A symmetric matrix represented in eigenvalue decomposition. More...

#include <vpdt_eigen_sym_matrix.h>

Public Types
typedef vpdt_field_default< T, n >::type	vector
	the data type used for vectors. More...

typedef vpdt_field_traits< vector >::matrix_type	matrix
	the data type used for matrices. More...

Public Member Functions
	vpdt_eigen_sym_matrix (unsigned int var_dim=n)
	Constructor. More...

	vpdt_eigen_sym_matrix (const matrix &evec, const vector &eval)
	Constructor - from eigenvectors and eigenvalues. More...

	vpdt_eigen_sym_matrix (const matrix &m)
	Constructor - from symmetric matrix. More...

unsigned int	dimension () const
	Return the dimension. More...

const matrix &	eigenvectors () const
	Access to the eigenvectors. More...

const vector &	eigenvalues () const
	Access to the eigenvalues. More...

void	set_eigenvectors (const matrix &m)
	Set the eigenvectors. More...

void	set_eigenvalues (const vector &v)
	set the eigenvalues. More...

void	set_size (unsigned int dim)
	Set the size (if variable) and reset to default. More...

void	set_matrix (const matrix &m)
	set the eigenvectors and eigen values by decomposing m. More...

vpdt_eigen_sym_matrix< T, n > &	operator *= (const T &val)
	multiply the matrix by a scalar. More...

void	form_matrix (matrix &m) const
	Reform the matrix. More...

void	form_inverse (matrix &m) const
	compute the matrix inverse. More...

void	product (const vector &x, vector &y) const
	evaluate y = M * x. More...

void	inverse_product (const vector &x, vector &y) const
	evaluate y = M^-1 * x. More...

T	quad_form (const vector &x) const
	evaluate the Quadratic form x^t * M * x. More...

T	inverse_quad_form (const vector &x) const
	evaluate the inverse Quadratic form x^t * M^-1 * x. More...

T	determinant () const
	compute the determinant. More...

Private Member Functions
bool	are_evec_orthonormal () const
	return true if the eigenvectors are (approximately) orthonormal. More...

Private Attributes
matrix	eigen_vec_
	the matrix of eigenvectors. More...

vector	eigen_val_
	the vector of eigenvalues. More...

Detailed Description

template<class T, unsigned int n = 0>
class vpdt_eigen_sym_matrix< T, n >

A symmetric matrix represented in eigenvalue decomposition.

Definition at line 40 of file vpdt_eigen_sym_matrix.h.

Member Typedef Documentation

◆ matrix

template<class T, unsigned int n = 0>

typedef vpdt_field_traits<vector>::matrix_type vpdt_eigen_sym_matrix< T, n >::matrix

the data type used for matrices.

Definition at line 46 of file vpdt_eigen_sym_matrix.h.

◆ vector

template<class T, unsigned int n = 0>

typedef vpdt_field_default<T,n>::type vpdt_eigen_sym_matrix< T, n >::vector

the data type used for vectors.

Definition at line 44 of file vpdt_eigen_sym_matrix.h.

Constructor & Destructor Documentation

◆ vpdt_eigen_sym_matrix() [1/3]

template<class T, unsigned int n = 0>

vpdt_eigen_sym_matrix< T, n >::vpdt_eigen_sym_matrix ( unsigned int var_dim = n )

inline

Constructor.

Optionally initialize the dimension for when n==0. Otherwise var_dim is ignored

Definition at line 51 of file vpdt_eigen_sym_matrix.h.

◆ vpdt_eigen_sym_matrix() [2/3]

template<class T, unsigned int n = 0>

vpdt_eigen_sym_matrix< T, n >::vpdt_eigen_sym_matrix	(	const matrix &	evec,
		const vector &	eval
	)

inline

Constructor - from eigenvectors and eigenvalues.

Definition at line 60 of file vpdt_eigen_sym_matrix.h.

◆ vpdt_eigen_sym_matrix() [3/3]

template<class T, unsigned int n = 0>

vpdt_eigen_sym_matrix< T, n >::vpdt_eigen_sym_matrix ( const matrix & m )

inline

Constructor - from symmetric matrix.

Definition at line 67 of file vpdt_eigen_sym_matrix.h.

Member Function Documentation

◆ are_evec_orthonormal()

template<class T, unsigned int n = 0>

bool vpdt_eigen_sym_matrix< T, n >::are_evec_orthonormal ( ) const

inlineprivate

return true if the eigenvectors are (approximately) orthonormal.

Definition at line 248 of file vpdt_eigen_sym_matrix.h.

◆ determinant()

template<class T, unsigned int n = 0>

T vpdt_eigen_sym_matrix< T, n >::determinant ( ) const

inline

compute the determinant.

Definition at line 232 of file vpdt_eigen_sym_matrix.h.

◆ dimension()

template<class T, unsigned int n = 0>

unsigned int vpdt_eigen_sym_matrix< T, n >::dimension ( ) const

inline

Return the dimension.

Definition at line 73 of file vpdt_eigen_sym_matrix.h.

◆ eigenvalues()

template<class T, unsigned int n = 0>

const vector& vpdt_eigen_sym_matrix< T, n >::eigenvalues ( ) const

inline

Access to the eigenvalues.

