(a(ncut)) for i .gt. ncut
+c
+c     ind(1:n) is an integer array which permuted in the same way as a(*).
+c-----------------------------------------------------------------------
+        real*8 tmp, abskey
+        integer itmp, first, last
+c-----
+        first = 1
+        last = n
+        if (ncut .lt. first .or. ncut .gt. last) return
+c
+c     outer loop -- while mid .ne. ncut do
+c
+ 1      mid = first
+        abskey = abs(a(mid))
+        do 2 j=first+1, last
+           if (abs(a(j)) .gt. abskey) then
+              mid = mid+1
+c     interchange
+              tmp = a(mid)
+              itmp = ind(mid)
+              a(mid) = a(j)
+              ind(mid) = ind(j)
+              a(j)  = tmp
+              ind(j) = itmp
+           endif
+ 2      continue
+c
+c     interchange
+c
+        tmp = a(mid)
+        a(mid) = a(first)
+        a(first)  = tmp
+c
+        itmp = ind(mid)
+        ind(mid) = ind(first)
+        ind(first) = itmp
+c
+c     test for while loop
+c
+        if (mid .eq. ncut) return
+        if (mid .gt. ncut) then
+           last = mid-1
+        else
+           first = mid+1
+        endif
+        goto 1
+c----------------end-of-qsplit------------------------------------------
+c-----------------------------------------------------------------------
+        end
diff --git a/ITSOL/itaux.f b/ITSOL/itaux.f
new file mode 100644
index 0000000..cfb1820
--- /dev/null
+++ b/ITSOL/itaux.f
@@ -0,0 +1,217 @@
+      subroutine runrc(n,rhs,sol,ipar,fpar,wk,guess,a,ja,ia,
+     +     au,jau,ju,solver)
+      implicit none
+      integer n,ipar(16),ia(n+1),ja(*),ju(*),jau(*)
+      real*8 fpar(16),rhs(n),sol(n),guess(n),wk(*),a(*),au(*)
+      external solver
+c-----------------------------------------------------------------------
+c     the actual tester. It starts the iterative linear system solvers
+c     with a initial guess suppied by the user.
+c
+c     The structure {au, jau, ju} is assumed to have the output from
+c     the ILU* routines in ilut.f.
+c
+c-----------------------------------------------------------------------
+c     local variables
+c
+      integer i, iou, its
+      real*8 res, dnrm2
+c     real dtime, dt(2), time
+c     external dtime
+      external dnrm2
+      save its,res
+c
+c     ipar(2) can be 0, 1, 2, please don't use 3
+c
+      if (ipar(2).gt.2) then
+         print *, 'I can not do both left and right preconditioning.'
+         return
+      endif
+c
+c     normal execution
+c
+      its = 0
+      res = 0.0D0
+c
+      do i = 1, n
+         sol(i) = guess(i)
+      enddo
+c
+      iou = 6
+      ipar(1) = 0
+c     time = dtime(dt)
+ 10   call solver(n,rhs,sol,ipar,fpar,wk)
+c
+c     output the residuals
+c
+      if (ipar(7).ne.its) then
+         write (iou, *) its, real(res)
+         its = ipar(7)
+      endif
+      res = fpar(5)
+c
+      if (ipar(1).eq.1) then
+         call amux(n, wk(ipar(8)), wk(ipar(9)), a, ja, ia)
+         goto 10
+      else if (ipar(1).eq.2) then
+         call atmux(n, wk(ipar(8)), wk(ipar(9)), a, ja, ia)
+         goto 10
+      else if (ipar(1).eq.3 .or. ipar(1).eq.5) then
+         call lusol(n,wk(ipar(8)),wk(ipar(9)),au,jau,ju)
+         goto 10
+      else if (ipar(1).eq.4 .or. ipar(1).eq.6) then
+         call lutsol(n,wk(ipar(8)),wk(ipar(9)),au,jau,ju)
+         goto 10
+      else if (ipar(1).le.0) then
+         if (ipar(1).eq.0) then
+            print *, 'Iterative sovler has satisfied convergence test.'
+         else if (ipar(1).eq.-1) then
+            print *, 'Iterative solver has iterated too many times.'
+         else if (ipar(1).eq.-2) then
+            print *, 'Iterative solver was not given enough work space.'
+            print *, 'The work space should at least have ', ipar(4),
+     &           ' elements.'
+         else if (ipar(1).eq.-3) then
+            print *, 'Iterative sovler is facing a break-down.'
+         else
+            print *, 'Iterative solver terminated. code =', ipar(1)
+         endif
+      endif
+c     time = dtime(dt)
+      write (iou, *) ipar(7), real(fpar(6))
+      write (iou, *) '# retrun code =', ipar(1),
+     +     '	convergence rate =', fpar(7)
+c     write (iou, *) '# total execution time (sec)', time
+c
+c     check the error
+c
+      call amux(n,sol,wk,a,ja,ia)
+      do i = 1, n
+         wk(n+i) = sol(i) -1.0D0
+         wk(i) = wk(i) - rhs(i)
+      enddo
+      write (iou, *) '# the actual residual norm is', dnrm2(n,wk,1)
+      write (iou, *) '# the error norm is', dnrm2(n,wk(1+n),1)
+c
+      if (iou.ne.6) close(iou)
+      return
+      end
+c-----end-of-runrc
+c-----------------------------------------------------------------------
+      function distdot(n,x,ix,y,iy)
+      integer n, ix, iy
+      real*8 distdot, x(*), y(*), ddot
+      external ddot
+      distdot = ddot(n,x,ix,y,iy)
+      return
+      end
+c-----end-of-distdot
+c-----------------------------------------------------------------------
+c
+      function afun (x,y,z)
+      real*8 afun, x,y, z 
+      afun = -1.0D0
+      return 
+      end
+      
+      function bfun (x,y,z)
+      real*8 bfun, x,y, z 
+      bfun = -1.0D0
+      return 
+      end
+      
+      function cfun (x,y,z)
+      real*8 cfun, x,y, z 
+      cfun = -1.0D0
+      return 
+      end
+      
+      function dfun (x,y,z)
+      real*8 dfun, x,y, z, gammax, gammay, alpha
+      common /func/ gammax, gammay, alpha
+      dfun = gammax*exp(x*y)
+      return 
+      end
+      
+      function efun (x,y,z)
+      real*8 efun, x,y, z, gammax, gammay, alpha
+      common /func/ gammax, gammay, alpha
+      efun = gammay*exp(-x*y) 
+      return 
+      end
+      
+      function ffun (x,y,z)
+      real*8 ffun, x,y, z 
+      ffun = 0.0D0
+      return 
+      end
+      
+      function gfun (x,y,z)
+      real*8 gfun, x,y, z, gammax, gammay, alpha
+      common /func/ gammax, gammay, alpha
+      gfun = alpha 
+      return 
+      end
+      
+      function hfun (x,y,z)
+      real*8 hfun, x,y, z, gammax, gammay, alpha
+      common /func/ gammax, gammay, alpha
+      hfun = alpha * sin(gammax*x+gammay*y-z)
+      return 
+      end
+      
+
+      function betfun(side, x, y, z)
+      real*8 betfun, x, y, z
+      character*2 side
+      betfun = 1.0
+      return
+      end
+
+      function gamfun(side, x, y, z)
+      real*8 gamfun, x, y, z
+      character*2 side
+      if (side.eq.'x2') then
+         gamfun = 5.0
+      else if (side.eq.'y1') then
+         gamfun = 2.0
+      else if (side.eq.'y2') then
+         gamfun = 7.0
+      else
+         gamfun = 0.0
+      endif
+      return
+      end
+c-----------------------------------------------------------------------
+c     functions for the block PDE's 
+c-----------------------------------------------------------------------
+      subroutine afunbl (nfree,x,y,z,coeff)
+      return
+      end
+c     
+      subroutine bfunbl (nfree,x,y,z,coeff)
+      return 
+      end
+      
+      subroutine cfunbl (nfree,x,y,z,coeff)
+c     
+      return 
+      end
+      
+      subroutine dfunbl (nfree,x,y,z,coeff)
+      
+      return
+      end
+c     
+      subroutine efunbl (nfree,x,y,z,coeff)
+      return 
+      end
+c     
+      subroutine ffunbl (nfree,x,y,z,coeff)
+      return 
+      end
+c     
+      subroutine gfunbl (nfree,x,y,z,coeff)
+      return 
+      end
+      
diff --git a/ITSOL/iters.f b/ITSOL/iters.f
new file mode 100644
index 0000000..f00c7d7
--- /dev/null
+++ b/ITSOL/iters.f
@@ -0,0 +1,3586 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c         Basic Iterative Solvers with Reverse Communication           c
+c----------------------------------------------------------------------c
+c     This file currently has several basic iterative linear system    c
+c     solvers. They are:                                               c
+c     CG       -- Conjugate Gradient Method                            c
+c     CGNR     -- Conjugate Gradient Method (Normal Residual equation) c
+c     BCG      -- Bi-Conjugate Gradient Method                         c
+c     DBCG     -- BCG with partial pivoting                            c
+c     BCGSTAB  -- BCG stabilized                                       c
+c     TFQMR    -- Transpose-Free Quasi-Minimum Residual method         c
+c     FOM      -- Full Orthogonalization Method                        c
+c     GMRES    -- Generalized Minimum RESidual method                  c
+c     FGMRES   -- Flexible version of Generalized Minimum              c
+c                 RESidual method                                      c
+c     DQGMRES  -- Direct versions of Quasi Generalize Minimum          c
+c                 Residual method                                      c
+c----------------------------------------------------------------------c
+c     They all have the following calling sequence:
+c      subroutine solver(n, rhs, sol, ipar, fpar, w)
+c      integer n, ipar(16)
+c      real*8 rhs(n), sol(n), fpar(16), w(*)
+c     Where
+c     (1) 'n' is the size of the linear system,
+c     (2) 'rhs' is the right-hand side of the linear system,
+c     (3) 'sol' is the solution to the linear system,
+c     (4) 'ipar' is an integer parameter array for the reverse
+c     communication protocol,
+c     (5) 'fpar' is an floating-point parameter array storing
+c     information to and from the iterative solvers.
+c     (6) 'w' is the work space (size is specified in ipar)
+c
+c     They are preconditioned iterative solvers with reverse
+c     communication. The preconditioners can be applied from either
+c     from left or right or both (specified by ipar(2), see below).
+c
+c     Author: Kesheng John Wu (kewu@mail.cs.umn.edu) 1993
+c
+c     NOTES:
+c
+c     (1) Work space required by each of the iterative solver
+c     routines is as follows:
+c       CG      == 5 * n
+c       CGNR    == 5 * n
+c       BCG     == 7 * n
+c       DBCG    == 11 * n
+c       BCGSTAB == 8 * n
+c       TFQMR   == 11 * n
+c       FOM     == (n+3)*(m+2) + (m+1)*m/2 (m = ipar(5), default m=15)
+c       GMRES   == (n+3)*(m+2) + (m+1)*m/2 (m = ipar(5), default m=15)
+c       FGMRES  == 2*n*(m+1) + (m+1)*m/2 + 3*m + 2 (m = ipar(5),
+c                  default m=15)
+c       DQGMRES == n + lb * (2*n+4) (lb=ipar(5)+1, default lb = 16)
+c
+c     (2) ALL iterative solvers require a user-supplied DOT-product
+c     routine named DISTDOT. The prototype of DISTDOT is
+c
+c     real*8 function distdot(n,x,ix,y,iy)
+c     integer n, ix, iy
+c     real*8 x(1+(n-1)*ix), y(1+(n-1)*iy)
+c
+c     This interface of DISTDOT is exactly the same as that of
+c     DDOT (or SDOT if real == real*8) from BLAS-1. It should have
+c     same functionality as DDOT on a single processor machine. On a
+c     parallel/distributed environment, each processor can perform
+c     DDOT on the data it has, then perform a summation on all the
+c     partial results.
+c
+c     (3) To use this set of routines under SPMD/MIMD program paradigm,
+c     several things are to be noted: (a) 'n' should be the number of
+c     vector elements of 'rhs' that is present on the local processor.
+c     (b) if RHS(i) is on processor j, it is expected that SOL(i)
+c     will be on the same processor, i.e. the vectors are distributed
+c     to each processor in the same way. (c) the preconditioning and
+c     stopping criteria specifications have to be the same on all
+c     processor involved, ipar and fpar have to be the same on each
+c     processor. (d) DISTDOT should be replaced by a distributed
+c     dot-product function.
+c
+c     ..................................................................
+c     Reverse Communication Protocols
+c
+c     When a reverse-communication routine returns, it could be either
+c     that the routine has terminated or it simply requires the caller
+c     to perform one matrix-vector multiplication. The possible matrices
+c     that involve in the matrix-vector multiplications are:
+c     A       (the matrix of the linear system),
+c     A^T     (A transposed),
+c     Ml^{-1} (inverse of the left preconditioner),
+c     Ml^{-T} (inverse of the left preconditioner transposed),
+c     Mr^{-1} (inverse of the right preconditioner),
+c     Mr^{-T} (inverse of the right preconditioner transposed).
+c     For all the matrix vector multiplication, v = A u. The input and
+c     output vectors are supposed to be part of the work space 'w', and
+c     the starting positions of them are stored in ipar(8:9), see below.
+c
+c     The array 'ipar' is used to store the information about the solver.
+c     Here is the list of what each element represents:
+c
+c     ipar(1) -- status of the call/return.
+c     A call to the solver with ipar(1) == 0 will initialize the
+c     iterative solver. On return from the iterative solver, ipar(1)
+c     carries the status flag which indicates the condition of the
+c     return. The status information is divided into two categories,
+c     (1) a positive value indicates the solver requires a matrix-vector
+c     multiplication,
+c     (2) a non-positive value indicates termination of the solver.
+c     Here is the current definition:
+c       1 == request a matvec with A,
+c       2 == request a matvec with A^T,
+c       3 == request a left preconditioner solve (Ml^{-1}),
+c       4 == request a left preconditioner transposed solve (Ml^{-T}),
+c       5 == request a right preconditioner solve (Mr^{-1}),
+c       6 == request a right preconditioner transposed solve (Mr^{-T}),
+c      10 == request the caller to perform stopping test,
+c       0 == normal termination of the solver, satisfied the stopping
+c            criteria,
+c      -1 == termination because iteration number is greater than the
+c            preset limit,
+c      -2 == return due to insufficient work space,
+c      -3 == return due to anticipated break-down / divide by zero,
+c            in the case where Arnoldi procedure is used, additional
+c            error code can be found in ipar(12), where ipar(12) is
+c            the error code of orthogonalization procedure MGSRO:
+c               -1: zero input vector
+c               -2: input vector contains abnormal numbers
+c               -3: input vector is a linear combination of others
+c               -4: trianguler system in GMRES/FOM/etc. has nul rank
+c      -4 == the values of fpar(1) and fpar(2) are both <= 0, the valid
+c            ranges are 0 <= fpar(1) < 1, 0 <= fpar(2), and they can
+c            not be zero at the same time
+c      -9 == while trying to detect a break-down, an abnormal number is
+c            detected.
+c     -10 == return due to some non-numerical reasons, e.g. invalid
+c            floating-point numbers etc.
+c
+c     ipar(2) -- status of the preconditioning:
+c       0 == no preconditioning
+c       1 == left preconditioning only
+c       2 == right preconditioning only
+c       3 == both left and right preconditioning
+c
+c     ipar(3) -- stopping criteria (details of this will be
+c     discussed later).
+c
+c     ipar(4) -- number of elements in the array 'w'. if this is less
+c     than the desired size, it will be over-written with the minimum
+c     requirement. In which case the status flag ipar(1) = -2.
+c
+c     ipar(5) -- size of the Krylov subspace (used by GMRES and its
+c     variants), e.g. GMRES(ipar(5)), FGMRES(ipar(5)),
+c     DQGMRES(ipar(5)).
+c
+c     ipar(6) -- maximum number of matrix-vector multiplies, if not a
+c     positive number the iterative solver will run till convergence
+c     test is satisfied.
+c
+c     ipar(7) -- current number of matrix-vector multiplies. It is
+c     incremented after each matrix-vector multiplication. If there
+c     is preconditioning, the counter is incremented after the
+c     preconditioning associated with each matrix-vector multiplication.
+c
+c     ipar(8) -- pointer to the input vector to the requested matrix-
+c     vector multiplication.
+c
+c     ipar(9) -- pointer to the output vector of the requested matrix-
+c     vector multiplication.
+c
+c     To perform v = A * u, it is assumed that u is w(ipar(8):ipar(8)+n-1)
+c     and v is stored as w(ipar(9):ipar(9)+n-1).
+c
+c     ipar(10) -- the return address (used to determine where to go to
+c     inside the iterative solvers after the caller has performed the
+c     requested services).
+c
+c     ipar(11) -- the result of the external convergence test
+c     On final return from the iterative solvers, this value
+c     will be reflected by ipar(1) = 0 (details discussed later)
+c
+c     ipar(12) -- error code of MGSRO, it is
+c                  1 if the input vector to MGSRO is linear combination
+c                    of others,
+c                  0 if MGSRO was successful,
+c                 -1 if the input vector to MGSRO is zero,
+c                 -2 if the input vector contains invalid number.
+c
+c     ipar(13) -- number of initializations. During each initilization
+c                 residual norm is computed directly from M_l(b - A x).
+c
+c     ipar(14) to ipar(16) are NOT defined, they are NOT USED by
+c     any iterative solver at this time.
+c
+c     Information about the error and tolerance are stored in the array
+c     FPAR. So are some internal variables that need to be saved from
+c     one iteration to the next one. Since the internal variables are
+c     not the same for each routine, we only define the common ones.
+c
+c     The first two are input parameters:
+c     fpar(1) -- the relative tolerance,
+c     fpar(2) -- the absolute tolerance (details discussed later),
+c
+c     When the iterative solver terminates,
+c     fpar(3) -- initial residual/error norm,
+c     fpar(4) -- target residual/error norm,
+c     fpar(5) -- current residual norm (if available),
+c     fpar(6) -- current residual/error norm,
+c     fpar(7) -- convergence rate,
+c
+c     fpar(8:10) are used by some of the iterative solvers to save some
+c     internal information.
+c
+c     fpar(11) -- number of floating-point operations. The iterative
+c     solvers will add the number of FLOPS they used to this variable,
+c     but they do NOT initialize it, nor add the number of FLOPS due to
+c     matrix-vector multiplications (since matvec is outside of the
+c     iterative solvers). To insure the correct FLOPS count, the
+c     caller should set fpar(11) = 0 before invoking the iterative
+c     solvers and account for the number of FLOPS from matrix-vector
+c     multiplications and preconditioners.
+c
+c     fpar(12:16) are not used in current implementation.
+c
+c     Whether the content of fpar(3), fpar(4) and fpar(6) are residual
+c     norms or error norms depends on ipar(3). If the requested
+c     convergence test is based on the residual norm, they will be
+c     residual norms. If the caller want to test convergence based the
+c     error norms (estimated by the norm of the modifications applied
+c     to the approximate solution), they will be error norms.
+c     Convergence rate is defined by (Fortran 77 statement)
+c     fpar(7) = log10(fpar(3) / fpar(6)) / (ipar(7)-ipar(13))
+c     If fpar(7) = 0.5, it means that approximately every 2 (= 1/0.5)
+c     steps the residual/error norm decrease by a factor of 10.
+c
+c     ..................................................................
+c     Stopping criteria,
+c
+c     An iterative solver may be terminated due to (1) satisfying
+c     convergence test; (2) exceeding iteration limit; (3) insufficient
+c     work space; (4) break-down. Checking of the work space is
+c     only done in the initialization stage, i.e. when it is called with
+c     ipar(1) == 0. A complete convergence test is done after each
+c     update of the solutions. Other conditions are monitored
+c     continuously.
+c
+c     With regard to the number of iteration, when ipar(6) is positive,
+c     the current iteration number will be checked against it. If
+c     current iteration number is greater the ipar(6) than the solver
+c     will return with status -1. If ipar(6) is not positive, the
+c     iteration will continue until convergence test is satisfied.
+c
+c     Two things may be used in the convergence tests, one is the
+c     residual 2-norm, the other one is 2-norm of the change in the
+c     approximate solution. The residual and the change in approximate
+c     solution are from the preconditioned system (if preconditioning
+c     is applied). The DQGMRES and TFQMR use two estimates for the
+c     residual norms. The estimates are not accurate, but they are
+c     acceptable in most of the cases. Generally speaking, the error
+c     of the TFQMR's estimate is less accurate.
+c
+c     The convergence test type is indicated by ipar(3). There are four
+c     type convergence tests: (1) tests based on the residual norm;
+c     (2) tests based on change in approximate solution; (3) caller
+c     does not care, the solver choose one from above two on its own;
+c     (4) caller will perform the test, the solver should simply continue.
+c     Here is the complete definition:
+c      -2 == || dx(i) || <= rtol * || rhs || + atol
+c      -1 == || dx(i) || <= rtol * || dx(1) || + atol
+c       0 == solver will choose test 1 (next)
+c       1 == || residual || <= rtol * || initial residual || + atol
+c       2 == || residual || <= rtol * || rhs || + atol
+c     999 == caller will perform the test
+c     where dx(i) denote the change in the solution at the ith update.
+c     ||.|| denotes 2-norm. rtol = fpar(1) and atol = fpar(2).
+c
+c     If the caller is to perform the convergence test, the outcome
+c     should be stored in ipar(11).
+c     ipar(11) = 0 -- failed the convergence test, iterative solver
+c     should continue
+c     ipar(11) = 1 -- satisfied convergence test, iterative solver
+c     should perform the clean up job and stop.
+c
+c     Upon return with ipar(1) = 10,
+c     ipar(8)  points to the starting position of the change in
+c              solution Sx, where the actual solution of the step is
+c              x_j = x_0 + M_r^{-1} Sx.
+c              Exception: ipar(8) < 0, Sx = 0. It is mostly used by
+c              GMRES and variants to indicate (1) Sx was not necessary,
+c              (2) intermediate result of Sx is not computed.
+c     ipar(9)  points to the starting position of a work vector that
+c              can be used by the caller.
+c
+c     NOTE: the caller should allow the iterative solver to perform
+c     clean up job after the external convergence test is satisfied,
+c     since some of the iterative solvers do not directly
+c     update the 'sol' array. A typical clean-up stage includes
+c     performing the final update of the approximate solution and
+c     computing the convergence information (e.g. values of fpar(3:7)).
+c
+c     NOTE: fpar(4) and fpar(6) are not set by the accelerators (the
+c     routines implemented here) if ipar(3) = 999.
+c
+c     ..................................................................
+c     Usage:
+c
+c     To start solving a linear system, the user needs to specify
+c     first 6 elements of the ipar, and first 2 elements of fpar.
+c     The user may optionally set fpar(11) = 0 if one wants to count
+c     the number of floating-point operations. (Note: the iterative
+c     solvers will only add the floating-point operations inside
+c     themselves, the caller will have to add the FLOPS from the
+c     matrix-vector multiplication routines and the preconditioning
+c     routines in order to account for all the arithmetic operations.)
+c
+c     Here is an example:
+c     ipar(1) = 0	! always 0 to start an iterative solver
+c     ipar(2) = 2	! right preconditioning
+c     ipar(3) = 1	! use convergence test scheme 1
+c     ipar(4) = 10000	! the 'w' has 10,000 elements
+c     ipar(5) = 10	! use *GMRES(10) (e.g. FGMRES(10))
+c     ipar(6) = 100	! use at most 100 matvec's
+c     fpar(1) = 1.0E-6	! relative tolerance 1.0E-6
+c     fpar(2) = 1.0E-10 ! absolute tolerance 1.0E-10
+c     fpar(11) = 0.0	! clearing the FLOPS counter
+c
+c     After the above specifications, one can start to call an iterative
+c     solver, say BCG. Here is a piece of pseudo-code showing how it can
+c     be done,
+c
+c 10   call bcg(n,rhs,sol,ipar,fpar,w)
+c      if (ipar(1).eq.1) then
+c         call amux(n,w(ipar(8)),w(ipar(9)),a,ja,ia)
+c         goto 10
+c      else if (ipar(1).eq.2) then
+c         call atmux(n,w(ipar(8)),w(ipar(9)),a,ja,ia)
+c         goto 10
+c      else if (ipar(1).eq.3) then
+c         left preconditioner solver
+c         goto 10
+c      else if (ipar(1).eq.4) then
+c         left preconditioner transposed solve
+c         goto 10
+c      else if (ipar(1).eq.5) then
+c         right preconditioner solve
+c         goto 10
+c      else if (ipar(1).eq.6) then
+c         right preconditioner transposed solve
+c         goto 10
+c      else if (ipar(1).eq.10) then
+c         call my own stopping test routine
+c         goto 10
+c      else if (ipar(1).gt.0) then
+c         ipar(1) is an unspecified code
+c      else
+c         the iterative solver terminated with code = ipar(1)
+c      endif
+c
+c     This segment of pseudo-code assumes the matrix is in CSR format,
+c     AMUX and ATMUX are two routines from the SPARSKIT MATVEC module.
+c     They perform matrix-vector multiplications for CSR matrices,
+c     where w(ipar(8)) is the first element of the input vectors to the
+c     two routines, and w(ipar(9)) is the first element of the output
+c     vectors from them. For simplicity, we did not show the name of
+c     the routine that performs the preconditioning operations or the
+c     convergence tests.
+c-----------------------------------------------------------------------
+      subroutine cg(n, rhs, sol, ipar, fpar, w)
+      implicit none
+      integer n, ipar(16)
+      real*8 rhs(n), sol(n), fpar(16), w(n,*)
+c-----------------------------------------------------------------------
+c     This is a implementation of the Conjugate Gradient (CG) method
+c     for solving linear system.
+c
+c     NOTE: This is not the PCG algorithm. It is a regular CG algorithm.
+c     To be consistent with the other solvers, the preconditioners are
+c     applied by performing Ml^{-1} A Mr^{-1} P in place of A P in the
+c     CG algorithm.  PCG uses the preconditioner differently.
+c
+c     fpar(7) is used here internally to store <r, r>.
+c     w(:,1) -- residual vector
+c     w(:,2) -- P, the conjugate direction
+c     w(:,3) -- A P, matrix multiply the conjugate direction
+c     w(:,4) -- temporary storage for results of preconditioning
+c     w(:,5) -- change in the solution (sol) is stored here until
+c               termination of this solver
+c-----------------------------------------------------------------------
+c     external functions used
+c
+      real*8 distdot
+      logical stopbis, brkdn
+      external distdot, stopbis, brkdn, bisinit
+c
+c     local variables
+c
+      integer i
+      real*8 alpha
+      logical lp,rp
+      save
+c
+c     check the status of the call
+c
+      if (ipar(1).le.0) ipar(10) = 0
+      goto (10, 20, 40, 50, 60, 70, 80), ipar(10)
+c
+c     initialization
+c
+      call bisinit(ipar,fpar,5*n,1,lp,rp,w)
+      if (ipar(1).lt.0) return
+c
+c     request for matrix vector multiplication A*x in the initialization
+c
+      ipar(1) = 1
+      ipar(8) = n+1
+      ipar(9) = ipar(8) + n
+      ipar(10) = 1
+      do i = 1, n
+         w(i,2) = sol(i)
+      enddo
+      return
+ 10   ipar(7) = ipar(7) + 1
+      ipar(13) = 1
+      do i = 1, n
+         w(i,2) = rhs(i) - w(i,3)
+      enddo
+      fpar(11) = fpar(11) + n
+c
+c     if left preconditioned
+c
+      if (lp) then
+         ipar(1) = 3
+         ipar(9) = 1
+         ipar(10) = 2
+         return
+      endif
+c
+ 20   if (lp) then
+         do i = 1, n
+            w(i,2) = w(i,1)
+         enddo
+      else
+         do i = 1, n
+            w(i,1) = w(i,2)
+         enddo
+      endif
+c
+      fpar(7) = distdot(n,w,1,w,1)
+      fpar(11) = fpar(11) + 2 * n
+      fpar(3) = sqrt(fpar(7))
+      fpar(5) = fpar(3)
+      if (abs(ipar(3)).eq.2) then
+         fpar(4) = fpar(1) * sqrt(distdot(n,rhs,1,rhs,1)) + fpar(2)
+         fpar(11) = fpar(11) + 2 * n
+      else if (ipar(3).ne.999) then
+         fpar(4) = fpar(1) * fpar(3) + fpar(2)
+      endif
+c
+c     before iteration can continue, we need to compute A * p, which
+c     includes the preconditioning operations
+c
+ 30   if (rp) then
+         ipar(1) = 5
+         ipar(8) = n + 1
+         if (lp) then
+            ipar(9) = ipar(8) + n
+         else
+            ipar(9) = 3*n + 1
+         endif
+         ipar(10) = 3
+         return
+      endif
+c
+ 40   ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = n + 1
+      endif
+      if (lp) then
+         ipar(9) = 3*n+1
+      else
+         ipar(9) = n+n+1
+      endif
+      ipar(10) = 4
+      return
+c
+ 50   if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = n+n+1
+         ipar(10) = 5
+         return
+      endif
+c
+c     continuing with the iterations
+c
+ 60   ipar(7) = ipar(7) + 1
+      alpha = distdot(n,w(1,2),1,w(1,3),1)
+      fpar(11) = fpar(11) + 2*n
+      if (brkdn(alpha,ipar)) goto 900
+      alpha = fpar(7) / alpha
+      do i = 1, n
+         w(i,5) = w(i,5) + alpha * w(i,2)
+         w(i,1) = w(i,1) - alpha * w(i,3)
+      enddo
+      fpar(11) = fpar(11) + 4*n
+c
+c     are we ready to terminate ?
+c
+      if (ipar(3).eq.999) then
+         ipar(1) = 10
+         ipar(8) = 4*n + 1
+         ipar(9) = 3*n + 1
+         ipar(10) = 6
+         return
+      endif
+ 70   if (ipar(3).eq.999) then
+         if (ipar(11).eq.1) goto 900
+      else if (stopbis(n,ipar,1,fpar,w,w(1,2),alpha)) then
+         goto 900
+      endif
+c
+c     continue the iterations
+c
+      alpha = fpar(5)*fpar(5) / fpar(7)
+      fpar(7) = fpar(5)*fpar(5)
+      do i = 1, n
+         w(i,2) = w(i,1) + alpha * w(i,2)
+      enddo
+      fpar(11) = fpar(11) + 2*n
+      goto 30
+c
+c     clean up -- necessary to accommodate the right-preconditioning
+c
+ 900  if (rp) then
+         if (ipar(1).lt.0) ipar(12) = ipar(1)
+         ipar(1) = 5
+         ipar(8) = 4*n + 1
+         ipar(9) = ipar(8) - n
+         ipar(10) = 7
+         return
+      endif
+ 80   if (rp) then
+         call tidycg(n,ipar,fpar,sol,w(1,4))
+      else
+         call tidycg(n,ipar,fpar,sol,w(1,5))
+      endif
+c
+      return
+      end
+c-----end-of-cg
+c-----------------------------------------------------------------------
+      subroutine cgnr(n,rhs,sol,ipar,fpar,wk)
+      implicit none
+      integer n, ipar(16)
+      real*8 rhs(n),sol(n),fpar(16),wk(n,*)
+c-----------------------------------------------------------------------
+c     CGNR -- Using CG algorithm solving A x = b by solving
+c     Normal Residual equation: A^T A x = A^T b
+c     As long as the matrix is not singular, A^T A is symmetric
+c     positive definite, therefore CG (CGNR) will converge.
+c
+c     Usage of the work space:
+c     wk(:,1) == residual vector R
+c     wk(:,2) == the conjugate direction vector P
+c     wk(:,3) == a scratch vector holds A P, or A^T R
+c     wk(:,4) == a scratch vector holds intermediate results of the
+c                preconditioning
+c     wk(:,5) == a place to hold the modification to SOL
+c
+c     size of the work space WK is required = 5*n
+c-----------------------------------------------------------------------
+c     external functions used
+c
+      real*8 distdot
+      logical stopbis, brkdn
+      external distdot, stopbis, brkdn, bisinit
+c
+c     local variables
+c
+      integer i
+      real*8 alpha, zz, zzm1
+      logical lp, rp
+      save
+c
+c     check the status of the call
+c
+      if (ipar(1).le.0) ipar(10) = 0
+      goto (10, 20, 40, 50, 60, 70, 80, 90, 100, 110), ipar(10)
+c
+c     initialization
+c
+      call bisinit(ipar,fpar,5*n,1,lp,rp,wk)
+      if (ipar(1).lt.0) return
+c
+c     request for matrix vector multiplication A*x in the initialization
+c
+      ipar(1) = 1
+      ipar(8) = 1
+      ipar(9) = 1 + n
+      ipar(10) = 1
+      do i = 1, n
+         wk(i,1) = sol(i)
+      enddo
+      return
+ 10   ipar(7) = ipar(7) + 1
+      ipar(13) = ipar(13) + 1
+      do i = 1, n
+         wk(i,1) = rhs(i) - wk(i,2)
+      enddo
+      fpar(11) = fpar(11) + n
+c
+c     if left preconditioned, precondition the initial residual
+c
+      if (lp) then
+         ipar(1) = 3
+         ipar(10) = 2
+         return
+      endif
+c
+ 20   if (lp) then
+         do i = 1, n
+            wk(i,1) = wk(i,2)
+         enddo
+      endif
+c
+      zz = distdot(n,wk,1,wk,1)
+      fpar(11) = fpar(11) + 2 * n
+      fpar(3) = sqrt(zz)
+      fpar(5) = fpar(3)
+      if (abs(ipar(3)).eq.2) then
+         fpar(4) = fpar(1) * sqrt(distdot(n,rhs,1,rhs,1)) + fpar(2)
+         fpar(11) = fpar(11) + 2 * n
+      else if (ipar(3).ne.999) then
+         fpar(4) = fpar(1) * fpar(3) + fpar(2)
+      endif
+c
+c     normal iteration begins here, first half of the iteration
+c     computes the conjugate direction
+c
+ 30   continue
+c
+c     request the caller to perform a A^T r --> wk(:,3)
+c
+      if (lp) then
+         ipar(1) = 4
+         ipar(8) = 1
+         if (rp) then
+            ipar(9) = n + n + 1
+         else
+            ipar(9) = 3*n + 1
+         endif
+         ipar(10) = 3
+         return
+      endif
+c
+ 40   ipar(1) = 2
+      if (lp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = 1
+      endif
+      if (rp) then
+         ipar(9) = 3*n + 1
+      else
+         ipar(9) = n + n + 1
+      endif
+      ipar(10) = 4
+      return
+c
+ 50   if (rp) then
+         ipar(1) = 6
+         ipar(8) = ipar(9)
+         ipar(9) = n + n + 1
+         ipar(10) = 5
+         return
+      endif
+c
+ 60   ipar(7) = ipar(7) + 1
+      zzm1 = zz
+      zz = distdot(n,wk(1,3),1,wk(1,3),1)
+      fpar(11) = fpar(11) + 2 * n
+      if (brkdn(zz,ipar)) goto 900
+      if (ipar(7).gt.3) then
+         alpha = zz / zzm1
+         do i = 1, n
+            wk(i,2) = wk(i,3) + alpha * wk(i,2)
+         enddo
+         fpar(11) = fpar(11) + 2 * n
+      else
+         do i = 1, n
+            wk(i,2) = wk(i,3)
+         enddo
+      endif
+c
+c     before iteration can continue, we need to compute A * p
+c
+      if (rp) then
+         ipar(1) = 5
+         ipar(8) = n + 1
+         if (lp) then
+            ipar(9) = ipar(8) + n
+         else
+            ipar(9) = 3*n + 1
+         endif
+         ipar(10) = 6
+         return
+      endif
+c
+ 70   ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = n + 1
+      endif
+      if (lp) then
+        ipar(9) = 3*n+1
+      else
+         ipar(9) = n+n+1
+      endif
+      ipar(10) = 7
+      return
+c
+ 80   if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = n+n+1
+         ipar(10) = 8
+         return
+      endif
+c
+c     update the solution -- accumulate the changes in w(:,5)
+c
+ 90   ipar(7) = ipar(7) + 1
+      alpha = distdot(n,wk(1,3),1,wk(1,3),1)
+      fpar(11) = fpar(11) + 2 * n
+      if (brkdn(alpha,ipar)) goto 900
+      alpha = zz / alpha
+      do i = 1, n
+         wk(i,5) = wk(i,5) + alpha * wk(i,2)
+         wk(i,1) = wk(i,1) - alpha * wk(i,3)
+      enddo
+      fpar(11) = fpar(11) + 4 * n
+c
+c     are we ready to terminate ?
+c
+      if (ipar(3).eq.999) then
+         ipar(1) = 10
+         ipar(8) = 4*n + 1
+         ipar(9) = 3*n + 1
+         ipar(10) = 9
+         return
+      endif
+ 100  if (ipar(3).eq.999) then
+         if (ipar(11).eq.1) goto 900
+      else if (stopbis(n,ipar,1,fpar,wk,wk(1,2),alpha)) then
+         goto 900
+      endif
+c
+c     continue the iterations
+c
+      goto 30
+c
+c     clean up -- necessary to accommodate the right-preconditioning
+c
+ 900  if (rp) then
+         if (ipar(1).lt.0) ipar(12) = ipar(1)
+         ipar(1) = 5
+         ipar(8) = 4*n + 1
+         ipar(9) = ipar(8) - n
+         ipar(10) = 10
+         return
+      endif
+ 110  if (rp) then
+         call tidycg(n,ipar,fpar,sol,wk(1,4))
+      else
+         call tidycg(n,ipar,fpar,sol,wk(1,5))
+      endif
+      return
+      end
+c-----end-of-cgnr
+c-----------------------------------------------------------------------
+      subroutine bcg(n,rhs,sol,ipar,fpar,w)
+      implicit none
+      integer n, ipar(16)
+      real*8  fpar(16), rhs(n), sol(n), w(n,*)
+c-----------------------------------------------------------------------
+c     BCG: Bi Conjugate Gradient method. Programmed with reverse
+c     communication, see the header for detailed specifications
+c     of the protocol.
+c
+c     in this routine, before successful return, the fpar's are
+c     fpar(3) == initial residual norm
+c     fpar(4) == target residual norm
+c     fpar(5) == current residual norm
+c     fpar(7) == current rho (rhok = <r, s>)
+c     fpar(8) == previous rho (rhokm1)
+c
+c     w(:,1) -- r, the residual
+c     w(:,2) -- s, the dual of the 'r'
+c     w(:,3) -- p, the projection direction
+c     w(:,4) -- q, the dual of the 'p'
+c     w(:,5) -- v, a scratch vector to store A*p, or A*q.
+c     w(:,6) -- a scratch vector to store intermediate results
+c     w(:,7) -- changes in the solution
+c-----------------------------------------------------------------------
+c     external routines used
+c
+      real*8 distdot
+      logical stopbis,brkdn
+      external distdot, stopbis, brkdn
+c
+      real*8 one
+      parameter(one=1.0D0)
+c
+c     local variables
+c
+      integer i
+      real*8 alpha
+      logical rp, lp
+      save
+c
+c     status of the program
+c
+      if (ipar(1).le.0) ipar(10) = 0
+      goto (10, 20, 40, 50, 60, 70, 80, 90, 100, 110), ipar(10)
+c
+c     initialization, initial residual
+c
+      call bisinit(ipar,fpar,7*n,1,lp,rp,w)
+      if (ipar(1).lt.0) return
+c
+c     compute initial residual, request a matvecc
+c
+      ipar(1) = 1
+      ipar(8) = 3*n+1
+      ipar(9) = ipar(8) + n
+      do i = 1, n
+         w(i,4) = sol(i)
+      enddo
+      ipar(10) = 1
+      return
+ 10   ipar(7) = ipar(7) + 1
+      ipar(13) = ipar(13) + 1
+      do i = 1, n
+         w(i,1) = rhs(i) - w(i,5)
+      enddo
+      fpar(11) = fpar(11) + n
+      if (lp) then
+         ipar(1) = 3
+         ipar(8) = 1
+         ipar(9) = n+1
+         ipar(10) = 2
+         return
+      endif
+c
+ 20   if (lp) then
+         do i = 1, n
+            w(i,1) = w(i,2)
+            w(i,3) = w(i,2)
+            w(i,4) = w(i,2)
+         enddo
+      else
+         do i = 1, n
+            w(i,2) = w(i,1)
+            w(i,3) = w(i,1)
+            w(i,4) = w(i,1)
+         enddo
+      endif
+c
+      fpar(7) = distdot(n,w,1,w,1)
+      fpar(11) = fpar(11) + 2 * n
+      fpar(3) = sqrt(fpar(7))
+      fpar(5) = fpar(3)
+      fpar(8) = one
+      if (abs(ipar(3)).eq.2) then
+         fpar(4) = fpar(1) * sqrt(distdot(n,rhs,1,rhs,1)) + fpar(2)
+         fpar(11) = fpar(11) + 2 * n
+      else if (ipar(3).ne.999) then
+         fpar(4) = fpar(1) * fpar(3) + fpar(2)
+      endif
+      if (ipar(3).ge.0.and.fpar(5).le.fpar(4)) then
+         fpar(6) = fpar(5)
+         goto 900
+      endif
+c
+c     end of initialization, begin iteration, v = A p
+c
+ 30   if (rp) then
+         ipar(1) = 5
+         ipar(8) = n + n + 1
+         if (lp) then
+            ipar(9) = 4*n + 1
+         else
+            ipar(9) = 5*n + 1
+         endif
+         ipar(10) = 3
+         return
+      endif
+c
+ 40   ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = n + n + 1
+      endif
+      if (lp) then
+         ipar(9) = 5*n + 1
+      else
+         ipar(9) = 4*n + 1
+      endif
+      ipar(10) = 4
+      return
+c
+ 50   if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = 4*n + 1
+         ipar(10) = 5
+         return
+      endif
+c
+ 60   ipar(7) = ipar(7) + 1
+      alpha = distdot(n,w(1,4),1,w(1,5),1)
+      fpar(11) = fpar(11) + 2 * n
+      if (brkdn(alpha,ipar)) goto 900
+      alpha = fpar(7) / alpha
+      do i = 1, n
+         w(i,7) = w(i,7) + alpha * w(i,3)
+         w(i,1) = w(i,1) - alpha * w(i,5)
+      enddo
+      fpar(11) = fpar(11) + 4 * n
+      if (ipar(3).eq.999) then
+         ipar(1) = 10
+         ipar(8) = 6*n + 1
+         ipar(9) = 5*n + 1
+         ipar(10) = 6
+         return
+      endif
+ 70   if (ipar(3).eq.999) then
+         if (ipar(11).eq.1) goto 900
+      else if (stopbis(n,ipar,1,fpar,w,w(1,3),alpha)) then
+         goto 900
+      endif
+c
+c     A^t * x
+c
+      if (lp) then
+         ipar(1) = 4
+         ipar(8) = 3*n + 1
+         if (rp) then
+            ipar(9) = 4*n + 1
+         else
+            ipar(9) = 5*n + 1
+         endif
+         ipar(10) = 7
+         return
+      endif
+c
+ 80   ipar(1) = 2
+      if (lp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = 3*n + 1
+      endif
+      if (rp) then
+         ipar(9) = 5*n + 1
+      else
+         ipar(9) = 4*n + 1
+      endif
+      ipar(10) = 8
+      return
+c
+ 90   if (rp) then
+         ipar(1) = 6
+         ipar(8) = ipar(9)
+         ipar(9) = 4*n + 1
+         ipar(10) = 9
+         return
+      endif
+c
+ 100  ipar(7) = ipar(7) + 1
+      do i = 1, n
+         w(i,2) = w(i,2) - alpha * w(i,5)
+      enddo
+      fpar(8) = fpar(7)
+      fpar(7) = distdot(n,w,1,w(1,2),1)
+      fpar(11) = fpar(11) + 4 * n
+      if (brkdn(fpar(7), ipar)) return
+      alpha = fpar(7) / fpar(8)
+      do i = 1, n
+         w(i,3) = w(i,1) + alpha * w(i,3)
+         w(i,4) = w(i,2) + alpha * w(i,4)
+      enddo
+      fpar(11) = fpar(11) + 4 * n
+c
+c     end of the iterations
+c
+      goto 30
+c
+c     some clean up job to do
+c
+ 900  if (rp) then
+         if (ipar(1).lt.0) ipar(12) = ipar(1)
+         ipar(1) = 5
+         ipar(8) = 6*n + 1
+         ipar(9) = ipar(8) - n
+         ipar(10) = 10
+         return
+      endif
+ 110  if (rp) then
+         call tidycg(n,ipar,fpar,sol,w(1,6))
+      else
+         call tidycg(n,ipar,fpar,sol,w(1,7))
+      endif
+      return
+c-----end-of-bcg
+      end
+c-----------------------------------------------------------------------
+      subroutine bcgstab(n, rhs, sol, ipar, fpar, w)
+      implicit none
+      integer n, ipar(16)
+      real*8 rhs(n), sol(n), fpar(16), w(n,8)
+c-----------------------------------------------------------------------
+c     BCGSTAB --- Bi Conjugate Gradient stabilized (BCGSTAB)
+c     This is an improved BCG routine. (1) no matrix transpose is
+c     involved. (2) the convergence is smoother.
+c
+c
+c     Algorithm:
+c     Initialization - r = b - A x, r0 = r, p = r, rho = (r0, r),
+c     Iterate -
+c     (1) v = A p
+c     (2) alpha = rho / (r0, v)
+c     (3) s = r - alpha v
+c     (4) t = A s
+c     (5) omega = (t, s) / (t, t)
+c     (6) x = x + alpha * p + omega * s
+c     (7) r = s - omega * t
+c     convergence test goes here
+c     (8) beta = rho, rho = (r0, r), beta = rho * alpha / (beta * omega)
+c         p = r + beta * (p - omega * v)
+c
+c     in this routine, before successful return, the fpar's are
+c     fpar(3) == initial (preconditionied-)residual norm
+c     fpar(4) == target (preconditionied-)residual norm
+c     fpar(5) == current (preconditionied-)residual norm
+c     fpar(6) == current residual norm or error
+c     fpar(7) == current rho (rhok = <r, r0>)
+c     fpar(8) == alpha
+c     fpar(9) == omega
+c
+c     Usage of the work space W
+c     w(:, 1) = r0, the initial residual vector
+c     w(:, 2) = r, current residual vector
+c     w(:, 3) = s
+c     w(:, 4) = t
+c     w(:, 5) = v
+c     w(:, 6) = p
+c     w(:, 7) = tmp, used in preconditioning, etc.
+c     w(:, 8) = delta x, the correction to the answer is accumulated
+c               here, so that the right-preconditioning may be applied
+c               at the end
+c-----------------------------------------------------------------------
+c     external routines used
+c
+      real*8 distdot
+      logical stopbis, brkdn
+      external distdot, stopbis, brkdn
+c
+      real*8 one
+      parameter(one=1.0D0)
+c
+c     local variables
+c
+      integer i
+      real*8 alpha,beta,rho,omega
+      logical lp, rp
+      save lp, rp
+c
+c     where to go
+c
+      if (ipar(1).gt.0) then
+         goto (10, 20, 40, 50, 60, 70, 80, 90, 100, 110) ipar(10)
+      else if (ipar(1).lt.0) then
+         goto 900
+      endif
+c
+c     call the initialization routine
+c
+      call bisinit(ipar,fpar,8*n,1,lp,rp,w)
+      if (ipar(1).lt.0) return
+c
+c     perform a matvec to compute the initial residual
+c
+      ipar(1) = 1
+      ipar(8) = 1
+      ipar(9) = 1 + n
+      do i = 1, n
+         w(i,1) = sol(i)
+      enddo
+      ipar(10) = 1
+      return
+ 10   ipar(7) = ipar(7) + 1
+      ipar(13) = ipar(13) + 1
+      do i = 1, n
+         w(i,1) = rhs(i) - w(i,2)
+      enddo
+      fpar(11) = fpar(11) + n
+      if (lp) then
+         ipar(1) = 3
+         ipar(10) = 2
+         return
+      endif
+c
+ 20   if (lp) then
+         do i = 1, n
+            w(i,1) = w(i,2)
+            w(i,6) = w(i,2)
+         enddo
+      else
+         do i = 1, n
+            w(i,2) = w(i,1)
+            w(i,6) = w(i,1)
+         enddo
+      endif
+c
+      fpar(7) = distdot(n,w,1,w,1)
+      fpar(11) = fpar(11) + 2 * n
+      fpar(5) = sqrt(fpar(7))
+      fpar(3) = fpar(5)
+      if (abs(ipar(3)).eq.2) then
+         fpar(4) = fpar(1) * sqrt(distdot(n,rhs,1,rhs,1)) + fpar(2)
+         fpar(11) = fpar(11) + 2 * n
+      else if (ipar(3).ne.999) then
+         fpar(4) = fpar(1) * fpar(3) + fpar(2)
+      endif
+      if (ipar(3).ge.0) fpar(6) = fpar(5)
+      if (ipar(3).ge.0 .and. fpar(5).le.fpar(4) .and.
+     +     ipar(3).ne.999) then
+         goto 900
+      endif
+c
+c     beginning of the iterations
+c
+c     Step (1), v = A p
+ 30   if (rp) then
+         ipar(1) = 5
+         ipar(8) = 5*n+1
+         if (lp) then
+            ipar(9) = 4*n + 1
+         else
+            ipar(9) = 6*n + 1
+         endif
+         ipar(10) = 3
+         return
+      endif
+c
+ 40   ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = 5*n+1
+      endif
+      if (lp) then
+         ipar(9) = 6*n + 1
+      else
+         ipar(9) = 4*n + 1
+      endif
+      ipar(10) = 4
+      return
+ 50   if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = 4*n + 1
+         ipar(10) = 5
+         return
+      endif
+c
+ 60   ipar(7) = ipar(7) + 1
+c
+c     step (2)
+      alpha = distdot(n,w(1,1),1,w(1,5),1)
+      fpar(11) = fpar(11) + 2 * n
+      if (brkdn(alpha, ipar)) goto 900
+      alpha = fpar(7) / alpha
+      fpar(8) = alpha
+c
+c     step (3)
+      do i = 1, n
+         w(i,3) = w(i,2) - alpha * w(i,5)
+      enddo
+      fpar(11) = fpar(11) + 2 * n
+c
+c     Step (4): the second matvec -- t = A s
+c
+      if (rp) then
+         ipar(1) = 5
+         ipar(8) = n+n+1
+         if (lp) then
+            ipar(9) = ipar(8)+n
+         else
+            ipar(9) = 6*n + 1
+         endif
+         ipar(10) = 6
+         return
+      endif
+c
+ 70   ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = n+n+1
+      endif
+      if (lp) then
+         ipar(9) = 6*n + 1
+      else
+         ipar(9) = 3*n + 1
+      endif
+      ipar(10) = 7
+      return
+ 80   if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = 3*n + 1
+         ipar(10) = 8
+         return
+      endif
+ 90   ipar(7) = ipar(7) + 1
+c
+c     step (5)
+      omega = distdot(n,w(1,4),1,w(1,4),1)
+      fpar(11) = fpar(11) + n + n
+      if (brkdn(omega,ipar)) goto 900
+      omega = distdot(n,w(1,4),1,w(1,3),1) / omega
+      fpar(11) = fpar(11) + n + n
+      if (brkdn(omega,ipar)) goto 900
+      fpar(9) = omega
+      alpha = fpar(8)
+c
+c     step (6) and (7)
+      do i = 1, n
+         w(i,7) = alpha * w(i,6) + omega * w(i,3)
+         w(i,8) = w(i,8) + w(i,7)
+         w(i,2) = w(i,3) - omega * w(i,4)
+      enddo
+      fpar(11) = fpar(11) + 6 * n + 1
+c
+c     convergence test
+      if (ipar(3).eq.999) then
+         ipar(1) = 10
+         ipar(8) = 7*n + 1
+         ipar(9) = 6*n + 1
+         ipar(10) = 9
+         return
+      endif
+      if (stopbis(n,ipar,2,fpar,w(1,2),w(1,7),one))  goto 900
+ 100  if (ipar(3).eq.999.and.ipar(11).eq.1) goto 900
+c
+c     step (8): computing new p and rho
+      rho = fpar(7)
+      fpar(7) = distdot(n,w(1,2),1,w(1,1),1)
+      omega = fpar(9)
+      beta = fpar(7) * fpar(8) / (fpar(9) * rho)
+      do i = 1, n
+         w(i,6) = w(i,2) + beta * (w(i,6) - omega * w(i,5))
+      enddo
+      fpar(11) = fpar(11) + 6 * n + 3
+      if (brkdn(fpar(7),ipar)) goto 900
+c
+c     end of an iteration
+c
+      goto 30
+c
+c     some clean up job to do
+c
+ 900  if (rp) then
+         if (ipar(1).lt.0) ipar(12) = ipar(1)
+         ipar(1) = 5
+         ipar(8) = 7*n + 1
+         ipar(9) = ipar(8) - n
+         ipar(10) = 10
+         return
+      endif
+ 110  if (rp) then
+         call tidycg(n,ipar,fpar,sol,w(1,7))
+      else
+         call tidycg(n,ipar,fpar,sol,w(1,8))
+      endif
+c
+      return
+c-----end-of-bcgstab
+      end
+c-----------------------------------------------------------------------
+      subroutine tfqmr(n, rhs, sol, ipar, fpar, w)
+      implicit none
+      integer n, ipar(16)
+      real*8 rhs(n), sol(n), fpar(16), w(n,*)
+c-----------------------------------------------------------------------
+c     TFQMR --- transpose-free Quasi-Minimum Residual method
+c     This is developed from BCG based on the principle of Quasi-Minimum
+c     Residual, and it is transpose-free.
+c
+c     It uses approximate residual norm.
+c
+c     Internally, the fpar's are used as following:
+c     fpar(3) --- initial residual norm squared
+c     fpar(4) --- target residual norm squared
+c     fpar(5) --- current residual norm squared
+c
+c     w(:,1) -- R, residual
+c     w(:,2) -- R0, the initial residual
+c     w(:,3) -- W
+c     w(:,4) -- Y
+c     w(:,5) -- Z
+c     w(:,6) -- A * Y
+c     w(:,7) -- A * Z
+c     w(:,8) -- V
+c     w(:,9) -- D
+c     w(:,10) -- intermediate results of preconditioning
+c     w(:,11) -- changes in the solution
+c-----------------------------------------------------------------------
+c     external functions
+c
+      real*8 distdot
+      logical brkdn
+      external brkdn, distdot
+c
+      real*8 one,zero
+      parameter(one=1.0D0,zero=0.0D0)
+c
+c     local variables
+c
+      integer i
+      logical lp, rp
+      real*8 eta,sigma,theta,te,alpha,rho,tao
+      save
+c
+c     status of the call (where to go)
+c
+      if (ipar(1).le.0) ipar(10) = 0
+      goto (10,20,40,50,60,70,80,90,100,110), ipar(10)
+c
+c     initializations
+c
+      call bisinit(ipar,fpar,11*n,2,lp,rp,w)
+      if (ipar(1).lt.0) return
+      ipar(1) = 1
+      ipar(8) = 1
+      ipar(9) = 1 + 6*n
+      do i = 1, n
+         w(i,1) = sol(i)
+      enddo
+      ipar(10) = 1
+      return
+ 10   ipar(7) = ipar(7) + 1
+      ipar(13) = ipar(13) + 1
+      do i = 1, n
+         w(i,1) = rhs(i) - w(i,7)
+         w(i,9) = zero
+      enddo
+      fpar(11) = fpar(11) + n
+c
+      if (lp) then
+         ipar(1) = 3
+         ipar(9) = n+1
+         ipar(10) = 2
+         return
+      endif
+ 20   continue
+      if (lp) then
+         do i = 1, n
+            w(i,1) = w(i,2)
+            w(i,3) = w(i,2)
+         enddo
+      else
+         do i = 1, n
+            w(i,2) = w(i,1)
+            w(i,3) = w(i,1)
+         enddo
+      endif
+c
+      fpar(5) = sqrt(distdot(n,w,1,w,1))
+      fpar(3) = fpar(5)
+      tao = fpar(5)
+      fpar(11) = fpar(11) + n + n
+      if (abs(ipar(3)).eq.2) then
+         fpar(4) = fpar(1) * sqrt(distdot(n,rhs,1,rhs,1)) + fpar(2)
+         fpar(11) = fpar(11) + n + n
+      else if (ipar(3).ne.999) then
+         fpar(4) = fpar(1) * tao + fpar(2)
+      endif
+      te = zero
+      rho = zero
+c
+c     begin iteration
+c
+ 30   sigma = rho
+      rho = distdot(n,w(1,2),1,w(1,3),1)
+      fpar(11) = fpar(11) + n + n
+      if (brkdn(rho,ipar)) goto 900
+      if (ipar(7).eq.1) then
+         alpha = zero
+      else
+         alpha = rho / sigma
+      endif
+      do i = 1, n
+         w(i,4) = w(i,3) + alpha * w(i,5)
+      enddo
+      fpar(11) = fpar(11) + n + n
+c
+c     A * x -- with preconditioning
+c
+      if (rp) then
+         ipar(1) = 5
+         ipar(8) = 3*n + 1
+         if (lp) then
+            ipar(9) = 5*n + 1
+         else
+            ipar(9) = 9*n + 1
+         endif
+         ipar(10) = 3
+         return
+      endif
+c
+ 40   ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = 3*n + 1
+      endif
+      if (lp) then
+         ipar(9) = 9*n + 1
+      else
+         ipar(9) = 5*n + 1
+      endif
+      ipar(10) = 4
+      return
+c
+ 50   if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = 5*n + 1
+         ipar(10) = 5
+         return
+      endif
+ 60   ipar(7) = ipar(7) + 1
+      do i = 1, n
+         w(i,8) = w(i,6) + alpha * (w(i,7) + alpha * w(i,8))
+      enddo
+      sigma = distdot(n,w(1,2),1,w(1,8),1)
+      fpar(11) = fpar(11) + 6 * n
+      if (brkdn(sigma,ipar)) goto 900
+      alpha = rho / sigma
+      do i = 1, n
+         w(i,5) = w(i,4) - alpha * w(i,8)
+      enddo
+      fpar(11) = fpar(11) + 2*n
+c
+c     the second A * x
+c
+      if (rp) then
+         ipar(1) = 5
+         ipar(8) = 4*n + 1
+         if (lp) then
+            ipar(9) = 6*n + 1
+         else
+            ipar(9) = 9*n + 1
+         endif
+         ipar(10) = 6
+         return
+      endif
+c
+ 70   ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = 4*n + 1
+      endif
+      if (lp) then
+         ipar(9) = 9*n + 1
+      else
+         ipar(9) = 6*n + 1
+      endif
+      ipar(10) = 7
+      return
+c
+ 80   if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = 6*n + 1
+         ipar(10) = 8
+         return
+      endif
+ 90   ipar(7) = ipar(7) + 1
+      do i = 1, n
+         w(i,3) = w(i,3) - alpha * w(i,6)
+      enddo
+c
+c     update I
+c
+      theta = distdot(n,w(1,3),1,w(1,3),1) / (tao*tao)
+      sigma = one / (one + theta)
+      tao = tao * sqrt(sigma * theta)
+      fpar(11) = fpar(11) + 4*n + 6
+      if (brkdn(tao,ipar)) goto 900
+      eta = sigma * alpha
+      sigma = te / alpha
+      te = theta * eta
+      do i = 1, n
+         w(i,9) = w(i,4) + sigma * w(i,9)
+         w(i,11) = w(i,11) + eta * w(i,9)
+         w(i,3) = w(i,3) - alpha * w(i,7)
+      enddo
+      fpar(11) = fpar(11) + 6 * n + 6
+      if (ipar(7).eq.1) then
+         if (ipar(3).eq.-1) then
+            fpar(3) = eta * sqrt(distdot(n,w(1,9),1,w(1,9),1))
+            fpar(4) = fpar(1)*fpar(3) + fpar(2)
+            fpar(11) = fpar(11) + n + n + 4
+         endif
+      endif
+c
+c     update II
+c
+      theta = distdot(n,w(1,3),1,w(1,3),1) / (tao*tao)
+      sigma = one / (one + theta)
+      tao = tao * sqrt(sigma * theta)
+      fpar(11) = fpar(11) + 8 + 2*n
+      if (brkdn(tao,ipar)) goto 900
+      eta = sigma * alpha
+      sigma = te / alpha
+      te = theta * eta
+      do i = 1, n
+         w(i,9) = w(i,5) + sigma * w(i,9)
+         w(i,11) = w(i,11) + eta * w(i,9)
+      enddo
+      fpar(11) = fpar(11) + 4*n + 3
+c
+c     this is the correct over-estimate
+c      fpar(5) = sqrt(real(ipar(7)+1)) * tao
+c     this is an approximation
+      fpar(5) = tao
+      if (ipar(3).eq.999) then
+         ipar(1) = 10
+         ipar(8) = 10*n + 1
+         ipar(9) = 9*n + 1
+         ipar(10) = 9
+         return
+      else if (ipar(3).lt.0) then
+         fpar(6) = eta * sqrt(distdot(n,w(1,9),1,w(1,9),1))
+         fpar(11) = fpar(11) + n + n + 2
+      else
+         fpar(6) = fpar(5)
+      endif
+      if (fpar(6).gt.fpar(4) .and. (ipar(7).lt.ipar(6)
+     +     .or. ipar(6).le.0)) goto 30
+ 100  if (ipar(3).eq.999.and.ipar(11).eq.0) goto 30
+c
+c     clean up
+c
+ 900  if (rp) then
+         if (ipar(1).lt.0) ipar(12) = ipar(1)
+         ipar(1) = 5
+         ipar(8) = 10*n + 1
+         ipar(9) = ipar(8) - n
+         ipar(10) = 10
+         return
+      endif
+ 110  if (rp) then
+         call tidycg(n,ipar,fpar,sol,w(1,10))
+      else
+         call tidycg(n,ipar,fpar,sol,w(1,11))
+      endif
+c
+      return
+      end
+c-----end-of-tfqmr
+c-----------------------------------------------------------------------
+      subroutine fom(n, rhs, sol, ipar, fpar, w)
+      implicit none
+      integer n, ipar(16)
+      real*8 rhs(n), sol(n), fpar(16), w(*)
+c-----------------------------------------------------------------------
+c     This a version of The Full Orthogonalization Method (FOM) 
+c     implemented with reverse communication. It is a simple restart 
+c     version of the FOM algorithm and is implemented with plane 
+c     rotations similarly to GMRES.
+c
+c  parameters:
+c  ----------- 
+c     ipar(5) == the dimension of the Krylov subspace
+c     after every ipar(5) iterations, the FOM will restart with
+c     the updated solution and recomputed residual vector.
+c
+c     the work space in `w' is used as follows:
+c     (1) the basis for the Krylov subspace, size n*(m+1);
+c     (2) the Hessenberg matrix, only the upper triangular
+c     portion of the matrix is stored, size (m+1)*m/2 + 1
+c     (3) three vectors, all are of size m, they are
+c     the cosine and sine of the Givens rotations, the third one holds
+c     the residuals, it is of size m+1.
+c
+c     TOTAL SIZE REQUIRED == (n+3)*(m+2) + (m+1)*m/2
+c     Note: m == ipar(5). The default value for this is 15 if
+c     ipar(5) <= 1.
+c-----------------------------------------------------------------------
+c     external functions used
+c
+      real*8 distdot
+      external distdot
+c
+      real*8 one, zero
+      parameter(one=1.0D0, zero=0.0D0)
+c
+c     local variables, ptr and p2 are temporary pointers,
+c     hes points to the Hessenberg matrix,
+c     vc, vs point to the cosines and sines of the Givens rotations
+c     vrn points to the vectors of residual norms, more precisely
+c     the right hand side of the least square problem solved.
+c
+      integer i,ii,idx,k,m,ptr,p2,prs,hes,vc,vs,vrn
+      real*8 alpha, c, s 
+      logical lp, rp
+      save
+c
+c     check the status of the call
+c
+      if (ipar(1).le.0) ipar(10) = 0
+      goto (10, 20, 30, 40, 50, 60, 70) ipar(10)
+c
+c     initialization
+c
+      if (ipar(5).le.1) then
+         m = 15
+      else
+         m = ipar(5)
+      endif
+      idx = n * (m+1)
+      hes = idx + n
+      vc = hes + (m+1) * m / 2 + 1
+      vs = vc + m
+      vrn = vs + m
+      i = vrn + m + 1
+      call bisinit(ipar,fpar,i,1,lp,rp,w)
+      if (ipar(1).lt.0) return
+c
+c     request for matrix vector multiplication A*x in the initialization
+c
+ 100  ipar(1) = 1
+      ipar(8) = n+1
+      ipar(9) = 1
+      ipar(10) = 1
+      k = 0
+      do i = 1, n
+         w(n+i) = sol(i)
+      enddo
+      return
+ 10   ipar(7) = ipar(7) + 1
+      ipar(13) = ipar(13) + 1
+      if (lp) then
+         do i = 1, n
+            w(n+i) = rhs(i) - w(i)
+         enddo
+         ipar(1) = 3
+         ipar(10) = 2
+         return
+      else
+         do i = 1, n
+            w(i) = rhs(i) - w(i)
+         enddo
+      endif
+      fpar(11) = fpar(11) + n
+c
+ 20   alpha = sqrt(distdot(n,w,1,w,1))
+      fpar(11) = fpar(11) + 2*n + 1
+      if (ipar(7).eq.1 .and. ipar(3).ne.999) then
+         if (abs(ipar(3)).eq.2) then
+            fpar(4) = fpar(1) * sqrt(distdot(n,rhs,1,rhs,1)) + fpar(2)
+            fpar(11) = fpar(11) + 2*n
+         else
+            fpar(4) = fpar(1) * alpha + fpar(2)
+         endif
+         fpar(3) = alpha
+      endif
+      fpar(5) = alpha
+      w(vrn+1) = alpha
+      if (alpha.le.fpar(4) .and. ipar(3).ge.0 .and. ipar(3).ne.999) then
+         ipar(1) = 0
+         fpar(6) = alpha
+         goto 300
+      endif
+      alpha = one / alpha
+      do ii = 1, n
+         w(ii) = alpha * w(ii)
+      enddo
+      fpar(11) = fpar(11) + n
+c
+c     request for (1) right preconditioning
+c     (2) matrix vector multiplication
+c     (3) left preconditioning
+c
+ 110  k = k + 1
+      if (rp) then
+         ipar(1) = 5
+         ipar(8) = k*n - n + 1
+         if (lp) then
+            ipar(9) = k*n + 1
+         else
+            ipar(9) = idx + 1
+         endif
+         ipar(10) = 3
+         return
+      endif
+c
+ 30   ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = (k-1)*n + 1
+      endif
+      if (lp) then
+         ipar(9) = idx + 1
+      else
+         ipar(9) = 1 + k*n
+      endif
+      ipar(10) = 4
+      return
+c
+ 40   if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = k*n + 1
+         ipar(10) = 5
+         return
+      endif
+c
+c     Modified Gram-Schmidt orthogonalization procedure
+c     temporary pointer 'ptr' is pointing to the current column of the
+c     Hessenberg matrix. 'p2' points to the new basis vector
+c
+ 50   ipar(7) = ipar(7) + 1
+      ptr = k * (k - 1) / 2 + hes
+      p2 = ipar(9)
+      call mgsro(.false.,n,n,k+1,k+1,fpar(11),w,w(ptr+1),
+     $     ipar(12))
+      if (ipar(12).lt.0) goto 200
+c
+c     apply previous Givens rotations to column.
+c
+      p2 = ptr + 1
+      do i = 1, k-1
+         ptr = p2
+         p2 = p2 + 1
+         alpha = w(ptr)
+         c = w(vc+i)
+         s = w(vs+i)
+         w(ptr) = c * alpha + s * w(p2)
+         w(p2) = c * w(p2) - s * alpha
+      enddo
+c
+c     end of one Arnoldi iteration, alpha will store the estimated
+c     residual norm at current stage
+c
+      fpar(11) = fpar(11) + 6*k
+
+      prs = vrn+k
+      alpha = fpar(5) 
+      if (w(p2) .ne. zero) alpha = abs(w(p2+1)*w(prs)/w(p2)) 
+      fpar(5) = alpha
+c
+      if (k.ge.m .or. (ipar(3).ge.0 .and. alpha.le.fpar(4))
+     +     .or. (ipar(6).gt.0 .and. ipar(7).ge.ipar(6)))
+     +     goto 200
+c
+      call givens(w(p2), w(p2+1), c, s)
+      w(vc+k) = c
+      w(vs+k) = s
+      alpha = - s * w(prs)
+      w(prs) = c * w(prs)
+      w(prs+1) = alpha
+c
+      if (w(p2).ne.zero) goto 110
+c
+c     update the approximate solution, first solve the upper triangular
+c     system, temporary pointer ptr points to the Hessenberg matrix,
+c     prs points to the right-hand-side (also the solution) of the system.
+c
+ 200  ptr = hes + k * (k + 1) / 2
+      prs = vrn + k
+      if (w(ptr).eq.zero) then
+c
+c     if the diagonal elements of the last column is zero, reduce k by 1
+c     so that a smaller trianguler system is solved
+c
+         k = k - 1
+         if (k.gt.0) then
+            goto 200
+         else
+            ipar(1) = -3
+            ipar(12) = -4
+            goto 300
+         endif
+      endif
+      w(prs) = w(prs) / w(ptr)
+      do i = k-1, 1, -1
+         ptr = ptr - i - 1
+         do ii = 1, i
+            w(vrn+ii) = w(vrn+ii) - w(prs) * w(ptr+ii)
+         enddo
+         prs = prs - 1
+         w(prs) = w(prs) / w(ptr)
+      enddo
+c
+      do ii = 1, n
+         w(ii) = w(ii) * w(prs)
+      enddo
+      do i = 1, k-1
+         prs = prs + 1
+         ptr = i*n
+         do ii = 1, n
+            w(ii) = w(ii) + w(prs) * w(ptr+ii)
+         enddo
+      enddo
+      fpar(11) = fpar(11) + 2*(k-1)*n + n + k*(k+1)
+c
+      if (rp) then
+         ipar(1) = 5
+         ipar(8) = 1
+         ipar(9) = idx + 1
+         ipar(10) = 6
+         return
+      endif
+c
+ 60   if (rp) then
+         do i = 1, n
+            sol(i) = sol(i) + w(idx+i)
+         enddo
+      else
+         do i = 1, n
+            sol(i) = sol(i) + w(i)
+         enddo
+      endif
+      fpar(11) = fpar(11) + n
+c
+c     process the complete stopping criteria
+c
+      if (ipar(3).eq.999) then
+         ipar(1) = 10
+         ipar(8) = -1
+         ipar(9) = idx + 1
+         ipar(10) = 7
+         return
+      else if (ipar(3).lt.0) then
+         if (ipar(7).le.m+1) then
+            fpar(3) = abs(w(vrn+1))
+            if (ipar(3).eq.-1) fpar(4) = fpar(1)*fpar(3)+fpar(2)
+         endif
+         alpha = abs(w(vrn+k))
+      endif
+      fpar(6) = alpha
+c
+c     do we need to restart ?
+c
+ 70   if (ipar(12).ne.0) then
+         ipar(1) = -3
+         goto 300
+      endif
+      if (ipar(7).lt.ipar(6) .or. ipar(6).le.0) then
+         if (ipar(3).ne.999) then
+            if (fpar(6).gt.fpar(4)) goto 100
+         else
+            if (ipar(11).eq.0) goto 100
+         endif
+      endif
+c
+c     termination, set error code, compute convergence rate
+c
+      if (ipar(1).gt.0) then
+         if (ipar(3).eq.999 .and. ipar(11).eq.1) then
+            ipar(1) = 0
+         else if (ipar(3).ne.999 .and. fpar(6).le.fpar(4)) then
+            ipar(1) = 0
+         else if (ipar(7).ge.ipar(6) .and. ipar(6).gt.0) then
+            ipar(1) = -1
+         else
+            ipar(1) = -10
+         endif
+      endif
+ 300  if (fpar(3).ne.zero .and. fpar(6).ne.zero .and.
+     +     ipar(7).gt.ipar(13)) then
+         fpar(7) = log10(fpar(3) / fpar(6)) / dble(ipar(7)-ipar(13))
+      else
+         fpar(7) = zero
+      endif
+      return
+      end
+c-----end-of-fom-------------------------------------------------------- 
+c-----------------------------------------------------------------------
+      subroutine gmres(n, rhs, sol, ipar, fpar, w)
+      implicit none
+      integer n, ipar(16)
+      real*8 rhs(n), sol(n), fpar(16), w(*)
+c-----------------------------------------------------------------------
+c     This a version of GMRES implemented with reverse communication.
+c     It is a simple restart version of the GMRES algorithm.
+c
+c     ipar(5) == the dimension of the Krylov subspace
+c     after every ipar(5) iterations, the GMRES will restart with
+c     the updated solution and recomputed residual vector.
+c
+c     the space of the `w' is used as follows:
+c     (1) the basis for the Krylov subspace, size n*(m+1);
+c     (2) the Hessenberg matrix, only the upper triangular
+c     portion of the matrix is stored, size (m+1)*m/2 + 1
+c     (3) three vectors, all are of size m, they are
+c     the cosine and sine of the Givens rotations, the third one holds
+c     the residuals, it is of size m+1.
+c
+c     TOTAL SIZE REQUIRED == (n+3)*(m+2) + (m+1)*m/2
+c     Note: m == ipar(5). The default value for this is 15 if
+c     ipar(5) <= 1.
+c-----------------------------------------------------------------------
+c     external functions used
+c
+      real*8 distdot
+      external distdot
+c
+      real*8 one, zero
+      parameter(one=1.0D0, zero=0.0D0)
+c
+c     local variables, ptr and p2 are temporary pointers,
+c     hess points to the Hessenberg matrix,
+c     vc, vs point to the cosines and sines of the Givens rotations
+c     vrn points to the vectors of residual norms, more precisely
+c     the right hand side of the least square problem solved.
+c
+      integer i,ii,idx,k,m,ptr,p2,hess,vc,vs,vrn
+      real*8 alpha, c, s
+      logical lp, rp
+      save
+c
+c     check the status of the call
+c
+      if (ipar(1).le.0) ipar(10) = 0
+      goto (10, 20, 30, 40, 50, 60, 70) ipar(10)
+c
+c     initialization
+c
+      if (ipar(5).le.1) then
+         m = 15
+      else
+         m = ipar(5)
+      endif
+      idx = n * (m+1)
+      hess = idx + n
+      vc = hess + (m+1) * m / 2 + 1
+      vs = vc + m
+      vrn = vs + m
+      i = vrn + m + 1
+      call bisinit(ipar,fpar,i,1,lp,rp,w)
+      if (ipar(1).lt.0) return
+c
+c     request for matrix vector multiplication A*x in the initialization
+c
+ 100  ipar(1) = 1
+      ipar(8) = n+1
+      ipar(9) = 1
+      ipar(10) = 1
+      k = 0
+      do i = 1, n
+         w(n+i) = sol(i)
+      enddo
+      return
+ 10   ipar(7) = ipar(7) + 1
+      ipar(13) = ipar(13) + 1
+      if (lp) then
+         do i = 1, n
+            w(n+i) = rhs(i) - w(i)
+         enddo
+         ipar(1) = 3
+         ipar(10) = 2
+         return
+      else
+         do i = 1, n
+            w(i) = rhs(i) - w(i)
+         enddo
+      endif
+      fpar(11) = fpar(11) + n
+c
+ 20   alpha = sqrt(distdot(n,w,1,w,1))
+      fpar(11) = fpar(11) + 2*n
+      if (ipar(7).eq.1 .and. ipar(3).ne.999) then
+         if (abs(ipar(3)).eq.2) then
+            fpar(4) = fpar(1) * sqrt(distdot(n,rhs,1,rhs,1)) + fpar(2)
+            fpar(11) = fpar(11) + 2*n
+         else
+            fpar(4) = fpar(1) * alpha + fpar(2)
+         endif
+         fpar(3) = alpha
+      endif
+      fpar(5) = alpha
+      w(vrn+1) = alpha
+      if (alpha.le.fpar(4) .and. ipar(3).ge.0 .and. ipar(3).ne.999) then
+         ipar(1) = 0
+         fpar(6) = alpha
+         goto 300
+      endif
+      alpha = one / alpha
+      do ii = 1, n
+         w(ii) = alpha * w(ii)
+      enddo
+      fpar(11) = fpar(11) + n
+c
+c     request for (1) right preconditioning
+c     (2) matrix vector multiplication
+c     (3) left preconditioning
+c
+ 110  k = k + 1
+      if (rp) then
+         ipar(1) = 5
+         ipar(8) = k*n - n + 1
+         if (lp) then
+            ipar(9) = k*n + 1
+         else
+            ipar(9) = idx + 1
+         endif
+         ipar(10) = 3
+         return
+      endif
+c
+ 30   ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = (k-1)*n + 1
+      endif
+      if (lp) then
+         ipar(9) = idx + 1
+      else
+         ipar(9) = 1 + k*n
+      endif
+      ipar(10) = 4
+      return
+c
+ 40   if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = k*n + 1
+         ipar(10) = 5
+         return
+      endif
+c
+c     Modified Gram-Schmidt orthogonalization procedure
+c     temporary pointer 'ptr' is pointing to the current column of the
+c     Hessenberg matrix. 'p2' points to the new basis vector
+c
+ 50   ipar(7) = ipar(7) + 1
+      ptr = k * (k - 1) / 2 + hess
+      p2 = ipar(9)
+      call mgsro(.false.,n,n,k+1,k+1,fpar(11),w,w(ptr+1),
+     $     ipar(12))
+      if (ipar(12).lt.0) goto 200
+c
+c     apply previous Givens rotations and generate a new one to eliminate
+c     the subdiagonal element.
