Basic linear algebra functions. More...

#include "gmm_scaled.h"
#include "gmm_transposed.h"
#include "gmm_conjugated.h"

Functions
template<typename L >
void	gmm::clear (L &l)
	clear (fill with zeros) a vector or matrix.

template<typename L >
size_type	gmm::nnz (const L &l)
	count the number of non-zero entries of a vector or matrix.

template<typename L >
void	gmm::fill (L &l, typename gmm::linalg_traits< L >::value_type x)
	*‍/ More...

template<typename L >
void	gmm::fill_random (L &l)
	fill a vector or matrix with random value (uniform [-1,1]).

template<typename L >
void	gmm::fill_random (L &l, double cfill)
	*‍/ More...

template<typename V >
void	gmm::resize (V &v, size_type n)
	*‍/ More...

template<typename M >
void	gmm::resize (M &v, size_type m, size_type n)
	*‍/ More...

template<typename M >
void	gmm::reshape (M &v, size_type m, size_type n)
	*‍/ More...

template<typename V1 , typename V2 >
strongest_value_type< V1, V2 >::value_type	gmm::vect_sp (const V1 &v1, const V2 &v2)
	*‍/ More...

template<typename MATSP , typename V1 , typename V2 >
strongest_value_type3< V1, V2, MATSP >::value_type	gmm::vect_sp (const MATSP &ps, const V1 &v1, const V2 &v2)
	scalar product between two vectors, using a matrix. More...

template<typename V1 , typename V2 >
strongest_value_type< V1, V2 >::value_type	gmm::vect_hp (const V1 &v1, const V2 &v2)
	*‍/ More...

template<typename MATSP , typename V1 , typename V2 >
strongest_value_type3< V1, V2, MATSP >::value_type	gmm::vect_hp (const MATSP &ps, const V1 &v1, const V2 &v2)
	Hermitian product with a matrix.

template<typename M >
linalg_traits< M >::value_type	gmm::mat_trace (const M &m)
	Trace of a matrix.

template<typename V >
number_traits< typename linalg_traits< V >::value_type >::magnitude_type	gmm::vect_norm2_sqr (const V &v)
	squared Euclidean norm of a vector.

template<typename V >
number_traits< typename linalg_traits< V >::value_type >::magnitude_type	gmm::vect_norm2 (const V &v)
	Euclidean norm of a vector.

template<typename V1 , typename V2 >
number_traits< typename linalg_traits< V1 >::value_type >::magnitude_type	gmm::vect_dist2_sqr (const V1 &v1, const V2 &v2)
	squared Euclidean distance between two vectors

template<typename V1 , typename V2 >
number_traits< typename linalg_traits< V1 >::value_type >::magnitude_type	gmm::vect_dist2 (const V1 &v1, const V2 &v2)
	Euclidean distance between two vectors.

template<typename M >
number_traits< typename linalg_traits< M >::value_type >::magnitude_type	gmm::mat_euclidean_norm_sqr (const M &m)
	*‍/ More...

template<typename M >
number_traits< typename linalg_traits< M >::value_type >::magnitude_type	gmm::mat_euclidean_norm (const M &m)
	Euclidean norm of a matrix.

template<typename V >
number_traits< typename linalg_traits< V >::value_type >::magnitude_type	gmm::vect_norm1 (const V &v)
	1-norm of a vector

template<typename V1 , typename V2 >
number_traits< typename linalg_traits< V1 >::value_type >::magnitude_type	gmm::vect_dist1 (const V1 &v1, const V2 &v2)
	1-distance between two vectors

template<typename V >
number_traits< typename linalg_traits< V >::value_type >::magnitude_type	gmm::vect_norminf (const V &v)
	Infinity norm of a vector.

template<typename V1 , typename V2 >
number_traits< typename linalg_traits< V1 >::value_type >::magnitude_type	gmm::vect_distinf (const V1 &v1, const V2 &v2)
	Infinity distance between two vectors.

template<typename M >
number_traits< typename linalg_traits< M >::value_type >::magnitude_type	gmm::mat_norm1 (const M &m)
	*‍/ More...

