Class Cholesky<T extends MatrixMixin<T,?,?,?>>

java.lang.Object

org.flag4j.linalg.decompositions.chol.Cholesky<T>

Type Parameters:

T - The type of matrix to compute the Cholesky decomposition of.

All Implemented Interfaces:

Decomposition<T>

Direct Known Subclasses:

ComplexCholesky, RealCholesky

public abstract class Cholesky<T extends MatrixMixin<T,?,?,?>>
extends Object
implements Decomposition<T>

This abstract class specifies methods for computing the Cholesky decomposition of a positive-definite matrix.

The Cholesky decomposition is essentially a special case of the LU decomposition for Hermitian positive-definite matrices where the upper triangular matrix is the Hermitian transpose of the lower triangular matrix.

Given a Hermitian positive-definite matrix A, the Cholesky decomposition will decompose it into A=LL^H where L is a lower triangular matrix and L^H is the conjugate transpose of L.

If A is a real valued symmetric positive-definite matrix, then the decomposition simplifies to A=LL^T.

Field Summary

Fields

Modifier and Type	Field	Description
protected static final double	DEFAULT_POS_DEF_TOLERANCE	Default tolerance for considering a value along the diagonal of L to be non-positive.
protected T	L	The lower triangular matrix, L, resulting from the Cholesky decomposition A=LLH.

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	Cholesky(boolean enforceHermitian)	Constructs a Cholesky decomposer.

Method Summary

Modifier and Type	Method	Description
T	getL()	Gets the L matrix computed by the Cholesky decomposition A=LLH.
T	getLH()	Gets the LH matrix computed by the Cholesky decomposition A=LLH.

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.flag4j.linalg.decompositions.Decomposition

decompose

Field Details

DEFAULT_POS_DEF_TOLERANCE

protected static final double DEFAULT_POS_DEF_TOLERANCE

Default tolerance for considering a value along the diagonal of L to be non-positive.

See Also:

• Constant Field Values

L

protected T extends MatrixMixin<T,?,?,?> L

The lower triangular matrix, L, resulting from the Cholesky decomposition A=LL^H.

Constructor Details

Cholesky

protected Cholesky(boolean enforceHermitian)

Constructs a Cholesky decomposer.

Parameters:

enforceHermitian - Flag indicating if the matrix to be decomposed should be explicitly checked to be Hermitian (true). If false, no check will be made and the matrix will be treated as if it were Hermitian and only the lower half of the matrix will be accessed.

Method Details

getL

public T getL()

Gets the L matrix computed by the Cholesky decomposition A=LL^H.

Returns:

The L matrix from the Cholesky decomposition A=LL^H.

getLH

public T getLH()

Gets the L^H matrix computed by the Cholesky decomposition A=LL^H.

Returns:

The L^H matrix from the Cholesky decomposition A=LL^H.