+c
+      p2 = ptr + 1
+      do i = 1, k-1
+         ptr = p2
+         p2 = p2 + 1
+         alpha = w(ptr)
+         c = w(vc+i)
+         s = w(vs+i)
+         w(ptr) = c * alpha + s * w(p2)
+         w(p2) = c * w(p2) - s * alpha
+      enddo
+      call givens(w(p2), w(p2+1), c, s)
+      w(vc+k) = c
+      w(vs+k) = s
+      p2 = vrn + k
+      alpha = - s * w(p2)
+      w(p2) = c * w(p2)
+      w(p2+1) = alpha
+c
+c     end of one Arnoldi iteration, alpha will store the estimated
+c     residual norm at current stage
+c
+      fpar(11) = fpar(11) + 6*k + 2
+      alpha = abs(alpha)
+      fpar(5) = alpha
+      if (k.lt.m .and. .not.(ipar(3).ge.0 .and. alpha.le.fpar(4))
+     +     .and. (ipar(6).le.0 .or. ipar(7).lt.ipar(6))) goto 110
+c
+c     update the approximate solution, first solve the upper triangular
+c     system, temporary pointer ptr points to the Hessenberg matrix,
+c     p2 points to the right-hand-side (also the solution) of the system.
+c
+ 200  ptr = hess + k * (k + 1) / 2
+      p2 = vrn + k
+      if (w(ptr).eq.zero) then
+c
+c     if the diagonal elements of the last column is zero, reduce k by 1
+c     so that a smaller trianguler system is solved [It should only
+c     happen when the matrix is singular, and at most once!]
+c
+         k = k - 1
+         if (k.gt.0) then
+            goto 200
+         else
+            ipar(1) = -3
+            ipar(12) = -4
+            goto 300
+         endif
+      endif
+      w(p2) = w(p2) / w(ptr)
+      do i = k-1, 1, -1
+         ptr = ptr - i - 1
+         do ii = 1, i
+            w(vrn+ii) = w(vrn+ii) - w(p2) * w(ptr+ii)
+         enddo
+         p2 = p2 - 1
+         w(p2) = w(p2) / w(ptr)
+      enddo
+c
+      do ii = 1, n
+         w(ii) = w(ii) * w(p2)
+      enddo
+      do i = 1, k-1
+         ptr = i*n
+         p2 = p2 + 1
+         do ii = 1, n
+            w(ii) = w(ii) + w(p2) * w(ptr+ii)
+         enddo
+      enddo
+      fpar(11) = fpar(11) + 2*k*n - n + k*(k+1)
+c
+      if (rp) then
+         ipar(1) = 5
+         ipar(8) = 1
+         ipar(9) = idx + 1
+         ipar(10) = 6
+         return
+      endif
+c
+ 60   if (rp) then
+         do i = 1, n
+            sol(i) = sol(i) + w(idx+i)
+         enddo
+      else
+         do i = 1, n
+            sol(i) = sol(i) + w(i)
+         enddo
+      endif
+      fpar(11) = fpar(11) + n
+c
+c     process the complete stopping criteria
+c
+      if (ipar(3).eq.999) then
+         ipar(1) = 10
+         ipar(8) = -1
+         ipar(9) = idx + 1
+         ipar(10) = 7
+         return
+      else if (ipar(3).lt.0) then
+         if (ipar(7).le.m+1) then
+            fpar(3) = abs(w(vrn+1))
+            if (ipar(3).eq.-1) fpar(4) = fpar(1)*fpar(3)+fpar(2)
+         endif
+         fpar(6) = abs(w(vrn+k))
+      else
+         fpar(6) = fpar(5)
+      endif
+c
+c     do we need to restart ?
+c
+ 70   if (ipar(12).ne.0) then
+         ipar(1) = -3
+         goto 300
+      endif
+      if ((ipar(7).lt.ipar(6) .or. ipar(6).le.0) .and.
+     +     ((ipar(3).eq.999.and.ipar(11).eq.0) .or.
+     +     (ipar(3).ne.999.and.fpar(6).gt.fpar(4)))) goto 100
+c
+c     termination, set error code, compute convergence rate
+c
+      if (ipar(1).gt.0) then
+         if (ipar(3).eq.999 .and. ipar(11).eq.1) then
+            ipar(1) = 0
+         else if (ipar(3).ne.999 .and. fpar(6).le.fpar(4)) then
+            ipar(1) = 0
+         else if (ipar(7).ge.ipar(6) .and. ipar(6).gt.0) then
+            ipar(1) = -1
+         else
+            ipar(1) = -10
+         endif
+      endif
+ 300  if (fpar(3).ne.zero .and. fpar(6).ne.zero .and.
+     +     ipar(7).gt.ipar(13)) then
+         fpar(7) = log10(fpar(3) / fpar(6)) / dble(ipar(7)-ipar(13))
+      else
+         fpar(7) = zero
+      endif
+      return
+      end
+c-----end-of-gmres
+c-----------------------------------------------------------------------
+      subroutine dqgmres(n, rhs, sol, ipar, fpar, w)
+      implicit none
+      integer n, ipar(16)
+      real*8 rhs(n), sol(n), fpar(16), w(*)
+c-----------------------------------------------------------------------
+c     DQGMRES -- Flexible Direct version of Quasi-General Minimum
+c     Residual method. The right preconditioning can be varied from
+c     step to step.
+c
+c     Work space used = n + lb * (2*n+4)
+c     where lb = ipar(5) + 1 (default 16 if ipar(5) <= 1)
+c-----------------------------------------------------------------------
+c     local variables
+c
+      real*8 one,zero,deps
+      parameter(one=1.0D0,zero=0.0D0)
+      parameter(deps=1.0D-33)
+c
+      integer i,ii,j,jp1,j0,k,ptrw,ptrv,iv,iw,ic,is,ihm,ihd,lb,ptr
+      real*8 alpha,beta,psi,c,s,distdot
+      logical lp,rp,full
+      external distdot,bisinit
+      save
+c
+c     where to go
+c
+      if (ipar(1).le.0) ipar(10) = 0
+      goto (10, 20, 40, 50, 60, 70) ipar(10)
+c
+c     locations of the work arrays. The arrangement is as follows:
+c     w(1:n) -- temporary storage for the results of the preconditioning
+c     w(iv+1:iw) -- the V's
+c     w(iw+1:ic) -- the W's
+c     w(ic+1:is) -- the COSINEs of the Givens rotations
+c     w(is+1:ihm) -- the SINEs of the Givens rotations
+c     w(ihm+1:ihd) -- the last column of the Hessenberg matrix
+c     w(ihd+1:i) -- the inverse of the diagonals of the Hessenberg matrix
+c
+      if (ipar(5).le.1) then
+         lb = 16
+      else
+         lb = ipar(5) + 1
+      endif
+      iv = n
+      iw = iv + lb * n
+      ic = iw + lb * n
+      is = ic + lb
+      ihm = is + lb
+      ihd = ihm + lb
+      i = ihd + lb
+c
+c     parameter check, initializations
+c
+      full = .false.
+      call bisinit(ipar,fpar,i,1,lp,rp,w)
+      if (ipar(1).lt.0) return
+      ipar(1) = 1
+      if (lp) then
+         do ii = 1, n
+            w(iv+ii) = sol(ii)
+         enddo
+         ipar(8) = iv+1
+         ipar(9) = 1
+      else
+         do ii = 1, n
+            w(ii) = sol(ii)
+         enddo
+         ipar(8) = 1
+         ipar(9) = iv+1
+      endif
+      ipar(10) = 1
+      return
+c
+ 10   ipar(7) = ipar(7) + 1
+      ipar(13) = ipar(13) + 1
+      if (lp) then
+         do i = 1, n
+            w(i) = rhs(i) - w(i)
+         enddo
+         ipar(1) = 3
+         ipar(8) = 1
+         ipar(9) = iv+1
+         ipar(10) = 2
+         return
+      else
+         do i = 1, n
+            w(iv+i) = rhs(i) - w(iv+i)
+         enddo
+      endif
+      fpar(11) = fpar(11) + n
+c
+ 20   alpha = sqrt(distdot(n, w(iv+1), 1, w(iv+1), 1))
+      fpar(11) = fpar(11) + (n + n)
+      if (abs(ipar(3)).eq.2) then
+         fpar(4) = fpar(1) * sqrt(distdot(n,rhs,1,rhs,1)) + fpar(2)
+         fpar(11) = fpar(11) + 2*n
+      else if (ipar(3).ne.999) then
+         fpar(4) = fpar(1) * alpha + fpar(2)
+      endif
+      fpar(3) = alpha
+      fpar(5) = alpha
+      psi = alpha
+      if (alpha.le.fpar(4)) then
+         ipar(1) = 0
+         fpar(6) = alpha
+         goto 80
+      endif
+      alpha = one / alpha
+      do i = 1, n
+         w(iv+i) = w(iv+i) * alpha
+      enddo
+      fpar(11) = fpar(11) + n
+      j = 0
+c
+c     iterations start here
+c
+ 30   j = j + 1
+      if (j.gt.lb) j = j - lb
+      jp1 = j + 1
+      if (jp1.gt.lb) jp1 = jp1 - lb
+      ptrv = iv + (j-1)*n + 1
+      ptrw = iv + (jp1-1)*n + 1
+      if (.not.full) then
+         if (j.gt.jp1) full = .true.
+      endif
+      if (full) then
+         j0 = jp1+1
+         if (j0.gt.lb) j0 = j0 - lb
+      else
+         j0 = 1
+      endif
+c
+c     request the caller to perform matrix-vector multiplication and
+c     preconditioning
+c
+      if (rp) then
+         ipar(1) = 5
+         ipar(8) = ptrv
+         ipar(9) = ptrv + iw - iv
+         ipar(10) = 3
+         return
+      else
+         do i = 0, n-1
+            w(ptrv+iw-iv+i) = w(ptrv+i)
+         enddo
+      endif
+c
+ 40   ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = ptrv
+      endif
+      if (lp) then
+         ipar(9) = 1
+      else
+         ipar(9) = ptrw
+      endif
+      ipar(10) = 4
+      return
+c
+ 50   if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = ptrw
+         ipar(10) = 5
+         return
+      endif
+c
+c     compute the last column of the Hessenberg matrix
+c     modified Gram-schmidt procedure, orthogonalize against (lb-1)
+c     previous vectors
+c
+ 60   continue
+      call mgsro(full,n,n,lb,jp1,fpar(11),w(iv+1),w(ihm+1),
+     $     ipar(12))
+      if (ipar(12).lt.0) then
+         ipar(1) = -3
+         goto 80
+      endif
+      beta = w(ihm+jp1)
+c
+c     incomplete factorization (QR factorization through Givens rotations)
+c     (1) apply previous rotations [(lb-1) of them]
+c     (2) generate a new rotation
+c
+      if (full) then
+         w(ihm+jp1) = w(ihm+j0) * w(is+jp1)
+         w(ihm+j0) = w(ihm+j0) * w(ic+jp1)
+      endif
+      i = j0
+      do while (i.ne.j)
+         k = i+1
+         if (k.gt.lb) k = k - lb
+         c = w(ic+i)
+         s = w(is+i)
+         alpha = w(ihm+i)
+         w(ihm+i) = c * alpha + s * w(ihm+k)
+         w(ihm+k) = c * w(ihm+k) - s * alpha
+         i = k
+      enddo
+      call givens(w(ihm+j), beta, c, s)
+      if (full) then
+         fpar(11) = fpar(11) + 6 * lb
+      else
+         fpar(11) = fpar(11) + 6 * j
+      endif
+c
+c     detect whether diagonal element of this column is zero
+c
+      if (abs(w(ihm+j)).lt.deps) then
+         ipar(1) = -3
+         goto 80
+      endif
+      w(ihd+j) = one / w(ihm+j)
+      w(ic+j) = c
+      w(is+j) = s
+c
+c     update the W's (the conjugate directions) -- essentially this is one
+c     step of triangular solve.
+c
+      ptrw = iw+(j-1)*n + 1
+      if (full) then
+         do i = j+1, lb
+            alpha = -w(ihm+i)*w(ihd+i)
+            ptr = iw+(i-1)*n+1
+            do ii = 0, n-1
+               w(ptrw+ii) = w(ptrw+ii) + alpha * w(ptr+ii)
+            enddo
+         enddo
+      endif
+      do i = 1, j-1
+         alpha = -w(ihm+i)*w(ihd+i)
+         ptr = iw+(i-1)*n+1
+         do ii = 0, n-1
+            w(ptrw+ii) = w(ptrw+ii) + alpha * w(ptr+ii)
+         enddo
+      enddo
+c
+c     update the solution to the linear system
+c
+      alpha = psi * c * w(ihd+j)
+      psi = - s * psi
+      do i = 1, n
+         sol(i) = sol(i) + alpha * w(ptrw-1+i)
+      enddo
+      if (full) then
+         fpar(11) = fpar(11) + lb * (n+n)
+      else
+         fpar(11) = fpar(11) + j * (n+n)
+      endif
+c
+c     determine whether to continue,
+c     compute the desired error/residual norm
+c
+      ipar(7) = ipar(7) + 1
+      fpar(5) = abs(psi)
+      if (ipar(3).eq.999) then
+         ipar(1) = 10
+         ipar(8) = -1
+         ipar(9) = 1
+         ipar(10) = 6
+         return
+      endif
+      if (ipar(3).lt.0) then
+         alpha = abs(alpha)
+         if (ipar(7).eq.2 .and. ipar(3).eq.-1) then
+            fpar(3) = alpha*sqrt(distdot(n, w(ptrw), 1, w(ptrw), 1))
+            fpar(4) = fpar(1) * fpar(3) + fpar(2)
+            fpar(6) = fpar(3)
+         else
+            fpar(6) = alpha*sqrt(distdot(n, w(ptrw), 1, w(ptrw), 1))
+         endif
+         fpar(11) = fpar(11) + 2 * n
+      else
+         fpar(6) = fpar(5)
+      endif
+      if (ipar(1).ge.0 .and. fpar(6).gt.fpar(4) .and. (ipar(6).le.0
+     +     .or. ipar(7).lt.ipar(6))) goto 30
+ 70   if (ipar(3).eq.999 .and. ipar(11).eq.0) goto 30
+c
+c     clean up the iterative solver
+c
+ 80   fpar(7) = zero
+      if (fpar(3).ne.zero .and. fpar(6).ne.zero .and.
+     +     ipar(7).gt.ipar(13))
+     +     fpar(7) = log10(fpar(3) / fpar(6)) / dble(ipar(7)-ipar(13))
+      if (ipar(1).gt.0) then
+         if (ipar(3).eq.999 .and. ipar(11).ne.0) then
+            ipar(1) = 0
+         else if (fpar(6).le.fpar(4)) then
+            ipar(1) = 0
+         else if (ipar(6).gt.0 .and. ipar(7).ge.ipar(6)) then
+            ipar(1) = -1
+         else
+            ipar(1) = -10
+         endif
+      endif
+      return
+      end
+c-----end-of-dqgmres
+c-----------------------------------------------------------------------
+      subroutine fgmres(n, rhs, sol, ipar, fpar, w)
+      implicit none
+      integer n, ipar(16)
+      real*8 rhs(n), sol(n), fpar(16), w(*)
+c-----------------------------------------------------------------------
+c     This a version of FGMRES implemented with reverse communication.
+c
+c     ipar(5) == the dimension of the Krylov subspace
+c
+c     the space of the `w' is used as follows:
+c     >> V: the bases for the Krylov subspace, size n*(m+1);
+c     >> W: the above bases after (left-)multiplying with the
+c     right-preconditioner inverse, size m*n;
+c     >> a temporary vector of size n;
+c     >> the Hessenberg matrix, only the upper triangular portion
+c     of the matrix is stored, size (m+1)*m/2 + 1
+c     >> three vectors, first two are of size m, they are the cosine
+c     and sine of the Givens rotations, the third one holds the
+c     residuals, it is of size m+1.
+c
+c     TOTAL SIZE REQUIRED == n*(2m+1) + (m+1)*m/2 + 3*m + 2
+c     Note: m == ipar(5). The default value for this is 15 if
+c     ipar(5) <= 1.
+c-----------------------------------------------------------------------
+c     external functions used
+c
+      real*8 distdot
+      external distdot
+c
+      real*8 one, zero
+      parameter(one=1.0D0, zero=0.0D0)
+c
+c     local variables, ptr and p2 are temporary pointers,
+c     hess points to the Hessenberg matrix,
+c     vc, vs point to the cosines and sines of the Givens rotations
+c     vrn points to the vectors of residual norms, more precisely
+c     the right hand side of the least square problem solved.
+c
+      integer i,ii,idx,iz,k,m,ptr,p2,hess,vc,vs,vrn
+      real*8 alpha, c, s
+      logical lp, rp
+      save
+c
+c     check the status of the call
+c
+      if (ipar(1).le.0) ipar(10) = 0
+      goto (10, 20, 30, 40, 50, 60) ipar(10)
+c
+c     initialization
+c
+      if (ipar(5).le.1) then
+         m = 15
+      else
+         m = ipar(5)
+      endif
+      idx = n * (m+1)
+      iz = idx + n
+      hess = iz + n*m
+      vc = hess + (m+1) * m / 2 + 1
+      vs = vc + m
+      vrn = vs + m
+      i = vrn + m + 1
+      call bisinit(ipar,fpar,i,1,lp,rp,w)
+      if (ipar(1).lt.0) return
+c
+c     request for matrix vector multiplication A*x in the initialization
+c
+ 100  ipar(1) = 1
+      ipar(8) = n+1
+      ipar(9) = 1
+      ipar(10) = 1
+      k = 0
+      do ii = 1, n
+         w(ii+n) = sol(ii)
+      enddo
+      return
+ 10   ipar(7) = ipar(7) + 1
+      ipar(13) = ipar(13) + 1
+      fpar(11) = fpar(11) + n
+      if (lp) then
+         do i = 1, n
+            w(n+i) = rhs(i) - w(i)
+         enddo
+         ipar(1) = 3
+         ipar(10) = 2
+         return
+      else
+         do i = 1, n
+            w(i) = rhs(i) - w(i)
+         enddo
+      endif
+c
+ 20   alpha = sqrt(distdot(n,w,1,w,1))
+      fpar(11) = fpar(11) + n + n
+      if (ipar(7).eq.1 .and. ipar(3).ne.999) then
+         if (abs(ipar(3)).eq.2) then
+            fpar(4) = fpar(1) * sqrt(distdot(n,rhs,1,rhs,1)) + fpar(2)
+            fpar(11) = fpar(11) + 2*n
+         else
+            fpar(4) = fpar(1) * alpha + fpar(2)
+         endif
+         fpar(3) = alpha
+      endif
+      fpar(5) = alpha
+      w(vrn+1) = alpha
+      if (alpha.le.fpar(4) .and. ipar(3).ge.0 .and. ipar(3).ne.999) then
+         ipar(1) = 0
+         fpar(6) = alpha
+         goto 300
+      endif
+      alpha = one / alpha
+      do ii = 1, n
+         w(ii) = w(ii) * alpha
+      enddo
+      fpar(11) = fpar(11) + n
+c
+c     request for (1) right preconditioning
+c     (2) matrix vector multiplication
+c     (3) left preconditioning
+c
+ 110  k = k + 1
+      if (rp) then
+         ipar(1) = 5
+         ipar(8) = k*n - n + 1
+         ipar(9) = iz + ipar(8)
+         ipar(10) = 3
+         return
+      else
+         do ii = 0, n-1
+            w(iz+k*n-ii) = w(k*n-ii)
+         enddo
+      endif
+c
+ 30   ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = (k-1)*n + 1
+      endif
+      if (lp) then
+         ipar(9) = idx + 1
+      else
+         ipar(9) = 1 + k*n
+      endif
+      ipar(10) = 4
+      return
+c
+ 40   if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = k*n + 1
+         ipar(10) = 5
+         return
+      endif
+c
+c     Modified Gram-Schmidt orthogonalization procedure
+c     temporary pointer 'ptr' is pointing to the current column of the
+c     Hessenberg matrix. 'p2' points to the new basis vector
+c
+ 50   ptr = k * (k - 1) / 2 + hess
+      p2 = ipar(9)
+      ipar(7) = ipar(7) + 1
+      call mgsro(.false.,n,n,k+1,k+1,fpar(11),w,w(ptr+1),
+     $     ipar(12))
+      if (ipar(12).lt.0) goto 200
+c
+c     apply previous Givens rotations and generate a new one to eliminate
+c     the subdiagonal element.
+c
+      p2 = ptr + 1
+      do i = 1, k-1
+         ptr = p2
+         p2 = p2 + 1
+         alpha = w(ptr)
+         c = w(vc+i)
+         s = w(vs+i)
+         w(ptr) = c * alpha + s * w(p2)
+         w(p2) = c * w(p2) - s * alpha
+      enddo
+      call givens(w(p2), w(p2+1), c, s)
+      w(vc+k) = c
+      w(vs+k) = s
+      p2 = vrn + k
+      alpha = - s * w(p2)
+      w(p2) = c * w(p2)
+      w(p2+1) = alpha
+      fpar(11) = fpar(11) + 6 * k
+c
+c     end of one Arnoldi iteration, alpha will store the estimated
+c     residual norm at current stage
+c
+      alpha = abs(alpha)
+      fpar(5) = alpha
+      if (k.lt.m .and. .not.(ipar(3).ge.0 .and. alpha.le.fpar(4))
+     +      .and. (ipar(6).le.0 .or. ipar(7).lt.ipar(6))) goto 110
+c
+c     update the approximate solution, first solve the upper triangular
+c     system, temporary pointer ptr points to the Hessenberg matrix,
+c     p2 points to the right-hand-side (also the solution) of the system.
+c
+ 200  ptr = hess + k * (k + 1 ) / 2
+      p2 = vrn + k
+      if (w(ptr).eq.zero) then
+c
+c     if the diagonal elements of the last column is zero, reduce k by 1
+c     so that a smaller trianguler system is solved [It should only
+c     happen when the matrix is singular!]
+c
+         k = k - 1
+         if (k.gt.0) then
+            goto 200
+         else
+            ipar(1) = -3
+            ipar(12) = -4
+            goto 300
+         endif
+      endif
+      w(p2) = w(p2) / w(ptr)
+      do i = k-1, 1, -1
+         ptr = ptr - i - 1
+         do ii = 1, i
+            w(vrn+ii) = w(vrn+ii) - w(p2) * w(ptr+ii)
+         enddo
+         p2 = p2 - 1
+         w(p2) = w(p2) / w(ptr)
+      enddo
+c
+      do i = 0, k-1
+         ptr = iz+i*n
+         do ii = 1, n
+            sol(ii) = sol(ii) + w(p2)*w(ptr+ii)
+         enddo
+         p2 = p2 + 1
+      enddo
+      fpar(11) = fpar(11) + 2*k*n + k*(k+1)
+c
+c     process the complete stopping criteria
+c
+      if (ipar(3).eq.999) then
+         ipar(1) = 10
+         ipar(8) = -1
+         ipar(9) = idx + 1
+         ipar(10) = 6
+         return
+      else if (ipar(3).lt.0) then
+         if (ipar(7).le.m+1) then
+            fpar(3) = abs(w(vrn+1))
+            if (ipar(3).eq.-1) fpar(4) = fpar(1)*fpar(3)+fpar(2)
+         endif
+         fpar(6) = abs(w(vrn+k))
+      else if (ipar(3).ne.999) then
+         fpar(6) = fpar(5)
+      endif
+c
+c     do we need to restart ?
+c
+ 60   if (ipar(12).ne.0) then
+         ipar(1) = -3
+         goto 300
+      endif
+      if ((ipar(7).lt.ipar(6) .or. ipar(6).le.0).and.
+     +     ((ipar(3).eq.999.and.ipar(11).eq.0) .or.
+     +     (ipar(3).ne.999.and.fpar(6).gt.fpar(4)))) goto 100
+c
+c     termination, set error code, compute convergence rate
+c
+      if (ipar(1).gt.0) then
+         if (ipar(3).eq.999 .and. ipar(11).eq.1) then
+            ipar(1) = 0
+         else if (ipar(3).ne.999 .and. fpar(6).le.fpar(4)) then
+            ipar(1) = 0
+         else if (ipar(7).ge.ipar(6) .and. ipar(6).gt.0) then
+            ipar(1) = -1
+         else
+            ipar(1) = -10
+         endif
+      endif
+ 300  if (fpar(3).ne.zero .and. fpar(6).ne.zero .and.
+     $     ipar(7).gt.ipar(13)) then
+         fpar(7) = log10(fpar(3) / fpar(6)) / dble(ipar(7)-ipar(13))
+      else
+         fpar(7) = zero
+      endif
+      return
+      end
+c-----end-of-fgmres
+c-----------------------------------------------------------------------
+      subroutine dbcg (n,rhs,sol,ipar,fpar,w)
+      implicit none
+      integer n,ipar(16)
+      real*8 rhs(n), sol(n), fpar(16), w(n,*)
+c-----------------------------------------------------------------------
+c Quasi GMRES method for solving a linear
+c system of equations a * sol = y.  double precision version.
+c this version is without restarting and without preconditioning.
+c parameters :
+c -----------
+c n     = dimension of the problem
+c
+c y     = w(:,1) a temporary storage used for various operations
+c z     = w(:,2) a work vector of length n.
+c v     = w(:,3:4) size n x 2
+c w     = w(:,5:6) size n x 2
+c p     = w(:,7:9) work array of dimension n x 3
+c del x = w(:,10)  accumulation of the changes in solution
+c tmp   = w(:,11)  a temporary vector used to hold intermediate result of
+c                  preconditioning, etc.
+c
+c sol   = the solution of the problem . at input sol must contain an
+c         initial guess to the solution.
+c    ***  note:   y is destroyed on return.
+c
+c-----------------------------------------------------------------------
+c subroutines and functions called:
+c 1) matrix vector multiplication and preconditioning through reverse
+c     communication
+c
+c 2) implu, uppdir, distdot (blas)
+c-----------------------------------------------------------------------
+c aug. 1983  version.    author youcef saad. yale university computer
+c science dept. some  changes made july 3, 1986.
+c references: siam j. sci. stat. comp., vol. 5, pp. 203-228 (1984)
+c-----------------------------------------------------------------------
+c     local variables
+c
+      real*8 one,zero
+      parameter(one=1.0D0,zero=0.0D0)
+c
+      real*8 t,sqrt,distdot,ss,res,beta,ss1,delta,x,zeta,umm
+      integer k,j,i,i2,ip2,ju,lb,lbm1,np,indp
+      logical lp,rp,full, perm(3)
+      real*8 ypiv(3),u(3),usav(3)
+      external tidycg
+      save
+c
+c     where to go
+c
+      if (ipar(1).le.0) ipar(10) = 0
+      goto (110, 120, 130, 140, 150, 160, 170, 180, 190, 200) ipar(10)
+c
+c     initialization, parameter checking, clear the work arrays
+c
+      call bisinit(ipar,fpar,11*n,1,lp,rp,w)
+      if (ipar(1).lt.0) return
+      perm(1) = .false.
+      perm(2) = .false.
+      perm(3) = .false.
+      usav(1) = zero
+      usav(2) = zero
+      usav(3) = zero
+      ypiv(1) = zero
+      ypiv(2) = zero
+      ypiv(3) = zero
+c-----------------------------------------------------------------------
+c     initialize constants for outer loop :
+c-----------------------------------------------------------------------
+      lb = 3
+      lbm1 = 2
+c
+c     get initial residual vector and norm
+c
+      ipar(1) = 1
+      ipar(8) = 1
+      ipar(9) = 1 + n
+      do i = 1, n
+         w(i,1) = sol(i)
+      enddo
+      ipar(10) = 1
+      return
+ 110  ipar(7) = ipar(7) + 1
+      ipar(13) = ipar(13) + 1
+      if (lp) then
+         do i = 1, n
+            w(i,1) = rhs(i) - w(i,2)
+         enddo
+         ipar(1) = 3
+         ipar(8) = 1
+         ipar(9) = n+n+1
+         ipar(10) = 2
+         return
+      else
+         do i = 1, n
+            w(i,3) = rhs(i) - w(i,2)
+         enddo
+      endif
+      fpar(11) = fpar(11) + n
+c
+ 120  fpar(3) = sqrt(distdot(n,w(1,3),1,w(1,3),1))
+      fpar(11) = fpar(11) + n + n
+      fpar(5) = fpar(3)
+      fpar(7) = fpar(3)
+      zeta = fpar(3)
+      if (abs(ipar(3)).eq.2) then
+         fpar(4) = fpar(1) * sqrt(distdot(n,rhs,1,rhs,1)) + fpar(2)
+         fpar(11) = fpar(11) + 2*n
+      else if (ipar(3).ne.999) then
+         fpar(4) = fpar(1) * zeta + fpar(2)
+      endif
+      if (ipar(3).ge.0.and.fpar(5).le.fpar(4)) then
+         fpar(6) = fpar(5)
+         goto 900
+      endif
+c
+c     normalize first arnoldi vector
+c
+      t = one/zeta
+      do 22 k=1,n
+         w(k,3) = w(k,3)*t
+         w(k,5) = w(k,3)
+ 22   continue
+      fpar(11) = fpar(11) + n
+c
+c     initialize constants for main loop
+c
+      beta = zero
+      delta = zero
+      i2 = 1
+      indp = 0
+      i = 0
+c
+c     main loop: i = index of the loop.
+c
+c-----------------------------------------------------------------------
+ 30   i = i + 1
+c
+      if (rp) then
+         ipar(1) = 5
+         ipar(8) = (1+i2)*n+1
+         if (lp) then
+            ipar(9) = 1
+         else
+            ipar(9) = 10*n + 1
+         endif
+         ipar(10) = 3
+         return
+      endif
+c
+ 130  ipar(1) = 1
+      if (rp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = (1+i2)*n + 1
+      endif
+      if (lp) then
+         ipar(9) = 10*n + 1
+      else
+         ipar(9) = 1
+      endif
+      ipar(10) = 4
+      return
+c
+ 140  if (lp) then
+         ipar(1) = 3
+         ipar(8) = ipar(9)
+         ipar(9) = 1
+         ipar(10) = 5
+         return
+      endif
+c
+c     A^t * x
+c
+ 150  ipar(7) = ipar(7) + 1
+      if (lp) then
+         ipar(1) = 4
+         ipar(8) = (3+i2)*n + 1
+         if (rp) then
+            ipar(9) = n + 1
+         else
+            ipar(9) = 10*n + 1
+         endif
+         ipar(10) = 6
+         return
+      endif
+c
+ 160  ipar(1) = 2
+      if (lp) then
+         ipar(8) = ipar(9)
+      else
+         ipar(8) = (3+i2)*n + 1
+      endif
+      if (rp) then
+         ipar(9) = 10*n + 1
+      else
+         ipar(9) = n + 1
+      endif
+      ipar(10) = 7
+      return
+c
+ 170  if (rp) then
+         ipar(1) = 6
+         ipar(8) = ipar(9)
+         ipar(9) = n + 1
+         ipar(10) = 8
+         return
+      endif
+c-----------------------------------------------------------------------
+c     orthogonalize current v against previous v's and
+c     determine relevant part of i-th column of u(.,.) the
+c     upper triangular matrix --
+c-----------------------------------------------------------------------
+ 180  ipar(7) = ipar(7) + 1
+      u(1) = zero
+      ju = 1
+      k = i2
+      if (i .le. lbm1) ju = 0
+      if (i .lt. lb) k = 0
+ 31   if (k .eq. lbm1) k=0
+      k=k+1
+c
+      if (k .ne. i2) then
+         ss  = delta
+         ss1 = beta
+         ju = ju + 1
+         u(ju) = ss
+      else
+         ss = distdot(n,w(1,1),1,w(1,4+k),1)
+         fpar(11) = fpar(11) + 2*n
+         ss1= ss
+         ju = ju + 1
+         u(ju) = ss
+      endif
+c
+      do 32  j=1,n
+         w(j,1) = w(j,1) - ss*w(j,k+2)
+         w(j,2) = w(j,2) - ss1*w(j,k+4)
+ 32   continue
+      fpar(11) = fpar(11) + 4*n
+c
+      if (k .ne. i2) goto 31
+c
+c     end of Mod. Gram. Schmidt loop
+c
+      t = distdot(n,w(1,2),1,w(1,1),1)
+c
+      beta   = sqrt(abs(t))
+      delta  = t/beta
+c
+      ss = one/beta
+      ss1 = one/ delta
+c
+c     normalize and insert new vectors
+c
+      ip2 = i2
+      if (i2 .eq. lbm1) i2=0
+      i2=i2+1
+c
+      do 315 j=1,n
+         w(j,i2+2)=w(j,1)*ss
+         w(j,i2+4)=w(j,2)*ss1
+ 315  continue
+      fpar(11) = fpar(11) + 4*n
+c-----------------------------------------------------------------------
+c     end of orthogonalization.
+c     now compute the coefficients u(k) of the last
+c     column of the  l . u  factorization of h .
+c-----------------------------------------------------------------------
+      np = min0(i,lb)
+      full = (i .ge. lb)
+      call implu(np, umm, beta, ypiv, u, perm, full)
+c-----------------------------------------------------------------------
+c     update conjugate directions and solution
+c-----------------------------------------------------------------------
+      do 33 k=1,n
+         w(k,1) = w(k,ip2+2)
+ 33   continue
+      call uppdir(n, w(1,7), np, lb, indp, w, u, usav, fpar(11))
+c-----------------------------------------------------------------------
+      if (i .eq. 1) goto 34
+      j = np - 1
+      if (full) j = j-1
+      if (.not.perm(j)) zeta = -zeta*ypiv(j)
+ 34   x = zeta/u(np)
+      if (perm(np))goto 36
+      do 35 k=1,n
+         w(k,10) = w(k,10) + x*w(k,1)
+ 35   continue
+      fpar(11) = fpar(11) + 2 * n
+c-----------------------------------------------------------------------
+ 36   if (ipar(3).eq.999) then
+         ipar(1) = 10
+         ipar(8) = 9*n + 1
+         ipar(9) = 10*n + 1
+         ipar(10) = 9
+         return
+      endif
+      res = abs(beta*zeta/umm)
+      fpar(5) = res * sqrt(distdot(n, w(1,i2+2), 1, w(1,i2+2), 1))
+      fpar(11) = fpar(11) + 2 * n
+      if (ipar(3).lt.0) then
+         fpar(6) = x * sqrt(distdot(n,w,1,w,1))
+         fpar(11) = fpar(11) + 2 * n
+         if (ipar(7).le.3) then
+            fpar(3) = fpar(6)
+            if (ipar(3).eq.-1) then
+               fpar(4) = fpar(1) * sqrt(fpar(3)) + fpar(2)
+            endif
+         endif
+      else
+         fpar(6) = fpar(5)
+      endif
+c---- convergence test -----------------------------------------------
+ 190  if (ipar(3).eq.999.and.ipar(11).eq.0) then
+         goto 30
+      else if (fpar(6).gt.fpar(4) .and. (ipar(6).gt.ipar(7) .or.
+     +        ipar(6).le.0)) then
+         goto 30
+      endif
+c-----------------------------------------------------------------------
+c     here the fact that the last step is different is accounted for.
+c-----------------------------------------------------------------------
+      if (.not. perm(np)) goto 900
+      x = zeta/umm
+      do 40 k = 1,n
+         w(k,10) = w(k,10) + x*w(k,1)
+ 40   continue
+      fpar(11) = fpar(11) + 2 * n
+c
+c     right preconditioning and clean-up jobs
+c
+ 900  if (rp) then
+         if (ipar(1).lt.0) ipar(12) = ipar(1)
+         ipar(1) = 5
+         ipar(8) = 9*n + 1
+         ipar(9) = ipar(8) + n
+         ipar(10) = 10
+         return
+      endif
+ 200  if (rp) then
+         call tidycg(n,ipar,fpar,sol,w(1,11))
+      else
+         call tidycg(n,ipar,fpar,sol,w(1,10))
+      endif
+      return
+      end
+c-----end-of-dbcg-------------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine implu(np,umm,beta,ypiv,u,permut,full)
+      real*8 umm,beta,ypiv(*),u(*),x, xpiv
+      logical full, perm, permut(*)
+      integer np,k,npm1
+c-----------------------------------------------------------------------
+c     performs implicitly one step of the lu factorization of a
+c     banded hessenberg matrix.
+c-----------------------------------------------------------------------
+      if (np .le. 1) goto 12
+      npm1 = np - 1
+c
+c     -- perform  previous step of the factorization-
+c
+      do 6 k=1,npm1
+         if (.not. permut(k)) goto 5
+         x=u(k)
+         u(k) = u(k+1)
+         u(k+1) = x
+ 5       u(k+1) = u(k+1) - ypiv(k)*u(k)
+ 6    continue
+c-----------------------------------------------------------------------
+c     now determine pivotal information to be used in the next call
+c-----------------------------------------------------------------------
+ 12   umm = u(np)
+      perm = (beta .gt. abs(umm))
+      if (.not. perm) goto 4
+      xpiv = umm / beta
+      u(np) = beta
+      goto 8
+ 4    xpiv = beta/umm
+ 8    permut(np) = perm
+      ypiv(np) = xpiv
+      if (.not. full) return
+c     shift everything up if full...
+      do 7 k=1,npm1
+         ypiv(k) = ypiv(k+1)
+         permut(k) = permut(k+1)
+ 7    continue
+      return
+c-----end-of-implu
+      end
+c-----------------------------------------------------------------------
+      subroutine uppdir(n,p,np,lbp,indp,y,u,usav,flops)
+      real*8 p(n,lbp), y(*), u(*), usav(*), x, flops
+      integer k,np,n,npm1,j,ju,indp,lbp
+c-----------------------------------------------------------------------
+c     updates the conjugate directions p given the upper part of the
+c     banded upper triangular matrix u.  u contains the non zero
+c     elements of the column of the triangular matrix..
+c-----------------------------------------------------------------------
+      real*8 zero
+      parameter(zero=0.0D0)
+c
+      npm1=np-1
+      if (np .le. 1) goto 12
+      j=indp
+      ju = npm1
+ 10   if (j .le. 0) j=lbp
+      x = u(ju) /usav(j)
+      if (x .eq. zero) goto 115
+      do 11 k=1,n
+         y(k) = y(k) - x*p(k,j)
+ 11   continue
+      flops = flops + 2*n
+ 115  j = j-1
+      ju = ju -1
+      if (ju .ge. 1) goto 10
+ 12   indp = indp + 1
+      if (indp .gt. lbp) indp = 1
+      usav(indp) = u(np)
+      do 13 k=1,n
+         p(k,indp) = y(k)
+ 13   continue
+ 208  return
+c-----------------------------------------------------------------------
+c-------end-of-uppdir---------------------------------------------------
+      end
+      subroutine givens(x,y,c,s)
+      real*8 x,y,c,s
+c-----------------------------------------------------------------------
+c     Given x and y, this subroutine generates a Givens' rotation c, s.
+c     And apply the rotation on (x,y) ==> (sqrt(x**2 + y**2), 0).
+c     (See P 202 of "matrix computation" by Golub and van Loan.)
+c-----------------------------------------------------------------------
+      real*8 t,one,zero
+      parameter (zero=0.0D0,one=1.0D0)
+c
+      if (x.eq.zero .and. y.eq.zero) then
+         c = one
+         s = zero
+      else if (abs(y).gt.abs(x)) then
+         t = x / y
+         x = sqrt(one+t*t)
+         s = sign(one / x, y)
+         c = t*s
+      else if (abs(y).le.abs(x)) then
+         t = y / x
+         y = sqrt(one+t*t)
+         c = sign(one / y, x)
+         s = t*c
+      else
+c
+c     X or Y must be an invalid floating-point number, set both to zero
+c
+         x = zero
+         y = zero
+         c = one
+         s = zero
+      endif
+      x = abs(x*y)
+c
+c     end of givens
+c
+      return
+      end
+c-----end-of-givens
+c-----------------------------------------------------------------------
+      logical function stopbis(n,ipar,mvpi,fpar,r,delx,sx)
+      implicit none
+      integer n,mvpi,ipar(16)
+      real*8 fpar(16), r(n), delx(n), sx, distdot
+      external distdot
+c-----------------------------------------------------------------------
+c     function for determining the stopping criteria. return value of
+c     true if the stopbis criteria is satisfied.
+c-----------------------------------------------------------------------
+      if (ipar(11) .eq. 1) then
+         stopbis = .true.
+      else
+         stopbis = .false.
+      endif
+      if (ipar(6).gt.0 .and. ipar(7).ge.ipar(6)) then
+         ipar(1) = -1
+         stopbis = .true.
+      endif
+      if (stopbis) return
+c
+c     computes errors
+c
+      fpar(5) = sqrt(distdot(n,r,1,r,1))
+      fpar(11) = fpar(11) + 2 * n
+      if (ipar(3).lt.0) then
+c
+c     compute the change in the solution vector
+c
+         fpar(6) = sx * sqrt(distdot(n,delx,1,delx,1))
+         fpar(11) = fpar(11) + 2 * n
+         if (ipar(7).lt.mvpi+mvpi+1) then
+c
+c     if this is the end of the first iteration, set fpar(3:4)
+c
+            fpar(3) = fpar(6)
+            if (ipar(3).eq.-1) then
+               fpar(4) = fpar(1) * fpar(3) + fpar(2)
+            endif
+         endif
+      else
+         fpar(6) = fpar(5)
+      endif
+c
+c     .. the test is struct this way so that when the value in fpar(6)
+c       is not a valid number, STOPBIS is set to .true.
+c
+      if (fpar(6).gt.fpar(4)) then
+         stopbis = .false.
+         ipar(11) = 0
+      else
+         stopbis = .true.
+         ipar(11) = 1
+      endif
+c
+      return
+      end
+c-----end-of-stopbis
+c-----------------------------------------------------------------------
+      subroutine tidycg(n,ipar,fpar,sol,delx)
+      implicit none
+      integer i,n,ipar(16)
+      real*8 fpar(16),sol(n),delx(n)
+c-----------------------------------------------------------------------
+c     Some common operations required before terminating the CG routines
+c-----------------------------------------------------------------------
+      real*8 zero
+      parameter(zero=0.0D0)
+c
+      if (ipar(12).ne.0) then
+         ipar(1) = ipar(12) 
+      else if (ipar(1).gt.0) then
+         if ((ipar(3).eq.999 .and. ipar(11).eq.1) .or.
+     +        fpar(6).le.fpar(4)) then
+            ipar(1) = 0
+         else if (ipar(7).ge.ipar(6) .and. ipar(6).gt.0) then
+            ipar(1) = -1
+         else
+            ipar(1) = -10
+         endif
+      endif
+      if (fpar(3).gt.zero .and. fpar(6).gt.zero .and.
+     +     ipar(7).gt.ipar(13)) then
+         fpar(7) = log10(fpar(3) / fpar(6)) / dble(ipar(7)-ipar(13))
+      else
+         fpar(7) = zero
+      endif
+      do i = 1, n
+         sol(i) = sol(i) + delx(i)
+      enddo
+      return
+      end
+c-----end-of-tidycg
+c-----------------------------------------------------------------------
+      logical function brkdn(alpha, ipar)
+      implicit none
+      integer ipar(16)
+      real*8 alpha, beta, zero, one
+      parameter (zero=0.0D0, one=1.0D0)
+c-----------------------------------------------------------------------
+c     test whether alpha is zero or an abnormal number, if yes,
+c     this routine will return .true.
+c
+c     If alpha == 0, ipar(1) = -3,
+c     if alpha is an abnormal number, ipar(1) = -9.
+c-----------------------------------------------------------------------
+      brkdn = .false.
+      if (alpha.gt.zero) then
+         beta = one / alpha
+         if (.not. beta.gt.zero) then
+            brkdn = .true.
+            ipar(1) = -9
+         endif
+      else if (alpha.lt.zero) then
+         beta = one / alpha
+         if (.not. beta.lt.zero) then
+            brkdn = .true.
+            ipar(1) = -9
+         endif
+      else if (alpha.eq.zero) then
+         brkdn = .true.
+         ipar(1) = -3
+      else
+         brkdn = .true.
+         ipar(1) = -9
+      endif
+      return
+      end
+c-----end-of-brkdn
+c-----------------------------------------------------------------------
+      subroutine bisinit(ipar,fpar,wksize,dsc,lp,rp,wk)
+      implicit none
+      integer i,ipar(16),wksize,dsc
+      logical lp,rp
+      real*8  fpar(16),wk(*)
+c-----------------------------------------------------------------------
+c     some common initializations for the iterative solvers
+c-----------------------------------------------------------------------
+      real*8 zero, one
+      parameter(zero=0.0D0, one=1.0D0)
+c
+c     ipar(1) = -2 inidcate that there are not enough space in the work
+c     array
+c
+      if (ipar(4).lt.wksize) then
+         ipar(1) = -2
+         ipar(4) = wksize
+         return
+      endif
+c
+      if (ipar(2).gt.2) then
+         lp = .true.
+         rp = .true.
+      else if (ipar(2).eq.2) then
+         lp = .false.
+         rp = .true.
+      else if (ipar(2).eq.1) then
+         lp = .true.
+         rp = .false.
+      else
+         lp = .false.
+         rp = .false.
+      endif
+      if (ipar(3).eq.0) ipar(3) = dsc
+c     .. clear the ipar elements used
+      ipar(7) = 0
+      ipar(8) = 0
+      ipar(9) = 0
+      ipar(10) = 0
+      ipar(11) = 0
+      ipar(12) = 0
+      ipar(13) = 0
+c
+c     fpar(1) must be between (0, 1), fpar(2) must be positive,
+c     fpar(1) and fpar(2) can NOT both be zero
+c     Normally return ipar(1) = -4 to indicate any of above error
+c
+      if (fpar(1).lt.zero .or. fpar(1).ge.one .or. fpar(2).lt.zero .or.
+     &     (fpar(1).eq.zero .and. fpar(2).eq.zero)) then
+         if (ipar(1).eq.0) then
+            ipar(1) = -4
+            return
+         else
+            fpar(1) = 1.0D-6
+            fpar(2) = 1.0D-16
+         endif
+      endif
+c     .. clear the fpar elements
+      do i = 3, 10
+         fpar(i) = zero
+      enddo
+      if (fpar(11).lt.zero) fpar(11) = zero
+c     .. clear the used portion of the work array to zero
+      do i = 1, wksize
+         wk(i) = zero
+      enddo
+c
+      return
+c-----end-of-bisinit
+      end
+c-----------------------------------------------------------------------
+      subroutine mgsro(full,lda,n,m,ind,ops,vec,hh,ierr)
+      implicit none
+      logical full
+      integer lda,m,n,ind,ierr
+      real*8  ops,hh(m),vec(lda,m)
+c-----------------------------------------------------------------------
+c     MGSRO  -- Modified Gram-Schmidt procedure with Selective Re-
+c               Orthogonalization
+c     The ind'th vector of VEC is orthogonalized against the rest of
+c     the vectors.
+c
+c     The test for performing re-orthogonalization is performed for
+c     each indivadual vectors. If the cosine between the two vectors
+c     is greater than 0.99 (REORTH = 0.99**2), re-orthogonalization is
+c     performed. The norm of the 'new' vector is kept in variable NRM0,
+c     and updated after operating with each vector.
+c
+c     full   -- .ture. if it is necessary to orthogonalize the ind'th
+c               against all the vectors vec(:,1:ind-1), vec(:,ind+2:m)
+c               .false. only orthogonalize againt vec(:,1:ind-1)
+c     lda    -- the leading dimension of VEC
+c     n      -- length of the vector in VEC
+c     m      -- number of vectors can be stored in VEC
+c     ind    -- index to the vector to be changed
+c     ops    -- operation counts
+c     vec    -- vector of LDA X M storing the vectors
+c     hh     -- coefficient of the orthogonalization
+c     ierr   -- error code
+c               0 : successful return
+c               -1: zero input vector
+c               -2: input vector contains abnormal numbers
+c               -3: input vector is a linear combination of others
+c
+c     External routines used: real*8 distdot
+c-----------------------------------------------------------------------
+      integer i,k
+      real*8  nrm0, nrm1, fct, thr, distdot, zero, one, reorth
+      parameter (zero=0.0D0, one=1.0D0, reorth=0.98D0)
+      external distdot
+c
+c     compute the norm of the input vector
+c
+      nrm0 = distdot(n,vec(1,ind),1,vec(1,ind),1)
+      ops = ops + n + n
+      thr = nrm0 * reorth
+      if (nrm0.le.zero) then
+         ierr = - 1
+         return
+      else if (nrm0.gt.zero .and. one/nrm0.gt.zero) then
+         ierr = 0
+      else
+         ierr = -2
+         return
+      endif
+c
+c     Modified Gram-Schmidt loop
+c
+      if (full) then
+         do 40 i = ind+1, m
+            fct = distdot(n,vec(1,ind),1,vec(1,i),1)
+            hh(i) = fct
+            do 20 k = 1, n
+               vec(k,ind) = vec(k,ind) - fct * vec(k,i)
+ 20         continue
+            ops = ops + 4 * n + 2
+            if (fct*fct.gt.thr) then
+               fct = distdot(n,vec(1,ind),1,vec(1,i),1)
+               hh(i) = hh(i) + fct
+               do 30 k = 1, n
+                  vec(k,ind) = vec(k,ind) - fct * vec(k,i)
+ 30            continue
+               ops = ops + 4*n + 1
+            endif
+            nrm0 = nrm0 - hh(i) * hh(i)
+            if (nrm0.lt.zero) nrm0 = zero
+            thr = nrm0 * reorth
+ 40      continue
+      endif
+c
+      do 70 i = 1, ind-1
+         fct = distdot(n,vec(1,ind),1,vec(1,i),1)
+         hh(i) = fct
+         do 50 k = 1, n
+            vec(k,ind) = vec(k,ind) - fct * vec(k,i)
+ 50      continue
+         ops = ops + 4 * n + 2
+         if (fct*fct.gt.thr) then
+            fct = distdot(n,vec(1,ind),1,vec(1,i),1)
+            hh(i) = hh(i) + fct
+            do 60 k = 1, n
+               vec(k,ind) = vec(k,ind) - fct * vec(k,i)
+ 60         continue
+            ops = ops + 4*n + 1
+         endif
+         nrm0 = nrm0 - hh(i) * hh(i)
+         if (nrm0.lt.zero) nrm0 = zero
+         thr = nrm0 * reorth
+ 70   continue
+c
+c     test the resulting vector
+c
+      nrm1 = sqrt(distdot(n,vec(1,ind),1,vec(1,ind),1))
+      ops = ops + n + n
+ 75   hh(ind) = nrm1
+      if (nrm1.le.zero) then
+         ierr = -3
+         return
+      endif
+c
+c     scale the resulting vector
+c
+      fct = one / nrm1
+      do 80 k = 1, n
+         vec(k,ind) = vec(k,ind) * fct
+ 80   continue
+      ops = ops + n + 1
+c
+c     normal return
+c
+      ierr = 0
+      return
+c     end surbotine mgsro
+      end
diff --git a/ITSOL/makefile b/ITSOL/makefile
new file mode 100644
index 0000000..41bbeb7
--- /dev/null
+++ b/ITSOL/makefile
@@ -0,0 +1,27 @@
+FFLAGS =
+F77 = f77
+
+#F77 = cf77
+#FFLAGS = -Wf"-dp"
+
+LIBS =  ../libskit.a ../UNSUPP/BLAS1/blas1.o
+
+riters.ex:  riters.o iters.o ilut.o itaux.o $(LIBS)
+	$(F77) $(FFLAGS) -o riters.ex riters.o itaux.o $(LIBS)
+
+rilut.ex: rilut.o ilut.o iters.o itaux.o $(LIBS)
+	$(F77) $(FFLAGS) -o rilut.ex rilut.o itaux.o $(LIBS)
+
+riter2.ex: riter2.o iters.o ilut.o itaux.o $(LIBS)
+	$(F77) $(FFLAGS) -o riter2.ex riter2.o itaux.o $(LIBS)
+
+clean:
+	rm -f *.o *.ex core *.trace
+
+../UNSUPP/BLAS1/blas1.o:
+	(cd ../UNSUPP/BLAS1; $(F77) $(FFLAGS) -c blas1.f)
+
+../libskit.a:
+	(cd ..; $(MAKE) $(MAKEFLAGS) libskit.a)
+
+
diff --git a/ITSOL/rilut.f b/ITSOL/rilut.f
new file mode 100644
index 0000000..ddf4a70
--- /dev/null
+++ b/ITSOL/rilut.f
@@ -0,0 +1,285 @@
+      program rilut
+c-----------------------------------------------------------------------
+c     test program for ilut preconditioned gmres.
+c     this program generates a sparse matrix using
+c     matgen and then solves a linear system with an 
+c     artificial rhs.
+c-----------------------------------------------------------------------
+      implicit none 
+c 
+      integer nmax, nzmax 
+      parameter (nmax=5000,nzmax=100000)
+      integer ia(nmax),ja(nzmax),jau(nzmax),ju(nzmax),iw(nmax*3),
+     &     iperm(nmax*2),ipar(16), levs(nzmax) 
+      real*8  a(nzmax),x(nmax),y(nmax),au(nzmax),vv(nmax,20),
+     *     xran(nmax),rhs(nmax),al(nmax),fpar(16)
+c     real t(2), t1, etime
+c
+      integer nx,ny,nz,n,j,k,ierr,meth,lfil,nwk,im,maxits,iout
+      real*8 tol,permtol,eps,alph,gammax,gammay,alpha 
+      external gmres
+c     
+      common /func/ gammax, gammay, alpha
+c-----------------------------------------------------------------------
+c     pde to be discretized is :
+c---------------------------
+c     
+c     -Lap u + gammax exp (xy)delx u + gammay exp (-xy) dely u +alpha u
+c     
+c     where Lap = 2-D laplacean, delx = part. der. wrt x,
+c     dely = part. der. wrt y.
+c     gammax, gammay, and alpha are passed via the commun func.
+c     
+c-----------------------------------------------------------------------
+c     
+c     data for PDE:
+c     
+      nx = 30 
+      ny = 30 
+      nz = 1
+      alpha = -50.0
+      gammax = 10.0
+      gammay = 10.0
+c     
+c     data for preconditioner
+c     
+      nwk = nzmax 
+c     
+c     data for GMRES
+c     
+      im   = 10
+      eps  = 1.0D-07
+      maxits = 100 
+      iout = 6
+      permtol = 1.0
+      ipar(2) = 2
+      ipar(3) = 2
+      ipar(4) = 20*nmax
+      ipar(5) = im
+      ipar(6) = maxits
+      fpar(1) = eps
+      fpar(2) = 2.22D-16
+c     
+c     same initial guess for gmres 
+c     
+c--------------------------------------------------------------
+c     call gen57 to generate matrix in compressed sparse row format
+c--------------------------------------------------------------
+c     
+c     define part of the boundary condition here
+c     
+      al(1) = 0.0
+      al(2) = 1.0
+      al(3) = 0.0
+      al(4) = 0.0
+      al(5) = 0.0
+      al(6) = 0.0
+      call gen57pt(nx,ny,nz,al,0,n,a,ja,ia,ju,rhs) 
+c
+c     zero initial guess to the iterative solvers
+c
+      do j=1, n
+         xran(j) = 0.d0
+      enddo
+      print *, 'RILUT:  generated a finite difference matrix'
+      print *, '        grid size = ', nx, ' X ', ny, ' X ', nz
+      print *, '        matrix size = ', n
+c--------------------------------------------------------------
+c     gnerate right han side = A * (1,1,1,...,1)**T
+c--------------------------------------------------------------
+      do  k=1,n
+         x(k) = 1.0
+      enddo
+      call amux(n, x, y, a, ja, ia)
+c--------------------------------------------------------------
+c     test all different methods available:
+c     ILU0, MILU0, ILUT and with different values of tol and lfil
+c     ( from cheaper to more expensive preconditioners)
+c     The more accurate the preconditioner the fewer iterations 
+c     are required in pgmres, in general. 
+c     
+c--------------------------------------------------------------
+      do 200 meth = 1, 15 
+         goto (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) meth
+ 1       continue
+         write (iout,*) ' +++++ ILU(0) Preconditioner ++++ '
+c        t1 = etime(t)    
+         call ilu0 (n, a, ja, ia, au, jau, ju, iw, ierr)
+c        t1 = etime(t) - t1 
+         goto 100
+ 2       continue
+         write (iout,*) ' +++++ MILU(0) Preconditioner ++++ '
+c        t1 = etime(t)    
+         call milu0 (n, a, ja, ia, au, jau, ju, iw, ierr)
+c        t1 = etime(t) - t1 
+         goto 100
+ 3       continue
+         write (iout,*) ' +++++ ILUT Preconditioner ++++ '
+         write (iout,*) ' +++++ tol = 0.0001, lfil=5 ++++ '
+         tol  = 0.0001
+         lfil = 5
+c     
+c        t1 = etime(t)       
+         call ilut (n,a,ja,ia,lfil,tol,au,jau,ju,nwk,vv,iw,ierr)
+c         t1 = etime(t) - t1 
+         goto 100
+ 4       continue
+         write (iout,*) ' +++++ ILUT Preconditioner ++++ '
+         write (iout,*) ' +++++ tol = 0.0001, lfil=10 ++++ '
+         tol = 0.0001
+         lfil = 10
+c     
+c        t1 = etime(t)       
+         call ilut (n,a,ja,ia,lfil,tol,au,jau,ju,nwk,vv,iw,ierr)
+
+c        t1 = etime(t) - t1 
+         goto 100
+ 5       continue
+         write (iout,*) ' +++++ ILUT Preconditioner ++++ '
+         write (iout,*) ' +++++ tol = .0001, lfil=15 ++++ '
+         tol = 0.0001 
+         lfil = 15 
+c     
+c        t1 = etime(t)    
+         call ilut (n,a,ja,ia,lfil,tol,au,jau,ju,nwk,vv,iw,ierr)
+c        t1 = etime(t) - t1 
+         goto 100
+ 6       continue
+         write (iout,*) ' +++++ ILUTP Preconditioner ++++ '
+         write (iout,*) ' +++++ tol = 0.0001, lfil=5 ++++ '
+         tol  = 0.0001
+         lfil = 5
+c     
+c        t1 = etime(t)
+         call ilutp(n,a,ja,ia,lfil,tol,permtol,n,au,jau,ju,nwk,
+     *        vv,iw,iperm,ierr)
+c        t1 = etime(t) - t1 
+         goto 100
+ 7       continue
+         write (iout,*) ' +++++ ILUTP Preconditioner ++++ '
+         write (iout,*) ' +++++ tol = 0.0001, lfil=10 ++++ '
+         tol = 0.0001
+         lfil = 10
+c     
+c        t1 = etime(t)
+         call ilutp(n,a,ja,ia,lfil,tol,permtol,n,au,jau,ju,nwk,
+     *        vv,iw,iperm,ierr)
+c        t1 = etime(t) - t1 
+         goto 100
+c-----------------------------------------------------------------------------
+ 8       continue
+         write (iout,*) ' +++++ ILUTP Preconditioner ++++ '
+         write (iout,*) ' +++++ tol = .0001, lfil=15 ++++ '
+         tol = 0.0001
+         lfil = 15
+c     
+c        t1 = etime(t)
+         call ilutp(n,a,ja,ia,lfil,tol,permtol,n,au,jau,ju,nwk,
+     *        vv,iw,iperm,ierr)
+c        t1 = etime(t) - t1 
+         goto 100 
+ 9      continue
+         write (iout,*) ' +++++ ILUK Preconditioner ++++ '
+         write (iout,*) ' +++++       lfil=0        ++++ '
+         lfil = 0 
+c        t1 = etime(t)
+         call iluk(n,a,ja,ia,lfil,au,jau,ju,levs,nwk,vv,iw,ierr)
+         print *, ' nnz for a =', ia(n+1) - ia(1) 
+         print *, ' nnz for ilu =', jau(n+1) -jau(1) + n 
+c        t1 = etime(t) - t1 
+         goto 100 
+c
+ 10      continue
+         write (iout,*) ' +++++ ILUK Preconditioner ++++ '
+         write (iout,*) ' +++++       lfil=1        ++++ '
+         lfil = 1 
+c        t1 = etime(t)
+         call iluk(n,a,ja,ia,lfil,au,jau,ju,levs,nwk,vv,iw,ierr)
+         print *, ' nnz for a =', ia(n+1) - ia(1) 
+         print *, ' nnz for ilu =', jau(n+1) -jau(1) + n 
+c        t1 = etime(t) - t1 
+         goto 100 
+c
+ 11      continue
+         write (iout,*) ' +++++ ILUK Preconditioner ++++ '
+         write (iout,*) ' +++++       lfil=3        ++++ '
+         lfil = 3 
+c        t1 = etime(t)
+         call iluk(n,a,ja,ia,lfil,au,jau,ju,levs,nwk,vv,iw,ierr)
+         print *, ' nnz for a =', ia(n+1) - ia(1) 
+         print *, ' nnz for ilu =', jau(n+1) -jau(1) + n 
+c        t1 = etime(t) - t1 
+         goto 100 
+c
+ 12      continue
+         write (iout,*) ' +++++ ILUK Preconditioner ++++ '
+         write (iout,*) ' +++++       lfil=6        ++++ '
+         lfil = 6
+c        t1 = etime(t)
+         call iluk(n,a,ja,ia,lfil,au,jau,ju,levs,nwk,vv,iw,ierr)
+         print *, ' nnz for a =', ia(n+1) - ia(1) 
+         print *, ' nnz for ilu =', jau(n+1) -jau(1) + n 
+c        t1 = etime(t) - t1 
+         goto 100 
+c
+ 13      continue
+c----------------------------------------------------------------------- 
+        write (iout,*) ' +++++ ILUD Preconditioner ++++ '
+        write (iout,*) ' +++++ tol=0.075, alpha=0.0 ++++ '
+        tol = 0.075 
+        alph= 0.0 
+c        t1 = etime(t)
+        call ilud(n,a,ja,ia,alph,tol,au,jau,ju,nwk,vv,iw,ierr)
+c
+        print *, ' nnz for a =', ia(n+1) - ia(1) 
+        print *, ' nnz for ilu =', jau(n+1) -jau(1) + n 
+c        t1 = etime(t) - t1 
+        goto 100 
+c
+ 14      continue
+        write (iout,*) ' +++++ ILUD Preconditioner ++++ '
+        write (iout,*) ' +++++ tol=0.075, alpha=1.0 ++++ '
+        tol = 0.075 
+        alph=1.0 
+c        t1 = etime(t)
+        call ilud(n,a,ja,ia,alph,tol,au,jau,ju,nwk,vv,iw,ierr)
+        print *, ' nnz for a =', ia(n+1) - ia(1) 
+        print *, ' nnz for ilu =', jau(n+1) -jau(1) + n 
+c        t1 = etime(t) - t1 
+        goto 100 
+ 
+ 15      continue
+        write (iout,*) ' +++++ ILUD Preconditioner ++++ '
+        write (iout,*) ' +++++ tol=0.01, alpha=1.0 ++++ '
+        tol = 0.01
+c        t1 = etime(t)
+        call ilud(n,a,ja,ia,alph,tol,au,jau,ju,nwk,vv,iw,ierr)
+        print *, ' nnz for a =', ia(n+1) - ia(1) 
+        print *, ' nnz for ilu =', jau(n+1) -jau(1) + n 
+c        t1 = etime(t) - t1 
+c        goto 100 
+c
+ 100     continue
+c     
+c     check that return was succesful
+c     
+c        print *, ' ILU factorization time ', t1 
+         print *, ' Precon set-up returned with ierr ', ierr
+         if (ierr .ne. 0) goto 200
+c--------------------------------------------------------------
+c     call GMRES
+c--------------------------------------------------------------
+         call runrc(n,y,x,ipar,fpar,vv,xran,a,ja,ia,au,jau,ju,
+     +        gmres)
+         print *, 'GMRES return status = ', ipar(1)
+         write (iout,*) '     ' 
+ 200  continue
+c     
+c----------------------------------------------------------
+c     
+      write (iout,*) ' **** SOLUTION ****  '
+      write(iout, 111) (x(k),k=1,n) 
+ 111  format (5d15.5)
+      stop
+      end
+
diff --git a/ITSOL/riter2.f b/ITSOL/riter2.f
new file mode 100644
index 0000000..01b50d6
--- /dev/null
+++ b/ITSOL/riter2.f
@@ -0,0 +1,102 @@
+      program riters
+c-----------------------------------------------------------------------
+c test program for iters -- the basic iterative solvers
+c
+c     this program reads a Harwell/Boeing matrix from standard input
+c     and solves the linear system with an artifical right-hand side
+c     (the solution is a vector of (1,1,...,1)^T)
+c-----------------------------------------------------------------------
+c      implicit none
+c      implicit real*8 (a-h,o-z)
+      integer nmax, nzmax, maxits,lwk
+      parameter (nmax=5000,nzmax=100000,maxits=60,lwk=nmax*40)
+      integer ia(nmax),ja(nzmax),jau(nzmax),ju(nzmax),iw(nmax*3)
+      integer ipar(16),i,lfil,nwk,nrow,ierr
+      real*8  a(nzmax),sol(nmax),rhs(nmax),au(nzmax),wk(nmax*40)
+      real*8  xran(nmax), fpar(16), tol
+      character guesol*2, title*72, key*8, type*3
+      external cg,bcg,dbcg,bcgstab,tfqmr,gmres,fgmres,dqgmres
+      external cgnr, fom, runrc, ilut
+c
+c     set the parameters for the iterative solvers
+c
+      ipar(2) = 2
+      ipar(3) = 1
+      ipar(4) = lwk
+      ipar(5) = 16
+      ipar(6) = maxits
+      fpar(1) = 1.0D-5
+      fpar(2) = 1.0D-10
+c--------------------------------------------------------------
+c     read in a matrix from standard input
+c--------------------------------------------------------------
+      iounit = 5
+      job = 2
+      nrhs = 0
+      call readmt (nmax,nzmax,job,iounit,a,ja,ia,a,nrhs,
+     *     guesol,nrow,ncol,nnz,title,key,type,ierr)
+      print *, 'READ the matrix ', key, type
+      print *, title
+      print *
+c
+c     set-up the preconditioner ILUT(15, 1E-4) ! new definition of lfil
+c
+      lfil = 15
+      tol = 1.0D-4 ! this is too high for ilut for saylr1
+      tol = 1.0D-7
+      nwk = nzmax
+      call ilut (nrow,a,ja,ia,lfil,tol,au,jau,ju,nwk,
+     *     wk,iw,ierr)
+      ipar(2) = 2
+c
+c     generate a linear system with known solution
+c
+      do i = 1, nrow
+         sol(i) = 1.0D0
+         xran(i) = 0.D0
+      end do
+      call amux(nrow, sol, rhs, a, ja, ia)
+      print *, ' '
+      print *, '	*** CG ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     cg)
+      print *, ' '
+      print *, '	*** BCG ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     bcg)
+      print *, ' '
+      print *, '	*** DBCG ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     dbcg)
+      print *, ' '
+      print *, '	*** CGNR ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     cgnr)
+      print *, ' '
+      print *, '	*** BCGSTAB ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     bcgstab)
+      print *, ' '
+      print *, '	*** TFQMR ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     tfqmr)
+      print *, ' '
+      print *, '	*** FOM ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     fom)
+      print *, ' '
+      print *, '	*** GMRES ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     gmres)
+      print *, ' '
+      print *, '	*** FGMRES ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     fgmres)
+      print *, ' '
+      print *, '	*** DQGMRES ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     dqgmres)
+      stop
+      end
+c-----end-of-main
+c-----------------------------------------------------------------------
diff --git a/ITSOL/riters.f b/ITSOL/riters.f
new file mode 100644
index 0000000..1ad8e69
--- /dev/null
+++ b/ITSOL/riters.f
@@ -0,0 +1,129 @@
+      program riters
+c-----------------------------------------------------------------------
+c test program for iters -- the basic iterative solvers
+c
+c     this program generates a sparse matrix using
+c     GEN57PT and then solves a linear system with an 
+c     artificial rhs (the solution is a vector of (1,1,...,1)^T).
+c-----------------------------------------------------------------------
+c      implicit none
+c      implicit real*8 (a-h,o-z)
+      integer nmax, nzmax, maxits,lwk
+      parameter (nmax=5000,nzmax=100000,maxits=60,lwk=nmax*40)
+      integer ia(nmax),ja(nzmax),jau(nzmax),ju(nzmax),iw(nmax*3)
+      integer ipar(16),nx,ny,nz,i,lfil,nwk,nrow,ierr
+      real*8  a(nzmax),sol(nmax),rhs(nmax),au(nzmax),wk(nmax*40)
+      real*8  xran(nmax), fpar(16), al(nmax)
+      real*8  gammax,gammay,alpha,tol
+      external gen57pt,cg,bcg,dbcg,bcgstab,tfqmr,gmres,fgmres,dqgmres
+      external cgnr, fom, runrc, ilut
+c     
+      common /func/ gammax, gammay, alpha
+c-----------------------------------------------------------------------  
+c pde to be discretized is :
+c---------------------------
+c
+c -Lap u + gammax exp (xy)delx u + gammay exp (-xy) dely u +alpha u
+c
+c where Lap = 2-D laplacean, delx = part. der. wrt x,
+c dely = part. der. wrt y.
+c gammax, gammay, and alpha are passed via the commun func.
+c 
+c-----------------------------------------------------------------------  
+c
+c data for PDE:
+c
+      nx = 6
+      ny = 6
+      nz = 1
+      alpha = 0.0
+      gammax = 0.0
+      gammay = 0.0
+c
+c     set the parameters for the iterative solvers
+c
+      ipar(2) = 2
+      ipar(3) = 1
+      ipar(4) = lwk
+      ipar(5) = 10 
+      ipar(6) = maxits
+      fpar(1) = 1.0D-5
+      fpar(2) = 1.0D-10
+c--------------------------------------------------------------
+c call GEN57PT to generate matrix in compressed sparse row format
+c
+c     al(1:6) are used to store part of the boundary conditions
+c     (see documentation on GEN57PT.)
+c--------------------------------------------------------------
+      al(1) = 0.0
+      al(2) = 0.0
+      al(3) = 0.0
+      al(4) = 0.0
+      al(5) = 0.0
+      al(6) = 0.0
+      nrow = nx * ny * nz
+      call gen57pt(nx,ny,nz,al,0,nrow,a,ja,ia,ju,rhs)
+      print *, 'RITERS: generated a finite difference matrix'
+      print *, '        grid size = ', nx, ' X ', ny, ' X ', nz
+      print *, '        matrix size = ', nrow
+c
+c     set-up the preconditioner ILUT(15, 1E-4)  ! new definition of lfil
+c
+      lfil = 3
+      tol = 1.0D-4
+      nwk = nzmax
+      call ilut (nrow,a,ja,ia,lfil,tol,au,jau,ju,nwk,
+     *     wk,iw,ierr)
+      ipar(2) = 2
+c
+c     generate a linear system with known solution
+c
+      do i = 1, nrow
+         sol(i) = 1.0D0
+         xran(i) = 0.d0
+      end do
+      call amux(nrow, sol, rhs, a, ja, ia)
+      print *, ' '
+      print *, '	*** CG ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     cg)
+      print *, ' '
+      print *, '	*** BCG ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     bcg)
+      print *, ' '
+      print *, '	*** DBCG ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     dbcg)
+      print *, ' '
+      print *, '	*** CGNR ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     cgnr)
+      print *, ' '
+      print *, '	*** BCGSTAB ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     bcgstab)
+      print *, ' '
+      print *, '	*** TFQMR ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     tfqmr)
+      print *, ' '
+      print *, '	*** FOM ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     fom)
+      print *, ' '
+      print *, '	*** GMRES ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     gmres)
+      print *, ' '
+      print *, '	*** FGMRES ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     fgmres)
+      print *, ' '
+      print *, '	*** DQGMRES ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     dqgmres)
+      stop
+      end
+c-----end-of-main
+c-----------------------------------------------------------------------
diff --git a/ITSOL/riters_sav b/ITSOL/riters_sav
new file mode 100644
index 0000000..d4bc99a
--- /dev/null
+++ b/ITSOL/riters_sav
@@ -0,0 +1,129 @@
+      program riters
+c-----------------------------------------------------------------------
+c test program for iters -- the basic iterative solvers
+c
+c     this program generates a sparse matrix using
+c     GEN57PT and then solves a linear system with an 
+c     artificial rhs (the solution is a vector of (1,1,...,1)^T).
+c-----------------------------------------------------------------------
+c      implicit none
+c      implicit real*8 (a-h,o-z)
+      integer nmax, nzmax, maxits,lwk
+      parameter (nmax=5000,nzmax=100000,maxits=60,lwk=nmax*40)
+      integer ia(nmax),ja(nzmax),jau(nzmax),ju(nzmax),iw(nmax*3)
+      integer ipar(16),nx,ny,nz,i,lfil,nwk,nrow,ierr
+      real*8  a(nzmax),sol(nmax),rhs(nmax),au(nzmax),wk(nmax*40)
+      real*8  xran(nmax), fpar(16), al(nmax)
+      real*8  gammax,gammay,alpha,tol
+      external gen57pt,cg,bcg,dbcg,bcgstab,tfqmr,gmres,fgmres,dqgmres
+      external cgnr, fom, runrc, ilut
+c     
+      common /func/ gammax, gammay, alpha
+c-----------------------------------------------------------------------  
+c pde to be discretized is :
+c---------------------------
+c
+c -Lap u + gammax exp (xy)delx u + gammay exp (-xy) dely u +alpha u
+c
+c where Lap = 2-D laplacean, delx = part. der. wrt x,
+c dely = part. der. wrt y.
+c gammax, gammay, and alpha are passed via the commun func.
+c 
+c-----------------------------------------------------------------------  
+c
+c data for PDE:
+c
+      nx = 50
+      ny = 50
+      nz = 1
+      alpha = -50.0
+      gammax = 10.0
+      gammay = 10.0
+c
+c     set the parameters for the iterative solvers
+c
+      ipar(2) = 2
+      ipar(3) = 1
+      ipar(4) = lwk
+      ipar(5) = 16
+      ipar(6) = maxits
+      fpar(1) = 1.0D-5
+      fpar(2) = 1.0D-10
+c--------------------------------------------------------------
+c call GEN57PT to generate matrix in compressed sparse row format
+c
+c     al(1:6) are used to store part of the boundary conditions
+c     (see documentation on GEN57PT.)
+c--------------------------------------------------------------
+      al(1) = 0.0
+      al(2) = 0.0
+      al(3) = 0.0
+      al(4) = 0.0
+      al(5) = 0.0
+      al(6) = 0.0
+      nrow = nx * ny * nz
+      call gen57pt(nx,ny,nz,al,0,nrow,a,ja,ia,ju,rhs)
+      print *, 'RITERS: generated a finite difference matrix'
+      print *, '        grid size = ', nx, ' X ', ny, ' X ', nz
+      print *, '        matrix size = ', nrow
+c
+c     set-up the preconditioner ILUT(15, 1E-4)  ! new definition of lfil
+c
+      lfil = 15
+      tol = 1.0D-4
+      nwk = nzmax
+      call ilut (nrow,a,ja,ia,lfil,tol,au,jau,ju,nwk,
+     *     wk,iw,ierr)
+      ipar(2) = 2
+c
+c     generate a linear system with known solution
+c
+      do i = 1, nrow
+         sol(i) = 1.0D0
+         xran(i) = 0.d0
+      end do
+      call amux(nrow, sol, rhs, a, ja, ia)
+      print *, ' '
+      print *, '	*** CG ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     cg)
+      print *, ' '
+      print *, '	*** BCG ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     bcg)
+      print *, ' '
+      print *, '	*** DBCG ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     dbcg)
+      print *, ' '
+      print *, '	*** CGNR ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     cgnr)
+      print *, ' '
+      print *, '	*** BCGSTAB ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     bcgstab)
+      print *, ' '
+      print *, '	*** TFQMR ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     tfqmr)
+      print *, ' '
+      print *, '	*** FOM ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     fom)
+      print *, ' '
+      print *, '	*** GMRES ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     gmres)
+      print *, ' '
+      print *, '	*** FGMRES ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     fgmres)
+      print *, ' '
+      print *, '	*** DQGMRES ***'
+      call runrc(nrow,rhs,sol,ipar,fpar,wk,xran,a,ja,ia,au,jau,ju,
+     +     dqgmres)
+      stop
+      end
+c-----end-of-main
+c-----------------------------------------------------------------------
diff --git a/ITSOL/runilut.f b/ITSOL/runilut.f
new file mode 100644
index 0000000..8eb817f
--- /dev/null
+++ b/ITSOL/runilut.f
@@ -0,0 +1,264 @@
+      program runall 
+c-----------------------------------------------------------------------
+c     not present: CG and FGMRES 
+c-----------------------------------------------------------------------
+c     program for running all examples -- for book tables.
+c-----------------------------------------------------------------------
+      parameter (nmax=10000,np1=nmax+1,nt2=2*nmax,nzmax = 100000,
+     *     lw=31*nmax,nzumax = 20*nzmax) 
+c-----------------------------------------------------------------------
+      implicit none 
+c
+      integer ia(nt2),ja(nzmax),jlu(nzumax),levs(nzumax),ju(nmax+1) 
+      real*8 wk(lw),rhs(nmax),a(nzmax),alu(nzumax)
+      integer jw(nt2), iperm(nt2) 
+      real*8 w(nt2),sol(nt2) 
+      integer n, mbloc 
+      character guesol*2, title*72, key*8, type*3 
+c-----------------------------------------------------------------------
+      integer iout,lfil,j,k,maxits,i,ncol,numat,mat,iwk,nnz,ipo,ipi,iin,
+     *   job,nrhs,im,outf,ipre,its,ierr,ipre1,ipre2,lf,it,itp,
+     *     icode,imat,kk,lfinc, niter  
+      character*50 filnam
+      integer iters(20) 
+c
+c     up to 10 matrices 
+c
+      real*8 droptol, dropinc, t, permtol, tol, eps, rand, alph, dnrm2 
+c
+c-----------------------------------------------------------------------
+      data iin/4/, iout/8/ 
+c-----------------------------------------------------------------------
+      iwk = nzumax 
+c
+c read in matrix pathname from file. == then read matrix itself 
+c
+      open (2, file ='matfile')
+      read (2,*)  numat
+      i=20
+c-----------------------------------------------------------------------
+      open (iin,file='inputs')
+      read (iin,*) alph 
+      read (iin,*) im, maxits 
+      read (iin,*) eps 
+      read (iin,*) ipre1, ipre2, niter 
+      read (iin,*) tol, dropinc, permtol 
+      read (iin,*) lf, lfinc 
+      outf = 30
+c     
+c     BIG MATRIX LOOP
+c
+c-----------------------------------------------------------------------
+c     LOOP THROUGH MATRICES 
+c-----------------------------------------------------------------------
+      do 300 mat =1, numat
+         read (2,'(a50)') filnam 
+         imat = 20 
+         open (imat,file =filnam) 
+         write (7,*) filnam 
+         job = 3
+         nrhs = nmax 
+         call readmt (nmax,nzmax,job,imat,a,ja,ia, rhs, nrhs,
+     *        guesol,n,ncol,nnz,title,key,type,ierr)
+c-----------------------------------------------------------------------
+         rewind(imat)
+         write (7,*) ' -- read -- returned with  ierr = ', ierr 
+         write (7,*) ' matrix ', filnam 
+         write (7,*) ' *** n  =  ', n, ' nnz ', nnz   
+         if (ierr .ne. 0) stop ' not able to read *** ' 
+c     
+c     sort matrix 
+c     
+         call csort(n,a,ja,ia,jlu,.true.) 
