org.apache.commons.math4.linear

## Class CholeskyDecomposition

• public class CholeskyDecomposition
extends 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:

Since:
2.0 (changed to concrete class in 3.0)
MathWorld, Wikipedia
• ### 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

All 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.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, 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