Package org.apache.commons.math.linear

Class CholeskyDecompositionImpl

java.lang.Object

org.apache.commons.math.linear.CholeskyDecompositionImpl

All Implemented Interfaces:

CholeskyDecomposition

public class CholeskyDecompositionImpl
extends 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

See Also:

• MathWorld
• Wikipedia

Field Summary

Fields

Modifier and Type	Field	Description
static final double	DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD	Default threshold below which diagonal elements are considered null and matrix not positive definite.
static final double	DEFAULT_RELATIVE_SYMMETRY_THRESHOLD	Default threshold above which off-diagonal elements are considered too different and matrix not symmetric.

Constructor Summary

Constructors

Constructor	Description
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

Modifier and Type	Method	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 Details

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 Details

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 Details

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