Added missing SVN properties to some *.java files in package o.a.c.m.linear
git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1177938 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Sebastien Brisard
parent
ba15d2764e
commit
ef6e900827
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@ -1,307 +1,307 @@
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math.linear;
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import org.apache.commons.math.exception.DimensionMismatchException;
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import org.apache.commons.math.util.FastMath;
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/**
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* Calculates the Cholesky decomposition of a matrix.
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* <p>The Cholesky decomposition of a real symmetric positive-definite
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* matrix A consists of a lower triangular matrix L with same size such
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* that: A = LL<sup>T</sup>. In a sense, this is the square root of A.</p>
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* <p>This class is based on the class with similar name from the
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* <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
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* following changes:</p>
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* <ul>
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* <li>a {@link #getLT() getLT} method has been added,</li>
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* <li>the {@code isspd} method has been removed, since the constructor of
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* this class throws a {@link NonPositiveDefiniteMatrixException} when a
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* matrix cannot be decomposed,</li>
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* <li>a {@link #getDeterminant() getDeterminant} method has been added,</li>
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* <li>the {@code solve} method has been replaced by a {@link #getSolver()
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* getSolver} method and the equivalent method provided by the returned
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* {@link DecompositionSolver}.</li>
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* </ul>
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*
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* @see <a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>
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* @see <a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a>
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* @version $Id: CholeskyDecomposition.java 1173481 2011-09-21 03:45:37Z celestin $
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* @since 2.0 (changed to concrete class in 3.0)
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*/
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public class CholeskyDecomposition {
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/**
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* Default threshold above which off-diagonal elements are considered too different
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* and matrix not symmetric.
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*/
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public static final double DEFAULT_RELATIVE_SYMMETRY_THRESHOLD = 1.0e-15;
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/**
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* Default threshold below which diagonal elements are considered null
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* and matrix not positive definite.
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*/
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public static final double DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD = 1.0e-10;
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/** Row-oriented storage for L<sup>T</sup> matrix data. */
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private double[][] lTData;
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/** Cached value of L. */
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private RealMatrix cachedL;
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/** Cached value of LT. */
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private RealMatrix cachedLT;
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/**
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* Calculates the Cholesky decomposition of the given matrix.
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* <p>
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* Calling this constructor is equivalent to call {@link
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* #CholeskyDecompositionImpl(RealMatrix, double, double)} with the
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* thresholds set to the default values {@link
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* #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD} and {@link
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* #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD}
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* </p>
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* @param matrix the matrix to decompose
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* @throws NonSquareMatrixException if the matrix is not square.
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* @throws NonSymmetricMatrixException if the matrix is not symmetric.
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* @throws NonPositiveDefiniteMatrixException if the matrix is not
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* strictly positive definite.
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* @see #CholeskyDecompositionImpl(RealMatrix, double, double)
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* @see #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
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* @see #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
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*/
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public CholeskyDecomposition(final RealMatrix matrix) {
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this(matrix, DEFAULT_RELATIVE_SYMMETRY_THRESHOLD,
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DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD);
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}
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/**
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* Calculates the Cholesky decomposition of the given matrix.
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* @param matrix the matrix to decompose
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* @param relativeSymmetryThreshold threshold above which off-diagonal
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* elements are considered too different and matrix not symmetric
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* @param absolutePositivityThreshold threshold below which diagonal
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* elements are considered null and matrix not positive definite
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* @throws NonSquareMatrixException if the matrix is not square.
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* @throws NonSymmetricMatrixException if the matrix is not symmetric.
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* @throws NonPositiveDefiniteMatrixException if the matrix is not
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* strictly positive definite.
