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

Class Doolittle

java.lang.Object

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

All Implemented Interfaces:

LUDecomposition, java.io.Serializable

public class Doolittle
extends java.lang.Object
implements LUDecomposition

Doolittle algorithm is an LU decomposition of a square matrix. This implementation uses column/partial pivoting. 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)

Not every non-singular matrix can be LU decomposed but some singular matrix can have valid LU decomposition. For example, the following singular matrix has LU decomposition. \[ \begin{bmatrix} 1 & 0 & 0\\ 0 & 0 & 2\\ 0 & 1 & -1 \end{bmatrix} \] On the other hand, the LU decomposition with pivoting always exists, even if the matrix is singular.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
Doolittle(Matrix A) Run the Doolittle algorithm on a square matrix for LU decomposition.
Doolittle(Matrix A, boolean usePivoting, double epsilon) Run the Doolittle algorithm on a square matrix for LU decomposition.

Method Summary

Modifier and Type	Method and Description
LowerTriangularMatrix	L() Get the lower triangular matrix L as in the LU decomposition.
PermutationMatrix	P() Get the permutation matrix P as in P * A = L * U.
UpperTriangularMatrix	U() Get the upper triangular matrix U as in the LU decomposition.

Methods inherited from class java.lang.Object

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

Constructor Detail

Doolittle

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

Run the Doolittle algorithm on a square matrix for LU decomposition.

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)

Run the Doolittle algorithm on a square matrix for LU decomposition.

Parameters:

A - a square matrix

Throws:

java.lang.IllegalArgumentException - if A is not square

Method Detail

L

public LowerTriangularMatrix L()

Description copied from interface: LUDecomposition

Get the lower triangular matrix L as in the LU decomposition.

Specified by:

L in interface LUDecomposition

Returns:

L

U

public UpperTriangularMatrix U()

Description copied from interface: LUDecomposition

Get the upper triangular matrix U as in the LU decomposition.

Specified by:

U in interface LUDecomposition

Returns:

U

P

public PermutationMatrix P()

Description copied from interface: LUDecomposition

Get the permutation matrix P as in P * A = L * U.

Specified by:

P in interface LUDecomposition

Returns:

P