numerical::symmetric_eigen Class Reference

The eigenvalues and eigenvectors of a real symmetric matrix. More...

#include <decomposition.hpp>

Collaboration diagram for numerical::symmetric_eigen:

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

Private Member Functions
void	extract_sorted (const buffer< double > &diagonal, const buffer< double > &v)
	Sorts the eigenvalues diagonal ascending and reorders v's columns to match.

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

Detailed Description

The eigenvalues and eigenvectors of a real symmetric matrix.

By default the matrix is reduced to tridiagonal form by Householder reflections and the tridiagonal is diagonalised by divide and conquer (eigen_method::divide_and_conquer), the method of LAPACK's dsyevd, most of its work in matrix products; implicit QL (eigen_method::tridiagonal_ql, dsyev's) and cyclic Jacobi rotations (eigen_method::jacobi) are the alternatives. Whichever, the eigenvalues are real and the eigenvectors orthonormal. The eigenvalues are returned in ascending order, with vectors j-th column the eigenvector of values [j] (A = V Λ Vᵀ). Real symmetric only (the complex Hermitian case is hermitian_eigen). Only the lower triangle is read, as numpy.linalg.eigh reads it by default: the upper one is taken to mirror it.

Definition at line 4401 of file decomposition.hpp.

Constructor & Destructor Documentation

symmetric_eigen()

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

inlineexplicit

Diagonalises input.

Parameters

[in]	input	A real symmetric matrix (its lower triangle is read).
[in]	method	The algorithm.

Exceptions

dimension_error	If input is not square.
convergence_error	If the method did not converge within its bound.

Definition at line 4412 of file decomposition.hpp.

Member Function Documentation

extract_sorted()

void numerical::symmetric_eigen::extract_sorted ( const buffer< double > &  diagonal, const buffer< double > &  v  )

inlineprivate

Sorts the eigenvalues diagonal ascending and reorders v's columns to match.

Definition at line 4498 of file decomposition.hpp.

values()

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

inlinenoexcept

The eigenvalues, ascending.

Definition at line 4478 of file decomposition.hpp.

vectors() [1/2]

matrix< double > numerical::symmetric_eigen::vectors ( ) &&

inline

The eigenvectors, moved out of an expiring decomposition.

Definition at line 4490 of file decomposition.hpp.

vectors() [2/2]

const matrix< double > & numerical::symmetric_eigen::vectors ( ) const &

inlinenoexcept

The eigenvectors as columns, ordered to match values.

Definition at line 4484 of file decomposition.hpp.

Member Data Documentation

n_

std::size_t numerical::symmetric_eigen::n_

private

The matrix order.

Definition at line 4521 of file decomposition.hpp.

values_

vector<double> numerical::symmetric_eigen::values_

private

Eigenvalues, ascending.

Definition at line 4522 of file decomposition.hpp.

vectors_

matrix<double> numerical::symmetric_eigen::vectors_

private

Eigenvectors as columns.

Definition at line 4523 of file decomposition.hpp.

---

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

• include/numerical/decomposition.hpp