numerical::eigen_decomposition< T > Class Template Reference

The eigenvalues, and optionally the right eigenvectors, of a general square matrix, as numpy.linalg.eig. More...

#include <eigen.hpp>

Collaboration diagram for numerical::eigen_decomposition< T >:

Public Member Functions
	eigen_decomposition (const matrix< T > &input, bool vectors=true)
	Decomposes input.
const vector< std::complex< double > > &	values () const noexcept
	The eigenvalues, in the order of the Schur form.
const matrix< std::complex< double > > &	vectors () const &noexcept
	The eigenvectors as columns, ordered to match values (empty where they were not computed).
matrix< std::complex< double > >	vectors () &&
	The eigenvectors, moved out of an expiring decomposition.
bool	real () const noexcept
	Whether every eigenvalue is real (a real matrix's whose Schur form has no 2 × 2 block): its vectors are then real too.

Private Member Functions
void	finish (std::complex< double > *row, const std::complex< double > &value, double) const
	Normalises the eigenvector row (a row of Vᵀ) of a real matrix's eigenvalue value, as dgeev: a real one to unit norm; a pair's first to unit norm, its largest component real, its second the first's conjugate (the row above).
void	finish (std::complex< double > *row, const std::complex< double > &, const std::complex< double > &) const
	Normalises the eigenvector row of a complex matrix, as zgeev: to unit norm, its largest component real and positive.

Private Attributes
std::size_t	n_
	The matrix order.
vector< std::complex< double > >	values_
	The eigenvalues.
matrix< std::complex< double > >	vectors_
	The eigenvectors as columns.
bool	real_ {true}
	Whether all eigenvalues are real.

Detailed Description

template<typename T>
class numerical::eigen_decomposition< T >

The eigenvalues, and optionally the right eigenvectors, of a general square matrix, as numpy.linalg.eig.

T is double or std::complex<double>; the eigenvalues and vectors are complex either way (real says whether a real matrix's are all real). Column j of vectors is the eigenvector of values [j], A V = V Λ, each of unit norm with its component of largest modulus real.

Definition at line 2979 of file eigen.hpp.

Constructor & Destructor Documentation

eigen_decomposition()

template<typename T >

numerical::eigen_decomposition< T >::eigen_decomposition ( const matrix< T > &  input, bool  vectors = true  )

inlineexplicit

Decomposes input.

Parameters

[in]	input	A square matrix.
[in]	vectors	Whether to compute the eigenvectors (the eigenvalues alone cost a third as much).

Exceptions

dimension_error	If input is not square.
non_finite_error	If an entry is infinite or NaN.
convergence_error	If the QR iterations did not converge.

Definition at line 2991 of file eigen.hpp.

Member Function Documentation

finish() [1/2]

template<typename T >

void numerical::eigen_decomposition< T >::finish ( std::complex< double > *  row, const std::complex< double > &  , const std::complex< double > &    ) const

inlineprivate

Normalises the eigenvector row of a complex matrix, as zgeev: to unit norm, its largest component real and positive.

Definition at line 3139 of file eigen.hpp.

finish() [2/2]

template<typename T >

void numerical::eigen_decomposition< T >::finish ( std::complex< double > *  row, const std::complex< double > &  value, double    ) const

inlineprivate

Normalises the eigenvector row (a row of Vᵀ) of a real matrix's eigenvalue value, as dgeev: a real one to unit norm; a pair's first to unit norm, its largest component real, its second the first's conjugate (the row above).

Definition at line 3116 of file eigen.hpp.

real()

template<typename T >

bool numerical::eigen_decomposition< T >::real ( ) const

inlinenoexcept

Whether every eigenvalue is real (a real matrix's whose Schur form has no 2 × 2 block): its vectors are then real too.

Definition at line 3106 of file eigen.hpp.

values()

template<typename T >

const vector< std::complex< double > > & numerical::eigen_decomposition< T >::values ( ) const

inlinenoexcept

The eigenvalues, in the order of the Schur form.

Definition at line 3087 of file eigen.hpp.

vectors() [1/2]

template<typename T >

matrix< std::complex< double > > numerical::eigen_decomposition< T >::vectors ( ) &&

inline

The eigenvectors, moved out of an expiring decomposition.

Definition at line 3099 of file eigen.hpp.

vectors() [2/2]

template<typename T >

const matrix< std::complex< double > > & numerical::eigen_decomposition< T >::vectors ( ) const &

inlinenoexcept

The eigenvectors as columns, ordered to match values (empty where they were not computed).

Definition at line 3093 of file eigen.hpp.

Member Data Documentation

n_

template<typename T >

std::size_t numerical::eigen_decomposition< T >::n_

private

The matrix order.

Definition at line 3146 of file eigen.hpp.

real_

template<typename T >

bool numerical::eigen_decomposition< T >::real_ {true}

private

Whether all eigenvalues are real.

Definition at line 3149 of file eigen.hpp.

values_

template<typename T >

vector<std::complex<double> > numerical::eigen_decomposition< T >::values_

private

The eigenvalues.

Definition at line 3147 of file eigen.hpp.

vectors_

template<typename T >

matrix<std::complex<double> > numerical::eigen_decomposition< T >::vectors_

private

The eigenvectors as columns.

Definition at line 3148 of file eigen.hpp.

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The documentation for this class was generated from the following file:

• include/numerical/eigen.hpp