fr.cnes.sirius.patrius.math.linear

Class LUDecomposition

java.lang.Object

fr.cnes.sirius.patrius.math.linear.LUDecomposition

All Implemented Interfaces:

Decomposition

public class LUDecomposition
extends Object
implements Decomposition

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• the solve and isNonSingular methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.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)

Version:

$Id: LUDecomposition.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

MathWorld, Wikipedia

Constructor Summary

Constructors

Constructor and Description
LUDecomposition(RealMatrix matrix) Simple constructor.
LUDecomposition(RealMatrix matrix, double singularityThreshold) Constructor used to set the singularity threshold.

Method Summary

Modifier and Type	Method and Description
static Function<RealMatrix,Decomposition>	decompositionBuilder(double singularityThreshold) Builder for decomposition.
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() Gets 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)

Simple constructor. The singularity threshold defaults to 1e-11.

The decomposition is directly computed on the input matrix

Parameters:

matrix - The matrix to decompose.

Throws:

NonSquareMatrixException - if matrix is not square.

See Also:

LUDecomposition(RealMatrix, double)

LUDecomposition

public LUDecomposition(RealMatrix matrix,
                       double singularityThreshold)

Constructor used to set the singularity threshold.

The decomposition is directly computed on the input 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()

Gets a solver for finding the A × X = B solution in exact linear sense.

Specified by:

getSolver in interface Decomposition

Returns:

the decomposition solver.

decompositionBuilder

public static Function<RealMatrix,Decomposition> decompositionBuilder(double singularityThreshold)

Builder for decomposition.

Parameters:

singularityThreshold - Singularity threshold

Returns:

decomposition