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Merged RectangularCholeskyDecomposition and RectangularCholeskyDecompositionImpl (see MATH-662). 

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1175105 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Sebastien Brisard 2011-09-24 04:54:28 +00:00
parent 18323639c9
commit b4764661a3
3 changed files with 120 additions and 164 deletions
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127
src/main/java/org/apache/commons/math/linear/RectangularCholeskyDecomposition.java
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@ -17,11 +17,10 @@
package org.apache.commons.math.linear; package org.apache.commons.math.linear;
import org.apache.commons.math.util.FastMath;
/** /**
* An interface to classes that implement an algorithm to calculate a * Calculates the rectangular Cholesky decomposition of a matrix.
* rectangular variation of Cholesky decomposition of a real symmetric
* positive semidefinite matrix.
* <p>The rectangular Cholesky decomposition of a real symmetric positive * <p>The rectangular Cholesky decomposition of a real symmetric positive
* semidefinite matrix A consists of a rectangular matrix B with the same * semidefinite matrix A consists of a rectangular matrix B with the same
* number of rows such that: A is almost equal to BB<sup>T</sup>, depending * number of rows such that: A is almost equal to BB<sup>T</sup>, depending
@ -38,12 +37,118 @@ package org.apache.commons.math.linear;
* linear systems, so it does not provide any {@link DecompositionSolver * linear systems, so it does not provide any {@link DecompositionSolver
* decomposition solver}.</p> * decomposition solver}.</p>
* *
* @see CholeskyDecomposition * @see <a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>
* @see org.apache.commons.math.random.CorrelatedRandomVectorGenerator * @see <a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a>
* @version $Id$ * @version $Id$
* @since 3.0 * @since 2.0 (changed to concrete class in 3.0)
*/ */
public interface RectangularCholeskyDecomposition { public class RectangularCholeskyDecomposition {
/** Permutated Cholesky root of the symmetric positive semidefinite matrix. */
private final RealMatrix root;
/** Rank of the symmetric positive semidefinite matrix. */
private int rank;
/**
* Decompose a symmetric positive semidefinite matrix.
*
* @param matrix Symmetric positive semidefinite matrix.
* @param small Diagonal elements threshold under which column are
* considered to be dependent on previous ones and are discarded.
* @exception NonPositiveDefiniteMatrixException if the matrix is not
* positive semidefinite.
*/
public RectangularCholeskyDecomposition(RealMatrix matrix, double small)
throws NonPositiveDefiniteMatrixException {
int order = matrix.getRowDimension();
double[][] c = matrix.getData();
double[][] b = new double[order][order];
int[] swap = new int[order];
int[] index = new int[order];
for (int i = 0; i < order; ++i) {
index[i] = i;
}
int r = 0;
for (boolean loop = true; loop;) {
// find maximal diagonal element
swap[r] = r;
for (int i = r + 1; i < order; ++i) {
int ii = index[i];
int isi = index[swap[i]];
if (c[ii][ii] > c[isi][isi]) {
swap[r] = i;
}
}
// swap elements
if (swap[r] != r) {
int tmp = index[r];
index[r] = index[swap[r]];
index[swap[r]] = tmp;
}
// check diagonal element
int ir = index[r];
if (c[ir][ir] < small) {
if (r == 0) {
throw new NonPositiveDefiniteMatrixException(c[ir][ir], ir, small);
}
// check remaining diagonal elements
for (int i = r; i < order; ++i) {
if (c[index[i]][index[i]] < -small) {
// there is at least one sufficiently negative diagonal element,
// the symmetric positive semidefinite matrix is wrong
throw new NonPositiveDefiniteMatrixException(c[index[i]][index[i]], i, small);
}
}
// all remaining diagonal elements are close to zero, we consider we have
// found the rank of the symmetric positive semidefinite matrix
++r;
loop = false;
} else {
// transform the matrix
double sqrt = FastMath.sqrt(c[ir][ir]);
b[r][r] = sqrt;
double inverse = 1 / sqrt;
for (int i = r + 1; i < order; ++i) {
int ii = index[i];
double e = inverse * c[ii][ir];
b[i][r] = e;
c[ii][ii] -= e * e;
for (int j = r + 1; j < i; ++j) {
int ij = index[j];
double f = c[ii][ij] - e * b[j][r];
c[ii][ij] = f;
c[ij][ii] = f;
}
}
// prepare next iteration
loop = ++r < order;
}
}
// build the root matrix
rank = r;
root = MatrixUtils.createRealMatrix(order, r);
for (int i = 0; i < order; ++i) {
for (int j = 0; j < r; ++j) {
root.setEntry(index[i], j, b[i][j]);
}
}
}
/** Get the root of the covariance matrix. /** Get the root of the covariance matrix.
* The root is the rectangular matrix <code>B</code> such that * The root is the rectangular matrix <code>B</code> such that
@ -51,7 +156,9 @@ public interface RectangularCholeskyDecomposition {
* @return root of the square matrix * @return root of the square matrix
* @see #getRank() * @see #getRank()
*/ */
RealMatrix getRootMatrix(); public RealMatrix getRootMatrix() {
return root;
}
/** Get the rank of the symmetric positive semidefinite matrix. /** Get the rank of the symmetric positive semidefinite matrix.
* The r is the number of independent rows in the symmetric positive semidefinite * The r is the number of independent rows in the symmetric positive semidefinite
@ -60,6 +167,8 @@ public interface RectangularCholeskyDecomposition {
* @return r of the square matrix. * @return r of the square matrix.
* @see #getRootMatrix() * @see #getRootMatrix()
*/ */
int getRank(); public int getRank() {
return rank;
}
} }

