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-rw-r--r--src/de/lmu/ifi/dbs/elki/math/linearalgebra/VMath.java284
1 files changed, 163 insertions, 121 deletions
diff --git a/src/de/lmu/ifi/dbs/elki/math/linearalgebra/VMath.java b/src/de/lmu/ifi/dbs/elki/math/linearalgebra/VMath.java
index 6b8cdc31..fc514a65 100644
--- a/src/de/lmu/ifi/dbs/elki/math/linearalgebra/VMath.java
+++ b/src/de/lmu/ifi/dbs/elki/math/linearalgebra/VMath.java
@@ -4,7 +4,7 @@ package de.lmu.ifi.dbs.elki.math.linearalgebra;
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
- Copyright (C) 2013
+ Copyright (C) 2014
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
@@ -75,16 +75,17 @@ public final class VMath {
*/
public static final double[] randomNormalizedVector(final int dimensionality) {
final double[] v = new double[dimensionality];
- for (int i = 0; i < dimensionality; i++) {
+ for(int i = 0; i < dimensionality; i++) {
v[i] = Math.random();
}
double norm = euclideanLength(v);
- if (norm != 0) {
- for (int row = 0; row < v.length; row++) {
+ if(norm != 0) {
+ for(int row = 0; row < v.length; row++) {
v[row] /= norm;
}
return v;
- } else {
+ }
+ else {
return randomNormalizedVector(dimensionality);
}
}
@@ -120,7 +121,7 @@ public final class VMath {
*/
public static final double[][] transpose(final double[] v) {
double[][] re = new double[v.length][1];
- for (int i = 0; i < v.length; i++) {
+ for(int i = 0; i < v.length; i++) {
re[i][0] = v[i];
}
return re;
@@ -136,7 +137,7 @@ public final class VMath {
public static final double[] plus(final double[] v1, final double[] v2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
final double[] result = new double[v1.length];
- for (int i = 0; i < result.length; i++) {
+ for(int i = 0; i < result.length; i++) {
result[i] = v1[i] + v2[i];
}
return result;
@@ -153,7 +154,7 @@ public final class VMath {
public static final double[] plusTimes(final double[] v1, final double[] v2, final double s2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
final double[] result = new double[v1.length];
- for (int i = 0; i < result.length; i++) {
+ for(int i = 0; i < result.length; i++) {
result[i] = v1[i] + v2[i] * s2;
}
return result;
@@ -170,7 +171,7 @@ public final class VMath {
public static final double[] timesPlus(final double[] v1, final double s1, final double[] v2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
final double[] result = new double[v1.length];
- for (int i = 0; i < result.length; i++) {
+ for(int i = 0; i < result.length; i++) {
result[i] = v1[i] * s1 + v2[i];
}
return result;
@@ -188,7 +189,7 @@ public final class VMath {
public static final double[] timesPlusTimes(final double[] v1, final double s1, final double[] v2, final double s2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
final double[] result = new double[v1.length];
- for (int i = 0; i < result.length; i++) {
+ for(int i = 0; i < result.length; i++) {
result[i] = v1[i] * s1 + v2[i] * s2;
}
return result;
@@ -203,7 +204,7 @@ public final class VMath {
*/
public static final double[] plusEquals(final double[] v1, final double[] v2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v1[i] += v2[i];
}
return v1;
@@ -219,7 +220,7 @@ public final class VMath {
*/
public static final double[] plusTimesEquals(final double[] v1, final double[] v2, final double s2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v1[i] += s2 * v2[i];
}
return v1;
@@ -235,7 +236,7 @@ public final class VMath {
*/
public static final double[] timesPlusEquals(final double[] v1, final double s1, final double[] v2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v1[i] = v1[i] * s1 + v2[i];
}
return v1;
@@ -252,7 +253,7 @@ public final class VMath {
*/
public static final double[] timesPlusTimesEquals(final double[] v1, final double s1, final double[] v2, final double s2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v1[i] = v1[i] * s1 + v2[i] * s2;