+         job = 0
+         call roscal(n,job,1,a,ja,ia,wk,a,ja,ia,ierr)
+         call coscal(n,job,1,a,ja,ia,wk,a,ja,ia,ierr)
+c-----------------------------------------------------------------------
+c     LOOP THROUGH PRECONDITONERS
+c-----------------------------------------------------------------------
+         droptol = tol 
+         lfil = lf  
+         kk = 0 
+         do 500 ipre = ipre1, ipre2 
+c----------------------------------------------------------------------- 
+c     ipre = 1 --> ILUD
+c     ipre = 2 --> ILUT
+c     ipre = 3 --> ILUDP
+c     ipre = 4 --> ILUTP
+c     ipre = 5 --> ILUK 
+c-----------------------------------------------------------------------
+            lfil = lf
+            droptol = tol 
+            do 350 itp =1, niter 
+               do k=1,n
+                  sol(k) = 1.0 
+               enddo
+c     
+               call amux (n, sol, rhs, a, ja, ia)
+c     
+               goto (1,2,3,4) ipre 
+c     
+ 1             continue 
+               call ilud (n,a,ja,ia,alph,droptol,alu,jlu,ju,iwk,
+     *              w,jw,ierr)
+               if (ierr .ne. 0) write (7,*) ' ilud ierr = ', ierr 
+               call stb_test(n,rhs,alu,jlu,ju,t)
+               write (7,*) ' ILUD-drpt =', droptol, ' stbtest = ', t
+               write (7,*) '  --- fill-in =', jlu(n+1)-jlu(1) 
+c     
+               goto 100
+ 2             continue
+c     
+               call ilutn (n,a,ja,ia,lfil,droptol,alu,jlu,ju,iwk,w,jw,
+     *              ierr)
+               if (ierr .ne. 0) write (7,*) ' ILUT ierr = ', ierr 
+               call stb_test(n,rhs,alu,jlu,ju,t)
+               write (7,*) ' ILUT-drpt =', droptol, 
+     *              ' lfil = ', lfil, ' stbtest = ', t 
+               write (7,*) '  --- fill-in =', jlu(n+1)-jlu(1) 
+c     
+               goto 100
+c
+c     pivoting codes
+c 
+ 3             continue
+               mbloc = n 
+               call iludp (n,a,ja,ia,alph,droptol,permtol,mbloc,alu,
+     *              jlu,ju,iwk,w,jw,iperm,ierr)
+               if (ierr .ne. 0) write (7,*) ' ilud ierr = ', ierr 
+               call stb_test(n,rhs,alu,jlu,ju,t)
+               write (7,*) ' ILUD-drpt =', droptol, ' stbtest = ', t
+               write (7,*) '  --- fill-in =', jlu(n+1)-jlu(1) 
+               goto 100 
+ 4             continue
+               mbloc = n
+               call ilutpn (n,a,ja,ia,lfil,droptol,permtol,mbloc,alu,
+     *              jlu,ju,iwk,w,jw,iperm,ierr) 
+               if (ierr .ne. 0) write (7,*) ' milutp ierr = ', ierr 
+c     
+               call stb_test(n,rhs,alu,jlu,ju,t)
+               write (7,*) ' ILUTP-drpt =', droptol, 
+     *              ' lfil = ', lfil, ' stbtest = ', t 
+               write (7,*) '  --- fill-in =', jlu(n+1)-jlu(1) 
+
+               goto 100
+ 5             continue
+c     
+               call ilukn(n,a,ja,ia,lfil,alu,jlu,ju,levs,iwk,w,jw,ierr)
+               if (ierr .ne. 0) write (7,*) ' ILUT ierr = ', ierr 
+               call stb_test(n,rhs,alu,jlu,ju,t)
+               write (7,*) ' ILUK -- lfil = ', lfil,' stbtest = ', t 
+               write (7,*) '  --- fill-in =', jlu(n+1)-jlu(1) 
+c               goto 100
+c     ----------- 
+c     big loop --
+c     -----------
+ 100        continue 
+            
+            do 11 k=1,n
+               sol(k) = 1.0 
+ 11         continue
+            
+            call amux (n, sol, rhs, a, ja, ia)
+            do 12 j=1, n
+               sol(j) = rand(j) 
+ 12         continue       
+            its = 0 
+c-----------------------------------------------------------------------
+ 10         continue 
+c     
+            call fgmr (n,im,rhs,sol,it,wk,ipo,ipi,eps,maxits,0,icode)
+c-----------------------------------------------------------------------
+            if (icode.eq.1) then
+               call amux(n, wk(ipo), wk(ipi), a, ja, ia)
+               its =  its+1 
+               goto 10
+            else if (icode.eq.3 .or. icode.eq.5) then
+c     
+c     output the residuals here ...
+c     
+               if (ipre .eq. 0) then 
+c     NOPRE
+                  call dcopy(n, wk(ipo),1,wk(ipi),1)
+               else
+                  call lusol(n,wk(ipo),wk(ipi),alu,jlu,ju)
+               endif
+               goto 10
+            endif
+c     
+c     done *** 
+c     
+            call amux(n,sol,wk,a,ja,ia)
+c     
+            do i = 1, n
+               wk(n+i) = sol(i) -1.0D0
+               wk(i) = wk(i) - rhs(i)
+            end do
+c     
+            kk = kk+1 
+            iters(kk) = its
+c     res(kk) = dnrm2(n,wk,1) 
+c     err(kk) = dnrm2(n,wk(n+1),1) 
+            write (iout, *) '# actual residual norm ', dnrm2(n,wk,1)
+            write (iout, *) '# error norm ', dnrm2(n,wk(1+n),1)
+c     
+            droptol = droptol*dropinc
+            lfil = lfil + lfinc 
+c
+c     pivoting codes
+c 
+            if (ipre .ge. 3)  then
+               do k=1, ia(n+1)-1 
+                  ja(k) = iperm(ja(k)) 
+               enddo
+            endif
+ 350        continue
+c     
+ 500     continue
+         call entline(outf,filnam,iters,kk) 
+         close (imat) 
+ 300  continue 
+      stop
+c-------------end-of-main-program-ilut_solve_new------------------------
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      function distdot(n,x,ix,y,iy)
+      integer n, ix, iy
+      real*8 distdot, x(*), y(*), ddot
+      external ddot
+      distdot = ddot(n,x,ix,y,iy)
+      return
+c-----end-of-distdot
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine entline(outf,mat,its,kk) 
+      implicit none 
+      integer outf, kk,its(kk),k
+      character mat*70
+c      real*8 err(kk), res(kk) 
+c----------------------------------------------------------------------- 
+      write(outf,100)  mat(19:29),(its(k),k=1,8)
+ 100  format
+     * (a,' & ', 8(i4,' & '),'\\\\ \\hline') 
+      return
+      end 
+c-----------------------------------------------------------------------
+      subroutine stb_test(n,sol,alu,jlu,ju,tmax)      
+      implicit none
+      integer n, jlu(*),ju(*) 
+      real*8 sol(n),alu(*),tmax
+c----------------------------------------------------------------------- 
+      real*8 max, t, abs
+      integer j
+c
+      call lusol(n,sol,sol,alu,jlu,ju)
+c      
+      tmax = 0.0 
+      do j=1, n
+         t = abs(sol(j)) 
+         tmax = max(t,tmax) 
+      enddo
+      return
+      end 
diff --git a/ITSOL/saylr1 b/ITSOL/saylr1
new file mode 100644
index 0000000..a5a0f2f
--- /dev/null
+++ b/ITSOL/saylr1
@@ -0,0 +1,367 @@
+1UNSYMMETRIC MATRIX OF PAUL SAYLOR - 14 BY 17 2D GRID   MAY, 1983         SAYLR1
+           363            24           113           226             0
+RUA                      238           238          1128             0
+(10I8)          (10I8)          (5E16.8)                                
+       1       4       8      12      16      20      24      28      32      36
+      40      44      48      52      55      59      64      69      74      79
+      84      89      94      99     104     109     114     119     123     127
+     132     137     142     147     152     157     162     167     172     177
+     182     187     191     195     200     205     210     215     220     225
+     230     235     240     245     250     255     259     263     268     273
+     278     283     288     293     298     303     308     313     318     323
+     327     331     336     341     346     351     356     361     366     371
+     376     381     386     391     395     399     404     409     414     419
+     424     429     434     439     444     449     454     459     463     467
+     472     477     482     487     492     497     502     507     512     517
+     522     527     531     535     540     545     550     555     560     565
+     570     575     580     585     590     595     599     603     608     613
+     618     623     628     633     638     643     648     653     658     663
+     667     671     676     681     686     691     696     701     706     711
+     716     721     726     731     735     739     744     749     754     759
+     764     769     774     779     784     789     794     799     803     807
+     812     817     822     827     832     837     842     847     852     857
+     862     867     871     875     880     885     890     895     900     905
+     910     915     920     925     930     935     939     943     948     953
+     958     963     968     973     978     983     988     993     998    1003
+    1007    1011    1016    1021    1026    1031    1036    1041    1046    1051
+    1056    1061    1066    1071    1075    1078    1082    1086    1090    1094
+    1098    1102    1106    1110    1114    1118    1122    1126    1129
+       1       2      15       1       2       3      16       2       3       4
+      17       3       4       5      18       4       5       6      19       5
+       6       7      20       6       7       8      21       7       8       9
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diff --git a/LGPL b/LGPL
new file mode 100644
index 0000000..b1e3f5a
--- /dev/null
+++ b/LGPL
@@ -0,0 +1,504 @@
+		  GNU LESSER GENERAL PUBLIC LICENSE
+		       Version 2.1, February 1999
+
+ Copyright (C) 1991, 1999 Free Software Foundation, Inc.
+     59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+[This is the first released version of the Lesser GPL.  It also counts
+ as the successor of the GNU Library Public License, version 2, hence
+ the version number 2.1.]
+
+			    Preamble
+
+  The licenses for most software are designed to take away your
+freedom to share and change it.  By contrast, the GNU General Public
+Licenses are intended to guarantee your freedom to share and change
+free software--to make sure the software is free for all its users.
+
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+specially designated software packages--typically libraries--of the
+Free Software Foundation and other authors who decide to use it.  You
+can use it too, but we suggest you first think carefully about whether
+this license or the ordinary General Public License is the better
+strategy to use in any particular case, based on the explanations below.
+
+  When we speak of free software, we are referring to freedom of use,
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+you have the freedom to distribute copies of free software (and charge
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+it if you want it; that you can change the software and use pieces of
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+
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+it.  And you must show them these terms so they know their rights.
+
+  We protect your rights with a two-step method: (1) we copyright the
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+
+  Finally, software patents pose a constant threat to the existence of
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+
+  Most GNU software, including some libraries, is covered by the
+ordinary GNU General Public License.  This license, the GNU Lesser
+General Public License, applies to certain designated libraries, and
+is quite different from the ordinary General Public License.  We use
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+
+  When a program is linked with a library, whether statically or using
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+Public License permits more lax criteria for linking other code with
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+
+  We call this license the "Lesser" General Public License because it
+does Less to protect the user's freedom than the ordinary General
+Public License.  It also provides other free software developers Less
+of an advantage over competing non-free programs.  These disadvantages
+are the reason we use the ordinary General Public License for many
+libraries.  However, the Lesser license provides advantages in certain
+special circumstances.
+
+  For example, on rare occasions, there may be a special need to
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+library does the same job as widely used non-free libraries.  In this
+case, there is little to gain by limiting the free library to free
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+
+  In other cases, permission to use a particular library in non-free
+programs enables a greater number of people to use a large body of
+free software.  For example, permission to use the GNU C Library in
+non-free programs enables many more people to use the whole GNU
+operating system, as well as its variant, the GNU/Linux operating
+system.
+
+  Although the Lesser General Public License is Less protective of the
+users' freedom, it does ensure that the user of a program that is
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+  The precise terms and conditions for copying, distribution and
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+former contains code derived from the library, whereas the latter must
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+
+		  GNU LESSER GENERAL PUBLIC LICENSE
+   TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
+
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diff --git a/MATGEN/FDIF/README b/MATGEN/FDIF/README
new file mode 100644
index 0000000..0abf798
--- /dev/null
+++ b/MATGEN/FDIF/README
@@ -0,0 +1,31 @@
+This directory contains the routines that generate finite difference
+matrices from a second order elliptic operator.
+
+      1) 5-pt and 7-pt matrices on rectangular regions discretizing
+           elliptic operators of the form: 
+
+         L u == delx( a delx u ) + dely ( b dely u) + delz ( c delz u ) + 
+                delx ( d u ) + dely (e u) + delz( f u ) + g u = h u
+
+         with Boundary conditions,
+		 alpha del u / del n + beta u = gamma
+	 on a rectangular 1-D, 2-D or 3-D grid using centered
+	 difference scheme or upwind scheme.
+ 
+         The functions a, b, ..., h are known through the
+         subroutines  afun, bfun, ..., hfun in the file
+         functns.f. The alpha is a constant on each side of the
+	 rectanglar domain. the beta and the gamma are defined
+	 by the functions betfun and gamfun (see functns.f for
+	 examples).
+
+      2) block version of the finite difference matrices (several degrees of
+         freedom per grid point. ) It only generates the matrix (without
+	 the right-hand-side), only Dirichlet Boundary conditions are used.
+
+genmat.f ---- the matrix generation routines.
+functns.f --- functions used by the genmat.f
+
+to test the 5-point/7-point matrix please see mak57pt
+to test the block version of the 5-point/7-point matrix see mak57bl
+
diff --git a/MATGEN/FDIF/functns.f b/MATGEN/FDIF/functns.f
new file mode 100644
index 0000000..329f1ef
--- /dev/null
+++ b/MATGEN/FDIF/functns.f
@@ -0,0 +1,171 @@
+c-----------------------------------------------------------------------
+c     contains the functions needed for defining the PDE poroblems. 
+c
+c     first for the scalar 5-point and 7-point PDE 
+c-----------------------------------------------------------------------
+      function afun (x,y,z)
+      real*8 afun, x,y,z 
+      afun = -1.0d0
+      return 
+      end
+
+      function bfun (x,y,z)
+      real*8 bfun, x,y,z 
+      bfun = -1.0d0
+      return 
+      end
+
+      function cfun (x,y,z)
+      real*8 cfun, x,y,z 
+      cfun = -1.0d0
+      return 
+      end
+
+      function dfun (x,y,z)
+      real*8 dfun, x,y,z 
+      data gamma /100.0/ 
+c     dfun = gamma * exp( x * y )
+      dfun = 10.d0
+      return 
+      end
+
+      function efun (x,y,z)
+      real*8 efun, x,y,z
+      data gamma /100.0/ 
+c     efun = gamma * exp( (- x) * y ) 
+      efun = 0.d0
+      return 
+      end
+
+      function ffun (x,y,z)
+      real*8 ffun, x,y,z 
+      ffun = 0.0
+      return 
+      end
+
+      function gfun (x,y,z)
+      real*8 gfun, x,y,z 
+      gfun = 0.0 
+      return 
+      end
+
+      function hfun(x, y, z)
+      real*8 hfun, x, y, z
+      hfun = 0.0
+      return
+      end
+
+      function betfun(side, x, y, z)
+      real*8 betfun, x, y, z
+      character*2 side
+      betfun = 1.0
+      return
+      end
+
+      function gamfun(side, x, y, z)
+      real*8 gamfun, x, y, z
+      character*2 side
+      if (side.eq.'x2') then
+         gamfun = 5.0
+      else if (side.eq.'y1') then
+         gamfun = 2.0
+      else if (side.eq.'y2') then
+         gamfun = 7.0
+      else
+         gamfun = 0.0
+      endif
+      return
+      end
+
+c-----------------------------------------------------------------------
+c     functions for the block PDE's 
+c-----------------------------------------------------------------------
+      subroutine afunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+         coeff((j-1)*nfree+j) = -1.0d0
+ 2    continue
+      return 
+      end
+
+      subroutine bfunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+         coeff((j-1)*nfree+j) = -1.0d0
+ 2    continue
+      return 
+      end
+
+      subroutine cfunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+         coeff((j-1)*nfree+j) = -1.0d0
+ 2    continue
+      return 
+      end
+
+      subroutine dfunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+ 2    continue
+      return 
+      end
+
+      subroutine efunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+ 2    continue
+      return 
+      end
+
+      subroutine ffunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+ 2    continue
+      return 
+      end
+
+      subroutine gfunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+ 2    continue
+      return 
+      end
+c-----------------------------------------------------------------------
+c     The material property function xyk for the 
+c     finite element problem 
+c-----------------------------------------------------------------------
+      subroutine xyk(nel,xyke,x,y,ijk,node)
+      implicit real*8 (a-h,o-z)
+      dimension xyke(2,2), x(*), y(*), ijk(node,*)
+c     
+c     this is the identity matrix.
+c     
+      xyke(1,1) = 1.0d0
+      xyke(2,2) = 1.0d0
+      xyke(1,2) = 0.0d0
+      xyke(2,1) = 0.0d0
+
+      return
+      end
diff --git a/MATGEN/FDIF/genmat.f b/MATGEN/FDIF/genmat.f
new file mode 100644
index 0000000..9d648e9
--- /dev/null
+++ b/MATGEN/FDIF/genmat.f
@@ -0,0 +1,1279 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c    MATRIX GENERATION ROUTINES  -- FINITE DIFFERENCE MATRICES         c
+c----------------------------------------------------------------------c
+c contents:                                                            c
+c----------                                                            c
+c gen57pt  : generates 5-point and 7-point matrices.                   c
+c gen57bl  : generates block 5-point and 7-point matrices.             c
+c                                                                      c
+c supporting routines:                                                 c
+c---------                                                             c
+c gensten  : generate the stencil (point version)                      c
+c bsten    : generate the stencil (block version)                      c
+c fdaddbc  : finite difference add boundary conditions                 c
+c fdreduce : reduce the system to eliminate node with known values     c
+c clrow    : clear a row of a CSR matrix                               c
+c lctcsr   : locate the position of A(i,j) in CSR format               c
+c----------------------------------------------------------------------c
+      subroutine gen57pt(nx,ny,nz,al,mode,n,a,ja,ia,iau,rhs)
+      integer ja(*),ia(*),iau(*), nx, ny, nz, mode, n
+      real*8 a(*), rhs(*), al(6)
+c-----------------------------------------------------------------------
+c On entry:
+c
+c nx      = number of grid points in x direction
+c ny	  = number of grid points in y direction
+c nz	  = number of grid points in z direction
+c al      = array of size 6, carries the coefficient alpha of the
+c           boundary conditions
+c mode    = what to generate:
+c           < 0 : generate the graph only,
+c           = 0 : generate the matrix,
+c           > 0 : generate the matrix and the right-hand side.
+c
+c On exit:
+c
+c n       = number of nodes with unknown values, ie number of rows
+c           in the matrix
+c
+c a,ja,ia = resulting matrix in row-sparse format
+c
+c iau     = integer*n, containing the poisition of the diagonal element
+c           in the a, ja, ia structure
+c
+c rhs     = the right-hand side
+c
+c External functions needed (must be supplied by caller)
+c     afun, bfun, cfun, dfun, efun, ffun, gfun, hfun
+c     betfun, gamfun
+c They have the following prototype:
+c     real*8 function xfun(x, y, z)
+c     real*8 x, y, z
+c-----------------------------------------------------------------------
+c This subroutine computes the sparse matrix in compressed sparse row
+c format for the elliptic equation:
+c       d    du    d    du    d    du      du     du     du
+c L u = --(A --) + --(B --) + --(C --) + D -- + E -- + F -- + G u = H u
+c       dx   dx    dy   dy    dz   dz      dx     dy     dz
+c
+c with general Mixed Boundary conditions, on a rectangular 1-D,
+c 2-D or 3-D grid using 2nd order centered difference schemes.
+c
+c The functions a, b, ..., g, h are known through the
+c as afun, bfun, ..., gfun, hfun in this subroutine.
+c NOTE: To obtain the correct matrix, any function that is not
+c needed should be set to zero.  For example for two-dimensional
+c problems, nz should be set to 1 and the functions cfun and ffun
+c should be zero functions.
+c
+c The Boundary condition is specified in the following form:
+c           du
+c     alpha -- + beta u = gamma
+c           dn
+c Where alpha is constant at each side of the boundary surfaces.  Alpha
+c is represented by parameter al.  It is expected to an array that
+c contains enough elements to specify the boundaries for the problem,
+c 1-D case needs two elements, 2-D needs 4 and 3-D needs 6.  The order
+c of the boundaries in the array is left(west), right(east),
+c bottom(south), top(north), front, rear.  Beta and gamma are functions
+c of type real with three arguments x, y, z.  These two functions are
+c known subroutine 'addbc' as betfun and gamfun.  They should following
+c the same notion as afun ... hfun.  For more restriction on afun ...
+c hfun, please read the documentation follows the subroutine 'getsten',
+c and, for more on betfun and gamfun, please refer to the documentation
+c under subroutine 'fdaddbc'.
+c
+c The nodes are ordered using natural ordering, first x direction, then
+c y, then z.  The mesh size h is uniform and determined by grid points
+c in the x-direction.
+c
+c The domain specified for the problem is [0 .ge. x .ge. 1],
+c [0 .ge. y .ge. (ny-1)*h] and [0 .ge. z .ge. (nz-1)*h], where h is
+c 1 / (nx-1).  Thus if non-Dirichlet boundary condition is specified,
+c the mesh will have nx points along the x direction, ny along y and
+c nz along z.  For 1-D case, both y and z value are assumed to zero
+c when calling relavent functions that have three parameters.
+c Similarly, for 2-D case, z is assumed to be zero.
+c
+c About the expectation of nx, ny and nz:
+c nx is required to be .gt. 1 always;
+c if the second dimension is present in the problem, then ny should be
+c .gt. 1, else 1;
+c if the third dimension is present in the problem, nz .gt. 1, else 1.
+c when ny is 1, nz must be 1.
+c-----------------------------------------------------------------------
+c
+c     stencil [1:7] has the following meaning:
+c
+c     center point = stencil(1)
+c     west point = stencil(2)
+c     east point = stencil(3)
+c     south point = stencil(4)
+c     north point = stencil(5)
+c     front point = stencil(6)
+c     back point = stencil(7)
+c
+c     al[1:6] carry the coefficient alpha in the similar order
+c
+c     west  side = al(1)
+c     east  side = al(2)
+c     south side = al(3)
+c     north side = al(4)
+c     front side = al(5)
+c     back  side = al(6)
+c
+c                           al(4)
+c                           st(5)
+c                            |
+c                            |
+c                            |           al(6)
+c                            |          .st(7)
+c                            |     .
+c         al(1)              | .             al(2)
+c         st(2) ----------- st(1) ---------- st(3)
+c                       .    |
+c                   .        |
+c               .            |
+c            st(6)           |
+c            al(5)           |
+c                            |
+c                           st(4)
+c                           al(3)
+c
+c-------------------------------------------------------------------
+c     some constants
+c
+      real*8 one
+      parameter (one=1.0D0)
+c
+c     local variables
+c
+      integer ix, iy, iz, kx, ky, kz, node, iedge
+      real*8  r, h, stencil(7)
+      logical value, genrhs
+c
+c     nx has to be larger than 1
+c
+      if (nx.le.1) return
+      h = one / dble(nx-1)
+c
+c     the mode
+c
+      value = (mode.ge.0)
+      genrhs = (mode.gt.0)
+c
+c     first generate the whole matrix as if the boundary condition does
+c     not exist
+c
+      kx = 1
+      ky = nx
+      kz = nx*ny
+      iedge = 1
+      node = 1
+      do 100 iz = 1,nz
+         do 90 iy = 1,ny
+            do 80 ix = 1,nx
+               ia(node) = iedge
+c
+c     compute the stencil at the current node
+c
+               if (value) call
+     &              getsten(nx,ny,nz,mode,ix-1,iy-1,iz-1,stencil,h,r)
+c     west
+               if (ix.gt.1) then
+                  ja(iedge)=node-kx
+		  if (value) a(iedge) = stencil(2)
+                  iedge=iedge + 1
+               end if
+c     south
+               if (iy.gt.1) then
+                  ja(iedge)=node-ky
+		  if (value) a(iedge) = stencil(4)
+                  iedge=iedge + 1
+               end if
+c     front plane
+               if (iz.gt.1) then
+                  ja(iedge)=node-kz
+		  if (value) a(iedge) = stencil(6)
+                  iedge=iedge + 1
+               endif
+c     center node
+               ja(iedge) = node
+               iau(node) = iedge
+               if (value) a(iedge) = stencil(1)
+               iedge = iedge + 1
+c     east
+               if (ix.lt.nx) then
+                  ja(iedge)=node+kx
+		  if (value) a(iedge) = stencil(3)
+                  iedge=iedge + 1
+               end if
+c     north
+               if (iy.lt.ny) then
+                  ja(iedge)=node+ky
+		  if (value) a(iedge) = stencil(5)
+                  iedge=iedge + 1
+               end if
+c     back plane
+               if (iz.lt.nz) then
+                  ja(iedge)=node+kz
+                  if (value) a(iedge) = stencil(7)
+                  iedge=iedge + 1
+               end if
+c     the right-hand side
+               if (genrhs) rhs(node) = r
+               node=node+1
+ 80         continue
+ 90      continue
+ 100  continue
+      ia(node)=iedge
+c
+c     Add in the boundary conditions
+c
+      call fdaddbc(nx,ny,nz,a,ja,ia,iau,rhs,al,h)
+c
+c     eliminate the boudary nodes from the matrix
+c
+      call fdreduce(nx,ny,nz,al,n,a,ja,ia,iau,rhs,stencil)
+c
+c     done
+c
+      return
+c-----end-of-gen57pt----------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine getsten (nx,ny,nz,mode,kx,ky,kz,stencil,h,rhs)
+      integer nx,ny,nz,mode,kx,ky,kz
+      real*8 stencil(*),h,rhs,afun,bfun,cfun,dfun,efun,ffun,gfun,hfun
+      external afun,bfun,cfun,dfun,efun,ffun,gfun,hfun
+c-----------------------------------------------------------------------
+c     This subroutine calculates the correct stencil values for
+c     centered difference discretization of the elliptic operator
+c     and the right-hand side
+c
+c L u = delx( A delx u ) + dely ( B dely u) + delz ( C delz u ) +
+c	delx ( D u ) + dely (E u) + delz( F u ) + G u = H
+c
+c   For 2-D problems the discretization formula that is used is:
+c
+c h**2 * Lu == A(i+1/2,j)*{u(i+1,j) - u(i,j)} +
+c	       A(i-1/2,j)*{u(i-1,j) - u(i,j)} +
+c              B(i,j+1/2)*{u(i,j+1) - u(i,j)} +
+c              B(i,j-1/2)*{u(i,j-1) - u(i,j)} +
+c              (h/2)*D(i,j)*{u(i+1,j) - u(i-1,j)} +
+c              (h/2)*E(i,j)*{u(i,j+1) - u(i,j-1)} +
+c              (h/2)*E(i,j)*{u(i,j+1) - u(i,j-1)} +
+c              (h**2)*G(i,j)*u(i,j)
+c-----------------------------------------------------------------------
+c     some constants
+c
+      real*8 zero, half
+      parameter (zero=0.0D0,half=0.5D0)
+c
+c     local variables
+c
+      integer k
+      real*8 hhalf,cntr, x, y, z, coeff
+c
+c     if mode < 0, we shouldn't have come here
+c
+      if (mode .lt. 0) return
+c
+      do 200 k=1,7
+         stencil(k) = zero
+ 200  continue
+c
+      hhalf = h*half
+      x = h*dble(kx)
+      y = h*dble(ky)
+      z = h*dble(kz)
+      cntr = zero
+c     differentiation wrt x:
+      coeff = afun(x+hhalf,y,z)
+      stencil(3) = stencil(3) + coeff
+      cntr = cntr + coeff
+c
+      coeff = afun(x-hhalf,y,z)
+      stencil(2) = stencil(2) + coeff
+      cntr = cntr + coeff
+c
+      coeff = dfun(x,y,z)*hhalf
+      stencil(3) = stencil(3) + coeff
+      stencil(2) = stencil(2) - coeff
+      if (ny .le. 1) goto 99
+c
+c     differentiation wrt y:
+c
+      coeff = bfun(x,y+hhalf,z)
+      stencil(5) = stencil(5) + coeff
+      cntr = cntr + coeff
+c
+      coeff = bfun(x,y-hhalf,z)
+      stencil(4) = stencil(4) + coeff
+      cntr = cntr + coeff
+c
+      coeff = efun(x,y,z)*hhalf
+      stencil(5) = stencil(5) + coeff
+      stencil(4) = stencil(4) - coeff
+      if (nz .le. 1) goto 99
+c
+c differentiation wrt z:
+c
+      coeff = cfun(x,y,z+hhalf)
+      stencil(7) = stencil(7) + coeff
+      cntr = cntr + coeff
+c
+      coeff = cfun(x,y,z-hhalf)
+      stencil(6) = stencil(6) + coeff
+      cntr = cntr + coeff
+c
+      coeff = ffun(x,y,z)*hhalf
+      stencil(7) = stencil(7) + coeff
+      stencil(6) = stencil(6) - coeff
+c
+c contribution from function G:
+c
+ 99   coeff = gfun(x,y,z)
+      stencil(1) = h*h*coeff - cntr
+c
+c     the right-hand side
+c
+      if (mode .gt. 0) rhs = h*h*hfun(x,y,z)
+c
+      return
+c------end-of-getsten---------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine gen57bl (nx,ny,nz,nfree,na,n,a,ja,ia,iau,stencil)
+c     implicit real*8 (a-h,o-z)
+      integer ja(*),ia(*),iau(*),nx,ny,nz,nfree,na,n
+      real*8 a(na,1), stencil(7,1)
+c--------------------------------------------------------------------
+c This subroutine computes the sparse matrix in compressed
+c format for the elliptic operator
+c
+c L u = delx( a . delx u ) + dely ( b . dely u) + delz ( c . delz u ) +
+c	delx ( d . u ) + dely (e . u) + delz( f . u ) + g . u
+c
+c Here u is a vector of nfree componebts and each of the functions
+c a, b, c, d, e, f, g   is an (nfree x nfree) matrix depending of
+c the coordinate (x,y,z).
+c with Dirichlet Boundary conditions, on a rectangular 1-D,
+c 2-D or 3-D grid using centered difference schemes.
+c
+c The functions a, b, ..., g are known through the
+c subroutines  afunbl, bfunbl, ..., gfunbl. (user supplied) .
+c
+c uses natural ordering, first x direction, then y, then z
+c mesh size h is uniform and determined by grid points
+c in the x-direction.
+c 
+c The output matrix is in Block -- Sparse Row format. 
+c
+c--------------------------------------------------------------------
+c parameters:
+c-------------
+c Input:
+c ------
+c nx      = number of points in x direction
+c ny	  = number of points in y direction
+c nz	  = number of points in z direction
+c nfree   = number of degrees of freedom per point
+c na	  = first dimension of array a as declared in calling
+c           program. Must be .ge. nfree**2
+c
+c Output: 
+c ------ 
+c n	  = dimension of matrix (output)
+c
+c a, ja, ia = resulting matrix in  Block Sparse Row format
+c           a(1:nfree**2, j ) contains a nonzero block and ja(j) 
+c           contains the (block) column number of this block.
+c           the block dimension of the matrix is n (output) and 
+c           therefore the total number of (scalar) rows is n x nfree.
+c     
+c iau     = integer*n containing the position of the diagonal element
+c           in the a, ja, ia structure
+c
+c Work space:
+c------------ 
+c stencil =  work array of size (7,nfree**2) [stores local stencils]
+c
+c--------------------------------------------------------------------
+c
+c     stencil (1:7,*) has the following meaning:
+c
+c     center point = stencil(1)
+c     west point   = stencil(2)
+c     east point   = stencil(3)
+c     south point  = stencil(4)
+c     north point  = stencil(5)
+c     front point  = stencil(6)
+c     back point   = stencil(7)
+c
+c
+c                           st(5)
+c                            |
+c                            |
+c                            |
+c                            |          .st(7)
+c                            |     .
+c                            | .
+c         st(2) ----------- st(1) ---------- st(3)
+c                       .    |
+c                   .        |
+c               .            |
+c            st(6)           |
+c                            |
+c                            |
+c                           st(4)
+c
+c-------------------------------------------------------------------
+c     some constants
+c
+      real*8 one
+      parameter (one=1.0D0)
+c
+c     local variables
+c
+      integer iedge,ix,iy,iz,k,kx,ky,kz,nfree2,node
+      real*8  h
+c
+      h = one/dble(nx+1)
+      kx = 1
+      ky = nx
+      kz = nx*ny
+      nfree2 = nfree*nfree
+      iedge = 1
+      node = 1
+      do 100 iz = 1,nz
+         do 90 iy = 1,ny
+            do 80 ix = 1,nx
+               ia(node) = iedge
+               call bsten(nx,ny,nz,ix,iy,iz,nfree,stencil,h)
+c     west
+               if (ix.gt.1) then
+                  ja(iedge)=node-kx
+	          do 4 k=1,nfree2
+		     a(k,iedge) = stencil(2,k)
+ 4		  continue
+                  iedge=iedge + 1
+               end if
+c     south
+               if (iy.gt.1) then
+                  ja(iedge)=node-ky
+	          do 5 k=1,nfree2
+		     a(k,iedge) = stencil(4,k)
+ 5		  continue
+                  iedge=iedge + 1
+               end if
+c     front plane
+               if (iz.gt.1) then
+                  ja(iedge)=node-kz
+	          do 6 k=1,nfree2
+		     a(k,iedge) = stencil(6,k)
+ 6		  continue
+                  iedge=iedge + 1
+               endif
+c     center node
+               ja(iedge) = node
+               iau(node) = iedge
+               do 7 k=1,nfree2
+                  a(k,iedge) = stencil(1,k)
+ 7             continue
+               iedge = iedge + 1
+c     -- upper part
+c     east
+               if (ix.lt.nx) then
+                  ja(iedge)=node+kx
+	          do 8 k=1,nfree2
+		     a(k,iedge) = stencil(3,k)
+ 8		  continue
+                  iedge=iedge + 1
+               end if
+c     north
+               if (iy.lt.ny) then
+                  ja(iedge)=node+ky
+	          do 9 k=1,nfree2
+		     a(k,iedge) = stencil(5,k)
+ 9		  continue
+                  iedge=iedge + 1
+               end if
+c     back plane
+               if (iz.lt.nz) then
+                  ja(iedge)=node+kz
+	          do 10 k=1,nfree2
+                     a(k,iedge) = stencil(7,k)
+ 10		  continue
+                  iedge=iedge + 1
+               end if
+c------next node -------------------------
+               node=node+1
+ 80         continue
+ 90      continue
+ 100  continue
+c     
+c     -- new version of BSR -- renumbering removed. 
+c     change numbering of nodes so that each ja(k) will contain the
+c     actual column number in the original matrix of entry (1,1) of each
+c     block (k).
+c      do 101 k=1,iedge-1
+c         ja(k) = (ja(k)-1)*nfree+1
+c 101  continue
+c
+c      n = (node-1)*nfree
+      n = node-1 
+      ia(node)=iedge
+      return
+c--------------end-of-gen57bl-------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine bsten (nx,ny,nz,kx,ky,kz,nfree,stencil,h)
+c-----------------------------------------------------------------------
+c     This subroutine calcultes the correct block-stencil values for
+c     centered difference discretization of the elliptic operator
+c     (block version of stencil)
+c
+c L u = delx( a delx u ) + dely ( b dely u) + delz ( c delz u ) +
+c       d delx ( u ) + e dely (u) + f delz( u ) + g u
+c
+c   For 2-D problems the discretization formula that is used is:
+c
+c h**2 * Lu == a(i+1/2,j)*{u(i+1,j) - u(i,j)} +
+c	       a(i-1/2,j)*{u(i-1,j) - u(i,j)} +
+c              b(i,j+1/2)*{u(i,j+1) - u(i,j)} +
+c              b(i,j-1/2)*{u(i,j-1) - u(i,j)} +
+c              (h/2)*d(i,j)*{u(i+1,j) - u(i-1,j)} +
+c              (h/2)*e(i,j)*{u(i,j+1) - u(i,j-1)} +
+c              (h/2)*e(i,j)*{u(i,j+1) - u(i,j-1)} +
+c              (h**2)*g(i,j)*u(i,j)
+c-----------------------------------------------------------------------
+c     some constants
+c
+      real*8  zero,half
+      parameter(zero=0.0D0,half=0.5D0)
+c
+c     local variables
+c
+      integer i,k,kx,ky,kz,nfree,nfree2,nx,ny,nz
+      real*8 stencil(7,*), cntr(225), coeff(225),h,h2,hhalf,x,y,z
+c------------
+      if (nfree .gt. 15) then
+         print *, ' ERROR ** nfree too large '
+         stop
+      endif
+c
+      nfree2 = nfree*nfree
+      do 200 k=1, nfree2
+         cntr(k) = zero
+         do 199 i=1,7
+            stencil(i,k) = zero
+ 199     continue
+ 200  continue
+c------------
+      hhalf = h*half
+      h2 = h*h
+      x = h*dble(kx)
+      y = h*dble(ky)
+      z = h*dble(kz)
+c differentiation wrt x:
+      call afunbl(nfree,x+hhalf,y,z,coeff)
+      do 1 k=1, nfree2
+      stencil(3,k) = stencil(3,k) + coeff(k)
+      cntr(k) = cntr(k) + coeff(k)
+ 1    continue
+c
+      call afunbl(nfree,x-hhalf,y,z,coeff)
+      do 2 k=1, nfree2
+         stencil(2,k) = stencil(2,k) + coeff(k)
+         cntr(k) = cntr(k) + coeff(k)
+ 2    continue
+c
+      call dfunbl(nfree,x,y,z,coeff)
+      do 3 k=1, nfree2
+         stencil(3,k) = stencil(3,k) + coeff(k)*hhalf
+         stencil(2,k) = stencil(2,k) - coeff(k)*hhalf
+ 3    continue
+      if (ny .le. 1) goto 99
+c
+c differentiation wrt y:
+c
+      call bfunbl(nfree,x,y+hhalf,z,coeff)
+      do 4 k=1,nfree2
+         stencil(5,k) = stencil(5,k) + coeff(k)
+         cntr(k) = cntr(k) + coeff(k)
+ 4    continue
+c
+      call bfunbl(nfree,x,y-hhalf,z,coeff)
+      do 5 k=1, nfree2
+         stencil(4,k) = stencil(4,k) + coeff(k)
+         cntr(k) = cntr(k) + coeff(k)
+ 5    continue
+c
+      call efunbl(nfree,x,y,z,coeff)
+      do 6 k=1, nfree2
+         stencil(5,k) = stencil(5,k) + coeff(k)*hhalf
+         stencil(4,k) = stencil(4,k) - coeff(k)*hhalf
+ 6    continue
+      if (nz .le. 1) goto 99
+c
+c differentiation wrt z:
+c
+      call cfunbl(nfree,x,y,z+hhalf,coeff)
+      do 7 k=1, nfree2
+         stencil(7,k) = stencil(7,k) + coeff(k)
+         cntr(k) = cntr(k) + coeff(k)
+ 7    continue
+c
+      call cfunbl(nfree,x,y,z-hhalf,coeff)
+      do 8 k=1, nfree2
+         stencil(6,k) = stencil(6,k) + coeff(k)
+         cntr(k) = cntr(k) + coeff(k)
+ 8    continue
+c
+      call ffunbl(nfree,x,y,z,coeff)
+      do 9 k=1, nfree2
+         stencil(7,k) = stencil(7,k) + coeff(k)*hhalf
+         stencil(6,k) = stencil(6,k) - coeff(k)*hhalf
+ 9    continue
+c
+c discretization of  product by g:
+c
+ 99   call gfunbl(nfree,x,y,z,coeff)
+      do 10 k=1, nfree2
+         stencil(1,k) = h2*coeff(k) - cntr(k)
+ 10   continue
+c
+      return
+c------------end of bsten-----------------------------------------------
+c-----------------------------------------------------------------------
+      end
+      subroutine fdreduce(nx,ny,nz,alpha,n,a,ja,ia,iau,rhs,stencil)
+      implicit none
+      integer nx,ny, nz, n, ia(*), ja(*), iau(*)
+      real*8  alpha(*), a(*), rhs(*), stencil(*)
+c-----------------------------------------------------------------------
+c This subroutine tries to reduce the size of the matrix by looking
+c for Dirichlet boundary conditions at each surface and solve the boundary
+c value and modify the right-hand side of related nodes, then clapse all
+c the boundary nodes.
+c-----------------------------------------------------------------------
+c     parameters
+c
+      real*8   zero
+      parameter(zero=0.0D0)
+c
+c     local variables
+c
+      integer  i,j,k,kx,ky,kz,lx,ux,ly,uy,lz,uz,node,nbnode,lk,ld,iedge
+      real*8   val
+      integer  lctcsr
+      external lctcsr
+c
+c     The first half of this subroutine will try to change the right-hand
+c     side of all the nodes that has a neighbor with Dirichlet boundary
+c     condition, since in this case the value of the boundary point is
+c     known.
+c     Then in the second half, we will try to eliminate the boundary
+c     points with known values (with Dirichlet boundary condition).
+c
+      kx = 1
+      ky = nx
+      kz = nx*ny
+      lx = 1
+      ux = nx
+      ly = 1
+      uy = ny
+      lz = 1
+      uz = nz
+c
+c     Here goes the first part. ----------------------------------------
+c
+c     the left (west) side
+c
+      if (alpha(1) .eq. zero) then
+         lx = 2
+         do 10 k = 1, nz
+            do 11 j = 1, ny
+               node = (k-1)*kz + (j-1)*ky + 1
+               nbnode = node + kx
+               lk = lctcsr(nbnode, node, ja, ia)
+               ld = iau(node)
+               val = rhs(node)/a(ld)
+c     modify the rhs
+               rhs(nbnode) = rhs(nbnode) - a(lk)*val
+ 11         continue
+ 10      continue
+      endif
+c
+c     right (east) side
+c
+      if (alpha(2) .eq. zero) then
+         ux = nx - 1
+         do 20 k = 1, nz
+            do 21 j = 1, ny
+               node = (k-1)*kz + (j-1)*ky + nx
+               nbnode = node - kx
+               lk = lctcsr(nbnode, node, ja, ia)
+               ld = iau(node)
+               val = rhs(node)/a(ld)
+c     modify the rhs
+               rhs(nbnode) = rhs(nbnode) - a(lk)*val
+ 21         continue
+ 20      continue
+      endif
+c
+c     if it's only 1-D, skip the following part
+c
+      if (ny .le. 1) goto 100
+c
+c     the bottom (south) side
+c
+      if (alpha(3) .eq. zero) then
+         ly = 2
+         do 30 k = 1, nz
+            do 31 i = lx, ux
+               node = (k-1)*kz + i
+               nbnode = node + ky
+               lk = lctcsr(nbnode, node, ja, ia)
+               ld = iau(node)
+               val = rhs(node)/a(ld)
+c     modify the rhs
+               rhs(nbnode) = rhs(nbnode) - a(lk)*val
+ 31         continue
+ 30      continue
+      endif
+c
+c     top (north) side
+c
+      if (alpha(4) .eq. zero) then
+         uy = ny - 1
+         do 40 k = 1, nz
+            do 41 i = lx, ux
+               node = (k-1)*kz + i + (ny-1)*ky
+               nbnode = node - ky
+               lk = lctcsr(nbnode, node, ja, ia)
+               ld = iau(node)
+               val = rhs(node)/a(ld)
+c     modify the rhs
+               rhs(nbnode) = rhs(nbnode) - a(lk)*val
+ 41         continue
+ 40      continue
+      endif
+c
+c     if only 2-D skip the following section on z
+c
+      if (nz .le. 1) goto 100
+c
+c     the front surface
+c
+      if (alpha(5) .eq. zero) then
+         lz = 2
+         do 50 j = ly, uy
+            do 51 i = lx,  ux
+               node = (j-1)*ky + i
+               nbnode = node + kz
+               lk = lctcsr(nbnode, node, ja, ia)
+               ld = iau(node)
+               val = rhs(node)/a(ld)
+c     modify the rhs
+               rhs(nbnode) = rhs(nbnode) - a(lk)*val
+ 51         continue
+ 50      continue
+      endif
+c
+c     rear surface
+c
+      if (alpha(6) .eq. zero) then
+         uz = nz - 1
+         do 60 j = ly, uy
+            do 61 i = lx, ux
+               node = (nz-1)*kz + (j-1)*ky + i
+               nbnode = node - kz
+               lk = lctcsr(nbnode, node, ja, ia)
+               ld = iau(node)
+               val = rhs(node)/a(ld)
+c     modify the rhs
+               rhs(nbnode) = rhs(nbnode) - a(lk)*val
+ 61         continue
+ 60      continue
+      endif
+c
+c     now the second part ----------------------------------------------
+c
+c     go through all the actual nodes with unknown values, collect all
+c     of them to form a new matrix in compressed sparse row format.
+c
+ 100  kx = 1
+      ky = ux - lx + 1
+      kz = (uy - ly + 1) * ky
+      node = 1
+      iedge = 1
+      do 80 k = lz, uz
+         do 81 j = ly, uy
+            do 82 i = lx, ux
+c
+c     the corresponding old node number
+               nbnode = ((k-1)*ny + j-1)*nx + i
+c
+c     copy the row into local stencil, copy is done is the exact
+c     same order as the stencil is written into array a
+               lk = ia(nbnode)
+               if (i.gt.1) then
+                  stencil(2) = a(lk)
+                  lk = lk + 1
+               end if
+               if (j.gt.1) then
+                  stencil(4) = a(lk)
+                  lk = lk + 1
+               end if
+               if (k.gt.1) then
+                  stencil(6) = a(lk)
+                  lk = lk + 1
+               end if
+               stencil(1) = a(lk)
+               lk = lk + 1
+               if (i.lt.nx) then
+                  stencil(3) = a(lk)
+                  lk = lk + 1
+               endif
+               if (j.lt.ny) then
+                  stencil(5) = a(lk)
+                  lk = lk + 1
+               end if
+               if (k.lt.nz) stencil(7) = a(lk)
+c
+c     first the ia pointer -- points to the beginning of each row
+               ia(node) = iedge
+c
+c     move the values from the local stencil to the new matrix
+c
+c     the neighbor on the left (west)
+               if (i.gt.lx) then
+                  ja(iedge)=node-kx
+                  a(iedge) =stencil(2)
+                  iedge=iedge + 1
+               end if
+c     the neighbor below (south)
+               if (j.gt.ly) then
+                  ja(iedge)=node-ky
+                  a(iedge)=stencil(4)
+                  iedge=iedge + 1
+               end if
+c     the neighbor in the front
+               if (k.gt.lz) then
+                  ja(iedge)=node-kz
+                  a(iedge)=stencil(6)
+                  iedge=iedge + 1
+               endif
+c     center node (itself)
+               ja(iedge) = node
+               iau(node) = iedge
+               a(iedge) = stencil(1)
+               iedge = iedge + 1
+c     the neighbor to the right (east)
+               if (i.lt.ux) then
+                  ja(iedge)=node+kx
+                  a(iedge)=stencil(3)
+                  iedge=iedge + 1
+               end if
+c     the neighbor above (north)
+               if (j.lt.uy) then
+                  ja(iedge)=node+ky
+                  a(iedge)=stencil(5)
+                  iedge=iedge + 1
+               end if
+c     the neighbor at the back
+               if (k.lt.uz) then
+                  ja(iedge)=node+kz
+                  a(iedge)=stencil(7)
+                  iedge=iedge + 1
+               end if
+c     the right-hand side
+               rhs(node) = rhs(nbnode)
+c------next node -------------------------
+               node=node+1
+c
+ 82         continue
+ 81      continue
+ 80   continue
+c
+      ia(node) = iedge
+c
+c     the number of nodes in the final matrix is stored in n
+c
+      n = node - 1
+      return
+c-----------------------------------------------------------------------
+      end
+c-----end of fdreduce-----------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine fdaddbc(nx,ny,nz,a,ja,ia,iau,rhs,al,h)
+      integer nx, ny, nz, ia(nx*ny*nz), ja(7*nx*ny*nz), iau(nx*ny*nz)
+      real*8  h, al(6), a(7*nx*ny*nz), rhs(nx*ny*nz)
+c-----------------------------------------------------------------------
+c This subroutine will add the boundary condition to the linear system
+c consutructed without considering the boundary conditions
+c
+c The Boundary condition is specified in the following form:
+c           du
+c     alpha -- + beta u = gamma
+c           dn
+c Alpha is stored in array AL.  The six side of the boundary appares
+c in AL in the following order: left(west), right(east), bottom(south),
+c top(north), front, back(rear). (see also the illustration in gen57pt)
+c Beta and gamma appears as the functions, betfun and gamfun.
+c They have the following prototype
+c
+c real*8 function xxxfun(x, y, z)
+c real*8 x, y, z
+c
+c where x, y, z are vales in the range of [0, 1][0, (ny-1)*h]
+c [0, (nz-1)*h]
+c
+c At the corners or boundary lines, the boundary conditions are applied
+c in the follow order:
+c 1) if one side is Dirichlet boundary condition, the Dirichlet boundary
+c    condition is used;
+c 2) if more than one sides are Dirichlet, the Direichlet condition
+c    specified for X direction boundary will overwrite the one specified
+c    for Y direction boundary which in turn has priority over Z
+c     direction boundaries.
+c 3) when all sides are non-Dirichlet, the average values are used.
+c-----------------------------------------------------------------------
+c     some constants
+c
+      real*8   half,zero,one,two
+      parameter(half=0.5D0,zero=0.0D0,one=1.0D0,two=2.0D0)
+c
+c     local variables
+c
+      character*2 side
+      integer  i,j,k,kx,ky,kz,node,nbr,ly,uy,lx,ux
+      real*8   coeff, ctr, hhalf, x, y, z
+      real*8   afun, bfun, cfun, dfun, efun, ffun, gfun, hfun
+      external afun, bfun, cfun, dfun, efun, ffun, gfun, hfun
+      real*8   betfun, gamfun
+      integer  lctcsr
+      external lctcsr, betfun, gamfun
+c
+      hhalf = half * h
+      kx = 1
+      ky = nx
+      kz = nx*ny
+c
+c     In 3-D case, we need to go through all 6 faces one by one. If
+c     the actual dimension is lower, test on ny is performed first.
+c     If ny is less or equals to 1, then the value of nz is not
+c     checked.
+c-----
+c     the surface on the left (west) side
+c     Concentrate on the contribution from the derivatives related to x,
+c     The terms with derivative of x was assumed to be:
+c
+c     a(3/2,j,k)*[u(2,j,k)-u(1,j,k)] + a(1/2,j,k)*[u(0,j,k)-u(1,j,k)] +
+c     h*d(1,j,k)*[u(2,j,k)-u(0,j,k)]/2
+c
+c     But they actually are:
+c
+c     2*{a(3/2,j,k)*[u(2,j,k)-u(1,j,k)] -
+c     h*a(1,j,k)*[beta*u(1,j,k)-gamma]/alpha]} +
+c     h*h*d(1,j,k)*[beta*u(1,j,k)-gamma]/alpha
+c
+c     Therefore, in terms of local stencil the right neighbor of a node
+c     should be changed to 2*a(3/2,j,k),
+c     The matrix never contains the left neighbor on this border, nothing
+c     needs to be done about it.
+c     The following terms should be added to the center stencil:
+c     -a(3/2,j,k) + a(1/2,j,k) + [h*d(1,j,k)-2*a(1,j,k)]*h*beta/alpha
+c
+c     And these terms should be added to the corresponding right-hand side
+c     [h*d(1,j,k)-2*a(1,j,k)]*h*gamma/alpha
+c
+c     Obviously, the formula do not apply for the Dirichlet Boundary
+c     Condition, where alpha will be zero. In that case, we simply set
+c     all the elements in the corresponding row to zero(0), then let
+c     the diagonal element be beta, and the right-hand side be gamma.
+c     Thus the value of u at that point will be set. Later on point
+c     like this will be removed from the matrix, since they are of
+c     know value before solving the system.(not done in this subroutine)
+c
+      x = zero
+      side = 'x1'
+      do 20 k = 1, nz
+         z = (k-1)*h
+         do 21 j = 1, ny
+            y = (j-1)*h
+            node = 1+(j-1)*ky+(k-1)*kz
+c
+c     check to see if it's Dirichlet Boundary condition here
+c
+            if (al(1) .eq. zero) then
+               call clrow(node, a, ja, ia)
+               a(iau(node)) = betfun(side,x,y,z)
+               rhs(node) = gamfun(side,x,y,z)
+            else
+c
+c     compute the terms formulated above to modify the matrix.
+c
+c     the right neighbor is stroed in nbr'th posiiton in the a
+               nbr = lctcsr(node, node+kx, ja, ia)
+c
+               coeff = two*afun(x,y,z)
+               ctr = (h*dfun(x,y,z) - coeff)*h/al(1)
+               rhs(node) = rhs(node) + ctr * gamfun(side,x,y,z)
+               ctr = afun(x-hhalf,y,z) + ctr * betfun(side,x,y,z)
+               coeff = afun(x+hhalf,y,z)
+               a(iau(node)) = a(iau(node)) - coeff + ctr
+               a(nbr) = two*coeff
+            end if
+ 21      continue
+ 20   continue
+c
+c     the right (east) side boudary, similarly, the contirbution from
+c     the terms containing the derivatives of x were assumed to be
+c
+c     a(nx+1/2,j,k)*[u(nx+1,j,k)-u(nx,j,k)] +
+c     a(nx-1/2,j,k)*[u(nx-1,j,k)-u(nx,j,k)] +
+c     d(nx,j,k)*[u(nx+1,j,k)-u(nx-1,j,k)]*h/2
+c
+c     Actualy they are:
+c
+c     2*{h*a(nx,j,k)*[gamma-beta*u(nx,j,k)]/alpha +
+c     a(nx-1/2,j,k)*[u(nx-1,j,k)-u(nx,j,k)]} +
+c     h*h*d(nx,j,k)*[gamma-beta*u(nx,j,k)]/alpha
+c
+c     The left stencil has to be set to 2*a(nx-1/2,j,k)
+c
+c     The following terms have to be added to the center stencil:
+c
+c     -a(nx-1/2,j,k)+a(nx+1/2,j,k)-[2*a(nx,j,k)+h*d(nx,j,k)]*beta/alpha
+c
+c     The following terms have to be added to the right-hand side:
+c
+c     -[2*a(nx,j,k)+h*d(nx,j,k)]*h*gamma/alpha
+c
+      x = one
+      side = 'x2'
+      do 22 k = 1, nz
+         z = (k-1)*h
+         do 23 j = 1, ny
+            y = (j-1)*h
+            node = (k-1)*kz + j*ky
+c
+            if (al(2) .eq. zero) then
+               call clrow(node, a, ja, ia)
+               a(iau(node)) = betfun(side,x,y,z)
+               rhs(node) = gamfun(side,x,y,z)
+            else
+               nbr = lctcsr(node, node-kx, ja, ia)
+c
+               coeff = two*afun(x,y,z)
+               ctr = (coeff + h*dfun(x,y,z))*h/al(2)
+               rhs(node) = rhs(node) - ctr * gamfun(side,x,y,z)
+               ctr = afun(x+hhalf,y,z) - ctr * betfun(side,x,y,z)
+               coeff = afun(x-hhalf,y,z)
+               a(iau(node)) = a(iau(node)) - coeff + ctr
+               a(nbr) = two*coeff
+            end if
+ 23      continue
+ 22   continue
+c
+c     If only one dimension, return now
+c
+      if (ny .le. 1) return
+c
+c     the bottom (south) side suface, This similar to the situation
+c     with the left side, except all the function and realted variation
+c     should be on the y.
+c
+c     These two block if statment here is to resolve the possible conflict
+c     of assign the boundary value differently by different side of the
+c     Dirichlet Boundary Conditions. They ensure that the edges that have
+c     be assigned a specific value will not be reassigned.
+c
+      if (al(1) .eq. zero) then
+         lx = 2
+      else
+         lx = 1
+      end if
+      if (al(2) .eq. zero) then
+         ux = nx-1
+      else
+         ux = nx
+      end if
+      y = zero
+      side = 'y1'
+      do 24 k = 1, nz
+         z = (k-1)*h
+         do 25 i = lx, ux
+            x = (i-1)*h
+            node = i + (k-1)*kz
+c
+            if (al(3) .eq. zero) then
+               call clrow(node, a, ja, ia)
+               a(iau(node)) = betfun(side,x,y,z)
+               rhs(node) = gamfun(side,x,y,z)
+            else
+               nbr = lctcsr(node, node+ky, ja, ia)
+c
+               coeff = two*bfun(x,y,z)
+               ctr = (h*efun(x,y,z) - coeff)*h/al(3)
+               rhs(node) = rhs(node) + ctr * gamfun(side,x,y,z)
+               ctr = bfun(x,y-hhalf,z) + ctr * betfun(side,x,y,z)
+               coeff = bfun(x,y+hhalf,z)
+               a(iau(node)) = a(iau(node)) - coeff + ctr
+               a(nbr) = two*coeff
+            end if
+ 25      continue
+ 24   continue
+c
+c     The top (north) side, similar to the right side
+c
+      y = (ny-1) * h
+      side = 'y2'
+      do 26 k = 1, nz
+         z = (k-1)*h
+         do 27 i = lx, ux
+            x = (i-1)*h
+            node = (k-1)*kz+(ny-1)*ky + i
+c
+            if (al(4) .eq. zero) then
+               call clrow(node, a, ja, ia)
+               a(iau(node)) = betfun(side,x,y,z)
+               rhs(node) = gamfun(side,x,y,z)
+            else
+               nbr = lctcsr(node, node-ky, ja, ia)
+c
+               coeff = two*bfun(x,y,z)
+               ctr = (coeff + h*efun(x,y,z))*h/al(4)
+               rhs(node) = rhs(node) - ctr * gamfun(side,x,y,z)
+               ctr = bfun(x,y+hhalf,z) - ctr * betfun(side,x,y,z)
+               coeff = bfun(x,y-hhalf,z)
+               a(iau(node)) = a(iau(node)) - coeff + ctr
+               a(nbr) = two*coeff
+            end if
+ 27      continue
+ 26   continue
+c
+c     If only has two dimesion to work on, return now
+c
+      if (nz .le. 1) return
+c
+c     The front side boundary
+c
+c     If the edges of the surface has been decided by Dirichlet Boundary
+c     Condition, then leave them alone.
+c
+      if (al(3) .eq. zero) then
+         ly = 2
+      else
+         ly = 1
+      end if
+      if (al(4) .eq. zero) then
+         uy = ny-1
+      else
+         uy = ny
+      end if
+c
+      z = zero
+      side = 'z1'
+      do 28 j = ly, uy
+         y = (j-1)*h
+         do 29 i = lx, ux
+            x = (i-1)*h
+            node = i + (j-1)*ky
+c
+            if (al(5) .eq. zero) then
+               call clrow(node, a, ja, ia)
+               a(iau(node)) = betfun(side,x,y,z)
+               rhs(node) = gamfun(side,x,y,z)
+            else
+               nbr = lctcsr(node, node+kz, ja, ia)
+c
+               coeff = two*cfun(x,y,z)
+               ctr = (h*ffun(x,y,z) - coeff)*h/al(5)
+               rhs(node) = rhs(node) + ctr * gamfun(side,x,y,z)
+               ctr = cfun(x,y,z-hhalf) + ctr * betfun(side,x,y,z)
+               coeff = cfun(x,y,z+hhalf)
+               a(iau(node)) = a(iau(node)) - coeff + ctr
+               a(nbr) = two*coeff
+            end if
+ 29      continue
+ 28   continue
+c
+c     Similiarly for the top side of the boundary suface
+c
+      z = (nz - 1) * h
+      side = 'z2'
+      do 30 j = ly, uy
+         y = (j-1)*h
+         do 31 i = lx, ux
+            x = (i-1)*h
+            node = (nz-1)*kz + (j-1)*ky + i
+c
+            if (al(6) .eq. zero) then
+               call clrow(node, a, ja, ia)
+               a(iau(node)) = betfun(side,x,y,z)
+               rhs(node) = gamfun(side,x,y,z)
+            else
+               nbr = lctcsr(node, node-kz, ja, ia)
+c
+               coeff = two*cfun(x,y,z)
+               ctr = (coeff + h*ffun(x,y,z))*h/al(6)
+               rhs(node) = rhs(node) - ctr * gamfun(side,x,y,z)
+               ctr = cfun(x,y,z+hhalf) - ctr * betfun(side,x,y,z)
+               coeff = cfun(x,y,z-hhalf)
+               a(iau(node)) = a(iau(node)) - coeff + ctr
+               a(nbr) = two*coeff
+            end if
+ 31      continue
+ 30   continue
+c
+c     all set
+c
+      return
+c-----------------------------------------------------------------------
+      end
+c-----end of fdaddbc----------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine clrow(i, a, ja, ia)
+      integer i, ja(*), ia(*), k
+      real *8 a(*)
+c-----------------------------------------------------------------------
+c     clear the row i to all zero, but still keep the structure of the
+c     CSR matrix
+c-----------------------------------------------------------------------
+      do 10 k = ia(i), ia(i+1)-1
+         a(k) = 0.0D0
+ 10   continue
+c
+      return
+c-----end of clrow------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      function lctcsr(i,j,ja,ia)
+      integer lctcsr, i, j, ja(*), ia(*), k
+c-----------------------------------------------------------------------
+c     locate the position of a matrix element in a CSR format
+c     returns -1 if the desired element is zero
+c-----------------------------------------------------------------------
+      lctcsr = -1
+      k = ia(i)
+ 10   if (k .lt. ia(i+1) .and. (lctcsr .eq. -1)) then
+         if (ja(k) .eq. j) lctcsr = k
+         k = k + 1
+         goto 10
+      end if
+c
+      return
+c-----------------------------------------------------------------------
+      end
+c-----end of lctcsr-----------------------------------------------------
+
+
diff --git a/MATGEN/FDIF/makefile b/MATGEN/FDIF/makefile
new file mode 100644
index 0000000..18978d2
--- /dev/null
+++ b/MATGEN/FDIF/makefile
@@ -0,0 +1,21 @@
+FFLAGS = 
+F77 = f77
+
+#F77 = cf77
+#FFLAGS = -Wf"-dp"
+
+FILES1 = rgen5pt.o functns.o 
+
+gen5.ex:	$(FILES1) ../../libskit.a 
+	$(F77) $(FFLAGS) -o gen5.ex $(FILES1) ../../libskit.a 
+
+FILES2 = rgenblk.o functns.o 
+genbl.ex:	$(FILES2)  ../../libskit.a 
+	$(F77) $(FFLAGS) -o genbl.ex $(FILES2) ../../libskit.a 
+
+clean:
+	rm -f *.o *.ex core *.trace
+
+../../libskit.a:
+	(cd ../..; $(MAKE) $(MAKEFLAGS) libskit.a)
+
diff --git a/MATGEN/FDIF/rgen5pt.f b/MATGEN/FDIF/rgen5pt.f
new file mode 100644
index 0000000..fb736f8
--- /dev/null
+++ b/MATGEN/FDIF/rgen5pt.f
@@ -0,0 +1,66 @@
+      program fivept
+c-----------------------------------------------------------------------
+c main program for generating 5 point and 7-point matrices in the
+c Harwell-Boeing format.  Creates a file with containing a 
+c harwell-boeing matrix. typical session:
+c user answer are after the colon
+c Enter nx, ny, nz  : 10 10 1
+c Filename for matrix: test.mat
+c output matrix in data file : test.mat
+c
+c nz = 1 will create a 2-D problem
+c
+c-----------------------------------------------------------------------
+      integer nmx, nxmax
+      parameter (nxmax = 50, nmx = nxmax*nxmax)
+c      implicit none 
+      integer ia(nmx),ja(7*nmx),iau(nmx)
+      real*8 a(7*nmx),rhs(nmx),al(6)
+      character title*72, key*8, type*3, matfile*50, guesol*2
+c-----------------------------------------------------------------------    
+      integer nx, ny, nz, iout, n, ifmt, job
+      write (6,*)  '  '
+      write(6,'(22hEnter  nx, ny, nz   : ,$)') 
+      read (5,*) nx, ny, nz 
+      write(6,'(22hFilename for matrix : ,$)') 
+      read(5,'(a50)') matfile
+      open (unit=7,file=matfile)
+c
+c     boundary condition is partly specified here
+c
+c      al(1) = 1.0D0
+c      al(2) = 0.0D0
+c      al(3) = 2.3D1
+c      al(4) = 0.4D0
+c      al(5) = 0.0D0
+c      al(6) = 8.2D-2
+       al(1) = 0.0D0
+       al(2) = 0.0D0
+       al(3) = 0.0D1
+       al(4) = 0.0D0
+       al(5) = 0.0D0
+       al(6) = 0.0D0 
+c
+      call gen57pt (nx,ny,nz,al,0,n,a,ja,ia,iau,rhs)
+      iout = 7
+c
+c     write out the matrix
+c
+      guesol='NN'
+      title = 
+     *     ' 5-POINT TEST MATRIX FROM SPARSKIT                    '
+c          '123456789012345678901234567890123456789012345678901234567890
+      type  = 'RUA' 
+      key ='SC5POINT'
+C           12345678 
+      ifmt = 15
+      job = 2
+c   upper part only??  
+c      call getu (n, a, ja, ia, a, ja, ia) 
+      call prtmt (n,n,a,ja,ia,rhs,guesol,title,key,type,
+     1     ifmt,job,iout) 
+      write (6,*) ' output matrix in data file : ', matfile
+c     
+      stop
+      end
+      
diff --git a/MATGEN/FDIF/rgenblk.f b/MATGEN/FDIF/rgenblk.f
new file mode 100644
index 0000000..4df0c7a
--- /dev/null
+++ b/MATGEN/FDIF/rgenblk.f
@@ -0,0 +1,63 @@
+      program bfivept
+c-----------------------------------------------------------------------
+c main program for generating BLOCK 5 point and 7-point matrices in the
+c Harwell-Boeing format.  Creates a file with containing a 
+c harwell-boeing matrix. 
+c
+c max block size = 5
+c max number of grid points = 8000  = ( nx * ny * nz .le. 8000) 
+c matrix dimension =  (nx*ny*nz* Block-size**2) .le. 8000 * 25= 200,000
+c
+c typical session:
+c Enter nx, ny, nz : 10 10 1 
+c enter block-size : 4
+c enter filename for matrix: test.mat 
+c output matrix in data file : test.mat 
+c
+c nz =1 will create a 2-D problem
+c-----------------------------------------------------------------------
+      parameter (nxmax = 20, nmx = nxmax*nxmax*nxmax, ntot=nmx*25) 
+      integer ia(ntot),ja(ntot),iau(ntot), iao(ntot),jao(ntot)
+      real*8 stencil(7,100), a(ntot), ao(ntot) 
+      character title*72,key*8,type*3, matfile*50, guesol*2
+c-----------------------------------------------------------------------
+      write (6,*)  '  '
+      write(6,'(22hEnter  nx, ny, nz   : ,$)') 
+      read (5,*) nx, ny, nz 
+      write(6,'(22hnfree (Block size)  : ,$)') 
+      read (5,*) nfree 
+     
+      write(6,'(22hFilename for matrix : ,$)') 
+
+      read(5,'(a50)') matfile
+      open (unit=7,file=matfile) 
+c
+      write (6,*) ' output in data file : ', matfile
+
+c------------------------------------------------------
+      na = nfree*nfree
+c
+      call gen57bl (nx,ny,nz,nfree,na,n,a,ja,ia,iau,stencil)
+c------------------------------------------------------
+
+      print *, ' n=', n, ' nfree ', nfree, ' na =', na
+
+      call bsrcsr(1,n,nfree, na, a, ja, ia, ao, jao, iao)
+      n = n * nfree ! Apr. 21, 1995
+
+      guesol='NN'
+
+      title =
+     *     ' BLOCK 5-POINT TEST MATRIX FROM SPARSKIT               '
+      type  = 'RUA'
+      key   = 'BLOCK5PT'
+C              12345678 
+      ifmt = 15
+      job = 2
+      iout = 7
+      call prtmt (n,n,ao,jao,iao,rhs,guesol,title,key,type,
+     1     ifmt,job,iout) 
+      print *, ' output in data file : ', matfile
+c
+      stop
+      end
diff --git a/MATGEN/FEM/README b/MATGEN/FEM/README
new file mode 100644
index 0000000..cd1745b
--- /dev/null
+++ b/MATGEN/FEM/README
@@ -0,0 +1,26 @@
+---------------------------------------------------------------
+
+                 SPARSKIT  Modules  FEM
+
+---------------------------------------------------------------
+
+    This directory contains the SPARSKIT FEM module,
+    a matrix generator for finite element matrices.
+
+contents:
+=========
+
+    convdif.f  == a driver to generate a matrix and some associated plots 
+    functns2.o == functions needed by the driver -- define the coefficients
+                  of the PDE
+    meshes.f   == set of sample meshes defined as inout to the driver
+    makefile   == a makefile for an executable to generate a sample mesh 
+    elmtlib2.f == a small finite element library 
+
+mat.hb is a test matrix.
+
+Two output files are provided:  mat.ps and msh.ps.  You may wish to save
+these to another name before running the test program so that you may
+compare your output to these files.
+
+-----------------------------------------------------------------------  
diff --git a/MATGEN/FEM/convdif.f b/MATGEN/FEM/convdif.f
new file mode 100644
index 0000000..e58fd8a
--- /dev/null
+++ b/MATGEN/FEM/convdif.f
@@ -0,0 +1,131 @@
+      program convdif 
+c-----------------------------------------------------------------------
+c this driver will generate a finite element matrix for the
+c convection-diffusion problem 
+c
+c                  - Div ( K(x,y) Grad u ) + C grad u = f
+c                    u = 0 on boundary 
+c 
+c (Dirichlet boundary conditions). 
+c----------------------------------------------------------------------- 
+c this code will prompt for desired mesh (from 0 to 9, with one being
+c a user input one) and will general the matrix in harewell-Boeing format
+c in the file mat.hb. It also generates two post script files, one 
+c showing the pattern of the matrix (mat.ps) and the other showing the
+c corresponding mesh (msh.ps).
+c-----------------------------------------------------------------------
+c the structure and organization of the fem codes follow very closely 
+c that of the book by Noborou Kikuchi (Finite element methods in 
+c mechanics,   Cambridge Univ. press, 1986). 
+c-----------------------------------------------------------------------
+c coded Y. Saad and S. Ma -- this version dated August 11, 1993 
+c----------------------------------------------------------------------- 
+      implicit none 
+      integer maxnx, maxnel
+      parameter (maxnx = 8000, maxnel = 15000)
+      real*8 a(7*maxnx),x(maxnx),y(maxnx),f(3*maxnx)
+      integer ijk(3,maxnel),ichild(12,maxnel),iparnts(2,maxnx),
+     *     ia(maxnx),ja(7*maxnx),iwk(maxnx),jwk(maxnx),nodcode(maxnx),
+     *     iperm(maxnx)
+c 
+      character matfile*20, title*72, munt*2,key*8, type*3
+      real size 
+c     
+      integer iin,node,nx,nelx,iout,ndeg,na,nmesh,nref,nxmax,nelmax,nb,
+     *    ii,nxnew, nelxnew,ierr,job,n,ncol,mode,ptitle,ifmt 
+      external xyk, funb, func, fung
+      data iin/7/,node/3/,nx/0/,nelx/0/,iout/8/,ndeg/12/, na/3000/
+c--------------------------------------------------------------
+c choose starting mesh   --- 
+c--------------------------------------------------------------
+c     files for output 
+c 
+      open(unit=10,file='mat.hb') 
+      open(unit=11,file='msh.ps') 
+      open(unit=12,file='mat.ps') 
+c-----------------------------------------------------------------------
+      print *, ' enter chosen mesh '
+      read (*,*) nmesh
+      if (nmesh .eq. 0) then 
+         print *, 'enter input file for initial mesh '
+         read(*,'(a20)') matfile
+         open (unit=7,file=matfile)
+      endif
+c----------------------------------------------------------------------- 
+      print *, ' Enter the number of refinements desired '
+      read (*,*) nref
+      call inmesh (nmesh,iin,nx,nelx,node,x,y,nodcode,ijk,iperm) 
+c
+c     ...REFINE THE GRID
+c 
+      nxmax = maxnx
+      nelmax= maxnel
+      nb = 0 
+      do 10 ii = 1, nref
+c     
+c     estimate the number nx and nelx at next refinement level.
+c
+         call checkref(nx,nelx,ijk,node,nodcode,nb,nxnew,nelxnew)
+         if (nxnew .gt. nxmax .or. nelxnew .gt. nelmax) then
+	    print *, ' Was able to do only ', ii-1 ,'  refinements'
+	    goto 11
+         endif
+c
+c     ...if OK refine  all elements 
+c     
+         call refall(nx,nelx,ijk,node,ndeg,x,y,ichild,iparnts,nodcode,
+     *        nxmax, nelmax, ierr)
+         if (ierr .ne. 0) print *, '** ERROR IN REFALL : ierr =',ierr 
+ 10   continue
+ 11   continue
+c-----------------------------------------------------------------------
+      job = 0
+c-----------------------------------------------------------------------
+c     assemble the matrix in CSR format 
+c----------------------------------------------------------------------- 
+      call assmbo (nx,nelx,node,ijk,nodcode,x,y,
+     *     a,ja,ia,f,iwk,jwk,ierr,xyk,funb,func,fung) 
+      n = nx 
+c----------------------Harewell-Boeing matrix---------------------------
+c---------------------1---------2---------3---------5---------6
+c            12345678901234567890123456789012345678901234567890
+      title='1Sample matrix from SPARSKIT  ' 
+      key = 'SPARSKIT'
+      type = 'rua'
+      ifmt = 6
+      job = 2 
+      call prtmt (n,n,a,ja,ia,f,'NN',title,key,type,ifmt,job,10)       
+c----------------------Plot of mesh-------------------------------------
+c----------------------------------------------------------------------- 
+      size = 6.0 
+      munt = 'in' 
+      mode = 0 
+      title ='Finite element mesh ' 
+      ptitle = 1
+      call psgrid (nx,ja,ia,x,y,title,ptitle,size,munt,11) 
+c      hsize  = 5.6 
+c      vsize = 5.6 
+c      xleft = 0.0
+c      bot = 0.0
+c      job = 30 
+c      call texgrd(nx,ja,ia,x,y,munt,size,vsize,hsize,
+c     *     xleft,bot,job,title,ptitle,ijk,node,nelx,11) 
+c----------------------Plot of matrix-pattern---------------------------
+c----------------------------------------------------------------------- 
+      size = 5.5
+      mode = 0
+      title = 'Assembled Matrix'
+      ptitle = 1
+      ncol = 0
+      iout = 12
+      call pspltm(n,n,mode,ja,ia,title,ptitle,size,munt,ncol,iwk,12) 
+c      xleft = 0.00 
+c      bot = 0.70 
+c      job =  0
+c      call texplt(nx,nx,mode,ja,ia,munt,size,vsize,hsize,xleft,bot,
+c     *     job,title,ptitle,ncol,iwk,12) 
+      stop
+c-----end-of-program-convdif--------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
diff --git a/MATGEN/FEM/elmtlib2.f b/MATGEN/FEM/elmtlib2.f
new file mode 100644
index 0000000..90f4cec
--- /dev/null
+++ b/MATGEN/FEM/elmtlib2.f
@@ -0,0 +1,1501 @@
+      subroutine refall(nx, nelx,ijk,node,ndeg,x,y,
+     *     ichild,iparnts,nodcode,nxmax,nelmax,ierr)
+      implicit real*8  (a-h,o-z)
+      integer nx, nelx, node, ndeg, nxmax, nelmax 
+      integer ichild(ndeg,1),iparnts(2,nx),ijk(node,*), nodcode(nx)
+      integer midnode(20),inod(20) 
+      real*8  x(*),y(*)
+c-------------------------------------------------------------
+c refines a finite element grid using triangular elements.
+c uses mid points to refine all the elements of the grid.
+c
+c nx	= number of nodes at input
+c nelx	= number of elements at input
+c ijk	= connectivity matrix: for node k, ijk(*,k) point to the
+c         nodes of element k. 
+c node  = first dimension of array ijk [should be >=3] 
+c ndeg	= first dimension of array ichild which is at least as large
+c         as the max degree of each node
+c x,y   = real*8 arrays containing the x(*) and y(*) coordinates 
+c	  resp. of the nodes.
+c ichild= list of the children of a node: ichild(1,k) stores 
+c         the position in ichild(*,k)  of the last child so far.
+c         (local use)
+c iparnts= list of the 2 parents of each node.
+c         (local use)
+c nodcode= boundary information list for each node with the
+c	   following meaning:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point.
+c corner elements are used only to generate the grid by refinement 
+c since they do not  correspond to real elements. 
