jmathlib.toolbox.jmathlib.matrix._private.Jama
Class LUDecomposition

java.lang.Object
  extended by jmathlib.toolbox.jmathlib.matrix._private.Jama.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

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(double[][] A)
          LU Decomposition
LUDecomposition(Matrix A)
           
 
Method Summary
 double det()
          Determinant
 double[] getDoublePivot()
          Return pivot permutation vector as a one-dimensional double array
 double[][] getDoublePivotAsArray()
           
 double[][] getL()
          Return lower triangular factor
 int[] getPivot()
          Return pivot permutation vector
 double[][] getU()
          Return upper triangular factor
 boolean isNonsingular()
          Is the matrix nonsingular?
 double[][] solve(double[][] B)
          Solve A*X = B
 double[][] 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

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)

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

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

getDoublePivotAsArray

public double[][] getDoublePivotAsArray()

det

public double det()
Determinant

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

solve

public double[][] 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.

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

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