MVT API

math.matrix
Class LUDecomposition

java.lang.Object
  |
  +--math.matrix.LUDecomposition
All 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 < 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.

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
 
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.

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

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.

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