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* @see #CholeskyDecompositionImpl(RealMatrix)
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* @see #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
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* @see #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
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*/
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public CholeskyDecomposition(final RealMatrix matrix,
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final double relativeSymmetryThreshold,
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final double absolutePositivityThreshold) {
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if (!matrix.isSquare()) {
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throw new NonSquareMatrixException(matrix.getRowDimension(),
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matrix.getColumnDimension());
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}
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final int order = matrix.getRowDimension();
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lTData = matrix.getData();
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cachedL = null;
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cachedLT = null;
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// check the matrix before transformation
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for (int i = 0; i < order; ++i) {
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final double[] lI = lTData[i];
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// check off-diagonal elements (and reset them to 0)
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for (int j = i + 1; j < order; ++j) {
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final double[] lJ = lTData[j];
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final double lIJ = lI[j];
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final double lJI = lJ[i];
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final double maxDelta =
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relativeSymmetryThreshold * FastMath.max(FastMath.abs(lIJ), FastMath.abs(lJI));
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if (FastMath.abs(lIJ - lJI) > maxDelta) {
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throw new NonSymmetricMatrixException(i, j, relativeSymmetryThreshold);
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}
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lJ[i] = 0;
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}
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}
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// transform the matrix
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for (int i = 0; i < order; ++i) {
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final double[] ltI = lTData[i];
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// check diagonal element
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if (ltI[i] <= absolutePositivityThreshold) {
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throw new NonPositiveDefiniteMatrixException(ltI[i], i, absolutePositivityThreshold);
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}
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ltI[i] = FastMath.sqrt(ltI[i]);
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final double inverse = 1.0 / ltI[i];
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for (int q = order - 1; q > i; --q) {
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ltI[q] *= inverse;
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final double[] ltQ = lTData[q];
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for (int p = q; p < order; ++p) {
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ltQ[p] -= ltI[q] * ltI[p];
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}
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}
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}
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}
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/**
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* Returns the matrix L of the decomposition.
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* <p>L is an lower-triangular matrix</p>
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* @return the L matrix
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*/
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public RealMatrix getL() {
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if (cachedL == null) {
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cachedL = getLT().transpose();
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}
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return cachedL;
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}
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/**
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* Returns the transpose of the matrix L of the decomposition.
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* <p>L<sup>T</sup> is an upper-triangular matrix</p>
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* @return the transpose of the matrix L of the decomposition
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*/
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public RealMatrix getLT() {
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if (cachedLT == null) {
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cachedLT = MatrixUtils.createRealMatrix(lTData);
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}
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// return the cached matrix
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return cachedLT;
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}
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/**
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* Return the determinant of the matrix
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* @return determinant of the matrix
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*/
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public double getDeterminant() {
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double determinant = 1.0;
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for (int i = 0; i < lTData.length; ++i) {
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double lTii = lTData[i][i];
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determinant *= lTii * lTii;
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}
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return determinant;
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}
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/**
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* Get a solver for finding the A × X = B solution in least square sense.
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* @return a solver
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*/
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public DecompositionSolver getSolver() {
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return new Solver(lTData);
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}
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/** Specialized solver. */
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private static class Solver implements DecompositionSolver {
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/** Row-oriented storage for L<sup>T</sup> matrix data. */
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private final double[][] lTData;
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/**
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* Build a solver from decomposed matrix.
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* @param lTData row-oriented storage for L<sup>T</sup> matrix data
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*/
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private Solver(final double[][] lTData) {
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this.lTData = lTData;
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}
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/** {@inheritDoc} */
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public boolean isNonSingular() {
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// if we get this far, the matrix was positive definite, hence non-singular
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return true;
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}
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/** {@inheritDoc} */
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public RealVector solve(final RealVector b) {
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final int m = lTData.length;
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if (b.getDimension() != m) {
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throw new DimensionMismatchException(b.getDimension(), m);
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}
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final double[] x = b.toArray();
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// Solve LY = b
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for (int j = 0; j < m; j++) {
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final double[] lJ = lTData[j];
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x[j] /= lJ[j];
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final double xJ = x[j];
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for (int i = j + 1; i < m; i++) {
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x[i] -= xJ * lJ[i];
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}
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}
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// Solve LTX = Y
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for (int j = m - 1; j >= 0; j--) {
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x[j] /= lTData[j][j];
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final double xJ = x[j];
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for (int i = 0; i < j; i++) {
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x[i] -= xJ * lTData[i][j];
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}
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}
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return new ArrayRealVector(x, false);
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}
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/** {@inheritDoc} */
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public RealMatrix solve(RealMatrix b) {
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final int m = lTData.length;
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if (b.getRowDimension() != m) {
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throw new DimensionMismatchException(b.getRowDimension(), m);
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}
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final int nColB = b.getColumnDimension();
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final double[][] x = b.getData();
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// Solve LY = b
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for (int j = 0; j < m; j++) {
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final double[] lJ = lTData[j];
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final double lJJ = lJ[j];
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final double[] xJ = x[j];
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for (int k = 0; k < nColB; ++k) {
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xJ[k] /= lJJ;
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}
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for (int i = j + 1; i < m; i++) {
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final double[] xI = x[i];
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final double lJI = lJ[i];
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for (int k = 0; k < nColB; ++k) {
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xI[k] -= xJ[k] * lJI;
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}
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}
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}
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// Solve LTX = Y
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for (int j = m - 1; j >= 0; j--) {
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final double lJJ = lTData[j][j];
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final double[] xJ = x[j];
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for (int k = 0; k < nColB; ++k) {
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xJ[k] /= lJJ;
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}
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for (int i = 0; i < j; i++) {
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final double[] xI = x[i];
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final double lIJ = lTData[i][j];
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for (int k = 0; k < nColB; ++k) {
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xI[k] -= xJ[k] * lIJ;
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}
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}
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}
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return new Array2DRowRealMatrix(x);
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}
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/** {@inheritDoc} */
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public RealMatrix getInverse() {
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return solve(MatrixUtils.createRealIdentityMatrix(lTData.length));
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}
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}
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}
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/*
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* 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.
