Module imagingbook.common

Package imagingbook.common.math.eigen

Class EigenDecompositionApache

java.lang.Object

imagingbook.common.math.eigen.EigenDecompositionApache

All Implemented Interfaces:

RealEigenDecomposition

public class EigenDecompositionApache
extends Object
implements RealEigenDecomposition

An implementation of RealEigenDecomposition, which merely wraps an instance of EigenDecomposition as provided by the Apache Commons Math library. Note this works only for square matrices and symmetry and zero tolerances cannot be specified, default values are always used. The Jama version (EigenDecompositionJama) generally appears to be more flexible and robust.

Version:

2022/11/24

See Also:

• EigenDecompositionJama
• Eigensolver2x2

Constructor Summary

Constructors

Constructor	Description
EigenDecompositionApache(RealMatrix M)	Constructor, calculates the eigen decomposition of the specified matrix, which must be square but does not need to be symmetric.

Method Summary

Modifier and Type	Method	Description
RealVector	getEigenvector(int k)	Returns the k-th eigenvector, i.e., the k-th column vector of the matrix returned by RealEigenDecomposition.getV().
EigenDecomposition	getInternalDecomposition()	Returns the underlying Apache eigendecomposition instance, mainly for debugging.
double	getRealEigenvalue(int k)	Returns the real part of the k-th eigenvalue
double[]	getRealEigenvalues()	Returns a vector holding the real parts of the eigenvalues
RealMatrix	getV()	Return the matrix of eigenvectors, which are its column vectors.
boolean	hasComplexEigenvalues()	Returns whether the calculated eigenvalues are complex or real.

Methods inherited from class java.lang.Object

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

Methods inherited from interface imagingbook.common.math.eigen.RealEigenDecomposition

getD

Constructor Details

EigenDecompositionApache

public EigenDecompositionApache(RealMatrix M)

Constructor, calculates the eigen decomposition of the specified matrix, which must be square but does not need to be symmetric.

Parameters:

M - the matrix to decompose

Method Details

hasComplexEigenvalues

public boolean hasComplexEigenvalues()

Description copied from interface: RealEigenDecomposition

Returns whether the calculated eigenvalues are complex or real.

Specified by:

hasComplexEigenvalues in interface RealEigenDecomposition

Returns:

true if any of the eigenvalues is complex, false otherwise

getRealEigenvalue

public double getRealEigenvalue(int k)

Description copied from interface: RealEigenDecomposition

Returns the real part of the k-th eigenvalue

Specified by:

getRealEigenvalue in interface RealEigenDecomposition

Parameters:

k - index of the eigenvalue @param k index of the eigenvector (0-based)

Returns:

real part of the k-th eigenvalue

getRealEigenvalues

public double[] getRealEigenvalues()

Description copied from interface: RealEigenDecomposition

Returns a vector holding the real parts of the eigenvalues

Specified by:

getRealEigenvalues in interface RealEigenDecomposition

Returns:

real(diag(D))

getEigenvector

public RealVector getEigenvector(int k)

Description copied from interface: RealEigenDecomposition

Returns the k-th eigenvector, i.e., the k-th column vector of the matrix returned by RealEigenDecomposition.getV().

Specified by:

getEigenvector in interface RealEigenDecomposition

Parameters:

k - index of the eigenvector (0-based)

Returns:

the k-th eigenvector (instance of RealVector)

getV

public RealMatrix getV()

Description copied from interface: RealEigenDecomposition

Return the matrix of eigenvectors, which are its column vectors.

Specified by:

getV in interface RealEigenDecomposition

Returns:

the matrix of eigenvectors

getInternalDecomposition

public EigenDecomposition getInternalDecomposition()

Returns the underlying Apache eigendecomposition instance, mainly for debugging.

Returns:

the Apache eigendecomposition instance