org.apache.commons.math3.linear
Class FieldLUDecomposition<T extends FieldElement<T>>

java.lang.Object
  extended by org.apache.commons.math3.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.

Since:
2.0 (changed to concrete class in 3.0)
Version:
$Id: FieldLUDecomposition.java 1416643 2012-12-03 19:37:14Z tn $
See Also:
MathWorld, Wikipedia

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


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