}
return v1;
@@ -267,7 +268,7 @@ public final class VMath {
*/
public static final double[] plus(final double[] v1, final double d) {
final double[] result = new double[v1.length];
- for (int i = 0; i < result.length; i++) {
+ for(int i = 0; i < result.length; i++) {
result[i] = v1[i] + d;
}
return result;
@@ -281,7 +282,7 @@ public final class VMath {
* @return Modified vector
*/
public static final double[] plusEquals(final double[] v1, final double d) {
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v1[i] += d;
}
return v1;
@@ -296,7 +297,7 @@ public final class VMath {
*/
public static final double[] minus(final double[] v1, final double[] v2) {
final double[] sub = new double[v1.length];
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
sub[i] = v1[i] - v2[i];
}
return sub;
@@ -312,7 +313,7 @@ public final class VMath {
*/
public static final double[] minusTimes(final double[] v1, final double[] v2, final double s2) {
final double[] sub = new double[v1.length];
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
sub[i] = v1[i] - v2[i] * s2;
}
return sub;
@@ -328,7 +329,7 @@ public final class VMath {
*/
public static final double[] timesMinus(final double[] v1, final double s1, final double[] v2) {
final double[] sub = new double[v1.length];
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
sub[i] = v1[i] * s1 - v2[i];
}
return sub;
@@ -345,7 +346,7 @@ public final class VMath {
*/
public static final double[] timesMinusTimes(final double[] v1, final double s1, final double[] v2, final double s2) {
final double[] sub = new double[v1.length];
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
sub[i] = v1[i] * s1 - v2[i] * s2;
}
return sub;
@@ -360,7 +361,7 @@ public final class VMath {
*/
public static final double[] minusEquals(final double[] v1, final double[] v2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v1[i] -= v2[i];
}
return v1;
@@ -376,7 +377,7 @@ public final class VMath {
*/
public static final double[] minusTimesEquals(final double[] v1, final double[] v2, final double s2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v1[i] -= v2[i] * s2;
}
return v1;
@@ -392,7 +393,7 @@ public final class VMath {
*/
public static final double[] timesMinusEquals(final double[] v1, final double s1, final double[] v2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v1[i] = v1[i] * s1 - v2[i];
}
return v1;
@@ -409,7 +410,7 @@ public final class VMath {
*/
public static final double[] timesMinusTimesEquals(final double[] v1, final double s1, final double[] v2, final double s2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v1[i] = v1[i] * s1 - v2[i] * s2;
}
return v1;
@@ -424,7 +425,7 @@ public final class VMath {
*/
public static final double[] minus(final double[] v1, final double d) {
final double[] result = new double[v1.length];
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
result[i] = v1[i] - d;
}
return result;
@@ -438,7 +439,7 @@ public final class VMath {
* @return v1 = v1 - d
*/
public static final double[] minusEquals(final double[] v1, final double d) {
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v1[i] -= d;
}
return v1;
@@ -453,7 +454,7 @@ public final class VMath {
*/
public static final double[] times(final double[] v1, final double s1) {
final double[] v = new double[v1.length];
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v[i] = v1[i] * s1;
}
return v;
@@ -467,7 +468,7 @@ public final class VMath {
* @return v1 = v1 * s1
*/
public static final double[] timesEquals(final double[] v1, final double s) {
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
v1[i] *= s;
}
return v1;
@@ -484,8 +485,8 @@ public final class VMath {
assert (m2.length == 1) : ERR_MATRIX_INNERDIM;
final int columndimension = m2[0].length;
final double[][] re = new double[v1.length][columndimension];
