Package org.hipparchus.linear

Class SemiDefinitePositiveCholeskyDecomposition

java.lang.Object

org.hipparchus.linear.SemiDefinitePositiveCholeskyDecomposition

public class SemiDefinitePositiveCholeskyDecomposition
extends Object

Calculates the Cholesky decomposition of a positive semidefinite matrix.

The classic Cholesky decomposition (CholeskyDecomposition) applies to real symmetric positive-definite matrix. This class extends the Cholesky decomposition to positive semidefinite matrix. The main application is for estimation based on the Unscented Kalman Filter.

Since:

2.2

See Also:

• "J. Hartikainen, A. Solin, and S. Särkkä. Optimal filtering with Kalman filters and smoothers, Dept. of Biomedica Engineering and Computational Sciences, Aalto University School of Science, Aug. 2011."

Field Summary

Fields

Modifier and Type	Field	Description
static final double	POSITIVITY_THRESHOLD	Default threshold below which elements are not considered positive.

Constructor Summary

Constructors

Constructor	Description
SemiDefinitePositiveCholeskyDecomposition(RealMatrix matrix)	Calculates the Cholesky decomposition of the given matrix.
SemiDefinitePositiveCholeskyDecomposition(RealMatrix matrix, double positivityThreshold)	Calculates the Cholesky decomposition of the given matrix.

Method Summary

Modifier and Type	Method	Description
RealMatrix	getL()	Returns the matrix L of the decomposition.
RealMatrix	getLT()	Returns the transpose of the matrix L of the decomposition.

Methods inherited from class java.lang.Object

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

Field Details

POSITIVITY_THRESHOLD

public static final double POSITIVITY_THRESHOLD

Default threshold below which elements are not considered positive.

See Also:

• Constant Field Values

Constructor Details

SemiDefinitePositiveCholeskyDecomposition

public SemiDefinitePositiveCholeskyDecomposition(RealMatrix matrix)

Calculates the Cholesky decomposition of the given matrix.

Parameters:

matrix - the matrix to decompose

Throws:

MathIllegalArgumentException - if the matrix is not square.

See Also:

• SemiDefinitePositiveCholeskyDecomposition(RealMatrix, double)
• POSITIVITY_THRESHOLD

SemiDefinitePositiveCholeskyDecomposition

public SemiDefinitePositiveCholeskyDecomposition(RealMatrix matrix,
 double positivityThreshold)

Calculates the Cholesky decomposition of the given matrix.

Parameters:

matrix - the matrix to decompose

positivityThreshold - threshold below which elements are not considered positive

Throws:

MathIllegalArgumentException - if the matrix is not square.

Method Details

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