org.openmali.decomposition
Class LUDecomposition

java.lang.Object
  extended by org.openmali.decomposition.LUDecomposition

public class LUDecomposition
extends java.lang.Object

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 < 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.


Constructor Summary
LUDecomposition(MatrixMxNf A)
          LU Decomposition.
 
Method Summary
 float det()
           
 MatrixMxNf getL()
           
 int[] getPivot()
           
 MatrixMxNf getU()
           
 boolean isNonsingular()
          Is the matrix nonsingular?
 MatrixMxNf solve(MatrixMxNf B)
          Solves 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(MatrixMxNf A)
LU Decomposition.

Parameters:
A - Rectangular matrix
Method Detail

isNonsingular

public final boolean isNonsingular()
Is the matrix nonsingular?

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

getL

public MatrixMxNf getL()
Returns:
lower triangular factor.

getU

public MatrixMxNf getU()
Returns:
upper triangular factor.

getPivot

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

det

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

solve

public final MatrixMxNf solve(MatrixMxNf B)
Solves 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.