jhplot.math
Class LUDecomposition

java.lang.Object
  extended by jhplot.math.LUDecomposition

public class LUDecomposition
extends 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. In other words, assuming P the permutation Matrix, P*A = 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(double[][] A)
          LU Decomposition
 
Method Summary
 double det()
          Determinant
 double[][] getL()
          Return lower triangular factor
 double[][] getP()
          Return pivot permutation vector
 double[][] getU()
          Return upper triangular factor
 boolean isNonsingular()
          Is the matrix nonsingular?
 double[][] solve(double[][] B)
          Solve A*X = B
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

LUDecomposition

public LUDecomposition(double[][] 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 double[][] getL()
Return lower triangular factor

Returns:
L

getU

public double[][] getU()
Return upper triangular factor

Returns:
U

getP

public double[][] getP()
Return pivot permutation vector

Returns:
piv

det

public double det()
Determinant

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

solve

public double[][] solve(double[][] 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:
IllegalArgumentException - Matrix row dimensions must agree.
RuntimeException - Matrix is singular.


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