org.apache.commons.math3.linear
Class LUDecomposition

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• the solve and isNonSingular methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.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

Version:

$Id: LUDecomposition.java 3720 2012-03-16 16:34:17Z CardosoP $

See Also:

MathWorld, Wikipedia

Constructor Summary

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

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