net.mumie.mathletfactory.math.number.numeric

Class Eigenvalue2x2

java.lang.Object

net.mumie.mathletfactory.math.number.numeric.Eigenvalue2x2

public class Eigenvalue2x2
extends java.lang.Object

Contains methods for the computation of eigenvalues and eigenvectors of a real 2x2-matrix given as an array of MNumber entries.

Author:

Liu, Mrose

Document status:

finished

Constructor Summary

Constructors

Constructor and Description
Eigenvalue2x2()

Method Summary

Methods

Modifier and Type	Method and Description
static MNumber[]	eigenvalue(MNumber[] matrix) Computes the (real or complex) eigenvalues of matrix.
static MNumber[]	eigenvector(MNumber[] matrix) Computes the normalized eigenvectors which belong to the eigenvalues given by eigenvalue.
static MNumber[]	eigenvectorOfSymmetricMatrix(MNumber[] matrix) Computes the orthonormalized eigenvectors of the symmetric 2x2-matrix.
static boolean	realEigenvaluesExist(MNumber[] matrix) Checks whether matrix has real eigenvalues.

Methods inherited from class java.lang.Object

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

Constructor Detail

Eigenvalue2x2

public Eigenvalue2x2()

Method Detail

realEigenvaluesExist

public static boolean realEigenvaluesExist(MNumber[] matrix)

Checks whether matrix has real eigenvalues.

Parameters:

matrix - a MNumber[] holding rowwise a 2x2-matrix.

Returns:

a boolean which is true if matrix has only real eigenvalues.

Throws:

java.lang.IllegalArgumentException - if the length of matrix is |=4.

eigenvalue

public static MNumber[] eigenvalue(MNumber[] matrix)

Computes the (real or complex) eigenvalues of matrix.

Parameters:

matrix - a MNumber[] holding rowwise a 2x2-matrix.

Returns:

a MNumber[] holding the eigenvalues of matrix.

Throws:

java.lang.IllegalArgumentException - if the length of matrix is |=4.

eigenvector

public static MNumber[] eigenvector(MNumber[] matrix)

Computes the normalized eigenvectors which belong to the eigenvalues given by eigenvalue. If two different eigenvectors exist, (v_11, v_12, v_21, v_22) is returned, where v_1 is the eigenvector belonging to the first eigenvalue and v_2 is the eigenvector belonging to the second eigenvalue. If only one eigenvector exists, this eigenvector is returned.

Parameters:

matrix - a MNumber[] holding rowwise a 2x2-matrix.

Returns:

a MNumber[] holding the eigenvectors of matrix.

Throws:

java.lang.IllegalArgumentException - if the length of matrix is |=4.

eigenvectorOfSymmetricMatrix

public static MNumber[] eigenvectorOfSymmetricMatrix(MNumber[] matrix)

Computes the orthonormalized eigenvectors of the symmetric 2x2-matrix.

Parameters:

matrix - a MNumber[] holding rowwise a symmetric 2x2-matrix.

Returns:

a MNumber[] holding the orthonormalized eigenvectors of matrix.

Throws:

java.lang.IllegalArgumentException - if the length of matrix is |=4 or if matrix is not symmetric.