Package gov.nih.mipav.model.algorithms

Class ModifiedCholeskyFactorization

  • public class ModifiedCholeskyFactorization
extends java.lang.Object
    Copyright (c) 2015, Sheung Hun Cheng and Nicholas J. Higham All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. modified-cholesky contains MATLAB functions that compute a modified Cholesky factorization of a symmetric and possibly indefinite matrix. The algorithm is from S. H. Cheng and N.J. Higham. "[A modified Cholesky algorithm based on a symmetric indefinite factorization](http://dx.doi.org/10.1137/S0895479896302898)". SIAM J. Matrix Anal. Appl., 19(4):1097-1110, 1998. and uses LDL^T factorization with a symmetric form of rook pivoting proposed by Ashcraft, Grimes, and Lewis. The functions here are based on code originally written by Bobby Cheng and Nick Higham in 1996. Modified Cholesky algorithm based on LDL' factorization. % [L D,P,D0,rho] = modchol_ldlt_m(A,delta) computes a modified % Cholesky factorization P*(A + E)*P' = L*D*L', where % P is a permutation matrix, L is unit lower triangular, % and D is block diagonal and positive definite with 1-by-1 and 2-by-2 % diagonal blocks. Thus A+E is symmetric positive definite, but E is % not explicitly computed. Also returned is a block diagonal D0 such % that P*A*P' = L*D0*L'. If A is sufficiently positive definite then % E = 0 and D = D0. Rho is the growth factor for the factorization. % The algorithm sets the smallest eigenvalue of D to the tolerance % delta, which defaults to sqrt(eps)*norm(A,'fro'). % The LDL' factorization is compute using a symmetric form of rook % pivoting proposed by Ashcraft, Grimes and Lewis. % % This routine does not exploit symmetry and is not designed to be % efficient. % Authors: Bobby Cheng and Nick Higham, 1996; revised 2015. Ported to Java by William Gandler from the file modchol_ldlt_m.m.

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private double[][] Ain  
      private double[][] D  
      private double delta  
      private double[][] DMC  
      private double epsilon  
      private double[][] L  
      private double[][] P  
      private double[] rho  

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      void run()  
      void test_modchol()  

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Field Detail

      • Ain

        private double[][] Ain

      • delta

        private double delta

      • L

        private double[][] L

      • DMC

        private double[][] DMC

      • P

        private double[][] P

      • D

        private double[][] D

      • rho

        private double[] rho

      • epsilon

        private double epsilon

    • Constructor Detail

      • ModifiedCholeskyFactorization

        public ModifiedCholeskyFactorization()

      • ModifiedCholeskyFactorization

        public ModifiedCholeskyFactorization​(double[][] Ain,
                                     double delta,
                                     double[][] L,
                                     double[][] DMC,
                                     double[][] P,
                                     double[][] D,
                                     double[] rho)

    • Method Detail

      • test_modchol

        public void test_modchol()

      • run

        public void run()