+c nxmax  = maximum number of nodes allowed. If during the algorithm
+c          the number of nodes being created exceeds nxmax then 
+c	   refall  quits without modifying the (x,y) xoordinates
+c	   and nx, nelx. ijk is modified. Also ierr is set to 1.
+c nelmax = same as above for number of elements allowed. See ierr..
+c ierr	 = error message: 
+c	   0 --> normal return
+c	   1 --> refall quit because nxmax  was exceeded.
+c	   2 --> refall quit because nelmax was exceeded.
+c--------------------------------------------------------------
+c---------------------------------------------------------------  
+c inilitialize lists of children and parents --
+c data structure is as follows
+c ichild(1,k) stores the position of last child of node k so far in list
+c ichild(j,k) , j .ge. 2 = list of children of node k.
+c iparnts(1,k) and iparnts(2,k) are the two parents of node k. 
+c---------------------------------------------------------------  
+c------ do a first check :
+      if (nx .ge. nxmax) goto 800
+      if (nelx .ge. nelmax) goto 900
+c------ initialize
+      do 1 k=1,nx
+         do 2 j=2,ndeg
+            ichild(j,k) = 0
+ 2       continue
+         ichild(1,k) = 1
+         iparnts(1,k)= 0
+         iparnts(2,k)= 0
+ 1    continue
+c------- initialize nelxnew and nxnew 
+      nelxnew = nelx
+      nxnew   = nx
+      ierr    = 0
+c--------------------------------------------------------------
+c main loop: scan all elements
+c--------------------------------------------------------------
+c     do 100 nel = nelx,1,-1
+      do 100 nel = 1, nelx
+c note : interesting question which order is best for parallelism?
+c alternative order: do 100 nel = nelx, 1, -1
+c
+c------ unpack nodes of element
+         do 101 i=1,node
+            inod(i) = ijk(i,nel)
+c convention: node after last node = first node. 
+            inod(node+i) = inod(i)
+            midnode(i) = 0
+ 101     continue
+c--------------------------------------------------------------
+c for each new potential node determine if it has already been 
+c numbered. a potential node is the middle of any two nodes ..
+c-------------------------------------------------------------- 
+         do 80 ii=1,node
+        	k1 = inod(ii)
+	        k2 = inod(ii+1)
+c------- test for current pair :
+                last = ichild(1,k1)
+                do 21 k=2,last
+                   jchild = ichild(k,k1) 
+                   ipar1 = iparnts(1,jchild)
+                   ipar2 = iparnts(2,jchild)
+                   if( (ipar1 .eq. k1 .and. ipar2 .eq. k2) .or. 
+     *                  (ipar2 .eq. k1 .and. ipar1 .eq. k2)) then
+c node has already been created and numbered ....
+                      midnode(ii) = jchild
+c... therefore it must be an internal node
+                      nodcode(jchild) = 0
+c... and no new node to create.
+                      goto 80
+                   endif
+c-----------------------------------------------------	    
+ 21         continue
+c     
+c else  create a new node
+c
+            nxnew = nxnew + 1
+            if (nxnew .gt. nxmax) goto 800
+c-------
+            x(nxnew) = (x(k1) + x(k2))*0.5
+            y(nxnew) = (y(k1) + y(k2))*0.5
+            midnode(ii) = nxnew
+c
+c update nodcode information -- normally min0(nodcode(k1),nodcode(k2))
+c 
+            nodcode(nxnew) = min0(1,nodcode(k1),nodcode(k2))
+c     
+c update parents and children's lists
+c 
+            iparnts(1,nxnew) = k1
+            iparnts(2,nxnew) = k2
+c     
+            last = last+1
+            ichild(last,k1) = nxnew
+            ichild(1,k1) = last
+c     
+            last = ichild(1,k2)+1
+            ichild(last,k2) = nxnew
+            ichild(1,k2) = last
+c     
+ 80      continue		
+c
+c------- replace current element by new one
+c
+         do 81 i=1,node
+            jnod = midnode(i)
+            ijk(i,nel) = jnod
+ 81      continue
+c-------create new elements
+         do 82 ii=1, node
+            nelxnew = nelxnew+1
+            if (nelxnew .gt. nelmax) goto 900
+            ijk(1,nelxnew) = inod(ii)
+            k = ii
+            do jj=2,node
+               ijk(jj,nelxnew) = midnode(k)
+               k = k+2
+               if (k .gt. node) k =  k-node
+           enddo
+ 82     continue
+c------ done !
+ 100  continue
+      nx = nxnew
+      nelx = nelxnew
+      return
+ 800  ierr = 1
+      return
+ 900  ierr = 2
+      return
+      end
+c
+      subroutine checkref(nx,nelx,ijk,node,nodcode,
+     *     nbound,  nxnew,nelxnew) 
+c-------------------------------------------------------------	
+c returns the expected the new number of nodes and 
+c elemnts of refall is applied to current grid once.
+c
+c nx	= number of nodes at input
+c nelx	= number of elements at input
+c ijk	= connectivity matrix: for node k, ijk(*,k) point to the
+c         nodes of element k.
+c nbound  = number of boundary points on entry - enter zero if
+c	     unknown
+c
+c nodcode= boundary information list for each node with the
+c	   following meaning:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point.
+c
+c nxnew  = new number of nodes if refall were to be applied
+c nelxnew = same for nelx.
+c--------------------------------------------------------------
+       integer ijk(node,1),nodcode(nx)
+c
+	nelxnew = nelx*4
+c
+c count the number of boundary nodes
+c
+	if (nbound .ne. 0) goto 2
+	do 1 j=1, nx
+	if (nodcode(j) .ge. 1) nbound = nbound+1
+ 1	continue
+c number of edges=[3*(number of elmts) + number of bound nodes ]/ 2
+ 2	continue
+	nxnew = nx + (3*nelx+nbound)/2
+	nbound = 2*nbound
+	return
+	end				
+c----------------------------------------------------------------------- 
+	subroutine unassbl (a,na,f,nx,nelx,ijk,nodcode,
+     *			   node,x,y,ierr,xyk)
+c----------------------------------------------------------------------- 
+c a      = un-assembled matrix on output
+c na	 = 1-st dimension of a.  a(na,node,node)
+c
+c f      = right hand side (global load vector) in un-assembled form
+c nx     = number of nodes at input
+c nelx	 = number of elements at input
+c ijk	 = connectivity matrix: for node k, ijk(*,k) point to the
+c          nodes of element k.
+c node	 = total number of nodal points in each element
+c	   also second dimension of a.
+c
+c nodcode= boundary information list for each node with the
+c	   following meaning:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point (corner points
+c
+c x,y   = real*8 arrays containing the $x$ and $y$ coordinates 
+c	  resp. of the nodes.
+c         K11, K22, and K12 at that element.
+c ierr	= error message integer . 
+c	  ierr = 0 --> normal return
+c	  ierr = 1 --> negative area encountered (due to bad 
+c	           numbering of nodes of an element)
+c
+c xyk	= subroutine defining the material properties at each 
+c         element. Form: 
+c 	call xyk(nel,xyke,x,y,ijk,node) 
+c--------------------------------------------------------------
+	implicit real*8 (a-h,o-z)
+        dimension a(na,node,node),ijk(node,1),x(1),y(1),f(node,1),
+     *	    ske(3,3),fe(3),xe(3),ye(3),xyke(2,2)
+            integer nodcode(1)
+	 external xyk
+
+c--------------------------------------------------------------
+c   initialize
+c--------------------------------------------------------------
+	do 100 i=1, node 
+	do 100 j=1, nx
+               f(i,j) = 0.0d0
+ 100	continue
+c---------------------------------------------------
+c main loop
+c--------------------------------------------------- 
+	do 102 nel=1, nelx
+c
+c get coordinetes of nodal points
+c 
+	do 104 i=1, node
+	j = ijk(i,nel)
+	xe(i) = x(j)
+	ye(i) = y(j)
+ 104	continue
+c
+c compute determinant
+c
+ 	det=xe(2)*(ye(3)-ye(1))+xe(3)*(ye(1)-ye(2))+xe(1)*(ye(2)-ye(3))
+        if ( det .le. 0.) then
+          print *, 'nel', nel, ' det = ' , det
+          print *, xe(1), xe(2), xe(3)
+          print *, ye(1), ye(2), ye(3)
+        end if
+c
+c set material properties
+c 
+	call xyk(xyke,x,y)
+c
+c construct element stiffness matrix
+c
+	ierr = 0
+	call estif3(nel,ske,fe,det,xe,ye,xyke,ierr)
+	if (ierr .ne. 0) then
+          write (*,*) 'ERROR: estif3 gave an error',ierr
+          return
+        endif
+c	write (8,'(9f8.4)') ((ske(i,j),j=1,3),i=1,3)
+c assemble: add element stiffness matrix to global matrix
+c 
+	do 120 ka=1, node
+            f(ka,nel) = fe(ka)
+        do 108 kb = 1,node
+            a(nel,ka,kb) = ske(ka,kb)
+ 108	continue
+ 120	continue
+ 102	continue
+        return
+	end
+c-----------------------------------------------------------------------
+	subroutine unassbl_lstif(a, na, f, nx, nelx, ijk, nodcode,
+     *  	           node, x, y, ierr, xyk, funb, func, fung)
+c----------------------------------------------------------------------- 
+c a      = un-assembled matrix on output
+c
+c na	 = 1-st dimension of a.  a(na,node,node)
+c
+c f      = right hand side (global load vector) in un-assembled form
+c
+c nx     = number of nodes at input
+c
+c nelx	 = number of elements at input
+c
+c ijk	 = connectivity matrix: for node k, ijk(*,k) point to the
+c          nodes of element k.
+c
+c nodcode= boundary information list for each node with the
+c	   following meaning:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point (corner points
+c
+c node	 = total number of nodal points in each element
+c	   also second dimension of a.
+c
+c x,y   = real*8 arrays containing the $x$ and $y$ coordinates 
+c	  resp. of the nodes.
+c         K11, K22, and K12 at that element.
+c
+c ierr	= error message integer . 
+c	  ierr = 0 --> normal return
+c	  ierr = 1 --> negative area encountered (due to bad 
+c	           numbering of nodes of an element)
+c
+c xyk	= subroutine defining the material properties at each 
+c         element. Form:  	call xyk(xyke,x,y) 
+c
+c funb, = functions needed for the definition of lstif3 problem
+c func,
+c fung
+c--------------------------------------------------------------
+c moulitsa@cs.umn.edu : It uses lstif3 problem
+c--------------------------------------------------------------
+      implicit real*8 (a-h,o-z)
+      dimension a(na,node,node), ijk(node,1), x(1), y(1), f(node,1),
+     &          ske(3,3), fe(3), xe(3), ye(3) 
+      integer nodcode(1)
+      external xyk, funb, func, fung
+c--------------------------------------------------------------
+c   initialize
+c--------------------------------------------------------------
+      do i=1, node 
+	do j=1, nx
+          f(i,j) = 0.0d0
+        end do
+      end do
+
+c---------------------------------------------------
+c main loop
+c--------------------------------------------------- 
+      do nel=1, nelx
+c
+c get coordinetes of nodal points
+c 
+	do i=1, node
+	  j = ijk(i,nel)
+	  xe(i) = x(j)
+	  ye(i) = y(j)
+        end do
+c
+c compute determinant
+c
+c	det=xe(2)*(ye(3)-ye(1))+xe(3)*(ye(1)-ye(2))+xe(1)*(ye(2)-ye(3))
+c       if ( det .le. 0.) then
+c         print *, 'nel', nel, ' det = ' , det
+c         print *, xe(1), xe(2), xe(3)
+c         print *, ye(1), ye(2), ye(3)
+c       end if
+c
+c construct element stiffness matrix
+c
+	ierr = 0
+
+        call lstif3(ske, fe, xe, ye, xyk, funb, func, fung)
+c	write (8,'(9f8.4)') ((ske(i,j),j=1,3),i=1,3)
+c
+c assemble: add element stiffness matrix to global matrix
+c 
+	do ka=1, node
+          f(ka,nel) = fe(ka)
+          do kb = 1,node
+            a(nel,ka,kb) = ske(ka,kb)
+          end do
+        end do
+
+      end do
+
+      return
+      end
+c----------------------------------------------------------------------- 
+	subroutine assmbo (nx, nelx, node, ijk, nodcode, x, y, a, ja, 
+     *                  ia, f, iwk, jwk, ierr, xyk, funb, func, fung)
+c----------------------------------------------------------------------- 
+c nx     = number of nodes at input
+c
+c nelx	 = number of elements at input
+c
+c node	 = total number of nodal points in each element
+c
+c ijk	 = connectivity matrix: for node k, ijk(*,k) point to the
+c          nodes of element k.
+c
+c nodcode= boundary information list for each node with the
+c	   following meaning:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point (corner points
+c
+c x,y   = real arrays containing the $x$ and $y$ coordinates 
+c	  resp. of the nodes.
+c
+c a,ja,ia= assembled matrix on output
+c
+c f      = right hand side (global load vector) 
+c
+c iwk,jwk = two integer work arrays.
+c
+c ierr	= error message integer . 
+c	  ierr = 0 --> normal return
+c	  ierr = 1 --> negative area encountered (due to bad 
+c	           numbering of nodes of an element)
+c
+c xyk	= subroutine defining the material properties at each 
+c         element. Form: 
+c 	call xyk(nel,xyke,x,y,ijk,node) with on return
+c         xyke =  material constant matrices. 
+c         for each element nel, xyke(1,nel),xyke(2,nel) 
+c         and xyke(3,nel) represent the constants
+c         K11, K22, and K12 at that element.
+c--------------------------------------------------------------
+c moulitsa@cs.umn.edu : It has been modified so as to handle
+c      more types of domains/meshes i.e.  |\ /|
+c                                         | X |
+c                                         |/ \|
+c--------------------------------------------------------------
+      implicit real*8  (a-h,o-z)
+      dimension a(*),ijk(node,1),x(1),y(1),f(1),ske(3,3),fe(3),
+     *      xe(3),ye(3),iwk(1),jwk(1)
+      integer ia(1), ja(*), nodcode(1)
+      external xyk, funb, func, fung
+
+c--------------------------------------------------------------
+c   initialize
+c--------------------------------------------------------------
+      do i=1,nx 
+        f(i) = 0.0 
+      end do
+c initialize  pointer arrays.
+      do k=1,nx+1
+        ia(k) = 1
+        jwk(k) = 0
+      end do
+      do k=1,nelx
+        do j=1,node
+          knod = ijk(j,k)
+          ia(knod) = ia(knod) + 2
+        end do
+      end do
+c---------------------------------------------------
+      do k=1, nx
+	if (nodcode(k) .ge.1 ) ia(k)=ia(k)+1
+      end do
+c
+      ksav = ia(1)
+      ia(1) = 1
+      do j=2, nx+1
+        ksavn = ia(j)
+        ia(j) = ia(j-1) +  ksav
+        iwk(j-1) = ia(j-1)-1
+        ksav = ksavn
+      end do
+
+c-----------------
+c main loop
+c-----------------
+      do nel=1, nelx
+c
+c get coordinates of nodal points
+c
+	do i=1, node
+	  j = ijk(i,nel)
+          xe(i) = x(j)
+          ye(i) = y(j)
+        end do
+c
+c compute determinant
+c
+c 	det=xe(2)*(ye(3)-ye(1))+xe(3)*(ye(1)-ye(2))+xe(1)*(ye(2)-ye(3))
+c
+c set material properties
+c 
+c	call xyk(nel,xyke,x,y,ijk,node)
+c
+c construct element stiffness matrix
+c
+        ierr = 0
+c
+c	call evalg(nel, fe, xe, ye, fung, ierr)
+c	call estif3(nel,ske,fe,det,xe,ye,xyke,ierr)
+        call lstif3(ske, fe, xe, ye, xyk, funb, func, fung)
+        if (ierr .ne. 0) return
+c
+c assemble: add element stiffness matrix to global matrix
+c 
+        do ka=1, node
+          ii = ijk(ka,nel)
+	  f(ii) = f(ii) + fe(ka)
+c
+c unpack row into jwk1
+c
+	  irowst = ia(ii)
+	  ilast  = iwk(ii) 
+          do k=irowst,ilast 
+	    jwk(ja(k)) = k
+          end do
+c
+	  do kb = 1,node
+c
+c column number = jj
+c
+            jj = ijk(kb,nel)
+	    k = jwk(jj)
+	    if (k .eq. 0) then
+	      ilast = ilast+1
+	      jwk(jj) = ilast
+	      ja(ilast) = jj
+	      a(ilast) = ske(ka,kb)
+	    else 
+	      a(k) = a(k) + ske(ka,kb)
+	    endif
+          end do
+c refresh jwk
+          do k=irowst,ilast 
+	    jwk(ja(k)) = 0
+          end do
+          iwk(ii) = ilast 
+        end do
+c
+      end do
+
+c squeeze away the zero entries
+c added so as to handle more type of domains/meshes
+      do i=1, nx
+        ista=ia(i)
+        isto=ia(i+1)-1
+        do j=ista, isto
+          if (ja(j) .EQ. 0) then
+            iwk(i)=j-ista
+            go to 200
+          end if
+        end do
+ 200    continue
+      end do
+
+      do i=2, nx
+        ksav=ia(i)
+        ia(i)=ia(i-1)+iwk(i-1)
+        ksavn=ia(i)
+        do j=0, iwk(i)-1
+          ja(ksavn+j)=ja(ksav+j)
+          a(ksavn+j) = a(ksav+j)
+        end do
+      end do
+      ia(nx+1)=ia(nx)+iwk(nx)
+
+      return
+      end
+c-----------------------------------------------------------------------
+	subroutine assmbo2 (nx, nelx, node, ijk, nodcode, x, y, a, ja,
+     *                   ia, f, iwk, jwk, ierr, xyk, funb, func, fung)
+c----------------------------------------------------------------------- 
+c nx     = number of nodes at input
+c
+c nelx	 = number of elements at input
+c
+c node	 = total number of nodal points in each element
+c
+c ijk	 = connectivity matrix: for node k, ijk(*,k) point to the
+c          nodes of element k.
+c
+c nodcode= boundary information list for each node with the
+c	   following meaning:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point (corner points
+c
+c x,y   = real arrays containing the $x$ and $y$ coordinates 
+c	  resp. of the nodes.
+c
+c a,ja,ia= assembled matrix on output
+c
+c f      = right hand side (global load vector) 
+c
+c iwk,jwk = two integer work arrays.
+c
+c ierr	= error message integer . 
+c	  ierr = 0 --> normal return
+c	  ierr = 1 --> negative area encountered (due to bad 
+c	           numbering of nodes of an element)
+c
+c xyk	= subroutine defining the material properties at each 
+c         element. Form: 
+c 	call xyk(nel,xyke,x,y,ijk,node) with on return
+c         xyke =  material constant matrices. 
+c         for each element nel, xyke(1,nel),xyke(2,nel) 
+c         and xyke(3,nel) represent the constants
+c         K11, K22, and K12 at that element.
+c--------------------------------------------------------------
+c
+c moulitsa@cs.umn.edu : This routine yields the same results
+c   as assmbo. It differs in that it constructs the ia array
+c   by creating a list with the adjacent nodes for each node
+c
+c--------------------------------------------------------------
+      implicit real*8  (a-h,o-z)
+      dimension a(*),ijk(node,1),x(1),y(1),f(1),ske(3,3),fe(3),
+     *      xe(3),ye(3),iwk(1),jwk(1), kwk(500)
+      integer ia(1), ja(*), nodcode(1)
+      external xyk, funb, func, fung
+
+c--------------------------------------------------------------
+c   initialize
+c--------------------------------------------------------------
+      do i=1,nx 
+        f(i) = 0.0 
+        iwk(i) = 0
+        kwk(i) = 0
+      end do
+
+c iwk : how many elements a node belongs to
+      do k=1,nelx
+        do j=1,node
+          knod = ijk(j,k)
+          iwk(knod) = iwk(knod) + 1
+        end do
+      end do
+c
+c iwk : prepare for csr like format
+      ksav=iwk(1)
+      iwk(1)=1
+      do j=2, nx+1
+        ksavn = iwk(j)
+        iwk(j) = iwk(j-1) +  ksav
+        ksav = ksavn
+      end do
+c
+c jwk : list of elements a node belongs to
+      k=1
+      do i=1,nelx
+        do j=1,node
+          knod = ijk(j,i)
+          k=iwk(knod)
+          jwk(k)=i
+          iwk(knod)=iwk(knod)+1
+        end do
+      end do
+
+c iwk : transform iwk back to what it was
+      do i=nx+1,2,-1
+        iwk(i)=iwk(i-1)
+      end do
+      iwk(1)=1
+
+c kwk : mark edges that a node is associated with
+      nedges=1
+      ia(1)=1
+      do i=1,nx
+        kwk(i)=i
+        do j=iwk(i), iwk(i+1)-1
+          do k=1, node
+            knod = ijk(k,jwk(j))
+            if ( kwk(knod) .NE. i) then
+              kwk(knod) = i
+              nedges=nedges+1
+            end if
+          end do
+        end do
+        ia(i+1)=nedges
+      end do
+      do i=2,nx+1
+        ia(i)=ia(i)+i-1
+        iwk(i-1)=ia(i-1)-1
+        jwk(i)=0
+      end do
+      jwk(1)=0
+            
+c-----------------
+c main loop
+c-----------------
+      do nel=1, nelx
+c
+c get coordinates of nodal points
+c
+	do i=1, node
+	  j = ijk(i,nel)
+          xe(i) = x(j)
+          ye(i) = y(j)
+        end do
+c
+c compute determinant
+c
+c 	det=xe(2)*(ye(3)-ye(1))+xe(3)*(ye(1)-ye(2))+xe(1)*(ye(2)-ye(3))
+c
+c set material properties
+c 
+c	call xyk(nel,xyke,x,y,ijk,node)
+c
+c construct element stiffness matrix
+c
+        ierr = 0
+c
+c	call evalg(nel, fe, xe, ye, fung, ierr)
+c	call estif3(nel,ske,fe,det,xe,ye,xyke,ierr)
+        call lstif3(ske, fe, xe, ye, xyk, funb, func, fung)
+        if (ierr .ne. 0) return
+c
+c assemble: add element stiffness matrix to global matrix
+c 
+        do ka=1, node
+          ii = ijk(ka,nel)
+	  f(ii) = f(ii) + fe(ka)
+c
+c unpack row into jwk1
+c
+	  irowst = ia(ii)
+	  ilast  = iwk(ii) 
+          do k=irowst,ilast 
+	    jwk(ja(k)) = k
+          end do
+c
+	  do kb = 1,node
+c
+c column number = jj
+c
+            jj = ijk(kb,nel)
+	    k = jwk(jj)
+	    if (k .eq. 0) then
+	      ilast = ilast+1
+	      jwk(jj) = ilast
+	      ja(ilast) = jj
+	      a(ilast) = ske(ka,kb)
+	    else 
+	      a(k) = a(k) + ske(ka,kb)
+	    endif
+          end do
+c refresh jwk
+          do k=irowst,ilast 
+	    jwk(ja(k)) = 0
+          end do
+          iwk(ii) = ilast 
+        end do
+c
+      end do
+
+      return
+      end
+c----------------------------------------------------------------------- 
+	subroutine chkelmt (nx, x, y, nelx, ijk, node)
+	implicit real*8 (a-h,o-z)
+	dimension ijk(node,1),x(1),y(1)
+c----------------------------------------------------------------------- 
+c this subsourine checks the labeling within each elment and reorders
+c the nodes in they ar not correctly ordered.
+c----------------------------------------------------------------------- 
+	do 1 nel =1, nelx
+ 	det = x(ijk(2,nel))*(y(ijk(3,nel))-y(ijk(1,nel)))+
+     *        x(ijk(3,nel))*(y(ijk(1,nel))-y(ijk(2,nel)))+
+     *        x(ijk(1,nel))*(y(ijk(2,nel))-y(ijk(3,nel)))
+c
+c if determinant negative exchange last two nodes of elements.
+c
+	if (det .lt. 0.0d0) then
+	    j = ijk(2,nel)
+	    ijk(2,nel) = ijk(3,nel)
+	    ijk(3,nel) = j
+	endif
+ 1	continue
+c
+	return			
+	end			 
+c----------------------------------------------------------------------- 
+      SUBROUTINE DLAUNY(X,Y,NODES,ELMNTS,NEMAX,NELMNT)
+      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
+c 
+C code written by P.K. Sweby
+c simple delauney triangulation routine (non optimal)
+c
+C     ******************************************************************
+C     *                                                                *
+C     * Performs a Delaunay triangularisation of a region given a set  *
+C     * of mesh points.                                                *
+C     *   X,Y    :- 1D arrays holding coordinates of mesh points.      *
+C     *             dimensioned AT LEAST NODES+3.                      *
+C     *   NODES  :- number of mesh points.                             *
+C     *   ELMNTS :- INTEGER array, dimensioned NEMAX x 3, which on exit*
+C     *             contains the index of global nodes associated with *
+C     *             each element.                                      *
+C     *   NELMNT :- on exit contains the number of elements in the     *
+C     *             triangularisation.                                 *
+C     *                                                                *
+C     *                                   P.K.Sweby                    *
+C     *                                                                *
+C     ******************************************************************
+C
+      INTEGER ELMNTS
+      DIMENSION X(NODES),Y(NODES),ELMNTS(NEMAX,3)
+C
+      PI=4.0*ATAN(1.0)
+C
+C     Calculate artificial nodes NODES+i i=1,2,3,4 and construct first
+C     two (artificial) elements.
+C
+      XMIN=X(1)
+      XMAX=X(1)
+      YMIN=Y(1)
+      YMAX=Y(1)
+      DO 10 I=2,NODES
+      XMIN=MIN(XMIN,X(I))
+      XMAX=MAX(XMAX,X(I))
+      YMIN=MIN(YMIN,Y(I))
+      YMAX=MAX(YMAX,Y(I))
+ 10   CONTINUE
+      DX=XMAX-XMIN
+      DY=YMAX-YMIN
+      XL=XMIN-4.0*DX
+      XR=XMAX+4.0*DX
+      YL=YMIN-4.0*DY
+      YR=YMAX+4.0*DY
+      X(NODES+1)=XL
+      Y(NODES+1)=YL
+      X(NODES+2)=XL
+      Y(NODES+2)=YR
+      X(NODES+3)=XR
+      Y(NODES+3)=YR
+      X(NODES+4)=XR
+      Y(NODES+4)=YL
+      ELMNTS(1,1)=NODES+1
+      ELMNTS(1,2)=NODES+2
+      ELMNTS(1,3)=NODES+3
+      ELMNTS(2,1)=NODES+3
+      ELMNTS(2,2)=NODES+4
+      ELMNTS(2,3)=NODES+1
+      NELMNT=2
+      DO 90 IN=1,NODES
+C
+C     Add one mesh point at a time and remesh locally if necessary
+C
+      NDEL=0
+      NEWEL=0
+      DO 40 IE=1,NELMNT
+C
+C     Is point IN insided circumcircle of element IE ?
+C
+      I1=ELMNTS(IE,1)
+      I2=ELMNTS(IE,2)
+      I3=ELMNTS(IE,3)
+      X2=X(I2)-X(I1)
+      X3=X(I3)-X(I1)
+      Y2=Y(I2)-Y(I1)
+      Y3=Y(I3)-Y(I1)
+      Z=(X2*(X2-X3)+Y2*(Y2-Y3))/(Y2*X3-Y3*X2)
+      CX=0.5*(X3-Z*Y3)
+      CY=0.5*(Y3+Z*X3)
+      R2=CX**2+CY**2
+      RN2=((X(IN)-X(I1)-CX)**2+(Y(IN)-Y(I1)-CY)**2)
+      IF(RN2.GT.R2)GOTO 40
+C
+C     Yes it is inside,create new elements and mark old for deletion.
+C
+      DO 30 J=1,3
+      DO 20 K=1,3
+      ELMNTS(NELMNT+NEWEL+J,K)=ELMNTS(IE,K)
+ 20   CONTINUE
+      ELMNTS(NELMNT+NEWEL+J,J)=IN
+ 30   CONTINUE
+      NEWEL=NEWEL+3
+      ELMNTS(IE,1)=0
+      NDEL=NDEL+1
+C
+ 40   CONTINUE
+C
+C     If IN was inside circumcircle of more than 1 element then will
+C     have created 2 identical new elements: delete them both.
+C
+      IF(NDEL.GT.1)THEN
+          DO 60 IE=NELMNT+1,NELMNT+NEWEL-1
+          DO 60 JE=IE+1,NELMNT+NEWEL
+          MATCH=0
+          DO 50 K=1,3
+          DO 50 L=1,3
+          IF(ELMNTS(IE,K).EQ.ELMNTS(JE,L))MATCH=MATCH+1
+ 50       CONTINUE
+          IF(MATCH.EQ.3)THEN
+              ELMNTS(IE,1)=0
+              ELMNTS(JE,1)=0
+              NDEL=NDEL+2
+          ENDIF
+ 60       CONTINUE
+      ENDIF
+C
+C     Delete any elements
+C
+      NN=NELMNT+NEWEL
+      IE=1
+ 70   CONTINUE
+      IF(ELMNTS(IE,1).EQ.0)THEN
+          DO 80 J=IE,NN-1
+          DO 80 K=1,3
+          ELMNTS(J,K)=ELMNTS(J+1,K)
+ 80       CONTINUE
+          NN=NN-1
+          IE=IE-1
+      ENDIF
+      IE=IE+1
+      IF(IE.LE.NN)GOTO 70
+      NELMNT=NN
+ 90   CONTINUE
+C
+C     Finally remove elements containing artificial nodes
+C
+      IE=1
+ 100  CONTINUE
+      NART=0
+      DO 110 L=1,3
+      IF(ELMNTS(IE,L).GT.NODES)NART=NART+1
+ 110  CONTINUE
+      IF(NART.GT.0)THEN
+          DO 120 J=IE,NN-1
+          DO 120 K=1,3
+          ELMNTS(J,K)=ELMNTS(J+1,K)
+ 120      CONTINUE
+          NELMNT=NELMNT-1
+          IE=IE-1
+      ENDIF
+      IE=IE+1
+      IF(IE.LE.NELMNT)GOTO 100
+      RETURN
+      END
+c-----------------------------------------------------------------------
+      subroutine estif3(nel,ske,fe,det,xe,ye,xyke,ierr)
+c----------------------------------------------------------------------- 
+c this subroutine constructs the element stiffness matrix for heat
+c condution problem
+c
+c                  - Div ( K(x,y) Grad u ) = f
+c                    u = 0 on boundary
+c
+c using 3-node triangular elements arguments:
+c nel	= element number
+c ske	= element stiffness matrix
+c fe	= element load vector
+c det	= 2*area of the triangle
+c xy, ye= coordinates of the three nodal points in an element.
+c xyke  = material constants (kxx, kxy, kyx, kyy)
+c
+c------------------------------------------------------------------------
+	implicit real*8 (a-h,o-z)
+	dimension ske(3,3), fe(3), xe(3), ye(3), dn(3,2),xyke(2,2)
+c
+c initialize
+c
+	area = 0.5*det
+c
+	do 200 i=1,3
+	do 200 j=1,3
+	ske(i,j) = 0.0d0
+ 200	continue
+c
+c get first gradient of shape function
+c
+	call gradi3(nel,xe,ye,dn,det,ierr)
+	if (ierr .ne. 0) return
+c
+	do 100 i=1,3
+	do 100 j=1,3
+	t = 0.0d0
+	do 102 k=1,2
+	do 102 l=1,2
+ 102	t = t+xyke(k,l)*dn(i,k)*dn(j,l)
+ 100	ske(i,j) = t*area
+c
+	return
+	end
+c-------------------------------------------------------
+        subroutine gradi3(nel, xe, ye, dn, det,ierr)
+c-------------------------------------------------------
+c constructs the first derivative of the shape functions.
+c arguments:
+c nel	= element nuumber
+c xy, ye= coordinates of the three nodal points in an element.
+c dn	= gradients (1-st derivatives) of the shape functions.
+c area	= area of the triangle
+c
+c------------------------------------------------------- 
+   	implicit real*8 (a-h,o-z)
+	dimension xe(3), ye(3), dn(3,2)
+        data eps/1.d-17/
+c compute area
+	ierr = 0 
+	if (det .le. eps) goto 100
+c
+	dn(1,1) = (ye(2)-ye(3))/det
+	dn(2,1) = (ye(3)-ye(1))/det
+	dn(3,1) = (ye(1)-ye(2))/det
+	dn(1,2) = (xe(3)-xe(2))/det
+	dn(2,2) = (xe(1)-xe(3))/det
+	dn(3,2) = (xe(2)-xe(1))/det
+c
+	return
+c
+ 100	continue
+	ierr = 3
+  	write(iout,*) 'ERROR:negative area encountered at elmt: ',nel
+c	write(iout,*) det,(xe(i),ye(i),i=1,3)
+	return
+	end
+c----------------------------------------------------------------------- 
+        subroutine hsourc (indic,nx,nelx,node,x,y,ijk,fs,f) 
+	implicit real*8 (a-h,o-z) 
+        real*8 x(*),y(*),fs(*),f(*),xe(3),ye(3),det,areao3
+	integer ijk(node,*)
+c
+c generates the load vector f in assembled/unassembled form from the
+c the element contributions fs. 
+c indic = indicates if f is to be assembled (1) or not (zero) 
+c note: f(*) not initilazed. because might use values from boundary 
+c conditions.
+c 
+	jnod = 0
+	do 130 nel = 1,nelx
+c
+c get coordinates of nodal points
+c	
+	do 104 i=1, node
+	j = ijk(i,nel)
+	xe(i) = x(j)
+	ye(i) = y(j)
+ 104	continue
+c
+c compute determinant
+c
+	det=xe(2)*(ye(3)-ye(1))+xe(3)*(ye(1)-ye(2))+xe(1)*(ye(2)-ye(3))
+c area3 = area/3 
+	areao3 = det/6.0
+c 
+c contributions to nodes in the element
+c 
+	if (indic .eq. 0) then
+	   do 115 ka=1,node
+	   jnod = jnod+1
+	   f(jnod) = fs(nel)*areao3
+ 115	   continue
+	else
+	    do 120 ka=1, node
+            ii = ijk(ka,nel)
+	    f(ii) = f(ii) + fs(nel)*areao3
+ 120	    continue
+	endif 
+c
+ 130	continue
+	return
+        end
+c----- end of hsourc --------------------------------------------------- 
+c-----------------------------------------------------------------------
+      subroutine bound (nx,nelx,ijk,nodcode,node,nint,iperm,
+     *             x,y,wk,iwk)
+c-----------------------------------------------------------------------
+c this routine counts the number of boundary points and 
+c reorders the points in such a way that the boundary nodes
+c are last.
+c 
+c nx, nelx, ijk, nodcode, node: see other subroutines
+c iperm = permutation array from old orderin to new ordering,
+c iwk   = reverse permutation array or return.
+c wk	= real work array
+c On return
+c x, y, nodecode, are permuted
+c ijk  is updated according to new oerdering.
+c nint = number of interior points.
+c 
+c-----------------------------------------------------------------------
+      implicit real*8  (a-h,o-z)
+      dimension ijk(node,1),x(1),y(1),wk(1),iwk(1),iperm(1),
+     *     nodcode(1)
+
+c     put all boundary points at the end, backwards
+      nint = 1
+      nbound = nx
+      do 1 j=1, nx
+         if (nodcode(j) .eq. 0) then
+            iperm(nint) = j
+            nint = nint+1
+         else
+            iperm(nbound) = j
+            nbound = nbound-1
+         endif
+ 1    continue
+c-------------------------------------------------------------------
+      nint = nint-1
+c     
+c permute x's
+c   
+      do 2 k=1, nx
+         wk(k) = x(k)
+ 2    continue
+      do 3 k=1,nx
+         x(k) = wk(iperm(k))
+ 3    continue
+c 
+c     permute the y's
+c
+      do 4 k=1, nx
+         wk(k) = y(k)
+ 4    continue
+      do 5 k=1, nx
+         y(k) = wk(iperm(k))
+ 5    continue
+c 
+c     permute the boundary information
+c
+      do 6 k=1, nx
+         iwk(k) = nodcode(k)
+ 6    continue 
+      do 7 k=1,nx
+         nodcode(k) = iwk(iperm(k))
+ 7    continue
+c
+c     get reverse permutation
+c
+      do 8 k=1, nx
+         iwk(iperm(k)) = k
+ 8    continue
+c
+c     update the elements connectivity matrix
+c
+      do 10 nel = 1, nelx
+         do 9 j=1, node
+            knod = ijk(j,nel)
+            ijk(j,nel) = iwk(knod) 
+ 9       continue
+ 10   continue
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine symbound (nx,nelx,ijk,nodcode,node,nint,
+     *     iperm,wk,iwk)
+c-----------------------------------------------------------------------
+c     this routine is a symbolic version of routine bound.
+c     
+c   nx, nelx, ijk, nodcode, node: see other subroutines
+c   iperm = permutation array from old orderin to new ordering,
+c   iwk   = reverse permutation array or return.
+c   wk	  = real work array
+c   On return
+c   ijk   = is updated according to new oerdering.
+c   nint  = number of interior points.
+c 
+c-----------------------------------------------------------------------
+	implicit real*8  (a-h,o-z)
+	dimension ijk(node,1),wk(1),iwk(1),iperm(1),
+     *		  nodcode(1)
+
+c put all boundary points at the end, backwards
+	nint = 1
+	nbound = nx
+	do 1 j=1, nx
+	if (nodcode(j) .eq. 0) then
+	  iperm(nint) = j
+	  nint = nint+1
+	else
+	iperm(nbound) = j
+	nbound = nbound-1
+	endif
+ 1	continue
+c-------------------------------------------------------------------
+	nint = nint-1
+c 
+c permute the boundary information
+c
+	do 6 k=1, nx
+           iwk(k) = nodcode(k)
+ 6      continue 
+	do 7 k=1,nx
+           nodcode(k) = iwk(iperm(k))
+ 7	continue
+c
+c get reverse permutation
+c
+	do 8 k=1, nx
+           iwk(iperm(k)) = k
+ 8	continue
+c
+c update the elements connectivity matrix
+c
+	do 10 nel = 1, nelx
+	   do 9 j=1, node
+	      knod = ijk(j,nel)
+              ijk(j,nel) = iwk(knod) 
+ 9	   continue
+ 10	continue
+	return
+	end    
+c----------------------------------------------------------------------- 
+	subroutine diric (nx,nint,a,ja,ia, f)
+c--------------------------------------------------------------
+c this routine takes into account the boundary conditions
+c and removes the unnecessary boundary points.
+c--------------------------------------------------------------
+	implicit real*8  (a-h,o-z)
+	dimension a(*),ia(*),ja(*),f(*)
+c call extract from UNARY
+	call submat (nx,1,1,nint,1,nint,a,ja,ia,nr,nc,a,ja,ia)
+        write (*,*) 'nr=',nr,'nc=',nc
+	return
+c----------- end of diric ------------------------------------- 
+	end
+c-----------------------------------------------------------------------
+	subroutine symdiric (nx,nint,a,ja,ia, f)
+c--------------------------------------------------------------
+c this routine takes into account the boundary conditions
+c and removes the unnecessary boundary points.
+c--------------------------------------------------------------
+	implicit real*8  (a-h,o-z)
+	dimension a(*),ia(*),ja(*),f(*)
+c     call submat from UNARY, with job = 0,
+c     meaning no movement of real values.
+	call submat (nx,0,1,nint,1,nint,a,ja,ia,nr,nc,a,ja,ia)
+	return
+c----------- end of symdiric ------------------------------------- 
+	end
+c-----------------------------------------------------------------------
+      subroutine cleannods (nx,x,y,nelx,ijk,node,nodcode,iperm) 
+c      implicit none 
+      integer nx,nelx,node,ijk(node,nelx),nodcode(*),iperm(nx) 
+      real*8 x(nx),y(nx)
+c-----------------------------------------------------------------------
+c     this routine removes the nodes that do not belong to any element
+c     (spurious points) and relabels the ijk array accordingly.
+c-----------------------------------------------------------------------
+      integer nel,i,k,j,indx
+c
+      do j=1, nx
+         iperm(j) = 0
+      enddo
+c     
+      do nel = 1, nelx
+         do i=1,node
+            k = ijk(i,nel) 
+            iperm(k) = nel 
+         enddo
+      enddo
+c
+      indx = 0 
+      do j =1, nx
+         if (iperm(j) .ne. 0) then
+            indx = indx+1
+            iperm(indx) = j
+            x(indx) = x(j)
+            y(indx) = y(j) 
+            nodcode(indx) = nodcode(j) 
+         endif
+      enddo
+c     
+c     update nx
+c     
+      nx = indx
+c     
+c     old number to new numbers
+c     
+      do j =1, nx 
+         iperm(nx+iperm(j)) = j 
+      enddo 
+c     
+c     
+c     change all node numbers in ijk
+c     
+      do nel = 1, nelx
+         do i=1,node
+            k = ijk(i,nel) 
+            k = iperm(nx+k) 
+            ijk(i,nel) = k
+         enddo
+      enddo
+      return
+c-----------------------------------------------------------------------
+c-----end-of-cleannod---------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+      subroutine cleanel (nelx,ijk,node,nodcode,nodexc) 
+c      implicit none
+      integer nelx,node,nodexc,ijk(node,nelx),nodcode(*)
+c-----------------------------------------------------------------------
+c     this routine remove certain types of elements from the mesh
+c     An element whose nodes are all labelled by the same label 
+c     nodexc are removed. nelx is changed accordingly on return.
+c-----------------------------------------------------------------------
+      logical exclude
+      integer nel, i,k 
+      nel = 1
+ 1    continue
+      exclude = .true. 
+      do i=1,node
+         k = ijk(i,nel) 
+         exclude = (exclude .and. nodcode(k).eq. nodexc) 
+      enddo
+c     
+      if (exclude) then
+         do i=1,node
+            ijk(i,nel) = ijk(i,nelx) 
+         enddo
+         nelx = nelx - 1
+      else
+         nel = nel+1
+      endif
+      if (nel .le. nelx) goto 1
+      return
+c-----------------------------------------------------------------------
+c-----end-of-cleanel---------------------------------------------------- 
+      end
+
+	subroutine lstif3(ske, fe, xe, ye, 
+     1	   xyk, funb, func, fung)
+c---------------------------------------------------------------------------
+c
+c  This subroutine computes the local stiffness matrix for the 
+c   Diffusion-Convection Equation with the 
+c    variable cofficients, 'K(x,y), B(x,y), C(x,y) '
+c
+c  -Div( K(x,y) T(x,y)) + B(x,y) Tx + C(x,y) Ty = G
+c
+c   Here K(x,y) is a 2x2 Matrix, where each entry is a function of x and y.
+c
+c   K, B, C and G need to be supplied by user.
+c    They need to be defined as externals in the calling routines.
+c
+c   PSI(i,x,y) : i-th shape fucntions on the standard triangle N, i=1, 2, 3
+c      where N is the following.
+c
+c             (-1,1)
+c                .
+c                . .
+c		 .   .
+c		 .       .
+c		 . . . . . . (1,-1)
+c	       (-1,-1)
+c
+c   Local stiffness matrix is obtained by integral on the current 
+c   element. To do so, change the current coordinates to N 
+c    by Affine mapping, sending
+c
+c    (xe(1),ye(1))   ---> (-1,-1)
+c    (xe(2),ye(2))   ---> (1,-1)
+c    (xe(3),ye(3))   ---> (-1,1) .
+c
+c    Then we perform the integration on N
+c     by Gaussian Quadrature with 9 points.
+c
+c---------------------------------------------------------------------------
+c
+c  on entry
+c  ---------
+c
+c   xe       = x coordinates of the nodes in the current element.
+c   ye       = y coordinates of the nodes in the current element.
+c   xyk      = subroutine defining the function K(x,y). 
+c   funb     = function defining the function b(x,y).
+c   func     = function defining the function c(x,y).
+c   fung     = function defining the function g(x,y).
+c
+c---------------------------------------------------------------------------
+c
+c  on return
+c  ---------
+c
+c   ske : Local Stiffness Matrix.( 3x3 in this subroutine.)
+c   fe  : Local Load Vector.
+c
+c---------------------------------------------------------------------------
+	implicit real*8(a-h,o-z)
+	dimension ske(3,3), fe(3), xe(3), ye(3), dn(3,2), 
+     1            xyke(2,2), wei(9), gau1(9), gau2(9)
+	external xyk, funb, func, fung
+
+c  Gau1 and Gau2 are the Gaussian Quadrature Points for the Traingle N,
+c   and Wei, are the corresponding weights.
+c
+c   They are derived from the 1-D case by Reiterated integrals.
+c
+	data gau1/-0.8, -0.1127016654, 0.5745966692, -0.8872983346, -0.5, 
+     1        -0.1127016654,  -0.9745966692, -0.8872983346, -0.8 /
+	data gau2/3*-0.7745966692, 3*0., 3*0.7745966692 /
+	data wei/0.2738575107, 0.4381720172, 0.2738551072, 0.2469135803, 
+     1     0.3950617284, 0.2469135803, 0.03478446464, 
+     2     0.05565514341, 0.03478446464 /
+
+	npt = 9
+
+c
+c    Compute the Affine mappings from the current triangle to the
+c     standard triangle N. Integration will be performed on that
+c     triangle by Gaussian quadrature.
+c
+c    T = A X + B
+c   
+c    A11, A12, A21, A22, B1, B2 will denote the entries of
+c     A & B.
+c
+	x1 = xe(1)
+	x2 = xe(2)
+	x3 = xe(3)
+	y1 = ye(1)
+	y2 = ye(2)
+	y3 = ye(3)
+
+	rj1 = (x3-x1)*(y2-y3) - (x2-x3)*(y3-y1)
+	rj2 = (x3-x1)*(y1-y2) - (x1-x2)*(y3-y1)
+	a11 = 2*(y1-y3)/rj1
+	a12 = 2*(x3-x1)/rj1
+	a21 = 2*(y1-y2)/rj2
+	a22 = 2*(x2-x1)/rj2
+	b1 = 1. - a11*x2 - a12*y2
+	b2 = -1. - a21*x2 - a22*y2
+
+c
+c  Compute the first order partial derivatives of the shape functions.
+c   dn(i,1) and dn(i,2) are the first order partial derivativ of i-th shape function
+c    with respect to x and y, respectively.
+c
+	dn(1,1) = -0.5*(a11+a21)
+	dn(1,2) = -0.5*(a12+a22)
+	dn(2,1) = 0.5*a11
+	dn(2,2) = 0.5*a12
+	dn(3,1) = 0.5*a21
+	dn(3,2) = 0.5*a22
+c  Compute the Jacobian associated with T.
+	Rja = a11*a22 - a12*a21
+c
+c  Find the inverse mapping of T
+c
+
+	u11 = a22/rja
+	u12 = -a12/Rja
+	u21 = -a21/rja
+	u22 = a11/rja
+	v1 = -u11*b1 - u12*b2
+	v2 = -u21*b1 - u22*b2
+
+	do 200 i = 1 , 3
+	  T4 = 0.
+	do 220 j = 1 , 3
+	  T1 = 0.
+	  T2 = 0.
+	  T3 = 0.
+	  do 250 k = 1, npt
+	    r = gau1(k)
+	    s = gau2(k)
+	    w = wei(k)
+
+	    x = u11*r + u12*s + v1
+	    y = u21*r + u22*s + v2
+
+	    call xyk(xyke, x, y)
+
+	    derv2 = dn(i,1)*dn(j,1)*xyke(1,1) 
+     1            + dn(i,2)*dn(j,2)*xyke(2,2)
+     2            + dn(i,1)*dn(j,2)*xyke(1,2)
+     3            + dn(i,2)*dn(j,1)*xyke(2,1)
+	    if(j .eq. 1) then
+	      T4 = T4 + w*fung(x,y)*psi(i,r,s)
+	    endif
+
+	    T1 = T1 + w*derv2
+	    T2 = T2 + w*funb(x,y)*psi(i,r,s)
+	    T3 = T3 + w*func(x,y)*psi(i,r,s)
+250	  continue
+	
+	ske(i,j) = (T1 + T2*dn(j,1) + T3*dn(j,2))/Rja
+220	continue	
+	fe(i) = T4/Rja
+200	continue
+
+	return
+	end
+c--- end of lstif3 ---------------------------------------------------------
+c---------------------------------------------------------------------------
+C  Piecewise linear fucntions on triangle.
+	function psi(i,r,s)
+	implicit real*8(a-h,o-z)
+
+	goto (100,200,300) ,i
+
+100	  psi = -(r+s)/2.
+	return
+200	  psi = (r+1.)/2.
+	return
+300	  psi = (s+1.)/2.
+	return
+	end
diff --git a/MATGEN/FEM/femgen.f b/MATGEN/FEM/femgen.f
new file mode 100644
index 0000000..41cf66c
--- /dev/null
+++ b/MATGEN/FEM/femgen.f
@@ -0,0 +1,620 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c      MATRIX GENERATION ROUTINES - FINITE ELEMENT MATRICES            c
+c----------------------------------------------------------------------c
+c contents:                                                            c
+c----------                                                            c
+c genfea       : generates finite element matrices in assembled form   c
+c genfea_wbc   : generates finite element matrices in assembled form   c
+c                without applying the boundary conditions              c
+c genfeu       : generates finite element matrices in unassembled form c
+c genfeu_wbc   : generates finite element matrices in unassembled form c
+c                without applying the boundary conditions              c
+c genfeu_lstif : generates finite element matrices in unassembled form c
+c                using the lstif problem appearing in elmtlib2.f       c
+c assmb1       : assembles an unassembled matrix (produced by genfeu)  c
+c----------------------------------------------------------------------c
+      subroutine genfea (nx,nelx,node,job,x,y,ijk,nodcode,fs,nint,
+     *     a,ja,ia,f,iwk,jwk,ierr,xyk)
+c-----------------------------------------------------------------------
+c this subroutine generates a finite element matrix in assembled form.
+c the matrix is assembled in compressed sparse row format. See genfeu
+c for matrices in unassembled form. The user must provide the grid, 
+c (coordinates x, y and connectivity matrix ijk) as well as some 
+c information on the nodes (nodcode) and the material properties 
+c (the function K(x,y) above) in the form of a subroutine xyk. 
+c----------------------------------------------------------------------
+c
+c on entry:
+c ---------
+c 
+c nx	    = integer . the number of nodes in the grid . 
+c nelx	    = integer . the number of elements in the grid.
+c node      = integer = the number of nodes per element (should be
+c             set to three in this version). also the first dimension
+c             of ijk
+c job	    = integer. If job=0, it is assumed that there is no heat
+c             source (i.e. fs = 0) and the right hand side
+c             produced will therefore be a zero vector.
+c             If job = 1 on entry then the contributions from the
+c             heat source in each element are taken into account.
+c 
+c x, y      = two real arrays containing the coordinates of the nodes.
+c 
+c ijk       =  an integer array containing the connectivity matrix.
+c              ijk(i,nel), i=1,2,..node, is the list of the nodes
+c              constituting the element nel, ans listed in 
+c              counter clockwise order.
+c
+c nodcode   = an integer array containing the boundary information for
+c             each node with the following meaning.
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner node. [This node and the
+c             corresponmding element are discarded.]
+c
+c fs	    = real array of length nelx on entry containing the heat 
+c             source for each element (job = 1 only) 
+c
+c xyk	    = subroutine defining the material properties at each 
+c	      element. Form: 
+c 	      call xyk(nel,xyke,x,y,ijk,node) with on return
+c             xyke =  material constant matrices. 
+c	      for each element nel, xyke(1,nel),xyke(2,nel) 
+c             and xyke(3,nel) represent the constants
+c             K11, K22, and K12 at that element.
+c                           
+c on return
+c --------- 
+c nint	    = integer. The number of active (nonboundary) nodes. Also 
+c             equal to the dimension of the assembled matrix.
+c
+c a, ja, ia = assembled matrix in compressed sparse row format.
+c
+c f	    = real array containing the right hand for the linears 
+c             system to solve.
+c 
+c ierr	    = integer. Error message. If (ierr .ne. 0) on return
+c             it means that one of the elements has a negative or zero
+c             area probably because of a bad ordering of the nodes 
+c             (see ijk above). Use the subroutine chkelmt to reorder
+c             the nodes properly if necessary.
+c iwk, jwk  = two integer work arrays of length nx each.
+c
+c-----------------------------------------------------------------------
+      real*8 a(*),x(*),y(*),f(*),fs(*)
+      integer ijk(node,*), nodcode(*),ia(*),ja(*),iwk(*),jwk(*)
+      external xyk, funb, func, fung 
+c     
+      ierr = 0 
+c     
+c     take into boundary conditions to remove boundary nodes.
+c     
+      call bound (nx,nelx,ijk,nodcode,node,nint,jwk,
+     *     x,y,f,iwk)
+c     
+c     assemble the matrix
+c     
+       call assmbo (nx,nelx,node,ijk,nodcode,x,y,
+     *     a,ja,ia,f,iwk,jwk,ierr,xyk, funb, func, fung)
+c     
+c     if applicable (job .eq. 1) get heat source function
+c     
+      indic = 1
+      if (job .eq. 1) 
+     *     call hsourc (indic,nx,nelx,node,x,y,ijk,fs,f) 
+c     
+c     call diric for Dirichlet conditions
+c     
+      call diric(nx,nint,a,ja,ia,f)
+c     done
+      return
+c------end of genfea ---------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+      subroutine genfea_wbc (nx,nelx,node,job,x,y,ijk,nodcode,fs,
+     *     a,ja,ia,f,iwk,jwk,ierr,xyk)
+c-----------------------------------------------------------------------
+c this subroutine generates a finite element matrix in assembled form.
+c the matrix is assembled in compressed sparse row format. See genfeu
+c for matrices in unassembled form. The user must provide the grid, 
+c (coordinates x, y and connectivity matrix ijk) as well as some 
+c information on the nodes (nodcode) and the material properties 
+c (the function K(x,y) above) in the form of a subroutine xyk. 
+c----------------------------------------------------------------------
+c Irene Moulitsas, moulitsa@cs.umn.edu  : It does not apply boundary
+c                 conditions; variable nint is eliminated
+c----------------------------------------------------------------------
+c
+c on entry:
+c ---------
+c 
+c nx	    = integer . the number of nodes in the grid . 
+c nelx	    = integer . the number of elements in the grid.
+c node      = integer = the number of nodes per element (should be
+c             set to three in this version). also the first dimension
+c             of ijk
+c job	    = integer. If job=0, it is assumed that there is no heat
+c             source (i.e. fs = 0) and the right hand side
+c             produced will therefore be a zero vector.
+c             If job = 1 on entry then the contributions from the
+c             heat source in each element are taken into account.
+c 
+c x, y      = two real arrays containing the coordinates of the nodes.
+c 
+c ijk       =  an integer array containing the connectivity matrix.
+c              ijk(i,nel), i=1,2,..node, is the list of the nodes
+c              constituting the element nel, ans listed in 
+c              counter clockwise order.
+c
+c nodcode   = an integer array containing the boundary information for
+c             each node with the following meaning.
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner node. [This node and the
+c             corresponmding element are discarded.]
+c
+c fs	    = real array of length nelx on entry containing the heat 
+c             source for each element (job = 1 only) 
+c
+c xyk	    = subroutine defining the material properties at each 
+c	      element. Form: 
+c 	      call xyk(nel,xyke,x,y,ijk,node) with on return
+c             xyke =  material constant matrices. 
+c	      for each element nel, xyke(1,nel),xyke(2,nel) 
+c             and xyke(3,nel) represent the constants
+c             K11, K22, and K12 at that element.
+c                           
+c on return
+c --------- 
+c a, ja, ia = assembled matrix in compressed sparse row format.
+c
+c f	    = real array containing the right hand for the linears 
+c             system to solve.
+c 
+c ierr	    = integer. Error message. If (ierr .ne. 0) on return
+c             it means that one of the elements has a negative or zero
+c             area probably because of a bad ordering of the nodes 
+c             (see ijk above). Use the subroutine chkelmt to reorder
+c             the nodes properly if necessary.
+c iwk, jwk  = two integer work arrays of length nx each.
+c
+c-----------------------------------------------------------------------
+      real*8 a(*),x(*),y(*),f(*),fs(*)
+      integer ijk(node,*), nodcode(*),ia(*),ja(*),iwk(*),jwk(*)
+      external xyk, funb, func, fung 
+c     
+      ierr = 0 
+c     
+c     assemble the matrix
+c     
+       call assmbo (nx,nelx,node,ijk,nodcode,x,y,
+     *     a,ja,ia,f,iwk,jwk,ierr,xyk, funb, func, fung)
+c     
+c     if applicable (job .eq. 1) get heat source function
+c     
+      indic = 1
+      if (job .eq. 1) 
+     *     call hsourc (indic,nx,nelx,node,x,y,ijk,fs,f) 
+c
+c     done
+      return
+c------end of genfea_wbc -----------------------------------------------
+c-----------------------------------------------------------------------
+       end
+c----------------------------------------------------------------------- 
+      subroutine genfeu (nx,nelx,node,job,x,y,ijk,nodcode,fs,
+     *     nint,a,na,f,iwk,jwk,ierr,xyk)
+c-----------------------------------------------------------------------
+c this subroutine generates finite element matrices for heat 
+c condution problem 
+c
+c                  - Div ( K(x,y) Grad u ) = f
+c                    u = 0 on boundary 
+c 
+c (with Dirichlet boundary conditions). The matrix is returned 
+c in unassembled form. The user must provide the grid, 
+c (coordinates x, y and connectivity matrix ijk) as well as some 
+c information on the nodes (nodcode) and the material properties 
+c (the function K(x,y) above) in the form of a subroutine xyk. 
+c
+c----------------------------------------------------------------------
+c
+c on entry:
+c ---------
+c 
+c nx	    = integer . the number of nodes in the grid . 
+c nelx	    = integer . the number of elements in the grid.
+c node      = integer = the number of nodes per element (should be
+c             set to three in this version). also the first dimension
+c             of ijk
+c job	    = integer. If job=0, it is assumed that there is no heat
+c             source (i.e. fs = 0) and the right hand side
+c             produced will therefore be a zero vector.
+c             If job = 1 on entry then the contributions from the
+c             heat source in each element are taken into account.
+c 
+c na	    = integer. The first dimension of the array a. 
+c             a is declared as an array of dimension a(na,node,node).
+c
+c x, y      = two real arrays containing the coordinates of the nodes.
+c 
+c ijk       =  an integer array containing the connectivity matrix.
+c              ijk(i,nel), i=1,2,..node, is the list of the nodes
+c              constituting the element nel, ans listed in 
+c              counter clockwise order.
+c
+c xyk	    = subroutine defining the material properties at each 
+c	      element. Form: 
+c 	      call xyk(nel,xyke,x,y,ijk,node) with on return
+c             xyke =  material constant matrices. 
+c	      for each element nel, xyke(1,nel),xyke(2,nel) 
+c             and xyke(3,nel) represent the constants
+c             K11, K22, and K12 at that element.
+c                           
+c nodcode   = an integer array containing the boundary information for
+c             each node with the following meaning.
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner node. [This node and the
+c             corresponmding element are discarded.]
+c
+c fs	    = real array of length nelx on entry containing the heat 
+c             source for each element (job = 1 only) 
+c                           
+c on return
+c --------- 
+c nint	    = integer. The number of active (nonboundary) nodes. Also 
+c             equal to the dimension of the assembled matrix.
+c
+c a         = matrix in unassembled form. a(nel,*,*) contains the 
+c             element matrix for element nel.
+c
+c f	    = real array containing the right hand for the linears 
+c             system to solve, in assembled form. 
+c 
+c ierr	    = integer. Error message. If (ierr .ne. 0) on return
+c             it means that one of the elements has a negative or zero
+c             area probably because of a bad ordering of the nodes 
+c             (see ijk above). Use the subroutine chkelmt to reorder
+c             the nodes properly if necessary.
+c iwk, jwk  = two integer work arrays of length nx each.
+c
+c-----------------------------------------------------------------------
+      real*8 a(na,node,node),x(*),y(*),f(*), fs(*)
+      integer ijk(node,*), nodcode(*),iwk(*),jwk(*)
+      external xyk
+c     
+      ierr = 0 
+c     
+c     take boundary conditions into account to move boundary nodes to
+c     the end..
+c     
+      call bound (nx,nelx,ijk,nodcode,node,nint,jwk,
+     *     x,y,f,iwk)
+c     
+c     assemble the matrix
+c     
+      call unassbl (a,na,f,nx,nelx,ijk,nodcode,
+     *     node,x,y,ierr,xyk) 
+c     
+c     if applicable (job .eq. 1) get heat source function
+c     
+      indic = 0
+      if (job .eq. 1) 
+     *     call hsourc (indic,nx,nelx,node,x,y,ijk,fs,f) 
+c     
+c     done
+c     
+      return
+      end
+c----- end of genfeu ---------------------------------------------------- 
+      subroutine genfeu_wbc (nx,nelx,node,job,x,y,ijk,nodcode,fs,
+     *          a,na,f,iwk,jwk,ierr,xyk)
+c-----------------------------------------------------------------------
+c this subroutine generates finite element matrices for heat 
+c condution problem 
+c
+c                  - Div ( K(x,y) Grad u ) = f
+c                    u = 0 on boundary 
+c 
+c (with Dirichlet boundary conditions). The matrix is returned 
+c in unassembled form. The user must provide the grid, 
+c (coordinates x, y and connectivity matrix ijk) as well as some 
+c information on the nodes (nodcode) and the material properties 
+c (the function K(x,y) above) in the form of a subroutine xyk. 
+c
+c----------------------------------------------------------------------
+c moulitsa@cs   : It does not apply boundary conditions
+c                 variable nint is eliminated
+c----------------------------------------------------------------------
+c
+c on entry:
+c ---------
+c 
+c nx	    = integer . the number of nodes in the grid . 
+c nelx	    = integer . the number of elements in the grid.
+c node      = integer = the number of nodes per element (should be
+c             set to three in this version). also the first dimension
+c             of ijk
+c job	    = integer. If job=0, it is assumed that there is no heat
+c             source (i.e. fs = 0) and the right hand side
+c             produced will therefore be a zero vector.
+c             If job = 1 on entry then the contributions from the
+c             heat source in each element are taken into account.
+c 
+c na	    = integer. The first dimension of the array a. 
+c             a is declared as an array of dimension a(na,node,node).
+c
+c x, y      = two real arrays containing the coordinates of the nodes.
+c 
+c ijk       =  an integer array containing the connectivity matrix.
+c              ijk(i,nel), i=1,2,..node, is the list of the nodes
+c              constituting the element nel, ans listed in 
+c              counter clockwise order.
+c
+c xyk	    = subroutine defining the material properties at each 
+c	      element. Form: 
+c 	      call xyk(nel,xyke,x,y,ijk,node) with on return
+c             xyke =  material constant matrices. 
+c	      for each element nel, xyke(1,nel),xyke(2,nel) 
+c             and xyke(3,nel) represent the constants
+c             K11, K22, and K12 at that element.
+c                           
+c nodcode   = an integer array containing the boundary information for
+c             each node with the following meaning.
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner node. [This node and the
+c             corresponmding element are discarded.]
+c
+c fs	    = real array of length nelx on entry containing the heat 
+c             source for each element (job = 1 only) 
+c                           
+c on return
+c --------- 
+c a         = matrix in unassembled form. a(nel,*,*) contains the 
+c             element matrix for element nel.
+c
+c f	    = real array containing the right hand for the linears 
+c             system to solve, in assembled form. 
+c 
+c ierr	    = integer. Error message. If (ierr .ne. 0) on return
+c             it means that one of the elements has a negative or zero
+c             area probably because of a bad ordering of the nodes 
+c             (see ijk above). Use the subroutine chkelmt to reorder
+c             the nodes properly if necessary.
+c iwk, jwk  = two integer work arrays of length nx each.
+c
+c-----------------------------------------------------------------------
+      real*8 a(na,node,node),x(*),y(*),f(*), fs(*)
+      integer ijk(node,*), nodcode(*),iwk(*),jwk(*)
+      external xyk
+c     
+      ierr = 0 
+c     
+c     assemble the matrix
+c     
+      call unassbl (a,na,f,nx,nelx,ijk,nodcode,
+     *     node,x,y,ierr,xyk) 
+c     
+c     if applicable (job .eq. 1) get heat source function
+c     
+      indic = 0
+      if (job .eq. 1) 
+     *     call hsourc (indic,nx,nelx,node,x,y,ijk,fs,f) 
+c     
+c     done
+c     
+      return
+      end
+c----- end of genfeu_wbc ----------------------------------------------- 
+      subroutine genfeu_lstif (nx,nelx,node,job,x,y,ijk,nodcode,fs,
+     *          a,na,f,iwk,jwk,ierr,xyk)
+c-----------------------------------------------------------------------
+c this subroutine generates finite element matrices using unassmbl_lstif.
+c The matrix is returned in unassembled form.
+c The user must provide the grid, coordinates x, y and connectivity matrix
+c ijk) as well as some information on the nodes (nodcode) and the material
+c properties (the function K(x,y) above) in the form of a subroutine xyk. 
+c
+c----------------------------------------------------------------------
+c moulitsa@cs.umn.edu   : It does not apply boundary conditions
+c                         variable nint is eliminated
+c----------------------------------------------------------------------
+c
+c on entry:
+c ---------
+c 
+c nx	    = integer . the number of nodes in the grid . 
+c nelx	    = integer . the number of elements in the grid.
+c node      = integer = the number of nodes per element (should be
+c             set to three in this version). also the first dimension
+c             of ijk
+c job	    = integer. If job=0, it is assumed that there is no heat
+c             source (i.e. fs = 0) and the right hand side
+c             produced will therefore be a zero vector.
+c             If job = 1 on entry then the contributions from the
+c             heat source in each element are taken into account.
+c 
+c na	    = integer. The first dimension of the array a. 
+c             a is declared as an array of dimension a(na,node,node).
+c
+c x, y      = two real arrays containing the coordinates of the nodes.
+c 
+c ijk       =  an integer array containing the connectivity matrix.
+c              ijk(i,nel), i=1,2,..node, is the list of the nodes
+c              constituting the element nel, ans listed in 
+c              counter clockwise order.
+c
+c xyk	    = subroutine defining the material properties at each 
+c	      element. Form: 
+c 	      call xyk(nel,xyke,x,y,ijk,node) with on return
+c             xyke =  material constant matrices. 
+c	      for each element nel, xyke(1,nel),xyke(2,nel) 
+c             and xyke(3,nel) represent the constants
+c             K11, K22, and K12 at that element.
+c                           
+c nodcode   = an integer array containing the boundary information for
+c             each node with the following meaning.
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner node. [This node and the
+c             corresponmding element are discarded.]
+c
+c fs	    = real array of length nelx on entry containing the heat 
+c             source for each element (job = 1 only) 
+c                           
+c on return
+c --------- 
+c a         = matrix in unassembled form. a(nel,*,*) contains the 
+c             element matrix for element nel.
+c
+c f	    = real array containing the right hand for the linears 
+c             system to solve, in assembled form. 
+c 
+c ierr	    = integer. Error message. If (ierr .ne. 0) on return
+c             it means that one of the elements has a negative or zero
+c             area probably because of a bad ordering of the nodes 
+c             (see ijk above). Use the subroutine chkelmt to reorder
+c             the nodes properly if necessary.
+c iwk, jwk  = two integer work arrays of length nx each.
+c
+c-----------------------------------------------------------------------
+      real*8 a(na,node,node),x(*),y(*),f(*), fs(*)
+      integer ijk(node,*), nodcode(*),iwk(*),jwk(*)
+      external xyk, funb, func, fung
+c     
+      ierr = 0 
+c     
+c     assemble the matrix
+c     
+      call unassbl_lstif (a,na,f,nx,nelx,ijk,nodcode,
+     *     node,x,y,ierr,xyk,funb,func,fung) 
+c     
+c     if applicable (job .eq. 1) get heat source function
+c     
+      indic = 0
+      if (job .eq. 1) 
+     *     call hsourc (indic,nx,nelx,node,x,y,ijk,fs,f) 
+c     
+c     done
+c     
+      return
+      end
+c----- end of genfeu_lstif ---------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine assmb1 (u,nu,a,ja,ia,fu,f,nx,nelx,ijk,nodcode,
+     *     node,iwk,jwk)
+c--------------------------------------------------------------
+c u	 = unassembled matrix u(na,node,node)
+c nu	 = 1-st dimension of u
+c a,ja,ia= assembled matrix on output
+c fu	 = unassembled right hand side
+c f      = right hand side (global load vector) assembled
+c nx     = number of nodes at input
+c nelx	 = number of elements at input
+c ijk	 = connectivity matrix: for node k, ijk(*,k) point to the
+c          nodes of element k.
+c node	 = total number of nodal points in each element
+c
+c nodcode= boundary information list for each node with the
+c	   following meaning:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point (corner points
+c
+c x,y   = real*8 arrays containing the $x$ and $y$ coordinates 
+c	  resp. of the nodes.
+c         K11, K22, and K12 at that element.
+c iwk,jwk = two integer work arrays.
+c ierr	= error message integer . 
+c	  ierr = 0 --> normal return
+c	  ierr = 1 --> negative area encountered (due to bad 
+c	           numbering of nodes of an element- see
+c		   message printed in unit iout). not used..
+c iout	= output unit (not used here).
+c--------------------------------------------------------------
+      implicit real*8 (a-h,o-z)
+      real*8 u(nu,node,node),a(*),fu(node,*),f(*)
+      integer ja(*),ia(*),ijk(node,*),iwk(*),jwk(*),nodcode(*)
+c     max number of nonzeros per row allowed  = 200
+c--------------------------------------------------------------
+c     initialize
+c--------------------------------------------------------------
+      do 100 i=1,nx 
+         f(i) = 0.0d0 
+ 100  continue
+c     
+c     initialize  pointer arrays.
+c     
+      do 5 k=1,nx+1
+         ia(k) = 1
+         jwk(k) = 0
+ 5    continue
+      do 6 k=1,nelx
+         do 59 j=1,node
+            knod = ijk(j,k)
+            ia(knod) = ia(knod) + 1
+ 59      continue
+ 6    continue
+c---------------------------------------------------
+      do 7 k=1, nx
+         if (nodcode(k) .ge.1 ) ia(k)=ia(k)+1
+ 7    continue
+c     
+      ksav = ia(1)
+      ia(1) = 1
+      do 101 j=2, nx+1
+         ksavn = ia(j)
+         ia(j) = ia(j-1) +  ksav
+         iwk(j-1) = ia(j-1)-1
+         ksav = ksavn
+ 101  continue
+c-----------------
+c     main loop
+c-----------------
+      do 102 nel=1, nelx
+c     
+c     get nodal points
+c     
+         do 120 ka=1, node
+            ii = ijk(ka,nel)
+            f(ii) = f(ii) + fu(ka,nel)
+c     
+c     unpack row into jwk1
+c     
+            irowst = ia(ii)
+            ilast  = iwk(ii) 
+            do 109 k=irowst,ilast 
+               jwk(ja(k)) = k
+ 109        continue
+c     
+            do 108 kb = 1,node
+c     
+c     column number = jj
+c     
+               jj = ijk(kb,nel)
+               k = jwk(jj)
+               if (k .eq. 0) then
+                  ilast = ilast+1
+                  jwk(jj) = ilast
+                  ja(ilast) = jj
+                  a(ilast) = u(nel,ka,kb) 
+               else 
+                  a(k) = a(k) + u(nel,ka,kb)
+               endif
+ 108        continue
+c     refresh jwk
+            do 119 k=irowst,ilast 
+               jwk(ja(k)) = 0
+ 119        continue
+            iwk(ii) = ilast 
+ 120     continue
+c     
+ 102  continue
+      return
+c---------end-of-assmb1---------------------------------------------- 
+      end
+c--------------------------------------------------------------------
diff --git a/MATGEN/FEM/functns2.f b/MATGEN/FEM/functns2.f
new file mode 100644
index 0000000..090536c
--- /dev/null
+++ b/MATGEN/FEM/functns2.f
@@ -0,0 +1,225 @@
+c-----------------------------------------------------------------------
+c     contains the functions needed for defining the PDE poroblems. 
+c
+c     first for the scalar 5-point and 7-point PDE 
+c-----------------------------------------------------------------------
+      function afun (x,y,z)
+      real*8 afun, x,y,z 
+      afun = -1.0
+      return 
+      end
+
+      function bfun (x,y,z)
+      real*8 bfun, x,y,z 
+      bfun = -1.0
+      return 
+      end
+
+      function cfun (x,y,z)
+      real*8 cfun, x,y,z 
+      cfun = -1.0d0
+      return 
+      end
+
+      function dfun (x,y,z)
+      real*8 dfun, x,y,z 
+      dfun = 10.d0
+      return 
+      end
+
+      function efun (x,y,z)
+      real*8 efun, x,y,z
+      efun = 0.0d0
+      return 
+      end
+
+      function ffun (x,y,z)
+      real*8 ffun, x,y,z 
+      ffun = 0.0
+      return 
+      end
+
+      function gfun (x,y,z)
+      real*8 gfun, x,y,z 
+      gfun = 0.0 
+      return 
+      end
+
+      function hfun(x, y, z)
+      real*8 hfun, x, y, z
+      hfun = 0.0
+      return
+      end
+
+      function betfun(side, x, y, z)
+      real*8 betfun, x, y, z
+      character*2 side
+      betfun = 1.0
+      return
+      end
+
+      function gamfun(side, x, y, z)
+      real*8 gamfun, x, y, z
+      character*2 side
+      if (side.eq.'x2') then
+         gamfun = 5.0
+      else if (side.eq.'y1') then
+         gamfun = 2.0
+      else if (side.eq.'y2') then
+         gamfun = 7.0
+      else
+         gamfun = 0.0
+      endif
+      return
+      end
+
+c-----------------------------------------------------------------------
+c     functions for the block PDE's 
+c-----------------------------------------------------------------------
+      subroutine afunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+         coeff((j-1)*nfree+j) = -1.0d0
+ 2    continue
+      return 
+      end
+
+      subroutine bfunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+         coeff((j-1)*nfree+j) = -1.0d0
+ 2    continue
+      return 
+      end
+
+      subroutine cfunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+         coeff((j-1)*nfree+j) = -1.0d0
+ 2    continue
+      return 
+      end
+
+      subroutine dfunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+ 2    continue
+      return 
+      end
+
+      subroutine efunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+ 2    continue
+      return 
+      end
+
+      subroutine ffunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+ 2    continue
+      return 
+      end
+
+      subroutine gfunbl (nfree,x,y,z,coeff)
+      real*8 x, y, z, coeff(100) 
+      do 2 j=1, nfree
+         do 1 i=1, nfree
+            coeff((j-1)*nfree+i) = 0.0d0
+ 1       continue
+ 2    continue
+      return 
+      end
+c-----------------------------------------------------------------------
+c     The material property function xyk for the 
+c     finite element problem 
+c-----------------------------------------------------------------------
+c        subroutine xyk(nel,xyke,x,y,ijk,node)
+c        implicit real*8 (a-h,o-z)
+c        dimension xyke(2,2), x(*), y(*), ijk(node,*)
+cc
+cc this is the identity matrix.
+cc
+c        xyke(1,1) = 1.0d0
+c        xyke(2,2) = 1.0d0
+c        xyke(1,2) = 0.0d0
+c        xyke(2,1) = 0.0d0
+cc
+c        return
+c        end
+c
+        subroutine xyk (xyke, x, y)
+        implicit real*8(a-h,o-z)
+        dimension xyke(2,2)
+
+        xyke(1,1) = 1.
+        xyke(1,1) = exp(x+y)
+        xyke(1,2) = 0.
+        xyke(2,1) = 0.
+        xyke(2,2) = 1.
+        xyke(2,2) = exp(x+y)
+        return
+        end
+
+        function funb(x,y)
+        implicit real*8(a-h,o-z)
+
+        funb = 0.
+        funb = 2.5
+        funb = 2*x
+        return
+        end
+
+        function func(x,y)
+        implicit real*8(a-h,o-z)
+
+        func = 0.
+        func = -1.5
+        func = -5*y
+        return
+        end
+
+        function fung(x,y)
+c  Right hand side corresponding to the exact solution of
+c   u = exp(x+y)*x*(1.-x)*y*(1.-y)
+c   (That exact solution is defined in the function exact)
+        implicit real*8(a-h,o-z)
+
+c        fung = 1. + x
+c        fung = 2*y*(1.-y) + 2*x*(1.-x)
+c        fung = 2*y*(1.-y) + 2*x*(1.-x) +2.5*(1-2*x)*y*(1-y) 
+c     1        - 1.5*(1.-2*y)*x*(1-x)
+        r = exp(x+y)
+        fung = r*r*((x*x+3.*x)*y*(1.-y) +
+     1                    (y*y+3.*y)*x*(1.-x)) 
+     2          + r*(r-2.*x)*(x*x+x-1.)*y*(1.-y)
+     3                + r*(r+5.*y)*(y*y+y-1.)*x*(1.-x)
+        return
+        end
+
+         function exact(x,y)
+C  Exact Solution.
