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From "Phil Steitz" <>
Subject RE: [PATCH] Cholesky decomposition
Date Mon, 13 Dec 2004 21:29:00 GMT
Thanks for the patch!  It may take a little while for us to apply it, since we need to discuss
the strategy for extending the 1.0 matrix classes.  It would be great if you could open a
Bugzilla ticket and attach the code below in a java class.  Don't worry about the name, but
do include the apache license on top.  A corresponding class including junit tests would also
help. Thanks!

	-----Original Message----- 
	From: Peter [] 
	Sent: Mon 12/13/2004 2:31 PM 
	Subject: [PATCH] Cholesky decomposition

	This method implements the Cholesky decomposition of a RealMatrix. It
	can be easily modified to be incorporated under the RealMatrix class and
	to decompose BigMatrixes as well.
	I hope you place it in the next release.
	Peter P. Lupo
	Computer Science barchelor student. UFRJ-Brazil
	     * Computes the cholesky decomposition of matrix. The return is a lower triangular matrix
that may be empty and also coincide with the original matrix. The method only uses the upper
right part of the matrix, which must be square, symmetric and positive-definite by definition.
	     * @param matrix
	     *            The matrix to decompose.
	     * @return
	     *            The matrix with the result, which is lower triangular and has the same
dimensions of the original matrix.
	     * @exception InvalidMatrixException
	     *                if matrix is not square, symmetric or positive-definite.
	    public static RealMatrix choleskyDecomposition(RealMatrix matrix) {
	        if (!matrix.isSquare()) throw new InvalidMatrixException("Not a
	square/symmetric matrix."); //"matrix" is not square
	        if (!matrix.equals(matrix.transpose())) throw new
	InvalidMatrixException("Not a symmetric matrix."); //"matrix" is not square
	        double[][] matrixData = matrix.copy().getData();
	        double[][] cholesky = new
	        for (int i = 0; i < matrix.getColumnDimension(); i++) {
	            double[] ithRowOfL = cholesky[i];
	            double[] ithRowOfA = matrixData[i];
	            for (int j = i; j < matrix.getRowDimension(); j++) {
	                double[] jthRowOfL = cholesky[j];
	                double sum = ithRowOfA[j];
	                for (int k = i - 1; k >= 0; k--){
	                    sum -= ithRowOfL[k] * jthRowOfL[k];
	                if (i == j) {
	                    if (sum <= 0)throw new InvalidMatrixException("Not a
	positive definite matrix."); //"matrix", with rounding errors is not
	positive definite
	                    if (cholesky != null){
	                        cholesky[j][i] = Math.sqrt(sum);
	                } else {
	                    if (cholesky != null){
	                        cholesky[j][i] = sum / cholesky[i][i];
	                    if (i < j){
	                        cholesky[i][j] = 0;
	        return new RealMatrixImpl(cholesky);
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