Jama

Class LUDecomposition

Implemented Interfaces:
java.io.Serializable

public class LUDecomposition
extends java.lang.Object
implements java.io.Serializable

LU Decomposition.

For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If m <32n, then L is m-by-m and U is m-by-n.

The LU decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if isNonsingular() returns false.

See Also:
Serialized Form

Constructor Summary

LUDecomposition(Matrix A)
LU Decomposition

Method Summary

double
det()
Determinant
double[]
getDoublePivot()
Return pivot permutation vector as a one-dimensional double array
Matrix
getL()
Return lower triangular factor
int[]
getPivot()
Return pivot permutation vector
Matrix
getU()
Return upper triangular factor
boolean
isNonsingular()
Is the matrix nonsingular?
Matrix
solve(Matrix B)
Solve A*X = B

Constructor Details

LUDecomposition

public LUDecomposition(Matrix A)
LU Decomposition
Parameters:
A - Rectangular matrix

Method Details

det

public double det()
Determinant
Returns:
det(A)

getDoublePivot

public double[] getDoublePivot()
Return pivot permutation vector as a one-dimensional double array
Returns:
(double) piv

getL

public Matrix getL()
Return lower triangular factor
Returns:
L

getPivot

public int[] getPivot()
Return pivot permutation vector
Returns:
piv

getU

public Matrix getU()
Return upper triangular factor
Returns:
U

isNonsingular

public boolean isNonsingular()
Is the matrix nonsingular?
Returns:
true if U, and hence A, is nonsingular.

solve

public Matrix solve(Matrix B)
Solve A*X = B
Parameters:
B - A Matrix with as many rows as A and any number of columns.
Returns:
X so that L*U*X = B(piv,:)