edu.jas.jlinalg

Class GaussElimination<C extends edu.jas.structure.RingElem<C>>

java.lang.Object

edu.jas.jlinalg.GaussElimination<C>

Type Parameters:

C - coefficient ring element type

public class GaussElimination<C extends edu.jas.structure.RingElem<C>>
extends java.lang.Object

Algorithms related to Gaussian elimination. Conversion to JLinAlg classes and delegation to JLinAlg algorithms.

Author:

Heinz Kredel

Constructor Summary

Constructors

Constructor and Description
GaussElimination()

Method Summary

Modifier and Type	Method and Description
edu.jas.poly.GenPolynomial<C>	characteristicPolynomial(edu.jas.vector.GenMatrix<C> a) Characteristic polynomial of a matrix.
C	determinant(edu.jas.vector.GenMatrix<C> a) Determinant of a matrix.
edu.jas.vector.GenMatrix<C>	gaussElimination(edu.jas.vector.GenMatrix<C> a) Gauss elimination of a matrix.
edu.jas.vector.GenMatrix<C>	gaussJordanElimination(edu.jas.vector.GenMatrix<C> a) Gauss-Jordan elimination of a matrix.
edu.jas.vector.GenMatrix<C>	inverse(edu.jas.vector.GenMatrix<C> a) Inverse of a matrix.
boolean	isNullSpace(edu.jas.vector.GenMatrix<C> a, edu.jas.vector.GenMatrix<C> n) Test if n is a null space for the linear system: a n = 0.
edu.jas.vector.GenMatrix<C>	nullSpace(edu.jas.vector.GenMatrix<C> a) Null space, generating system of solutions of a linear system: a x = 0.
int	rank(edu.jas.vector.GenMatrix<C> a) Rank of a matrix.
edu.jas.vector.GenVector<C>	solve(edu.jas.vector.GenMatrix<C> a, edu.jas.vector.GenVector<C> b) Solve a linear system: a x = b.
C	trace(edu.jas.vector.GenMatrix<C> a) Trace of a matrix.

Methods inherited from class java.lang.Object

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

Constructor Detail

GaussElimination

public GaussElimination()

Method Detail

solve

public edu.jas.vector.GenVector<C> solve(edu.jas.vector.GenMatrix<C> a,
                                         edu.jas.vector.GenVector<C> b)

Solve a linear system: a x = b.

Parameters:

a - matrix

b - vector of right hand side

Returns:

a solution vector x

nullSpace

public edu.jas.vector.GenMatrix<C> nullSpace(edu.jas.vector.GenMatrix<C> a)

Null space, generating system of solutions of a linear system: a x = 0.

Parameters:

a - matrix

Returns:

matrix of generating system of solution vectors x

isNullSpace

public boolean isNullSpace(edu.jas.vector.GenMatrix<C> a,
                           edu.jas.vector.GenMatrix<C> n)

Test if n is a null space for the linear system: a n = 0.

Parameters:

a - matrix

n - matrix

Returns:

true, if n is a nullspace of a, else false

characteristicPolynomial

public edu.jas.poly.GenPolynomial<C> characteristicPolynomial(edu.jas.vector.GenMatrix<C> a)

Characteristic polynomial of a matrix.

Parameters:

a - matrix

Returns:

characteristic polynomial of a

determinant

public C determinant(edu.jas.vector.GenMatrix<C> a)

Determinant of a matrix.

Parameters:

a - matrix

Returns:

determinant of a

trace

public C trace(edu.jas.vector.GenMatrix<C> a)

Trace of a matrix.

Parameters:

a - matrix

Returns:

trace of a

rank

public int rank(edu.jas.vector.GenMatrix<C> a)

Rank of a matrix.

Parameters:

a - matrix

Returns:

rank of a

gaussElimination

public edu.jas.vector.GenMatrix<C> gaussElimination(edu.jas.vector.GenMatrix<C> a)

Gauss elimination of a matrix.

Parameters:

a - matrix

Returns:

Gauss elimination of a

gaussJordanElimination

public edu.jas.vector.GenMatrix<C> gaussJordanElimination(edu.jas.vector.GenMatrix<C> a)

Gauss-Jordan elimination of a matrix.

Parameters:

a - matrix

Returns:

Gauss-Jordan elimination of a

inverse

public edu.jas.vector.GenMatrix<C> inverse(edu.jas.vector.GenMatrix<C> a)

Inverse of a matrix.

Parameters:

a - matrix

Returns:

inverse matrix of a