org.jmatrices.dbl.decomposition
Class LUDecomposition

java.lang.Object
  extended byorg.jmatrices.dbl.decomposition.LUDecomposition

public class LUDecomposition
extends java.lang.Object

LUDecomposition

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 < n, 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.

http://www.hku.hk/cc/sp2/software/hpf/Course/HTMLQuestionsnode65.html http://csep10.phys.utk.edu/guidry/phys594/lectures/linear_algebra/lanotes/node3.html

The code is basically JAMA code with modifications made to fit in the scheme of things.

Author: purangp

Date: 08.03.2004 Time: 23:37:48


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 getPivotMatrix()
          Return pivot permutation vector
 Matrix getU()
          Return upper triangular factor
 boolean isNonsingular()
          Is the matrix nonsingular?
 boolean isSingular()
           
 Matrix solve(Matrix B)
          Solve A*X = B
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

LUDecomposition

public LUDecomposition(Matrix a)
LU Decomposition

Parameters:
a - Rectangular matrix
Method Detail

isNonsingular

public boolean isNonsingular()
Is the matrix nonsingular?

Returns:
true if U, and hence A, is nonsingular.

isSingular

public boolean isSingular()

getL

public Matrix getL()
Return lower triangular factor

Returns:
L

getU

public Matrix getU()
Return upper triangular factor

Returns:
U

getPivot

public int[] getPivot()
Return pivot permutation vector

Returns:
piv

getDoublePivot

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

Returns:
(double) piv

getPivotMatrix

public Matrix getPivotMatrix()
Return pivot permutation vector

Returns:
piv

det

public double det()
Determinant

Returns:
det(A)
Throws:
java.lang.IllegalArgumentException - Matrix must be square

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,:)
Throws:
java.lang.IllegalArgumentException - Matrix row dimensions must agree.
java.lang.RuntimeException - Matrix is singular.