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Supported by Index-Structures

de.lmu.ifi.dbs.elki.math.linearalgebra
Class LUDecomposition

java.lang.Object
  extended by de.lmu.ifi.dbs.elki.math.linearalgebra.LUDecomposition
All Implemented Interfaces:
Serializable

public class LUDecomposition
extends Object
implements 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

Field Summary
private  double[][] LU
          Array for internal storage of decomposition.
private  int m
          Row and column dimensions, and pivot sign.
private  int n
          Row and column dimensions, and pivot sign.
private  int[] piv
          Internal storage of pivot vector.
private  int pivsign
          Row and column dimensions, and pivot sign.
private static long serialVersionUID
          Serial version
 
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
 

Field Detail

serialVersionUID

private static final long serialVersionUID
Serial version

See Also:
Constant Field Values

LU

private double[][] LU
Array for internal storage of decomposition.


m

private int m
Row and column dimensions, and pivot sign.


n

private int n
Row and column dimensions, and pivot sign.


pivsign

private int pivsign
Row and column dimensions, and pivot sign.


piv

private int[] piv
Internal storage of pivot vector.

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:
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:
IllegalArgumentException - Matrix row dimensions must agree.
RuntimeException - Matrix is singular.

Release 0.3 (2010-03-31_1612)