- for (int j = 0; j < columndimension; j++) {
- for (int i = 0; i < v1.length; i++) {
+ for(int j = 0; j < columndimension; j++) {
+ for(int i = 0; i < v1.length; i++) {
re[i][j] = v1[i] * m2[0][j];
}
}
@@ -503,9 +504,9 @@ public final class VMath {
assert (m2.length == v1.length) : ERR_MATRIX_INNERDIM;
final int columndimension = m2[0].length;
final double[][] re = new double[1][columndimension];
- for (int j = 0; j < columndimension; j++) {
+ for(int j = 0; j < columndimension; j++) {
double s = 0;
- for (int k = 0; k < v1.length; k++) {
+ for(int k = 0; k < v1.length; k++) {
s += v1[k] * m2[k][j];
}
re[0][j] = s;
@@ -523,7 +524,7 @@ public final class VMath {
public static final double transposeTimes(final double[] v1, final double[] v2) {
assert (v2.length == v1.length) : ERR_MATRIX_INNERDIM;
double s = 0;
- for (int k = 0; k < v1.length; k++) {
+ for(int k = 0; k < v1.length; k++) {
s += v1[k] * v2[k];
}
return s;
@@ -540,8 +541,8 @@ public final class VMath {
assert (m2[0].length == 1) : ERR_MATRIX_INNERDIM;
final double[][] re = new double[v1.length][m2.length];
- for (int j = 0; j < m2.length; j++) {
- for (int i = 0; i < v1.length; i++) {
+ for(int j = 0; j < m2.length; j++) {
+ for(int i = 0; i < v1.length; i++) {
re[i][j] = v1[i] * m2[j][0];
}
}
@@ -557,8 +558,8 @@ public final class VMath {
*/
public static final double[][] timesTranspose(final double[] v1, final double[] v2) {
final double[][] re = new double[v1.length][v2.length];
- for (int j = 0; j < v2.length; j++) {
- for (int i = 0; i < v1.length; i++) {
+ for(int j = 0; j < v2.length; j++) {
+ for(int i = 0; i < v1.length; i++) {
re[i][j] = v1[i] * v2[j];
}
}
@@ -566,7 +567,8 @@ public final class VMath {
}
/**
- * Returns the scalar product (dot product) of this vector and the specified vector v.
+ * Returns the scalar product (dot product) of this vector and the specified
+ * vector v.
*
* This is the same as transposeTimes.
*
@@ -577,21 +579,36 @@ public final class VMath {
public static final double scalarProduct(final double[] v1, final double[] v2) {
assert (v1.length == v2.length) : ERR_VEC_DIMENSIONS;
double scalarProduct = 0.0;
- for (int row = 0; row < v1.length; row++) {
+ for(int row = 0; row < v1.length; row++) {
scalarProduct += v1[row] * v2[row];
}
return scalarProduct;
}
/**
+ * Squared Euclidean length of the vector
+ *
+ * @param v1 vector
+ * @return squared Euclidean length of this vector
+ */
+ public static final double squareSum(final double[] v1) {
+ double acc = 0.0;
+ for(int row = 0; row < v1.length; row++) {
+ final double v = v1[row];
+ acc += v * v;
+ }
+ return acc;
+ }
+
+ /**
* Euclidean length of the vector
*
* @param v1 vector
- * @return euclidean length of this vector
+ * @return Euclidean length of this vector
*/
public static final double euclideanLength(final double[] v1) {
double acc = 0.0;
- for (int row = 0; row < v1.length; row++) {
+ for(int row = 0; row < v1.length; row++) {
final double v = v1[row];
acc += v * v;
}
@@ -607,8 +624,8 @@ public final class VMath {
public static final double[] normalize(final double[] v1) {
double norm = euclideanLength(v1);
double[] re = new double[v1.length];
- if (norm != 0) {
- for (int row = 0; row < v1.length; row++) {
+ if(norm != 0) {
+ for(int row = 0; row < v1.length; row++) {
re[row] = v1[row] / norm;
}
}
@@ -623,8 +640,8 @@ public final class VMath {
*/
public static final double[] normalizeEquals(final double[] v1) {
double norm = euclideanLength(v1);
- if (norm != 0) {
- for (int row = 0; row < v1.length; row++) {
+ if(norm != 0) {
+ for(int row = 0; row < v1.length; row++) {
v1[row] /= norm;
}
}
@@ -643,7 +660,7 @@ public final class VMath {
final int columndimension = m2[0].length;
double[] sum = new double[v1.length];
- for (int i = 0; i < columndimension; i++) {
+ for(int i = 0; i < columndimension; i++) {
// TODO: optimize - copy less.
