com.numericalmethod.suanshu.matrix.doubles.factorization.eigen

Class Eigen

java.lang.Object

com.numericalmethod.suanshu.matrix.doubles.factorization.eigen.Eigen

All Implemented Interfaces:

Spectrum, java.io.Serializable

public class Eigen
extends java.lang.Object
implements Spectrum

Given a square matrix A, an eigenvalue λ and its associated eigenvector v are defined by Av = λv. We first find the eigenvalues and then the eigenvector space by solving a system of homogeneous linear equations. That is, (A - λ)v = 0.

TODO: For the moment, we compute both real and complex eigenvalues, but we do not compute the eigenvectors for complex eigenvalues.

The R equivalent function is eigen.

See Also:

Wikipedia: Eigenvalue algorithm, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	Eigen.Method the methods available to compute eigenvalues and eigenvectors

Constructor Summary

Constructors

Constructor and Description
Eigen(Matrix A) Compute the eigenvalues and eigenvectors for a square matrix.
Eigen(Matrix A, Eigen.Method method, double epsilon) Compute the eigenvalues and eigenvectors for a square matrix.

Method Summary

Modifier and Type	Method and Description
java.lang.Number	getEigenvalue(int i) Get the i-th eigenvalue.
java.util.List<java.lang.Number>	getEigenvalues() Get all the eigenvalues.
EigenProperty	getProperty(int i) Get the i-th EigenProperty.
EigenProperty	getProperty(java.lang.Number eigenvalue) Get the EigenProperty by eigenvalue.
double[]	getRealEigenvalues() Get all real eigenvalues.
int	size() Get the number of distinct eigenvalues.

Methods inherited from class java.lang.Object

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

Constructor Detail

Eigen

public Eigen(Matrix A,
             Eigen.Method method,
             double epsilon)

Compute the eigenvalues and eigenvectors for a square matrix. For each eigenvalue, there are infinitely many associated eigenvectors, which forms a vector space. This implementation computes a set of linearly independent basis, any linear combination of them qualifies as an eigenvector.

TODO: For the moment, we compute both real and complex eigenvalues, but we do not compute the eigenvectors for complex eigenvalues.

Parameters:

A - a square matrix

method - the eigen decomposition algorithm, c.f., Eigen.Method

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Throws:

java.lang.IllegalArgumentException - if A is not square

Eigen

public Eigen(Matrix A)

Compute the eigenvalues and eigenvectors for a square matrix.

Parameters:

A - a square matrix

See Also:

Wikipedia: QR algorithm

Method Detail

size

public int size()

Get the number of distinct eigenvalues.

Returns:

the number of distinct eigenvalues

getEigenvalues

public java.util.List<java.lang.Number> getEigenvalues()

Description copied from interface: Spectrum

Get all the eigenvalues.

Specified by:

getEigenvalues in interface Spectrum

Returns:

the eigenvalues

getRealEigenvalues

public double[] getRealEigenvalues()

Get all real eigenvalues. The eigenvalues are sorted in descending order.

Returns:

all real eigenvalues

getEigenvalue

public java.lang.Number getEigenvalue(int i)

Get the i-th eigenvalue. The eigenvalues are sorted in descending order. The index counts from 0 to agree with the List<Number> convention.

Parameters:

i - an index, counting from 0

Returns:

return the i-th eigenvalue

getProperty

public EigenProperty getProperty(java.lang.Number eigenvalue)

Get the EigenProperty by eigenvalue. Note that the number passed in must be exactly the same as the eigenvalue in binary representation. Passing in an approximate number (up to precision) will likely result in an unmatched error, i.e., null returned.

Parameters:

eigenvalue - an eigenvalue

Returns:

the EigenProperty of the eigenvalue

getProperty

public EigenProperty getProperty(int i)

Get the i-th EigenProperty. The eigenvalues are sorted in descending order. The index counts from 0 to agree with the List<Number> convention.

Parameters:

i - the index, counting from 0

Returns:

the i-th EigenProperty