Definition at line 79 of file vpdt_eigen_sym_matrix.h.

◆ eigenvectors()

template<class T, unsigned int n = 0>

const matrix& vpdt_eigen_sym_matrix< T, n >::eigenvectors ( ) const

inline

Access to the eigenvectors.

Definition at line 76 of file vpdt_eigen_sym_matrix.h.

◆ form_inverse()

template<class T, unsigned int n = 0>

void vpdt_eigen_sym_matrix< T, n >::form_inverse ( matrix & m ) const

inline

compute the matrix inverse.

m = eigen_vec_ * inverse(diag(eigen_val_)) * eigen_vec_.transpose()

Definition at line 141 of file vpdt_eigen_sym_matrix.h.

◆ form_matrix()

template<class T, unsigned int n = 0>

void vpdt_eigen_sym_matrix< T, n >::form_matrix ( matrix & m ) const

inline

Reform the matrix.

m = eigen_vec_ * diag(eigen_val_) * eigen_vec_.transpose()

Definition at line 120 of file vpdt_eigen_sym_matrix.h.

◆ inverse_product()

template<class T, unsigned int n = 0>

void vpdt_eigen_sym_matrix< T, n >::inverse_product	(	const vector &	x,
		vector &	y
	)		const

inline

evaluate y = M^-1 * x.

Definition at line 182 of file vpdt_eigen_sym_matrix.h.

◆ inverse_quad_form()

template<class T, unsigned int n = 0>

T vpdt_eigen_sym_matrix< T, n >::inverse_quad_form ( const vector & x ) const

inline

evaluate the inverse Quadratic form x^t * M^-1 * x.

Definition at line 215 of file vpdt_eigen_sym_matrix.h.

◆ operator *=()

template<class T, unsigned int n = 0>

vpdt_eigen_sym_matrix<T,n>& vpdt_eigen_sym_matrix< T, n >::operator *= ( const T & val )

inline

multiply the matrix by a scalar.

Definition at line 110 of file vpdt_eigen_sym_matrix.h.

◆ product()

template<class T, unsigned int n = 0>

void vpdt_eigen_sym_matrix< T, n >::product	(	const vector &	x,
		vector &	y
	)		const

inline

evaluate y = M * x.

Definition at line 164 of file vpdt_eigen_sym_matrix.h.

◆ quad_form()

template<class T, unsigned int n = 0>

T vpdt_eigen_sym_matrix< T, n >::quad_form ( const vector & x ) const

inline

evaluate the Quadratic form x^t * M * x.

Definition at line 200 of file vpdt_eigen_sym_matrix.h.

◆ set_eigenvalues()

template<class T, unsigned int n = 0>

void vpdt_eigen_sym_matrix< T, n >::set_eigenvalues ( const vector & v )

inline

set the eigenvalues.

Definition at line 89 of file vpdt_eigen_sym_matrix.h.

◆ set_eigenvectors()

template<class T, unsigned int n = 0>

void vpdt_eigen_sym_matrix< T, n >::set_eigenvectors ( const matrix & m )

inline

Set the eigenvectors.

Definition at line 82 of file vpdt_eigen_sym_matrix.h.

◆ set_matrix()

template<class T, unsigned int n = 0>

void vpdt_eigen_sym_matrix< T, n >::set_matrix ( const matrix & m )

inline

set the eigenvectors and eigen values by decomposing m.

Definition at line 101 of file vpdt_eigen_sym_matrix.h.

◆ set_size()

template<class T, unsigned int n = 0>

void vpdt_eigen_sym_matrix< T, n >::set_size ( unsigned int dim )

inline

Set the size (if variable) and reset to default.

Definition at line 92 of file vpdt_eigen_sym_matrix.h.

Member Data Documentation

◆ eigen_val_

template<class T, unsigned int n = 0>

vector vpdt_eigen_sym_matrix< T, n >::eigen_val_

private

the vector of eigenvalues.

Definition at line 245 of file vpdt_eigen_sym_matrix.h.

◆ eigen_vec_

template<class T, unsigned int n = 0>

matrix vpdt_eigen_sym_matrix< T, n >::eigen_vec_

private

the matrix of eigenvectors.

Definition at line 243 of file vpdt_eigen_sym_matrix.h.

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

core/vpdl/vpdt/vpdt_eigen_sym_matrix.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<class T, unsigned int n = 0> class vpdt_eigen_sym_matrix< T, n >

Member Typedef Documentation

◆ matrix

◆ vector

Constructor & Destructor Documentation

◆ vpdt_eigen_sym_matrix() [1/3]

◆ vpdt_eigen_sym_matrix() [2/3]

◆ vpdt_eigen_sym_matrix() [3/3]

Member Function Documentation

◆ are_evec_orthonormal()

◆ determinant()

◆ dimension()

◆ eigenvalues()

◆ eigenvectors()

◆ form_inverse()

◆ form_matrix()

◆ inverse_product()

◆ inverse_quad_form()

◆ operator *=()

◆ product()

◆ quad_form()

◆ set_eigenvalues()

◆ set_eigenvectors()

◆ set_matrix()

◆ set_size()

Member Data Documentation

◆ eigen_val_

◆ eigen_vec_

template<class T, unsigned int n = 0>
class vpdt_eigen_sym_matrix< T, n >