CholeskyDecomposition
org.apache.commons.math3.linear

## Class 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 = LLT. 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:

MathWorld, Wikipedia
• ### Field Summary

Fields
Modifier and TypeField 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 TypeMethod 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.
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.
Constant Field Values
• ### 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.

LT 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