Package org.hipparchus.linear

Class OrderedComplexEigenDecomposition

java.lang.Object

org.hipparchus.linear.ComplexEigenDecomposition

org.hipparchus.linear.OrderedComplexEigenDecomposition

public class OrderedComplexEigenDecomposition
extends ComplexEigenDecomposition

Given a matrix A, it computes a complex eigen decomposition A = VDV^{T}. It ensures that eigen values in the diagonal of D are in ascending order.

Field Summary

Fields inherited from class org.hipparchus.linear.ComplexEigenDecomposition

DEFAULT_EIGENVECTORS_EQUALITY, DEFAULT_EPSILON, DEFAULT_EPSILON_AV_VD_CHECK

Constructor Summary

Constructors

Constructor	Description
OrderedComplexEigenDecomposition(RealMatrix matrix)	Constructor for the decomposition.
OrderedComplexEigenDecomposition(RealMatrix matrix, double eigenVectorsEquality, double epsilon, double epsilonAVVDCheck)	Constructor for decomposition.
OrderedComplexEigenDecomposition(RealMatrix matrix, double eigenVectorsEquality, double epsilon, double epsilonAVVDCheck, Comparator<Complex> eigenValuesComparator)	Constructor for decomposition.

Method Summary

Modifier and Type	Method	Description
FieldMatrix<Complex>	getVT()	Getter VT.

Methods inherited from class org.hipparchus.linear.ComplexEigenDecomposition

checkDefinition, findEigenValues, findEigenVectors, getD, getDeterminant, getEigenvalues, getEigenvector, getV, hasComplexEigenvalues, matricesToEigenArrays

Methods inherited from class java.lang.Object

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

Constructor Detail

OrderedComplexEigenDecomposition

public OrderedComplexEigenDecomposition(RealMatrix matrix)

Constructor for the decomposition.

Parameters:

matrix - real matrix.

OrderedComplexEigenDecomposition

public OrderedComplexEigenDecomposition(RealMatrix matrix,
                                        double eigenVectorsEquality,
                                        double epsilon,
                                        double epsilonAVVDCheck)

Constructor for decomposition.

The eigenVectorsEquality threshold is used to ensure the L∞-normalized eigenvectors found using inverse iteration are different from each other. if $min(|e_i-e_j|,|e_i+e_j|)$ is smaller than this threshold, the algorithm considers it has found again an already known vector, so it drops it and attempts a new inverse iteration with a different start vector. This value should be much larger than epsilon which is used for convergence

This constructor calls OrderedComplexEigenDecomposition(RealMatrix, double, double, double, Comparator) with a comparator using real ordering as the primary sort order and imaginary ordering as the secondary sort order..

Parameters:

matrix - real matrix.

eigenVectorsEquality - threshold below which eigenvectors are considered equal

epsilon - Epsilon used for internal tests (e.g. is singular, eigenvalue ratio, etc.)

epsilonAVVDCheck - Epsilon criteria for final AV=VD check

Since:

1.9

OrderedComplexEigenDecomposition

public OrderedComplexEigenDecomposition(RealMatrix matrix,
                                        double eigenVectorsEquality,
                                        double epsilon,
                                        double epsilonAVVDCheck,
                                        Comparator<Complex> eigenValuesComparator)

Constructor for decomposition.

The eigenVectorsEquality threshold is used to ensure the L∞-normalized eigenvectors found using inverse iteration are different from each other. if $min(|e_i-e_j|,|e_i+e_j|)$ is smaller than this threshold, the algorithm considers it has found again an already known vector, so it drops it and attempts a new inverse iteration with a different start vector. This value should be much larger than epsilon which is used for convergence

Parameters:

matrix - real matrix.

eigenVectorsEquality - threshold below which eigenvectors are considered equal

epsilon - Epsilon used for internal tests (e.g. is singular, eigenvalue ratio, etc.)

epsilonAVVDCheck - Epsilon criteria for final AV=VD check

eigenValuesComparator - comparator for sorting eigen values

Since:

3.0

Method Detail

getVT

public FieldMatrix<Complex> getVT()

Getter VT.

Overrides:

getVT in class ComplexEigenDecomposition

Returns:

VT.