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java.lang.Object org.jmatrices.dbl.decomposition.LUDecomposition
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 |
public LUDecomposition(Matrix a)
a
- Rectangular matrixMethod Detail |
public boolean isNonsingular()
public boolean isSingular()
public Matrix getL()
public Matrix getU()
public int[] getPivot()
public double[][] getDoublePivot()
public Matrix getPivotMatrix()
public double det()
java.lang.IllegalArgumentException
- Matrix must be squarepublic Matrix solve(Matrix B)
B
- A Matrix with as many rows as A and any number of columns.
java.lang.IllegalArgumentException
- Matrix row dimensions must agree.
java.lang.RuntimeException
- Matrix is singular.
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