org.apache.commons.math.linear
Class CholeskyDecompositionImpl

java.lang.Object
  org.apache.commons.math.linear.CholeskyDecompositionImpl

All Implemented Interfaces:

CholeskyDecomposition

public class CholeskyDecompositionImpl
extends java.lang.Object
implements CholeskyDecomposition

Calculates the Cholesky decomposition of a matrix.

The Cholesky decomposition of a real symmetric positive-definite matrix A consists of a lower triangular matrix L with same size that satisfy: A = LL^TQ = I). In a sense, this is the square root of A.

Since:

2.0

Version:

$Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $

See Also:

MathWorld, Wikipedia

Nested Class Summary

private static class

CholeskyDecompositionImpl.Solver Specialized solver.

Field Summary

private RealMatrix	cachedL Cached value of L.
private RealMatrix	cachedLT Cached value of LT.
static double	DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD Default threshold below which diagonal elements are considered null and matrix not positive definite.
static double	DEFAULT_RELATIVE_SYMMETRY_THRESHOLD Default threshold above which off-diagonal elements are considered too different and matrix not symmetric.
private double[][]	lTData Row-oriented storage for LT matrix data.

Constructor Summary

CholeskyDecompositionImpl(RealMatrix matrix)
Calculates the Cholesky decomposition of the given matrix.

CholeskyDecompositionImpl(RealMatrix matrix, double relativeSymmetryThreshold, double absolutePositivityThreshold)
Calculates the Cholesky decomposition of the given matrix.

Method Summary

double	getDeterminant() Return the determinant of the matrix
RealMatrix	getL() Returns the matrix L of the decomposition.
RealMatrix	getLT() Returns the transpose of the matrix L of the decomposition.
DecompositionSolver	getSolver() Get a solver for finding the A × X = B solution in least square sense.

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_RELATIVE_SYMMETRY_THRESHOLD

public static final double DEFAULT_RELATIVE_SYMMETRY_THRESHOLD

Default threshold above which off-diagonal elements are considered too different and matrix not symmetric.

See Also:

Constant Field Values

DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD

public static final double DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD

Default threshold below which diagonal elements are considered null and matrix not positive definite.

See Also:

Constant Field Values

lTData

private double[][] lTData

Row-oriented storage for L^T matrix data.

cachedL

private RealMatrix cachedL

Cached value of L.

cachedLT

private RealMatrix cachedLT

Cached value of LT.

Constructor Detail

CholeskyDecompositionImpl

public CholeskyDecompositionImpl(RealMatrix matrix)
                          throws NonSquareMatrixException,
                                 NotSymmetricMatrixException,
                                 NotPositiveDefiniteMatrixException

Calculates the Cholesky decomposition of the given matrix.

Calling this constructor is equivalent to call CholeskyDecompositionImpl(RealMatrix, double, double) with the thresholds set to the default values DEFAULT_RELATIVE_SYMMETRY_THRESHOLD and DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD

Parameters:

matrix - the matrix to decompose

Throws:

NonSquareMatrixException - if matrix is not square

NotSymmetricMatrixException - if matrix is not symmetric

NotPositiveDefiniteMatrixException - if the matrix is not strictly positive definite

See Also:

CholeskyDecompositionImpl(RealMatrix, double, double), DEFAULT_RELATIVE_SYMMETRY_THRESHOLD, DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD

CholeskyDecompositionImpl

public CholeskyDecompositionImpl(RealMatrix matrix,
                                 double relativeSymmetryThreshold,
                                 double absolutePositivityThreshold)
                          throws NonSquareMatrixException,
                                 NotSymmetricMatrixException,
                                 NotPositiveDefiniteMatrixException

Calculates the Cholesky decomposition of the given matrix.

Parameters:

matrix - the matrix to decompose

relativeSymmetryThreshold - threshold above which off-diagonal elements are considered too different and matrix not symmetric

absolutePositivityThreshold - threshold below which diagonal elements are considered null and matrix not positive definite

Throws:

NonSquareMatrixException - if matrix is not square

NotSymmetricMatrixException - if matrix is not symmetric

NotPositiveDefiniteMatrixException - if the matrix is not strictly positive definite

See Also:

CholeskyDecompositionImpl(RealMatrix), DEFAULT_RELATIVE_SYMMETRY_THRESHOLD, DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD

Method Detail

getL

public RealMatrix getL()

Returns the matrix L of the decomposition.

L is an lower-triangular matrix

Specified by:

getL in interface CholeskyDecomposition

Returns:

the L matrix

getLT

public RealMatrix getLT()

Returns the transpose of the matrix L of the decomposition.

L^T is an upper-triangular matrix

Specified by:

getLT in interface CholeskyDecomposition

Returns:

the transpose of the matrix L of the decomposition

getDeterminant

public double getDeterminant()

Return the determinant of the matrix

Specified by:

getDeterminant in interface CholeskyDecomposition

Returns:

determinant of the matrix

getSolver

public DecompositionSolver getSolver()

Get a solver for finding the A × X = B solution in least square sense.

Specified by:

getSolver in interface CholeskyDecomposition

Returns:

a solver