LUDecomposition (Apache Commons Math 3.6.1 API)

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

```
public class LUDecomposition
extends Object
```
Calculates the LUP-decomposition of a square matrix.
The LUP-decomposition of a matrix A consists of three matrices L, U and P that satisfy: P×A = L×U. L is lower triangular (with unit diagonal terms), U is upper triangular and P is a permutation matrix. All matrices are m×m.

As shown by the presence of the P matrix, this decomposition is implemented using partial pivoting.

This class is based on the class with similar name from the JAMA library.
- a getP method has been added,
- the det method has been renamed as getDeterminant,
- the getDoublePivot method has been removed (but the int based getPivot method has been kept),
- the solve and isNonSingular methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.
Since:

2.0 (changed to concrete class in 3.0)

See Also:
MathWorld, Wikipedia

Constructor Summary

Constructors
Constructor and Description
`LUDecomposition(RealMatrix matrix)` Calculates the LU-decomposition of the given matrix.
`LUDecomposition(RealMatrix matrix, double singularityThreshold)` Calculates the LU-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`	`getP()` Returns the P rows permutation matrix.
`int[]`	`getPivot()` Returns the pivot permutation vector.
`DecompositionSolver`	`getSolver()` Get a solver for finding the A × X = B solution in exact linear sense.
`RealMatrix`	`getU()` Returns the matrix U of the decomposition.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - LUDecomposition
```
public LUDecomposition(RealMatrix matrix)
```
    Calculates the LU-decomposition of the given matrix. This constructor uses 1e-11 as default value for the singularity threshold.
    
    Parameters:
    matrix - Matrix to decompose.
    
    Throws:
    
    NonSquareMatrixException - if matrix is not square.
  - LUDecomposition
```
public LUDecomposition(RealMatrix matrix,
               double singularityThreshold)
```
    Calculates the LU-decomposition of the given matrix.
    
    Parameters:
    matrix - The matrix to decompose.
    singularityThreshold - threshold (based on partial row norm) under which a matrix is considered singular
    
    Throws:
    
    NonSquareMatrixException - if matrix is not square
- Method Detail
  - getL
```
public RealMatrix getL()
```
    Returns the matrix L of the decomposition.
    L is a lower-triangular matrix
    
    Returns:
    the L matrix (or null if decomposed matrix is singular)
  - getU
```
public RealMatrix getU()
```
    Returns the matrix U of the decomposition.
    U is an upper-triangular matrix
    
    Returns:
    the U matrix (or null if decomposed matrix is singular)
  - getP
```
public RealMatrix getP()
```
    Returns the P rows permutation matrix.
    P is a sparse matrix with exactly one element set to 1.0 in each row and each column, all other elements being set to 0.0.
    
    The positions of the 1 elements are given by the pivot permutation vector.
    
    Returns:
    the P rows permutation matrix (or null if decomposed matrix is singular)
    See Also:
    getPivot()
  - getPivot
```
public int[] getPivot()
```
    Returns the pivot permutation vector.
    
    Returns:
    the pivot permutation vector
    See Also:
    getP()
  - 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 exact linear sense.
    
    Returns:
    a solver

Class LUDecomposition

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

LUDecomposition

LUDecomposition

Method Detail

getL

getU

getP

getPivot

getDeterminant

getSolver