double[] v_i = getCol(m2, i);
plusTimesEquals(sum, v_i, scalarProduct(v1, v_i));
@@ -705,7 +722,7 @@ public final class VMath {
*/
public static final double[][] unitMatrix(final int dim) {
final double[][] e = new double[dim][dim];
- for (int i = 0; i < dim; i++) {
+ for(int i = 0; i < dim; i++) {
e[i][i] = 1;
}
return e;
@@ -731,8 +748,8 @@ public final class VMath {
*/
public static final double[][] random(final int m, final int n) {
final double[][] A = new double[m][n];
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
+ for(int i = 0; i < m; i++) {
+ for(int j = 0; j < n; j++) {
A[i][j] = Math.random();
}
}
@@ -748,7 +765,7 @@ public final class VMath {
*/
public static final double[][] identity(final int m, final int n) {
final double[][] A = new double[m][n];
- for (int i = 0; i < Math.min(m, n); i++) {
+ for(int i = 0; i < Math.min(m, n); i++) {
A[i][i] = 1.0;
}
return A;
@@ -763,7 +780,7 @@ public final class VMath {
*/
public static final double[][] diagonal(final double[] v1) {
final double[][] result = new double[v1.length][v1.length];
- for (int i = 0; i < v1.length; i++) {
+ for(int i = 0; i < v1.length; i++) {
result[i][i] = v1[i];
}
return result;
@@ -778,7 +795,7 @@ public final class VMath {
public static final double[][] copy(final double[][] m1) {
final int columndimension = m1[0].length;
final double[][] X = new double[m1.length][columndimension];
- for (int i = 0; i < m1.length; i++) {
+ for(int i = 0; i < m1.length; i++) {
System.arraycopy(m1[i], 0, X[i], 0, columndimension);
}
return X;
@@ -793,7 +810,7 @@ public final class VMath {
public static final double[] rowPackedCopy(final double[][] m1) {
final int columndimension = m1[0].length;
double[] vals = new double[m1.length * columndimension];
- for (int i = 0; i < m1.length; i++) {
+ for(int i = 0; i < m1.length; i++) {
System.arraycopy(m1[i], 0, vals, i * columndimension, columndimension);
}
return vals;
@@ -808,8 +825,8 @@ public final class VMath {
public static final double[] columnPackedCopy(final double[][] m1) {
final int columndimension = m1[0].length;
final double[] vals = new double[m1.length * columndimension];
- for (int i = 0; i < m1.length; i++) {
- for (int j = 0; j < columndimension; j++) {
+ for(int i = 0; i < m1.length; i++) {
+ for(int j = 0; j < columndimension; j++) {
vals[i + j * m1.length] = m1[i][j];
}
}
@@ -828,7 +845,7 @@ public final class VMath {
*/
public static final double[][] getMatrix(final double[][] m1, final int r0, final int r1, final int c0, final int c1) {
final double[][] X = new double[r1 - r0 + 1][c1 - c0 + 1];
- for (int i = r0; i <= r1; i++) {
+ for(int i = r0; i <= r1; i++) {
System.arraycopy(m1[i], c0, X[i - r0], 0, c1 - c0 + 1);
}
return X;
@@ -844,8 +861,8 @@ public final class VMath {
*/
public static final double[][] getMatrix(final double[][] m1, final int[] r, final int[] c) {
final double[][] X = new double[r.length][c.length];
- for (int i = 0; i < r.length; i++) {
- for (int j = 0; j < c.length; j++) {
+ for(int i = 0; i < r.length; i++) {
+ for(int j = 0; j < c.length; j++) {
X[i][j] = m1[r[i]][c[j]];
}
}
@@ -863,7 +880,7 @@ public final class VMath {
*/
public static final double[][] getMatrix(final double[][] m1, final int[] r, final int c0, final int c1) {
final double[][] X = new double[r.length][c1 - c0 + 1];
- for (int i = 0; i < r.length; i++) {
+ for(int i = 0; i < r.length; i++) {
System.arraycopy(m1[r[i]], c0, X[i], 0, c1 - c0 + 1);
}
return X;
@@ -880,8 +897,8 @@ public final class VMath {
*/
