fr.cnes.sirius.patrius.math.linear

Class FieldLUDecomposition<T extends FieldElement<T>>

java.lang.Object

fr.cnes.sirius.patrius.math.linear.FieldLUDecomposition<T>

Type Parameters:

T - the type of the field elements

public class FieldLUDecomposition<T extends FieldElement<T>>
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: PA = LU, L is lower triangular, and U is upper triangular and P is a permutation matrix. All matrices are m×m.

Since field elements do not provide an ordering operator, the permutation matrix is computed here only in order to avoid a zero pivot element, no attempt is done to get the largest pivot element.

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• the solve and isNonSingular methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.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: FieldLUDecomposition.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

MathWorld, Wikipedia

Constructor Summary

Constructors

Constructor and Description
FieldLUDecomposition(FieldMatrix<T> matrix) Calculates the LU-decomposition of the given matrix.

Method Summary

Modifier and Type	Method and Description
T	getDeterminant() Return the determinant of the matrix.
FieldMatrix<T>	getL() Returns the matrix L of the decomposition.
FieldMatrix<T>	getP() Returns the P rows permutation matrix.
int[]	getPivot() Returns the pivot permutation vector.
FieldDecompositionSolver<T>	getSolver() Get a solver for finding the A × X = B solution in exact linear sense.
FieldMatrix<T>	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

FieldLUDecomposition

public FieldLUDecomposition(FieldMatrix<T> matrix)

Calculates the LU-decomposition of the given matrix.

Parameters:

matrix - The matrix to decompose.

Throws:

NonSquareMatrixException - if matrix is not square

Method Detail

getL

public FieldMatrix<T> 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 FieldMatrix<T> 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 FieldMatrix<T> 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 T getDeterminant()

Return the determinant of the matrix.

Returns:

determinant of the matrix

getSolver

public FieldDecompositionSolver<T> getSolver()

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

Returns:

a solver