+         implicit real*8(a-h,o-z)
+
+         exact = exp(x+y)*x*(1.-x)*y*(1.-y)
+
+         return
+         end
diff --git a/MATGEN/FEM/makefile b/MATGEN/FEM/makefile
new file mode 100644
index 0000000..2bc6e21
--- /dev/null
+++ b/MATGEN/FEM/makefile
@@ -0,0 +1,20 @@
+FFLAGS = 
+F77 = f77
+
+#F77 = cf77
+#FFLAGS = -Wf"-dp"
+
+FILES = convdif.o functns2.o
+
+fem.ex:	$(FILES)  ../../UNSUPP/PLOTS/psgrd.o ../../libskit32.a 
+	$(F77) $(FFLAGS) -o fem.ex $(FILES) ../../UNSUPP/PLOTS/psgrd.o ../../libskit32.a 
+
+clean:
+	rm -f *.o *.ex core *.trace
+
+../../libskit.a:
+	(cd ../..; $(MAKE) $(MAKEFLAGS) libskit.a)
+
+../../UNSUPP/PLOTS/psgrd.o: ../../UNSUPP/PLOTS/psgrd.f
+	(cd ../../UNSUPP/PLOTS; $(F77) $(FFLAGS) -c psgrd.f)
+
diff --git a/MATGEN/FEM/mat.hb b/MATGEN/FEM/mat.hb
new file mode 100644
index 0000000..1444ca1
--- /dev/null
+++ b/MATGEN/FEM/mat.hb
@@ -0,0 +1,513 @@
+1Sample matrix from SPARSKIT                                            SPARSKIT
+           509            19            92           398             0
+rua                      369           369          2385             0
+(20I4)          (26I3)          (6D12.6)            (6D12.6)            
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diff --git a/MATGEN/FEM/meshes.f b/MATGEN/FEM/meshes.f
new file mode 100644
index 0000000..7e59850
--- /dev/null
+++ b/MATGEN/FEM/meshes.f
@@ -0,0 +1,986 @@
+      subroutine inmesh (nmesh,iin,nx,nelx,node,x,y,nodcode,ijk,iperm)
+      implicit none 
+      real*8 x(*),y(*)
+      integer nmesh,iin,nx,nelx,node,nodcode(nx),ijk(node,nelx), 
+     *     iperm(nx) 
+c-----------------------------------------------------------------------
+c this subroutine selects and initializes a mesh among a few
+c choices. So far there are 9 initial meshes provided and the user can
+c also enter his own mesh as a 10th option. 
+c 
+c on entry:
+c--------- 
+c nmesh	    = integer indicating the mesh chosen. nmesh=1,...,9
+c             corresponds to one of the 9 examples supplied by
+c             SPARSKIT. nmesh = 0 is a user supplied initial mesh.
+c             see below for additional information for the format.
+c iin       = integer containing the I/O unit number where to read
+c             the data from in case nmesh = 1. A dummy integer 
+c             otherwise.
+c node      = integer = the number of nodes per element (should be
+c             set to node=3 in this version). node is also the first 
+c             dimension of the array ijk.
+c
+c on return
+c ---------
+c nx	    = integer . the number of nodes
+c nelx	    = integer . the number of elements
+c x, y      = two real arrays containing the coordinates of the nodes.
+c nodcode   = an integer array containing the boundary information for
+c             each node with the following meaning.
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner node. 
+c                           
+c ijk(node,*)= an integer array containing the connectivity matrix.
+c
+c-----------------------------------------------------------------------
+c format for user supplied mesh (when nmesh = 7) 
+c
+c option nmesh = 0, is a user definied initial mesh. 
+c--------- 
+c format is as follows:
+c line 1: two integers, the first containing the number of nodes 
+c         the second the number of elements.
+c line 2: to line nx+1:  node information.
+c        enter the following, one line per node:
+c     * the number of the node in the numbering chosen (integer 
+c          taking the values 1 to nx), followed by,
+c        * the coordinates of the nodes (2 reals)  followed by 
+c	   the boundary information, an integer taking one of the 
+c          values 0, 1, or 2,  with the meaning explained above.
+c
+c line nx+2 to nx+nelx+1: connectivity matrix
+c       enter the following one line per element: 
+c       * number of the element in the numbering chosen, followed by
+c       * The three numbers of the nodes (according to the above numbering
+c       of the nodes) that constitute the element, in a counter clock-wise
+c       order (this is in fact not important since it is checked by the
+c       subroutine chkelemt). 
+c
+c AN EXAMPLE: consisting on one single element (a triangle) 
+c------------ 
+c    3    1
+c    1    0.0000    0.0000    2    
+c    2    4.0000    0.0000    2     
+c    3    0.0000    4.0000    2                  
+c    1    1    2    3
+c
+c----------------------------------------------------------------------- 
+c     local variables      
+      integer i, j, ii
+c
+c     print *, ' ----- nmesh = ', nmesh 
+      goto (10,1,2,3,4,5,6,7,8,9) nmesh+1 
+ 1    continue
+      call fmesh1  (nx,nelx,node,x,y,nodcode,ijk)
+      goto 18
+ 2    continue
+      call fmesh2  (nx,nelx,node,x,y,nodcode,ijk)
+      goto 18
+ 3    continue
+      call fmesh3  (nx,nelx,node,x,y,nodcode,ijk)
+      goto 18
+ 4    continue
+      call fmesh4  (nx,nelx,node,x,y,nodcode,ijk)
+      goto 18
+ 5    continue
+      call fmesh5  (nx,nelx,node,x,y,nodcode,ijk)
+      goto 18
+ 6    continue
+      call fmesh6 (nx,nelx,node,x,y,nodcode,ijk)
+      goto 18
+ 7    continue
+      call fmesh7 (nx,nelx,node,x,y,nodcode,ijk,iperm) 
+      goto 18
+ 8    continue
+      call fmesh8 (nx,nelx,node,x,y,nodcode,ijk,iperm) 
+      goto 18
+ 9    continue
+      call fmesh9(nx,nelx,node,x,y,nodcode,ijk,iperm) 
+      goto 18
+ 10   continue
+c
+c-------option 0 : reading mesh from IO unit iin.
+c
+      read (iin,*) nx, nelx
+c     
+      do 16 i=1,nx
+         read(iin,*) ii,x(ii),y(ii),nodcode(ii)
+ 16   continue
+      do 17 i=1,nelx
+         read(iin,*) ii,(ijk(j,ii),j=1,node)
+         if (ii. gt. nelx) nelx = ii
+ 17   continue
+c-----------------------------------------------------------------------
+ 18    continue
+c     and return
+      return
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      subroutine fmesh1 (nx,nelx,node,x,y,nodcode,ijk)
+c--------------------------------------------------------------
+c 
+c initial mesh for a simple square with two elemnts
+c      3             4
+c       --------------
+c       |          . |
+c       |   2    .   |
+c       |      .     |
+c       |   .    1   |
+c       | .          |
+c       --------------
+c      1              2
+c--------------------------------------------------------------
+c input parameters: node = first dimensoin of ijk (must be .ge. 3)
+c output parameters:
+c    nx    = number of nodes
+c    nelx = number of elemnts
+c    (x(1:nx), y(1:nx)) = coordinates of nodes
+c    nodcode(1:nx) = integer code for each node with the 
+c	    following meening:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point.
+c   ijk(1:3,1:nelx) = connectivity matrix. for a given element
+c	    number nel, ijk(k,nel), k=1,2,3 represent the nodes
+c	    composing the element nel.
+c--------------------------------------------------------------
+      implicit real*8 (a-h,o-z)
+      dimension x(*),y(*),nodcode(*),ijk(node,*)
+      real*8 x1(4),y1(4)
+      integer ijk1(2),ijk2(2),ijk3(2)
+c--------------------------------------------------------------
+c coordinates of nodal points
+c--------------------------------------------------------------
+      data  x1/0.0, 1.0, 0.0, 1.0/
+      data  y1/0.0, 0.0, 1.0, 1.0/
+c
+c------------------|--|
+c elements         1  2
+c------------------|--|
+      data ijk1   /1, 1/
+      data ijk2   /2, 4/
+      data ijk3   /4, 3/
+c
+      nx = 4
+c
+      do 1 k=1, nx
+         x(k) = x1(k)
+         y(k) = y1(k)
+         nodcode(k) = 1
+ 1    continue
+c     
+      nodcode(2) = 2
+      nodcode(3) = 2
+c
+      nelx = 2
+c
+      do  2 k=1,nelx
+         ijk(1,k) = ijk1(k) 
+         ijk(2,k) = ijk2(k)
+         ijk(3,k) = ijk3(k)
+ 2    continue
+c
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine fmesh2 (nx,nelx,node,x,y,nodcode,ijk)
+c---------------------------------------------------------------
+c initial mesh for a simple D-shaped region with 4 elemnts
+c       6
+c       | .
+c       |    .
+c       |      .
+c       |   4     .
+c       |           .
+c     4 -------------- 5
+c       |          . |
+c       |   3    .   |
+c       |      .     |
+c       |   .    2   |
+c       | .          |
+c       --------------
+c       | 2         . 3
+c       |         .
+c       |   1   .
+c       |     .
+c       |  .
+c       |.
+c       1  
+c--------------------------------------------------------------
+c input parameters: node = first dimensoin of ijk (must be .ge. 3)
+c output parameters:
+c    nx    = number of nodes
+c    nelx = number of elemnts
+c    (x(1:nx), y(1:nx)) = coordinates of nodes
+c    nodcode(1:nx) = integer code for each node with the 
+c	    following meening:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point.
+c   ijk(1:3,1:nelx) = connectivity matrix. for a given element
+c	    number nel, ijk(k,nel), k=1,2,3 represent the nodes
+c	    composing the element nel.
+c
+c--------------------------------------------------------------
+      implicit real*8 (a-h,o-z)
+      dimension x(*),y(*),nodcode(*),ijk(node,*)
+      real*8 x1(6),y1(6)
+      integer ijk1(4),ijk2(4),ijk3(4)
+c--------------------------------------------------------------
+c coordinates of nodal points
+c--------------------------------------------------------------
+      data x1/0.0, 0.0, 1.0, 0.0, 1.0, 0.0/
+      data y1/0.0, 1.0, 1.0, 2.0, 2.0, 3.0/
+c
+c------------------|--|--|--|
+c elements         1  2  3  4
+c------------------|--|--|--|
+      data ijk1   /1, 2, 2, 4/
+      data ijk2   /3, 3, 5, 5/
+      data ijk3   /2, 5, 4, 6/
+c
+      nx = 6
+c
+      do 1 k=1, nx
+         x(k) = x1(k)
+         y(k) = y1(k)
+         nodcode(k) = 1
+ 1    continue
+c
+      nelx = 4
+c     
+      do  2 k=1,nelx
+         ijk(1,k) = ijk1(k) 
+         ijk(2,k) = ijk2(k)
+         ijk(3,k) = ijk3(k)
+ 2    continue
+c
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine fmesh3 (nx,nelx,node,x,y,nodcode,ijk)
+c---------------------------------------------------------------
+c initial mesh for a C-shaped region composed of 10 elements --
+c
+c
+c      10           11            12             
+c       ---------------------------
+c       |          . |          . |
+c       |  7     .   |   9    .   |
+c       |      .     |      .     |
+c       |   .    8   |   .   10   |
+c       | .          | .          |
+c     7 ---------------------------
+c       |          . |8           9
+c       |   5    .   |
+c       |      .     |
+c       |   .    6   |
+c     4 | .          |5           6
+c       ---------------------------
+c       |          . |          . |
+c       |   1    .   |  3     .   |
+c       |      .     |      .     |
+c       |   .    2   |   .   4    |
+c       | .          | .          |
+c       ---------------------------
+c      1             2            3
+c
+c--------------------------------------------------------------
+c input parameters: node = first dimensoin of ijk (must be .ge. 3)
+c    nx    = number of nodes
+c    nelx = number of elemnts
+c    (x(1:nx), y(1:nx)) = coordinates of nodes
+c    nodcode(1:nx) = integer code for each node with the 
+c	    following meening:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point.
+c   ijk(1:3,1:nelx) = connectivity matrix. for a given element
+c	    number nel, ijk(k,nel), k=1,2,3 represent the nodes
+c	    composing the element nel.
+c
+c--------------------------------------------------------------
+      implicit real*8 (a-h,o-z)
+      dimension x(*),y(*),nodcode(*),ijk(node,*)
+      real*8 x1(12),y1(12)
+      integer ijk1(10),ijk2(10),ijk3(10)
+c--------------------------------------------------------------
+c coordinates of nodal points
+c--------------------------------------------------------------
+      data x1/0.0,1.0,2.0,0.0,1.0,2.0,0.0,1.0,2.0,0.0,1.0,2.0/
+      data y1/0.0,0.0,0.0,1.0,1.0,1.0,2.0,2.0,2.0,3.0,3.0,3.0/
+c
+c------------------|--|--|--|--|--|--|---|---|---|
+c elements         1  2  3  4  5  6  7   8   9  10
+c------------------|--|--|--|--|--|--|---|---|---|
+      data ijk1   /1, 1, 2, 2, 4, 4, 7,  7,  8, 8/
+      data ijk2   /5, 2, 6, 3, 8, 5, 11, 8, 12, 9/
+      data ijk3   /4, 5, 5, 6, 7, 8, 10, 11,11, 12/
+c
+      nx = 12
+c
+      do 1 k=1, nx
+         x(k) = x1(k)
+         y(k) = y1(k)
+         nodcode(k) = 1
+ 1    continue
+c
+      nodcode(3) = 2
+      nodcode(10) = 2
+      nodcode(9) = 2
+c     
+      nelx = 10
+c     
+      do  2 k=1,nelx
+         ijk(1,k) = ijk1(k) 
+         ijk(2,k) = ijk2(k)
+         ijk(3,k) = ijk3(k)
+ 2    continue
+c
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine fmesh4 (nx,nelx,node,x,y,nodcode,ijk)
+c----------------------------------------------------------------------- 
+c initial mesh for a C-shaped region composed of 10 elements --
+c      10                   11 
+c       +------------------+ .
+c       | .                |    .
+c       |    .       8     |       . 12
+c       |        .         |  9   . |
+c       |     7      .     |   .    |
+c     7 |                . | .   10 |
+c       -------------------+--------+ 9
+c       |                 .| 8 
+c       |     5       .    |
+c       |         .        |
+c       |    .       6     |
+c       |.                 | 5      6
+c    4  +------------------+--------+ 
+c       |               .  | .   4  |
+c       |    1       .     |    .   |
+c       |        .         |  3    .| 3
+c       |    .        2    |    .
+c       | .                | .
+c       -------------------- 
+c       1                  2 
+c--------------------------------------------------------------
+c input parameters: node = first dimensoin of ijk (must be .ge. 3)
+c    nx    = number of nodes
+c    nelx = number of elemnts
+c    (x(1:nx), y(1:nx)) = coordinates of nodes
+c    nodcode(1:nx) = integer code for each node with the 
+c	    following meening:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point.
+c   ijk(1:3,1:nelx) = connectivity matrix. for a given element
+c	    number nel, ijk(k,nel), k=1,2,3 represent the nodes
+c	    composing the element nel.
+c
+c--------------------------------------------------------------
+      implicit real*8 (a-h,o-z)
+      dimension x(*),y(*),nodcode(*),ijk(node,*)
+      real*8 x1(12),y1(12)
+      integer ijk1(10),ijk2(10),ijk3(10)
+c--------------------------------------------------------------
+c coordinates of nodal points
+c--------------------------------------------------------------
+      data x1/0.0,1.0,1.5,0.0,1.0,1.5,0.0,1.0,1.5,0.0,1.0,1.5/
+      data y1/0.0,0.0,0.5,1.0,1.0,1.0,2.0,2.0,2.0,3.0,3.0,2.5/
+c
+c------------------|--|--|--|--|--|--|---|---|---|
+c elements         1  2  3  4  5  6  7   8   9  10
+c------------------|--|--|--|--|--|--|---|---|---|
+      data ijk1   /1, 1, 2, 5, 4, 4, 7, 10,  8, 8/
+      data ijk2   /5, 2, 3, 3, 8, 5, 8,  8, 12, 9/
+      data ijk3   /4, 5, 5, 6, 7, 8, 10, 11,11, 12/
+c
+      nx = 12
+c     
+      do 1 k=1, nx
+         x(k) = x1(k)
+         y(k) = y1(k)
+         nodcode(k) = 1
+ 1    continue
+c
+      nodcode(6) = 2
+      nodcode(9) = 2
+c
+      nelx = 10
+c     
+      do  2 k=1,nelx
+         ijk(1,k) = ijk1(k) 
+         ijk(2,k) = ijk2(k)
+         ijk(3,k) = ijk3(k)
+ 2    continue
+c     
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine fmesh5 (nx,nelx,node,x,y,nodcode,ijk)
+c---------------------------------------------------------------
+c     initial mesh for a whrench shaped region composed of 14 elements --
+c     
+c                                      13            15    
+c                                        . ----------.           |-3
+c                                      .   .   13  .   .         |
+c                                   .   12   .   .  14    .      |
+c 9        10        11       12  .            . 14        . 16  |
+c ----------------------------------------------------------     |-2
+c |       . |       . |       . |            . |                 |  
+c | 1   .   |  3  .   |  5  .   |    7   .     |                 |
+c |   .  2  |   .  4  |   .  6  |     .    8   |                 |
+c |.        |.        |.        | .            |                 |
+c -----------------------------------------------------------    |-1
+c 1         2         3       4  .           6 .           . 8   |
+c                                   .   9    .   .   11   .      |
+c                                      .   .  10    .   .        |
+c                                        .___________.           |-0
+c                                       5             7
+c
+c 0---------1--------2----------3--------------4-------------5
+c--------------------------------------------------------------
+c input parameters: node = first dimensoin of ijk (must be .ge. 3)
+c    nx    = number of nodes
+c    nelx = number of elemnts
+c    (x(1:nx), y(1:nx)) = coordinates of nodes
+c    nodcode(1:nx) = integer code for each node with the 
+c	    following meening:
+c	nodcode(i) = 0 -->  node i is internal
+c	nodcode(i) = 1 -->  node i is a boundary but not a corner point
+c	nodcode(i) = 2 -->  node i is a corner point.
+c   ijk(1:3,1:nelx) = connectivity matrix. for a given element
+c	    number nel, ijk(k,nel), k=1,2,3 represent the nodes
+c	    composing the element nel.
+c
+c--------------------------------------------------------------
+      implicit real*8 (a-h,o-z)
+      dimension x(*),y(*),nodcode(*),ijk(node,*)
+      real*8 x1(16),y1(16)
+      integer ijk1(14),ijk2(14),ijk3(14)
+c--------------------------------------------------------------
+c     coordinates of nodal points
+c--------------------------------------------------------------
+      data x1/0.,1.,2.,3.,3.5,4.,4.5,5.,0.,1.,2.,3.,3.5,4.,4.5,5./
+      data y1/1.,1.,1.,1.,0.,1.,0.,1.,2.,2.,2.,2.,3.,2.,3.,2./
+c     
+c------------------|--|--|--|--|--|--|---|---|---|--|---|---|---|
+c elements         1  2  3  4  5  6  7   8   9  10  11  12  13  14
+c------------------|--|--|--|--|--|--|---|---|---|--|---|---|---|
+      data ijk1   /1, 1, 2, 2, 3, 3, 4,  4,  4,  5, 6, 12, 14, 14/
+      data ijk2   /10,2,11, 3,12, 4,14,  6,  5,  7, 7, 14, 15, 16/
+      data ijk3   /9,10,10,11,11,12,12, 14,  6,  6, 8, 13, 13, 15/
+c
+      nx = 16
+c     
+      do 1 k=1, nx
+         x(k) = x1(k)
+         y(k) = y1(k)
+         nodcode(k) = 1
+ 1    continue
+c     
+      nodcode(9) = 2
+      nodcode(8) = 2
+      nodcode(16) = 2
+c     
+      nelx = 14
+c     
+      do  2 k=1,nelx
+         ijk(1,k) = ijk1(k) 
+         ijk(2,k) = ijk2(k)
+         ijk(3,k) = ijk3(k)
+ 2    continue
+c     
+      return
+      end
+c----------------------------------------------------------------------- 
+      subroutine fmesh6 (nx,nelx,node,x,y,nodcode,ijk)
+c---------------------------------------------------------------
+c this generates a finite element mesh for an ellipse-shaped 
+c domain.
+c---------------------------------------------------------------
+      implicit real*8 (a-h,o-z)
+      dimension x(*),y(*),nodcode(*),ijk(node,*), ijktr(200,3)
+      integer nel(200) 
+c--------------------------------------------------------------
+c     coordinates of nodal points
+c--------------------------------------------------------------
+      nd = 8 
+      nr = 3
+c     
+c     define axes of ellipse
+c     
+      a = 2.0
+      b = 1.30 
+c     
+      nx = 1
+      pi = 4.0* atan(1.0) 
+      theta = 2.0 * pi / real(nd)  
+      x(1) = 0.0
+      y(1) = 0.0 
+      delr = a / real(nr)
+      nx = 0
+      do i = 1, nr 
+         ar = real(i)*delr
+         br = ar*b / a
+         do j=1, nd 
+            nx = nx+1
+            x(nx) = a +ar*cos(real(j)*theta)
+            y(nx) = b +br*sin(real(j)*theta)
+c            write (13,*) ' nod ', nx, ' x,y', x(nx), y(nx) 
+            nodcode(nx) = 0
+            if (i .eq. nr) nodcode(nx) = 1
+         enddo
+      enddo
+c     
+      nemax = 200
+      call dlauny(x,y,nx,ijktr,nemax,nelx)
+c     
+c     print *, ' delauny -- nx, nelx ', nx, nelx
+      do 3 j=1,nx
+         nel(j) = 0
+ 3    continue
+c     transpose ijktr into ijk and count the number of 
+c     elemnts to which each node belongs
+c     
+      do 4 j=1, nelx
+         do 41 k=1, node
+	    i = ijktr(j,k)
+	    ijk(k,j) = i
+	    nel(i) = nel(i)+1
+ 41      continue
+ 4    continue
+c     
+c     take care of ordering within each element
+c     
+      call chkelmt (nx, x, y, nelx, ijk, node)
+c     
+      return
+      end
+c--------------------------------------------------------
+      subroutine fmesh7 (nx,nelx,node,x,y,nodcode,ijk,iperm)
+      implicit none 
+      real*8 x(*),y(*) 
+      integer nx,nelx,node,nodcode(nx),ijk(node,nelx),iperm(nx) 
+c---------------------------------------------------------------
+c     this generates a U-shaped domain with an elliptic inside.
+c     then a Delauney triangulation is used to generate the mesh.
+c     mesh needs to be post-processed -- see inmesh -- 
+c---------------------------------------------------------------
+      integer nr,nsec,i,k,nemax,j,nel(200),ijktr(200,3),nodexc
+      real*8 a,b,x1, y1, x2, y2, xcntr,ycntr, rad,pi,delr,xnew,ynew,
+     *     arx, ary, cos, sin, theta,excl   
+c--------------------------------------------------------------
+c     coordinates of nodal points
+c--------------------------------------------------------------
+      data x1/0.0/,y1/0.0/,x2/6.0/,y2/6.0/,nodexc/1/
+      xcntr = x2/3.0
+      ycntr = y2/2.0 
+      rad = 1.8
+      nsec = 20 
+      nr = 3 
+c
+c     exclusion zone near the boundary 
+c 
+      excl = 0.02*x2 
+c-----------------------------------------------------------------------
+c     enter the four corner points. 
+c-----------------------------------------------------------------------
+      nx = 1 
+      x(nx) = x1
+      y(nx) = y1
+      nodcode(nx) = 1
+      nx = nx+1
+      x(nx) = x2
+      y(nx) = y1
+      nodcode(nx) = 1
+      nx = nx+1
+      x(nx) = x2
+      y(nx) = y2 
+      nodcode(nx) = 1
+      nx = nx+1
+      x(nx) = x1
+      y(nx) = y2
+      nodcode(nx) = 1
+c     
+c     define axes of ellipse 
+c     
+      a = 2.0
+      b = 1.30
+c-----------------------------------------------------------------------
+      pi = 4.0*atan(1.0) 
+      delr = a / real(nr)
+      do 2 i = 1, nsec 
+         theta = 2.0 * real(i-1) * pi / real(nsec)  
+         xnew = xcntr + rad*cos(theta)
+         ynew = ycntr + rad*b*sin(theta)/a 
+         if ((xnew .ge. x2) .or. (xnew .le. x1) .or. (ynew .ge. y2)
+     *        .or. (ynew .le. y1)) goto 2 
+         nx = nx+1 
+         x(nx) = xnew 
+         y(nx) = ynew 
+         nodcode(nx) = nodexc 
+         arx = delr*cos(theta)
+         ary = delr*b*sin(theta)/a 
+c     
+c     while inside domain do: 
+c     
+ 1       continue 
+         xnew = x(nx) + arx 
+         ynew = y(nx) + ary 
+         if (xnew .ge. x2) then 
+            x(nx) = x2 
+            nodcode(nx) = 1
+         else if (xnew .le. x1) then
+            x(nx) = x1 
+            nodcode(nx) = 1         
+         else if (ynew .ge. y2) then 
+            y(nx) = y2 
+            nodcode(nx) = 1
+         else if (ynew .le. y1) then
+            y(nx) = y1 
+            nodcode(nx) = 1         
+         else
+            nx = nx+1 
+            x(nx) = xnew 
+            y(nx) = ynew 
+            nodcode(nx) = 0
+            call clos2bdr(nx,xnew,ynew,x,y,x1,x2,y1,y2,excl,nodcode)
+         endif 
+c        write (13,*) ' nod ', nx, ' x,y', x(nx), y(nx)
+c     *         ,' arx--ary ', arx, ary
+         arx = arx*1.2 
+         ary = ary*1.2
+         if (nodcode(nx) .le. 0) goto 1 
+ 2    continue 
+c     
+      nemax = 200
+      call dlauny(x,y,nx,ijktr,nemax,nelx)
+c     
+c     print *, ' delauny -- nx, nelx ', nx, nelx
+      do 3 j=1,nx
+         nel(j) = 0
+ 3    continue
+c     
+c     transpose ijktr into ijk and count the number of 
+c     elemnts to which each node belongs
+c     
+      do 4 j=1, nelx
+         do 41 k=1, node
+	    i = ijktr(j,k)
+	    ijk(k,j) = i
+	    nel(i) = nel(i)+1
+ 41      continue
+ 4    continue
+c
+c     this mesh needs cleaning up --
+c 
+      call cleanel (nelx,ijk, node,nodcode,nodexc) 
+      call cleannods(nx,x,y,nelx,ijk,node,nodcode,iperm)       
+c
+c     take care of ordering within each element
+c
+      call chkelmt (nx, x, y, nelx, ijk, node)
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine fmesh8 (nx,nelx,node,x,y,nodcode,ijk,iperm)
+      implicit none 
+      real*8 x(*),y(*) 
+      integer nx,nelx,node,nodcode(nx),ijk(node,nelx),iperm(nx) 
+c---------------------------------------------------------------
+c     this generates a small rocket type shape inside a rectangle
+c     then a Delauney triangulation is used to generate the mesh.
+c     mesh needs to be post-processed -- see inmesh -- 
+c---------------------------------------------------------------
+      integer nr,nsec,i,k,nemax,j,nel(1500),ijktr(1500,3),nodexc 
+      real*8 a,b,x1, y1, x2, y2, xcntr,ycntr, rad,pi,delr,xnew,ynew,
+     *     arx, ary, cos, sin, theta,radi,excl 
+c--------------------------------------------------------------
+c     coordinates of corners + some additional data 
+c--------------------------------------------------------------
+      data x1/0.0/,y1/0.0/,x2/6.0/,y2/6.0/,nodexc/3/  
+      xcntr = 4.0 
+      ycntr = y2/2.0 
+      rad = 0.6
+c
+c     exclusion zone near the boundary. 
+c 
+      excl = 0.02*x2 
+      nsec = 30
+      nr = 4
+c-----------------------------------------------------------------------
+c     enter the four corner points. 
+c-----------------------------------------------------------------------
+      nx = 1 
+      x(nx) = x1
+      y(nx) = y1
+      nodcode(nx) = 1
+      nx = nx+1
+      x(nx) = x2
+      y(nx) = y1
+      nodcode(nx) = 1
+      nx = nx+1
+      x(nx) = x2
+      y(nx) = y2 
+      nodcode(nx) = 1
+      nx = nx+1
+      x(nx) = x1
+      y(nx) = y2
+      nodcode(nx) = 1
+c     
+c     define axes of ellipse /circle / object
+c     
+      a = 2.0
+      b = 1.0
+c-----------------------------------------------------------------------
+      pi = 4.0*atan(1.0) 
+      delr = 2.0*rad / real(nr)
+      do 2 i = 1, nsec 
+         theta = 2.0*real(i-1) * pi / real(nsec) 
+         if (theta .gt. pi) theta = theta - 2.0*pi 
+         radi=rad*(1.0+0.05*((pi/2.0)**2-theta**2)**2)
+     *        /(1.0+0.05*(pi/2.0)**4) 
+         arx = radi*cos(theta)/real(nr) 
+         ary = radi*sin(theta)/real(nr) 
+c      a hack!
+c         arx = (abs(theta)+0.25)*cos(theta)/real(nr) 
+c         ary = (abs(theta)+0.25)*sin(theta)/real(nr) 
+c
+         xnew = xcntr + radi*cos(theta)
+         ynew = ycntr + radi*b*sin(theta)/a 
+         if ((xnew .ge. x2) .or. (xnew .le. x1) .or. (ynew .ge. y2)
+     *        .or. (ynew .le. y1)) goto 2 
+         nx = nx+1 
+         x(nx) = xnew 
+         y(nx) = ynew 
+         nodcode(nx) = nodexc 
+c     
+c     while inside domain do: 
+c     
+ 1       continue 
+         xnew = xnew  + arx 
+         ynew = ynew  + ary 
+         if (xnew .ge. x2) then 
+            x(nx) = x2 
+            nodcode(nx) = 1
+         else if (xnew .le. x1) then
+            x(nx) = x1 
+            nodcode(nx) = 1         
+         else if (ynew .ge. y2) then 
+            y(nx) = y2 
+            nodcode(nx) = 1
+         else if (ynew .le. y1) then
+            y(nx) = y1 
+            nodcode(nx) = 1         
+c
+c     else we can add this as interior point
+c 
+         else
+            nx = nx+1 
+            x(nx) = xnew 
+            y(nx) = ynew 
+            nodcode(nx) = 0
+c
+c     do something if point is too close to boundary 
+c 
+            call clos2bdr(nx,xnew,ynew,x,y,x1,x2,y1,y2,excl,nodcode)
+         endif
+c            
+         arx = arx*1.1
+         ary = ary*1.1 
+         if (nodcode(nx) .eq. 0) goto 1 
+ 2    continue 
+c     
+      nemax = 1500 
+      call dlauny(x,y,nx,ijktr,nemax,nelx)
+c     
+      print *, ' delauney -- nx, nelx ', nx, nelx
+      do 3 j=1,nx
+         nel(j) = 0
+ 3    continue
+c-----------------------------------------------------------------------     
+c     transpose ijktr into ijk and count the number of 
+c     elemnts to which each node belongs
+c----------------------------------------------------------------------- 
+      do 4 j=1, nelx
+         do 41 k=1, node
+	    i = ijktr(j,k)
+	    ijk(k,j) = i
+	    nel(i) = nel(i)+1
+ 41      continue
+ 4    continue
+c
+c     this mesh needs cleaning up --
+c 
+      call cleanel (nelx,ijk, node,nodcode,nodexc) 
+      call cleannods(nx,x,y,nelx,ijk,node,nodcode,iperm)       
+c
+c     take care of ordering within each element
+c
+      call chkelmt (nx, x, y, nelx, ijk, node)
+      return
+      end
+c-----------------------------------------------------------------------  
+      subroutine fmesh9 (nx,nelx,node,x,y,nodcode,ijk,iperm)
+      implicit none 
+      real*8 x(*),y(*) 
+      integer nx,nelx,node,nodcode(nx),ijk(node,nelx),iperm(nx) 
+c---------------------------------------------------------------
+c     this generates a U-shaped domain with an elliptic inside.
+c     then a Delauney triangulation is used to generate the mesh.
+c     mesh needs to be post-processed -- see inmesh -- 
+c---------------------------------------------------------------
+      integer nr,nsec,i,k,nemax,j,nel(1500),ijktr(1500,3),nodexc 
+      real*8 x1, y1, x2, y2, xcntr,ycntr, rad,pi,delr,xnew,ynew,
+     *     arx, ary, cos, sin, theta,excl   
+c--------------------------------------------------------------
+c     coordinates of nodal points
+c--------------------------------------------------------------
+      data x1/0.0/,y1/0.0/,x2/11.0/,y2/5.5/,nodexc/3/ 
+      xcntr = 1.50
+      ycntr = y2/2.0 
+      rad = 0.6
+      nsec = 30
+      nr = 3 
+c
+c-----------------------------------------------------------------------
+c     enter the four corner points. 
+c-----------------------------------------------------------------------
+      nx = 1 
+      x(nx) = x1
+      y(nx) = y1
+      nodcode(nx) = 1
+      nx = nx+1
+      x(nx) = x2
+      y(nx) = y1
+      nodcode(nx) = 1
+      nx = nx+1
+      x(nx) = x2
+      y(nx) = y2 
+      nodcode(nx) = 1
+      nx = nx+1
+      x(nx) = x1
+      y(nx) = y2
+      nodcode(nx) = 1
+c     
+c     define axes of ellipse 
+c     
+c-----------------------------------------------------------------------
+      pi = 4.0*atan(1.0) 
+      delr = rad / real(nr) 
+      do 2 i = 1, nsec 
+         theta = 2.0 * real(i-1) * pi / real(nsec)  
+         xnew = xcntr + rad*cos(theta)
+         ynew = ycntr + rad*sin(theta) 
+         if ((xnew .ge. x2) .or. (xnew .le. x1) .or. (ynew .ge. y2)
+     *        .or. (ynew .le. y1)) goto 2 
+         nx = nx+1 
+         x(nx) = xnew 
+         y(nx) = ynew 
+         nodcode(nx) = nodexc 
+         arx = delr*cos(theta)
+         ary = delr*sin(theta)
+c 
+c     exclusion zone near the boundary 
+c
+c         excl = 0.1*delr 
+         excl = 0.15*delr
+c     
+c     while inside domain do: 
+c     
+ 1       continue 
+         xnew = x(nx) + arx 
+         ynew = y(nx) + ary 
+         if (xnew .ge. x2) then 
+            x(nx) = x2 
+            nodcode(nx) = 1
+         else if (xnew .le. x1) then
+            x(nx) = x1 
+            nodcode(nx) = 1         
+         else if (ynew .ge. y2) then 
+            y(nx) = y2 
+            nodcode(nx) = 1
+         else if (ynew .le. y1) then
+            y(nx) = y1 
+            nodcode(nx) = 1         
+         else
+            nx = nx+1 
+            x(nx) = xnew 
+            y(nx) = ynew 
+            nodcode(nx) = 0
+            call clos2bdr(nx,xnew,ynew,x,y,x1,x2,y1,y2,excl,nodcode)
+         endif 
+         arx = arx*1.1 
+         ary = ary*1.1
+         excl = excl*1.1 
+         if (nodcode(nx) .le. 0) goto 1 
+ 2    continue 
+c     
+      nemax = 1500
+      call dlauny(x,y,nx,ijktr,nemax,nelx)
+c     
+c     print *, ' delauny -- nx, nelx ', nx, nelx
+      do 3 j=1,nx
+         nel(j) = 0
+ 3    continue
+c     
+c     transpose ijktr into ijk and count the number of 
+c     elemnts to which each node belongs
+c     
+      do 4 j=1, nelx
+         do 41 k=1, node
+	    i = ijktr(j,k)
+	    ijk(k,j) = i
+	    nel(i) = nel(i)+1
+ 41      continue
+ 4    continue
+c
+c     this mesh needs cleaning up --
+c 
+      call cleanel (nelx,ijk, node,nodcode,nodexc) 
+      call cleannods(nx,x,y,nelx,ijk,node,nodcode,iperm)       
+c
+c     take care of ordering within each element
+c
+      call chkelmt (nx, x, y, nelx, ijk, node)
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine clos2bdr (nx,xnew,ynew,x,y,x1,x2,y1,y2,excl,nodcode) 
+      implicit none 
+      integer nx,nodcode(nx)
+      real*8 x(nx),y(nx),xnew,ynew,x1,x2,y1,y2,excl 
+c----------------------------------------------------------------------- 
+c     takes care of case where a point generated is too close to the
+c     boundary  -- in this case projects the previous point to the
+c     rectangle boundary == that makes some exclusion criterion
+c     violated... does a simple job.
+c----------------------------------------------------------------------- 
+      if (xnew .ge. x2-excl) then
+         x(nx) = x2
+         y(nx) = y(nx-1) 
+         nodcode(nx) = 1 
+      endif
+      if (xnew .le. x1+excl) then
+         x(nx) = x1 
+         y(nx) = y(nx-1) 
+         nodcode(nx) = 1 
+      endif
+      if (ynew .ge. y2-excl) then
+         y(nx) = y2
+         x(nx) = x(nx-1) 
+         nodcode(nx) = 1 
+      endif
+      if (ynew .le. y1+excl) then
+         y(nx) = y1 
+         x(nx) = x(nx-1) 
+         nodcode(nx) = 1 
+      endif
+c     
+      return
+      end
diff --git a/MATGEN/FEM/semantic.cache b/MATGEN/FEM/semantic.cache
new file mode 100644
index 0000000..bf87e70
--- /dev/null
+++ b/MATGEN/FEM/semantic.cache
@@ -0,0 +1,16 @@
+;; Object FEM/
+;; SEMANTICDB Tags save file
+(semanticdb-project-database-file "FEM/"
+  :tables (list 
+   (semanticdb-table "makefile"
+    :major-mode 'makefile-mode
+    :tags '(("FFLAGS" variable nil nil [1 11]) ("F77" variable (:default-value ("f77")) nil [11 21]) ("FILES" variable (:default-value ("convdif.o" "functns2.o")) nil [54 83]) ("fem.ex" function (:arguments ("$(FILES)" "../../UNSUPP/PLOTS/psgrd.o" "../../libskit32.a")) nil [84 232]) ("clean" function nil nil [232 269]) ("../../libskit.a" function nil nil [269 331]) ("../../UNSUPP/PLOTS/psgrd.o" function (:arguments ("../../UNSUPP/PLOTS/psgrd.f")) nil [331 441]))
+    :file "makefile"
+    :pointmax 441
+    :unmatched-syntax 'nil
+    )
+   )
+  :file "semantic.cache"
+  :semantic-tag-version "2.0pre3"
+  :semanticdb-version "2.0pre3"
+  )
diff --git a/MATGEN/MISC/README b/MATGEN/MISC/README
new file mode 100644
index 0000000..96e8aa2
--- /dev/null
+++ b/MATGEN/MISC/README
@@ -0,0 +1,15 @@
+This directory contains the last two test problems as described in
+README of the directory above this one.
+
+ zlatev.f : three different codes to generate matrices from the 
+            Zlatev et. al. paper (see above). Contributed by E. Rothman
+            (Cornell).
+
+ rzlatev.f : driver for a test program for the zlatev code.
+
+ makzlatev :  makefiles. See above for details.
+
+ markov.f  : a main program followed by a subroutine to generate
+             markov chain matrices modeling random walk on a triang.
+             grid. There is one parameter to the subroutine. 
+
diff --git a/MATGEN/MISC/makefile b/MATGEN/MISC/makefile
new file mode 100644
index 0000000..bc0b41c
--- /dev/null
+++ b/MATGEN/MISC/makefile
@@ -0,0 +1,25 @@
+FFLAGS = 
+F77 = f77
+
+#F77 = cf77
+#FFLAGS = -Wf"-dp"
+
+FILES1 = rsobel.o
+FILES2 = rzlatev.o
+FILES3 = markov.o
+
+sobel.ex:	$(FILES1) ../../libskit.a 
+	$(F77) $(FFLAGS) -o sobel.ex $(FILES1)  ../../libskit.a 
+
+zlatev.ex:	$(FILES2) ../../libskit.a 
+	$(F77) $(FFLAGS) -o zlatev.ex $(FILES2)  ../../libskit.a 
+
+markov.ex:	$(FILES3) ../../libskit.a 
+	$(F77) $(FFLAGS) -o markov.ex $(FILES3)  ../../libskit.a 
+
+clean:
+	rm -f *.o *.ex core *.trace
+
+../../libskit.a:
+	(cd ../..; $(MAKE) $(MAKEFLAGS) libskit.a)
+
diff --git a/MATGEN/MISC/markov.f b/MATGEN/MISC/markov.f
new file mode 100644
index 0000000..00eb34f
--- /dev/null
+++ b/MATGEN/MISC/markov.f
@@ -0,0 +1,143 @@
+      program markov 
+c-----------------------------------------------------------------------
+c
+c program to generate a Markov chain matrix (to test eigenvalue routines
+c or algorithms for singular systems (in which case use I-A )) 
+c the matrix models  simple random walk on a triangular grid.
+c see additional comments in subroutine.
+c -----
+c just compile this segment and link to the rest of sparskit 
+c (uses subroutine prtmt from MATGEN)
+c will create a matrix in the HARWELL/BOEING format and put it in
+c the file markov.mat
+c
+c-----------------------------------------------------------------------
+      parameter (nmax=5000, nzmax= 4*nmax) 
+      real*8 a(nzmax) 
+      integer ja(nzmax), ia(nmax+1)
+c 
+      character title*72,key*8,type*3              
+      open (unit=11,file='markov.mat') 
+c
+c read - in grid size - will not accept too large grids.
+c
+      write (6,'(17hEnter grid-size: ,$)') 
+      read *, m
+      if (m*(m+1) .gt. 2*nmax ) then
+         print *, ' m too large - unable to produce matrix '
+         stop
+      endif
+c 
+c call generator. 
+c
+      call markgen (m, n, a, ja, ia)
+c-----------------------------------------------------------------------
+      title=' Test matrix from SPARSKIT - markov chain model           '
+      key = 'randwk01'
+      type = 'rua'
+      iout = 11
+      job = 2
+      ifmt = 10
+      call prtmt (n, n, a, ja, ia, x,'NN',title,
+     *     key, type,ifmt, job, iout) 
+      stop
+      end
+c     
+      subroutine markgen (m, n, a, ja, ia) 
+c-----------------------------------------------------------------------
+c matrix generator for a markov model of a random walk on a triang. grid
+c-----------------------------------------------------------------------
+c this subroutine generates a test matrix that models a random
+c walk on a triangular grid. This test example was used by 
+c G. W. Stewart ["{SRRIT} - a FORTRAN subroutine to calculate the 
+c dominant invariant subspaces of a real matrix", 
+c Tech. report. TR-514, University of Maryland (1978).] and in a few
+c papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34,
+c pp. 269-295 (1980) ]. These matrices provide reasonably easy 
+c test problems for eigenvalue algorithms. The transpose of the 
+c matrix  is stochastic and so it is known that one is an exact 
+c eigenvalue. One seeks the eigenvector of the transpose associated 
+c with the eigenvalue unity. The problem is to calculate the 
+c steady state probability distribution of the system, which is
+c the eigevector associated with the eigenvalue one and scaled in
+c such a way that the sum all the components is equal to one.
+c-----------------------------------------------------------------------
+c parameters
+c------------
+c on entry :
+c----------
+c m     = integer. number of points in each direction. 
+c
+c on return:
+c----------
+c n     = integer. The dimension of the matrix. (In fact n is known 
+c         to be equal to (m(m+1))/2      ) 
+c a, 
+c ja,
+c ia    = the matrix stored in CSR format.
+c
+c-----------------------------------------------------------------------
+c Notes: 1) the code will actually compute the transpose of the 
+c stochastic matrix that contains the transition probibilities.
+c        2) It should also be possible to have a matrix generator
+c with an additional parameter (basically redefining `half' below 
+c to be another parameter and changing the rest accordingly, but 
+c this is not as simple as it sounds). This is not likely to provide 
+c any more interesting matrices. 
+c-----------------------------------------------------------------------
+      real*8 a(*), cst, pd, pu, half 
+      integer ja(*), ia(*) 
+c----------------------------------------------------------------------- 
+      data half/0.5d0/
+c
+      cst = half/real(m-1)
+c     
+c     --- ix counts the grid point (natural ordering used), i.e.,
+c     --- the row number of the matrix.
+c     
+      ix = 0
+      jax = 1
+      ia(1) = jax 
+c
+c     sweep y coordinates
+c
+      do 20 i=1,m
+         jmax = m-i+1
+c
+c     sweep x coordinates
+c
+         do 10 j=1,jmax
+            ix = ix + 1
+            if (j .eq. jmax) goto 2
+            pd = cst*real(i+j-1) 
+c            
+c     north
+c
+            a(jax) = pd
+            if (i.eq. 1) a(jax) = a(jax)+pd
+            ja(jax) =  ix + 1
+            jax = jax+1
+c     east
+            a(jax) = pd
+            if (j .eq. 1) a(jax) = a(jax)+pd
+            ja(jax) = ix + jmax
+            jax = jax+1
+c     south
+ 2          pu = half - cst*real(i+j-3) 
+            if ( j .gt. 1) then 
+               a(jax) = pu
+               ja(jax) = ix-1 
+               jax = jax+1
+            endif 
+c     west
+            if ( i .gt. 1) then
+               a(jax) = pu
+               ja(jax) = ix - jmax - 1 
+               jax = jax+1
+            endif 
+            ia(ix+1) = jax 
+ 10      continue
+ 20   continue
+      n = ix 
+      return
+      end
diff --git a/MATGEN/MISC/rsobel.f b/MATGEN/MISC/rsobel.f
new file mode 100644
index 0000000..5a3afab
--- /dev/null
+++ b/MATGEN/MISC/rsobel.f
@@ -0,0 +1,14 @@
+      program rsobel
+      integer n, ia(1:200), ja(1:1000), ib(1:200), jb(1:1000)
+      integer nrowc, ncolc
+      integer ic(1:200), jc(1:1000), ierr
+      real*8  a(1:1000), b(1:1000), c(1:1000)
+
+      write (*, '(1x, 9hInput n:  ,$)')
+      read *, n
+      call sobel(n,nrowc,ncolc,c,jc,ic,a,ja,ia,b,jb,ib,1000,ierr)
+      print *, 'ierr =', ierr
+      print *, 'Nrow =', nrowc, '	Ncol =', ncolc
+      call dump(1, nrowc, .true., c, jc, ic, 6)
+      end
+
diff --git a/MATGEN/MISC/rzlatev.f b/MATGEN/MISC/rzlatev.f
new file mode 100644
index 0000000..25014af
--- /dev/null
+++ b/MATGEN/MISC/rzlatev.f
@@ -0,0 +1,108 @@
+      program zlatev
+c-----------------------------------------------------------------------
+c
+c test suite for zlatev matrices. generates three matrices and 
+c writes them in three different files in Harwell-Boeing format.
+c      zlatev1.mat  produced from matrf2 
+c      zlatev2.mat  produced from  dcn 
+c      zlatev3.mat  produced from  ecn
+c
+c-----------------------------------------------------------------------
+      parameter (nmax = 1000, nzmax=20*nmax)
+      implicit real*8 (a-h,o-z)
+      integer ia(nzmax), ja(nzmax), iwk(nmax)
+      real*8 a(nzmax)
+      character title*72, key*3,type*8, guesol*2
+c
+      open (unit=7,file='zlatev1.mat')
+      open (unit=8,file='zlatev2.mat')
+      open (unit=9,file='zlatev3.mat')
+c
+      m = 100
+      n = m
+      ic = n/2 
+      index = 10
+      alpha = 5.0
+      nn = nzmax
+c
+c call matrf2
+c 
+      call matrf2(m,n,ic,index,alpha,nn,nz,a,ia,ja,ierr) 
+      job = 1
+c      do 110 i = 1, nz
+c         print *, ia(i), ja(i), a(i)
+c 110  continue
+      call coicsr(n, nz, job, a, ja, ia, iwk) 
+c-----
+      title = ' 1st matrix from zlatev examples                '
+      type  = 'RUA'
+      key   = ' ZLATEV1'
+      iout  = 7
+      guesol='NN'
+c
+      ifmt = 3
+      job = 2
+c
+c write result in H-B format. 
+c 
+c Replaces prtmt with smms in order to print matrix in format for 
+c SMMS instead.
+c      call smms (n,1,n,0,a,ja,ia,iout)
+      call prtmt (n,n,a,ja,ia,rhs,guesol,title,type,key,
+     1	                  ifmt,job,iout) 
+
+c-------- second type of matrices dcn matrices ---------------
+       n = 200 
+       nn = nzmax 
+       ic = 20
+c-------------------------------------------------------
+c matrix of the type e(c,n)
+c-------------------------------------------------------
+       call dcn(a,ia,ja,n,ne,ic,nn,ierr)
+c---------------------------------------------------
+      call coicsr(n, ne, job, a, ja, ia, iwk) 
+      title = ' 2nd matrix from zlatev examples                '
+      iout = iout+1
+      guesol='NN'
+      type  = 'RUA'
+      key = ' ZLATEV2'
+c
+      ifmt = 3
+      job = 2
+c
+c write result in second file 
+c
+c Replaced prtmt with smms in order to print matrix in format for 
+c SMMS instead.
+c      call smms (n,1,n,0,a,ja,ia,iout)
+      call prtmt (n,n,a,ja,ia,rhs,guesol,title,type,key,
+     1	                  ifmt,job,iout) 
+c-------------------------------------------------------
+c matrix of the type e(c,n)
+c-------------------------------------------------------
+       n = 200 
+       ic = 20
+       nn = nzmax 
+c
+c call ecn
+c 
+      call ecn(n,ic,ne,ia,ja,a,nn,ierr)
+      call coicsr(n, ne, job, a, ja, ia, iwk) 
+      title = ' 3nd matrix from zlatev examples                '
+      guesol='NN'
+      type  = 'RUA'
+      key = ' ZLATEV3'
+      iout = iout+1
+c
+      ifmt = 3
+      job = 2
+c
+c write resulting matrix in third file
+c
+c Replaced prtmt with smms in order to print matrix in format for 
+c SMMS instead.
+c      call smms (n,1,n,0,a,ja,ia,iout)
+      call prtmt (n,n,a,ja,ia,rhs,guesol,title,type,key,
+     1	                  ifmt,job,iout) 
+      stop
+      end
diff --git a/MATGEN/MISC/sobel.f b/MATGEN/MISC/sobel.f
new file mode 100644
index 0000000..2a25193
--- /dev/null
+++ b/MATGEN/MISC/sobel.f
@@ -0,0 +1,158 @@
+      subroutine sobel(n,nrowc,ncolc,c,jc,ic,a,ja,ia,b,jb,ib,nzmax,ierr)
+      integer i, n, ia(*), ja(*), ib(*), jb(*)
+      integer nrowa, ncola, nrowb, ncolb, nrowc, ncolc, ipos
+      integer ic(*), jc(*), offset, ierr
+      real*8  a(*), b(*), c(*)
+c-----------------------------------------------------------------------
+c     This subroutine generates a matrix used in the statistical problem
+c     presented by Prof. Sobel. The matrix is formed by a series of
+c     small submatrix on or adjancent to the diagonal. The submatrix on
+c     the diagonal is square and the size goes like 1, 1, 2, 2, 3, 3,...
+c     Each of the diagonal block is a triadiagonal matrix, each of the
+c     off-diagonal block is a bidiagonal block. The values of elements
+c     in the off-diagonal block are all -1. So are the values of the
+c     elements on the sub- and super-diagonal of the blocks on the
+c     diagonal. The first element(1,1) of the diagonal block is alternating
+c     between 3 and 5, the rest of the diagonal elements (of the block
+c     on the diagonal) are 6.
+c-----------------------------------------------------------------------
+c     This subroutine calls following subroutines to generate the three
+c     thypes of submatrices:
+c     diagblk -- generates diagonal block.
+c     leftblk -- generates the block left of the diagonal one.
+c     rightblk-- generates the block right of the diagonal one.
+c-----------------------------------------------------------------------
+      if (n.lt.2) return
+
+      ipos = 1
+      offset = 1
+      call diagblk(1, nrowc, ncolc, c, jc, ic)
+      do 10 i=2, n-2
+         nrowa = nrowc
+         ncola = ncolc
+         call copmat (nrowc,c,jc,ic,a,ja,ia,1,1)
+         call rightblk(i-1, nrowb, ncolb, b,jb,ib)
+         call addblk(nrowa,ncola,a,ja,ia,ipos,ipos+offset,1,
+     $        nrowb,ncolb,b,jb,ib,nrowc,ncolc,c,jc,ic,nzmax,ierr)
+         call leftblk(i,nrowb,ncolb,b,jb,ib)
+         call addblk(nrowc,ncolc,c,jc,ic,ipos+offset,ipos,1,
+     $        nrowb,ncolb,b,jb,ib,nrowa,ncola,a,ja,ia,nzmax,ierr)
+         ipos = ipos + offset
+         call diagblk(i,nrowb,ncolb,b,jb,ib)
+         call addblk(nrowa,ncola,a,ja,ia,ipos,ipos,1,
+     $        nrowb,ncolb,b,jb,ib,nrowc,ncolc,c,jc,ic,nzmax,ierr)
+         offset = 1 + (i-1)/2
+ 10   continue
+      end
+c-----------------------------------------------------------------------
+      subroutine diagblk(n, nrow, ncol, a, ja, ia)
+      implicit none
+      integer n, nrow, ncol, ia(1:*), ja(1:*)
+      real*8  a(1:*)
+c-----------------------------------------------------------------------
+c     generates the diagonal block for the given problem.
+c-----------------------------------------------------------------------
+      integer i, k
+      nrow = 1 + (n-1)/2
+      ncol = nrow
+      k = 1
+      ia(1) = 1
+      ja(1) = 1
+      if (mod(n, 2) .eq. 1) then
+         a(1) = 3
+      else
+         a(1) = 5
+      end if
+      k = k + 1
+      if (ncol.gt.1) then
+         ja(2) = 2
+         a(2) = -1.0
+         k = k + 1
+      end if
+      
+      do 10 i = 2, nrow
+         ia(i) = k
+         ja(k) = i-1
+         a(k) = -1.0
+         k = k + 1
+         ja(k) = i
+         a(k) = 6.0
+         k = k + 1
+         if (i.lt.nrow) then
+            ja(k) = i + 1
+            a(k) = -1.0
+            k = k+1
+         end if
+ 10   continue
+      ia(nrow+1) = k
+      return
+c---------end-of-diagblk------------------------------------------------ 
+      end
+c-----------------------------------------------------------------------
+      subroutine leftblk(n, nrow, ncol, a, ja, ia)
+      implicit none
+      integer n, nrow, ncol, ja(1:*), ia(1:*)
+      real*8  a(1:*)
+c-----------------------------------------------------------------------
+c     Generate the subdiagonal block for the problem given.
+c-----------------------------------------------------------------------
+      integer i, k
+      nrow = 1 + (n-1)/2
+      ncol = n/2
+      k = 1
+      do 10 i = 1, nrow
+         ia(i) = k
+         if (nrow.ne.ncol) then
+            if (i.gt.1) then
+               ja(k) = i-1
+               a(k) = -1.0
+               k = k+1
+            end if
+         end if
+         if (i.le.ncol) then
+            ja(k) = i
+            a(k) = -1.0
+            k = k+1
+         end if
+         if (nrow.eq.ncol) then
+            if (i.lt.ncol) then
+               ja(k) = i+1
+               a(k) = -1.0
+               k = k+1
+            end if
+         end if
+ 10   continue
+      ia(nrow+1) = k
+      return
+c---------end-of-leftblk------------------------------------------------ 
+      end
+c-----------------------------------------------------------------------
+      subroutine rightblk(n, nrow, ncol, a, ja, ia)
+      implicit none
+      integer n, nrow, ncol, ja(1:*), ia(1:*)
+      real*8  a(1:*)
+      integer i, k
+      nrow = 1 + (n-1)/2
+      ncol = 1 + n/2
+      k = 1
+      do 10 i = 1, nrow
+         ia(i) = k
+         if (nrow.eq.ncol) then
+            if (i.gt.1) then
+               ja(k) = i-1
+               a(k) = -1.0
+               k = k+1
+            end if
+         end if
+         ja(k) = i
+         a(k) = -1.0
+         k = k+1
+         if (nrow.ne.ncol) then
+            ja(k) = i+1
+            a(k) = -1.0
+            k = k+1
+         end if
+ 10   continue
+      ia(nrow+1) = k
+c---------end-of-rightblk----------------------------------------------- 
+      end
diff --git a/MATGEN/MISC/zlatev.f b/MATGEN/MISC/zlatev.f
new file mode 100644
index 0000000..d20a7fd
--- /dev/null
+++ b/MATGEN/MISC/zlatev.f
@@ -0,0 +1,542 @@
+      SUBROUTINE MATRF2(M,N,C,INDEX,ALPHA,NN,NZ,A,SNR,RNR,FEJLM)
+C--------------------------------------------------------------------
+C
+C   PURPOSE
+C   -------
+C   The subroutine generates sparse (rectangular or square) matrices.
+C   The dimensions of the matrix and the average number of nonzero
+C   elements per row can be specified by the user. Moreover, the user
+C   can also change the sparsity pattern and the condition number of the
+C   matrix. The non-zero elements of the desired matrix will be
+C   accumulated (in an arbitrary order) in the first NZ positions of
+C   array A. The column and the row numbers of the non-zero element
+C   stored in A(I), I=1,...,NZ, will be found in SNR(I) and RNR(I),
+C   respectively. The matrix generated by this subroutine is of the
+C   class F(M,N,C,R,ALPHA) (see reference).
+C
+C   Note: If A is the sparse matrix of type F(M,N,C,R,ALPHA), then
+C
+C           min|A(i,j)| = 1/ALPHA,
+C
+C           max|A(i,j)| = max(INDEX*N - N,10*ALPHA).
+C
+C
+C   CONTRIBUTOR: Ernest E. Rothman
+C                Cornell Theory Center/Cornell National Supercomputer
+C                Facility.
+C                e-mail address: BITNET:   eer@cornellf
+C                                INTERNET: eer@cornellf.tn.cornell.edu
+C
+C   minor modifications by Y. Saad. April 26, 1990.
+C
+C   Note: This subroutine has been copied from the following reference.
+C         The allowable array sizes have been changed.
+C
+C   REFERENCE: Zlatev, Zahari; Schaumburg, Kjeld; Wasniewski, Jerzy;
+C      "A testing Scheme for Subroutines Solving Large Linear Problems",
+C      Computers and Chemistry, Vol. 5, No. 2-3, pp. 91-100, 1981.
+C
+C
+C   INPUT PARAMETERS
+C   ----------------
+C   M    - Integer. The number of rows in the desired matrix.
+C          N < M+1 < 9000001 must be specified.
+C
+C   N    - Integer. The number of columns in the desired matrix.
+C          21 < N < 9000001 must be specified.
+C
+C   C    - Integer. The sparsity pattern can be changed by means of this
+C          parameter.  10 < C < N-10  must be specified.
+C
+C   INDEX - Integer.  The average number of non-zero elements per row in
+C           the matrix will be equal to INDEX.
+C           1 < INDEX < N-C-8 must be specified.
+C
+C   ALPHA - Real. The condition number of the matrix can be changed
+C           BY THIS PARAMETER. ALPHA > 0.0 MUST BE SPECIFIED.
+C           If ALPHA is approximately equal to 1.0 then the generated
+C           matrix is well-conditioned. Large values of ALPHA will
+C           usually produce ill-conditioned matrices. Note that no
+C           round-off errors during the computations in this subroutine
+C           are made if ALPHA = 2**I (where I is an arbitrary integer
+C           which produces numbers in the machine range).
+C
+C   NN    - Integer. The length of arrays A, RNR, and SNR (see below).
+C           INDEX*M+109 < NN < 9000001 must be specified.
+C
+C
+C   OUTPUT PARAMETERS
+C   -----------------
+C   NZ    - Integer. The number of non-zero elements in the matrix.
+C
+C   A(NN) - Real array. The non-zero elements of the matrix generated
+C           are accumulated in the first NZ locations of array A.
+C
+C   SNR(NN) - INTEGER array. The column number of the non-zero element
+C           kept in A(I), I=1,...NZ, is stored in SNR(I).
+C
+C   RNR(NN) - Integer array. The row number of the non-zero element
+C           kept in A(I), I=1,...NZ, is stored in RNR(I).
+C
+C   FEJLM - Integer. FEJLM=0 indicates that the call is successful.
+C           Error diagnostics are given by means of positive values of
+C           this parameter as follows:
+C             FEJLM = 1    -  N       is out of range.
+C             FEJLM = 2    -  M       is out of range.
+C             FEJLM = 3    -  C       is out of range.
+C             FEJLM = 4    -  INDEX   is out of range.
+C             FEJLM = 5    -  NN      is out of range.
+C             FEJLM = 7    -  ALPHA   is out of range.
+C
+C
+C
+C
+      REAL*8 A, ALPHA, ALPHA1
+      INTEGER M, N, NZ, C, NN, FEJLM, M1, NZ1, RR1, RR2, RR3, K
+      INTEGER M2, N2
+      INTEGER SNR, RNR
+      DIMENSION A(NN), SNR(NN), RNR(NN)
+      M1 = M
+      FEJLM = 0
+      NZ1 = INDEX*M + 110
+      K = 1
+      ALPHA1 = ALPHA
+      INDEX1 = INDEX - 1
+C
+C  Check the parameters.
+C
+      IF(N.GE.22) GO TO 1
+2     FEJLM = 1
+      RETURN
+1     IF(N.GT.9000000) GO TO 2
+      IF(M.GE.N) GO TO 3
+4     FEJLM = 2
+      RETURN
+3     IF(M.GT.9000000) GO TO 4
+      IF(C.LT.11)GO TO 6
+      IF(N-C.GE.11)GO TO 5
+6     FEJLM = 3
+      RETURN
+5     IF(INDEX.LT.1) GO TO 12
+      IF(N-C-INDEX.GE.9)GO TO 13
+12    FEJLM = 4
+13    IF(NN.GE.NZ1)GO TO 7
+8     FEJLM = 5
+      RETURN
+7     IF(NN.GT.9000000)GO TO 8
+      IF(ALPHA.GT.0.0)GO TO 9
+      FEJLM = 6
+      RETURN
+9     CONTINUE
+C
+C  End of the error check. Begin to generate the non-zero elements of
+C  the required matrix.
+C
+      DO 20 I=1,N
+      A(I) = 1.0d0
+      SNR(I) = I
+20    RNR(I) = I
+      NZ = N
+      J1 = 1
+      IF(INDEX1.EQ.0) GO TO 81
+      DO 21 J = 1,INDEX1
+      J1 = -J1
+      DO 22 I=1,N
+      A(NZ+I) = dfloat(J1*J*I)
+      IF(I+C+J-1.LE.N)SNR(NZ+I) = I + C + J - 1
+      IF(I+C+J-1.GT.N)SNR(NZ+I) = C + I + J - 1 - N
+22    RNR(NZ + I) = I
+21    NZ = NZ + N
+81    RR1 = 10
+      RR2 = NZ
+      RR3 = 1
+25    CONTINUE
+      DO 26 I=1,RR1
+      A(RR2 + I) = ALPHA*dfloat(I)
+      SNR(RR2+I) = N - RR1 + I
+      RNR(RR2+I) = RR3
+26    CONTINUE
+      IF(RR1.EQ.1) GO TO 27
+      RR2 = RR2 + RR1
+      RR1 = RR1 - 1
+      RR3 = RR3 + 1
+      GO TO 25
+27    NZ = NZ + 55
+29    M1 = M1 - N
+      ALPHA = 1.0d0/ALPHA
+      IF(M1.LE.0) GO TO 28
+      N2 = K*N
+      IF(M1.GE.N)M2 = N
+      IF(M1.LT.N)M2 = M1
+      DO 30 I=1,M2
+      A(NZ+I) = ALPHA*dfloat(K+1)
+      SNR(NZ + I) = I
+30    RNR(NZ + I) = N2 + I
+      NZ = NZ + M2
+      IF(INDEX1.EQ.0) GO TO 82
+      J1 = 1
+      DO 41 J = 1,INDEX1
+      J1 = -J1
+      DO 42 I = 1,M2
+      A(NZ+I) = ALPHA*dFLOAT(J*J1)*(dfloat((K+1)*I)+1.0d0)
+      IF(I+C+J-1.LE.N)SNR(NZ+I) = I + C + J - 1
+      IF(I+C+J-1.GT.N)SNR(NZ+I) = C + I + J - 1 - N
+42    RNR(NZ + I) = N2 + I
+41    NZ = NZ +M2
+82    K = K + 1
+      GO TO 29
+28    CONTINUE
+      ALPHA = 1.0d0/ALPHA1
+      RR1 = 1
+      RR2 = NZ
+35    CONTINUE
+      DO 36 I = 1,RR1
+      A(RR2+I) = ALPHA*dfloat(RR1+1-I)
+      SNR(RR2+I) = I
+      RNR(RR2+I) = N - 10 + RR1
+36    CONTINUE
+      IF(RR1.EQ.10) GO TO 34
+      RR2 = RR2 + RR1
+      RR1 = RR1 + 1
+      GO TO 35
+34    NZ = NZ + 55
+      ALPHA = ALPHA1
+      RETURN
+      END
+      SUBROUTINE DCN(AR,IA,JA,N,NE,IC,NN,IERR)
+C-----------------------------------------------------------------------
+C
+C   PURPOSE
+C   -------
+C   The subroutine generates sparse (square) matrices of the type
+C   D(N,C).  This type of matrix has the following characteristics:
+C   1's in the diagonal, three bands at the distance C above the
+C   diagonal (and reappearing cyclicly under it), and a 10 x 10
+C   triangle of elements in the upper right-hand corner.
+C   Different software libraries require different storage schemes.
+C   This subroutine generates the matrix in the storage  by
+C   indices mode.
+C
+C
+C   Note: If A is the sparse matrix of type D(N,C), then
+C
+C       min|A(i,j)| = 1,     max|A(i,j)| = max(1000,N + 1)
+C
+C
+C
+C   CONTRIBUTOR: Ernest E. Rothman
+C                Cornell Theory Center/Cornell National Supercomputer
+C                Facility.
+C                e-mail address: BITNET:   eer@cornellf
+C                                INTERNET: eer@cornellf.tn.cornell.edu
+C
+C
+C   REFERENCE
+C   ---------
+C   1) Zlatev, Zahari; Schaumburg, Kjeld; Wasniewski, Jerzy;
+C      "A Testing Scheme for Subroutines Solving Large Linear Problems",
+C       Computers and Chemistry, Vol. 5, No. 2-3, pp. 91-100, 1981.
+C   2) Osterby, Ole and Zletev, Zahari;
+C      "Direct Methods for Sparse Matrices";
+C       Springer-Verlag 1983.
+C
+C
+C
+C   INPUT PARAMETERS
+C   ----------------
+C   N    - Integer. The size of the square matrix.
+C          N > 13 must be specified.
+C
+C   NN   - Integer. The dimension of integer arrays IA and JA and 
+C          real array AR. Must be at least NE.
+C
+C   IC   - Integer. The sparsity pattern can be changed by means of this
+C          parameter.  0 < IC < N-12  must be specified.
+C
+C
+C   OUTPUT PARAMETERS
+C   -----------------
+C   NE   - Integer. The number of nonzero elements in the sparse matrix
+C          of the type D(N,C). NE = 4*N + 55.
+C
+C   AR(NN) - Real array. (Double precision)
+C            Stored entries of a sparse matrix to be generated by this
+C            subroutine.
+C            NN is greater then or equal to, NE, the number of
+C            nonzeros including a mandatory diagonal entry for
+C            each row. Entries are stored by indices.
+C
+C   IA(NN) - Integer array.
+C            Pointers to specify rows for the stored nonzero entries
+C            in AR.
+C
+C   JA(NN) - Integer array.
+C            Pointers to specify columns for the stored nonzero entries
+C            in AR.
+C
+C   IERR   - Error parameter is returned as zero on successful
+C             execution of the subroutine.
+C             Error diagnostics are given by means of positive values
+C             of this parameter as follows:
+C             IERR = 1    -  N       is out of range.
+C             IERR = 2    -  IC      is out of range.
+C             IERR = 3    -  NN      is out of range.
+C
+C----------------------------------------------------------------------
+C
+      real*8 ar(nn)
+      integer ia(nn), ja(nn), ierr
+      ierr = 0
+c
+c
+c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+Check the input parameters:
+c
+      if(n.le.13)then
+         ierr = 1
+         return
+      endif
+      if(ic .le. 0 .or. ic .ge. n-12)then
+         ierr = 2
+         return
+      endif
+      ne = 4*n+55 
+      if(nn.lt.ne)then
+         ierr = 3
+         return
+      endif
+c
+c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+c
+c Begin to generate the nonzero elements as well as the row and column
+c pointers:
+c
+      do 20 i=1,n
+        ar(i) = 1.0d0
+        ia(i) = i
+        ja(i) = i
+20    continue
+      ilast = n
+      do 30 i=1,n-ic
+        it = ilast + i
+        ar(it) = 1.0 + dfloat(i)
+        ia(it) = i
+        ja(it) = i+ic
+30    continue
+      ilast = ilast + n-ic
+      do 40 i=1,n-ic-1
+        it = ilast + i
+        ar(it) = -dfloat(i)
+        ia(it) = i
+        ja(it) = i+ic+1
+40    continue
+      ilast = ilast + n-ic-1
+      do 50 i=1,n-ic-2
+        it = ilast + i
+        ar(it) = 16.0d0
+        ia(it) = i
+        ja(it) = i+ic+2
+50    continue
+      ilast = ilast + n-ic-2
+      icount = 0
+      do 70 j=1,10
+        do 60 i=1,11-j
+         icount = icount + 1
+         it = ilast + icount
+         ar(it) = 100.0d0 * dfloat(j)
+         ia(it) = i
+         ja(it) = n-11+i+j
+60    continue
+70    continue
+      icount = 0
+      ilast = 55 + ilast
+      do 80 i=n-ic+1,n
+        icount = icount + 1
+        it = ilast + icount
+        ar(it) = 1.0d0 + dfloat(i)
+        ia(it) = i
+        ja(it) = i-n+ic
+80    continue
+      ilast = ilast + ic
+      icount = 0
+      do 90 i=n-ic,n
+        icount = icount + 1
+        it = ilast + icount
+        ar(it) = -dfloat(i)
+        ia(it) = i
+        ja(it) = i-n+ic+1
+90    continue
+      ilast = ilast + ic + 1
+      icount = 0
+      do 100 i=n-ic-1,n
+        icount = icount + 1
+        it = ilast + icount
+        ar(it) = 16.0d0
+        ia(it) = i
+        ja(it) = i-n+ic+2
+100   continue
+c     ilast = ilast + ic + 2
+c     if(ilast.ne.4*n+55) then
+c     write(*,*)' ilast equal to ', ilast
+c     write(*,*)' ILAST, the number of nonzeros, should = ', 4*n + 55
+c     stop
+c     end if
+c
+c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+      return
+      end
+      SUBROUTINE ECN(N,IC,NE,IA,JA,AR,NN,IERR)
+C----------------------------------------------------------------------
+C
+C   PURPOSE
+C   -------
+C   The subroutine generates sparse (square) matrices of the type
+C   E(N,C).  This type of matrix has the following characteristics:
+C   Symmetric, positive-definite, N x N matrices with 4 in the diagonal
+C   and -1 in the two sidediagonal and in the two bands at the distance
+C   C from the diagonal. These matrices are similar to matrices obtained
+C   from using the five-point formula in the discretization of the
+C   elliptic PDE.
+C
+C
+C   Note: If A is the sparse matrix of type E(N,C), then
+C
+C       min|A(i,j)| = 1,     max|A(i,j)| = 4
+C
+C
+C
+C   CONTRIBUTOR: Ernest E. Rothman
+C                Cornell Theory Center/Cornell National Supercomputer
+C                Facility.
+C                e-mail address: BITNET:   eer@cornellf
+C                                INTERNET: eer@cornellf.tn.cornell.edu
+C
+C
+C   REFERENCE
+C   ---------
+C   1) Zlatev, Zahari; Schaumburg, Kjeld; Wasniewski, Jerzy;
+C      "A Testing Scheme for Subroutines Solving Large Linear Problems",
+C       Computers and Chemistry, Vol. 5, No. 2-3, pp. 91-100, 1981.
+C   2) Osterby, Ole and Zletev, Zahari;
+C      "Direct Methods for Sparse Matrices";
+C       Springer-Verlag 1983.
+C
+C
+C
+C   INPUT PARAMETERS
+C   ----------------
+C   N    - Integer. The size of the square matrix.
+C          N > 2 must be specified.
+C
+C   NN   - Integer. The dimension of integer arrays IA and JA and 
+C          real array AR. Must be at least NE.
+C
+C   NN  - Integer. The dimension of integer array JA. Must be at least
+C          NE.
+C
+C   IC   - Integer. The sparsity pattern can be changed by means of this
+C          parameter.  1 < IC < N   must be specified.
+C
+C
+C
+C   OUTPUT PARAMETERS
+C   -----------------
+C   NE   - Integer. The number of nonzero elements in the sparse matrix
+C          of the type E(N,C). NE = 5*N - 2*IC - 2 . 
+C
+C   AR(NN)  - Real array.
+C             Stored entries of the sparse matrix A.
+C             NE is the number of nonzeros including a mandatory
+C             diagonal entry for each row.
+C
+C   IA(NN)  - Integer array.(Double precision)
+C             Pointers to specify rows for the stored nonzero entries
+C             in AR.
+C
+C   JA(NN) - Integer array.
+C             Pointers to specify columns for the stored nonzero entries
+C             in AR.
+C
+C   IERR    - Error parameter is returned as zero on successful
+C             execution of the subroutine.
+C             Error diagnostics are given by means of positive values
+C             of this parameter as follows:
+C             IERR = 1    -  N       is out of range.
+C             IERR = 2    -  IC      is out of range.
+C             IERR = 3    -  NN      is out of range.
+C
+C---------------------------------------------------------------------
+C
+C
+      real*8 ar(nn)
+      integer ia(nn), ja(nn), n, ne, ierr
+      ierr = 0
+c
+c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+c
+Check the input parameters:
+c
+      if(n.le.2)then
+         ierr = 1
+         return
+      endif
+      if(ic.le.1.or.ic.ge.n)then
+         ierr = 2
+         return
+      endif
+c
+      ne = 5*n-2*ic-2 
+      if(nn.lt.ne)then
+         ierr = 3
+         return
+      endif
+c
+c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+c
+c Begin to generate the nonzero elements as well as the row and column
+c pointers:
+c
+      do 20 i=1,n
+      ar(i) = 4.0d0
+      ia(i) = i
+      ja(i) = i
+20    continue
+      ilast = n
+      do 30 i=1,n-1
+      it = ilast + i
+      ar(it) = -1.0d0
+      ia(it) = i+1
+      ja(it) = i
+30    continue
+      ilast = ilast + n - 1
+      do 40 i=1,n-1
+      it = ilast + i
+      ar(it) = -1.0d0
+      ia(it) = i
+      ja(it) = i+1
+40    continue
+      ilast = ilast + n-1
+      do 50 i=1,n-ic
+      it = ilast + i
+      ar(it) = -1.0d0
+      ia(it) = i+ic
+      ja(it) = i
+50    continue
+      ilast = ilast + n-ic
+      do 60 I=1,n-ic
+      it = ilast + i
+      ar(it) = -1.0d0
+      ia(it) = i
+      ja(it) = i+ic
+60    continue
+c      ilast = ilast + n-ic
+c      if(ilast.ne.5*n-2*ic-2) then
+c      write(*,*)' ilast equal to ', ilast
+c      write(*,*)' ILAST, the no. of nonzeros, should = ', 5*n-2*ic-2
+c      stop
+c      end if
+c
+c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+      return
+      end
+
diff --git a/MATGEN/README b/MATGEN/README
new file mode 100644
index 0000000..9e1564b
--- /dev/null
+++ b/MATGEN/README
@@ -0,0 +1,57 @@
+-------------------------------------------------------------
+		SPARSKIT MODULE MATGEN 
+-------------------------------------------------------------
+
+ The current directory MATGEN contains a few subroutines and
+ drivers for generating sparse matrices.
+
+      1) 5-pt and 7-pt matrices on rectangular regions discretizing
+           elliptic operators of the form: 
+
+         L u == delx( a delx u ) + dely ( b dely u) + delz ( c delz u ) + 
+                delx ( d u ) + dely (e u) + delz( f u ) + g u = h u
+
+         with Boundary conditions,
+		 alpha del u / del n + beta u = gamma
+	 on a rectangular 1-D, 2-D or 3-D grid using centered
+	 difference scheme or upwind scheme.
+ 
+         The functions a, b, ..., h are known through the
+         subroutines  afun, bfun, ..., hfun in the file
+         functns.f. The alpha is a constant on each side of the
+	 rectanglar domain. the beta and the gamma are defined
+	 by the functions betfun and gamfun (see functns.f for
+	 examples).
+
+      2) block version of the finite difference matrices (several degrees of
+         freedom per grid point. ) It only generates the matrix (without
+	 the right-hand-side), only Dirichlet Boundary conditions are used.
+
+      3) Finite element matrices for the convection-diffusion problem 
+
+                  - Div ( K(x,y) Grad u ) + C(x,y) Grad u = f
+                    u = 0 on boundary 
+
+	 (with Dirichlet boundary conditions). The matrix is returned 
+	 assembled in compressed sparse row format. See genfeu for 
+	 matrices in unassembled form. The user must provide the grid, 
+	 (coordinates x, y and connectivity matrix ijk) as well as some 
+	 information on the nodes (nodcode) and the material properties 
+	 (the function K(x,y) above) in the form of a subroutine xyk. 
+
+     4) Markov chain matrices arising from a random walk on a
+	trangular grid. Useful for testing nonsymmetric eigenvalue
+	codes. Has been suggested by G.W. Stewart in one of his
+	papers. Used by Y. Saad in several papers as a test problem 
+	for nonsymmetric eigenvalue methods.
+
+     5) Matrices from the paper by Z. Zlatev, K. Schaumburg, 
+        and J. Wasniewski. (``A testing scheme for subroutines solving
+        large linear problems.''  Computers and Chemistry, 5:91--100, 
+        1981.)
+
+----------------------------------------------------------------------
+     the items (1) and (2) are in directory FDIF,
+     the item (3) is in directory FEM
+     the items (4) and (5) are in directory MISC
+
diff --git a/ORDERINGS/README b/ORDERINGS/README
new file mode 100644
index 0000000..285a852
--- /dev/null
+++ b/ORDERINGS/README
@@ -0,0 +1,55 @@
+------------------------------------------------------------
+                     SPARSKIT MODULE ORDERINGS
+-------------------------------------------------------------
+
+ The current directory ORDERINGS contains a few subroutines for
+ finding some of the standard reorderings for a given matrix.