public static final double[][] getMatrix(final double[][] m1, final int r0, final int r1, final int[] c) {
final double[][] X = new double[r1 - r0 + 1][c.length];
- for (int i = r0; i <= r1; i++) {
- for (int j = 0; j < c.length; j++) {
+ for(int i = r0; i <= r1; i++) {
+ for(int j = 0; j < c.length; j++) {
X[i - r0][j] = m1[i][c[j]];
}
}
@@ -899,7 +916,7 @@ public final class VMath {
* @param m2 New values for m1(r0:r1,c0:c1)
*/
public static final void setMatrix(final double[][] m1, final int r0, final int r1, final int c0, final int c1, final double[][] m2) {
- for (int i = r0; i <= r1; i++) {
+ for(int i = r0; i <= r1; i++) {
System.arraycopy(m2[i - r0], 0, m1[i], c0, c1 - c0 + 1);
}
}
@@ -913,8 +930,8 @@ public final class VMath {
* @param m2 New values for m1(r(:),c(:))
*/
public static final void setMatrix(final double[][] m1, final int[] r, final int[] c, final double[][] m2) {
- for (int i = 0; i < r.length; i++) {
- for (int j = 0; j < c.length; j++) {
+ for(int i = 0; i < r.length; i++) {
+ for(int j = 0; j < c.length; j++) {
m1[r[i]][c[j]] = m2[i][j];
}
}
@@ -930,7 +947,7 @@ public final class VMath {
* @param m2 New values for m1(r(:),c0:c1)
*/
public static final void setMatrix(final double[][] m1, final int[] r, final int c0, final int c1, final double[][] m2) {
- for (int i = 0; i < r.length; i++) {
+ for(int i = 0; i < r.length; i++) {
System.arraycopy(m2[i], 0, m1[r[i]], c0, c1 - c0 + 1);
}
}
@@ -945,8 +962,8 @@ public final class VMath {
* @param m2 New values for m1(r0:r1,c(:))
*/
public static final void setMatrix(final double[][] m1, final int r0, final int r1, final int[] c, final double[][] m2) {
- for (int i = r0; i <= r1; i++) {
- for (int j = 0; j < c.length; j++) {
+ for(int i = r0; i <= r1; i++) {
+ for(int j = 0; j < c.length; j++) {
m1[i][c[j]] = m2[i - r0][j];
}
}
@@ -985,7 +1002,7 @@ public final class VMath {
*/
public static final double[] getCol(double[][] m1, int col) {
double[] ret = new double[m1.length];
- for (int i = 0; i < ret.length; i++) {
+ for(int i = 0; i < ret.length; i++) {
ret[i] = m1[i][col];
}
return ret;
@@ -1000,7 +1017,7 @@ public final class VMath {
*/
public static final void setCol(final double[][] m1, final int c, final double[] column) {
assert (column.length == m1.length) : ERR_DIMENSIONS;
- for (int i = 0; i < m1.length; i++) {
+ for(int i = 0; i < m1.length; i++) {
m1[i][c] = column[i];
}
}
@@ -1014,8 +1031,8 @@ public final class VMath {
public static final double[][] transpose(final double[][] m1) {
final int columndimension = getColumnDimensionality(m1);
final double[][] re = new double[columndimension][m1.length];
- for (int i = 0; i < m1.length; i++) {
- for (int j = 0; j < columndimension; j++) {
+ for(int i = 0; i < m1.length; i++) {
+ for(int j = 0; j < columndimension; j++) {
re[j][i] = m1[i][j];
}
}
@@ -1055,8 +1072,8 @@ public final class VMath {
public static final double[][] plusEquals(final double[][] m1, final double[][] m2) {
final int columndimension = getColumnDimensionality(m1);
assert (getRowDimensionality(m1) == getRowDimensionality(m2) && columndimension == getColumnDimensionality(m2)) : ERR_MATRIX_DIMENSIONS;
- for (int i = 0; i < m1.length; i++) {
- for (int j = 0; j < columndimension; j++) {
+ for(int i = 0; i < m1.length; i++) {
+ for(int j = 0; j < columndimension; j++) {
m1[i][j] += m2[i][j];
}
}
@@ -1074,8 +1091,8 @@ public final class VMath {
public static final double[][] plusTimesEquals(final double[][] m1, final double[][] m2, final double s2) {
