Package org.hipparchus.linear

Class ComplexEigenDecomposition

java.lang.Object

org.hipparchus.linear.ComplexEigenDecomposition

Direct Known Subclasses:

OrderedComplexEigenDecomposition

public class ComplexEigenDecomposition
extends Object

Given a matrix A, it computes a complex eigen decomposition A = VDV^{T}. It checks the definition in runtime using AV = VD. Complex Eigen Decomposition, it differs from the EigenDecomposition since it computes the eigen vectors as complex eigen vectors (if applicable). Compute complex eigen values from the schur transform. Compute complex eigen vectors based on eigen values and the inverse iteration method. see: https://en.wikipedia.org/wiki/Inverse_iteration https://en.wikiversity.org/wiki/Shifted_inverse_iteration http://www.robots.ox.ac.uk/~sjrob/Teaching/EngComp/ecl4.pdf http://www.math.ohiou.edu/courses/math3600/lecture16.pdf

Constructor Summary

Constructors

Constructor	Description
ComplexEigenDecomposition(RealMatrix matrix)	Constructor for decomposition.

Method Summary

Modifier and Type	Method	Description
protected void	checkDefinition(RealMatrix matrix)	Check definition of the decomposition in runtime.
protected void	findEigenValues(RealMatrix matrix)	Compute eigen values using the Schur transform.
protected void	findEigenVectors(FieldMatrix<Complex> matrix)	Compute the eigen vectors using the inverse power method.
FieldMatrix<Complex>	getD()	Getter D.
double	getDeterminant()	Computes the determinant.
Complex[]	getEigenvalues()	Getter of the eigen values.
FieldVector<Complex>	getEigenvector(int i)	Getter of the eigen vectors.
FieldMatrix<Complex>	getV()	Getter V.
FieldMatrix<Complex>	getVT()	Getter VT.
boolean	hasComplexEigenvalues()	Confirm if there are complex eigen values.

Methods inherited from class java.lang.Object

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

Constructor Detail

ComplexEigenDecomposition

public ComplexEigenDecomposition(RealMatrix matrix)

Constructor for decomposition.

Parameters:

matrix - real matrix.

Method Detail

getEigenvalues

public Complex[] getEigenvalues()

Getter of the eigen values.

Returns:

igen values.

getEigenvector

public FieldVector<Complex> getEigenvector(int i)

Getter of the eigen vectors.

Parameters:

i - which eigen vector.

Returns:

eigen vector.

hasComplexEigenvalues

public boolean hasComplexEigenvalues()

Confirm if there are complex eigen values.

Returns:

true if there are complex eigen values.

getDeterminant

public double getDeterminant()

Computes the determinant.

Returns:

the determinant.

getV

public FieldMatrix<Complex> getV()

Getter V.

Returns:

V.

getD

public FieldMatrix<Complex> getD()

Getter D.

Returns:

D.

getVT

public FieldMatrix<Complex> getVT()

Getter VT.

Returns:

VT.

findEigenValues

protected void findEigenValues(RealMatrix matrix)

Compute eigen values using the Schur transform.

Parameters:

matrix - real matrix to compute eigen values.

findEigenVectors

protected void findEigenVectors(FieldMatrix<Complex> matrix)

Compute the eigen vectors using the inverse power method.

Parameters:

matrix - real matrix to compute eigen vectors.

checkDefinition

protected void checkDefinition(RealMatrix matrix)

Check definition of the decomposition in runtime.

Parameters:

matrix - matrix to be decomposed.