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

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.factorization.eigen.EigenDecomposition

public class EigenDecomposition
extends java.lang.Object

Let A be a square, diagonalizable N × N matrix with N linearly independent eigenvectors. Then A can be factorized as Q * D * Q' = A. Q is the square N × N matrix whose i-th column is the eigenvector of A, and D is the diagonal matrix whose diagonal elements are the corresponding eigenvalues.

See Also:

Wikipedia: Eigendecomposition of a matrix

Constructor Summary

EigenDecomposition(Matrix A)
Run the eigen decomposition on a square matrix.

EigenDecomposition(Matrix A, double epsilon)
Run the eigen decomposition on a square matrix.

Method Summary

DiagonalMatrix	D() Get the diagonal matrix D as in Q * D * Q' = A.
Matrix	Q() Get Q as in Q * D * Q' = A.
Matrix	Qt() Get Q' as in Q * D * Q' = A.

Methods inherited from class java.lang.Object

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

Constructor Detail

EigenDecomposition

public EigenDecomposition(Matrix A,
                          double epsilon)

Run the eigen decomposition on a square matrix.

Parameters:

A - a square, diagonalizable matrix

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

EigenDecomposition

public EigenDecomposition(Matrix A)

Run the eigen decomposition on a square matrix.

Parameters:

A - a square, diagonalizable matrix

Method Detail

D

public DiagonalMatrix D()

Get the diagonal matrix D as in Q * D * Q' = A.

Note that for the moment we support only real eigenvalues.

Returns:

D

Q

public Matrix Q()

Get Q as in Q * D * Q' = A.

Note that for the moment we support only real eigenvalues.

Returns:

Q

Qt

public Matrix Qt()

Get Q' as in Q * D * Q' = A.

Note that for the moment we support only real eigenvalues.

Returns:

Q.t()