numerical::hermitian_eigen Class Reference

The eigenvalues and eigenvectors of a complex Hermitian matrix. More...

#include <decomposition.hpp>

Collaboration diagram for numerical::hermitian_eigen:

Public Member Functions
	hermitian_eigen (const matrix< std::complex< double > > &input, eigen_method method=eigen_method::divide_and_conquer)
	Diagonalises input.
const vector< double > &	values () const noexcept
	The eigenvalues, ascending.
const matrix< std::complex< double > > &	vectors () const &noexcept
	The eigenvectors as columns, ordered to match values.
matrix< std::complex< double > >	vectors () &&
	The eigenvectors, moved out of an expiring decomposition.

Private Attributes
std::size_t	n_
	The matrix order.
vector< double >	values_
	Eigenvalues, ascending.
matrix< std::complex< double > >	vectors_
	Eigenvectors as columns.

Detailed Description

The eigenvalues and eigenvectors of a complex Hermitian matrix.

The matrix is reduced to a real symmetric tridiagonal by Householder reflections and unit phases (the method of LAPACK's zheevd), which the divide and conquer of symmetric_eigen diagonalises (implicit QL, zheev's, on request). The eigenvalues are real and returned in ascending order, with vectors j-th column the eigenvector of values [j] (A = V Λ Vᴴ, V unitary). Only the lower triangle is read and the imaginary part of the diagonal is ignored, as numpy.linalg.eigh reads a matrix by default.

Definition at line 4536 of file decomposition.hpp.

Constructor & Destructor Documentation

hermitian_eigen()

numerical::hermitian_eigen::hermitian_eigen ( const matrix< std::complex< double > > &  input, eigen_method  method = eigen_method::divide_and_conquer  )

inlineexplicit

Diagonalises input.

Parameters

[in]	input	A complex Hermitian matrix (its lower triangle is read).
[in]	method	The algorithm for the tridiagonal: eigen_method::divide_and_conquer or eigen_method::tridiagonal_ql.

Exceptions

std::invalid_argument	If method is eigen_method::jacobi, which has no complex form here.
dimension_error	If input is not square.
non_finite_error	If an entry is infinite or NaN.
convergence_error	If an iteration (implicit QL or the secular equation) did not converge within its bound (not observed).

Definition at line 4551 of file decomposition.hpp.

Member Function Documentation

values()

const vector< double > & numerical::hermitian_eigen::values ( ) const

inlinenoexcept

The eigenvalues, ascending.

Definition at line 4604 of file decomposition.hpp.

vectors() [1/2]

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

inline

The eigenvectors, moved out of an expiring decomposition.

Definition at line 4616 of file decomposition.hpp.

vectors() [2/2]

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

inlinenoexcept

The eigenvectors as columns, ordered to match values.

Definition at line 4610 of file decomposition.hpp.

Member Data Documentation

n_

std::size_t numerical::hermitian_eigen::n_

private

The matrix order.

Definition at line 4623 of file decomposition.hpp.

values_

vector<double> numerical::hermitian_eigen::values_

private

Eigenvalues, ascending.

Definition at line 4624 of file decomposition.hpp.

vectors_

matrix<std::complex<double> > numerical::hermitian_eigen::vectors_

private

Eigenvectors as columns.

Definition at line 4625 of file decomposition.hpp.

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

• include/numerical/decomposition.hpp