org.apache.commons.math3.linear

Class CholeskyDecomposition

java.lang.Object

org.apache.commons.math3.linear.CholeskyDecomposition

public class CholeskyDecomposition
extends java.lang.Object

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 such that: A = LL^T. In a sense, this is the square root of A.

This class is based on the class with similar name from the JAMA library, with the following changes:

• a getLT method has been added,
• the isspd method has been removed, since the constructor of this class throws a NonPositiveDefiniteMatrixException when a matrix cannot be decomposed,
• a getDeterminant method has been added,
• the solve method has been replaced by a getSolver method and the equivalent method provided by the returned DecompositionSolver.

Since:

2.0 (changed to concrete class in 3.0)

See Also:

MathWorld, Wikipedia

Field Summary

Fields

Modifier and Type	Field and Description
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.

Constructor Summary

Constructors

Constructor and Description
CholeskyDecomposition(RealMatrix matrix) Calculates the Cholesky decomposition of the given matrix.
CholeskyDecomposition(RealMatrix matrix, double relativeSymmetryThreshold, double absolutePositivityThreshold) Calculates the Cholesky decomposition of the given matrix.

Method Summary

Modifier and Type	Method and Description
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

equals, 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

Constructor Detail

CholeskyDecomposition

public CholeskyDecomposition(RealMatrix matrix)

Calculates the Cholesky decomposition of the given matrix.

Calling this constructor is equivalent to call CholeskyDecomposition(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 the matrix is not square.

NonSymmetricMatrixException - if the matrix is not symmetric.

NonPositiveDefiniteMatrixException - if the matrix is not strictly positive definite.

See Also:

CholeskyDecomposition(RealMatrix, double, double), DEFAULT_RELATIVE_SYMMETRY_THRESHOLD, DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD

CholeskyDecomposition

public CholeskyDecomposition(RealMatrix matrix,
                             double relativeSymmetryThreshold,
                             double absolutePositivityThreshold)

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 the matrix is not square.

NonSymmetricMatrixException - if the matrix is not symmetric.

NonPositiveDefiniteMatrixException - if the matrix is not strictly positive definite.

See Also:

CholeskyDecomposition(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

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

Returns:

the transpose of the matrix L of the decomposition

getDeterminant

public double getDeterminant()

Return the determinant of the matrix

Returns:

determinant of the matrix

getSolver

public DecompositionSolver getSolver()

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

Returns:

a solver