org.apache.commons.math.linear

## Class CholeskyDecompositionImpl

• java.lang.Object
• org.apache.commons.math.linear.CholeskyDecompositionImpl
• All Implemented Interfaces:
CholeskyDecomposition

```public class CholeskyDecompositionImpl
extends java.lang.Object
implements CholeskyDecomposition```
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 that satisfy: A = LLTQ = I). In a sense, this is the square root of A.

Since:
2.0
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
`CholeskyDecompositionImpl(RealMatrix matrix)`
Calculates the Cholesky decomposition of the given matrix.
```CholeskyDecompositionImpl(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

`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

Specified by:
`getL` in interface `CholeskyDecomposition`
Returns:
the L matrix
• #### getLT

`public RealMatrix getLT()`
Returns the transpose of the matrix L of the decomposition.

LT is an upper-triangular matrix

Specified by:
`getLT` in interface `CholeskyDecomposition`
Returns:
the transpose of the matrix L of the decomposition
• #### getDeterminant

`public double getDeterminant()`
Return the determinant of the matrix
Specified by:
`getDeterminant` in interface `CholeskyDecomposition`
Returns:
determinant of the matrix
• #### getSolver

`public DecompositionSolver getSolver()`
Get a solver for finding the A × X = B solution in least square sense.
Specified by:
`getSolver` in interface `CholeskyDecomposition`
Returns:
a solver