final int columndimension = getColumnDimensionality(m1);
assert (getRowDimensionality(m1) == getRowDimensionality(m2) && columndimension == getColumnDimensionality(m2)) : ERR_MATRIX_DIMENSIONS;
- for (int i = 0; i < m1.length; i++) {
- for (int j = 0; j < columndimension; j++) {
+ for(int i = 0; i < m1.length; i++) {
+ for(int j = 0; j < columndimension; j++) {
m1[i][j] += s2 * m2[i][j];
}
}
@@ -1115,8 +1132,8 @@ public final class VMath {
public static final double[][] minusEquals(final double[][] m1, final double[][] m2) {
final int columndimension = getColumnDimensionality(m1);
assert (getRowDimensionality(m1) == getRowDimensionality(m2) && columndimension == getColumnDimensionality(m2)) : ERR_MATRIX_DIMENSIONS;
- for (int i = 0; i < m1.length; i++) {
- for (int j = 0; j < columndimension; j++) {
+ for(int i = 0; i < m1.length; i++) {
+ for(int j = 0; j < columndimension; j++) {
m1[i][j] -= m2[i][j];
}
}
@@ -1133,10 +1150,10 @@ public final class VMath {
*/
public static final double[][] minusTimesEquals(final double[][] m1, final double[][] m2, final double s2) {
assert (getRowDimensionality(m1) == getRowDimensionality(m2) && getColumnDimensionality(m1) == getColumnDimensionality(m2)) : ERR_MATRIX_DIMENSIONS;
- for (int i = 0; i < m1.length; i++) {
+ for(int i = 0; i < m1.length; i++) {
final double[] row1 = m1[i];
final double[] row2 = m2[i];
- for (int j = 0; j < row1.length; j++) {
+ for(int j = 0; j < row1.length; j++) {
row1[j] -= s2 * row2[j];
}
}
@@ -1162,9 +1179,9 @@ public final class VMath {
* @return m1 = s1 * m1, overwriting m1
*/
public static final double[][] timesEquals(final double[][] m1, final double s1) {
- for (int i = 0; i < m1.length; i++) {
+ for(int i = 0; i < m1.length; i++) {
final double[] row = m1[i];
- for (int j = 0; j < row.length; j++) {
+ for(int j = 0; j < row.length; j++) {
row[j] *= s1;
}
}
@@ -1186,17 +1203,17 @@ public final class VMath {
final double[][] r2 = new double[m1.length][bcolumndimension];
// Optimized ala Jama. jik order.
final double[] Bcolj = new double[columndimension];
- for (int j = 0; j < bcolumndimension; j++) {
+ for(int j = 0; j < bcolumndimension; j++) {
// Make a linear copy of column j from B
// TODO: use column getter from B?
- for (int k = 0; k < columndimension; k++) {
+ for(int k = 0; k < columndimension; k++) {
Bcolj[k] = m2[k][j];
}
// multiply it with each row from A
- for (int i = 0; i < m1.length; i++) {
+ for(int i = 0; i < m1.length; i++) {
final double[] Arowi = m1[i];
double s = 0;
- for (int k = 0; k < columndimension; k++) {
+ for(int k = 0; k < columndimension; k++) {
s += Arowi[k] * Bcolj[k];
}
r2[i][j] = s;
@@ -1216,10 +1233,10 @@ public final class VMath {
assert (v2.length == getColumnDimensionality(m1)) : ERR_MATRIX_INNERDIM;
final double[] re = new double[m1.length];
// multiply it with each row from A
- for (int i = 0; i < m1.length; i++) {
+ for(int i = 0; i < m1.length; i++) {
final double[] Arowi = m1[i];
double s = 0;
- for (int k = 0; k < Arowi.length; k++) {
+ for(int k = 0; k < Arowi.length; k++) {
s += Arowi[k] * v2[k];
}
re[i] = s;
@@ -1239,9 +1256,9 @@ public final class VMath {
assert (v2.length == m1.length) : ERR_MATRIX_INNERDIM;
final double[] re = new double[columndimension];
// multiply it with each row from A
- for (int i = 0; i < columndimension; i++) {
+ for(int i = 0; i < columndimension; i++) {
double s = 0;
- for (int k = 0; k < m1.length; k++) {
+ for(int k = 0; k < m1.length; k++) {
s += m1[k][i] * v2[k];
}
re[i] = s;
@@ -1262,15 +1279,15 @@ public final class VMath {