template<typename M >
number_traits< typename linalg_traits< M >::value_type >::magnitude_type	gmm::mat_norminf (const M &m)
	*‍/ More...

template<typename M >
number_traits< typename linalg_traits< M >::value_type >::magnitude_type	gmm::mat_maxnorm (const M &m)
	*‍/ More...

template<typename L >
void	gmm::clean (L &l, double threshold)
	Clean a vector or matrix (replace near-zero entries with zeroes). More...

template<typename L1 , typename L2 >
void	gmm::copy (const L1 &l1, L2 &l2)
	*‍/ More...

template<typename L1 , typename L2 >
void	gmm::add (const L1 &l1, L2 &l2)
	*‍/ More...

template<typename L1 , typename L2 , typename L3 >
void	gmm::add (const L1 &l1, const L2 &l2, L3 &l3)
	*‍/ More...

template<typename L1 , typename L2 , typename L3 >
void	gmm::mult (const L1 &l1, const L2 &l2, L3 &l3)
	*‍/ More...

template<typename L1 , typename L2 , typename L3 >
void	gmm::mult_add (const L1 &l1, const L2 &l2, L3 &l3)
	*‍/ More...

template<typename MAT >
bool	gmm::is_symmetric (const MAT &A, magnitude_of_linalg(MAT) tol=magnitude_of_linalg(MAT)(-1))
	*‍/ More...

template<typename MAT >
bool	gmm::is_hermitian (const MAT &A, magnitude_of_linalg(MAT) tol=magnitude_of_linalg(MAT)(-1))
	*‍/ More...

Detailed Description

Basic linear algebra functions.

Author: Yves Renard Yves..nosp@m.Rena.nosp@m.rd@in.nosp@m.sa-l.nosp@m.yon.f.nosp@m.r

Date: October 13, 2002.

Definition in file gmm_blas.h.

Function Documentation

◆ fill()

template<typename L >

void gmm::fill	(	L &	l,
		typename gmm::linalg_traits< L >::value_type	x
	)

inline

*‍/

fill a vector or matrix with x.

Definition at line 104 of file gmm_blas.h.

◆ fill_random()

template<typename L >

void gmm::fill_random	(	L &	l,
		double	cfill
	)

inline

*‍/

fill a vector or matrix with random value.

Parameters

l	a vector or matrix.
cfill	probability of a non-zero value.

Definition at line 155 of file gmm_blas.h.

◆ resize() [1/2]

template<typename V >

void gmm::resize	(	V &	v,
		size_type	n
	)

inline

*‍/

resize a vector.

Definition at line 210 of file gmm_blas.h.

◆ resize() [2/2]

template<typename M >

void gmm::resize	(	M &	v,
		size_type	m,
		size_type	n
	)

inline

*‍/

resize a matrix

Definition at line 232 of file gmm_blas.h.

◆ reshape()

template<typename M >

void gmm::reshape	(	M &	v,
		size_type	m,
		size_type	n
	)

inline

*‍/

reshape a matrix

Definition at line 251 of file gmm_blas.h.

◆ vect_sp() [1/2]

template<typename V1 , typename V2 >

strongest_value_type<V1,V2>::value_type gmm::vect_sp	(	const V1 &	v1,
		const V2 &	v2
	)

inline

*‍/

scalar product between two vectors

Definition at line 264 of file gmm_blas.h.

◆ vect_sp() [2/2]

template<typename MATSP , typename V1 , typename V2 >

strongest_value_type3<V1,V2,MATSP>::value_type gmm::vect_sp	(	const MATSP &	ps,
		const V1 &	v1,
		const V2 &	v2
	)

inline

scalar product between two vectors, using a matrix.

Parameters

ps	the matrix of the scalar product.
v1	the first vector
v2	the second vector

Definition at line 279 of file gmm_blas.h.

◆ vect_hp()

template<typename V1 , typename V2 >

strongest_value_type<V1,V2>::value_type gmm::vect_hp	(	const V1 &	v1,
		const V2 &	v2
	)

inline

*‍/

Hermitian product.

Definition at line 512 of file gmm_blas.h.