|
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
|
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* distributed under the License is distributed on an "AS IS" BASIS,
|
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
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* See the License for the specific language governing permissions and
|
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* limitations under the License.
|
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*/
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package org.apache.commons.math.linear;
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import org.apache.commons.math.exception.DimensionMismatchException;
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import org.apache.commons.math.util.FastMath;
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/**
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* Calculates the Cholesky decomposition of a matrix.
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* <p>The Cholesky decomposition of a real symmetric positive-definite
|
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* matrix A consists of a lower triangular matrix L with same size such
|
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* that: A = LL<sup>T</sup>. In a sense, this is the square root of A.</p>
|
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* <p>This class is based on the class with similar name from the
|
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* <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
|
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* following changes:</p>
|
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* <ul>
|
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* <li>a {@link #getLT() getLT} method has been added,</li>
|
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* <li>the {@code isspd} method has been removed, since the constructor of
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* this class throws a {@link NonPositiveDefiniteMatrixException} when a
|
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* matrix cannot be decomposed,</li>
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* <li>a {@link #getDeterminant() getDeterminant} method has been added,</li>
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* <li>the {@code solve} method has been replaced by a {@link #getSolver()
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* getSolver} method and the equivalent method provided by the returned
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* {@link DecompositionSolver}.</li>
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* </ul>
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*
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* @see <a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>
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* @see <a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a>
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* @version $Id$
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* @since 2.0 (changed to concrete class in 3.0)
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*/
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public class CholeskyDecomposition {
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/**
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* Default threshold above which off-diagonal elements are considered too different
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* and matrix not symmetric.
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*/
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public static final double DEFAULT_RELATIVE_SYMMETRY_THRESHOLD = 1.0e-15;
|
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/**
|
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* Default threshold below which diagonal elements are considered null
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* and matrix not positive definite.
|
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*/
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public static final double DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD = 1.0e-10;
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/** Row-oriented storage for L<sup>T</sup> matrix data. */
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private double[][] lTData;
|
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/** Cached value of L. */
|
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private RealMatrix cachedL;
|
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/** Cached value of LT. */
|
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private RealMatrix cachedLT;
|
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|
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/**
|
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* Calculates the Cholesky decomposition of the given matrix.
|
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* <p>
|
||||
* Calling this constructor is equivalent to call {@link
|
||||
* #CholeskyDecompositionImpl(RealMatrix, double, double)} with the
|
||||
* thresholds set to the default values {@link
|
||||
* #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD} and {@link
|
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* #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD}
|
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* </p>
|
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* @param matrix the matrix to decompose
|
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* @throws NonSquareMatrixException if the matrix is not square.
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* @throws NonSymmetricMatrixException if the matrix is not symmetric.
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* @throws NonPositiveDefiniteMatrixException if the matrix is not
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* strictly positive definite.
