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/*
 * This software is a cooperative product of The MathWorks and the National
 * Institute of Standards and Technology (NIST) which has been released to the
 * public domain. Neither The MathWorks nor NIST assumes any responsibility
 * whatsoever for its use by other parties, and makes no guarantees, expressed
 * or implied, about its quality, reliability, or any other characteristic.
 */

/*
 * CholeskyDecomposition.java
 * Copyright (C) 1999 The Mathworks and NIST
 *
 */

package weka.core.matrix;

import weka.core.RevisionHandler;
import weka.core.RevisionUtils;

import java.io.Serializable;

/** 
 * Cholesky Decomposition.
 * 

* For a symmetric, positive definite matrix A, the Cholesky decomposition is * an lower triangular matrix L so that A = L*L'. *

* If the matrix is not symmetric or positive definite, the constructor * returns a partial decomposition and sets an internal flag that may * be queried by the isSPD() method. *

* Adapted from the JAMA package. * * @author The Mathworks and NIST * @author Fracpete (fracpete at waikato dot ac dot nz) * @version $Revision: 5953 $ */ public class CholeskyDecomposition implements Serializable, RevisionHandler { /** for serialization */ private static final long serialVersionUID = -8739775942782694701L; /** * Array for internal storage of decomposition. * @serial internal array storage. */ private double[][] L; /** * Row and column dimension (square matrix). * @serial matrix dimension. */ private int n; /** * Symmetric and positive definite flag. * @serial is symmetric and positive definite flag. */ private boolean isspd; /** * Cholesky algorithm for symmetric and positive definite matrix. * * @param Arg Square, symmetric matrix. */ public CholeskyDecomposition(Matrix Arg) { // Initialize. double[][] A = Arg.getArray(); n = Arg.getRowDimension(); L = new double[n][n]; isspd = (Arg.getColumnDimension() == n); // Main loop. for (int j = 0; j < n; j++) { double[] Lrowj = L[j]; double d = 0.0; for (int k = 0; k < j; k++) { double[] Lrowk = L[k]; double s = 0.0; for (int i = 0; i < k; i++) { s += Lrowk[i]*Lrowj[i]; } Lrowj[k] = s = (A[j][k] - s)/L[k][k]; d = d + s*s; isspd = isspd & (A[k][j] == A[j][k]); } d = A[j][j] - d; isspd = isspd & (d > 0.0); L[j][j] = Math.sqrt(Math.max(d,0.0)); for (int k = j+1; k < n; k++) { L[j][k] = 0.0; } } } /** * Is the matrix symmetric and positive definite? * @return true if A is symmetric and positive definite. */ public boolean isSPD() { return isspd; } /** * Return triangular factor. * @return L */ public Matrix getL() { return new Matrix(L,n,n); } /** * Solve A*X = B * @param B A Matrix with as many rows as A and any number of columns. * @return X so that L*L'*X = B * @exception IllegalArgumentException Matrix row dimensions must agree. * @exception RuntimeException Matrix is not symmetric positive definite. */ public Matrix solve(Matrix B) { if (B.getRowDimension() != n) { throw new IllegalArgumentException("Matrix row dimensions must agree."); } if (!isspd) { throw new RuntimeException("Matrix is not symmetric positive definite."); } // Copy right hand side. double[][] X = B.getArrayCopy(); int nx = B.getColumnDimension(); // Solve L*Y = B; for (int k = 0; k < n; k++) { for (int j = 0; j < nx; j++) { for (int i = 0; i < k ; i++) { X[k][j] -= X[i][j]*L[k][i]; } X[k][j] /= L[k][k]; } } // Solve L'*X = Y; for (int k = n-1; k >= 0; k--) { for (int j = 0; j < nx; j++) { for (int i = k+1; i < n ; i++) { X[k][j] -= X[i][j]*L[i][k]; } X[k][j] /= L[k][k]; } } return new Matrix(X,n,nx); } /** * Returns the revision string. * * @return the revision */ public String getRevision() { return RevisionUtils.extract("$Revision: 5953 $"); } }





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