assert (m2.length == m1.length) : ERR_MATRIX_INNERDIM;
final double[][] re = new double[coldim1][coldim2];
final double[] Bcolj = new double[m1.length];
- for (int j = 0; j < coldim2; j++) {
+ for(int j = 0; j < coldim2; j++) {
// Make a linear copy of column j from B
- for (int k = 0; k < m1.length; k++) {
+ for(int k = 0; k < m1.length; k++) {
Bcolj[k] = m2[k][j];
}
// multiply it with each row from A
- for (int i = 0; i < coldim1; i++) {
+ for(int i = 0; i < coldim1; i++) {
double s = 0;
- for (int k = 0; k < m1.length; k++) {
+ for(int k = 0; k < m1.length; k++) {
s += m1[k][i] * Bcolj[k];
}
re[i][j] = s;
@@ -1282,6 +1299,7 @@ public final class VMath {
/**
* Linear algebraic matrix multiplication, a<sup>T</sup> * B * c
*
+ * @param a vector on the left
* @param B matrix
* @param c vector on the right
* @return Matrix product, a<sup>T</sup> * B * c
@@ -1289,10 +1307,10 @@ public final class VMath {
public static double transposeTimesTimes(final double[] a, final double[][] B, final double[] c) {
assert (B.length == a.length) : ERR_MATRIX_INNERDIM;
double sum = 0.0;
- for (int j = 0; j < B[0].length; j++) {
+ for(int j = 0; j < B[0].length; j++) {
// multiply it with each row from A
double s = 0;
- for (int k = 0; k < a.length; k++) {
+ for(int k = 0; k < a.length; k++) {
s += a[k] * B[k][j];
}
sum += s * c[j];
@@ -1310,13 +1328,13 @@ public final class VMath {
public static final double[][] timesTranspose(final double[][] m1, final double[][] m2) {
assert (getColumnDimensionality(m2) == getColumnDimensionality(m1)) : ERR_MATRIX_INNERDIM;
final double[][] re = new double[m1.length][m2.length];
- for (int j = 0; j < re.length; j++) {
+ for(int j = 0; j < re.length; j++) {
final double[] Browj = m2[j];
// multiply it with each row from A
- for (int i = 0; i < m1.length; i++) {
+ for(int i = 0; i < m1.length; i++) {
final double[] Arowi = m1[i];
double s = 0;
- for (int k = 0; k < Browj.length; k++) {
+ for(int k = 0; k < Browj.length; k++) {
s += Arowi[k] * Browj[k];
}
re[i][j] = s;
@@ -1338,17 +1356,17 @@ public final class VMath {
final double[][] re = new double[getColumnDimensionality(m1)][m2.length];
// Optimized ala Jama. jik order.
final double[] Acolj = new double[m1.length];
- for (int j = 0; j < re.length; j++) {
+ for(int j = 0; j < re.length; j++) {
// Make a linear copy of column j from B
- for (int k = 0; k < m1.length; k++) {
+ for(int k = 0; k < m1.length; k++) {
Acolj[k] = m1[k][j];
}
final double[] Xrow = re[j];
// multiply it with each row from A
- for (int i = 0; i < m2.length; i++) {
+ for(int i = 0; i < m2.length; i++) {
final double[] Browi = m2[i];
double s = 0;
- for (int k = 0; k < m1.length; k++) {
+ for(int k = 0; k < m1.length; k++) {
s += Browi[k] * Acolj[k];
}
Xrow[i] = s;
@@ -1358,6 +1376,28 @@ public final class VMath {
}
/**
+ * Linear algebraic matrix multiplication, (a-c)<sup>T</sup> * B * (a-c)
+ *
+ * @param B matrix
+ * @param a First vector
+ * @param c Center vector
+ * @return Matrix product, (a-c)<sup>T</sup> * B * (a-c)
+ */
+ public static double mahalanobisDistance(final double[][] B, final double[] a, final double[] c) {
+ assert (B.length == a.length && a.length == c.length) : ERR_MATRIX_INNERDIM;
+ double sum = 0.0;
+ for(int j = 0; j < B[0].length; j++) {
+ // multiply it with each row from A
+ double s = 0;
+ for(int k = 0; k < a.length; k++) {
+ s += (a[k] - c[k]) * B[k][j];
+ }
+ sum += s * (a[j] - c[j]);
+ }
+ return sum;
+ }
+
+ /**
* getDiagonal returns array of diagonal-elements.