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* @see #CholeskyDecompositionImpl(RealMatrix, double, double)
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* @see #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
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* @see #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
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*/
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public CholeskyDecomposition(final RealMatrix matrix) {
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this(matrix, DEFAULT_RELATIVE_SYMMETRY_THRESHOLD,
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DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD);
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}
|
||||
|
||||
/**
|
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* Calculates the Cholesky decomposition of the given matrix.
|
||||
* @param matrix the matrix to decompose
|
||||
* @param relativeSymmetryThreshold threshold above which off-diagonal
|
||||
* elements are considered too different and matrix not symmetric
|
||||
* @param absolutePositivityThreshold threshold below which diagonal
|
||||
* elements are considered null and matrix not positive definite
|
||||
* @throws NonSquareMatrixException if the matrix is not square.
|
||||
* @throws NonSymmetricMatrixException if the matrix is not symmetric.
|
||||
* @throws NonPositiveDefiniteMatrixException if the matrix is not
|
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* strictly positive definite.
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* @see #CholeskyDecompositionImpl(RealMatrix)
|
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* @see #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
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* @see #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
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*/
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public CholeskyDecomposition(final RealMatrix matrix,
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final double relativeSymmetryThreshold,
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final double absolutePositivityThreshold) {
|
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if (!matrix.isSquare()) {
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throw new NonSquareMatrixException(matrix.getRowDimension(),
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matrix.getColumnDimension());
|
||||
}
|
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|
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final int order = matrix.getRowDimension();
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lTData = matrix.getData();
|
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cachedL = null;
|
||||
cachedLT = null;
|
||||
|
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// check the matrix before transformation
|
||||
for (int i = 0; i < order; ++i) {
|
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final double[] lI = lTData[i];
|
||||
|
||||
// check off-diagonal elements (and reset them to 0)
|
||||
for (int j = i + 1; j < order; ++j) {
|
||||
final double[] lJ = lTData[j];
|
||||
final double lIJ = lI[j];
|
||||
final double lJI = lJ[i];
|
||||
final double maxDelta =
|
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relativeSymmetryThreshold * FastMath.max(FastMath.abs(lIJ), FastMath.abs(lJI));
|
||||
if (FastMath.abs(lIJ - lJI) > maxDelta) {
|
||||
throw new NonSymmetricMatrixException(i, j, relativeSymmetryThreshold);
|
||||
}
|
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lJ[i] = 0;
|
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}
|
||||
}
|
||||
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// transform the matrix
|
||||
for (int i = 0; i < order; ++i) {
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|
||||
final double[] ltI = lTData[i];
|
||||
|
||||
// check diagonal element
|
||||
if (ltI[i] <= absolutePositivityThreshold) {
|
||||
throw new NonPositiveDefiniteMatrixException(ltI[i], i, absolutePositivityThreshold);
|
||||
}
|
||||
|
||||
ltI[i] = FastMath.sqrt(ltI[i]);
|
||||
final double inverse = 1.0 / ltI[i];
|
||||
|
||||
for (int q = order - 1; q > i; --q) {
|
||||
ltI[q] *= inverse;
|
||||
final double[] ltQ = lTData[q];
|
||||
for (int p = q; p < order; ++p) {
|
||||
ltQ[p] -= ltI[q] * ltI[p];
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the matrix L of the decomposition.
|
||||
* <p>L is an lower-triangular matrix</p>
|
||||
* @return the L matrix
|
||||
*/
|
||||
public RealMatrix getL() {
|
||||
if (cachedL == null) {
|
||||
cachedL = getLT().transpose();
|
||||
}
|
||||
return cachedL;
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the transpose of the matrix L of the decomposition.
|
||||
* <p>L<sup>T</sup> is an upper-triangular matrix</p>
|
||||
* @return the transpose of the matrix L of the decomposition
|
||||
*/
|
||||
public RealMatrix getLT() {
|
||||
|
||||
if (cachedLT == null) {
|
||||
cachedLT = MatrixUtils.createRealMatrix(lTData);
|
||||
}
|
||||
|
||||
// return the cached matrix
|
||||
return cachedLT;
|
||||
}
|
||||
|
||||
/**
|
||||
* Return the determinant of the matrix
|
||||
* @return determinant of the matrix
|
||||
*/
|
||||
public double getDeterminant() {
|
||||
double determinant = 1.0;
|
||||
for (int i = 0; i < lTData.length; ++i) {
|
||||
double lTii = lTData[i][i];
|
||||
determinant *= lTii * lTii;
|
||||
}
|
||||
return determinant;
|
||||
}
|
||||
|
||||
/**
|
||||
* Get a solver for finding the A × X = B solution in least square sense.
