com.numericalmethod.suanshu.matrix.doubles.factorization.triangle
Class Doolittle

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.factorization.triangle.Doolittle

All Implemented Interfaces:

LUDecomposition

public class Doolittle
extends java.lang.Object
implements LUDecomposition

This class implements the Doolittle algorithm with column/partial pivoting for the LU decomposition of a square matrix. It iteratively fills the first row, then first column, then second row, second column, etc. Before each iteration, it swaps the rows so that the biggest entry in the column is on the main diagonal. If this biggest entry is 0, the Doolittle construction fails and throws a runtime exception.

On success, we have

P %*% A == L %*% U

where A is an n x n matrix, P is an n x n pivoting matrix, L is an n x n lower triangular matrix, U is an n x n upper triangular matrix.

That is,

P.multiply(A) == L.multiply(U)

Singular matrix can have valid LU decomposition.

Note that not every non-singular matrix can be factored as A = L %*% U. E.g., |1, 0, 0| |0, 0, 2| |0, 1, -1|

On the other hand, the LU decomposition with pivoting always exists, even if the matrix is singular.

Field Summary

int	dim the dimension of the square matrix A
double	epsilon a precision parameter: when a number |x| ≤ ε, it is considered 0
boolean	usePivoting true if partial pivoting is wanted, e.g., for numerical stability

Constructor Summary

Doolittle(Matrix A)
Construct an LU decomposition using the Doolittle algorithm.

Doolittle(Matrix A, boolean usePivoting, double epsilon)
Construct an LU decomposition using the Doolittle algorithm.

Method Summary

LowerTriangularMatrix	L() Get a copy of the lower triangular matrix L as in P %*% A == L %*% U
PermutationMatrix	P() Get a copy of the permutation matrix P as in P %*% A == L %*% U
UpperTriangularMatrix	U() Get a copy of the upper triangular matrix U as in P %*% A == L %*% U

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

dim

public final int dim

the dimension of the square matrix A

usePivoting

public final boolean usePivoting

true if partial pivoting is wanted, e.g., for numerical stability

epsilon

public final double epsilon

a precision parameter: when a number |x| ≤ ε, it is considered 0

Constructor Detail

Doolittle

public Doolittle(Matrix A,
                 boolean usePivoting,
                 double epsilon)

Construct an LU decomposition using the Doolittle algorithm.

Parameters:

A - a square matrix

usePivoting - true if partial pivoting is wanted, e.g., for numerical stability

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Throws:

java.lang.IllegalArgumentException - if A is not square

Doolittle

public Doolittle(Matrix A)

Construct an LU decomposition using the Doolittle algorithm.

Parameters:

A - a square matrix to which Doolittle is applied

Throws:

java.lang.IllegalArgumentException - if A is not square

Method Detail

L

public LowerTriangularMatrix L()

Description copied from interface: LUDecomposition

Get a copy of the lower triangular matrix L as in

P %*% A == L %*% U

Specified by:

L in interface LUDecomposition

Returns:

a copy of L

U

public UpperTriangularMatrix U()

Description copied from interface: LUDecomposition

Get a copy of the upper triangular matrix U as in

P %*% A == L %*% U

Specified by:

U in interface LUDecomposition

Returns:

a copy of U

P

public PermutationMatrix P()

Description copied from interface: LUDecomposition

Get a copy of the permutation matrix P as in

P %*% A == L %*% U

Specified by:

P in interface LUDecomposition

Returns:

a copy of P