152
src/main/java/org/apache/commons/math/linear/RectangularCholeskyDecompositionImpl.java
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@ -1,152 +0,0 @@
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math.linear;
import org.apache.commons.math.util.FastMath;
/**
* Calculates the rectangular Cholesky decomposition of a matrix.
* <p>The rectangular Cholesky decomposition of a real symmetric positive
* semidefinite matrix A consists of a rectangular matrix B with the same
* number of rows such that: A is almost equal to BB<sup>T</sup>, depending
* on a user-defined tolerance. In a sense, this is the square root of A.</p>
*
* @see <a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>
* @see <a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a>
* @version $Id$
* @since 2.0
*/
public class RectangularCholeskyDecompositionImpl implements RectangularCholeskyDecomposition {
/** Permutated Cholesky root of the symmetric positive semidefinite matrix. */
private final RealMatrix root;
/** Rank of the symmetric positive semidefinite matrix. */
private int rank;
/**
* Decompose a symmetric positive semidefinite matrix.
*
* @param matrix Symmetric positive semidefinite matrix.
* @param small Diagonal elements threshold under which column are
* considered to be dependent on previous ones and are discarded.
* @exception NonPositiveDefiniteMatrixException if the matrix is not
* positive semidefinite.
*/
public RectangularCholeskyDecompositionImpl(RealMatrix matrix, double small)
throws NonPositiveDefiniteMatrixException {
int order = matrix.getRowDimension();
double[][] c = matrix.getData();
double[][] b = new double[order][order];
int[] swap = new int[order];
int[] index = new int[order];
for (int i = 0; i < order; ++i) {
index[i] = i;
}
int r = 0;
for (boolean loop = true; loop;) {
// find maximal diagonal element
swap[r] = r;
for (int i = r + 1; i < order; ++i) {
int ii = index[i];
int isi = index[swap[i]];
if (c[ii][ii] > c[isi][isi]) {
swap[r] = i;
}
}
// swap elements
if (swap[r] != r) {
int tmp = index[r];
index[r] = index[swap[r]];
index[swap[r]] = tmp;
}
// check diagonal element
int ir = index[r];
if (c[ir][ir] < small) {
if (r == 0) {
throw new NonPositiveDefiniteMatrixException(c[ir][ir], ir, small);
}
// check remaining diagonal elements
for (int i = r; i < order; ++i) {
if (c[index[i]][index[i]] < -small) {
// there is at least one sufficiently negative diagonal element,
// the symmetric positive semidefinite matrix is wrong
throw new NonPositiveDefiniteMatrixException(c[index[i]][index[i]], i, small);
}
}
// all remaining diagonal elements are close to zero, we consider we have
// found the rank of the symmetric positive semidefinite matrix
++r;
loop = false;
} else {
// transform the matrix
double sqrt = FastMath.sqrt(c[ir][ir]);
b[r][r] = sqrt;
double inverse = 1 / sqrt;
for (int i = r + 1; i < order; ++i) {
int ii = index[i];
double e = inverse * c[ii][ir];
b[i][r] = e;
c[ii][ii] -= e * e;
for (int j = r + 1; j < i; ++j) {
int ij = index[j];
double f = c[ii][ij] - e * b[j][r];
c[ii][ij] = f;
c[ij][ii] = f;
}
}
// prepare next iteration
loop = ++r < order;
}
}
// build the root matrix
rank = r;
root = MatrixUtils.createRealMatrix(order, r);
for (int i = 0; i < order; ++i) {
for (int j = 0; j < r; ++j) {
root.setEntry(index[i], j, b[i][j]);
}
}
}
/** {@inheritDoc} */
public RealMatrix getRootMatrix() {
return root;
}
/** {@inheritDoc} */
public int getRank() {
return rank;
}
}

5
src/main/java/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.java
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@ -20,7 +20,6 @@ package org.apache.commons.math.random;
import org.apache.commons.math.exception.DimensionMismatchException; import org.apache.commons.math.exception.DimensionMismatchException;
import org.apache.commons.math.linear.RealMatrix; import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.linear.RectangularCholeskyDecomposition; import org.apache.commons.math.linear.RectangularCholeskyDecomposition;
import org.apache.commons.math.linear.RectangularCholeskyDecompositionImpl;
/** /**
* A {@link RandomVectorGenerator} that generates vectors with with * A {@link RandomVectorGenerator} that generates vectors with with
@ -95,7 +94,7 @@ public class CorrelatedRandomVectorGenerator
this.mean = mean.clone(); this.mean = mean.clone();
final RectangularCholeskyDecomposition decomposition = final RectangularCholeskyDecomposition decomposition =
new RectangularCholeskyDecompositionImpl(covariance, small); new RectangularCholeskyDecomposition(covariance, small);
root = decomposition.getRootMatrix(); root = decomposition.getRootMatrix();
this.generator = generator; this.generator = generator;
@ -124,7 +123,7 @@ public class CorrelatedRandomVectorGenerator
} }
final RectangularCholeskyDecomposition decomposition = final RectangularCholeskyDecomposition decomposition =
new RectangularCholeskyDecompositionImpl(covariance, small); new RectangularCholeskyDecomposition(covariance, small);
root = decomposition.getRootMatrix(); root = decomposition.getRootMatrix();
this.generator = generator; this.generator = generator;