+
+levset.f -- level set based algorithms
+
+   dblstr   : doubled stripe partitioner 
+   rdis     : recursive dissection partitioner
+   dse2way  : distributed site expansion usuing sites from dblstr 
+   dse      : distributed site expansion usuing sites from rdis
+   BFS      : Breadth-First search traversal algorithm 
+   add_lvst : routine to add a level -- used by BFS 
+   stripes  : finds the level set structure
+   stripes0 : finds a trivial one-way partitioning from level-sets 
+   perphn   : finds a pseudo-peripheral node and performs a BFS from it.
+   mapper4  : routine used by dse and dse2way to do center expansion
+   get_domns: routine to find subdomaine from linked lists found by 
+              mapper4. 
+   add_lk   : routine to add entry to linked list -- used by mapper4. 
+   find_ctr : routine to locate an approximate center of a subgraph. 
+   rversp   : routine to reverse a given permutation (e.g., for RCMK)
+   maskdeg  : integer function to compute the `masked' of a node
+
+color.f  --  algorithms for independent set ordering and multicolor
+            orderings
+
+   multic  : greedy algorithm for multicoloring 
+   indset0 : greedy algorithm for independent set ordering
+   indset1 : independent set ordering using minimal degree traversal
+   indset2 : independent set ordering with local minimization 
+   indset3 : independent set ordering by vertex cover algorithm
+
+ccn.f -- code for strongly connected components
+
+    blccnx : Driver routine to reduce the structure of a  matrix 
+             to its strongly connected components.
+    cconex : Main routine to compute the strongly connected components
+             of a (block diagonal) matrix.
+    anccnx : We put in ICCNEX the vertices marked in the component MCCNEX.
+    newcnx : We put in ICCNEX the vertices marked in the component
+             MCCNEX. We modify also the vector KPW.
+    blccn1 : Parallel computation of the connected components of a
+             matrix. The parallel loop is performed only if the matrix
+             has a block diagonal structure.
+    icopy  : We copy an integer vector into anothoer.
+    compos : We calculate the composition between two permutation
+             vectors.
+    invlpw : We calculate the inverse of a permutation vector.
+    numini : We initialize a vector to the identity.
+    tbzero : We initialize to ZERO an integer vector.
+    iplusa : Given two integers IALPHA and IBETA, for an integer vector 
+             IA we calculate IA(i) = ialpha + ibeta * ia(i)
diff --git a/ORDERINGS/ccn.f b/ORDERINGS/ccn.f
new file mode 100644
index 0000000..eee5836
--- /dev/null
+++ b/ORDERINGS/ccn.f
@@ -0,0 +1,709 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c          REORDERING ROUTINES -- STRONGLY CONNECTED COMPONENTS        c 
+c----------------------------------------------------------------------c
+c     Contributed by:
+C     Laura C. Dutto - email: dutto@cerca.umontreal.ca
+c                      July 1992 - Update: March 1994
+C-----------------------------------------------------------------------
+c     CONTENTS:
+c     --------
+c     blccnx : Driver routine to reduce the structure of a  matrix 
+c              to its strongly connected components.
+c     cconex : Main routine to compute the strongly connected components
+c              of a (block diagonal) matrix.
+c     anccnx : We put in ICCNEX the vertices marked in the component MCCNEX.
+c     newcnx : We put in ICCNEX the vertices marked in the component
+c              MCCNEX. We modify also the vector KPW.
+c     blccn1 : Parallel computation of the connected components of a
+c              matrix. The parallel loop is performed only if the matrix
+c              has a block diagonal structure.
+c     ccnicopy:We copy an integer vector into anothoer.
+c     compos : We calculate the composition between two permutation
+c              vectors.
+c     invlpw : We calculate the inverse of a permutation vector.
+c     numini : We initialize a vector to the identity.
+c     tbzero : We initialize to ZERO an integer vector.
+c     iplusa : Given two integers IALPHA and IBETA, for an integer vector 
+c              IA we calculate IA(i) = ialpha + ibeta * ia(i)
+C
+c----------------------------------------------------------------------c
+      subroutine BLCCNX(n, nbloc, nblcmx, nsbloc, job, lpw, amat, ja,
+     *                  ia, iout, ier, izs, nw)
+C-----------------------------------------------------------------------
+c     
+c     This routine determines if the matrix given by the structure
+c     IA et JA is irreductible. If not, it orders the unknowns such
+c     that all the consecutive unknowns in KPW between NSBLOC(i-1)+1
+c     and NSBLOC(i) belong to the ith component of the matrix.
+c     The numerical values of the matrix are in AMAT. They are modified
+c     only if JOB = 1 and if we have more than one connected component.
+c
+c     On entry:
+c     --------
+c     n      = row and column dimension of the matrix
+c     nblcmx = maximum number of connected components allowed. The size
+c              of NSBLOC is nblcmx + 1 (in fact, it starts at 0).
+c     job    = integer indicating the work to be done:
+c              job = 1  if the permutation LPW is modified, we
+c                       permute not only the structure of the matrix
+c                       but also its numerical values.
+c              job.ne.1 if the permutation LPW is modified, we permute 
+c                       the structure of the matrix ignoring real values.
+c     iout   = impression parameter. If 0 < iout < 100, we print
+c              comments and error messages on unit IOUT.
+c     nw     = length of the work vector IZS.
+c
+c     Input / output:
+c     --------------
+c     nbloc  = number of connected components of the matrix. If the
+c              matrix is not irreductible, nbloc > 1. We allow
+c              nbloc > 1 on entry; in this case we calculate the
+c              number of connected components in each previous one.
+c     nsbloc = integer array of length NBLOC + 1 containing the pointers
+c              to the first node of each component on the old (input)
+c              and on the new (output) ordering.
+c     lpw    = integer array of length N corresponding to the
+c              permutation of the unknowns. We allow LPW to be a vector 
+c              different from the identity on input.
+c     amat   = real*8 values of the matrix given by the structure IA, JA.
+c     ja     = integer array of length NNZERO (= IA(N+1)-IA(1)) corresponding
+c              to the column indices of nonzero elements of the matrix, stored
+c              rowwise. It is modified only if the matrix has more
+c              than one connected component.
+c     ia     = integer array of length N+1 corresponding to the
+c              pointer to the beginning of each row in JA (compressed
+c              sparse row storage). It is modified only if
+c              the matrix has more than one connected component.
+c
+c     On return:
+c     ----------
+c     ier    = integer. Error message. Normal return ier = 0.
+c
+c     Work space:
+c     ----------
+c     izs    = integer vector of length NW
+c
+C-----------------------------------------------------------------------
+C     Laura C. Dutto - email: dutto@cerca.umontreal.ca
+c                      July 1992 - Update: March 1994
+C-----------------------------------------------------------------------
+      integer izs(nw), lpw(n), nsbloc(0:nblcmx), ia(n+1), ja(*)
+      real*8 amat(*)
+      logical impr
+      character*6 chsubr
+C-----------------------------------------------------------------------
+      ier    = 0
+      impr   = iout.gt.0.and.iout.le.99
+      ntb    = ia(n+1) - 1
+      mxccex = max(nblcmx,20)
+c.....The matrix AMAT is a real*8 vector
+      ireal  = 2
+c
+c.....MXPTBL: maximal number of vertices by block
+      mxptbl = 0
+      do ibloc = 1, nbloc
+         mxptbl = max( mxptbl, nsbloc(ibloc) - nsbloc(ibloc-1))
+      enddo
+c
+      long1 = nbloc * mxptbl
+      long2 = nbloc * (mxccex+1)
+c.....Dynamic allocation of memory
+      iend   = 1
+      iiend  = iend
+      ilpw   = iiend 
+      ikpw   = ilpw   + n
+      ilccnx = ikpw   + long1
+      imark  = ilccnx + long2
+      iend   = imark  + n
+      if(iend .gt. nw) go to 220
+c
+      nbloc0 = nbloc
+      chsubr = 'BLCCN1'
+c.....We determine if the matrix has more than NBLOC0 connected components.
+      call BLCCN1(n, nbloc, nblcmx, nsbloc, izs(ilpw), izs(ikpw), ia,
+     *            ja, izs(imark), mxccex, izs(ilccnx), mxptbl, iout,
+     *            ier)
+      if(ier.ne.0) go to 210
+c
+      if(nbloc .gt. nbloc0) then
+c..........The matrix has more than NBLOC0 conneted components. So, we
+c..........modify the vectors IA and JA to take account of the new permutation.
+           nfree = iend - ikpw
+           call tbzero(izs(ikpw), nfree)
+           iiat  = ikpw
+           ijat  = iiat + n + 1
+           iamat = ijat + ntb
+           iend  = iamat
+           if(job .eq. 1) iend = iamat + ireal * ntb
+           if(iend .gt. nw) go to 220
+c
+c..........We copy IA and JA on IAT and JAT respectively
+           call ccnicopy(n+1, ia, izs(iiat))
+           call ccnicopy(ntb, ja, izs(ijat))
+           if(job .eq. 1) call dcopy(ntb, amat, 1, izs(iamat), 1)
+           call dperm(n, izs(iamat), izs(ijat), izs(iiat), amat,
+     *                ja, ia, izs(ilpw), izs(ilpw), job)
+           ipos = 1
+c..........We sort columns inside JA.
+           call csrcsc(n, job, ipos, amat, ja, ia, izs(iamat),
+     *                 izs(ijat), izs(iiat))
+           call csrcsc(n, job, ipos, izs(iamat), izs(ijat), izs(iiat),
+     *                 amat, ja, ia)
+      endif
+c.....We modify the ordering of unknowns in LPW
+      call compos(n, lpw, izs(ilpw))
+c
+ 120  nfree = iend - iiend
+      call tbzero(izs(iiend), nfree)
+      iend = iiend
+      return
+c
+ 210  IF(IMPR) WRITE(IOUT,310) chsubr,ier
+      go to 120
+ 220  IF(IMPR) WRITE(IOUT,320) nw, iend
+      if(ier.eq.0) ier = -1
+      go to 120
+c
+ 310  FORMAT(' ***BLCCNX*** ERROR IN ',a6,'. IER = ',i8)
+ 320  FORMAT(' ***BLCCNX*** THERE IS NOT ENOUGH MEMORY IN THE WORK',
+     1       ' VECTOR.'/13X,' ALLOWED MEMORY = ',I10,'  - NEEDED',
+     2       ' MEMORY = ',I10)
+      end 
+c **********************************************************************
+      subroutine CCONEX(n, icol0, mxccnx, lccnex, kpw, ia, ja, mark,
+     *                  iout, ier)
+C-----------------------------------------------------------------------
+c
+c     This routine determines if the matrix given by the structure
+c     IA and JA is irreductible. If not, it orders the unknowns such
+c     that all the consecutive unknowns in KPW between LCCNEX(i-1)+1
+c     and LCCNEX(i) belong to the ith component of the matrix.
+c     The structure of the matrix could be nonsymmetric.
+c     The diagonal vertices (if any) will belong to the last connected
+c     component (convention).
+c
+c     On entry:
+c     --------
+c     n      = row and column dimension of the matrix
+c     icol0  = the columns of the matrix are between ICOL0+1 and ICOL0+N
+c     iout   = impression parameter. If 0 < IOUT < 100, we print
+c              comments and error messages on unit IOUT.
+c     ia     = integer array of length N+1 corresponding to the
+c              pointer to the beginning of each row in JA (compressed
+c              sparse row storage).
+c     ja     = integer array of length NNZERO (= IA(N+1)-IA(1))
+c              corresponding to the column indices of nonzero elements
+c              of the matrix, stored rowwise.
+c
+c     Input/Output:
+c     ------------
+c     mxccnx = maximum number of connected components allowed on input,
+c              and number of connected components of the matrix, on output.
+c
+c     On return:
+c     ----------
+c     lccnex = integer array of length MXCCNX + 1 containing the pointers
+c              to the first node of each component, in the vector KPW.
+c     kpw    = integer array of length N corresponding to the
+c              inverse of permutation vector.
+c     ier    = integer. Error message. Normal return ier = 0.
+c
+c     Work space:
+c     ----------
+c     mark   = integer vector of length N
+c
+C-----------------------------------------------------------------------
+C     Laura C. Dutto - email: dutto@cerca.umontreal.ca
+c                      July 1992 - Update: March 1994
+C-----------------------------------------------------------------------
+      dimension ia(n+1), lccnex(0:mxccnx), kpw(n), ja(*), mark(n)
+      logical impr
+C-----------------------------------------------------------------------
+      ier    = 0
+      ipos = ia(1) - 1 
+      impr   = iout.gt.0.and.iout.le.99
+c
+      nccnex = 0
+c.....We initialize MARK to zero. At the end of the algorithm, it would
+c.....indicate the number of connected component associated with the vertex.
+c.....The number (-1) indicates that the row associated with this vertex
+c.....is a diagonal row. This value could be modified because we accept
+c.....a non symmetric matrix. All the diagonal vertices will be put in
+c.....the same connected component.
+      call tbzero(mark, n)
+c
+ 5    do i = 1,n
+         if(mark(i) .eq. 0) then
+              ideb = i
+              go to 15
+         endif
+      enddo
+      go to 35
+c
+ 15   if( ia(ideb+1) - ia(ideb) .eq. 1) then
+c..........The row is a diagonal row.
+           mark(ideb) = -1
+           go to 5
+      endif
+      iccnex = nccnex + 1
+      if(iccnex .gt. mxccnx) go to 220
+      index  = 0
+      newind = 0
+      jref   = 0
+      mark(ideb) = iccnex
+      index  = index + 1
+      kpw(index) = ideb
+c
+ 20   jref = jref + 1
+      ideb = kpw(jref)
+
+      do 30 ir = ia(ideb)-ipos, ia(ideb+1)-ipos-1
+         j = ja(ir) - icol0
+         mccnex = mark(j)
+         if(mccnex .le. 0) then
+              index = index + 1
+              kpw(index) = j
+              mark(j) = iccnex
+         else if( mccnex .eq. iccnex) then
+              go to 30
+         else if( mccnex .gt. iccnex) then
+c.............We realize that the connected component MCCNX is,
+c.............in fact, included in this one. We modify MARK and KPW.
+              call NEWCNX(n, mccnex, iccnex, index, kpw, mark)
+              if(mccnex .eq. nccnex) nccnex = nccnex - 1
+         else
+c.............We realize that the previously marked vertices belong,
+c.............in fact, to the connected component ICCNX. We modify MARK.
+              call ANCCNX(n, iccnex, mccnex, mark, nwindx)
+              iccnex = mccnex
+              newind = newind + nwindx
+         endif
+ 30   continue
+      if(jref .lt. index) go to 20
+c
+c.....We have finished with this connected component.
+      index = index + newind
+      if(iccnex .eq. nccnex+1) nccnex = nccnex + 1
+      go to 5
+c.......................................................................
+c
+c     We have partitioned the graph in its connected components!
+c
+c.......................................................................
+ 35   continue
+c
+c.....All the vertices have been already marked. Before modifying KPW
+c.....(if necessary), we put the diagonal vertex (if any) in the last
+c.....connected component.
+      call tbzero(lccnex(1), nccnex)
+c
+      idiag = 0
+      do i = 1, n
+         iccnex = mark(i)
+         if(iccnex .eq. -1) then
+              idiag = idiag + 1
+              if(idiag .eq. 1) then
+                   nccnex = nccnex + 1
+                   if(nccnex .gt. mxccnx) go to 220
+                   if(impr) write(iout,340)
+              endif
+              mark(i) = nccnex
+         else
+              lccnex(iccnex) = lccnex(iccnex) + 1
+         endif
+      enddo
+      if(idiag .ge. 1) lccnex(nccnex) = idiag
+c
+      if(nccnex .eq. 1) then
+         lccnex(nccnex) = n
+         go to 40
+      endif
+c
+      iccnex = 1
+ 8    if(iccnex .gt. nccnex) go to 12
+      if(lccnex(iccnex) .le. 0) then
+           do i = 1, n
+              if(mark(i) .ge. iccnex) mark(i) = mark(i) - 1
+           enddo
+           nccnex = nccnex - 1
+           do mccnex = iccnex, nccnex
+              lccnex(mccnex) = lccnex(mccnex + 1)
+           enddo
+      else
+           iccnex = iccnex + 1
+      endif
+      go to 8
+c
+ 12   index = 0
+      do iccnex = 1, nccnex
+         noeicc = lccnex(iccnex)
+         lccnex(iccnex) = index
+         index  = index + noeicc
+      enddo
+      if(index .ne. n) go to 210
+c
+c.....We define correctly KPW
+      do i = 1,n
+         iccnex = mark(i)
+         index = lccnex(iccnex) + 1
+         kpw(index) = i
+         lccnex(iccnex) = index
+      enddo
+c
+ 40   mxccnx = nccnex
+      lccnex(0) = nccnex
+      if(nccnex .eq. 1) call numini(n, kpw)
+      return
+c
+ 210  if(impr) write(iout,310) index,n
+      go to 235
+ 220  if(impr) write(iout,320) nccnex, mxccnx
+      go to 235
+ 235  ier = -1
+      return
+c
+ 310  format(' ***CCONEX*** ERROR TRYING TO DETERMINE THE NUMBER',
+     *       ' OF CONNECTED COMPONENTS.'/13X,' NUMBER OF MARKED',
+     *       ' VERTICES =',i7,3x,'TOTAL NUMBER OF VERTICES =',I7)
+ 320  format(' ***CCONEX*** THE ALLOWED NUMBER OF CONNECTED COMPONENTS',
+     *       ' IS NOT ENOUGH.'/13X,' NECESSARY NUMBER = ',I4,
+     *       5x,' ALLOWED NUMBER = ',I4)
+ 323  format(' ***CCONEX*** ERROR IN ',A6,'. IER = ',I8)
+ 340  format(/' ***CCONEX*** THE LAST CONNECTED COMPONENT WILL',
+     *       ' HAVE THE DIAGONAL VERTICES.')
+      end
+c **********************************************************************
+      subroutine ANCCNX(n, mccnex, iccnex, mark, ncount)
+C-----------------------------------------------------------------------
+c     
+c     We put in ICCNEX the vertices marked in the component MCCNEX.
+C
+C-----------------------------------------------------------------------
+c     include "NSIMPLIC"
+      dimension mark(n)
+C-----------------------------------------------------------------------
+C     Laura C. Dutto - email: dutto@cerca.umontreal.ca - December 1993
+C-----------------------------------------------------------------------
+      ncount = 0
+      do i = 1, n
+         if( mark(i) .eq. mccnex) then
+              mark(i) = iccnex
+              ncount  = ncount + 1
+         endif
+      enddo
+c
+      return
+      end
+c **********************************************************************
+      subroutine NEWCNX(n, mccnex, iccnex, index, kpw, mark)
+C-----------------------------------------------------------------------
+c     
+c     We put in ICCNEX the vertices marked in the component MCCNEX. We
+c     modify also the vector KPW.
+C
+C-----------------------------------------------------------------------
+c     include "NSIMPLIC"
+      dimension kpw(*), mark(n)
+C-----------------------------------------------------------------------
+C     Laura C. Dutto - email: dutto@cerca.umontreal.ca - December 1993
+C-----------------------------------------------------------------------
+      do i = 1, n
+         if( mark(i) .eq. mccnex) then
+              mark(i) = iccnex
+              index = index + 1
+              kpw(index) = i
+         endif
+      enddo
+c
+      return
+      end
+c **********************************************************************
+      subroutine BLCCN1(n, nbloc, nblcmx, nsbloc, lpw, kpw, ia, ja,
+     *                  mark, mxccex, lccnex, mxptbl, iout, ier)
+C-----------------------------------------------------------------------
+c     
+c     This routine determines if the matrix given by the structure
+c     IA et JA is irreductible. If not, it orders the unknowns such
+c     that all the consecutive unknowns in KPW between NSBLOC(i-1)+1
+c     and NSBLOC(i) belong to the ith component of the matrix.
+c
+c     On entry:
+c     --------
+c     n      = row and column dimension of the matrix
+c     nblcmx = The size of NSBLOC is nblcmx + 1 (in fact, it starts at 0).
+c     ia     = integer array of length N+1 corresponding to the
+c              pointer to the beginning of each row in JA (compressed
+c              sparse row storage).
+c     ja     = integer array of length NNZERO (= IA(N+1)-IA(1)) corresponding
+c              to the column indices of nonzero elements of the matrix,
+c              stored rowwise.
+c     mxccex = maximum number of connected components allowed by block.
+c     mxptbl = maximum number of points (or unknowns) in each connected
+c              component (mxptbl .le. n).
+c     iout   = impression parameter. If 0 < iout < 100, we print
+c              comments and error messages on unit IOUT.
+c
+c     Input/Output:
+c     ------------
+c     nbloc  = number of connected components of the matrix. If the
+c              matrix is not irreductible, nbloc > 1. We allow
+c              nbloc > 1 on entry; in this case we calculate the
+c              number of connected components in each previous one.
+c     nsbloc = integer array of length NBLOC + 1 containing the pointers
+c              to the first node of each component on the new ordering.
+c              Normally, on entry you put: NBLOC = 1, NSBLOC(0) = 0,
+c              NSBLOC(NBLOC) = N.
+c
+c     On return:
+c     ----------
+c     lpw    = integer array of length N corresponding to the
+c              permutation vector (the row i goes to lpw(i)).
+c     ier    = integer. Error message. Normal return ier = 0.
+c
+c     Work space:
+c     ----------
+c     kpw    = integer vector of length MXPTBL*NBLOC necessary for parallel
+c              computation.
+c     mark   = integer vector of length N
+c     lccnex = integer vector of length (MXCCEX+1)*NBLOC necessary for parallel
+c              computation.
+c
+C-----------------------------------------------------------------------
+C     Laura C. Dutto - e-mail: dutto@cerca.umontreal.ca
+c                      Juillet 1992. Update: March 1994
+C-----------------------------------------------------------------------
+      dimension lpw(n), kpw(mxptbl*nbloc), ia(n+1), ja(*),
+     *          lccnex((mxccex+1)*nbloc), nsbloc(0:nbloc), mark(n)
+      logical impr
+      character chsubr*6
+C-----------------------------------------------------------------------
+      ier  = 0
+      impr = iout.gt.0.and.iout.le.99
+      isor = 0
+c
+      chsubr = 'CCONEX'
+      newblc = 0
+C$DOACROSS if(nbloc.gt.1), LOCAL(ibloc, ik0, ik1, ins0, ntb0,
+C$&   nccnex, ilccnx, info, kpibl), REDUCTION(ier, newblc)
+      do 100 ibloc = 1,nbloc
+         ik0 = nsbloc(ibloc - 1)
+         ik1 = nsbloc(ibloc)
+         ntb0 = ia(ik0+1)
+         if(ia(ik1+1) - ntb0 .le. 1) go to 100
+         ntb0 = ntb0 - 1
+         ins0 = ik1 - ik0
+c........We need more memory place for KPW1 because of parallel computation
+         kpibl = (ibloc-1) * mxptbl
+         call numini( ins0, kpw(kpibl+1))
+         nccnex = mxccex
+         ilccnx = (mxccex+1) * (ibloc-1) + 1
+c.......................................................................
+c
+c        Call to the main routine: CCONEX
+c
+c.......................................................................
+         call cconex(ins0, ik0, nccnex, lccnex(ilccnx), kpw(kpibl+1), 
+     *               ia(ik0+1), ja(ntb0+1), mark(ik0+1), isor, info)
+         ier = ier + info
+         if(info .ne. 0 .or. nccnex .lt. 1) go to 100
+c
+c........We add the new connected components on NEWBLC
+         newblc = newblc + nccnex
+c........We define LPW different from the identity only if there are more 
+c........than one connected component in this block
+         if(nccnex .eq. 1) then
+              call numini(ins0, lpw(ik0+1))
+         else
+              call invlpw(ins0, kpw(kpibl+1), lpw(ik0+1))
+         endif
+         call iplusa(ins0, ik0, 1, lpw(ik0+1))
+ 100  continue
+c
+      if(ier .ne. 0) go to 218
+      if(newblc .eq. nbloc) go to 120
+      if(newblc .gt. nblcmx) go to 230
+c
+c.....We modify the number of blocks to indicate the number of connected 
+c.....components in the matrix.
+      newblc = 0
+      nsfin = 0
+CDIR$ NEXT SCALAR
+      do ibloc = 1, nbloc
+         ilccnx = (mxccex+1) * (ibloc-1) + 1
+         nccnex = lccnex(ilccnx)
+         if(nccnex .gt. 1 .and. impr) write(iout,420) ibloc,nccnex
+         lcc0 = 0
+CDIR$ NEXT SCALAR
+         do icc = 1,nccnex
+            newblc = newblc + 1
+            nsb = lccnex(ilccnx+icc)
+c...........Be careful! In LCCNEX we have the cumulated number of vertices 
+            nsbloc(newblc) = nsfin + nsb
+            if(nccnex .gt. 1 .and. impr) write(iout,425) icc,nsb-lcc0
+            lcc0 = nsb
+         enddo
+         nsfin = nsfin + nsb
+      enddo
+      nbloc = newblc
+c
+ 120  return
+c
+ 218  if(impr) write(iout,318) chsubr,ier
+      go to 120
+ 230  if(impr) write(iout,330) newblc,nblcmx
+      if(ier.eq.0) ier = -1
+      go to 120
+c
+ 318  format(' ***BLCCN1*** ERROR IN ',a6,'. IER = ',i8)
+ 330  format(' ***BLCCN1*** THE MEMORY SPACE ALLOWED FOR NSBLOC IS',
+     *       ' NOT ENOUGH.'/13X,' NUMBER (NECESSARY) OF CONNECTED',
+     *       ' COMPONENTS = ',I5/13X,' MAXIMAL NUMBER OF BLOCKS',14x,
+     *       '= ',i5)
+ 420  FORMAT(' *** The block ',i3,' has ',i3,' strongly connected',
+     *       ' components. The number of vertices by component is:')
+ 425  format(5x,'Component No.',i3,' - Number of vertices = ',i6)
+      end
+C***********************************************************************
+      SUBROUTINE CCNICOPY(N,IX,IY)
+C.......................................................................
+C     We copy the vector IX on the vector IY
+C.......................................................................
+      DIMENSION IX(n),IY(n)
+C.......................................................................
+      IF(N.LE.0) RETURN
+C$DOACROSS if(n .gt. 250), local(i)
+      DO 10 I = 1,N
+         IY(I) = IX(I)
+   10 CONTINUE
+C
+      RETURN
+      END
+c***********************************************************************
+      SUBROUTINE COMPOS(n, lpw0, lpw1)
+C-----------------------------------------------------------------------
+c
+c     We take account of the original order of unknowns. We put the
+c     final result on LPW0.
+c
+C-----------------------------------------------------------------------
+      DIMENSION lpw0(n), lpw1(n)
+C-----------------------------------------------------------------------
+c     Laura C. Dutto - Mars 1994
+C-----------------------------------------------------------------------
+C$DOACROSS if(n .gt. 250), local(i0)
+      do i0 = 1, n
+         lpw0(i0) = lpw1(lpw0(i0))
+      enddo
+c
+      return
+      end
+C **********************************************************************
+      SUBROUTINE INVLPW(n, lpw, kpw)
+c.......................................................................
+c 
+c     KPW is the inverse of LPW
+c
+c.......................................................................
+      dimension lpw(n), kpw(n)
+c.......................................................................
+c     Laura C. Dutto - Novembre 1993
+c.......................................................................
+C$DOACROSS if(n .gt. 200), local(i0, i1)
+      do i0 = 1, n
+         i1 = lpw(i0)
+         kpw(i1) = i0
+      enddo
+c
+      return
+      end
+C **********************************************************************
+      subroutine NUMINI(n, lpw)
+c.......................................................................
+      dimension lpw(n)
+c.......................................................................
+c
+c     The vector LPW is initialized as the identity.
+c
+c.......................................................................
+c     Laura C. Dutto - Novembre 1993
+c.......................................................................
+C$DOACROSS if(n .gt. 250), local(i)
+      do i=1,n
+         lpw(i) = i
+      enddo
+c
+      return
+      end
+C***********************************************************************
+      SUBROUTINE TBZERO(M,NMOT)
+C.......................................................................
+C     We initialize to ZERO an integer vector of length NMOT.
+C.......................................................................
+      DIMENSION M(NMOT)
+C.......................................................................
+      IF(NMOT.le.0) return
+C$DOACROSS if(nmot.gt.500), LOCAL(i)
+      DO 1 I=1,NMOT
+           M(I)=0
+ 1         CONTINUE
+      RETURN
+      END
+C **********************************************************************
+      SUBROUTINE IPLUSA (n, nalpha, nbeta, ia)
+c.......................................................................
+C
+c     We add NALPHA to each element of NBETA * IA:
+c
+c            ia(i) = nalpha + nbeta * ia(i)
+c
+c.......................................................................
+      integer ia(n)
+c.......................................................................
+c     Laura C. Dutto - February 1994
+c.......................................................................
+      if(n .le. 0) return
+c
+      nmax = 500
+      if(nalpha .eq. 0) then
+           if(nbeta .eq. 1) return
+           if(nbeta .eq. -1) then
+C$DOACROSS if(n .gt. nmax), local (i)
+                do i = 1, n
+                   ia(i) = - ia(i)
+                enddo
+           else
+C$DOACROSS if(n .gt. nmax/2), local (i)
+                do i = 1, n
+                   ia(i) = nbeta * ia(i)
+                enddo
+           endif
+           return
+      endif
+      if(nbeta .eq. 0) then
+C$DOACROSS if(n .gt. nmax), local (i)
+           do i = 1, n
+              ia(i) = nalpha
+           enddo
+           return
+      endif
+      if(nbeta .eq. -1) then
+C$DOACROSS if(n .gt. nmax/2), local (i)
+           do i = 1, n
+              ia(i) = nalpha - ia(i)
+           enddo
+      else if(nbeta .eq. 1) then
+C$DOACROSS if(n .gt. nmax/2), local (i)
+           do i = 1, n
+              ia(i) = nalpha + ia(i)
+           enddo
+      else
+C$DOACROSS if(n .gt. nmax/3), local (i)
+           do i = 1, n
+              ia(i) = nalpha + nbeta * ia(i)
+           enddo
+      endif
+c
+      return
+      end
diff --git a/ORDERINGS/color.f b/ORDERINGS/color.f
new file mode 100644
index 0000000..dcc5216
--- /dev/null
+++ b/ORDERINGS/color.f
@@ -0,0 +1,917 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c          REORDERING ROUTINES -- COLORING BASED ROUTINES              c 
+c----------------------------------------------------------------------c
+c contents:                                                            c
+c----------                                                            c
+c multic  : greedy algorithm for multicoloring                         c
+c indset0 : greedy algorithm for independent set ordering              c
+c indset1 : independent set ordering using minimal degree traversal    c
+c indset2 : independent set ordering with local minimization           c
+c indset3 : independent set ordering by vertex cover algorithm         c
+c HeapSort, FixHeap, HeapInsert, interchange, MoveBack, FiHeapM,       c
+c           FixHeapM, HeapInsertM,indsetr,rndperm, are utility         c
+c           routines for sorting, generating random permutations, etc. c
+c----------------------------------------------------------------------c
+      subroutine multic (n,ja,ia,ncol,kolrs,il,iord,maxcol,ierr) 
+      integer n, ja(*),ia(n+1),kolrs(n),iord(n),il(maxcol+1),ierr 
+c-----------------------------------------------------------------------
+c     multicoloring ordering -- greedy algorithm -- 
+c     determines the coloring permutation and sets up
+c     corresponding data structures for it.
+c-----------------------------------------------------------------------
+c on entry
+c -------- 
+c n     = row and column dimention of matrix
+c ja    = column indices of nonzero elements of matrix, stored rowwise.
+c ia    = pointer to beginning of each row in ja.
+c maxcol= maximum number of colors allowed -- the size of il is
+c         maxcol+1 at least. Note: the number of colors does not
+c         exceed the maximum degree of each node +1.
+c iord  = en entry iord gives the order of traversal of the nodes
+c         in the multicoloring algorithm. If there is no preference 
+c         then set iord(j)=j for j=1,...,n
+c
+c on return
+c --------- 
+c ncol  = number of colours found 
+c kolrs = integer array containing the color number assigned to each node 
+c il    = integer array containing the pointers to the
+c         beginning of each color set. In the permuted matrix
+c         the rows /columns il(kol) to il(kol+1)-1 have the same color.
+c iord  = permutation array corresponding to the multicolor ordering.
+c         row number i will become row nbumber iord(i) in permuted 
+c         matrix. (iord = destination permutation array).
+c ierr  = integer. Error message. normal return ierr = 0. If ierr .eq.1
+c         then the array il was overfilled. 
+c 
+c-----------------------------------------------------------------------
+c     
+      integer kol, i, j, k, maxcol, mycol 
+c     
+      ierr = 0
+      do 1 j=1, n
+         kolrs(j) = 0
+ 1    continue 
+      do 11 j=1, maxcol
+         il(j) = 0
+ 11   continue
+c     
+      ncol = 0
+c     
+c     scan all nodes 
+c     
+      do 4 ii=1, n
+         i = iord(ii) 
+c     
+c     look at adjacent nodes to determine colors already assigned
+c     
+         mcol = 0
+         do 2 k=ia(i), ia(i+1)-1
+            j = ja(k)
+            icol = kolrs(j)
+            if (icol .ne. 0) then
+               mcol = max(mcol,icol) 
+c     
+c     il used as temporary to record already assigned colors.
+c     
+               il(icol) = 1 
+            endif
+ 2       continue
+c     
+c     taken colors determined. scan il until a slot opens up.
+c     
+         mycol = 1
+ 3       if (il(mycol) .eq. 1) then
+            mycol = mycol+1 
+            if (mycol .gt. maxcol) goto 99
+            if (mycol .le. mcol) goto 3
+         endif
+c     
+c     reset il to zero for next nodes
+c     
+         do 35 j=1, mcol
+            il(j) = 0
+ 35      continue
+c     
+c     assign color and update number of colors so far
+c     
+         kolrs(i) = mycol
+         ncol = max(ncol,mycol)
+ 4    continue
+c     
+c     every node has now been colored. Count nodes of each color
+c     
+      do 6 j=1, n
+         kol = kolrs(j)+1
+         il(kol) = il(kol)+1
+ 6    continue
+c     
+c     set pointers il
+c     
+      il(1) = 1
+      do 7 j=1, ncol
+         il(j+1) = il(j)+il(j+1)
+ 7    continue
+c     
+c     set iord
+c     
+      do 8 j=1, n
+         kol = kolrs(j) 
+         iord(j) = il(kol)
+         il(kol) = il(kol)+1
+ 8    continue
+c     
+c     shift il back 
+c     
+      do 9 j=ncol,1,-1
+         il(j+1) = il(j)
+ 9    continue
+      il(1) = 1
+c     
+      return
+ 99   ierr = 1
+      return
+c----end-of-multic------------------------------------------------------
+c-----------------------------------------------------------------------
+      end
+c-----------------------------------------------------------------------
+
+      subroutine indset0 (n,ja,ia,nset,iord,riord,sym,iptr) 
+      integer n, nset, ja(*),ia(*),riord(*),iord(*) 
+      logical sym
+c---------------------------------------------------------------------- 
+c greedy algorithm for independent set ordering
+c----------------------------------------------------------------------
+c parameters:
+c ----------
+c n      = row dimension of matrix
+c ja, ia = matrix pattern in CRS format
+c nset   = (output) number of elements in the independent set
+c iord   = permutation array corresponding to the independent set 
+c          ordering. Row number i will become row number iord(i) in 
+c          permuted matrix.
+c riord  = reverse permutation array. Row number i in the permutated 
+c          matrix is row number riord(i) in original matrix. 
+c----------------------------------------------------------------------
+c notes: works for CSR, MSR, and CSC formats but assumes that the
+c matrix has a symmetric structure. 
+c---------------------------------------------------------------------- 
+c local variables
+c 
+      integer j, k1, k2, nod, k, mat
+      do 1 j=1, n
+         iord(j) = 0
+ 1    continue
+      nummat = 1
+      if (.not. sym) nummat = 2
+c     
+c     iord used as a marker
+c     
+      nset = 0
+      do 12  nod=1, n
+         if (iord(nod) .ne. 0) goto 12 
+         nset = nset+1
+         iord(nod) = 1
+c     
+c     visit all neighbors of current nod 
+c     
+         ipos = 0
+         do 45 mat=1, nummat
+            do 4 k=ia(ipos+nod), ia(ipos+nod+1)-1 
+               j = ja(k)
+               if (j .ne. nod) iord(j) = 2
+ 4          continue
+            ipos = iptr-1
+ 45      continue
+ 12   continue
+c     
+c     get permutation
+c     
+      k1 = 0 
+      k2 = nset 
+      do 6 j=1,n
+         if (iord(j) .eq. 1) then
+            k1 = k1+1
+            k = k1
+         else
+            k2 = k2+1
+            k = k2 
+         endif
+         riord(k) = j         
+         iord(j) = k
+ 6    continue
+      return
+c---------------------------------------------------------------------- 
+      end
+c----------------------------------------------------------------------
+      subroutine indset1 (n,ja,ia,nset,iord,riord,iw,sym,iptr) 
+      integer n, nset, iptr, ja(*),ia(*),riord(*),iord(*),iw(*)
+      logical sym
+c---------------------------------------------------------------------- 
+c greedy algorithm for independent set ordering -- with intial 
+c order of traversal given by that of min degree. 
+c----------------------------------------------------------------------
+c parameters:
+c ----------
+c n      = row dimension of matrix
+c ja, ia = matrix pattern in CRS format
+c nset   = (output) number of elements in the independent set
+c iord   = permutation array corresponding to the independent set 
+c          ordering. Row number i will become row number iord(i) in 
+c          permuted matrix.
+c riord  = reverse permutation array. Row number i in the permutated 
+c          matrix is row number riord(i) in original matrix. 
+c----------------------------------------------------------------------
+c notes: works for CSR, MSR, and CSC formats but assumes that the
+c matrix has a symmetric structure. 
+c---------------------------------------------------------------------- 
+c local variables
+      integer j,k1,k2,nummat,nod,k,ipos 
+c
+c     nummat is the number of matrices to loop through (A in symmetric
+c     pattern case (nummat=1) or A,and transp(A) otherwise (mummat=2) 
+c
+      if (sym) then
+         nummat = 1
+      else
+         nummat = 2
+      endif
+      iptrm1 = iptr-1
+c     
+c     initialize arrays
+c
+      do 1 j=1,n
+         iord(j) = j 
+         riord(j) = j 
+         iw(j) = 0 
+ 1    continue
+c     
+c     initialize degrees of all nodes
+c     
+      ipos = 0
+      do 100 imat =1,nummat
+         do 15 j=1,n
+            iw(j) = iw(j) + ia(ipos+j+1)-ia(ipos+j) 
+ 15      continue
+         ipos = iptrm1
+ 100  continue 
+c     
+c     call heapsort -- sorts nodes in increasing degree. 
+c     
+      call HeapSort (iw,iord,riord,n,n) 
+c     
+c     weights no longer needed -- use iw to store order of traversal.
+c     
+      do 16 j=1, n
+         iw(n-j+1) = iord(j)
+         iord(j) = 0
+ 16   continue
+c     
+c     iord used as a marker
+c     
+      nset = 0
+      do 12  ii = 1, n
+         nod = iw(ii) 
+         if (iord(nod) .ne. 0) goto 12 
+         nset = nset+1
+         iord(nod) = 1
+c     
+c     visit all neighbors of current nod 
+c     
+         ipos = 0
+         do 45 mat=1, nummat
+            do 4 k=ia(ipos+nod), ia(ipos+nod+1)-1 
+               j = ja(k)
+               if (j .ne. nod) iord(j) = 2
+ 4          continue
+            ipos = iptrm1 
+ 45      continue
+ 12   continue
+c     
+c     get permutation
+c     
+      k1 = 0 
+      k2 = nset 
+      do 6 j=1,n
+         if (iord(j) .eq. 1) then
+            k1 = k1+1
+            k = k1
+         else
+            k2 = k2+1
+            k = k2 
+         endif
+         riord(k) = j         
+         iord(j) = k
+ 6    continue
+      return
+c----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------
+      subroutine indset2(n,ja,ia,nset,iord,riord,iw,sym,iptr) 
+      integer n,nset,iptr,ja(*),ia(*),riord(n),iord(n),iw(n) 
+      logical sym 
+c---------------------------------------------------------------------- 
+c greedy algorithm for independent set ordering -- local minimization
+c using heap strategy -- 
+c----------------------------------------------------------------------
+c This version for BOTH unsymmetric and symmetric patterns
+c----------------------------------------------------------------------
+c on entry
+c -------- 
+c n     = row and column dimension of matrix
+c ja    = column indices of nonzero elements of matrix,stored rowwise.
+c ia    = pointer to beginning of each row in ja.
+c sym   = logical indicating whether the matrix has a symmetric pattern.
+c         If not the transpose must also be provided -- appended to the
+c         ja, ia structure -- see description of iptr next.
+c iptr  = in case the matrix has an unsymmetric pattern,the transpose
+c         is assumed to be stored in the same arrays ia,ja. iptr is the
+c         location in ia of the pointer to the first row of transp(A).
+c         more generally, ia(iptr),...,ia(iptr+n) are the pointers to 
+c         the beginnings of rows 1, 2, ...., n+1 (row n+1 is fictitious)
+c         of the transpose of A in the array ja. For example,when using 
+c         the msr format,one can write:
+c          iptr = ja(n+1)
+c          ipos = iptr+n+2                ! get the transpose of A:
+c          call csrcsc (n,0,ipos,a,ja,ja,a,ja,ja(iptr))    ! and then:
+c          call indset(n,ja,ja,nset,iord,riord,iwk,.false.,iptr) 
+c
+c iw    = work space of length n.
+c
+c on return: 
+c---------- 
+c nset  = integer. The number of unknowns in the independent set. 
+c iord  = permutation array corresponding to the new ordering. The 
+c         first nset unknowns correspond to the independent set.
+c riord = reverse permutation array.  
+c----------------------------------------------------------------------
+c local variables --
+c 
+      integer j,k1,k2,nummat,nod,k,ipos,i,last,lastlast,jold,jnew,
+     *     jo,jn 
+c
+c     nummat is the number of matrices to loop through (A in symmetric
+c     pattern case (nummat=1) or A,and transp(A) otherwise (mummat=2) 
+c
+      if (sym) then
+         nummat = 1
+      else
+         nummat = 2
+      endif
+      iptrm1 = iptr-1
+c
+c     initialize arrays
+c
+      do 1 j=1,n
+         iord(j) = j
+         riord(j) = j
+         iw(j) = 0 
+ 1    continue
+c
+c     initialize degrees of all nodes
+c
+      ipos = 0
+      do 100 imat =1,nummat
+         do 15 j=1,n
+            iw(j) = iw(j) + ia(ipos+j+1)-ia(ipos+j) 
+ 15      continue
+ 100     ipos = iptrm1
+c     
+c start by constructing a heap
+c 
+      do 2 i=n/2,1,-1 
+         j = i
+         call FixHeap (iw,iord,riord,j,j,n) 
+ 2    continue
+c     
+c main loop -- remove nodes one by one. 
+c 
+      last = n
+      nset = 0
+ 3    continue
+      lastlast = last
+      nod = iord(1) 
+c     
+c     move first element to end
+c 
+      call moveback (iw,iord,riord,last) 
+      last = last -1 
+      nset = nset + 1 
+c
+c     scan all neighbors of accepted node -- move them to back -- 
+c     
+      ipos = 0
+      do 101 imat =1,nummat      
+         do 5 k=ia(ipos+nod),ia(ipos+nod+1)-1
+            jold = ja(k)
+            jnew = riord(jold)
+            if (jold .eq. nod .or. jnew .gt. last) goto 5 
+            iw(jnew) = -1
+            call HeapInsert (iw,iord,riord,jnew,ichild,jnew) 
+            call moveback (iw,iord,riord,last) 
+            last = last -1 
+ 5       continue 
+         ipos = iptrm1
+ 101  continue
+c
+c update the degree of each edge
+c 
+         do 6 k=last+1,lastlast-1
+            jold = iord(k) 
+c     
+c     scan the neighbors of current node
+c     
+         ipos = 0
+         do 102 imat =1,nummat
+            do 61 i=ia(ipos+jold),ia(ipos+jold+1)-1 
+               jo = ja(i) 
+               jn = riord(jo) 
+c
+c     consider this node only if it has not been moved          
+c     
+               if (jn .gt. last) goto 61
+c     update degree of this neighbor 
+               iw(jn) = iw(jn)-1
+c     and fix the heap accordingly
+               call HeapInsert (iw,iord,riord,jn,ichild,jn)
+ 61         continue
+            ipos = iptrm1
+ 102     continue
+ 6    continue
+c
+c     stopping test -- end main "while"loop 
+c
+      if (last .gt. 1) goto 3
+      nset = nset + last
+c
+c     rescan all nodes one more time to determine the permutations 
+c
+      k1 = 0 
+      k2 = nset
+      do 7 j=n,1,-1
+         if (iw(j) .ge. 0) then
+            k1 = k1+1
+            k = k1
+         else
+            k2 = k2+1
+            k = k2 
+         endif
+         riord(k) = iord(j) 
+ 7    continue
+      do j=1,n
+         iord(riord(j)) = j
+      enddo
+      return
+c----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------
+      subroutine indset3(n,ja,ia,nset,iord,riord,iw,sym,iptr) 
+      integer n,nset,iptr,ja(*),ia(*),riord(n),iord(n),iw(n) 
+      logical sym 
+c---------------------------------------------------------------------- 
+c greedy algorithm for independent set ordering -- local minimization
+c using heap strategy -- VERTEX COVER ALGORITHM --  
+c ASSUMES MSR FORMAT (no diagonal element) -- ADD A SWITCH FOR CSR -- 
+c----------------------------------------------------------------------
+c This version for BOTH unsymmetric and symmetric patterns
+c----------------------------------------------------------------------
+c on entry
+c -------- 
+c n     = row and column dimension of matrix
+c ja    = column indices of nonzero elements of matrix,stored rowwise.
+c ia    = pointer to beginning of each row in ja.
+c sym   = logical indicating whether the matrix has a symmetric pattern.
+c         If not the transpose must also be provided -- appended to the
+c         ja, ia structure -- see description of iptr next.
+c iptr  = in case the matrix has an unsymmetric pattern,the transpose
+c         is assumed to be stored in the same arrays ia,ja. iptr is the
+c         location in ia of the pointer to the first row of transp(A).
+c         more generally, ia(iptr),...,ia(iptr+n) are the pointers to 
+c         the beginnings of rows 1, 2, ...., n+1 (row n+1 is fictitious)
+c         of the transpose of A in the array ja. For example,when using 
+c         the msr format,one can write:
+c          iptr = ja(n+1)
+c          ipos = iptr+n+2                ! get the transpose of A:
+c          call csrcsc (n,0,ipos,a,ja,ja,a,ja,ja(iptr))    ! and then:
+c          call indset(n,ja,ja,nset,iord,riord,iwk,.false.,iptr) 
+c
+c iw    = work space of length n.
+c
+c on return: 
+c---------- 
+c nset  = integer. The number of unknowns in the independent set. 
+c iord  = permutation array corresponding to the new ordering. The 
+c         first nset unknowns correspond to the independent set.
+c riord = reverse permutation array.  
+c----------------------------------------------------------------------
+c local variables --
+c 
+      integer j,nummat,nod,k,ipos,i,lastnset,jold,jnew
+c
+c     nummat is the number of matrices to loop through (A in symmetric
+c     pattern case (nummat=1) or A,and transp(A) otherwise (mummat=2) 
+c
+      if (sym) then
+         nummat = 1
+      else
+         nummat = 2
+      endif
+      iptrm1 = iptr-1
+c
+c     initialize arrays
+c
+      do 1 j=1,n
+         riord(j) = j
+         iord(j) = j
+         iw(j) = 0 
+ 1    continue
+c
+c     initialize degrees of all nodes
+c
+      nnz = 0
+      ipos = 0
+      do 100 imat =1,nummat
+         do 15 j=1,n
+            ideg = ia(ipos+j+1)-ia(ipos+j) 
+            iw(j) = iw(j) + ideg 
+            nnz = nnz + ideg
+ 15      continue
+ 100     ipos = iptrm1
+c
+c     number of edges
+c     
+         if (sym) then nnz = 2*nnz
+c     
+c start by constructing a Max heap
+c 
+      do 2 i=n/2,1,-1 
+         j = i
+         call FixHeapM (iw,riord,iord,j,j,n) 
+ 2    continue
+      nset = n
+c----------------------------------------------------------------------     
+c main loop -- remove nodes one by one. 
+c----------------------------------------------------------------------
+ 3    continue
+      lastnset = nset
+      nod = riord(1) 
+c     
+c     move first element to end
+c 
+      call movebackM (iw,riord,iord,nset) 
+      nnz = nnz - iw(nset) 
+      nset = nset -1 
+c
+c     scan all neighbors of accepted node -- 
+c     
+      ipos = 0
+      do 101 imat =1,nummat      
+         do 5 k=ia(ipos+nod),ia(ipos+nod+1)-1
+            jold = ja(k)
+            jnew = iord(jold)
+            if (jold .eq. nod .or. jnew .gt. nset) goto 5 
+            iw(jnew) = iw(jnew) - 1
+            nnz = nnz-1 
+            call FixHeapM (iw,riord,iord,jnew,jnew,nset) 
+ 5       continue 
+         ipos = iptrm1
+ 101  continue
+c      
+      if (nnz .gt. 0) goto 3
+      return
+c----------------------------------------------------------------------- 
+      end
+c-----------------------------------------------------------------------
+      subroutine HeapSort (a,ind,rind,n,ncut)
+      integer a(*),ind(n),rind(n),n, ncut 
+c----------------------------------------------------------------------  
+c integer version -- min heap sorts decreasinly. 
+c---------------------------------------------------------------------- 
+c sorts inger keys in array a increasingly and permutes the companion
+c array ind rind accrodingly. 
+c n    = size of array
+c ncut = integer indicating when to cut the process.the process is
+c        stopped after ncut outer steps of the heap-sort algorithm.
+c        The first ncut values are sorted and they are the smallest
+c        ncut values of the array.
+c----------------------------------------------------------------------
+c local variables 
+c
+      integer i,last, j,jlast
+c   
+c    Heap sort algorithm ---
+c    
+c    build heap 
+       do 1 i=n/2,1,-1 
+          j = i
+          call FixHeap (a,ind,rind,j,j,n) 
+ 1    continue
+c     
+c   done -- now remove keys one by one 
+c
+      jlast = max(2,n-ncut+1)
+      do 2 last=n,jlast,-1 
+         call moveback (a,ind,rind,last) 
+ 2    continue
+      return
+      end 
+c----------------------------------------------------------------------
+      subroutine FixHeap (a,ind,rind,jkey,vacant,last)
+      integer a(*),ind(*),rind(*),jkey,vacant,last
+c----------------------------------------------------------------------
+c     inserts a key (key and companion index) at the vacant position 
+c     in a (min) heap -
+c arguments
+c     a(1:last)    = real array
+c     ind(1:last)  = integer array -- permutation of initial data
+c     rind(1:last) = integer array -- reverse permutation 
+c     jkey         = position of key to be inserted. a(jkey) 
+c                    will be inserted into the heap
+c     vacant       = vacant where a key is to be inserted
+c     last         = number of elements in the heap.
+c----------------------------------------------------------------------
+c local variables 
+c
+      integer child,lchild,rchild,xkey
+      xkey = a(jkey) 
+      ikey = ind(jkey) 
+      lchild = 2*vacant
+ 1    continue 
+      rchild = lchild+1  
+      child = lchild  
+      if (rchild .le. last .and. a(rchild) .lt. a(child))
+     *     child = rchild 
+      if (xkey .le. a(child) .or. child .gt. last) goto 2 
+      a(vacant) = a(child) 
+      ind(vacant) = ind(child) 
+      rind(ind(vacant)) = vacant 
+      vacant = child 
+      lchild = 2*vacant 
+      if (lchild .le.  last) goto 1
+ 2    continue 
+      a(vacant) = xkey 
+      ind(vacant) = ikey 
+      rind(ikey) = vacant 
+      return
+c----------------------------------------------------------------------      
+      end
+c----------------------------------------------------------------------      
+      subroutine HeapInsert (a,ind,rind,jkey,child,node) 
+      integer a(*),ind(*),rind(*),jkey,child,node
+c----------------------------------------------------------------------
+c inserts a key to a heap from `node'. Checks values up
+c only -- i.e.,assumes that the subtree (if any) whose root
+c is node is such that the keys are all inferior to those
+c to ge inserted. 
+c 
+c child is where the key ended up.
+c---------------------------------------------------------------------- 
+c---- local variables 
+      integer parent,xkey,ikey
+      xkey = a(jkey) 
+      ikey = ind(jkey) 
+c      node = node + 1 
+      a(node) = xkey 
+      ind(node) = ikey 
+      rind(ikey) = node 
+      if (node .le. 1) return
+      child=node 
+ 1    parent = child/2  
+      if (a(parent) .le. a(child)) goto 2
+      call interchange(a,ind,rind,child,parent) 
+      child = parent 
+      if (child .gt. 1) goto 1 
+ 2    continue
+      return
+      end 
+c-----------------------------------------------------------------------
+      subroutine interchange (a,ind,rind,i,j)
+      integer a(*),ind(*),rind(*),i,j 
+      integer tmp,itmp
+      tmp = a(i)  
+      itmp = ind(i) 
+c
+      a(i) = a(j) 
+      ind(i) = ind(j) 
+c
+      a(j) = tmp
+      ind(j) = itmp 
+      rind(ind(j)) = j
+      rind(ind(i)) = i
+c
+      return
+      end 
+c----------------------------------------------------------------------
+      subroutine moveback (a,ind,rind,last) 
+      integer a(*),ind(*),rind(*),last 
+c moves the front key to the back and inserts the last
+c one back in from the top -- 
+c 
+c local variables 
+c
+      integer vacant,xmin 
+c
+         vacant = 1 
+         xmin = a(vacant)
+         imin = ind(vacant) 
+         call FixHeap(a,ind,rind,last,vacant,last-1) 
+         a(last) = xmin 
+        ind(last) = imin 
+         rind(ind(last)) = last
+c
+         return
+         end 
+c----------------------------------------------------------------------
+      subroutine FixHeapM (a,ind,rind,jkey,vacant,last)
+      integer a(*),ind(*),rind(*),jkey,vacant,last
+c----      
+c     inserts a key (key and companion index) at the vacant position 
+c     in a heap -  THIS IS A MAX HEAP VERSION
+c arguments
+c     a(1:last)    = real array
+c     ind(1:last)  = integer array -- permutation of initial data
+c     rind(1:last) = integer array -- reverse permutation 
+c     jkey         = position of key to be inserted. a(jkey) 
+c                    will be inserted into the heap
+c     vacant       = vacant where a key is to be inserted
+c     last         = number of elements in the heap.
+c----     
+c local variables 
+c
+      integer child,lchild,rchild,xkey
+      xkey = a(jkey) 
+      ikey = ind(jkey) 
+      lchild = 2*vacant
+ 1    continue 
+      rchild = lchild+1  
+      child = lchild  
+      if (rchild .le. last .and. a(rchild) .gt. a(child))
+     *     child = rchild 
+      if (xkey .ge. a(child) .or. child .gt. last) goto 2
+      a(vacant) = a(child) 
+      ind(vacant) = ind(child) 
+      rind(ind(vacant)) = vacant 
+      vacant = child 
+      lchild = 2*vacant 
+      if (lchild .le.  last) goto 1
+ 2    continue 
+      a(vacant) = xkey 
+      ind(vacant) = ikey 
+      rind(ikey) = vacant 
+      return
+      end
+c      
+      subroutine HeapInsertM (a,ind,rind,jkey,child,node) 
+      integer a(*),ind(*),rind(*),jkey,child,node
+c----------------------------------------------------------------------
+c inserts a key to a heap from `node'. Checks values up
+c only -- i.e.,assumes that the subtree (if any) whose root
+c is node is such that the keys are all inferior to those
+c to ge inserted. 
+c 
+c child is where the key ended up.
+c---------------------------------------------------------------------- 
+c---- local variables 
+      integer parent,xkey,ikey
+      xkey = a(jkey) 
+      ikey = ind(jkey) 
+c      node = node + 1 
+      a(node) = xkey 
+      ind(node) = ikey 
+      rind(ikey) = node 
+      if (node .le. 1) return
+      child=node 
+ 1    parent = child/2  
+      if (a(parent) .ge. a(child)) goto 2
+      call interchange(a,ind,rind,child,parent) 
+      child = parent 
+      if (child .gt. 1) goto 1 
+ 2    continue
+      return
+      end 
+c----------------------------------------------------------------------
+      subroutine movebackM (a,ind,rind,last) 
+      integer a(*),ind(*),rind(*),last 
+c----------------------------------------------------------------------
+c moves the front key to the back and inserts the last
+c one back in from the top --  MAX HEAP VERSION 
+c----------------------------------------------------------------------
+c 
+c local variables 
+c
+      integer vacant,xmin 
+c
+      vacant = 1 
+      xmin = a(vacant)
+      imin = ind(vacant) 
+      call FixHeapM(a,ind,rind,last,vacant,last-1) 
+      a(last) = xmin 
+      ind(last) = imin 
+      rind(ind(last)) = last
+c----------------------------------------------------------------------
+      return
+      end 
+c----------------------------------------------------------------------
+      subroutine indsetr (n,ja,ia,nset,iord,riord,sym,iptr) 
+      integer n, nset, ja(*),ia(*),riord(*),iord(*) 
+      logical sym
+c---------------------------------------------------------------------- 
+c greedy algorithm for independent set ordering -- RANDOM TRAVERSAL -- 
+c----------------------------------------------------------------------
+c parameters:
+c ----------
+c n      = row dimension of matrix
+c ja, ia = matrix pattern in CRS format
+c nset   = (output) number of elements in the independent set
+c iord   = permutation array corresponding to the independent set 
+c          ordering. Row number i will become row number iord(i) in 
+c          permuted matrix.
+c riord  = reverse permutation array. Row number i in the permutated 
+c          matrix is row number riord(i) in original matrix. 
+c----------------------------------------------------------------------
+c notes: works for CSR, MSR, and CSC formats but assumes that the
+c matrix has a symmetric structure. 
+c---------------------------------------------------------------------- 
+c local variables
+c 
+      integer j, k1, k2, nod, k, mat
+      do 1 j=1, n
+         iord(j) = 0
+ 1    continue
+c
+c generate random permutation
+c 
+      iseed = 0 
+      call rndperm(n, riord, iseed)
+      write (8,'(10i6)') (riord(j),j=1,n) 
+c
+      nummat = 1
+      if (.not. sym) nummat = 2
+c     
+c iord used as a marker
+c 
+      nset = 0
+      do 12  ii=1, n
+         nod = riord(ii) 
+         if (iord(nod) .ne. 0) goto 12 
+         nset = nset+1
+         iord(nod) = 1
+c
+c visit all neighbors of current nod 
+c     
+         ipos = 0
+         do 45 mat=1, nummat
+            do 4 k=ia(ipos+nod), ia(ipos+nod+1)-1 
+               j = ja(k)
+               if (j .ne. nod) iord(j) = 2
+ 4          continue
+            ipos = iptr-1
+ 45      continue
+ 12   continue
+c
+c get permutation
+c     
+      k1 = 0 
+      k2 = nset 
+      do 6 j=1,n
+         if (iord(j) .eq. 1) then
+            k1 = k1+1
+            k = k1
+         else
+            k2 = k2+1
+            k = k2 
+         endif
+            riord(k) = j         
+            iord(j) = k
+ 6    continue
+      return
+c----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------
+      subroutine rndperm(n,iord,iseed) 
+      integer n, iseed, iord(n) 
+c----------------------------------------------------------------------
+c this subroutine will generate a pseudo random permutation of the
+c n integers 1,2, ...,n.
+c iseed is the initial seed. any integer.
+c----------------------------------------------------------------------
+c local
+c
+      integer i, j, itmp 
+c----------------------------------------------------------------------
+      do j=1, n
+         iord(j) = j
+      enddo
+c
+      do i=1, n
+         j = mod(irand(0),n) + 1
+         itmp = iord(i) 
+         iord(i) = iord(j) 
+         iord(j) = itmp
+      enddo
+c----------------------------------------------------------------------
+      return
+c----------------------------------------------------------------------
+      end 
diff --git a/ORDERINGS/dsepart.f b/ORDERINGS/dsepart.f
new file mode 100644
index 0000000..72306c4
--- /dev/null
+++ b/ORDERINGS/dsepart.f
@@ -0,0 +1,980 @@
+c----------------------------------------------------------------------c
+c                          S P A R S K I T                             c
+c----------------------------------------------------------------------c
+c               REORDERING ROUTINES -- LEVEL SET BASED ROUTINES        c
+c----------------------------------------------------------------------c
+c dblstr   : doubled stripe partitioner 
+c rdis     : recursive dissection partitioner
+c dse2way  : distributed site expansion usuing sites from dblstr 
+c dse      : distributed site expansion usuing sites from rdis
+c------------- utility routines ----------------------------------------- 
+c BFS      : Breadth-First search traversal algorithm 
+c add_lvst : routine to add a level -- used by BFS 
+c stripes  : finds the level set structure
+c stripes0 : finds a trivial one-way partitioning from level-sets 
+c perphn   : finds a pseudo-peripheral node and performs a BFS from it.
+c mapper4  : routine used by dse and dse2way to do center expansion
+c get_domns: routine to find subdomaine from linked lists found by 
+c            mapper4. 
+c add_lk   : routine to add entry to linked list -- used by mapper4. 
+c find_ctr : routine to locate an approximate center of a subgraph. 
+c rversp   : routine to reverse a given permutation (e.g., for RCMK)
+c maskdeg  : integer function to compute the `masked' of a node
+c-----------------------------------------------------------------------
+      subroutine dblstr(n,ja,ia,ip1,ip2,nfirst,riord,ndom,map,mapptr,
+     *     mask,levels,iwk) 
+      implicit none
+      integer ndom,ja(*),ia(*),ip1,ip2,nfirst,riord(*),map(*),mapptr(*),
+     *     mask(*),levels(*),iwk(*),nextdom
+c-----------------------------------------------------------------------
+c     this routine does a two-way partitioning of a graph using 
+c     level sets recursively. First a coarse set is found by a
+c     simple cuthill-mc Kee type algorithm. Them each of the large
+c     domains is further partitioned into subsets using the same 
+c     technique. The ip1 and ip2 parameters indicate the desired number 
+c     number of partitions 'in each direction'. So the total number of
+c     partitions on return ought to be equal (or close) to ip1*ip2 
+c----------------------parameters----------------------------------------
+c on entry: 
+c---------
+c n      = row dimension of matrix == number of vertices in graph
+c ja, ia = pattern of matrix in CSR format (the ja,ia arrays of csr data
+c          structure)
+c ip1    = integer indicating the number of large partitions ('number of
+c          paritions in first direction') 
+c ip2    = integer indicating the number of smaller partitions, per 
+c          large partition, ('number of partitions in second direction') 
+c nfirst = number of nodes in the first level that is input in riord 
+c riord  = (also an ouput argument). on entry riord contains the labels  
+c          of the nfirst nodes that constitute the first level.   
+c on return:
+c-----------
+c ndom   = total number of partitions found 
+c map    = list of nodes listed partition by partition from partition 1
+c          to paritition ndom.
+c mapptr = pointer array for map. All nodes from position 
+c          k1=mapptr(idom),to position k2=mapptr(idom+1)-1 in map belong
+c          to partition idom.
+c work arrays:
+c-------------
+c mask   = array of length n, used to hold the partition number of each 
+c          node for the first (large) partitioning. 
+c          mask is also used as a marker of  visited nodes. 
+c levels = integer array of length .le. n used to hold the pointer 
+c          arrays for the various level structures obtained from BFS. 
+c 
+c-----------------------------------------------------------------------
+      integer n, j,idom,kdom,jdom,maskval,k,nlev,init,ndp1,numnod
+      maskval = 1 
+      do j=1, n
+         mask(j) = maskval 
+      enddo
+      iwk(1) = 0 
+      call BFS(n,ja,ia,nfirst,iwk,mask,maskval,riord,levels,nlev)      
+c
+c     init = riord(1) 
+c     call perphn (ja,ia,mask,maskval,init,nlev,riord,levels) 
+      call stripes (nlev,riord,levels,ip1,map,mapptr,ndom)
+c-----------------------------------------------------------------------
+      if (ip2 .eq. 1) return      
+      ndp1 = ndom+1
+c     
+c     pack info into array iwk 
+c 
+      do j = 1, ndom+1
+         iwk(j) = ndp1+mapptr(j)  
+      enddo
+      do j=1, mapptr(ndom+1)-1
+         iwk(ndp1+j) = map(j) 
+      enddo
+      do idom=1, ndom 
+         j = iwk(idom) 
+         numnod = iwk(idom+1) - iwk(idom) 
+         init = iwk(j) 
+         do k=j, iwk(idom+1)-1 
+         enddo
+      enddo
+
+      do idom=1, ndom 
+         do k=mapptr(idom),mapptr(idom+1)-1 
+            mask(map(k)) = idom
+         enddo
+      enddo
+      nextdom = 1 
+c
+c     jdom = counter for total number of (small) subdomains 
+c 
+      jdom = 1
+      mapptr(jdom) = 1 
+c----------------------------------------------------------------------- 
+      do idom =1, ndom
+         maskval = idom
+         nfirst = 1
+         numnod = iwk(idom+1) - iwk(idom) 
+         j = iwk(idom) 
+         init = iwk(j) 
+         nextdom = mapptr(jdom) 
+c  note:    old version uses iperm array 
+         call perphn(numnod,ja,ia,init,mask,maskval,
+     *        nlev,riord,levels)
+c          
+         call stripes (nlev,riord,levels,ip2,map(nextdom),
+     *        mapptr(jdom),kdom)
+c          
+         mapptr(jdom) = nextdom
+         do j = jdom,jdom+kdom-1
+            mapptr(j+1) = nextdom + mapptr(j+1)-1
+         enddo
+         jdom = jdom + kdom
+      enddo
+c
+      ndom = jdom - 1
+      return
+      end 
+c-----------------------------------------------------------------------
+      subroutine rdis(n,ja,ia,ndom,map,mapptr,mask,levels,size,iptr) 
+      implicit none
+      integer n,ja(*),ia(*),ndom,map(*),mapptr(*),mask(*),levels(*),
+     *     size(ndom),iptr(ndom)
+c-----------------------------------------------------------------------
+c     recursive dissection algorithm for partitioning.
+c     initial graph is cut in two - then each time, the largest set
+c     is cut in two until we reach desired number of domains.
+c----------------------------------------------------------------------- 
+c     input
+c     n, ja, ia = graph 
+c     ndom      = desired number of subgraphs
+c     output 
+c     ------
+c     map, mapptr  = pointer array data structure for domains. 
+c             if k1 = mapptr(i), k2=mapptr(i+1)-1 then 
+c             map(k1:k2) = points in domain number i
+c    work arrays:
+c    -------------
+c    mask(1:n)    integer 
+c    levels(1:n)  integer 
+c    size(1:ndom) integer 
+c    iptr(1:ndom) integer 
+c----------------------------------------------------------------------- 
+      integer idom,maskval,k,nlev,init,nextsiz,wantsiz,lev,ko,
+     *     maxsiz,j,nextdom  
+c-----------------------------------------------------------------------
+      idom = 1
+c-----------------------------------------------------------------------
+c     size(i) = size of domnain  i
+c     iptr(i)  = index of first element of domain i
+c-----------------------------------------------------------------------
+      size(idom) = n
+      iptr(idom) = 1
+      do j=1, n
+         mask(j) = 1 
+      enddo
+c     
+c     domain loop
+c
+ 1    continue
+c
+c     select domain with largest size
+c     
+      maxsiz = 0 
+      do j=1, idom
+         if (size(j) .gt. maxsiz) then
+            maxsiz = size(j)
+            nextdom = j
+         endif
+      enddo
+c
+c     do a Prphn/ BFS on nextdom
+c     
+      maskval = nextdom
+      init = iptr(nextdom) 
+      call perphn(n,ja,ia,init,mask,maskval,nlev,map,levels) 
+c
+c     determine next subdomain
+c
+      nextsiz = 0
+      wantsiz = maxsiz/2 
+      idom = idom+1
+      lev = nlev 
+      do while (nextsiz .lt. wantsiz) 
+         do k = levels(lev), levels(lev+1)-1
+            mask(map(k)) = idom
+        enddo
+        nextsiz = nextsiz + levels(lev+1) - levels(lev) 
+        lev = lev-1
+      enddo
+c
+      size(nextdom) = size(nextdom) - nextsiz
+      size(idom) = nextsiz
+c
+c     new initial point = last point of previous domain
+c
+       iptr(idom) = map(levels(nlev+1)-1) 
+c       iptr(idom) = map(levels(lev)+1) 
+c      iptr(idom) = 1 
+c
+c alternative 
+c      lev = 1 
+c      do while (nextsiz .lt. wantsiz) 
+c         do k = levels(lev), levels(lev+1)-1
+c            mask(map(k)) = idom
+c         enddo
+c         nextsiz = nextsiz + levels(lev+1) - levels(lev) 
+c         lev = lev+1
+c      enddo
+c
+c     set size of new domain and adjust previous one
+c
+c      size(idom) = nextsiz 
+c      size(nextdom) = size(nextdom) - nextsiz 
+c      iptr(idom) = iptr(nextdom) 
+c      iptr(nextdom) = map(levels(lev))
+
+      if (idom .lt. ndom) goto 1
+c
+c     domains found -- build data structure 
+c     
+      mapptr(1) = 1
+      do idom=1, ndom 
+         mapptr(idom+1) = mapptr(idom) + size(idom) 
+      enddo
+      do k=1, n
+         idom = mask(k) 
+         ko = mapptr(idom) 
+         map(ko) = k
+         mapptr(idom) = ko+1
+      enddo
+c
+c     reset pointers
+c     
+      do j = ndom,1,-1
+         mapptr(j+1) = mapptr(j) 
+      enddo
+      mapptr(1) = 1 
+c
+      return
+      end 
+c-----------------------------------------------------------------------
+      subroutine dse2way(n,ja,ia,ip1,ip2,nfirst,riord,ndom,dom,idom,
+     *     mask,jwk,link) 
+c-----------------------------------------------------------------------
+c     uses centers obtained from dblstr partition to get new partition
+c----------------------------------------------------------------------- 
+c     input: n, ja, ia   = matrix
+c     nfirst = number of first points 
+c     riord  = riord(1:nfirst) initial points 
+c     output 
+c     ndom   = number of domains
+c     dom, idom = pointer array structure for domains. 
+c     mask , jwk, link = work arrays,
+c-----------------------------------------------------------------------
+      implicit none 
+      integer n, ja(*), ia(*), ip1, ip2, nfirst, riord(*), dom(*),
+     *     idom(*), mask(*), jwk(*),ndom,link(*)  
+c
+c-----------------------------------------------------------------------
+c     local variables
+      integer i, mid,nsiz, maskval,init, outer, nouter, k
+      call dblstr(n,ja,ia,ip1,ip2,nfirst,riord,ndom,dom,idom,mask,
+     *     link,jwk)
+c
+      nouter = 3
+c----------------------------------------------------------------------- 
+
+      do outer =1, nouter 
+c
+c     set masks 
+c
+      do i=1, ndom
+         do k=idom(i),idom(i+1)-1
+            mask(dom(k)) = i
+         enddo
+      enddo
+c
+c     get centers 
+c 
+      do i =1, ndom
+         nsiz = idom(i+1) - idom(i) 
+         init = dom(idom(i))
+         maskval = i 
+c
+c         use link for local riord -- jwk for other arrays -- 
+c 
+         call find_ctr(n,nsiz,ja,ia,init,mask,maskval,link, 
+     *    jwk,mid,jwk(nsiz+1)) 
+         riord(i) = mid 
+      enddo
+c
+c     do level-set expansion from centers -- save previous diameter 
+c 
+      call mapper4(n,ja,ia,ndom,riord,jwk,mask,link) 
+      call get_domns2(ndom,riord,link,jwk,dom,idom)
+c----------------------------------------------------------------------- 
+      enddo 
+      return 
+      end 
+c----------------------------------------------------------------------- 
+      subroutine dse(n,ja,ia,ndom,riord,dom,idom,mask,jwk,link) 
+      implicit none 
+      integer n, ja(*), ia(*), ndom, riord(*), dom(*),
+     *     idom(*), mask(*), jwk(*),link(*)  
+c-----------------------------------------------------------------------
+c     uses centers produced from rdis to get a new partitioning -- 
+c     see calling sequence in rdis.. 
+c-----------------------------------------------------------------------
+c     local variables
+      integer i, mid, nsiz, maskval,init, outer, nouter, k 
+c-----------------------------------------------------------------------
+      nouter = 3
+c 
+      call rdis(n,ja,ia,ndom,dom,idom,mask,link,jwk,jwk(ndom+1)) 
+c
+c     initial points = 
+c
+      do outer =1, nouter 
+c
+c     set masks 
+c
+      do i=1, ndom
+         do k=idom(i),idom(i+1)-1
+            mask(dom(k)) = i
+         enddo
+      enddo
+c
+c     get centers 
+c 
+      do i =1, ndom
+         nsiz = idom(i+1) - idom(i) 
+         init = dom(idom(i))
+         maskval = i 
+c
+c         use link for local riord -- jwk for other arrays -- 
+c 
+
+         call find_ctr(n,nsiz,ja,ia,init,mask,maskval,link, 
+     *    jwk,mid,jwk(nsiz+1)) 
+         riord(i) = mid 
+      enddo
+c
+c     do level-set expansion from centers -- save previous diameter 
+c 
+      call mapper4(n,ja,ia,ndom,riord,jwk,mask,link) 
+      call get_domns2(ndom,riord,link,jwk,dom,idom)
+c----------------------------------------------------------------------- 
+      enddo 
+      return 
+      end 
+c----------------------------------------------------------------------- 
+      subroutine BFS(n,ja,ia,nfirst,iperm,mask,maskval,riord,levels,
+     *     nlev)
+      implicit none 
+      integer n,ja(*),ia(*),nfirst,iperm(n),mask(n),riord(*),levels(*),
+     *     nlev,maskval 
+c-----------------------------------------------------------------------
+c finds the level-structure (breadth-first-search or CMK) ordering for a
+c given sparse matrix. Uses add_lvst. Allows an set of nodes to be 
+c the initial level (instead of just one node). 
+c-------------------------parameters------------------------------------
+c on entry:
+c---------
+c     n      = number of nodes in the graph 
+c     ja, ia = pattern of matrix in CSR format (the ja,ia arrays of csr data
+c     structure)
+c     nfirst = number of nodes in the first level that is input in riord
+c     iperm  = integer array indicating in which order to  traverse the graph
+c     in order to generate all connected components. 
+c     if iperm(1) .eq. 0 on entry then BFS will traverse the nodes
+c     in the  order 1,2,...,n.
+c     
+c     riord  = (also an ouput argument). On entry riord contains the labels  
+c     of the nfirst nodes that constitute the first level.      
+c     
+c     mask   = array used to indicate whether or not a node should be 
+c     condidered in the graph. see maskval.
+c     mask is also used as a marker of  visited nodes. 
+c     
+c     maskval= consider node i only when:  mask(i) .eq. maskval 
+c     maskval must be .gt. 0. 
+c     thus, to consider all nodes, take mask(1:n) = 1. 
+c     maskval=1 (for example) 
+c     
+c     on return
+c     ---------
+c     mask   = on return mask is restored to its initial state. 
+c     riord  = `reverse permutation array'. Contains the labels of the nodes
+c     constituting all the levels found, from the first level to
+c     the last. 
+c     levels = pointer array for the level structure. If lev is a level
+c     number, and k1=levels(lev),k2=levels(lev+1)-1, then
+c     all the nodes of level number lev are:
+c     riord(k1),riord(k1+1),...,riord(k2) 
+c     nlev   = number of levels found
+c-----------------------------------------------------------------------
+c     
+      integer j, ii, nod, istart, iend 
+      logical permut
+      permut = (iperm(1) .ne. 0) 
+c     
+c     start pointer structure to levels 
+c     
+      nlev   = 0 
+c     
+c     previous end
+c     
+      istart = 0 
+      ii = 0
+c     
+c     current end 
+c     
+      iend = nfirst
+c     
+c     intialize masks to zero -- except nodes of first level -- 
+c     
+      do 12 j=1, nfirst 
+         mask(riord(j)) = 0 
+ 12   continue
+c-----------------------------------------------------------------------
+ 13   continue 
+c     
+ 1    nlev = nlev+1
+      levels(nlev) = istart + 1
+      call add_lvst (istart,iend,nlev,riord,ja,ia,mask,maskval) 
+      if (istart .lt. iend) goto 1
+ 2    ii = ii+1 
+      if (ii .le. n) then
+         nod = ii         
+         if (permut) nod = iperm(nod)          
+         if (mask(nod) .eq. maskval) then
+c     
+c     start a new level
+c
+            istart = iend
+            iend = iend+1 
+            riord(iend) = nod
+            mask(nod) = 0
+            goto 1
+         else 
+            goto 2
+         endif
+      endif
+c----------------------------------------------------------------------- 
+ 3    levels(nlev+1) = iend+1 
+      do j=1, iend
+         mask(riord(j)) = maskval 
+      enddo
+c----------------------------------------------------------------------- 
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine add_lvst(istart,iend,nlev,riord,ja,ia,mask,maskval) 
+      integer nlev, nod, riord(*), ja(*), ia(*), mask(*) 
+c-------------------------------------------------------------
+c     adds one level set to the previous sets.. 