◆ mat_euclidean_norm_sqr()

template<typename M >

number_traits<typename linalg_traits<M>::value_type>::magnitude_type gmm::mat_euclidean_norm_sqr ( const M & m )

inline

*‍/

squared Euclidean norm of a matrix.

Definition at line 627 of file gmm_blas.h.

◆ mat_norm1()

template<typename M >

number_traits<typename linalg_traits<M>::value_type>::magnitude_type gmm::mat_norm1 ( const M & m )

*‍/

1-norm of a matrix

Definition at line 783 of file gmm_blas.h.

◆ mat_norminf()

template<typename M >

number_traits<typename linalg_traits<M>::value_type>::magnitude_type gmm::mat_norminf ( const M & m )

*‍/

infinity-norm of a matrix.

Definition at line 837 of file gmm_blas.h.

◆ mat_maxnorm()

template<typename M >

number_traits<typename linalg_traits<M>::value_type>::magnitude_type gmm::mat_maxnorm ( const M & m )

*‍/

max-norm of a matrix.

Definition at line 871 of file gmm_blas.h.

◆ clean()

template<typename L >

void gmm::clean	(	L &	l,
		double	threshold
	)

inline

Clean a vector or matrix (replace near-zero entries with zeroes).

◆ copy()

template<typename L1 , typename L2 >

void gmm::copy	(	const L1 &	l1,
		L2 &	l2
	)

inline

*‍/

Copy vectors or matrices.

Parameters

l1	source vector or matrix.
l2	destination.

Definition at line 978 of file gmm_blas.h.

◆ add() [1/2]

template<typename L1 , typename L2 >

void gmm::add	(	const L1 &	l1,
		L2 &	l2
	)

inline

*‍/

Add two vectors or matrices

Parameters

l1
l2	contains on output, l2+l1.

Definition at line 1277 of file gmm_blas.h.

◆ add() [2/2]

template<typename L1 , typename L2 , typename L3 >

void gmm::add	(	const L1 &	l1,
		const L2 &	l2,
		L3 &	l3
	)

inline

*‍/

Addition of two vectors/matrices

Parameters

l1
l2
l3	contains l1+l2 on output

Definition at line 1434 of file gmm_blas.h.

◆ mult()

template<typename L1 , typename L2 , typename L3 >

void gmm::mult	(	const L1 &	l1,
		const L2 &	l2,
		L3 &	l3
	)

inline

*‍/

matrix-vector or matrix-matrix product.

Parameters

l1	a matrix.
l2	a vector or matrix.
l3	the product l1*l2.

Definition at line 1664 of file gmm_blas.h.

◆ mult_add()

template<typename L1 , typename L2 , typename L3 >

void gmm::mult_add	(	const L1 &	l1,
		const L2 &	l2,
		L3 &	l3
	)

inline

*‍/

Multiply-accumulate. l3 += l1*l2;

Definition at line 1791 of file gmm_blas.h.

◆ is_symmetric()

template<typename MAT >

bool gmm::is_symmetric	(	const MAT &	A,
		magnitude_of_linalg(MAT)	tol = `magnitude_of_linalg(MAT)(-1)`
	)

inline

*‍/

test if A is symmetric.

Parameters

A	a matrix.
tol	a threshold.

Definition at line 2179 of file gmm_blas.h.

◆ is_hermitian()

template<typename MAT >

bool gmm::is_hermitian	(	const MAT &	A,
		magnitude_of_linalg(MAT)	tol = `magnitude_of_linalg(MAT)(-1)`
	)

inline

*‍/

test if A is Hermitian.

Parameters

A	a matrix.
tol	a threshold.

Definition at line 2241 of file gmm_blas.h.

Functions

Detailed Description

Function Documentation

◆ fill()

◆ fill_random()

◆ resize() [1/2]

◆ resize() [2/2]

◆ reshape()

◆ vect_sp() [1/2]

◆ vect_sp() [2/2]

◆ vect_hp()

◆ mat_euclidean_norm_sqr()

◆ mat_norm1()

◆ mat_norminf()

◆ mat_maxnorm()

◆ clean()

◆ copy()

◆ add() [1/2]

◆ add() [2/2]

◆ mult()

◆ mult_add()

◆ is_symmetric()

◆ is_hermitian()