*
* @param m1 Input matrix
@@ -1366,7 +1406,7 @@ public final class VMath {
public static final double[] getDiagonal(final double[][] m1) {
final int dim = Math.min(getColumnDimensionality(m1), m1.length);
final double[] diagonal = new double[dim];
- for (int i = 0; i < dim; i++) {
+ for(int i = 0; i < dim; i++) {
diagonal[i] = m1[i][i];
}
return diagonal;
@@ -1379,17 +1419,18 @@ public final class VMath {
*/
public static final void normalizeColumns(final double[][] m1) {
final int columndimension = getColumnDimensionality(m1);
- for (int col = 0; col < columndimension; col++) {
+ for(int col = 0; col < columndimension; col++) {
double norm = 0.0;
- for (int row = 0; row < m1.length; row++) {
+ for(int row = 0; row < m1.length; row++) {
norm = norm + (m1[row][col] * m1[row][col]);
}
norm = Math.sqrt(norm);
- if (norm != 0) {
- for (int row = 0; row < m1.length; row++) {
+ if(norm != 0) {
+ for(int row = 0; row < m1.length; row++) {
m1[row][col] /= norm;
}
- } else {
+ }
+ else {
// TODO: else: throw an exception?
}
}
@@ -1409,11 +1450,12 @@ public final class VMath {
final int rcolumndimension = columndimension + ccolumndimension;
final double[][] result = new double[m1.length][rcolumndimension];
- for (int i = 0; i < rcolumndimension; i++) {
+ for(int i = 0; i < rcolumndimension; i++) {
// FIXME: optimize - excess copying!
- if (i < columndimension) {
+ if(i < columndimension) {
setCol(result, i, getCol(m1, i));
- } else {
+ }
+ else {
setCol(result, i, getCol(m2, i - columndimension));
}
}
@@ -1431,10 +1473,10 @@ public final class VMath {
double[][] v = copy(m1);
// FIXME: optimize - excess copying!
- for (int i = 1; i < columndimension; i++) {
+ for(int i = 1; i < columndimension; i++) {
final double[] u_i = getCol(m1, i);
final double[] sum = new double[m1.length];
- for (int j = 0; j < i; j++) {
+ for(int j = 0; j < i; j++) {
final double[] v_j = getCol(v, j);
double scalar = scalarProduct(u_i, v_j) / scalarProduct(v_j, v_j);
plusEquals(sum, times(v_j, scalar));
@@ -1478,25 +1520,25 @@ public final class VMath {
* @return true if delta smaller than maximum
*/
public static final boolean almostEquals(final double[][] m1, final double[][] m2, final double maxdelta) {
- if (m1 == m2) {
+ if(m1 == m2) {
return true;
}
- if (m2 == null) {
+ if(m2 == null) {
return false;
}
- if (m1.getClass() != m2.getClass()) {
+ if(m1.getClass() != m2.getClass()) {
return false;
}
- if (m1.length != m2.length) {
+ if(m1.length != m2.length) {
return false;
}
final int columndimension = getColumnDimensionality(m1);
- if (columndimension != getColumnDimensionality(m2)) {
+ if(columndimension != getColumnDimensionality(m2)) {
return false;
}
- for (int i = 0; i < m1.length; i++) {
- for (int j = 0; j < columndimension; j++) {
- if (Math.abs(m1[i][j] - m2[i][j]) > maxdelta) {
+ for(int i = 0; i < m1.length; i++) {
+ for(int j = 0; j < columndimension; j++) {
+ if(Math.abs(m1[i][j] - m2[i][j]) > maxdelta) {
return false;
}
}
generated by cgit v1.2.3 (git 2.25.1) at 2024-06-01 18:11:56 +0000