+c     span all nodes of previous mask
+c-------------------------------------------------------------
+      nod = iend
+      do 25 ir = istart+1,iend 
+         i = riord(ir)		
+         do 24 k=ia(i),ia(i+1)-1
+            j = ja(k)
+            if (mask(j) .eq. maskval) then
+               nod = nod+1 
+               mask(j) = 0
+               riord(nod) = j
+            endif 
+ 24      continue
+ 25   continue
+      istart = iend 
+      iend   = nod 
+      return
+      end 
+c----------------------------------------------------------------------- 
+      subroutine stripes (nlev,riord,levels,ip,map,mapptr,ndom)
+      implicit none
+      integer nlev,riord(*),levels(nlev+1),ip,map(*),
+     *    mapptr(*), ndom
+c-----------------------------------------------------------------------
+c    this is a post processor to BFS. stripes uses the output of BFS to 
+c    find a decomposition of the adjacency graph by stripes. It fills 
+c    the stripes level by level until a number of nodes .gt. ip is 
+c    is reached. 
+c---------------------------parameters-----------------------------------
+c on entry: 
+c --------
+c nlev   = number of levels as found by BFS 
+c riord  = reverse permutation array produced by BFS -- 
+c levels = pointer array for the level structure as computed by BFS. If 
+c          lev is a level number, and k1=levels(lev),k2=levels(lev+1)-1, 
+c          then all the nodes of level number lev are:
+c                      riord(k1),riord(k1+1),...,riord(k2) 
+c  ip    = number of desired partitions (subdomains) of about equal size.
+c 
+c on return
+c ---------
+c ndom     = number of subgraphs (subdomains) found 
+c map      = node per processor list. The nodes are listed contiguously
+c            from proc 1 to nproc = mpx*mpy. 
+c mapptr   = pointer array for array map. list for proc. i starts at 
+c            mapptr(i) and ends at mapptr(i+1)-1 in array map.
+c-----------------------------------------------------------------------
+c local variables. 
+c
+      integer ib,ktr,ilev,k,nsiz,psiz 
+      ndom = 1 
+      ib = 1
+c to add: if (ip .le. 1) then ...
+      nsiz = levels(nlev+1) - levels(1) 
+      psiz = (nsiz-ib)/max(1,(ip - ndom + 1)) + 1 
+      mapptr(ndom) = ib 
+      ktr = 0 
+      do 10 ilev = 1, nlev
+c
+c     add all nodes of this level to domain
+c     
+         do 3 k=levels(ilev), levels(ilev+1)-1
+            map(ib) = riord(k)
+            ib = ib+1
+            ktr = ktr + 1 
+            if (ktr .ge. psiz  .or. k .ge. nsiz) then 
+               ndom = ndom + 1
+               mapptr(ndom) = ib 
+               psiz = (nsiz-ib)/max(1,(ip - ndom + 1)) + 1 
+               ktr = 0
+            endif
+c
+ 3       continue
+ 10   continue
+      ndom = ndom-1
+      return 
+      end
+c-----------------------------------------------------------------------
+      subroutine stripes0 (ip,nlev,il,ndom,iptr)
+      integer ip, nlev, il(*), ndom, iptr(*)
+c-----------------------------------------------------------------------
+c     This routine is a simple level-set partitioner. It scans
+c     the level-sets as produced by BFS from one to nlev.
+c     each time the number of nodes in the accumulated set of
+c     levels traversed exceeds the parameter ip, this set defines 
+c     a new subgraph. 
+c-------------------------parameter-list---------------------------------
+c on entry:
+c --------
+c ip     = desired number of nodes per subgraph.
+c nlev   = number of levels found  as output by BFS
+c il     = integer array containing the pointer array for
+c          the level data structure as output by BFS. 
+c          thus il(lev+1) - il(lev) = the number of 
+c          nodes that constitute the level numbe lev.
+c on return
+c ---------
+c ndom   = number of sungraphs found
+c iptr   = pointer array for the sugraph data structure. 
+c          thus, iptr(idom) points to the first level that 
+c          consistutes the subgraph number idom, in the 
+c          level data structure. 
+c-----------------------------------------------------------------------
+      ktr = 0
+      iband = 1 
+      iptr(iband) = 1 
+c-----------------------------------------------------------------------
+
+      do 10 ilev = 1, nlev
+         ktr = ktr + il(ilev+1) - il(ilev)
+         if (ktr .gt. ip) then
+            iband = iband+1 
+            iptr(iband) = ilev+1
+            ktr = 0
+         endif
+c
+ 10   continue
+c-----------returning --------------------
+      iptr(iband) = nlev + 1 
+      ndom = iband-1
+      return
+c-----------------------------------------------------------------------
+c-----end-of-stripes0--------------------------------------------------- 
+      end
+c----------------------------------------------------------------------- 
+      integer function maskdeg (ja,ia,nod,mask,maskval) 
+      implicit none 
+      integer ja(*),ia(*),nod,mask(*),maskval
+c-----------------------------------------------------------------------
+      integer deg, k 
+      deg = 0 
+      do k =ia(nod),ia(nod+1)-1
+         if (mask(ja(k)) .eq. maskval) deg = deg+1 
+      enddo
+      maskdeg = deg 
+      return
+      end 
+c-----------------------------------------------------------------------
+      subroutine perphn(n,ja,ia,init,mask,maskval,nlev,riord,levels) 
+      implicit none
+      integer n,ja(*),ia(*),init,mask(*),maskval,
+     *     nlev,riord(*),levels(*)
+c-----------------------------------------------------------------------
+c     finds a peripheral node and does a BFS search from it. 
+c-----------------------------------------------------------------------
+c     see routine  dblstr for description of parameters
+c input:
+c-------
+c ja, ia  = list pointer array for the adjacency graph
+c mask    = array used for masking nodes -- see maskval
+c maskval = value to be checked against for determing whether or
+c           not a node is masked. If mask(k) .ne. maskval then
+c           node k is not considered.
+c init    = init node in the pseudo-peripheral node algorithm.
+c
+c output:
+c-------
+c init    = actual pseudo-peripherial node found.
+c nlev    = number of levels in the final BFS traversal.
+c riord   =
+c levels  =
+c----------------------------------------------------------------------- 
+      integer j,nlevp,deg,nfirst,mindeg,nod,maskdeg
+      integer iperm(1) 
+      nlevp = 0 
+ 1    continue
+      riord(1) = init
+      nfirst = 1 
+      iperm(1) = 0
+c
+      call BFS(n,ja,ia,nfirst,iperm,mask,maskval,riord,levels,nlev)
+      if (nlev .gt. nlevp) then 
+         mindeg = n+1 
+         do j=levels(nlev),levels(nlev+1)-1
+            nod = riord(j) 
+            deg = maskdeg(ja,ia,nod,mask,maskval)
+            if (deg .lt. mindeg) then
+               init = nod
+               mindeg = deg
+            endif 
+         enddo
+         nlevp = nlev 
+         goto 1 
+      endif
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine mapper4 (n,ja,ia,ndom,nodes,levst,marker,link)
+      implicit none 
+      integer n,ndom,ja(*),ia(*),marker(n),levst(2*ndom), 
+     *     nodes(*),link(*) 
+c-----------------------------------------------------------------------
+c     finds domains given ndom centers -- by doing a level set expansion 
+c-----------------------------------------------------------------------
+c     on entry:
+c     ---------
+c     n      = dimension of matrix 
+c     ja, ia = adajacency list of matrix (CSR format without values) -- 
+c     ndom   = number of subdomains (nr output by coarsen)  
+c     nodes  = array of size at least n. On input the first ndom entries
+c              of nodes should contain the labels of the centers of the 
+c              ndom domains from which to do the expansions. 
+c     
+c     on return 
+c     --------- 
+c     link  = linked list array for the ndom domains. 
+c     nodes = contains the list of nodes of the domain corresponding to
+c             link. (nodes(i) and link(i) are related to the same node). 
+c    
+c     levst = levst(j) points to beginning of subdomain j in link.
+c
+c     work arrays:
+c     ----------- 
+c     levst : work array of length 2*ndom -- contains the beginning and
+c     end of  current level in link. 
+c     beginning of last level in link for each processor.
+c     also ends in levst(ndom+i) 
+c     marker : work array of length n. 
+c
+c     Notes on implementation: 
+c     ----------------------- 
+c     for j .le. ndom link(j) is <0  and indicates the end of the
+c     linked list. The most recent element added to the linked
+c     list is added at the end of the list (traversal=backward) 
+c     For  j .le. ndom, the value of -link(j) is the size of 
+c     subdomain j. 
+c
+c-----------------------------------------------------------------------
+c     local variables 
+      integer mindom,j,lkend,nod,nodprev,idom,next,i,kk,ii,ilast,nstuck,
+     *     isiz, nsize 
+c     
+c     initilaize nodes and link arrays
+c
+      do 10 j=1, n
+         marker(j) = 0
+ 10   continue
+c     
+      do 11 j=1, ndom
+         link(j) = -1 
+         marker(nodes(j)) = j
+         levst(j) = j
+         levst(ndom+j) = j 
+ 11   continue
+c
+c     ii = next untouched node for restarting new connected component. 
+c 
+      ii = 0
+c     
+      lkend = ndom
+      nod   = ndom  
+      nstuck = 0 
+c-----------------------------------------------------------------------
+ 100  continue 
+      idom = mindom(n,ndom,link) 
+c-----------------------------------------------------------------------
+c     begin level-set loop 
+c-----------------------------------------------------------------------
+ 3    nodprev = nod 
+      ilast = levst(ndom+idom) 
+      levst(ndom+idom) = lkend       
+      next = levst(idom) 
+c     
+c     linked list traversal loop
+c 
+      isiz = 0 
+      nsize = link(idom) 
+ 1    i = nodes(next) 
+      isiz = isiz + 1 
+c     
+c     adjacency list traversal loop 
+c     
+      do 2 kk=ia(i), ia(i+1)-1
+         j = ja(kk) 
+         if (marker(j) .eq. 0) then 
+            call add_lk(j,nod,idom,ndom,lkend,levst,link,nodes,marker) 
+         endif
+ 2    continue
+c     
+c     if last element of the previous level not reached continue
+c     
+      if (next .gt. ilast) then
+         next = link(next) 
+         if (next .gt. 0) goto 1
+      endif
+c-----------------------------------------------------------------------
+c     end level-set traversal --  
+c-----------------------------------------------------------------------
+      if (nodprev .eq. nod) then
+c     
+c     link(idom) >0 indicates that set is stuck  --  
+c
+         link(idom) = -link(idom) 
+         nstuck = nstuck+1
+      endif
+c     
+      if (nstuck .lt. ndom) goto 100 
+c
+c     reset sizes -- 
+c 
+      do j=1, ndom
+         if (link(j) .gt. 0) link(j) = -link(j)
+      enddo
+c
+      if (nod .eq. n) return 
+c
+c     stuck. add first non assigned point to smallest domain
+c     
+ 20   ii = ii+1
+      if (ii .le. n) then
+         if (marker(ii) .eq. 0) then 
+            idom = 0 
+            isiz = n+1 
+            do 30 kk=ia(ii), ia(ii+1)-1
+               i = marker(ja(kk)) 
+               if (i .ne. 0) then 
+                  nsize = abs(link(i)) 
+                  if (nsize .lt. isiz) then 
+                     isiz = nsize
+                     idom = i 
+                  endif
+               endif
+ 30            continue
+c
+c     if no neighboring domain select smallest one 
+c
+               if (idom .eq. 0) idom = mindom(n,ndom,link) 
+c     
+c     add ii to sudomain idom at end of linked list  
+c     
+            call add_lk(ii,nod,idom,ndom,lkend,levst,link,nodes,marker) 
+            goto 3 
+         else
+            goto 20 
+         endif
+      endif
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine get_domns2(ndom,nodes,link,levst,riord,iptr)
+      implicit none 
+      integer ndom,nodes(*),link(*),levst(*),riord(*),iptr(*) 
+c-----------------------------------------------------------------------
+c     constructs the subdomains from its linked list data structure
+c-----------------------------------------------------------------------
+c     input:
+c     ndom  = number of subdomains
+c     nodes = sequence of nodes are produced by mapper4. 
+c     link  = link list array as produced by mapper4.
+c     on return:
+c----------
+c     riord = contains the nodes in each subdomain in succession.
+c     iptr  = pointer in riord for beginnning of each subdomain.
+c     Thus subdomain number i consists of nodes 
+c     riord(k1),riord(k1)+1,...,riord(k2) 
+c     where k1 = iptr(i), k2= iptr(i+1)-1
+c     
+c-----------------------------------------------------------------------
+c     local variables 
+      integer nod, j, next, ii 
+      nod = 1
+      iptr(1) = nod 
+      do 21 j=1, ndom 
+         next = levst(j)
+ 22      ii = nodes(next)
+         riord(nod) = ii 
+         nod = nod+1 
+         next = link(next) 
+         if (next .gt.  0) goto 22
+         iptr(j+1) = nod 
+ 21   continue
+c
+      return
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
+      function mindom(n, ndom, link) 
+      implicit none 
+      integer mindom, n, ndom, link(n) 
+c-----------------------------------------------------------------------
+c     returns  the domain with smallest size
+c----------------------------------------------------------------------- 
+c      locals
+c
+      integer i, nsize, isiz 
+c
+      isiz = n+1 
+      do 10 i=1, ndom
+         nsize = - link(i) 
+         if (nsize .lt. 0) goto 10 
+         if (nsize .lt. isiz) then 
+            isiz = nsize
+            mindom = i
+         endif
+ 10   continue
+      return
+      end 
+c-----------------------------------------------------------------------
+      subroutine add_lk(new,nod,idom,ndom,lkend,levst,link,nodes,marker) 
+      implicit none
+      integer new,nod,idom,ndom,lkend,levst(*),link(*),nodes(*),
+     *     marker(*) 
+c----------------------------------------------------------------------- 
+c     inserts new element to linked list from the tail.
+c----------------------------------------------------------------------- 
+c     adds one entry (new) to linked list and ipdates everything.
+c     new  = node to be added
+c     nod  = current number of marked nodes
+c     idom = domain to which new is to be added
+c     ndom = total number of domains
+c     lkend= location of end of structure (link and nodes)
+c     levst= pointer array for link, nodes
+c     link = link array 
+c     nodes= nodes array -- 
+c     marker = marker array == if marker(k) =0 then node k is not
+c              assigned yet. 
+c----------------------------------------------------------------------- 
+c      locals
+c     
+      integer ktop  
+      lkend = lkend + 1
+      nodes(lkend) = new
+      nod = nod+1 
+      marker(new) = idom 
+      ktop = levst(idom) 
+      link(lkend) = ktop 
+      link(idom) = link(idom)-1 
+      levst(idom) = lkend 
+      return
+c-----------------------------------------------------------------------
+c-------end-of-add_lk--------------------------------------------------- 
+      end 
+c----------------------------------------------------------------------- 
+      subroutine find_ctr(n,nsiz,ja,ia,init,mask,maskval,riord,
+     *     levels,center,iwk) 
+      implicit none
+      integer n,nsiz,ja(*),ia(*),init,mask(*),maskval,riord(*),
+     *     levels(*),center,iwk(*) 
+c-----------------------------------------------------------------------
+c     finds a center point of a subgraph -- 
+c-----------------------------------------------------------------------
+c     n, ja, ia = graph
+c     nsiz = size of current domain.
+c     init = initial node in search
+c     mask
+c     maskval 
+c-----------------------------------------------------------------------
+c     local variables 
+      integer midlev, nlev,newmask, k, kr, kl, init0, nlev0  
+      call perphn(n,ja,ia,init,mask,maskval,nlev,riord,levels)
+c-----------------------------------------------------------------------
+c     midlevel = level which cuts domain into 2 roughly equal-size 
+c     regions 
+c
+      midlev = 1
+      k = 0 
+ 1    continue
+      k = k + levels(midlev+1)-levels(midlev) 
+      if (k*2 .lt. nsiz) then
+         midlev = midlev+1
+         goto 1 
+      endif
+c-----------------------------------------------------------------------
+      newmask = n+maskval
+c     
+c     assign temporary masks to mid-level elements
+c     
+      do k=levels(midlev),levels(midlev+1)-1
+         mask(riord(k)) = newmask
+      enddo
+c     
+c     find pseudo-periph node for mid-level `line'
+c
+      kr = 1
+      kl = kr + nsiz 
+      init0 = riord(levels(midlev))
+      call perphn(n,ja,ia,init0,mask,newmask,nlev0,iwk(kr),iwk(kl)) 
+c-----------------------------------------------------------------------
+c     restore  mask to initial state 
+c-----------------------------------------------------------------------
+      do k=levels(midlev),levels(midlev+1)-1
+         mask(riord(k)) = maskval 
+      enddo
+c-----------------------------------------------------------------------
+c     define center 
+c-----------------------------------------------------------------------  
+      midlev = 1 + (nlev0-1)/2
+      k = iwk(kl+midlev-1)
+      center = iwk(k) 
+c----------------------------------------------------------------------- 
+      return 
+      end 
+c-----------------------------------------------------------------------
+      subroutine rversp (n, riord)
+      integer n, riord(n)
+c-----------------------------------------------------------------------
+c     this routine does an in-place reversing of the permutation array
+c     riord --
+c-----------------------------------------------------------------------
+      integer j, k
+      do 26 j=1,n/2
+         k = riord(j)
+         riord(j) = riord(n-j+1)
+         riord(n-j+1) = k
+ 26   continue
+      return
+      end
+c-----------------------------------------------------------------------
diff --git a/README b/README
new file mode 100644
index 0000000..417b582
--- /dev/null
+++ b/README
@@ -0,0 +1,108 @@
+-----------------------------------------------------------------------
+                   S P A R S K I T   V E R S I O N  2.
+----------------------------------------------------------------------- 
+
+Latest update : Tue Mar  8 11:01:12 CST 2005
+
+-----------------------------------------------------------------------
+
+Welcome  to SPARSKIT  VERSION  2.  SPARSKIT is  a  package of  FORTRAN
+subroutines  for working  with  sparse matrices.  It includes  general
+sparse  matrix  manipulation  routines  as  well as  a  few  iterative
+solvers, see detailed description of contents below.
+
+ Copyright (C) 2005, the Regents of the University of Minnesota 
+
+SPARSKIT is  free software; you  can redistribute it and/or  modify it
+under the terms of the  GNU Lesser General Public License as published
+by the  Free Software Foundation [version  2.1 of the  License, or any
+later version.]
+
+A copy of  the licencing agreement is attached in  the file LGPL.  For
+additional information  contact the Free Software  Foundation Inc., 59
+Temple Place - Suite 330, Boston, MA 02111, USA or visit the web-site
+ 
+ http://www.gnu.org/copyleft/lesser.html
+
+
+DISCLAIMER
+----------
+
+SPARSKIT  is distributed  in  the hope  that  it will  be useful,  but
+WITHOUT   ANY  WARRANTY;   without  even   the  implied   warranty  of
+MERCHANTABILITY  or FITNESS  FOR A  PARTICULAR PURPOSE.   See  the GNU
+Lesser General Public License for more details.
+
+For more information contact saad@cs.umn.edu
+
+
+---------------------------------------------------
+            S P A R S K I T   VERSION 2  
+---------------------------------------------------
+
+In this directory you will  find  all relevant subdirectories and  the
+Unix makefile which  will  compile all the   modules and make  a  unix
+library  libskit.a.   Please read  the makefile.    Making the library
+should be  the first thing  to do  when starting  to use  the package.
+Some  of  the    objects   will be  linked    into  a  library  called
+libskit.a. Others   will  not be  linked  but  can be used    by other
+makefiles for test  problems provided in  the subdirectories.  You can
+then  link    to  libskit.a  by   default  instead  of  the individual
+modules. (Please report   any  compilation problems or  (even   minor)
+warnings  immediatly to saad@cs.umn.edu). Once  this   is done, it  is
+recommended to run the test problems provided.  There are various test
+suites in  each of the subdirectories  and makefiles are available for
+each.     See  explanations in the   README   files in each individual
+subdirectory.
+
+You may also make and run  the test programs  using the dotests script
+provided in this directory.  Output from this script may be redirected
+into a file and compared to the sample output files out.xxx.  There is
+an  additional  script called sgrep  which  is  useful for looking for
+tools   in   all  the  subdirectories.    Read  the   sgrep  file  for
+instructions.
+
+----------------------------------------------------------------------- 
+
+ Here is some information on the SPARSKIT sub-directories.
+
+ BLASSM : Basic linear algebra with sparse matrices. 
+	  contains two modules: blassm.f and matvec.f
+
+ DOC    : contains the main documentation of the package
+
+ INFO   : information routine (new one) . Info2 (spectral 
+	  information) not available yet.
+
+ FORMATS: Contains the Format Conversion routines in
+	  formats.f and the manipulation routines in
+	  unary.f           
+
+ INOUT  : input output routines. contains the module inout.f
+
+ ITSOL  : contains the iterative solution package. Various 
+          iterative solvers and preconditioners are provided. 
+
+ MATGEN : matrix generation routines.
+	  contains the module genmat.f and several subroutines 
+	  called by it. Also contains zlatev.f (contributed
+	  by E. Rothman, from Cornell).
+ 
+ ORDERINGS: 
+          still in the works. But contains a few coloring routines 
+          and level-set related orderings -- (e.g., cuthill Mc Kee, etc.) 
+
+ UNSUPP : various `unsupported' routines and drivers.
+	  (misc. routines includind routines for 
+          plotting.. BLAS1 is also added for completeness) 
+
+ See the file "logfile" for a complete revision history. 
+
+ Report any problems, suggestions, etc.. to
+
+	Yousef Saad.
+	saad@cs.umn.edu
+
+ ----------------------------------------------------------------------- 
+
+ 
\ No newline at end of file
diff --git a/UNSUPP/BLAS1/blas1.f b/UNSUPP/BLAS1/blas1.f
new file mode 100644
index 0000000..35e198b
--- /dev/null
+++ b/UNSUPP/BLAS1/blas1.f
@@ -0,0 +1,670 @@
+      subroutine  dcopy(n,dx,incx,dy,incy)
+c
+c     copies a vector, x, to a vector, y.
+c     uses unrolled loops for increments equal to one.
+c     jack dongarra, linpack, 3/11/78.
+c
+      double precision dx(1),dy(1)
+      integer i,incx,incy,ix,iy,m,mp1,n
+c
+      if(n.le.0)return
+      if(incx.eq.1.and.incy.eq.1)go to 20
+c
+c        code for unequal increments or equal increments
+c          not equal to 1
+c
+      ix = 1
+      iy = 1
+      if(incx.lt.0)ix = (-n+1)*incx + 1
+      if(incy.lt.0)iy = (-n+1)*incy + 1
+      do 10 i = 1,n
+        dy(iy) = dx(ix)
+        ix = ix + incx
+        iy = iy + incy
+   10 continue
+      return
+c
+c        code for both increments equal to 1
+c
+c
+c        clean-up loop
+c
+   20 m = mod(n,7)
+      if( m .eq. 0 ) go to 40
+      do 30 i = 1,m
+        dy(i) = dx(i)
+   30 continue
+      if( n .lt. 7 ) return
+   40 mp1 = m + 1
+      do 50 i = mp1,n,7
+        dy(i) = dx(i)
+        dy(i + 1) = dx(i + 1)
+        dy(i + 2) = dx(i + 2)
+        dy(i + 3) = dx(i + 3)
+        dy(i + 4) = dx(i + 4)
+        dy(i + 5) = dx(i + 5)
+        dy(i + 6) = dx(i + 6)
+   50 continue
+      return
+      end
+
+      double precision function ddot(n,dx,incx,dy,incy)
+c
+c     forms the dot product of two vectors.
+c     uses unrolled loops for increments equal to one.
+c     jack dongarra, linpack, 3/11/78.
+c
+      double precision dx(1),dy(1),dtemp
+      integer i,incx,incy,ix,iy,m,mp1,n
+c
+      ddot = 0.0d0
+      dtemp = 0.0d0
+      if(n.le.0)return
+      if(incx.eq.1.and.incy.eq.1)go to 20
+c
+c        code for unequal increments or equal increments
+c          not equal to 1
+c
+      ix = 1
+      iy = 1
+      if(incx.lt.0)ix = (-n+1)*incx + 1
+      if(incy.lt.0)iy = (-n+1)*incy + 1
+      do 10 i = 1,n
+        dtemp = dtemp + dx(ix)*dy(iy)
+        ix = ix + incx
+        iy = iy + incy
+   10 continue
+      ddot = dtemp
+      return
+c
+c        code for both increments equal to 1
+c
+c
+c        clean-up loop
+c
+   20 m = mod(n,5)
+      if( m .eq. 0 ) go to 40
+      do 30 i = 1,m
+        dtemp = dtemp + dx(i)*dy(i)
+   30 continue
+      if( n .lt. 5 ) go to 60
+   40 mp1 = m + 1
+      do 50 i = mp1,n,5
+        dtemp = dtemp + dx(i)*dy(i) + dx(i + 1)*dy(i + 1) +
+     *   dx(i + 2)*dy(i + 2) + dx(i + 3)*dy(i + 3) + dx(i + 4)*dy(i + 4)
+   50 continue
+   60 ddot = dtemp
+      return
+      end
+c
+      double precision function dasum(n,dx,incx)
+c
+c     takes the sum of the absolute values.
+c     jack dongarra, linpack, 3/11/78.
+c
+      double precision dx(1),dtemp
+      integer i,incx,m,mp1,n,nincx
+c
+      dasum = 0.0d0
+      dtemp = 0.0d0
+      if(n.le.0)return
+      if(incx.eq.1)go to 20
+c
+c        code for increment not equal to 1
+c
+      nincx = n*incx
+      do 10 i = 1,nincx,incx
+        dtemp = dtemp + dabs(dx(i))
+   10 continue
+      dasum = dtemp
+      return
+c
+c        code for increment equal to 1
+c
+c
+c        clean-up loop
+c
+   20 m = mod(n,6)
+      if( m .eq. 0 ) go to 40
+      do 30 i = 1,m
+        dtemp = dtemp + dabs(dx(i))
+   30 continue
+      if( n .lt. 6 ) go to 60
+   40 mp1 = m + 1
+      do 50 i = mp1,n,6
+        dtemp = dtemp + dabs(dx(i)) + dabs(dx(i + 1)) + dabs(dx(i + 2))
+     *  + dabs(dx(i + 3)) + dabs(dx(i + 4)) + dabs(dx(i + 5))
+   50 continue
+   60 dasum = dtemp
+      return
+      end
+
+      subroutine daxpy(n,da,dx,incx,dy,incy)
+c
+c     constant times a vector plus a vector.
+c     uses unrolled loops for increments equal to one.
+c     jack dongarra, linpack, 3/11/78.
+c
+      double precision dx(1),dy(1),da
+      integer i,incx,incy,ix,iy,m,mp1,n
+c
+      if(n.le.0)return
+      if (da .eq. 0.0d0) return
+      if(incx.eq.1.and.incy.eq.1)go to 20
+c
+c        code for unequal increments or equal increments
+c          not equal to 1
+c
+      ix = 1
+      iy = 1
+      if(incx.lt.0)ix = (-n+1)*incx + 1
+      if(incy.lt.0)iy = (-n+1)*incy + 1
+      do 10 i = 1,n
+        dy(iy) = dy(iy) + da*dx(ix)
+        ix = ix + incx
+        iy = iy + incy
+   10 continue
+      return
+c
+c        code for both increments equal to 1
+c
+c
+c        clean-up loop
+c
+   20 m = mod(n,4)
+      if( m .eq. 0 ) go to 40
+      do 30 i = 1,m
+        dy(i) = dy(i) + da*dx(i)
+   30 continue
+      if( n .lt. 4 ) return
+   40 mp1 = m + 1
+      do 50 i = mp1,n,4
+        dy(i) = dy(i) + da*dx(i)
+        dy(i + 1) = dy(i + 1) + da*dx(i + 1)
+        dy(i + 2) = dy(i + 2) + da*dx(i + 2)
+        dy(i + 3) = dy(i + 3) + da*dx(i + 3)
+   50 continue
+      return
+      end
+      double precision function dnrm2 ( n, dx, incx)
+      integer          next
+      double precision   dx(1), cutlo, cuthi, hitest, sum, xmax,zero,one
+      data   zero, one /0.0d0, 1.0d0/
+c
+c     euclidean norm of the n-vector stored in dx() with storage
+c     increment incx .
+c     if    n .le. 0 return with result = 0.
+c     if n .ge. 1 then incx must be .ge. 1
+c
+c           c.l.lawson, 1978 jan 08
+c
+c     four phase method     using two built-in constants that are
+c     hopefully applicable to all machines.
+c         cutlo = maximum of  dsqrt(u/eps)  over all known machines.
+c         cuthi = minimum of  dsqrt(v)      over all known machines.
+c     where
+c         eps = smallest no. such that eps + 1. .gt. 1.
+c         u   = smallest positive no.   (underflow limit)
+c         v   = largest  no.            (overflow  limit)
+c
+c     brief outline of algorithm..
+c
+c     phase 1    scans zero components.
+c     move to phase 2 when a component is nonzero and .le. cutlo
+c     move to phase 3 when a component is .gt. cutlo
+c     move to phase 4 when a component is .ge. cuthi/m
+c     where m = n for x() real and m = 2*n for complex.
+c
+c     values for cutlo and cuthi..
+c     from the environmental parameters listed in the imsl converter
+c     document the limiting values are as follows..
+c     cutlo, s.p.   u/eps = 2**(-102) for  honeywell.  close seconds are
+c                   univac and dec at 2**(-103)
+c                   thus cutlo = 2**(-51) = 4.44089e-16
+c     cuthi, s.p.   v = 2**127 for univac, honeywell, and dec.
+c                   thus cuthi = 2**(63.5) = 1.30438e19
+c     cutlo, d.p.   u/eps = 2**(-67) for honeywell and dec.
+c                   thus cutlo = 2**(-33.5) = 8.23181d-11
+c     cuthi, d.p.   same as s.p.  cuthi = 1.30438d19
+c     data cutlo, cuthi / 8.232d-11,  1.304d19 /
+c     data cutlo, cuthi / 4.441e-16,  1.304e19 /
+      data cutlo, cuthi / 8.232d-11,  1.304d19 /
+c
+      if(n .gt. 0) go to 10
+         dnrm2  = zero
+         go to 300
+c
+   10 assign 30 to next
+      sum = zero
+      nn = n * incx
+c                                                 begin main loop
+      i = 1
+   20    go to next,(30, 50, 70, 110)
+   30 if( dabs(dx(i)) .gt. cutlo) go to 85
+      assign 50 to next
+      xmax = zero
+c
+c                        phase 1.  sum is zero
+c
+   50 if( dx(i) .eq. zero) go to 200
+      if( dabs(dx(i)) .gt. cutlo) go to 85
+c
+c                                prepare for phase 2.
+      assign 70 to next
+      go to 105
+c
+c                                prepare for phase 4.
+c
+  100 i = j
+      assign 110 to next
+      sum = (sum / dx(i)) / dx(i)
+  105 xmax = dabs(dx(i))
+      go to 115
+c
+c                   phase 2.  sum is small.
+c                             scale to avoid destructive underflow.
+c
+   70 if( dabs(dx(i)) .gt. cutlo ) go to 75
+c
+c                     common code for phases 2 and 4.
+c                     in phase 4 sum is large.  scale to avoid overflow.
+c
+  110 if( dabs(dx(i)) .le. xmax ) go to 115
+         sum = one + sum * (xmax / dx(i))**2
+         xmax = dabs(dx(i))
+         go to 200
+c
+  115 sum = sum + (dx(i)/xmax)**2
+      go to 200
+c
+c
+c                  prepare for phase 3.
+c
+   75 sum = (sum * xmax) * xmax
+c
+c
+c     for real or d.p. set hitest = cuthi/n
+c     for complex      set hitest = cuthi/(2*n)
+c
+   85 hitest = cuthi/float( n )
+c
+c                   phase 3.  sum is mid-range.  no scaling.
+c
+      do 95 j =i,nn,incx
+      if(dabs(dx(j)) .ge. hitest) go to 100
+   95    sum = sum + dx(j)**2
+      dnrm2 = dsqrt( sum )
+      go to 300
+c
+  200 continue
+      i = i + incx
+      if ( i .le. nn ) go to 20
+c
+c              end of main loop.
+c
+c              compute square root and adjust for scaling.
+c
+      dnrm2 = xmax * dsqrt(sum)
+  300 continue
+      return
+      end
+
+      subroutine  dscal(n,da,dx,incx)
+c     scales a vector by a constant.
+c     uses unrolled loops for increment equal to one.
+c     jack dongarra, linpack, 3/11/78.
+c
+      double precision da,dx(1)
+      integer i,incx,m,mp1,n,nincx
+c
+      if(n.le.0)return
+      if(incx.eq.1)go to 20
+c
+c        code for increment not equal to 1
+c
+      nincx = n*incx
+      do 10 i = 1,nincx,incx
+        dx(i) = da*dx(i)
+   10 continue
+      return
+c
+c        code for increment equal to 1
+c
+c
+c        clean-up loop
+c
+   20 m = mod(n,5)
+      if( m .eq. 0 ) go to 40
+      do 30 i = 1,m
+        dx(i) = da*dx(i)
+   30 continue
+      if( n .lt. 5 ) return
+   40 mp1 = m + 1
+      do 50 i = mp1,n,5
+        dx(i) = da*dx(i)
+        dx(i + 1) = da*dx(i + 1)
+        dx(i + 2) = da*dx(i + 2)
+        dx(i + 3) = da*dx(i + 3)
+        dx(i + 4) = da*dx(i + 4)
+   50 continue
+      return
+      end
+
+      subroutine  dswap (n,dx,incx,dy,incy)
+c
+c     interchanges two vectors.
+c     uses unrolled loops for increments equal one.
+c     jack dongarra, linpack, 3/11/78.
+c
+      double precision dx(1),dy(1),dtemp
+      integer i,incx,incy,ix,iy,m,mp1,n
+c
+      if(n.le.0)return
+      if(incx.eq.1.and.incy.eq.1)go to 20
+c
+c       code for unequal increments or equal increments not equal
+c         to 1
+c
+      ix = 1
+      iy = 1
+      if(incx.lt.0)ix = (-n+1)*incx + 1
+      if(incy.lt.0)iy = (-n+1)*incy + 1
+      do 10 i = 1,n
+        dtemp = dx(ix)
+        dx(ix) = dy(iy)
+        dy(iy) = dtemp
+        ix = ix + incx
+        iy = iy + incy
+   10 continue
+      return
+c
+c       code for both increments equal to 1
+c
+c
+c       clean-up loop
+c
+   20 m = mod(n,3)
+      if( m .eq. 0 ) go to 40
+      do 30 i = 1,m
+        dtemp = dx(i)
+        dx(i) = dy(i)
+        dy(i) = dtemp
+   30 continue
+      if( n .lt. 3 ) return
+   40 mp1 = m + 1
+      do 50 i = mp1,n,3
+        dtemp = dx(i)
+        dx(i) = dy(i)
+        dy(i) = dtemp
+        dtemp = dx(i + 1)
+        dx(i + 1) = dy(i + 1)
+        dy(i + 1) = dtemp
+        dtemp = dx(i + 2)
+        dx(i + 2) = dy(i + 2)
+        dy(i + 2) = dtemp
+   50 continue
+      return
+      end
+
+      integer function idamax(n,dx,incx)
+c
+c     finds the index of element having max. absolute value.
+c     jack dongarra, linpack, 3/11/78.
+c
+      double precision dx(1),dmax
+      integer i,incx,ix,n
+c
+      idamax = 0
+      if( n .lt. 1 ) return
+      idamax = 1
+      if(n.eq.1)return
+      if(incx.eq.1)go to 20
+c
+c        code for increment not equal to 1
+c
+      ix = 1
+      dmax = dabs(dx(1))
+      ix = ix + incx
+      do 10 i = 2,n
+         if(dabs(dx(ix)).le.dmax) go to 5
+         idamax = i
+         dmax = dabs(dx(ix))
+    5    ix = ix + incx
+   10 continue
+      return
+c
+c        code for increment equal to 1
+c
+   20 dmax = dabs(dx(1))
+      do 30 i = 2,n
+         if(dabs(dx(i)).le.dmax) go to 30
+         idamax = i
+         dmax = dabs(dx(i))
+   30 continue
+      return
+      end
+c
+      subroutine  drot (n,dx,incx,dy,incy,c,s)
+c
+c     applies a plane rotation.
+c     jack dongarra, linpack, 3/11/78.
+c
+      double precision dx(1),dy(1),dtemp,c,s
+      integer i,incx,incy,ix,iy,n
+c
+      if(n.le.0)return
+      if(incx.eq.1.and.incy.eq.1)go to 20
+c
+c       code for unequal increments or equal increments not equal
+c         to 1
+c
+      ix = 1
+      iy = 1
+      if(incx.lt.0)ix = (-n+1)*incx + 1
+      if(incy.lt.0)iy = (-n+1)*incy + 1
+      do 10 i = 1,n
+        dtemp = c*dx(ix) + s*dy(iy)
+        dy(iy) = c*dy(iy) - s*dx(ix)
+        dx(ix) = dtemp
+        ix = ix + incx
+        iy = iy + incy
+   10 continue
+      return
+c
+c       code for both increments equal to 1
+c
+   20 do 30 i = 1,n
+        dtemp = c*dx(i) + s*dy(i)
+        dy(i) = c*dy(i) - s*dx(i)
+        dx(i) = dtemp
+   30 continue
+      return
+      end
+c
+      subroutine drotg(da,db,c,s)
+c
+c     construct givens plane rotation.
+c     jack dongarra, linpack, 3/11/78.
+c
+      double precision da,db,c,s,roe,scale,r,z
+c
+      roe = db
+      if( dabs(da) .gt. dabs(db) ) roe = da
+      scale = dabs(da) + dabs(db)
+      if( scale .ne. 0.0d0 ) go to 10
+         c = 1.0d0
+         s = 0.0d0
+         r = 0.0d0
+         go to 20
+   10 r = scale*dsqrt((da/scale)**2 + (db/scale)**2)
+      r = dsign(1.0d0,roe)*r
+      c = da/r
+      s = db/r
+   20 z = 1.0d0
+      if( dabs(da) .gt. dabs(db) ) z = s
+      if( dabs(db) .ge. dabs(da) .and. c .ne. 0.0d0 ) z = 1.0d0/c
+      da = r
+      db = z
+      return
+      end
+c
+      subroutine  ccopy(n,cx,incx,cy,incy)
+c
+c     copies a vector, x, to a vector, y.
+c     jack dongarra, linpack, 3/11/78.
+c
+      complex cx(1),cy(1)
+      integer i,incx,incy,ix,iy,n
+c
+      if(n.le.0)return
+      if(incx.eq.1.and.incy.eq.1)go to 20
+c
+c        code for unequal increments or equal increments
+c          not equal to 1
+c
+      ix = 1
+      iy = 1
+      if(incx.lt.0)ix = (-n+1)*incx + 1
+      if(incy.lt.0)iy = (-n+1)*incy + 1
+      do 10 i = 1,n
+        cy(iy) = cx(ix)
+        ix = ix + incx
+        iy = iy + incy
+   10 continue
+      return
+c
+c        code for both increments equal to 1
+c
+   20 do 30 i = 1,n
+        cy(i) = cx(i)
+   30 continue
+      return
+      end
+      subroutine  cscal(n,ca,cx,incx)
+c
+c     scales a vector by a constant.
+c     jack dongarra, linpack,  3/11/78.
+c
+      complex ca,cx(1)
+      integer i,incx,n,nincx
+c
+      if(n.le.0)return
+      if(incx.eq.1)go to 20
+c
+c        code for increment not equal to 1
+c
+      nincx = n*incx
+      do 10 i = 1,nincx,incx
+        cx(i) = ca*cx(i)
+   10 continue
+      return
+c
+c        code for increment equal to 1
+c
+   20 do 30 i = 1,n
+        cx(i) = ca*cx(i)
+   30 continue
+      return
+      end
+c
+      subroutine  csrot (n,cx,incx,cy,incy,c,s)
+c
+c     applies a plane rotation, where the cos and sin (c and s) are real
+c     and the vectors cx and cy are complex.
+c     jack dongarra, linpack, 3/11/78.
+c
+      complex cx(1),cy(1),ctemp
+      real c,s
+      integer i,incx,incy,ix,iy,n
+c
+      if(n.le.0)return
+      if(incx.eq.1.and.incy.eq.1)go to 20
+c
+c       code for unequal increments or equal increments not equal
+c         to 1
+c
+      ix = 1
+      iy = 1
+      if(incx.lt.0)ix = (-n+1)*incx + 1
+      if(incy.lt.0)iy = (-n+1)*incy + 1
+      do 10 i = 1,n
+        ctemp = c*cx(ix) + s*cy(iy)
+        cy(iy) = c*cy(iy) - s*cx(ix)
+        cx(ix) = ctemp
+        ix = ix + incx
+        iy = iy + incy
+   10 continue
+      return
+c
+c       code for both increments equal to 1
+c
+   20 do 30 i = 1,n
+        ctemp = c*cx(i) + s*cy(i)
+        cy(i) = c*cy(i) - s*cx(i)
+        cx(i) = ctemp
+   30 continue
+      return
+      end
+      subroutine  cswap (n,cx,incx,cy,incy)
+c
+c     interchanges two vectors.
+c     jack dongarra, linpack, 3/11/78.
+c
+      complex cx(1),cy(1),ctemp
+      integer i,incx,incy,ix,iy,n
+c
+      if(n.le.0)return
+      if(incx.eq.1.and.incy.eq.1)go to 20
+c
+c       code for unequal increments or equal increments not equal
+c         to 1
+c
+      ix = 1
+      iy = 1
+      if(incx.lt.0)ix = (-n+1)*incx + 1
+      if(incy.lt.0)iy = (-n+1)*incy + 1
+      do 10 i = 1,n
+        ctemp = cx(ix)
+        cx(ix) = cy(iy)
+        cy(iy) = ctemp
+        ix = ix + incx
+        iy = iy + incy
+   10 continue
+      return
+c
+c       code for both increments equal to 1
+   20 do 30 i = 1,n
+        ctemp = cx(i)
+        cx(i) = cy(i)
+        cy(i) = ctemp
+   30 continue
+      return
+      end
+      subroutine  csscal(n,sa,cx,incx)
+c
+c     scales a complex vector by a real constant.
+c     jack dongarra, linpack, 3/11/78.
+c
+      complex cx(1)
+      real sa
+      integer i,incx,n,nincx
+c
+      if(n.le.0)return
+      if(incx.eq.1)go to 20
+c
+c        code for increment not equal to 1
+c
+      nincx = n*incx
+      do 10 i = 1,nincx,incx
+        cx(i) = cmplx(sa*real(cx(i)),sa*aimag(cx(i)))
+   10 continue
+      return
+c
+c        code for increment equal to 1
+c
+   20 do 30 i = 1,n
+        cx(i) = cmplx(sa*real(cx(i)),sa*aimag(cx(i)))
+   30 continue
+      return
+      end
+
diff --git a/UNSUPP/MATEXP/README b/UNSUPP/MATEXP/README
new file mode 100644
index 0000000..f2119e0
--- /dev/null
+++ b/UNSUPP/MATEXP/README
@@ -0,0 +1,20 @@
+
+ SUBDIRECTORY MATEXP 
+ -------------------
+ routines related to matrix exponentials. 
+
+ contents:
+---------- 
+ exppro.f    computes exp( t A) v
+ rexp.f      a simple test program for exppro.f
+ phipro.f    solves y'= A y + b
+ rphi.f      a simple test program for phipro.f
+ makefile    makefile for the test problems. make exp.ex will make
+             an executable for exppro, make phi.ex will test program for
+             phipro.f
+
+
+ feedback appreciated.  BEWARE: DOCUMENTATION MAY BE INACCURATE -
+ ---------------------  VERY LITTLE TESTING DONE WITH PHIPRO.F -- 
+                        
+
diff --git a/UNSUPP/MATEXP/exppro.f b/UNSUPP/MATEXP/exppro.f
new file mode 100644
index 0000000..8d46ba0
--- /dev/null
+++ b/UNSUPP/MATEXP/exppro.f
@@ -0,0 +1,593 @@
+      subroutine expprod (n, m, eps, tn, u, w, x, y, a, ioff, ndiag)
+      real*8 eps, tn 
+      real*8 a(n,ndiag), u(n,m+1), w(n), x(n), y(n)
+      integer n, m, ndiag, ioff(ndiag)
+
+c-----------------------------------------------------------------------
+c this subroutine computes an approximation to the vector
+c
+c        	w :=  exp( - A * tn ) * w
+c
+c for matrices stored in diagonal (DIA) format.
+c
+c this routine constitutes an interface for the routine exppro for
+c matrices stored in diagonal (DIA) format.
+c-----------------------------------------------------------------------
+c ARGUMENTS
+c---------- 
+c see exppro for meaning of parameters n, m, eps, tn, u, w, x, y.
+c 
+c a, ioff, and ndiag are the arguments of the matrix:
+c
+c a(n,ndiag) = a rectangular array with a(*,k) containing the diagonal 
+c              offset by ioff(k) (negative or positive or zero), i.e., 
+c              a(i,jdiag) contains the element A(i,i+ioff(jdiag)) in 
+c              the usual dense storage scheme.
+c 
+c ioff	     = integer array containing the offsets  of the ndiag diagonals
+c ndiag      = integer. the number of diagonals.
+c 
+c-----------------------------------------------------------------------
+c local variables 
+c 
+      integer indic, ierr
+
+      indic = 0
+ 101  continue
+      call exppro (n, m, eps, tn, u, w, x, y, indic, ierr) 
+      if (indic .eq. 1) goto 102
+c     
+c     matrix vector-product for diagonal storage --
+c     
+      call oped(n, x, y, a, ioff, ndiag)
+      goto 101
+ 102  continue
+      return
+      end
+c----------end-of-expprod-----------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine exppro (n, m, eps, tn, u, w, x, y, indic, ierr)
+c     implicit  real*8 (a-h,o-z)
+      integer n, m, indic, ierr
+      real*8 eps, tn, u(n,m+1), w(n), x(n), y(n) 
+c-----------------------------------------------------------------------
+c     
+c this subroutine computes an approximation to the vector
+c
+c        	w :=  exp( - A * tn ) * w
+c
+c where A is an arbitary matrix and w is a given input vector 
+c uses a dynamic estimation of internal time advancement (dt) 
+c----------------------------------------------------------------------- 
+c THIS IS A REVERSE COMMUNICATION IMPLEMENTATION. 
+c------------------------------------------------- 
+c USAGE: (see also comments on indic below).
+c------ 
+c
+c      indic = 0
+c 1    continue
+c      call exppro (n, m, eps, tn, u, w, x, y, indic)
+c      if (indic .eq. 1) goto 2 <-- indic .eq. 1 means job is finished
+c      call matvec(n, x, y)     <--- user's matrix-vec. product
+c                                    with x = input vector, and
+c                                     y = result = A * x.
+c      goto 1
+c 2    continue
+c      .....
+c
+c-----------------------------------------------------------------------
+c
+c en entry:
+c---------- 
+c n	= dimension of matrix
+c
+c m	= dimension of Krylov subspace (= degree of polynomial 
+c         approximation to the exponential used. )
+c
+c eps   = scalar indicating the relative error tolerated for the result. 
+c         the code will try to compute an answer such that 
+c         norm2(exactanswer-approximation) / norm2(w) .le. eps 
+c
+c tn	= scalar by which to multiply matrix. (may be .lt. 0)
+c         the code will compute an approximation to exp(- tn * A) w
+c         and overwrite the result onto w.
+c
+c u	= work array of size n*(m+1) (used to hold the Arnoldi basis )
+c
+c w	= real array of length n = input vector to  which exp(-A) is
+c         to be applied. this is also an output argument 
+c
+c x, y  = two real work vectors of length at least  n each. 
+c         see indic for usage.
+c
+c indic = integer used as indicator for the reverse communication.
+c         in the first call enter indic = 0. See below for more.
+c
+c on return:
+c-----------
+c 
+c w     = contains the resulting vector exp(-A * tn ) * w when 
+c         exppro has finished (see indic) 
+c
+c indic = indicator for the reverse communication protocole.
+c       * INDIC .eq. 1  means that exppro has finished and w contains the
+c         result. 
+c       * INDIC .gt. 1 ,  means that exppro has not finished and that
+c         it is requesting another matrix vector product before
+c         continuing. The user must compute Ax where A is the matrix
+c         and x is the vector provided by exppro, and return the 
+c         result in y. Then exppro must be called again without
+c         changing any other argument. typically this must be
+c         implemented in a loop with exppro being called as long
+c         indic is returned with a value .ne. 1.
+c
+c ierr  = error indicator. 
+c         ierr = 1 means phipro was called with indic=1 (not allowed)
+c         ierr = -1 means that the input is zero the solution has been 
+c         unchanged.
+c 
+c NOTES:  m should not exceed 60 in this version  (see mmax below)
+c-----------------------------------------------------------------------
+c written by Y. Saad -- version feb, 1991.
+c----------------------------------------------------------------------- 
+c For reference see following papers : 
+c (1) E. Gallopoulos and Y. Saad: Efficient solution of parabolic 
+c     equations by Krylov approximation methods. RIACS technical
+c     report 90-14.
+c (2) Y.Saad: Analysis of some Krylov subspace approximations to the
+c     matrix exponential operator. RIACS Tech report. 90-14 
+c-----------------------------------------------------------------------
+c local variables 
+c 
+      integer mmax
+      parameter (mmax=60) 
+      real*8 errst, tcur, told, dtl, beta, red, dabs, dble
+      real*8 hh(mmax+2,mmax+1), z(mmax+1)
+      complex*16   wkc(mmax+1) 
+      integer ih, job
+      logical verboz
+      data verboz/.true./
+      save
+c-----------------------------------------------------------------------
+c indic = 3  means  passing through only with result of y= Ax to exphes
+c indic = 2  means exphes has finished its job
+c indic = 1  means exppro has finished its job (real end)/
+c-----------------------------------------------------------------------
+      ierr = 0 
+      if (indic .eq. 3) goto 101
+      if (indic .eq. 1) then 
+         ierr = 1
+         return
+      endif
+c----- 
+      ih = mmax 
+      m  = min0(m,mmax) 
+      tcur = 0.0d0
+      dtl = tn-tcur
+      job = -1
+c-------------------- outer loop ----------------------------- 
+ 100  continue
+      if(verboz) print *,'In EXPPRO, current time = ', tcur ,'---------'
+c------------------------------------------------------------- 
+c ---- call exponential propagator --------------------------- 
+c------------------------------------------------------------- 
+      told = tcur 
+ 101  continue
+c     if (told + dtl .gt. tn) dtl = tn-told
+      call  exphes (n,m,dtl,eps,u,w,job,z,wkc,beta,errst,hh,ih,
+     *              x,y,indic,ierr) 
+c-----------------------------------------------------------------------
+      if (ierr .ne. 0) return
+      if (indic .ge. 3) return
+      tcur = told + dtl 
+      if(verboz) print *, ' tcur now = ', tcur, ' dtl = ', dtl
+c
+c     relative error 
+c      if(verboz) print *, ' beta', beta
+      errst = errst / beta
+c---------
+      if ((errst .le. eps) .and. ( (errst .gt. eps/100.0) .or.
+     *     (tcur .eq. tn))) goto 102
+c     
+c     use approximation :  [ new err ] = fact**m  * [cur. error]
+c     
+      red =  (0.5*eps / errst)**(1.0d0 /dble(m) ) 
+      dtl = dtl*red 
+      if (dabs(told+dtl) .gt. dabs(tn) )  dtl = tn-told
+      if(verboz) print *, ' red =',red,' , reducing dt to: ', dtl
+c-------
+      job = 1 
+      goto 101
+c-------
+ 102  continue 
+c
+      call project(n,m,u,z,w)
+c never go beyond tcur
+      job = 0
+      dtl = dmin1(dtl, tn-tcur)
+      if (dabs(tcur+dtl) .gt. dabs(tn)) dtl = tn-tcur 
+      if (dabs(tcur) .lt. dabs(tn)) goto 100
+      indic = 1
+c
+      return
+      end
+c----------end-of-expro-------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine exphes (n,m,dt,eps,u,w,job,z,wkc,beta,errst,hh,ih,
+     *                   x, y, indic,ierr) 
+c     implicit  real*8 (a-h,o-z)
+      integer n, m, job, ih, indic, ierr
+      real*8 hh(ih+2,m+1), u(n,m+1), w(n), z(m+1), x(n), y(n)
+      complex*16 wkc(m+1) 
+      real*8 dt, eps, beta, errst
+c-----------------------------------------------------------------------
+c this subroutine computes the Arnoldi basis and the corresponding 
+c coeffcient vector in the approximation 
+c 
+c        	w  ::= beta  Vm  ym 
+c               where ym = exp(- Hm *dt) * e1
+c
+c to the vector exp(-A dt) w where A is an arbitary matrix and 
+c w is a given input vector. In case job = 0 the arnoldi basis 
+c is recomputed. Otherwise the
+c code assumes assumes that  u(*) contains an already computed 
+c arnoldi basis and computes only the y-vector (which is stored in v(*))
+c-----------------------------------------------------------------------
+c on entry:
+c---------- 
+c n	= dimension of matrix
+c
+c m	= dimension of Krylov subspace (= degree of polynomial 
+c         approximation to the exponential used. )
+c
+c dt	= scalar by which to multiply matrix. Can be viewed
+c         as a time step. dt must be positive [to be fixed].
+c
+c eps   = scalar indicating the relative error tolerated for the result. 
+c         the code will try to compute an answer such that 
+c         norm2(exactanswer-approximation) / norm2(w) .le. eps 
+c
+c u	= work array of size n*(m+1) to contain the Arnoldi basis
+c
+c w	= real array of length n = input vector to  which exp(-A) is
+c         to be applied. 
+c
+c job	= integer. job indicator. If job .lt.  0 then the Arnoldi
+c         basis is recomputed. If job .gt. 0 then it is assumed
+c         that the user wants to use a previously computed Krylov
+c         subspace but a different dt. Thus the Arnoldi basis and
+c         the Hessenberg matrix Hm are not recomputed. 
+c	  In that case the user should not modify the values of beta
+c         and the matrices hh and u(n,*) when recalling phipro. 
+c         job = -1 : recompute basis and get an initial estimate for 
+c                    time step dt to be used.
+c         job = 0  : recompute basis and do not alter dt.
+c         job = 1  : do not recompute arnoldi basis. 
+c
+c z     = real work array of  size (m+1)
+c wkc   = complex*16 work array of size (m+1) 
+c
+c hh    = work array of size size at least (m+2)*(m+1)
+c
+c ih+2	= first dimension of hh as declared in the calling program.
+c         ih must be .ge. m.
+c 
+c-----------------------------------------------------------------------
+c on return:
+c-----------
+c w2	= resulting vector w2 = exp(-A *dt) * w
+c beta  = real equal to the 2-norm of w. Needed if exppro will
+c         be recalled with the same Krylov subspace and a different dt. 
+c errst = rough estimates of the 2-norm of the error.
+c hh	= work array of dimension at least (m+2) x (m+1)
+c
+c----------------------------------------------------------------------- 
+c local variables 
+c 
+      integer ndmax
+      parameter (ndmax=20) 
+      real*8 alp0, fnorm, t, rm, ddot, dabs, dsqrt, dsign,dble
+      complex*16 alp(ndmax+1), rd(ndmax+1)
+      integer i, j, k, ldg, i0, i1, m1 
+      logical verboz
+      data verboz/.true./
+      save
+c------use degree 14 chebyshev all the time -------------------------- 
+      if (indic .ge. 3) goto 60
+c
+c------input fraction expansion of rational function ------------------ 
+c chebyshev (14,14) 
+      ldg= 7
+      alp0 =  0.183216998528140087E-11
+      alp(1)=( 0.557503973136501826E+02,-0.204295038779771857E+03)
+      rd(1)=(-0.562314417475317895E+01, 0.119406921611247440E+01)
+      alp(2)=(-0.938666838877006739E+02, 0.912874896775456363E+02)
+      rd(2)=(-0.508934679728216110E+01, 0.358882439228376881E+01)
+      alp(3)=( 0.469965415550370835E+02,-0.116167609985818103E+02)
+      rd(3)=(-0.399337136365302569E+01, 0.600483209099604664E+01)
+      alp(4)=(-0.961424200626061065E+01,-0.264195613880262669E+01)
+      rd(4)=(-0.226978543095856366E+01, 0.846173881758693369E+01)
+      alp(5)=( 0.752722063978321642E+00, 0.670367365566377770E+00)
+      rd(5)=( 0.208756929753827868E+00, 0.109912615662209418E+02)
+      alp(6)=(-0.188781253158648576E-01,-0.343696176445802414E-01)
+      rd(6)=( 0.370327340957595652E+01, 0.136563731924991884E+02)
+      alp(7)=( 0.143086431411801849E-03, 0.287221133228814096E-03)
+      rd(7)=( 0.889777151877331107E+01, 0.166309842834712071E+02)
+c-----------------------------------------------------------------------
+c     
+c     if job .gt. 0 skip arnoldi process:
+c     
+      if (job .gt. 0) goto 2
+c------normalize vector w and put in first column of u -- 
+      beta = dsqrt(ddot(n,w,1,w,1)) 
+c-----------------------------------------------------------------------
+      if(verboz) print *, ' In EXPHES, beta ', beta 
+      if (beta .eq. 0.0d0) then
+         ierr = -1 
+         indic = 1
+         return
+      endif
+c
+      t = 1.0d0/beta 
+      do 25 j=1, n
+         u(j,1) = w(j)*t 
+ 25   continue
+c------------------Arnoldi loop ------------------------------------- 
+c      fnorm = 0.0d0
+      i1 = 1
+ 58   i = i1
+      i1 = i + 1
+      do 59 k=1, n
+         x(k) = u(k,i)
+ 59   continue
+      indic = 3
+      return
+ 60   continue
+      do 61 k=1, n
+         u(k,i1) = y(k) 
+ 61   continue
+      i0 =1
+c     
+c switch  for Lanczos version 
+c     i0 = max0(1, i-1)
+      call mgsr (n, i0, i1, u, hh(1,i))
+      fnorm = fnorm + ddot(i1, hh(1,i),1, hh(1,i),1)
+      if (hh(i1,i) .eq. 0.0) m = i
+      if  (i .lt. m) goto 58
+c--------------done with arnoldi loop ---------------------------------
+      rm = dble(m) 
+      fnorm = dsqrt( fnorm / rm )
+c-------get  : beta*e1 into z 
+      m1 = m+1 
+      do 4 i=1,m1
+         hh(i,m1) = 0.0
+ 4    continue
+c
+c     compute initial dt when  job .lt. 1 
+c
+      if (job .ge. 0) goto 2 
+c
+c     t = eps / beta 
+c     
+      t = eps 
+      do 41 k=1, m-1
+         t = t*(1.0d0 - dble(m-k)/rm ) 
+ 41   continue
+c
+      t = 2.0d0*rm* (t**(1.0d0/rm) )  / fnorm 
+      if(verboz) print *, ' t, dt = ', t, dt
+      t = dmin1(dabs(dt),t) 
+      dt = dsign(t, dt) 
+c     
+ 2    continue 
+      z(1) = beta 
+      do 3 k=2, m1
+         z(k) = 0.0d0 
+ 3    continue
+c-------get  : exp(H) * beta*e1
+      call hes(ldg,m1,hh,ih,dt,z,rd,alp,alp0,wkc)
+c-------error estimate 
+      errst = dabs(z(m1))
+      if(verboz) print *, ' error estimate =', errst 
+c-----------------------------------------------------------------------
+      indic = 2
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine mgsr (n, i0, i1, ss, r)
+c     implicit  real*8 (a-h,o-z)
+      integer n, i0, i1
+      real*8 ss(n,i1), r(i1)
+c-----------------------------------------------------------------------
+c modified gram - schmidt  with  partial  reortho. the vector ss(*,i1) is
+c orthogonalized against the first i vectors  of ss  (which  are  already
+c orthogonal).  the coefficients of the orthogonalization are returned in
+c the array r
+c------------------------------------------------------------------------
+c local variables 
+c 
+      integer i, j, k, it
+      real*8 hinorm, tet, ddot, t, dsqrt
+      data  tet/10.0d0/
+
+      do 53 j=1, i1
+         r(j) = 0.0d0
+ 53   continue
+      i = i1-1
+      it = 0
+ 54   hinorm = 0.0d0
+      it = it +1
+      if (i .eq. 0) goto 56
+c     
+      do 55 j=i0, i
+         t = ddot(n, ss(1,j),1,ss(1,i1),1)
+         hinorm = hinorm + t**2
+         r(j) = r(j) + t
+         call daxpy(n,-t,ss(1,j),1,ss(1,i1),1)
+ 55   continue
+      t = ddot(n, ss(1,i1), 1, ss(1,i1), 1)
+ 56   continue
+c     
+c     test for reorthogonalization see daniel et. al.
+c     two reorthogonalization allowed ---
+c     
+      if (t*tet .le. hinorm .and. it .lt. 2) goto 54
+      t =dsqrt(t)
+      r(i1)= t
+      if (t .eq. 0.0d0) return
+      t = 1.0d0/t
+      do 57  k=1,n
+         ss(k,i1) = ss(k,i1)*t
+ 57   continue
+      return
+      end
+c----------end-of-mgsr--------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine project(n,m,u,v,w)
+      integer n, m
+      real*8 u(n,m), v(m), w(n)
+c
+c     computes the vector w = u * v
+c
+c local variables 
+c
+      integer j, k
+
+      do 1 k=1,n
+         w(k) = 0.d0
+ 1    continue
+
+      do 100 j=1,m
+         do 99 k=1,n
+            w(k) = w(k) + v(j) * u(k,j) 
+ 99      continue
+ 100  continue
+      return
+      end
+c-----------------------------------------------------------------------     
+      subroutine hes (ndg,m1,hh,ih,dt,y,root,coef,coef0,w2)
+c     implicit  real*8 (a-h,o-z)
+      integer ndg, m1, ih 
+      real*8 hh(ih+2,m1), y(m1)
+      complex*16   coef(ndg), root(ndg), w2(m1)
+      real*8 dt, coef0
+c--------------------------------------------------------------------  
+c computes exp ( H dt) * y    (1)
+c where H = Hessenberg matrix (hh)
+c y	  = arbitrary vector.
+c ----------------------------
+c ndg	= number of poles as determined by getrat
+c m1    = dimension of hessenberg matrix
+c hh	= hessenberg matrix (real)
+c ih+2	= first dimension of hh
+c dt	= scaling factor used for hh (see (1)) 
+c y	= real vector. on return exp(H dt ) y is computed
+c         and overwritten on y.
+c root  = poles of the rational approximation to exp as
+c         computed by getrat
+c coef, 
+c coef0 = coefficients of partial fraction expansion 
+c         
+c  exp(t) ~ coef0 +  sum     Real [   coef(i) / (t - root(i)  ]
+c                  i=1,ndg  
+c
+c valid for real t.
+c coef0 is real, coef(*) is a complex array.
+c
+c--------------------------------------------------------------------  
+c local variables 
+c
+      integer m1max
+      parameter (m1max=61) 
+      complex*16 hloc(m1max+1,m1max), t, zpiv, dcmplx
+      real*8 yloc(m1max), dble
+      integer i, j, ii
+c     
+c      if (m1 .gt. m1max) print *, ' *** ERROR : In HES, M+1 TOO LARGE'
+c     
+c     loop associated with the poles.
+c     
+      do 10 j=1,m1
+         yloc(j) = y(j)
+         y(j)    = y(j)*coef0
+ 10   continue
+c     
+      do 8 ii = 1, ndg
+c     
+c     copy Hessenberg matrix into temporary
+c     
+         do 2 j=1, m1
+            do 1 i=1, j+1
+               hloc(i,j) = dcmplx( dt*hh(i,j) )
+ 1          continue
+            hloc(j,j) = hloc(j,j) - root(ii) 
+            w2(j)     = dcmplx(yloc(j)) 
+ 2       continue 
+c
+c forward solve 
+c 
+         do 4 i=2,m1
+            zpiv  = hloc(i,i-1) / hloc(i-1,i-1)
+            do 3 j=i,m1
+               hloc(i,j) = hloc(i,j) - zpiv*hloc(i-1,j)
+ 3          continue
+            w2(i)     = w2(i) - zpiv*w2(i-1)
+ 4       continue 
+c     
+c     backward solve
+c     
+         do 6 i=m1,1,-1 
+            t=w2(i)
+            do 5 j=i+1,m1
+               t = t-hloc(i,j)*w2(j)
+ 5          continue
+            w2(i) = t/hloc(i,i)
+ 6       continue
+c     
+c     accumulate result in y.
+c     
+         do 7 i=1,m1
+            y(i) = y(i) + dble ( coef(ii) * w2(i) ) 
+ 7       continue
+ 8    continue
+      return
+      end
+c----------end-of-hes---------------------------------------------------
+c----------------------------------------------------------------------- 
+      subroutine daxpy(n,t,x,indx,y,indy)
+      integer n, indx, indy
+      real*8 x(n), y(n), t
+c-------------------------------------------------------------------
+c does the following operation
+c y <--- y + t * x ,   (replace by the blas routine daxpy )
+c indx and indy are supposed to be one here
+c-------------------------------------------------------------------
+       integer k
+
+       do 1 k=1,n
+          y(k) = y(k) + x(k)*t
+1      continue
+       return
+       end
+c----------end-of-daxpy-------------------------------------------------
+c----------------------------------------------------------------------- 
+       function ddot(n,x,ix,y,iy)
+       integer n, ix, iy
+       real*8 ddot, x(n), y(n)
+c-------------------------------------------------------------------
+c computes the inner product t=(x,y) -- replace by blas routine ddot
+c-------------------------------------------------------------------
+       integer j
+       real*8 t
+
+       t = 0.0d0
+       do 10 j=1,n
+          t = t + x(j)*y(j)
+10     continue
+       ddot=t
+       return
+       end
+c----------end-of-ddot--------------------------------------------------
+c----------------------------------------------------------------------- 
+
+
diff --git a/UNSUPP/MATEXP/makefile b/UNSUPP/MATEXP/makefile
new file mode 100644
index 0000000..279b29a
--- /dev/null
+++ b/UNSUPP/MATEXP/makefile
@@ -0,0 +1,14 @@
+FFLAGS = 
+F77 = f77
+
+#F77 = cf77
+#FFLAGS = -Wf"-dp"
+
+FILES1 = rexp.o exppro.o 
+FILES2 = rphi.o phipro.o 
+
+exp.ex:		$(FILES1)
+	$(F77) $(FFLAGS) $(FILES1) -o exp.ex  
+
+phi.ex:		$(FILES2)
+	$(F77) $(FFLAGS) $(FILES2) -o phi.ex  
diff --git a/UNSUPP/MATEXP/phipro.f b/UNSUPP/MATEXP/phipro.f
new file mode 100644
index 0000000..c699469
--- /dev/null
+++ b/UNSUPP/MATEXP/phipro.f
@@ -0,0 +1,640 @@
+      subroutine phiprod (n, m, eps, tn, u, w, r, x, y, a, ioff, ndiag)
+      real*8 eps, tn 
+      real*8 a(n,ndiag), u(n,m+1), w(n), r(n), x(n), y(n)
+      integer n, m, ndiag, ioff(ndiag)
+
+c-----------------------------------------------------------------------
+c this subroutine computes an approximation to the vector
+c
+c   	w(tn) = w(t0) + tn *  phi( - A * tn ) * (r - A w(t0))
+c
+c where phi(z) = (1-exp(z)) / z
+c 
+c i.e. solves   dw/dt = - A w + r in [t0,t0+ tn] (returns only w(t0+tn))
+c 
+c for matrices stored in diagonal (DIA) format.
+c
+c this routine constitutes an interface for the routine phipro for
+c matrices stored in diagonal (DIA) format. The phipro routine uses
+c reverse communication and as a result does not depend on any
+c data structure of the matrix.
+
+c-----------------------------------------------------------------------
+c ARGUMENTS
+c---------- 
+c see phipro for meaning of parameters n, m, eps, tn, u, w, x, y.
+c 
+c a, ioff, and ndiag are the arguments of the matrix:
+c
+c a(n,ndiag) = a rectangular array with a(*,k) containing the diagonal 
+c              offset by ioff(k) (negative or positive or zero), i.e., 
+c              a(i,jdiag) contains the element A(i,i+ioff(jdiag)) in 
+c              the usual dense storage scheme.
+c 
+c ioff	     = integer array containing the offsets  of the ndiag diagonals
+c ndiag      = integer. the number of diagonals.
+c 
+c-----------------------------------------------------------------------
+c local variables 
+c 
+      integer indic, ierr
+
+      indic = 0
+ 101  continue
+      call phipro (n, m, eps, tn, w, r, u, x, y, indic, ierr)
+      if (indic .eq. 1) goto 102
+c     
+c     matrix vector-product for diagonal storage --
+c     
+      call oped(n, x, y, a, ioff, ndiag)
+      goto 101
+ 102  continue
+      return
+      end
+c----------end-of-phiprod----------------------------------------------- 
+c-----------------------------------------------------------------------
+      subroutine phipro (n, m, eps, tn, w, r, u, x, y, indic, ierr)
+c     implicit  real*8 (a-h,o-z)
+      integer n, m, indic, ierr
+      real*8 eps, tn, w(n), r(n), u(n,m+1), x(n), y(n) 
+c-----------------------------------------------------------------------
+c
+c this subroutine computes an approximation to the vector
+c
+c     w(tn) = w(t0) + tn *  phi( - A * tn ) * (r - A w(t0))
+c     where phi(z) = (1-exp(z)) / z
+c 
+c     i.e. solves dw/dt=-Aw+r in [t0,t0+tn] (returns w(t0+tn))
+c     t0 need not be known.
+c 
+c note that for w(t0)=0 the answer is    w=tn *phi(-tn * A) r
+c in other words this allows to compute phi(A tn) v. 
+c This code will work well only for cases where eigenvalues are
+c real (or nearly real) and positive. It has also been coded to 
+c work for cases where tn .lt. 0.0 (and A has real negative spectrum)
+c 
+c----------------------------------------------------------------------- 
+c
+c THIS IS A REVERSE COMMUNICATION IMPLEMENTATION. 
+c------------------------------------------------- 
+c USAGE: (see also comments on argument indic below).
+c------ 
+c
+c      indic = 0
+c 1    continue
+c      call phipro (n, m, eps, tn, u, w, x, y, indic)
+c      if (indic .eq. 1) goto 2 <-- indic .eq. 1 means phipro has finished
+c      call matvec(n, x, y)     <--- user's matrix-vec. product
+c                                    with x = input vector, and
+c                                     y = result = A * x.
+c      goto 1
+c 2    continue
+c      .....
+c
+c-----------------------------------------------------------------------
+c
+c en entry:
+c---------- 
+c n	= dimension of matrix
+c
+c m	= dimension of Krylov subspace (= degree of polynomial 
+c         approximation to the exponential used. )
+c
+c eps   = scalar indicating the relative error tolerated for the result. 
+c         the code will try to compute an answer such that 
+c         norm2(exactanswer-approximation) / norm2(w) .le. eps 
+c
+c tn	= scalar by which to multiply matrix. (may be .lt. 0)
+c         the code will compute a solution to dw/dt = -A w + r,
+c         and overwrite the result w(tn) onto in w.
+c
+c w	= real array of length n. Initial condition for the ODE system
+c         on input, result w(tn) on output (input and output argument) 
+c
+c r     = real array of length n. the constant term in the system 
+c         dw/dt = -A w + r to be solved.
+c
+c u	= work array of size n*(m+1) (used to hold the Arnoldi basis )
+c
+c x, y  = two real work vectors of length n each. x and y are used to
+c         carry the input and output vectors for the matrix-vector
+c         products y=Ax in the reverse communication protocole.
+c         see argument indic (return) below for details on their usage.
+c
+c indic = integer used as indicator for the reverse communication.
+c         in the first call enter indic = 0.
+c
+c ierr  = error indicator. 
+c         ierr = 1 means phipro was called with indic=1 (not allowed)
+c         ierr = -1 means that the input is zero the solution has been 
+c         unchanged.
+c 
+c on return:
+c-----------
+c 
+c w     = contains the result w(tn)=w(t0)+tn*phi(-A*tn)*(r-Aw(t0))
+c         when phipro has finished (as indicated by indic see below)
+c
+c indic = indicator for the reverse communication protocole.
+c       * INDIC .eq. 1  means that phipro has finished and w contains the
+c         result. 
+c       * INDIC .gt. 1 means that phipro has not finished and that 
+c         it is requesting another matrix vector product before
+c         continuing. The user must compute Ax where A is the matrix
+c         and x is the vector provided by phipro and return the 
+c         result in y. Then phipro must be called again without
+c         changing any other argument. typically this is best 
+c         implemented in a loop with phipro being called as long
+c         indic is returned with a value .ne. 1.
+c 
+c NOTES:  m should not exceed 60 in this version  (see mmax below)
+c-----------------------------------------------------------------------
+c local variables 
+c 
+      integer mmax
+      parameter (mmax=60) 
+      real*8 errst, tcur, told, dtl, beta, red, dabs, dble
+      real*8 hh(mmax+2,mmax+1), z(mmax+1)
+      complex*16   wkc(mmax+1) 
+      integer ih, k, job
+      logical verboz
+      data verboz/.true./
+      save
+c-----------------------------------------------------------------------
+c indic = 4  means  getting y=Ax needed in phipro 
+c indic = 3  means  passing through only with result of y= Ax to phihes
+c indic = 2  means phihes has finished its job
+c indic = 1  means phipro has finished its job (real end)/
+c-----------------------------------------------------------------------
+      ierr = 0 
+      if (indic .eq. 3) goto 101 
+      if (indic .eq. 4) goto 11
+      if (indic .eq. 1) then 
+         ierr = 1
+         return
+      endif
+c----- 
+      ih = mmax 
+      m  = min0(m,mmax) 
+      tcur = 0.0d0
+      dtl = tn - tcur
+      job = -1
+c-------------------- outer loop ----------------------------- 
+ 100  continue
+      if(verboz) print *,'In PHIPRO, current time = ', tcur ,'---------'
+c------------------------------------------------------------- 
+c ---- call phionential propagator --------------------------- 
+c------------------------------------------------------------- 
+      told = tcur 
+c
+c     if (told + dtl .gt. tn) dtl = tn-told
+c      construct initial vector for Arnoldi:  r - A w(old) 
+c
+      do 10 k=1, n
+         x(k) = w(k)
+ 10   continue
+      indic = 4
+      return
+ 11   continue
+      do 12 k=1, n
+         u(k,1) = r(k) - y(k)
+ 12   continue
+c
+ 101  continue
+      call phihes (n,m,dtl,eps,u,job,z,wkc,beta,errst,hh,ih,x, y,indic,
+     *            ierr) 
+c-----------------------------------------------------------------------
+      if (ierr .ne. 0) return
+      if (indic .eq. 3) return
+      tcur = told + dtl 
+      if(verboz) print *, ' tcur now = ', tcur, ' dtl = ', dtl
+c
+c     relative error 
+c      if(verboz) print *, ' beta', beta
+      errst = errst / beta
+c---------
+      if ((errst .le. eps) .and. ( (errst .gt. eps/100.0) .or.
+     *     (tcur .eq. tn))) goto 102
+c
+c     use approximation :  [ new err ] = fact**m  * [cur. error]
+c 
+      red =  (0.5*eps / errst)**(1.0d0 /dble(m) ) 
+      dtl = dtl*red
+      if (dabs(told+dtl) .gt. dabs(tn) )  dtl = tn-told
+      if(verboz) print *, ' red =',red,' , reducing dt to: ', dtl
+c-------
+      job = 1 
+      goto 101
+c-------
+ 102  continue 
+c
+      call project(n, m, w, dtl, u, z) 
+c never go beyond tcur
+      job = 0
+      dtl = dmin1(dtl, tn-tcur)
+      if (dabs(tcur+dtl) .gt. dabs(tn)) dtl = tn-tcur 
+      if (dabs(tcur) .lt. dabs(tn)) goto 100
+      indic = 1
+      return
+      end
+c----------end-of-phipro------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine phihes (n,m,dt,eps,u,job,z,wkc,beta,errst,hh,ih,
+     *                   x, y, indic,ierr) 
+c     implicit  real*8 (a-h,o-z)
+      integer n, m, job, ih, indic, ierr
+      real*8 hh(ih+2,m+1), u(n,m+1), z(m+1), x(n), y(n)
+      complex*16 wkc(m+1) 
+      real*8 dt, eps, beta, errst
+c-----------------------------------------------------------------------
+c this subroutine computes the Arnoldi basis Vm and the corresponding 
+c coeffcient vector ym in the approximation 
+c 
+c        	w  ::= beta  Vm  ym 
+c               where ym = phi(- Hm * dt) * e1
+c
+c to the vector phi(-A * dt) w where A is an arbitary matrix and 
+c w is a given input vector. The phi function is defined   by
+c               phi(z) = (1 - exp(z) ) / z  
+c 
+c In case job .lt.0 the arnoldi basis is recomputed. Otherwise the
+c code assumes assumes that  u(*) contains an already computed 
+c arnoldi basis and computes only the y-vector (which is stored in
+c v(*)). Three different options are available through the argument job. 
+c-----------------------------------------------------------------------
+c on entry:
+c---------- 
+c n	= dimension of matrix
+c
+c m	= dimension of Krylov subspace (= degree of polynomial 
+c         approximation to the phionential used. )
+c
+c dt	= scalar by which to multiply matrix. Can be viewed
+c         as a time step. dt must be positive [to be fixed].
+c
+c eps   = scalar indicating the relative error tolerated for the result. 
+c         the code will try to compute an answer such that 
+c         norm2(exactanswer-approximation) / norm2(w) .le. eps 
+c
+c u	= work array of size n*(m+1) to contain the Arnoldi basis
+c
+c w	= real array of length n = input vector to  which phi(-A) is
+c         to be applied. 
+c
+c job	= integer. job indicator. If job .lt.  0 then the Arnoldi
+c         basis is recomputed. If job .gt. 0 then it is assumed
+c         that the user wants to use a previously computed Krylov
+c         subspace but a different dt. Thus the Arnoldi basis and
+c         the Hessenberg matrix Hm are not recomputed. 
+c	  In that case the user should not modify the values of beta
+c         and the matrices hh and u(n,*) when recalling phipro. 
+c         job = -1 : recompute basis and get an initial estimate for 
+c                    time step dt to be used.
+c         job = 0  : recompute basis and do not alter dt.
+c         job = 1  : do not recompute arnoldi basis. 
+c
+c z     = real work array of  size (m+1)
+c wkc   = complex*16 work array of size (m+1) 
+c
+c hh    = work array of size size at least (m+2)*(m+1)
+c
+c ih+2	= first dimension of hh as declared in the calling program.
+c         ih must be .ge. m.
+c 
+c-----------------------------------------------------------------------
+c on return:
+c-----------
+c w2	= resulting vector w2 = phi(-A *dt) * w
+c beta  = real equal to the 2-norm of w. Needed if phipro will
+c         be recalled with the same Krylov subspace and a different dt. 
+c errst = rough estimates of the 2-norm of the error.
+c hh	= work array of dimension at least (m+2) x (m+1) 
+c
+c----------------------------------------------------------------------- 
+c local variables 
+c 
+      integer ndmax
+      parameter (ndmax=20) 
+      real*8 alp0, fnorm, t, rm, ddot, dabs, dsqrt, dsign,dble
+      complex*16 alp(ndmax+1), rd(ndmax+1)
+      integer i, j, k, ldg, i0, i1, m1 
+      logical verboz
+      data verboz/.true./
+      save
+c------use degree 14 chebyshev all the time -------------------------- 
+      if (indic .eq. 3) goto 60
+c
+c------get partial fraction expansion of rational function -----------
+c-----------------------------------------------------------------------
+c chebyshev (14,14) 
+c      ldg= 7
+c      alp0 =  0.183216998528140087E-11
+c      alp(1)=( 0.557503973136501826E+02,-0.204295038779771857E+03)
+c      rd(1)=(-0.562314417475317895E+01, 0.119406921611247440E+01)
+c      alp(2)=(-0.938666838877006739E+02, 0.912874896775456363E+02)
+c      rd(2)=(-0.508934679728216110E+01, 0.358882439228376881E+01)
+c      alp(3)=( 0.469965415550370835E+02,-0.116167609985818103E+02)
+c      rd(3)=(-0.399337136365302569E+01, 0.600483209099604664E+01)
+c      alp(4)=(-0.961424200626061065E+01,-0.264195613880262669E+01)
+c      rd(4)=(-0.226978543095856366E+01, 0.846173881758693369E+01)
+c      alp(5)=( 0.752722063978321642E+00, 0.670367365566377770E+00)
+c      rd(5)=( 0.208756929753827868E+00, 0.109912615662209418E+02)
+c      alp(6)=(-0.188781253158648576E-01,-0.343696176445802414E-01)
+c      rd(6)=( 0.370327340957595652E+01, 0.136563731924991884E+02)
+c      alp(7)=( 0.143086431411801849E-03, 0.287221133228814096E-03)
+c      rd(7)=( 0.889777151877331107E+01, 0.166309842834712071E+02)
+c-----------------------------------------------------------------------
+c Pade of  degree =  (4,4) 
+c
+c        ldg= 2
+c        alp(1)=(-0.132639894655051648E+03,-0.346517448171383875E+03)
+c        rd(1)=(-0.579242120564063611E+01, 0.173446825786912484E+01)
+c        alp(2)=( 0.926398946550511936E+02, 0.337809095284865179E+02)
+c        rd(2)=(-0.420757879435933546E+01, 0.531483608371348736E+01)
+c
+c Pade of degree =  8
+c
+        ldg= 4
+        alp(1)=( 0.293453004361944040E+05, 0.261671093076405813E+05)
+        rd(1)=(-0.104096815812822569E+02, 0.523235030527069966E+01)
+        alp(2)=(-0.212876889060526154E+05,-0.764943398790569044E+05)
+        rd(2)=(-0.111757720865218743E+02, 0.173522889073929320E+01)
+        alp(3)=(-0.853199767523084301E+04,-0.439758928252937039E+03)
+        rd(3)=(-0.873657843439934822E+01, 0.882888500094418304E+01)
+        alp(4)=( 0.330386145089576530E+03,-0.438315990671386316E+03)
+        rd(4)=(-0.567796789779646360E+01, 0.127078225972105656E+02)
+c
+      do 102 k=1, ldg
+         alp(k) = - alp(k) / rd(k)
+ 102  continue
+      alp0 = 0.0d0
+c     
+c     if job .gt. 0 skip arnoldi process:
+c     
+      if (job .gt. 0) goto 2
+c------normalize vector u and put in first column of u -- 
+      beta = dsqrt(ddot(n,u,1,u,1))
+c-----------------------------------------------------------------------
+      if(verboz) print *, ' In PHIHES, beta ', beta 
+      if (beta .eq. 0.0d0) then
+         ierr = -1
+         indic = 1
+         return
+      endif 
+c
+      t = 1.0d0/beta 
+      do 25 j=1, n
+         u(j,1) = u(j,1)*t 
+ 25   continue
+c------------------Arnoldi loop ----------------------------------------- 
+c      fnorm = 0.0d0
+      i1 = 1
+ 58   i = i1
+      i1 = i + 1
+      do 59 k=1, n
+         x(k) = u(k,i)
+ 59   continue
+      indic = 3
+      return
+ 60   continue
+      do 61 k=1, n
+         u(k,i1) = y(k) 
+ 61   continue
+      i0 =1
+c switch  for Lanczos version 
+c     i0 = max0(1, i-1)
+      call mgsr (n, i0, i1, u, hh(1,i))
+      fnorm = fnorm + ddot(i1, hh(1,i),1, hh(1,i),1)
+      if (hh(i1,i) .eq. 0.0) m = i
+      if  (i .lt. m) goto 58
+c--------------done with arnoldi loop ---------------------------------
+      rm = dble(m) 
+      fnorm = dsqrt( fnorm / rm )
+c------- put beta*e1 into z ------------------------------------------- 
+      m1 = m+1 
+      do 4 i=1,m1
+         hh(i,m1) = 0.0
+ 4    continue
+c     
+c     compute initial dt when  job .lt. 1 
+c
+      if (job .ge. 0) goto 2
+c
+      t = 2.0*eps 
+      do 41 k=1, m
+         t = 2.0*t*dble(k+1)/rm
+ 41   continue
+c
+      t = rm* (t**(1.0d0/rm) ) / fnorm 
+      if(verboz) print *, ' t, dt = ', t, dt
+      t = dmin1(dabs(dt),t) 
+      dt = dsign(t, dt) 
+c---------------------- get the vector phi(Hm)e_1 + estimate ----------- 
+ 2    continue 
+      z(1) = beta 
+      do 3 k=2, m1
+         z(k) = 0.0d0 
+ 3    continue
+c-------get  : phi(H) * beta*e1
+      call hes(ldg,m1,hh,ih,dt,z,rd,alp,alp0,wkc)
+c-------error estimate 
+      errst = dabs(z(m1))
+      if(verboz) print *, ' error estimate =', errst 
+c----------------------------------------------------------------------- 
+      indic = 2
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine mgsr (n, i0, i1, ss, r)
+c     implicit  real*8 (a-h,o-z)
+      integer n, i0, i1
+      real*8 ss(n,i1), r(i1)
+c-----------------------------------------------------------------------
+c modified gram - schmidt  with  partial  reortho. the vector ss(*,i1) is
+c orthogonalized against the first i vectors  of ss  (which  are  already
+c orthogonal).  the coefficients of the orthogonalization are returned in
+c the array r
+c------------------------------------------------------------------------
+c local variables 
+c 
+      integer i, j, k, it
+      real*8 hinorm, tet, ddot, t, dsqrt
+      data  tet/10.0d0/
+
+      do 53 j=1, i1
+         r(j) = 0.0d0
+ 53   continue
+      i = i1-1
+      it = 0
+ 54   hinorm = 0.0d0
+      it = it +1
+      if (i .eq. 0) goto 56
+c     
+      do 55 j=i0, i
+         t = ddot(n, ss(1,j),1,ss(1,i1),1)
+         hinorm = hinorm + t**2
+         r(j) = r(j) + t
+         call daxpy(n,-t,ss(1,j),1,ss(1,i1),1)
+ 55   continue
+      t = ddot(n, ss(1,i1), 1, ss(1,i1), 1)
+ 56   continue
+c     
+c     test for reorthogonalization see daniel et. al.
+c     two reorthogonalization allowed ---
+c     
+      if (t*tet .le. hinorm .and. it .lt. 2) goto 54
+      t =dsqrt(t)
+      r(i1)= t
+      if (t .eq. 0.0d0) return
+      t = 1.0d0/t
+      do 57  k=1,n
+         ss(k,i1) = ss(k,i1)*t
+ 57   continue
+      return
+      end
+c----------end-of-mgsr--------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine project(n, m, w, t, u, v) 
+      integer n, m
+      real*8 u(n,m), v(m), w(n), t, scal
+c
+c     computes the vector w = w + t * u * v
+c
+c local variables 
+c
+      integer j, k
+
+      do 100 j=1,m
+         scal = t*v(j) 
+         do 99 k=1,n
+            w(k) = w(k) + scal*u(k,j) 
+ 99      continue
+ 100  continue
+      return
+      end
+c-----------------------------------------------------------------------
+      subroutine hes (ndg,m1,hh,ih,dt,y,root,coef,coef0,w2)
+c     implicit  real*8 (a-h,o-z)
+      integer ndg, m1, ih 
+      real*8 hh(ih+2,m1), y(m1)
+      complex*16   coef(ndg), root(ndg), w2(m1)
+      real*8 dt, coef0
+c--------------------------------------------------------------------  
+c computes phi ( H dt) * y    (1)
+c where H = Hessenberg matrix (hh)
+c y	  = arbitrary vector.
+c ----------------------------
+c ndg	= number of poles as determined by getrat
+c m1    = dimension of hessenberg matrix
+c hh	= hessenberg matrix (real)
+c ih+2	= first dimension of hh
+c dt	= scaling factor used for hh (see (1)) 
+c y	= real vector. on return phi(H dt ) y is computed
+c         and overwritten on y.
+c root  = poles of the rational approximation to phi as
+c         computed by getrat
+c coef, 
+c coef0 = coefficients of partial fraction phiansion 
+c         
+c  phi(t) ~ coef0 +  sum     Real [   coef(i) / (t - root(i)  ]
+c                  i=1,ndg  
+c
+c valid for real t.
+c coef0 is real, coef(*) is a complex array.
+c
+c--------------------------------------------------------------------  
+c local variables 
+c
+      integer m1max
+      parameter (m1max=70) 
+      complex*16   hloc(m1max+1,m1max), t, zpiv, dcmplx
+      real*8 yloc(m1max), dble
+      integer i, j, ii
+c     
+c      if (m1 .gt. m1max) print *, ' *** ERROR : In HES, M+1 TOO LARGE'
+c     
+c     loop associated with the poles.
+c     
+      do 10 j=1,m1
+         yloc(j) = y(j)
+         y(j)    = y(j)*coef0
+ 10   continue
+c     
+      do 8 ii = 1, ndg
+c     
+c     copy Hessenberg matrix into temporary
+c     
+         do 2 j=1, m1
+            do 1 i=1, j+1
+               hloc(i,j) = dcmplx( dt*hh(i,j) )
+ 1          continue
+            hloc(j,j) = hloc(j,j) - root(ii) 
+            w2(j)     = dcmplx(yloc(j)) 
+ 2       continue 
+c
+c forward solve 
+c 
+         do 4 i=2,m1
+            zpiv  = hloc(i,i-1) / hloc(i-1,i-1)
+            do 3 j=i,m1
+               hloc(i,j) = hloc(i,j) - zpiv*hloc(i-1,j)
+ 3          continue
+            w2(i)     = w2(i) - zpiv*w2(i-1)
+ 4       continue 
+c     
+c     backward solve
+c     
+         do 6 i=m1,1,-1 
+            t=w2(i)
+            do 5 j=i+1,m1
+               t = t-hloc(i,j)*w2(j)
+ 5          continue
+            w2(i) = t/hloc(i,i)
+ 6       continue
+c     
+c     accumulate result in y.
+c     
+         do 7 i=1,m1
+            y(i) = y(i) + dble ( coef(ii) * w2(i) ) 
+ 7       continue
+ 8    continue
+      return
+      end
+c----------end-of-hes---------------------------------------------------
+c-----------------------------------------------------------------------
+      subroutine daxpy(n,t,x,indx,y,indy)
+      integer n, indx, indy
+      real*8 x(n), y(n), t
+c-------------------------------------------------------------------
+c does the following operation
+c y <--- y + t * x ,   (replace by the blas routine daxpy )
+c indx and indy are supposed to be one here
+c-------------------------------------------------------------------
+       integer k
+
+       do 1 k=1,n
+          y(k) = y(k) + x(k)*t
+1      continue
+       return
+       end
+c----------end-of-daxpy-------------------------------------------------
+c----------------------------------------------------------------------- 
+       function ddot(n,x,ix,y,iy)
+       integer n, ix, iy
+       real*8 ddot, x(n), y(n)
+c-------------------------------------------------------------------
+c computes the inner product t=(x,y) -- replace by blas routine ddot
+c-------------------------------------------------------------------
+       integer j
+       real*8 t
+        
+       t = 0.0d0
+       do 10 j=1,n
+          t = t + x(j)*y(j)
+10     continue
+       ddot=t
+       return
+       end
+c----------end-of-ddot--------------------------------------------------
+c----------------------------------------------------------------------- 
+
diff --git a/UNSUPP/MATEXP/rexp.f b/UNSUPP/MATEXP/rexp.f
new file mode 100644
index 0000000..c5629b0
--- /dev/null
+++ b/UNSUPP/MATEXP/rexp.f
@@ -0,0 +1,98 @@
+      	program exptest
+c-------------------------------------------------------------------
+c
+c Test program for exponential propagator using Arnoldi approach
+c This main program is a very simple test using diagonal matrices
+c (Krylov subspace methods are blind to the structure of the matrix
+c except for symmetry). This provides a good way of testing the
+c accuracy of the method as well as the error estimates.
+c
+c-------------------------------------------------------------------
+        implicit real*8 (a-h,o-z)
+        parameter (nmax = 400, ih0=60, ndmx=20,nzmax = 7*nmax)
+        real*8 a(nzmax), u(ih0*nmax), w(nmax),w1(nmax),x(nmax),y(nmax)
+	integer ioff(10) 
+	data iout/6/, a0/0.0/, b0/1.0/, epsmac/1.d-10/, eps /1.d-10/
+c
+c set dimension of matrix
+c
+	n = 100
+c--------------------------- define matrix -----------------------------
+c A is a single diagonal matrix (ndiag = 1 and ioff(1) = 0 ) 
+c-----------------------------------------------------------------------
+        ndiag = 1
+	ioff(1) = 0
+c
+c-------- entries in the diagonal are uniformly distributed. 
+c
+	h = 1.0d0 / real(n+1)
+        do 1 j=1, n
+	a(j) = real(j+1)* h 
+ 1	continue
+c-------- 
+        write (6,'(10hEnter tn: ,$)')
+	read (5,*) tn 
+c
+        write (6,'(36hEpsilon (desired relative accuracy): ,$)')
+	read (5,*)  eps 
+c------- 
+        write (6,'(36h m (= dimension of Krylov subspace): ,$)')
+	read (5,*)  m 
+c------- 
+c define initial conditions: chosen so that solution = (1,1,1,1..1)^T
+c-------
+	do 2 j=1,n
+	w(j) = dexp(a(j)*tn) 
+ 2	w1(j) = w(j) 
+c
+         call expprod (n, m, eps, tn, u, w, x, y, a, ioff, ndiag)
+c
+        print *, ' final answer '
+        print *, (w(k),k=1,20) 
+c        
+	do 4 k=1,n
+ 4	w1(k) = dexp(-a(k)*tn) * w1(k) 
+        print *, ' exact solution '
+        print *, (w1(k),k=1,20) 
+c
+c---------- computing actual 2-norm of error ------------------
+c
+	t = 0.0d0
+	do 47 k=1,n
+ 47	t = t+ (w1(k)-w(k))**2
+        t = dsqrt(t / ddot(n, w,1,w,1) )
+c
+        write (6,*) ' final error', t
+c--------------------------------------------------------------
+	stop
+	end
+c------- 
+	subroutine oped(n,x,y,diag,ioff,ndiag)
+c======================================================
+c this kernel performs a matrix by vector multiplication
+c for a diagonally structured  matrix stored in diagonal
+c format
+c======================================================
+	implicit real*8 (a-h,o-z)
+	real*8 x(n), y(n), diag(n,ndiag)
+	common nope, nmvec
+	integer j, n, ioff(ndiag)
+CDIR$ IVDEP
+	do 1 j=1, n
+		y(j) = 0.00
+ 1	continue	
+c
+	do 10 j=1,ndiag
+	io = ioff(j)
+	i1=max0(1,1-io)
+	i2=min0(n,n-io)
+CDIR$ IVDEP
+	do 9 k=i1,i2
+	y(k) = y(k)+diag(k,j)*x(k+io)
+ 9	continue
+ 10	continue
+	nmvec  = nmvec + 1 
+	nope = nope + 2*ndiag*n
+	return
+	end
+c
diff --git a/UNSUPP/MATEXP/rphi.f b/UNSUPP/MATEXP/rphi.f
new file mode 100644
index 0000000..17f75a4
--- /dev/null
+++ b/UNSUPP/MATEXP/rphi.f
@@ -0,0 +1,127 @@
+      program phitest 
+c-------------------------------------------------------------------
+c Test program for exponential propagator using Arnoldi approach
+c This main program is a very simple test using diagonal matrices
+c (Krylov subspace methods are blind to the structure of the matrix
+c except for symmetry). This provides a good way of testing the
+c accuracy of the method as well as the error estimates. This test
+c program tests the phi-function variant instead of the exponential.
+c
+c The subroutine phipro which is tested here computes an approximation 
+c to the vector
+c
+c   	w(tn) = w(t0) + tn *  phi( - A * tn ) * (r - A w(t0))
+c
+c where phi(z) = (1-exp(z)) / z
+c 
+c i.e. it solves dw/dt = -A w + r in [t0,t0+ tn] (returns only w(t0+tn))
+c 
+c In this program t0=0, tn is input by the user and A is a simple 
+c diagonal matrix. 
+c
+c-------------------------------------------------------------------
+      implicit real*8 (a-h,o-z)
+      parameter (nmax = 400, ih0=60, ndmx=20,nzmax = 7*nmax)
+      real*8 a(nzmax), u(ih0*nmax), w(nmax),w1(nmax),x(nmax),y(nmax),
+     *     r(nmax) 
+      integer ioff(10) 
+      data iout/6/,a0/0.0/,b0/1.0/,epsmac/1.d-10/,eps/1.d-10/
+c     
+c     dimendion of matrix
+c     
+      n = 100
+c---------------------------define matrix -----------------------------
+c     A is a single diagonal matrix (ndiag = 1 and ioff(1) = 0 ) 
+c-----------------------------------------------------------------------
+      ndiag = 1
+      ioff(1) = 0
+c
+c     entriesin the diagonal are uniformly distributed. 
+c     
+      h = 1.0d0 / real(n+1) 
+      do 1 j=1, n
+         a(j) = real(j+1)*h 
+ 1    continue
+c--------
+      write (6,'(10hEnter tn: ,$)')
+      read (5,*) tn 
+c     
+      write (6,'(36hEpsilon (desired relative accuracy): ,$)')
+      read (5,*)  eps 
+c-------
+      write (6,'(36h m (= dimension of Krylov subspace): ,$)')
+      read (5,*)  m 
+c     
+c     define initial conditions to be (1,1,1,1..1)^T
+c     
+      do 2 j=1,n
+         w(j) = 1.0 - 1.0/real(j+10)  
+         r(j) = 1.0
+         w1(j) = w(j) 
+ 2    continue
+c     
+c     
+c     HERE IT IS DONE IN 10 SUBSTEPS         
+c     nsteps = 10 
+c     tnh = tn/real(nsteps) 
+c     MARCHING LOOP 
+c     do jj =1, nsteps 
+c     call phiprod (n, m, eps, tnh, u, w, r, x, y, a, ioff, ndiag)         
+      call phiprod (n, m, eps, tn, u, w, r, x, y, a, ioff, ndiag)
+c     enddo
+      print *, ' final answer '
+      print *, (w(k),k=1,20) 
+c     
+c     exact solution 
+c     
+      do 4 k=1,n
+         w1(k)=w1(k)+((1.0 - dexp(-a(k)*tn) )/a(k))*(r(k)  
+     +        - a(k)*w1(k) ) 
+ 4    continue
+c     
+c     exact solution 
+c     
+      print *, ' exact answer '
+      print *, (w1(k),k=1,20) 
+c     
+c     computing actual 2-norm of error 
+c     
+      t = 0.0d0
+      do 47 k=1,n
+         t = t+ (w1(k)-w(k))**2 
+ 47   continue
+      t = dsqrt(t / ddot(n, w,1,w,1) )
+c     
+      write (6,*) ' final error', t
+c----------------------------------------------------------------------- 
+      stop
+      end
+c-----------------------------------------------------------------------
+	subroutine oped(n,x,y,diag,ioff,ndiag)
+c======================================================
+c this kernel performs a matrix by vector multiplication
+c for a diagonally structured  matrix stored in diagonal format
+c======================================================
+	implicit real*8 (a-h,o-z)
+	real*8 x(n), y(n), diag(n,ndiag)
+	common nope, nmvec
+	integer j, n, ioff(ndiag)
+CDIR$ IVDEP
+	do 1 j=1, n
+		y(j) = 0.00
+ 1	continue	
+c
+	do 10 j=1,ndiag
+	io = ioff(j)
+	i1=max0(1,1-io)
+	i2=min0(n,n-io)
+CDIR$ IVDEP
+	do 9 k=i1,i2
+	y(k) = y(k)+diag(k,j)*x(k+io)
+ 9	continue
+ 10	continue
+	nmvec  = nmvec + 1 
+	nope = nope + 2*ndiag*n
+	return
+	end
+c
diff --git a/UNSUPP/PLOTS/README b/UNSUPP/PLOTS/README
new file mode 100644
index 0000000..c555d1f
--- /dev/null
+++ b/UNSUPP/PLOTS/README
@@ -0,0 +1,19 @@
+
+		             ----------------- 
+		             Current contents:
+			     -----------------
+
+Some of the files that were originally in this directory 
+have been moved to the INOUT module, or were obsolte and removed.
+
+* psgrd.f contains subroutine "psgrid" which plots a symmetric graph.
+
+* texplt1.f contains subroutine "texplt" allows several matrices
+  in the same picture by calling texplt several times and exploiting job and
+  different shifts.
+
+* texgrid1.f contains subroutine "texgrd" which generates tex commands
+  for plotting a symmetric graph associated with a mesh. Allows  
+  several grids in the same picture by calling texgrd several times and 
+  exploiting job and different shifts. 
+
diff --git a/UNSUPP/PLOTS/psgrd.f b/UNSUPP/PLOTS/psgrd.f
new file mode 100644
index 0000000..3a6f4c5
--- /dev/null
+++ b/UNSUPP/PLOTS/psgrd.f
@@ -0,0 +1,190 @@
+      subroutine psgrid (npts,ja,ia,xx,yy,title,ptitle,size,munt,iunt) 
+c-----------------------------------------------------------------------
+c     plots a symmetric graph defined by ja,ia and the coordinates
+c     xx(*),yy(*) 
+c----------------------------------------------------------------------- 
+c npts   = number of points in mesh
+c ja, ia = connectivity of mesh -- as given by pattern of sparse
+c            matrix.
+c xx, yy = cordinates of the points. 
+c
+c title  = character*(*). a title of arbitrary length to be printed 
+c          as a caption to the figure. Can be a blank character if no
+c          caption is desired.
+c
+c ptitle = position of title; 0 under the drawing, else above
+c
+c size   = size of the drawing  
+c
+c munt   = units used for size : 'cm' or 'in'
+c
+c     iunt   = logical unit number where to write the matrix into.
+c----------------------------------------------------------------------- 
+      implicit none 
+      integer npts,ptitle,iunt, ja(*), ia(*) 
+      character title*(*), munt*2 
+      real*8 xx(npts),yy(npts) 
+      real size
+c----------------------------------------------------------------------- 
+c     local variables --------------------------------------------------
+c----------------------------------------------------------------------- 
+      integer nr,ii,k,ltit
+      real xi,yi,xj,yj,lrmrgn,botmrgn,xtit,ytit,ytitof,fnstit,siz,
+     *     xl,xr, yb,yt, scfct,u2dot,frlw,delt,paperx,conv,dimen,
+     *     haf,zero, xdim, ydim
+      real*8 xmin,xmax,ymin,ymax,max,min
+      integer j
+c-----------------------------------------------------------------------
+      integer LENSTR
+      external LENSTR
+c----------------------------------------------------------------------- 
+      data haf /0.5/, zero/0.0/, conv/2.54/
+      siz = size
+c
+c     get max and min dimensions
+c
+      xmin = xx(1) 
+      xmax = xmin 
+      ymin = yy(1)
+      ymax = ymin
+      do j=2, npts
+         xmax = max(xmax,xx(j))
+         xmin = min(xmin,xx(j))
+         ymax = max(ymax,yy(j))
+         ymin = min(ymin,yy(j))
+      enddo
+c----------------------------------------------------------------------- 
+c      n = npts
+      nr = npts 
+      xdim = xmax -xmin
+      ydim = ymax -ymin
+      dimen = max(xdim,ydim) 
+c-----------------------------------------------------------------------
+      print *, ' xmin', xmin, ' xmax', xmax 
+      print *, ' ymin', ymin, ' ymax', ymax, ' dimen ', dimen
+c-----------------------------------------------------------------------
+c
+c units (cm or in) to dot conversion factor and paper size
+c 
+      if (munt.eq.'cm' .or. munt.eq.'CM') then
+         u2dot = 72.0/conv
+         paperx = 21.0
+      else
+        u2dot = 72.0
+        paperx = 8.5*conv
+        siz = siz*conv
+      end if
+c
+c left and right margins (drawing is centered)
+c 
+      lrmrgn = (paperx-siz)/2.0
+c
+c bottom margin : 2 cm
+c
+      botmrgn = 2.0/dimen
+c     scaling factor
+      scfct = siz*u2dot/dimen
+c     frame line witdh
+      frlw = 0.25/dimen
+c     font siz for title (cm)
+      fnstit = 0.5/dimen
+      ltit = LENSTR(title)
+c
+c     position of title : centered horizontally
+c                     at 1.0 cm vertically over the drawing
+      ytitof = 1.0/dimen
+      xtit = paperx/2.0
+      ytit = botmrgn+siz*nr/dimen + ytitof
+c almost exact bounding box
+      xl = lrmrgn*u2dot - scfct*frlw/2
+      xr = (lrmrgn+siz)*u2dot + scfct*frlw/2
+      yb = botmrgn*u2dot - scfct*frlw/2
+      yt = (botmrgn+siz*ydim/dimen)*u2dot + scfct*frlw/2
+      if (ltit.gt.0) then
+        yt = yt + (ytitof+fnstit*0.70)*u2dot
+      end if
+c add some room to bounding box
+      delt = 10.0
+      xl = xl-delt
+      xr = xr+delt
+      yb = yb-delt
+      yt = yt+delt
+c
+c correction for title under the drawing
+c
+      if (ptitle.eq.0 .and. ltit.gt.0) then
+      ytit = botmrgn + fnstit*0.3
+      botmrgn = botmrgn + ytitof + fnstit*0.7
+      end if
+c
+c     begin output
+c
+      write(iunt,10) '%!'
+      write(iunt,10) '%%Creator: PSPLTM routine'
+      write(iunt,12) '%%BoundingBox:',xl,yb,xr,yt
+      write(iunt,10) '%%EndComments'
+      write(iunt,10) '/cm {72 mul 2.54 div} def'
+      write(iunt,10) '/mc {72 div 2.54 mul} def'
+      write(iunt,10) '/pnum { 72 div 2.54 mul 20 string'
+      write(iunt,10) 'cvs print ( ) print} def'
+      write(iunt,10)
+     1  '/Cshow {dup stringwidth pop -2 div 0 rmoveto show} def'
+c
+c     we leave margins etc. in cm so it is easy to modify them if
+c     needed by editing the output file
+c
+      write(iunt,10) 'gsave'
+      if (ltit.gt.0) then
+      write(iunt,*) '/Helvetica findfont',fnstit,' cm scalefont setfont'
+      write(iunt,*) xtit,' cm',ytit,' cm moveto'
+      write(iunt,'(3A)') '(',title(1:ltit),') Cshow'
+      end if
+c
+      write(iunt,*) lrmrgn,' cm ',botmrgn,' cm translate'
+      write(iunt,*) siz,' cm ',dimen,' div dup scale '
+c     
+c     draw a frame around the matrix  // REMOVED 
+c
+c       del = 0.005
+c       del2 = del*2.0 
+c       write(iunt,*) del, ' setlinewidth'
+c       write(iunt,10) 'newpath'
+c       write(iunt,11) -del2, -del2, ' moveto'
+c       write(iunt,11) dimen+del2,-del2,' lineto'
+c       write(iunt,11) dimen+del2, dimen+del2, ' lineto'
+c       write(iunt,11) -del2,dimen+del2,' lineto'
+c       write(iunt,10) 'closepath stroke'
+c     
+c----------- plotting loop ---------------------------------------------
+       write(iunt,*)  ' 0.01 setlinewidth'
+c
+       do 1 ii=1, npts 
+       
+c     if (mask(ii) .eq. 0) goto 1
+          xi = xx(ii) - xmin 
+          yi = yy(ii) - ymin
+c     write (iout+1,*) ' ******** ii pt', xi, yi, xmin, ymin 
+          do 2 k=ia(ii),ia(ii+1)-1 
+             j = ja(k) 
+             if (j .le. ii) goto 2 
+             xj = xx(j) - xmin 
+             yj = yy(j) - ymin
+c     write (iout+1,*) ' j pt -- j= ',j, 'pt=', xj, yj
+c
+c     draw a line from ii to j
+c
+             write(iunt,11) xi, yi, ' moveto '
+             write(iunt,11) xj, yj, ' lineto'
+             write(iunt,10) 'closepath stroke'
+ 2        continue 
+ 1     continue
+c-----------------------------------------------------------------------
+       write(iunt,10) 'showpage'
+       return
+c
+ 10   format (A)
+ 11   format (2F9.2,A)
+ 12   format (A,4F9.2)
+ 13   format (2F9.2,A)
+c-----------------------------------------------------------------------
+      end
diff --git a/UNSUPP/PLOTS/texgrid1.f b/UNSUPP/PLOTS/texgrid1.f
new file mode 100644
index 0000000..906099e
--- /dev/null
+++ b/UNSUPP/PLOTS/texgrid1.f
@@ -0,0 +1,242 @@
+      subroutine texgrd(npts,ja,ia,xx,yy,munt,size,vsize,hsize,
+     *     xleft,bot,job,title,ptitle,ijk,node,nelx,iunt)
+c-----------------------------------------------------------------------
+      integer npts,iunt,ptitle,ja(*),ia(*), ijk(node,*) 
+      character title*(*), munt*2 
+      real*8 xx(npts), yy(npts) 
+c-----------------------------------------------------------------------
+c     allows to have several grids in same picture by calling texgrd 
+c     several times and exploiting job and different shifts.  
+c-----------------------------------------------------------------------
+c     input arguments description :
+c     
+c npts   = number of rows in matrix
+c
+c ncol   = number of columns in matrix 
+c
+c mode   = integer indicating whether the matrix is stored in 
+c          CSR mode (mode=0) or CSC mode (mode=1) or MSR mode (mode=2) 
+c
+c ja     = column indices of nonzero elements when matrix is
+c          stored rowise. Row indices if stores column-wise.
+c ia     = integer array of containing the pointers to the 
+c          beginning of the columns in arrays a, ja.
+c
+c munt   = units used for sizes : either 'cm' or 'in'
+c
+c size   = size of the matrix box in 'munt' units 
+c
+c vsize  = vertical size of the frame containing the picture
+c          in 'munt' units 
+c
+c hsize  = horizontal size of the frame containing the picture 
+c          in 'munt' units 
+c
+c xleft  =  position of left border of matrix in 'munt' units 
+c
+c bot    =  position of bottom border of matrix in 'munt' units 
+c
+c job    = job indicator for preamble and post process
+c          can be viewed as a 2-digit number job = [job1,job2]      
+c          where job1 = job /10 , job2 = job - 10*job1 = mod(job,10)
+c          job2  relates to preamble/post processing:
+c          job2 = 0: all preambles+end-document lines 
+c          job2 = 1: preamble only
+c          job2 = 2: end-document only
+c          anything else:  no preamble or end-docuiment lines
+c       Useful for plotting several matrices in same frame.
+c
+c          job1 relates to the way in which the nodes and elements must
+c          be processed:
+c          job1  relates to options for the plot. 
+c          job1 = 0 : only a filled circle for the nodes, no labeling 
+c          job1 = 1 : labels the nodes (in a circle) 
+c          job1 = 2 : labels both nodes and elements. 
+c          job1 = 3 : no circles, no labels 
+c
+c title  = character*(*). a title of arbitrary length to be printed 
+c          as a caption to the matrix. Can be a blank character if no
+c          caption is desired. Can be put on top or bottom of matrix
+c          se ptitle.
+c
+c ptitle = position of title; 0 under the frame, else above
+c
+c nlines = number of separation lines to draw for showing a partionning
+c          of the matrix. enter zero if no partition lines are wanted.
+c
+c lines  = integer array of length nlines containing the coordinates of 
+c          the desired partition lines . The partitioning is symmetric: 
+c          a horizontal line across the matrix will be drawn in 
+c          between rows lines(i) and lines(i)+1 for i=1, 2, ..., nlines
+c          an a vertical line will be similarly drawn between columns
+c          lines(i) and lines(i)+1 for i=1,2,...,nlines 
+c
+c iunt   = logical unit number where to write the matrix into.
+c----------------------------------------------------------------------- 
+      real*8 xmin, xmax, ymin, ymax
+
+      n = npts 
+      siz = size
+      job1 = job /10 
+      job2 = job - 10*job1 
+c
+c     get max and min dimensions
+c
+      xmin = xx(1) 
+      xmax = xmin 
+      ymin = yy(1)
+      ymax = ymin
+c
+      do j=2, npts
+         xmax = max(xmax,xx(j))
+         xmin = min(xmin,xx(j))
+         ymax = max(ymax,yy(j))
+         ymin = min(ymin,yy(j))
+      enddo
+c----------------------------------------------------------------------- 
+      n = npts
+      xdim = xmax -xmin
+      ydim = ymax -ymin
+      dimen = max(xdim,ydim) 
+c-----------------------------------------------------------------------
+      print *, ' xmin', xmin, ' xmax', xmax 
+      print *, ' ymin', ymin, ' ymax', ymax, ' dimen ', dimen
+c-----------------------------------------------------------------------
+c
+c units (cm or in) to dot conversion factor and paper size
+c 
+      tdim = max(ydim,xdim) 
+      unit0 = size/tdim 
+      hsiz = hsize/unit0
+      vsiz = vsize/unit0
+      siz  = size/unit0 
+c
+c     size of little circle for each node -- cirr = in local units
+c     cirabs in inches (or cm) -- rad = radius in locl units --
+c 
+      cirabs = 0.15
+      if (job1 .le. 0) cirabs = 0.08
+      if (job1 .eq. 3) cirabs = 0.0 
+      cirr   = cirabs/unit0 
+      rad = cirr/2.0
+c
+c     begin document generation
+c 
+      if (job2 .le. 1) then 
+         write (iunt,*) ' \\documentstyle[epic,eepic,12pt]{article} '
+         write (iunt,*) ' \\begin{document}'
+         write (iunt,100) unit0, munt 
+         write (iunt,99) hsiz, vsiz 
+      else 
+c     redeclare unitlength 
+         write (iunt,100) unit0, munt 
+      endif 
+      if (job1 .le. 0) then 
+         write (iunt,101) cirr
+      else
+         write (iunt,102) cirr
+      endif 
+ 102  format('\\def\\cird{\\circle{',f5.2,'} }') 
+ 101   format('\\def\\cird{\\circle*{',f5.2,'} }') 
+ 99   format('\\begin{picture}(',f8.2,1h,,f8.2,1h)) 
+ 100  format(' \\setlength{\\unitlength}{',f5.3,a2,'}')
+c
+c     bottom margin between cir and title
+c
+      xs = xleft /  unit0 + (tdim - xdim)*0.5 + (hsiz - siz)*0.5 
+      ys = bot / unit0 - ymin
+c
+      xmargin = 0.30/unit0
+      if (munt .eq. 'cm' .or. munt .eq. 'CM') xmargin = xmargin*2.5
+      xtit = xs + xmin 
+      if (ptitle .eq. 0) then 
+         ytit = ys + ymin - xmargin 
+      else
+         ytit = ys + ymax + xmargin 
+      endif 
+      ltit = LENSTR(title)
+      write(iunt,111) xtit,ytit,xdim,xmargin,title(1:ltit) 
+c      
+ 111  format ('\\put(',F6.2,',',F6.2,
+     *     '){\\makebox(',F6.2,1h,,F6.2,'){',A,2h}}) 
+c      
+c     print all the circles if needed
+c 
+c ##### temporary for showing f
+c      write (iunt,102) 0.01      
+c      write (iunt,112)xs+xx(1), ys+yy(1) 
+c-----------------------------------------------------------------------
+      if (job1 .eq. 3) goto 230
+      do 22 i=1, npts 
+         x = xs + xx(i) 
+         y = ys + yy(i) 
+         write(iunt,112) x, y 
+ 112     format ('\\put(',F6.2,',',F6.2,'){\\cird}')
+c         write(iunt,113) x-rad, y-rad, cirr, cirr, i 
+c 113     format ('\\put(',F6.2,',',F6.2,
+c     *     '){\\makebox(',F6.2,1h,,F6.2,'){\\scriptsize ',i4,2h}}) 
+         if (job1 .ge. 1) then 
+            write(iunt,113) x, y, i 
+         endif
+ 113     format ('\\put(',F6.2,',',F6.2,
+     *        '){\\makebox(0.0,0.0){\\scriptsize ',i4,2h}}) 
+ 22   continue
+ 230  continue 
+c         
+c     number the elements if needed
+c
+      if (job1 .eq. 2) then
+         do 23 iel = 1, nelx 
+            x = 0.0
+            y = 0.0
+            do j=1, node
+               x = x+xx(ijk(j,iel)) 
+               y = y+yy(ijk(j,iel)) 
+            enddo
+            x = xs + x / real(node) 
+            y = ys + y / real(node) 
+            write(iunt,113) x, y, iel 
+ 23      continue
+      endif 
+c
+c     draw lines
+c
+      write (iunt,*) ' \\Thicklines '
+      do 1 ii=1, npts 
+         xi = xs+ xx(ii) 
+         yi = ys+ yy(ii) 
+         do 2 k=ia(ii),ia(ii+1)-1 
+            j = ja(k) 
+            if (j .le. ii) goto 2
+            xj = xs + xx(j) 
+            yj = ys + yy(j) 
+            xspan = xj - xi
+            yspan = yj - yi
+            tlen = sqrt(xspan**2 + yspan**2) 
+            if (abs(xspan) .gt. abs(yspan)) then
+               ss = yspan / tlen
+               cc = sqrt(abs(1.0 - ss**2))
+               cc = sign(cc,xspan) 
+            else
+               cc = xspan / tlen 
+               ss = sqrt(abs(1.0 - cc**2))
+               ss = sign(ss,yspan) 
+            endif
+c            print *, ' ss -- cc ', ss, cc 
+c            write(iunt,114)xi,yi,xj,yj
+            write(iunt,114)xi+cc*rad,yi+ss*rad,xj-cc*rad,yj-ss*rad 
+ 114        format('\\drawline(',f6.2,1h,,f6.2,')(',f6.2,1h,,f6.2,1h))
+c            tlen = tlen - 2.0*cirr
+c            write(iunt,114) xi+cc*cirr,yi+ss*cirr,cc,ss,tlen 
+c 114        format('\\put(',f6.2,1h,,f6.2,'){\\line(',
+c     *           f6.2,1h,,f6.2,'){',f6.2,'}}') 
+ 2       continue 
+ 1    continue
+c-----------------------------------------------------------------------
+      if (job2 .eq. 0 .or. job2 .eq. 2) then 
+         write (iunt,*) ' \\end{picture} '
+         write (iunt,*) ' \\end{document} '
+      endif
+c
+      return
+      end
diff --git a/UNSUPP/PLOTS/texplt1.f b/UNSUPP/PLOTS/texplt1.f
new file mode 100644
index 0000000..97f3661
--- /dev/null
+++ b/UNSUPP/PLOTS/texplt1.f
@@ -0,0 +1,243 @@
+      subroutine texplt(nrow,ncol,mode,ja,ia,munt,size,vsize,hsize,
+     *     xleft,bot,job,title,ptitle,nlines,lines,iunt)
+c-----------------------------------------------------------------------
+      integer nrow,ncol,mode,iunt,ptitle,ja(*),ia(*),lines(nlines) 
+      character title*(*), munt*2 
+c-----------------------------------------------------------------------
+c     allows to have several matrices in same picture by calling texplt
+c     several times and exploiting job and different shifts.  
+c-----------------------------------------------------------------------
+c     input arguments description :
+c     
+c nrow   = number of rows in matrix
+c
+c ncol   = number of columns in matrix 
+c
+c mode   = integer indicating whether the matrix is stored in 
+c          CSR mode (mode=0) or CSC mode (mode=1) or MSR mode (mode=2) 
+c
+c ja     = column indices of nonzero elements when matrix is
+c          stored rowise. Row indices if stores column-wise.
+c ia     = integer array of containing the pointers to the 
+c          beginning of the columns in arrays a, ja.
+c
+c munt   = units used for sizes : either 'cm' or 'in'
+c
+c size   = size of the matrix box in 'munt' units 
+c
+c vsize  = vertical size of the frame containing the picture
+c          in 'munt' units 
+c
+c hsize  = horizontal size of the frame containing the picture 
+c          in 'munt' units 
+c
+c xleft  =  position of left border of matrix in 'munt' units 
+c
+c bot    =  position of bottom border of matrix in 'munt' units 
+c
+c job    = job indicator for preamble and post process
+c          
+c          can be thought of as a 2-digit number job = [job1,job2]
+c          where job1 = job /10 , job2 = job - 10*job1 = mod(job,10)
+c          job2 = 0: all preambles+end-document lines 
+c          job2 = 1: preamble only
+c          job2 = 2: end-document only
+c          anything else for job2:  no preamble or end-docuiment lines
+c       Useful for plotting several matrices in same frame.
+c
+c          job1 indicates what to put for a nonzero dot.
+c          job1  relates to preamble/post processing:
+c          job1 = 0 : a filled squate 
+c          job1 = 1 : a filled circle 
+c          job1 = 2 : the message $a_{ij}$ where i,j are the trow/column
+c                     positions of the nonzero element. 
+c
+c title  = character*(*). a title of arbitrary length to be printed 
+c          as a caption to the matrix. Can be a blank character if no
+c          caption is desired. Can be put on top or bottom of matrix
+c          se ptitle.
+c
+c ptitle = position of title; 0 under the frame, else above
+c
+c nlines = number of separation lines to draw for showing a partionning
+c          of the matrix. enter zero if no partition lines are wanted.
+c
+c lines  = integer array of length nlines containing the coordinates of 
+c          the desired partition lines . The partitioning is symmetric: 
+c          a horizontal line across the matrix will be drawn in 
+c          between rows lines(i) and lines(i)+1 for i=1, 2, ..., nlines
+c          an a vertical line will be similarly drawn between columns
+c          lines(i) and lines(i)+1 for i=1,2,...,nlines 
+c
+c iunt   = logical unit number where to write the matrix into.
+c----------------------------------------------------------------------- 
+      data haf /0.5/, zero/0.0/, conv/2.54/
+c-----------------------------------------------------------------------
+      n = ncol 
+      if (mode .eq. 0) n = nrow 
+      job1 = job /10 
+      job2 = job - 10*job1 
+      maxdim = max(nrow, ncol)
+      rwid = real(ncol-1)
+      rht  = real(nrow-1)
+      unit0 = size/real(maxdim) 
+      hsiz = hsize/unit0
+      vsiz = vsize/unit0
+      siz  = size/unit0
+c     
+c     size of little box for each dot -- boxr = in local units
+c     boxabs in inches (or cm)
+c 
+      boxr   = 0.6
+      boxabs = unit0*boxr 
+c
+c     spaces between frame to nearest box
+c
+      space = 0.03/unit0+(1.0-boxr)/2.0 
+c
+c     begin document generation
+c  for very first call better have \unitlength set first..
+      if (job2 .le. 1) then 
+         write (iunt,*) ' \\documentstyle[epic,12pt]{article} '
+         write (iunt,*) ' \\begin{document}'
+         write (iunt,100) unit0, munt 
+         write (iunt,99) hsiz, vsiz 
+      else 
+c     redeclare unitlength 
+         write (iunt,100) unit0, munt 
+      endif 
+c----- always redefine units 
+
+      if (job1 .eq. 0) then
+         write (iunt,101) boxabs, boxabs
+      else 
+         write (iunt,102) boxabs/unit0
+      endif 
+ 100  format(' \\setlength{\\unitlength}{',f5.3,a2,'}') 
+ 99   format('\\begin{picture}(',f8.2,1h,,f8.2,1h)) 
+ 101  format('\\def\\boxd{\\vrule height',f7.4,'in width',f7.4,'in }') 
+ 102  format('\\def\\boxd{\\circle*{',f7.4,'}}')
+c
+c     draw a frame around the matrix
+c     get shifts from real inches to local units
+c
+      xs = xleft/unit0 + (hsiz-siz)*0.5
+      ys = bot/unit0
+c     
+      eps = 0.0 
+      xmin = xs 
+      xmax = xs +rwid + boxr + 2.0*space 
+      ymin = ys 
+      ymax = ys+rht + boxr + 2.0*space
+c     
+c     bottom margin between box and title
+c
+      xmargin = 0.30/unit0
+      if (munt .eq. 'cm' .or. munt .eq. 'CM') xmargin = xmargin*2.5
+      xtit = 0.5*(xmin+xmax) 
+      xtit = xmin
+      ytit = ymax 
+      if (ptitle .eq. 0) ytit = ymin - xmargin 
+      xdim = xmax-xmin
+      ltit = LENSTR(title)
+      write(iunt,111) xtit,ytit,xdim,xmargin,title(1:ltit) 
+c      
+ 111  format ('\\put(',F6.2,',',F6.2,
+     *     '){\\makebox(',F6.2,1h,F6.2,'){',A,2h}}) 
+c      
+      write(iunt,*)  ' \\thicklines'
+      write (iunt,108) xmin,ymin,xmax,ymin,xmax,ymax,
+     *     xmin,ymax,xmin,ymin
+ 108  format('\\drawline',1h(,f8.2,1h,,f8.2,1h), 
+     *     1h(,f8.2,1h,,f8.2,1h), 1h(,f8.2,1h,,f8.2,1h), 
+     *     1h(,f8.2,1h,,f8.2,1h), 1h(,f8.2,1h,,f8.2,1h)) 
+c     
+c     draw the separation lines 
+c     
+c      if (job1 .gt.0) then
+c         xs = xs + 0.25
+c         ys = ys + 0.25
+c      endif
+      write(iunt,*)  ' \\thinlines'
+      do 22 kol=1, nlines 
+         isep = lines(kol)
+c     
+c     horizontal lines 
+c     
+         yy =  ys + real(nrow-isep)  
+         write(iunt,109) xmin, yy, xmax, yy
+c     
+c     vertical lines 
+c     
+         xx = xs+real(isep) 
+         write(iunt,109) xx, ymin, xx, ymax 
+ 22   continue
+c     
+ 109  format('\\drawline',
+     *     1h(,f8.2,1h,,f8.2,1h), 1h(,f8.2,1h,,f8.2,1h)) 
+      
+c-----------plotting loop ---------------------------------------------
+c     
+c     add some space right of the frame and up from the bottom
+c     
+      xs = xs+space
+      ys = ys+space
+c-----------------------------------------------------------------------
+      do 1 ii=1, n
+         istart = ia(ii)
+         ilast  = ia(ii+1)-1 
+         if (mode .eq. 1) then
+            do 2 k=istart, ilast
+               if (job1 .le. 1) then               
+                  write(iunt,12) xs+real(ii-1),ys+real(nrow-ja(k)) 
+               else
+                  write(iunt,13) xs+real(ii-1),ys+real(nrow-ja(k)),
+     *                 ii,ja(k) 
+               endif
+ 2          continue 
+         else
+            y = ys+real(nrow-ii)
+            do 3 k=istart, ilast
+               if (job1 .le. 1) then
+                  write(iunt,12) xs+real(ja(k)-1), y 
+               else 
+                  write(iunt,13) xs+real(ja(k)-1), y, ii, ja(k) 
+               endif
+ 3          continue          
+c     add diagonal element if MSR mode.
+            if (mode .eq. 2) 
+     *           write(iunt,12) xs+real(ii-1), ys+real(nrow-ii) 
+         endif
+ 1    continue
+c-----------------------------------------------------------------------
+ 12   format ('\\put(',F6.2,',',F6.2,')','{\\boxd}') 
+ 13   format ('\\put(',F6.2,',',F6.2,')','{$a_{',i3,1h,,i3,'}$}')
+c-----------------------------------------------------------------------
+      if (job2 .eq. 0 .or. job2 .eq. 2) then 
+         write (iunt,*) ' \\end{picture} '
+         write (iunt,*) ' \\end{document} '
+      endif
+c
+      return
+      end
+      integer function lenstr0(s)
+c-----------------------------------------------------------------------
+c return length of the string S
+c-----------------------------------------------------------------------
+      character*(*) s
+      integer len
+      intrinsic len
+      integer n
+c----------------------------------------------------------------------- 
+      n = len(s)
+10    continue
+        if (s(n:n).eq.' ') then
+          n = n-1
+          if (n.gt.0) go to 10
+        end if
+      lenstr0 = n
+c
+      return
+c-----------------------------------------------------------------------
+      end
+c----------------------------------------------------------------------- 
diff --git a/UNSUPP/README b/UNSUPP/README
new file mode 100644
index 0000000..98e0bbc
--- /dev/null
+++ b/UNSUPP/README
@@ -0,0 +1,57 @@
+
+                         ----------
+                         | UNSUPP |
+                         ---------- 
+
+ This is meant to contain any  subroutine that is not part 
+ of SPARSKIT proper (for example preconditioners, iterative 
+ solvers, plotting and other tools,...) but which are
+ nevertheless provided with the understanding that they may
+ not be the best codes around or that there is further work
+ needed on them.. 
+
+ CONTRIBUTIONS REQUESTED. 
+ ----------------------- 
+		             ----------------- 
+		             Current contents:
+			     -----------------
+SUBDIRECTORY BLAS1
+------------------
+
+* blas1.f : includes subroutines:
+            dcopy : copies a vector, x, to a vector, y.
+            ddot  : dot product of two vectors.
+            csscal: scales a complex vector by a real constant.
+            cswap : interchanges two vectors.
+            csrot : applies a plane rotation.
+            cscal : scales a vector by a constant.
+            ccopy : copies a vector, x, to a vector, y.
+            drotg : construct givens plane rotation.
+            drot  : applies a plane rotation.
+            dswap : interchanges two vectors.
+            dscal : scales a vector by a constant.
+            daxpy : constant times a vector plus a vector.
+            
+SUBDIRECTORY PLOTS
+------------------ 
+
+* psgrd.f contains subroutine "psgrid" which plots a symmetric graph.
+
+* texplt1.f contains subroutine "texplt" allows several matrices
+  in the same picture by calling texplt several times and exploiting job and
+  different shifts.
+
+* texgrid1.f contains subroutine "texgrd" which generates tex commands
+  for plotting a symmetric graph associated with a mesh. Allows
+  several grids in the same picture by calling texgrd several times and
+  exploiting job and different shifts.
+
+
+ SUBDIRECTORY MATEXP   
+ -------------------
+ routines related to matrix exponentials. 
+
+
+* exppro.f    computes w=exp( t A) v   -- + a simple test program rexp.f 
+* phipro.f    computes w = phi(At)v, where phi(x)=(1-exp(x))/x;
+              Also allows to solve the P.D.E. system y'= A y + b  
diff --git a/dotests b/dotests
new file mode 100755
index 0000000..82aeddc
--- /dev/null
+++ b/dotests
@@ -0,0 +1,144 @@
+#!/bin/sh
+#
+# SPARSKIT script for making and running all test programs.
+# Last modified: May 9, 1994.
+
+make all
+cd BLASSM
+echo Making tests in BLASSM directory
+make mvec.ex
+make tester.ex
+cd ..
+cd FORMATS
+echo Making tests in FORMATS directory
+make un.ex
+make fmt.ex
+make rvbr.ex
+cd ..
+cd INFO
+echo Making tests in INFO directory
+make info1.ex
+cd ..
+cd INOUT
+echo Making tests in INOUT directory
+make chk.ex
+make hb2ps.ex
+make hb2pic.ex
+cd ..
+cd ITSOL
+echo Making tests in ITSOL directory
+make riters.ex
+make rilut.ex
+make riter2.ex
+cd ..
+cd MATGEN/FDIF
+echo Making tests in MATGEN/FDIF directory
+make gen5.ex
+make genbl.ex
+cd ../..
+cd MATGEN/FEM
+echo Making tests in MATGEN/FEM directory
+make fem.ex
+cd ../..
+cd MATGEN/MISC
+echo Making tests in MATGEN/MISC directory
+make sobel.ex
+make zlatev.ex
+make markov.ex
+cd ../..
+cd UNSUPP/MATEXP
+echo Making tests in UNSUPP/MATEXP directory
+make exp.ex
+make phi.ex
+cd ../..
+
+# run all test programs
+
+cd BLASSM
+echo Testing BLASSM/mvec.ex ---------------------------------------
+./mvec.ex
+echo Testing BLASSM/tester.ex ---------------------------------------
+./tester.ex
+cd ..
+cd FORMATS
+echo Testing FORMATS/un.ex ---------------------------------------
+./un.ex
+cat unary.mat
+echo Testing FORMATS/fmt.ex ---------------------------------------
+./fmt.ex
+grep ERROR *.mat
+ls -s *.mat
+echo Testing FORMATS/rvbr.ex ---------------------------------------
+./rvbr.ex
+cd ..
+cd INFO
+echo Testing INFO/info1.ex ---------------------------------------
+./info1.ex < saylr1
+cd ..
+cd INOUT
+echo Testing INOUT/chk.ex ---------------------------------------
+./chk.ex
+echo Testing INOUT/hb2ps.ex ---------------------------------------
+./hb2ps.ex < ../INFO/saylr1 > saylr1.ps
+echo Testing INOUT/hb2pic.ex ---------------------------------------
+./hb2pic.ex < ../INFO/saylr1 > saylr1.pic
+cd ..
+cd ITSOL
+echo Testing ITSOL/riters.ex ---------------------------------------
+./riters.ex
+echo Testing ITSOL/rilut.ex ---------------------------------------
+./rilut.ex
+echo Testing ITSOL/riter2.ex ---------------------------------------
+./riter2.ex < ../INFO/saylr1
+cd ..
+cd MATGEN/FDIF
+echo Testing MATGEN/FDIF/gen5.ex ---------------------------------------
+./gen5.ex << \EOF
+10 10 1
+testpt.mat
+EOF
+echo Testing MATGEN/FDIF/genbl.ex ---------------------------------------
+./genbl.ex << \EOF
+10 10 1
+4
+testbl.mat
+EOF
+cd ../..
+cd MATGEN/FEM
+echo Testing MATGEN/FEM/fem.ex ---------------------------------------
+./fem.ex << \EOF
+2
+2
+EOF
+cat mat.hb
+cd ../..
+cd MATGEN/MISC
+echo Testing MATGEN/MISC/sobel.ex ---------------------------------------
+./sobel.ex << \EOF
+10
+EOF
+echo Testing MATGEN/MISC/zlatev.ex ---------------------------------------
+./zlatev.ex
+cat zlatev1.mat
+cat zlatev2.mat
+cat zlatev3.mat
+echo Testing MATGEN/MISC/markov.ex ---------------------------------------
+./markov.ex << \EOF
+10
+EOF
+cat markov.mat
+cd ../..
+cd UNSUPP/MATEXP
+echo Testing UNSUPP/MATEXP/exp.ex ---------------------------------------
+./exp.ex << \EOF
+0.1
+0.00001
+10
+EOF
+echo Testing UNSUPP/MATEXP/phi.ex ---------------------------------------
+./phi.ex << \EOF
+0.1
+0.00001
+10
+EOF
+cd ../..
diff --git a/logfile b/logfile
new file mode 100644
index 0000000..918c71f
--- /dev/null
+++ b/logfile
@@ -0,0 +1,329 @@
+
+----------------------------------------------------------------------
+SPARSKIT Revision History
+------------------------------------------------------------------------
+
+May 9, 1994 (Version 2)
+
+Warning:
+The interface for gen57pt has changed.
+The interface for csrbnd has changed.
+The interface for bsrcsr has changed.
+
+New or rearranged modules: 
+ITSOL/ilut.f       -- four preconditioners (old UNSUPP/SOLVERS plus ilutp)
+ITSOL/iters.f      -- nine iterative solvers using reverse communication
+MATGEN             -- rearranged into three subdirectories: FDIF, FEM, MISC.
+MATGEN/MISC/sobel.f-- generate matrices from a statistical application
+ORDERINGS/ccn      -- routines for strongly connected components
+ORDERINGS/color.f  -- coloring based routines for reordering
+ORDERINGS/levset.f -- level set based routines for reordering
+UNSUPP/PLOTS       -- many routines have been moved to the INOUT module
+
+New format:  VBR (Variable block row)
+------------------------------------------------------------------------
+May 25, 1994
+Fixed a bug in FORMATS/unary.f/levels, found by Aart J.C. Bik, Leiden.
+------------------------------------------------------------------------
+June 3, 1994
+The symmetric and nonsymmetric carpenter square format has been renamed
+to the symmetric and unsymmetric sparse skyline format.  This is simply
+a name change for the functions:
+        csrucs to csruss
+        ucscsr to usscsr
+        csrscs to csrsss
+        scscsr to ssscsr  
+This is a new format that was not in version 1 of SPARSKIT.
+------------------------------------------------------------------------
+June 27, 1994
+
+The function ssrcsr has changed, to make it more flexible (K. Wu, UMN).
+The old version will still be available in xssrcsr, but may be deleted
+in the near future.  Please let us know of any bugs, or errors in the
+code documentation.
+
+The interface to msrcsr has changed, to make the function in place
+(R. Bramley, Indiana).
+
+A number of minor bug fixes to the INOUT module (R. Bramley, Indiana).
+
+ICOPY in ccn.f was renamed to CCNICOPY to eliminate name conflicts
+with other libraries.
+
+Very minor typographical fixes were made to the paper.* documentation.
+------------------------------------------------------------------------
+August 3, 1994
+
+dinfo13.f was modified very slightly to handle skew-symmetric matrices.
+------------------------------------------------------------------------
+August 8, 1994
+
+Bug fixed in usscsr (D. Su).
+
+Bug fixed in ssrcsr (K. Wu).
+------------------------------------------------------------------------
+August 18, 1994
+
+New, more efficient version of cooell.  The old version will still be 
+available in xcooell, but may be deleted in the near future.  (K. Wu)
+
+Bug fixed in INFO/infofun/ansym.  (K. Wu)
+------------------------------------------------------------------------
+September 22, 1994
+
+Bug fixed in FORMATS/unary/getdia.  (John Red-horse, Sandia)
+
+Changes to ITSOL/iters.f:
+Bug fix in TFQMR; initialization of workspace; number of matrix-vector
+multiplications reported now includes those done in initialization;
+added routine FOM (Full Orthogonalization Method).  (K. Wu)
+
+This version has only been tested on Solaris, and the test script 
+output is in out.new.  The other outputs are somewhat out of date.
+The changes have not been major; please let us know if you find
+any incompatibilities.  Thanks.  (E. Chow)
+------------------------------------------------------------------------
+October 10, 1994
+
+formats.f: revised ssrcsr to be able to sort the column of the matrix
+produced, revised cooell to fill the unused entries in AO,JAO with zero
+diagonal elements.  (K. Wu)
+
+unary.f: new routine clncsr for removing duplicate entries, sorting
+columns of the input matrix, it requires less work space than csort.
+(K. Wu)
+
+iters.f: bug fix in fom.  (K. Wu)
+
+chkfmt1.f (test program): bug fix in call to ssrcsr.
+
+dotests script: slight modification when running fmt.ex
+
+matvec.f: added atmuxr, Tranpose(A) times a vector, where A is rectangular
+in CSR format.  Also useful for A times a vector, where A is rectangular
+in CSC format.  Very similar to atmux.  (E. Chow)
+------------------------------------------------------------------------
+October 17, 1994
+
+Minor fix to ilut.f, proper stopping when maxits is a multiple of the
+Krylov subspace size.
+
+A number of changes to iters.f:
+(1) add reorthgonalization to the Modified Gram-Schmidt procedures;
+(2) check number of matrix-vector multiplications used at the end of
+evey Arnoldi step;
+(3) in the initialization stage of the iterative solvers, clear fpar
+elements to zero.
+------------------------------------------------------------------------
+November 16, 1994
+
+Selective reorthogonalization replaces reorthogonalization change
+of Oct. 17, 1994.
+------------------------------------------------------------------------
+November 23, 1994
+
+Added csrcsc2, a minor variation on csrcsc for rectangular matrices.
+csrcsc now calls csrcsc2.
+
+Removed a useless line in infofun.f that could give a compiler warning.
+
+In the ILUT preconditioner, lfil-1 new fill-ins for rows in the 
+strictly upper part was used.  This has been changed to lfil,
+to be consistent with the strictly lower part.
+
+Replaced levset.f with dsepart.f, which adds a number of new partitioners:
+rdis, dse2way, dse, in addition to the original dblstr.
+The new perphn subroutine no longer takes the iperm array.
+------------------------------------------------------------------------
+January 3, 1995
+
+FORMATS/formats.f:ellcsr  ia(1) was not set.  (Reported by J. Schoon.)
+------------------------------------------------------------------------
+January 30, 1995
+
+BLASSM/blassm.f:amub  fixed the documentation. (Reported by D. O'Leary.)
+------------------------------------------------------------------------
+February 27, 1995
+
+iters.f: the reverse communication protocol has been augmented to make
+performing users own convergence test easier. minor bug fixes.
+
+unary.f: subroutine clncsr is slightly changed so that it will remove
+zero entries. also minor corrections to its documentation.
+
+formats.f: subroutine ssrcsr is slightly changed so it may optionally
+remove zero entries. also minor corrections to its documentation.
+
+infofun.f: subroutine ansym is rewritten to compute the Frobineus norm
+of the pattern-nonsymmetric part directly insead of computing it from
+the difference between the Frobineus of the whole matrix and its
+pattern-symmetric part. This should make the answer of 'FAN' more
+reliable.
+------------------------------------------------------------------------
+March 21, 1995
+
+Bug fix in iters.f:fom.
+Also, FOM, GMRES, FGMRES modified so that if a zero pivot is 
+encountered in the triangular solve part of the algorithm,
+the solve is truncated.
+
+The latest output of the dotests script as run on a solaris 2 machine
+is in out.sol2.
+------------------------------------------------------------------------
+March 27, 1995
+
+Fixes to ILUT and ILUTP.
+Backed out of the change of Nov. 23, 1994.  The original code was
+correct (lenu includes the diagonal).
+A smaller drop tolerance than prescribed was used (namely, by
+the 1-norm of the row); this has now been fixed.
+------------------------------------------------------------------------
+April 12, 1995
+
+Minor fix in rilut.f.  A duplicate call to ilut has been removed.
+------------------------------------------------------------------------
+April 21, 1995
+
+Cleaner versions of ILUT and ILUTP.  Note that the interface has been
+changed slightly (workspace parameters have been coalesced), and the
+definition of lfil has changed.
+ILUK, the standard level ILU(k), has been added to ilut.f.
+Due to these changes, ilut.f, and rilut.f have changed.
+Also, riters.f riter2.f have changed where they call ilut.
+
+The Block Sparse Row (BSR) format has changed, so that entries are
+stored in A(ni,ni,nnz), rather than A(nnz,ni,ni), where the blocks
+are ni by ni, and there are nnz blocks.  This stores the entries of
+the blocks contiguously so that they may be passed to other subroutines.
+As a result of this change, the following codes have changed:
+FORMATS/formats.f:bsrcsr - additionally takes extra workspace
+FORMATS/formats.f:csrbsr
+MATGEN/FDID/genmat.f:gen57bl - output n is now block dimension
+FORMATS/chkfmt1.f
+FORMATS/rvbr.f
+MATGEN/FDIF/rgenblk.f
+BLASSM/rmatvec.f
+
+The latest output of the dotests script from our Solaris machines here
+is in out.04-21-95.
+------------------------------------------------------------------------
+April 22, 1995
+
+Now you can ask csrbsr to tell you the number of block nonzeros beforehand.
+Also, a minor fix if job.eq.0.
+------------------------------------------------------------------------
+April 25, 1995
+
+csrbsr cleaned up even more.
+------------------------------------------------------------------------
+May 22, 1995
+
+iters.f - fixed rare bug in bcg and bcgstab: termination test not done
+properly if they breakdown on the first step.
+------------------------------------------------------------------------
+July 27, 1995
+
+Fixed a bug in the header documentation for csrcsc(), describing
+the appending of data structures.  Detected by Dan Stanescu, Concordia.
+
+Fixed compilation errors in UNSUPP/PLOTS/texgrid1.f for IBM machines,
+detected by Regis Gras, Laboratoire CEPHAG.
+------------------------------------------------------------------------
+Sept. 22, 1995
+
+Fixed  a bug   in the ILUT/ILUTP  routines --   found by Larry  Wigton
+[Boeing]  This bug caused  small elements  to  be  stored in  L factor
+produced by  ILUT.  Recall that  the ILUT  codes have been  revised on
+April  21 line   above  and there  are   changes in  meanings   of the
+parameters and calling  sequences.   The drop strategy  used  has also
+been modified slightly.
+
+We also  added two new preconditioning  routines named ILUD  and ILUDP
+[The difference between these and ILUT is  that there is no control of
+storage. Drop strategy is controled by only one parameter (tol). [This
+should be bigger than in ILUT in general.]
+-----------------------------------------------------------------------
+Sept. 26, 1995
+
+infofun.f:ansym was improved again.
+-----------------------------------------------------------------------
+Feb 17th, 1996:
+ Bug fix in getdia (bug reported by Norm Fuchs, Purdue).
+-----------------------------------------------------------------------
+
+August 13th, 1996
+ 1. A few more fixes to ILUT, ILUTP [ILUTP did not give the same result as
+ ILUT when pivoting is not done. This is now fixed.
+ 2. Small bug in (SPARSKIT2/ITSOL/iters.f) subroutine tidycg reported
+ by Laura Dutto.
+ 3. documentation error in minor (SPARSKIT2/ITSOL/iters.f) subroutine 
+ FGMRES requires more storage than stated.
+
+Sep. 6, 1997 
+ one routine (dperm1) has been added to FORMATS/unary.f
+ (slightly modified from PSPARSIB).. YS 
+
+Nov. 20, 1997 
+ Implicit none caused some minor compilation problems because of
+ order of declarations [reported by Stefan Nilsson (Chalmers) and
+ Christer Andersson (NADA, Sweden)]. Fixed by changing order of
+ declarations. YS 
+
+-----------------------------------------------------------------------  
+
+Aug. 16th, 1998.
+ removed useless argument in function mindom (ORDERINGS/dsepart.f)  
+ added one option to gen57pt in MATGEN/FDIF/matgen.f
+
+Sept. 2nd 1998,
+ - fixed yet other compiler problems with double declarations of
+   integer n in ilut.f -- these show up with gnu f77. 
+ - fixed an incorrect declaration of arraw iwk in coicsr in 
+   FORMATS/formats (reported by Dan Lee -- bmw)
+ - removed unnecessary declaration of stopbis in tfqmr 
+ - lenr was not initialized in nonz() in infofun (reported by Massino 
+   Caspari). 
+ - a spurious "g" character was inadvertantly introduced in the previous
+   version. [reported by Mike Botchev (CWI, NL)..  
+
+Sept. 30th, 1998
+ - fixed a bug in routine apldia (in BLASSM/blassm.f). The code worked
+   only for in place cases. 
+----------------------------------------------------------------------- 
+
+June 16, 1999
+ - the  finite element matrix generation suite has been updated 
+   (I. Moulistas) - three files have changed elmtlib2.f  femgen.f meshes.f
+   in the directory MATGEN/FEM
+ - the finite difference matrix generation routione matgen.f has been 
+   changed [SPARSKIT2/MATGEN/FDIF/genmat.f] - bug reported by David
+   Hyson and corrected by Kesheng John Wu..
+ - Adoption of the GNU general public licencing - GNU licence agreement 
+   added and terms in the main README file changed.. 
+
+March 3, 2001: fix documentation glitch regarding size of w in ilut routine.
+
+July 12, 2001: iband was not initialized in bandwidth -- warning: quite
+   a few bugs found so far in infofun! 
+
+July 24, 2001: another bug in infofun (in ansym).. no fun YS. 
+   
+-----------------------------------------------------------------------
+
+Sep 2003: fixed returned nrhs in readmtc 
+
+Dec. 29th, 03 -- it looks like the March 3, 2001 correction was not done
+[mishandled versions!] -- put new version..
+
+Mar. 08, 2005: revamping of the old files in DOC - contributed by
+  Daniel Heiserer (Thanks!) 
+
+Mar. 08, 2005: Moved to the Lesser GNU license instead of GNU -
+
+Oct. 20, 2005: a few bug fixes reported by E. Canot (irisa). 
+
+Nov. 18, 2009: a bug in csort [made assumption that ncol<nrow] 
+               reported by L. M. Baker.
+-----------------------------------------------------------------------
+
+
diff --git a/makefile b/makefile
new file mode 100644
index 0000000..643f81b
--- /dev/null
+++ b/makefile
@@ -0,0 +1,153 @@
+#-----------------------------------------------------------------------
+#                     S P A R S K I T  makefile 
+#-----------------------------------------------------------------------
+#
+# There are three types of source files in SPARSKIT:
+# 1. library source files
+# 2. non-library and unsupported source files
+# 3. test programs
+#
+# Simply type "make" to make the SPARSKIT library.
+#
+# "make all" will additionally make all the unsupported objects.
+#
+# To make the test programs, use the makefiles in each subdirectory,
+# or see the dotests script.
+# There are no references to test programs in this makefile.
+# Some test programs use the non-library objects from other directories,
+# so do a "make all" before making test programs.
+#
+# Last Updated:  May 9, 1994.
+
+SHELL = /bin/sh
+F77 = f77 
+# F77 = f77 
+# AR = ar rcv 
+AR = ar -rcv 
+# OPT = -c 
+# OPT = -c -static -64 -mips4 -O3 -r10000
+OPT = -c -O
+
+# Cray options
+#F77 = cf77
+#AR = bld rv
+#OPT = -c -Wf"-dp" 
+
+#
+# library objects
+#
+OBJ =	BLASSM/blassm.o		\
+	BLASSM/matvec.o		\
+	FORMATS/formats.o	\
+	FORMATS/unary.o		\
+	INFO/infofun.o		\
+	INOUT/inout.o		\
+	ITSOL/ilut.o		\
+	ITSOL/iters.o		\
+	MATGEN/FDIF/genmat.o	\
+	MATGEN/FEM/elmtlib2.o	\
+	MATGEN/FEM/femgen.o	\
+	MATGEN/FEM/meshes.o	\
+	MATGEN/MISC/sobel.o	\
+	MATGEN/MISC/zlatev.o	\
+	ORDERINGS/ccn.o		\
+	ORDERINGS/color.o	\
+	ORDERINGS/dsepart.o
+
+#
+# non-library and unsupported objects
+#
+OBJ2 =	ITSOL/itaux.o		\
+	MATGEN/FDIF/functns.o	\
+	MATGEN/FEM/functns2.o	\
+	UNSUPP/BLAS1/blas1.o	\
+	UNSUPP/MATEXP/exppro.o	\
+	UNSUPP/MATEXP/phipro.o	\
+	UNSUPP/PLOTS/psgrd.o	\
+	UNSUPP/PLOTS/texgrid1.o	\
+	UNSUPP/PLOTS/texplt1.o
+
+DIRS =	.			\
+	BLASSM			\
+	FORMATS			\
+	INFO			\
+	INOUT			\
+	ITSOL			\
+	MATGEN/FDIF		\
+	MATGEN/FEM		\
+	MATGEN/MISC		\
+	ORDERINGS		\
+	UNSUPP/BLAS1		\
+	UNSUPP/MATEXP		\
+	UNSUPP/PLOTS
+
+lib libskit.a: $(OBJ) 
+	 $(AR) libskit.a  $(OBJ) 
+##	 ranlib libskit.a
+
+# do not ranlib on some architectures
+
+clean: 
+	@for dir in $(DIRS) ;\
+          do \
+          echo cleaning $$dir ;\
+          (cd $$dir; rm -f *~ *.o *.ex .,* fort.* ftn?? *.mat *.pic *.ps *.trace core) ;\
+          done
+
+tarit: 
+	(cd ..; tar cvf - SPARSKIT2 | gzip -c > SPARSKIT2.tar.gz) 
+
+all: $(OBJ) $(OBJ2) libskit.a
+
+BLASSM/blassm.o: BLASSM/blassm.f
+	(cd BLASSM ; $(F77)  $(OPT) blassm.f)
+BLASSM/matvec.o: BLASSM/matvec.f
+	(cd BLASSM ; $(F77)  $(OPT) matvec.f)
+FORMATS/formats.o: FORMATS/formats.f
+	(cd FORMATS ; $(F77)  $(OPT) formats.f)
+FORMATS/unary.o: FORMATS/unary.f
+	(cd FORMATS ; $(F77)  $(OPT) unary.f)
+INFO/infofun.o: INFO/infofun.f
+	(cd INFO ; $(F77)  $(OPT) infofun.f)
+INOUT/inout.o: INOUT/inout.f
+	(cd INOUT; $(F77)  $(OPT) inout.f)
+ITSOL/ilut.o: ITSOL/ilut.f
+	(cd ITSOL; $(F77)  $(OPT) ilut.f)
+ITSOL/iters.o: ITSOL/iters.f
+	(cd ITSOL; $(F77)  $(OPT) iters.f)
+ITSOL/itaux.o: ITSOL/itaux.f
+	(cd ITSOL; $(F77)  $(OPT) itaux.f)
+MATGEN/FDIF/genmat.o: MATGEN/FDIF/genmat.f
+	(cd MATGEN/FDIF ; $(F77)  $(OPT) genmat.f)
+MATGEN/FDIF/functns.o: MATGEN/FDIF/functns.f
+	(cd MATGEN/FDIF ; $(F77)  $(OPT) functns.f)
+MATGEN/FEM/elmtlib2.o: MATGEN/FEM/elmtlib2.f
+	(cd MATGEN/FEM ; $(F77)  $(OPT) elmtlib2.f)
+MATGEN/FEM/femgen.o: MATGEN/FEM/femgen.f
+	(cd MATGEN/FEM ; $(F77)  $(OPT) femgen.f)
+MATGEN/FEM/functns2.o : MATGEN/FEM/functns2.f 
+	(cd MATGEN/FEM ; $(F77)  $(OPT) functns2.f)
+MATGEN/FEM/meshes.o: MATGEN/FEM/meshes.f
+	(cd MATGEN/FEM ; $(F77)  $(OPT) meshes.f)
+MATGEN/MISC/sobel.o: MATGEN/MISC/sobel.f
+	(cd MATGEN/MISC ; $(F77)  $(OPT) sobel.f)
+MATGEN/MISC/zlatev.o: MATGEN/MISC/zlatev.f
+	(cd MATGEN/MISC ; $(F77)  $(OPT) zlatev.f)
+ORDERINGS/ccn.o: ORDERINGS/ccn.f
+	(cd ORDERINGS ; $(F77)  $(OPT) ccn.f)
+ORDERINGS/color.o: ORDERINGS/color.f
+	(cd ORDERINGS ; $(F77)  $(OPT) color.f)
+ORDERINGS/dsepart.o: ORDERINGS/dsepart.f
+	(cd ORDERINGS ; $(F77)  $(OPT) dsepart.f)
+UNSUPP/BLAS1/blas1.o: UNSUPP/BLAS1/blas1.f
+	(cd UNSUPP/BLAS1 ; $(F77)  $(OPT) blas1.f)
+UNSUPP/MATEXP/exppro.o: UNSUPP/MATEXP/exppro.f
+	(cd UNSUPP/MATEXP ; $(F77)  $(OPT) exppro.f)
+UNSUPP/MATEXP/phipro.o: UNSUPP/MATEXP/phipro.f
+	(cd UNSUPP/MATEXP ; $(F77)  $(OPT) phipro.f)
+UNSUPP/PLOTS/psgrd.o : UNSUPP/PLOTS/psgrd.f 
+	(cd UNSUPP/PLOTS ; $(F77) $(OPT) psgrd.f)
+UNSUPP/PLOTS/texgrid1.o : UNSUPP/PLOTS/texgrid1.f 
+	(cd UNSUPP/PLOTS ; $(F77) $(OPT) texgrid1.f)
+UNSUPP/PLOTS/texplt1.o : UNSUPP/PLOTS/texplt1.f 
+	(cd UNSUPP/PLOTS ; $(F77) $(OPT) texplt1.f)
diff --git a/sgrep b/sgrep
new file mode 100755
index 0000000..4fe735d
--- /dev/null
+++ b/sgrep
@@ -0,0 +1,5 @@
+# Usage: sgrep pattern
+# Searches all source files for 'pattern'.
+# Regular expressions should be enclosed in quotes "".
+
+find . -name '*.f' -exec grep "$*" /dev/null {} \;