Package elki.math.linearalgebra

Class CholeskyDecomposition

  • public class CholeskyDecomposition
extends java.lang.Object
    Cholesky Decomposition.

    For a symmetric, positive definite matrix A, the Cholesky decomposition is an lower triangular matrix L so that \( A = L L^T \).

    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.

    Since:
    0.1
    Author:
    Arthur Zimek

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private boolean isspd
      Symmetric and positive definite flag.
      private double[][] L
      Array for internal storage of decomposition.

    • Constructor Summary

      Constructors 
      Constructor Description
      CholeskyDecomposition​(double[][] A)
      Cholesky algorithm for symmetric and positive definite matrix.

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      double[][] getL()
      Return triangular factor.
      boolean isSPD()
      Is the matrix symmetric and positive definite?
      double[] solve​(double[] b)
      Solve A*X = b
      double[][] solve​(double[][] B)
      Solve A*X = B
      private double[][] solveL​(double[][] X)
      Solve L*Y = B
      double[] solveLInplace​(double[] X)
      Solve L*X = b, modifying X.
      double[] solveLtransposed​(double[] X)
      Solve L^T*X = Y
      private double[][] solveLtransposed​(double[][] X)
      Solve L^T*X = Y

      • Methods inherited from class java.lang.Object

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

    • Field Detail

      • L

        private double[][] L
        Array for internal storage of decomposition.

      • isspd

        private boolean isspd
        Symmetric and positive definite flag.

    • Constructor Detail

      • CholeskyDecomposition

        public CholeskyDecomposition​(double[][] A)
        Cholesky algorithm for symmetric and positive definite matrix.
        Parameters:
        A - Square, symmetric matrix.

    • Method Detail

      • isSPD

        public boolean isSPD()
        Is the matrix symmetric and positive definite?
        Returns:
        true if A is symmetric and positive definite.

      • getL

        public double[][] getL()
        Return triangular factor.
        Returns:
        L

      • solve

        public double[][] solve​(double[][] B)
        Solve A*X = B
        Parameters:
        B - A Matrix with as many rows as A and any number of columns.
        Returns:
        X so that L*L^T*X = B
        Throws:
        java.lang.IllegalArgumentException - Matrix row dimensions must agree.
        java.lang.RuntimeException - Matrix is not symmetric positive definite.

      • solveL

        private double[][] solveL​(double[][] X)
        Solve L*Y = B
        Parameters:
        X - Copy of B.
        Returns:
        X

      • solveLtransposed

        private double[][] solveLtransposed​(double[][] X)
        Solve L^T*X = Y
        Parameters:
        X - Solution of L*Y=B
        Returns:
        X

      • solve

        public double[] solve​(double[] b)
        Solve A*X = b
        Parameters:
        b - A column vector with as many rows as A.
        Returns:
        X so that L*L^T*X = b
        Throws:
        java.lang.IllegalArgumentException - Matrix row dimensions must agree.
        java.lang.RuntimeException - Matrix is not symmetric positive definite.

      • solveLInplace

        public double[] solveLInplace​(double[] X)
        Solve L*X = b, modifying X.
        Parameters:
        X - Copy of b.
        Returns:
        X

      • solveLtransposed

        public double[] solveLtransposed​(double[] X)
        Solve L^T*X = Y
        Parameters:
        X - Solution of L*Y=b
        Returns:
        X