org.apache.commons.math3.linear

## Class CholeskyDecomposition

- java.lang.Object
- org.apache.commons.math3.linear.CholeskyDecomposition

public class CholeskyDecompositionextends 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method has been replaced by a`getSolver`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`

.

- a

### 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

Methods 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.

### 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

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