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Class Jama.LUDecomposition

java.lang.Object
  |
  +--Jama.LUDecomposition

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, notifyAll, notify, 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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