CholeskyDecomposition (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.linear.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 = 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- the solve method has been replaced by a getSolver method and the equivalent method provided by the returned DecompositionSolver.
Since:

2.0 (changed to concrete class in 3.0)

See Also:
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

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.
    
    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

Class CholeskyDecomposition

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_RELATIVE_SYMMETRY_THRESHOLD

DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD

Constructor Detail

CholeskyDecomposition

CholeskyDecomposition

Method Detail

getL

getLT

getDeterminant

getSolver