|
||||
* @return a solver
|
||||
*/
|
||||
public DecompositionSolver getSolver() {
|
||||
return new Solver(lTData);
|
||||
}
|
||||
|
||||
/** Specialized solver. */
|
||||
private static class Solver implements DecompositionSolver {
|
||||
/** Row-oriented storage for L<sup>T</sup> matrix data. */
|
||||
private final double[][] lTData;
|
||||
|
||||
/**
|
||||
* Build a solver from decomposed matrix.
|
||||
* @param lTData row-oriented storage for L<sup>T</sup> matrix data
|
||||
*/
|
||||
private Solver(final double[][] lTData) {
|
||||
this.lTData = lTData;
|
||||
}
|
||||
|
||||
/** {@inheritDoc} */
|
||||
public boolean isNonSingular() {
|
||||
// if we get this far, the matrix was positive definite, hence non-singular
|
||||
return true;
|
||||
}
|
||||
|
||||
/** {@inheritDoc} */
|
||||
public RealVector solve(final RealVector b) {
|
||||
final int m = lTData.length;
|
||||
if (b.getDimension() != m) {
|
||||
throw new DimensionMismatchException(b.getDimension(), m);
|
||||
}
|
||||
|
||||
final double[] x = b.toArray();
|
||||
|
||||
// Solve LY = b
|
||||
for (int j = 0; j < m; j++) {
|
||||
final double[] lJ = lTData[j];
|
||||
x[j] /= lJ[j];
|
||||
final double xJ = x[j];
|
||||
for (int i = j + 1; i < m; i++) {
|
||||
x[i] -= xJ * lJ[i];
|
||||
}
|
||||
}
|
||||
|
||||
// Solve LTX = Y
|
||||
for (int j = m - 1; j >= 0; j--) {
|
||||
x[j] /= lTData[j][j];
|
||||
final double xJ = x[j];
|
||||
for (int i = 0; i < j; i++) {
|
||||
x[i] -= xJ * lTData[i][j];
|
||||
}
|
||||
}
|
||||
|
||||
return new ArrayRealVector(x, false);
|
||||
}
|
||||
|
||||
/** {@inheritDoc} */
|
||||
public RealMatrix solve(RealMatrix b) {
|
||||
final int m = lTData.length;
|
||||
if (b.getRowDimension() != m) {
|
||||
throw new DimensionMismatchException(b.getRowDimension(), m);
|
||||
}
|
||||
|
||||
final int nColB = b.getColumnDimension();
|
||||
final double[][] x = b.getData();
|
||||
|
||||
// Solve LY = b
|
||||
for (int j = 0; j < m; j++) {
|
||||
final double[] lJ = lTData[j];
|
||||
final double lJJ = lJ[j];
|
||||
final double[] xJ = x[j];
|
||||
for (int k = 0; k < nColB; ++k) {
|
||||
xJ[k] /= lJJ;
|
||||
}
|
||||
for (int i = j + 1; i < m; i++) {
|
||||
final double[] xI = x[i];
|
||||
final double lJI = lJ[i];
|
||||
for (int k = 0; k < nColB; ++k) {
|
||||
xI[k] -= xJ[k] * lJI;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Solve LTX = Y
|
||||
for (int j = m - 1; j >= 0; j--) {
|
||||
final double lJJ = lTData[j][j];
|
||||
final double[] xJ = x[j];
|
||||
for (int k = 0; k < nColB; ++k) {
|
||||
xJ[k] /= lJJ;
|
||||
}
|
||||
for (int i = 0; i < j; i++) {
|
||||
final double[] xI = x[i];
|
||||
final double lIJ = lTData[i][j];
|
||||
for (int k = 0; k < nColB; ++k) {
|
||||
xI[k] -= xJ[k] * lIJ;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return new Array2DRowRealMatrix(x);
|
||||
}
|
||||
|
||||
/** {@inheritDoc} */
|
||||
public RealMatrix getInverse() {
|
||||
return solve(MatrixUtils.createRealIdentityMatrix(lTData.length));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue