LUDecomposition

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jmat.data.matrixDecompositions
Class LUDecomposition

java.lang.Object
  jmat.data.matrixDecompositions.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. 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.

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.

Constructor Summary

LUDecomposition(jmat.data.Matrix A)
          LU Decomposition

Method Summary

double det()
          Determinant

jmat.data.Matrix getL()
          Return lower triangular factor

jmat.data.Matrix getP()
          Return pivot permutation vector

jmat.data.Matrix getU()
          Return upper triangular factor

boolean isNonsingular()
          Is the matrix nonsingular?

jmat.data.Matrix solve(jmat.data.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

LU

private double[][] LU

Array for internal storage of decomposition.

piv

private int[] piv

Internal storage of pivot vector.

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.

Constructor Detail