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.

This identity always holds:

T %*% A == U

where U is in the reduced row echelon form.

This implementation makes sure that the leading 1s are numerically 1, for future 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

Field Summary

double	epsilon a precision parameter: when a number |x| ≤ ε, it is considered 0
int	ncols number of columns
int	nrows number of rows
boolean	usePivoting true if partial pivoting is wanted, e.g., for numerical stability

Constructor Summary

GaussJordanElimination(Matrix A)
Construct an instance of the Gauss-Jordan Elimination algorithm.

GaussJordanElimination(Matrix A, boolean usePivoting, double epsilon)
Construct an instance of 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, such that T %*% A == U

Methods inherited from class java.lang.Object

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

Field Detail

nrows

public final int nrows

number of rows

ncols

public final int ncols

number of columns

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

GaussJordanElimination

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

Construct an instance of 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)

Construct an instance of 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, such that

T %*% A == U

Returns:

the reduced row echelon form matrix