SuanShu, a Java numerical and statistical library

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

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


public class GaussJordanEliminationextends 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.

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

SuanShu, a Java numerical and statistical library