com.numericalmethod.suanshu.matrix.doubles.factorization.gaussianelimination
Class GaussJordanElimination

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.factorization.gaussianelimination.GaussJordanElimination

public class GaussJordanElimination
extends java.lang.Object

Gauss-Jordan elimination performs elementary row operations to reduce a matrix to the reduced row echelon form. The three elementary row operations are: scaling rows, swapping rows, and adding multiples of a row to another row. That is, T * A == U where T is the transformation matrix, U is in the reduced row echelon form.

This implementation makes sure that the leading 1s are numerically 1 for comparison purpose. Suppose there is a leading 1 at [i,j], U.get(i, j) == 1 always returns true.

See Also:

• Wikipedia: Gauss-Jordan elimination
• Wikipedia: Row echelon form

Constructor Summary

GaussJordanElimination(Matrix A)
Run the Gauss-Jordan elimination algorithm.

GaussJordanElimination(Matrix A, boolean usePivoting, double epsilon)
Run the Gauss-Jordan elimination algorithm.

Method Summary

Matrix	T() Get the transformation matrix, T, such that T * A = U.
Matrix	U() Get the reduced row echelon form matrix, U, such that T * A = U.

Methods inherited from class java.lang.Object

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

Constructor Detail

GaussJordanElimination

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

Run the Gauss-Jordan elimination algorithm.

Parameters:

A - a 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

GaussJordanElimination

public GaussJordanElimination(Matrix A)

Run the Gauss-Jordan elimination algorithm.

Parameters:

A - a matrix

Method Detail

T

public Matrix T()

Get the transformation matrix, T, such that T * A = U.

Returns:

the transformation matrix T

U

public Matrix U()

Get the reduced row echelon form matrix, U, such that T * A = U.

Returns:

the reduced row echelon form matrix