home | career | drupal | java | mac | mysql | perl | scala | uml | unix  

Java example source code file (CholeskyDecomposition.java)

This example Java source code file (CholeskyDecomposition.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

array2drowrealmatrix, arrayrealvector, choleskydecomposition, decompositionsolver, default_absolute_positivity_threshold, default_relative_symmetry_threshold, nonpositivedefinitematrixexception, nonsymmetricmatrixexception, realmatrix, realvector, solver

The CholeskyDecomposition.java Java example source code

/*
 * 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.math3.linear;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.util.FastMath;


/**
 * Calculates the Cholesky decomposition of a matrix.
 * <p>The Cholesky decomposition of a real symmetric positive-definite
 * matrix A consists of a lower triangular matrix L with same size such
 * that: A = LL<sup>T. In a sense, this is the square root of A.

* <p>This class is based on the class with similar name from the * <a href="http://math.nist.gov/javanumerics/jama/">JAMA library, with the * following changes:</p> * <ul> * <li>a {@link #getLT() getLT} method has been added, * <li>the {@code isspd} method has been removed, since the constructor of * this class throws a {@link NonPositiveDefiniteMatrixException} when a * matrix cannot be decomposed,</li> * <li>a {@link #getDeterminant() getDeterminant} method has been added, * <li>the {@code solve} method has been replaced by a {@link #getSolver() * getSolver} method and the equivalent method provided by the returned * {@link DecompositionSolver}.</li> * </ul> * * @see <a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld * @see <a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia * @since 2.0 (changed to concrete class in 3.0) */ public class CholeskyDecomposition { /** * Default threshold above which off-diagonal elements are considered too different * and matrix not symmetric. */ public static final double DEFAULT_RELATIVE_SYMMETRY_THRESHOLD = 1.0e-15; /** * Default threshold below which diagonal elements are considered null * and matrix not positive definite. */ public static final double DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD = 1.0e-10; /** Row-oriented storage for L<sup>T matrix data. */ private double[][] lTData; /** Cached value of L. */ private RealMatrix cachedL; /** Cached value of LT. */ private RealMatrix cachedLT; /** * Calculates the Cholesky decomposition of the given matrix. * <p> * Calling this constructor is equivalent to call {@link * #CholeskyDecomposition(RealMatrix, double, double)} with the * thresholds set to the default values {@link * #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD} and {@link * #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD} * </p> * @param matrix the matrix to decompose * @throws NonSquareMatrixException if the matrix is not square. * @throws NonSymmetricMatrixException if the matrix is not symmetric. * @throws NonPositiveDefiniteMatrixException if the matrix is not * strictly positive definite. * @see #CholeskyDecomposition(RealMatrix, double, double) * @see #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD * @see #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD */ public CholeskyDecomposition(final RealMatrix matrix) { this(matrix, DEFAULT_RELATIVE_SYMMETRY_THRESHOLD, DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD); } /** * 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 * strictly positive definite. * @see #CholeskyDecomposition(RealMatrix) * @see #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD * @see #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD */ public CholeskyDecomposition(final RealMatrix matrix, final double relativeSymmetryThreshold, final double absolutePositivityThreshold) { if (!matrix.isSquare()) { throw new NonSquareMatrixException(matrix.getRowDimension(), matrix.getColumnDimension()); } final int order = matrix.getRowDimension(); lTData = matrix.getData(); cachedL = null; cachedLT = null; // check the matrix before transformation for (int i = 0; i < order; ++i) { 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 = relativeSymmetryThreshold * FastMath.max(FastMath.abs(lIJ), FastMath.abs(lJI)); if (FastMath.abs(lIJ - lJI) > maxDelta) { throw new NonSymmetricMatrixException(i, j, relativeSymmetryThreshold); } lJ[i] = 0; } } // transform the matrix for (int i = 0; i < order; ++i) { 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

* @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>LT is an upper-triangular matrix

* @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 matrix data. */ private final double[][] lTData; /** * Build a solver from decomposed matrix. * @param lTData row-oriented storage for L<sup>T 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); } /** * Get the inverse of the decomposed matrix. * * @return the inverse matrix. */ public RealMatrix getInverse() { return solve(MatrixUtils.createRealIdentityMatrix(lTData.length)); } } }

Other Java examples (source code examples)

Here is a short list of links related to this Java CholeskyDecomposition.java source code file:



my book on functional programming

 

new blog posts

 

Copyright 1998-2021 Alvin Alexander, alvinalexander.com
All Rights Reserved.

A percentage of advertising revenue from
pages under the /java/jwarehouse URI on this website is
paid back to open source projects.