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/*****************************************************************************
* *
* Small (Matlab/Octave) Toolbox for Kriging *
* *
* Copyright Notice *
* *
* Copyright (C) 2013 Alexandra Krauth, Elham Rahali & SUPELEC *
* *
* Authors: Julien Bect <julien.bect@centralesupelec.fr> *
* Alexandra Krauth <alexandrakrauth@gmail.com> *
* Elham Rahali <elham.rahali@gmail.com> *
* *
* Copying Permission Statement *
* *
* This file is part of *
* *
* STK: a Small (Matlab/Octave) Toolbox for Kriging *
* (http://sourceforge.net/projects/kriging) *
* *
* STK is free software: you can redistribute it and/or modify it under *
* the terms of the GNU General Public License as published by the Free *
* Software Foundation, either version 3 of the License, or (at your *
* option) any later version. *
* *
* STK 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 General Public *
* License for more details. *
* *
* You should have received a copy of the GNU General Public License *
* along with STK. If not, see <http://www.gnu.org/licenses/>. *
* *
****************************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "stk_mex.h"
#include "primes.h"
/*****************************************************************************
* *
* Subfunctions *
* *
****************************************************************************/
int vanDerCorput_RR2(unsigned int b, unsigned int n, double *h);
int compute_nb_digits(unsigned int n, unsigned int b);
double radical_inverse(int *digits, unsigned int nb_digits, unsigned int b);
int next_Mersenne_number(unsigned int b);
int construct_permutRR(unsigned int b, int* permut);
int construct_permutRR_Mersenne(unsigned int b, int* permut);
/*****************************************************************************
* *
* MEX entry point (mexFunction) *
* *
* STK_SAMPLING_VDC_RR2 computes the first N terms of the J^th *
* RR2-scrambled van der Corput sequence *
* *
* CALL: X = stk_sampling_vdc_rr2(N, J) *
* *
* Reference: Ladislav Kocis and William J. Whiten (1997) *
* Computational investigations of lowdiscrepancy sequences. *
* ACM Transactions on Mathematical Software, 23(2):266-294. *
* *
****************************************************************************/
#define N_IN prhs[0]
#define J_IN prhs[1]
#define X_OUT plhs[0]
void mexFunction
(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
int n_, j_, r;
unsigned int n, j;
double *h;
mxArray* xdata;
n_ = 0; j_ = 0;
/*--- Read input arguments -----------------------------------------------*/
if(nrhs != 2)
mexErrMsgIdAndTxt("STK:stk_sampling_vdc_rr2:nrhs", "Two inputs required.");
if ((mxReadScalar_int(N_IN, &n_) != 0) || (n_ <= 0))
mexErrMsgIdAndTxt("STK:stk_sampling_vdc_rr2:IncorrectArgument",
"First argument (n) must be a strictly positive "
"scalar integer.");
n = (unsigned int) n_;
if ((mxReadScalar_int(J_IN, &j_) != 0) || (j_ <= 0))
mexErrMsgIdAndTxt("STK:stk_sampling_vdc_rr2:IncorrectArgument",
"Second argument (j) must be a scrictly positive "
"scalar integer.");
j = (unsigned int) j_;
if (j > PRIMES_TABLE_SIZE)
mexErrMsgIdAndTxt("STK:stk_sampling_vdc_rr2:IncorrectArgument",
"Second argument (d) must be smaller than %d.",
PRIMES_TABLE_SIZE);
/*--- Do the actual computations in a subroutine -------------------------*/
xdata = mxCreateDoubleMatrix(n, 1, mxREAL);
h = mxGetPr(xdata);
if ((r = vanDerCorput_RR2(primes_table[j - 1], n, h)) != STK_OK)
mexErrMsgIdAndTxt("STK:stk_sampling_vdc_rr2:Sanity",
"vanDerCorput_RR2() failed with error code %d.", r);
/*--- Create output dataframe --------------------------------------------*/
if ((r = mexCallMATLAB(1, &X_OUT, 1, &xdata, "stk_dataframe")) != 0)
mexErrMsgIdAndTxt("STK:stk_sampling_vdc_rr2:Sanity",
"mexCallMATLAB() failed with error code %d.", r);
}
/*****************************************************************************
* *
* void vanDerCorput_RR2(unsigned int b, unsigned int N, double *result) *
* *
* Compute N terms of the RR2-scrambled van der Corput sequence in base b. *
* *
****************************************************************************/
int vanDerCorput_RR2
(unsigned int b, unsigned int N, double *result)
{
int i, j, c, nb_digits_max, nb_digits, quotient;
int *permut, *digits, *s_digits;
/*--- Check input arguments ----------------------------------------------*/
if (N == 0)
return STK_OK; /* we successfully did... nothing... */
if (b == 0) /* 0 is not a prime */
return STK_ERROR_DOMAIN;
/*--- Allocate temporary arrays ------------------------------------------*/
/* Create arrays to store base-b representations
(note: N is the biggest integer that we'll have to represent) */
if ((nb_digits_max = compute_nb_digits(N, b)) == -1)
return STK_ERROR_SANITY;
if ((digits = (int*) mxCalloc(nb_digits_max, sizeof(int))) == NULL)
return STK_ERROR_OOM;
if ((s_digits = (int*) mxCalloc(nb_digits_max, sizeof(int))) == NULL)
return STK_ERROR_OOM;
/* Create the permutation array */
if ((permut = (int*) mxCalloc(b, sizeof(int))) == NULL)
return STK_ERROR_OOM;
construct_permutRR(b, permut);
/*--- Compute N terms in the base-b of the sequence ----------------------*/
nb_digits = 1; /* number of digits required to represent 1 in base b */
c = b; /* number of iterations before we increment nb_digits */
/* note: the first term is always zero, that's why we start at i = 1 */
for (i = 1; i < N; i++)
{
if ((--c) == 0) /* we need to increase the number of digits */
{
nb_digits++;
c = i * (b - 1);
}
/* Compute the representation of i in base b
(no need to fill with zeros at the end) */
quotient = i;
j = 0;
while (quotient > 0)
{
digits[j] = quotient % b;
quotient = quotient / b;
j++;
}
/* Scramble the digits */
for(j = 0; j < nb_digits; j++)
s_digits[j] = permut[digits[j]];
/* Compute the i^th term using the radical inverse function */
result[i] = radical_inverse(s_digits, nb_digits, b);
}
/*--- Free temporary arrays ----------------------------------------------*/
mxFree(digits);
mxFree(s_digits);
mxFree(permut);
return STK_OK;
}
/*****************************************************************************
* *
* void construct_permutRR(unsigned int b, int* pi_b) *
* *
* Compute N terms of the RR2-scrambled van der Corput sequence in base b. *
* *
****************************************************************************/
int construct_permutRR
(unsigned int b, int* pi_b)
{
int i, j, b_max, *pi_b_max;
/* Find the smallest number of the form 2^k - 1 (Mersenne number) that is
greater than or equal to b. This number is not necessarily prime. */
b_max = next_Mersenne_number(b);
/* Create an auxiliary permutation of {0, 1, ..., b_max - 1} */
if ((pi_b_max = mxCalloc(b_max, sizeof(int))) == NULL)
return STK_ERROR_OOM;
construct_permutRR_Mersenne(b_max, pi_b_max);
/* Trim pi_b_max to get pi_b (note: the first element is always 0) */
j = 1;
for (i = 1; i < b; i++)
{
while (pi_b_max[j] > (b - 1))
j++;
pi_b[i] = pi_b_max[j++];
}
mxFree(pi_b_max);
return STK_OK;
}
/*****************************************************************************
* *
* int construct_permutRR_Mersenne(unsigned int b, int *permut) *
* *
* Construct the "reverse radix" permutation in the case where b is a *
* Mersenne number. *
* *
* Note: careful, we do not actually check that b is a Mersenne number *
* *
****************************************************************************/
int construct_permutRR_Mersenne
(unsigned int b, int *permut)
{
int i, j, direct, reversed, digits;
if ((digits = compute_nb_digits(b - 1, 2)) == -1)
return STK_ERROR_SANITY;
permut[0] = 0;
for (i = 1; i < b; i++)
{
direct = i;
reversed = 0;
for(j = 0; j < digits; j++)
{
reversed <<= 1;
reversed += (direct & 01);
direct >>= 1;
}
permut[i] = reversed;
}
return STK_OK;
}
/*****************************************************************************
* *
* int compute_nb_digits(unsigned int n, unsigned int b) *
* *
* Compute the number of digits required to represent n in base b. *
* *
****************************************************************************/
int compute_nb_digits
(unsigned int n, unsigned int b)
{
int nb_digits, quotient;
if ((b <= 0) || (n <= 0))
return -1;
nb_digits = 0;
quotient = n;
while (quotient > 0)
{
nb_digits++;
quotient = quotient / b;
}
return nb_digits;
}
/*****************************************************************************
* *
* double radical_inverse *
* (int *digits, unsigned int nb_digits, unsigned int b) *
* *
* Apply the base-b radical inverse transform to a number given through its *
* base-b representation *
* *
****************************************************************************/
double radical_inverse
(int *digits, unsigned int nb_digits, unsigned int b)
{
int i, b_pow_inv;
double sum;
b_pow_inv = 1;
sum = 0;
for (i = 0; i < nb_digits; i++)
{
b_pow_inv *= b;
sum += ((double) digits[i]) / ((double)b_pow_inv);
}
return sum;
}
/*****************************************************************************
* *
* int next_Mersenne_number(unsigned int b) *
* *
* Compute the first integer bigger than b that is of the form *
* *
* 2^k - 1, with k an integer *
* *
****************************************************************************/
int next_Mersenne_number
(unsigned int b)
{
int m = 0;
while (m < b)
{
m <<= 1;
m += 1;
}
return m;
}
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