Package org.flag4j.linalg

Class RowEchelon

java.lang.Object

org.flag4j.linalg.RowEchelon

public class RowEchelon
extends Object

This class contains several methods for computing row echelon, reduced row echelon, and extended reduced row echelon forms of a matrix.

Constructor Summary

Constructors

Constructor	Description
RowEchelon()

Method Summary

Modifier and Type	Method	Description
static CMatrix	erref(CMatrix A)	Computes the extended reduced row echelon form of a matrix.
static Matrix	erref(Matrix A)	Computes the extended reduced row echelon form of a matrix.
static CMatrix	ref(CMatrix A)	Computes a row echelon form of a Matrix.
static Matrix	ref(Matrix A)	Computes a row echelon form of a Matrix.
static CMatrix	rref(CMatrix A)	Computes the reduced row echelon form of a matrix.
static Matrix	rref(Matrix A)	Computes the reduced row echelon form of a matrix.

Methods inherited from class java.lang.Object

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

Constructor Details

RowEchelon

public RowEchelon()

Method Details

ref

public static Matrix ref(Matrix A)

Computes a row echelon form of a Matrix. For a reduced row echelon form use rref(Matrix).

Parameters:

A - The matrix for which to compute the row echelon form.

Returns:

A matrix in row echelon form which is row-equivalent to the matrix A.

ref

public static CMatrix ref(CMatrix A)

Computes a row echelon form of a Matrix. For a reduced row echelon form use rref(CMatrix).

Parameters:

A - The matrix for which to compute the row echelon form.

Returns:

A matrix in row echelon form which is row-equivalent to the matrix A.

rref

public static Matrix rref(Matrix A)

Computes the reduced row echelon form of a matrix. For a non-reduced row echelon form see ref(Matrix). The reduced row echelon form is unique.

Parameters:

A - The matrix for which to compute the reduced row echelon form.

Returns:

A matrix in reduced row echelon form which is row-equivalent to this matrix.

rref

public static CMatrix rref(CMatrix A)

Computes the reduced row echelon form of a matrix. For a non-reduced row echelon form see ref(CMatrix). The reduced row echelon form is unique.

Parameters:

A - The matrix for which to compute the reduced row echelon form.

Returns:

A matrix in reduced row echelon form which is row-equivalent to this matrix.

erref

public static Matrix erref(Matrix A)

Computes the extended reduced row echelon form of a matrix. This is equivalent to rref(A.augment(Matrix.I(A.numRows())))

Parameters:

A - Matrix for which to compute extended reduced row echelon form of.

Returns:

A matrix in reduced row echelon form which is row-equivalent to this matrix augmented with the appropriately sized identity matrix.

erref

public static CMatrix erref(CMatrix A)

Computes the extended reduced row echelon form of a matrix. This is equivalent to rref(A.augment(Matrix.I(A.numRows())))

Parameters:

A - Matrix for which to compute extended reduced row echelon form of.

Returns:

A matrix in reduced row echelon form which is row-equivalent to this matrix augmented with the appropriately sized identity matrix.