Package org.apache.commons.math.linear

Class LUDecompositionImpl

java.lang.Object

org.apache.commons.math.linear.LUDecompositionImpl

All Implemented Interfaces:

LUDecomposition

public class LUDecompositionImpl
extends java.lang.Object
implements LUDecomposition

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: PA = LU, L is lower triangular, and 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.

Since:

2.0

Constructor Summary

Constructors

Constructor	Description
LUDecompositionImpl(RealMatrix matrix)	Calculates the LU-decomposition of the given matrix.
LUDecompositionImpl(RealMatrix matrix, double singularityThreshold)	Calculates the LU-decomposition of the given matrix.

Method Summary

Modifier and Type	Method	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

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LUDecompositionImpl

public LUDecompositionImpl(RealMatrix matrix)
                    throws InvalidMatrixException

Calculates the LU-decomposition of the given matrix.

Parameters:

matrix - The matrix to decompose.

Throws:

InvalidMatrixException - if matrix is not square

LUDecompositionImpl

public LUDecompositionImpl(RealMatrix matrix,
                           double singularityThreshold)
                    throws NonSquareMatrixException

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 an lower-triangular matrix

Specified by:

getL in interface LUDecomposition

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

Specified by:

getU in interface LUDecomposition

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.

Specified by:

getP in interface LUDecomposition

Returns:

the P rows permutation matrix (or null if decomposed matrix is singular)

See Also:

LUDecomposition.getPivot()

getPivot

public int[] getPivot()

Returns the pivot permutation vector.

Specified by:

getPivot in interface LUDecomposition

Returns:

the pivot permutation vector

See Also:

LUDecomposition.getP()

getDeterminant

public double getDeterminant()

Return the determinant of the matrix

Specified by:

getDeterminant in interface LUDecomposition

Returns:

determinant of the matrix

getSolver

public DecompositionSolver getSolver()

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

Specified by:

getSolver in interface LUDecomposition

Returns:

a solver