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gmm_def.h 45.12 KiB
// -*- c++ -*- (enables emacs c++ mode)
//===========================================================================
//
// Copyright (C) 2002-2008 Yves Renard
//
// This file is a part of GETFEM++
//
// Getfem++ is free software; you can redistribute it and/or modify it
// under the terms of the GNU Lesser General Public License as published
// by the Free Software Foundation; either version 2.1 of the License, or
// (at your option) any later version.
// This program is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
// or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
// License for more details.
// You should have received a copy of the GNU Lesser General Public License
// along with this program; if not, write to the Free Software Foundation,
// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
//
// As a special exception, you may use this file as part of a free software
// library without restriction. Specifically, if other files instantiate
// templates or use macros or inline functions from this file, or you compile
// this file and link it with other files to produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License. This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.
//
//===========================================================================
/**@file gmm_def.h
@author Yves Renard <Yves.Renard@insa-lyon.fr>
@date October 13, 2002.
@brief Basic definitions and tools of GMM.
*/
#ifndef GMM_DEF_H__
#define GMM_DEF_H__
#include "gmm_ref.h"
#include <complex>
#ifndef M_PI
# define M_E 2.7182818284590452354 /* e */
# define M_LOG2E 1.4426950408889634074 /* 1/ln(2) */
# define M_LOG10E 0.43429448190325182765 /* 1/ln(10) */
# define M_LN2 0.69314718055994530942 /* ln(2) */
# define M_LN10 2.30258509299404568402 /* ln(10) */
# define M_PI 3.14159265358979323846 /* pi */
# define M_PI_2 1.57079632679489661923 /* pi/2 */
# define M_PI_4 0.78539816339744830962 /* pi/4 */
# define M_1_PI 0.31830988618379067154 /* 1/pi */
# define M_2_PI 0.63661977236758134308 /* 2/pi */
# define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
# define M_SQRT1_2 0.70710678118654752440 /* sqrt(2)/2 */
#endif
#ifndef M_PIl
# define M_PIl 3.1415926535897932384626433832795029L /* pi */
# define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */
# define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */
# define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */
# define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */
# define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */
#endif
namespace gmm {
typedef size_t size_type;
/* ******************************************************************** */
/* Specifier types */
/* ******************************************************************** */
/* not perfectly null, required by aCC 3.33 */
struct abstract_null_type {
abstract_null_type(int=0) {}
template <typename A,typename B,typename C> void operator()(A,B,C) {}
}; // specify an information lake.
struct linalg_true {};
struct linalg_false {};
template <typename V, typename W> struct linalg_and
{ typedef linalg_false bool_type; };
template <> struct linalg_and<linalg_true, linalg_true>
{ typedef linalg_true bool_type; };
template <typename V, typename W> struct linalg_or
{ typedef linalg_true bool_type; };
template <> struct linalg_and<linalg_false, linalg_false>
{ typedef linalg_false bool_type; };
struct linalg_const {}; // A reference is either linalg_const,
struct linalg_modifiable {}; // linalg_modifiable or linalg_false.
struct abstract_vector {}; // The object is a vector
struct abstract_matrix {}; // The object is a matrix
struct abstract_sparse {}; // sparse matrix or vector
struct abstract_skyline {}; // 'sky-line' matrix or vector
struct abstract_dense {}; // dense matrix or vector
struct abstract_indirect {}; // matrix given by the product with a vector
struct row_major {}; // matrix with a row access.
struct col_major {}; // matrix with a column access
struct row_and_col {}; // both accesses but row preference
struct col_and_row {}; // both accesses but column preference
template <typename T> struct transposed_type;
template<> struct transposed_type<row_major> {typedef col_major t_type;};
template<> struct transposed_type<col_major> {typedef row_major t_type;};
template<> struct transposed_type<row_and_col> {typedef col_and_row t_type;};
template<> struct transposed_type<col_and_row> {typedef row_and_col t_type;};
template <typename T> struct principal_orientation_type
{ typedef abstract_null_type potype; };
template<> struct principal_orientation_type<row_major>
{ typedef row_major potype; };
template<> struct principal_orientation_type<col_major>
{ typedef col_major potype; };
template<> struct principal_orientation_type<row_and_col>
{ typedef row_major potype; };
template<> struct principal_orientation_type<col_and_row>
{ typedef col_major potype; };
// template <typename V> struct linalg_traits;
template <typename V> struct linalg_traits {
typedef abstract_null_type this_type;
typedef abstract_null_type linalg_type;
typedef abstract_null_type value_type;
typedef abstract_null_type is_reference;
typedef abstract_null_type& reference;
typedef abstract_null_type* iterator;
typedef const abstract_null_type* const_iterator;
typedef abstract_null_type index_sorted;
typedef abstract_null_type storage_type;
typedef abstract_null_type origin_type;
typedef abstract_null_type const_sub_row_type;
typedef abstract_null_type sub_row_type;
typedef abstract_null_type const_row_iterator;
typedef abstract_null_type row_iterator; typedef abstract_null_type const_sub_col_type;
typedef abstract_null_type sub_col_type;
typedef abstract_null_type const_col_iterator;
typedef abstract_null_type col_iterator;
typedef abstract_null_type sub_orientation;
};
template <typename PT, typename V> struct vect_ref_type;
template <typename P, typename V> struct vect_ref_type<P *, V> {
typedef typename linalg_traits<V>::reference access_type;
typedef typename linalg_traits<V>::iterator iterator;
};
template <typename P, typename V> struct vect_ref_type<const P *, V> {
typedef typename linalg_traits<V>::value_type access_type;
typedef typename linalg_traits<V>::const_iterator iterator;
};
template <typename PT> struct const_pointer;
template <typename P> struct const_pointer<P *>
{ typedef const P* pointer; };
template <typename P> struct const_pointer<const P *>
{ typedef const P* pointer; };
template <typename PT> struct modifiable_pointer;
template <typename P> struct modifiable_pointer<P *>
{ typedef P* pointer; };
template <typename P> struct modifiable_pointer<const P *>
{ typedef P* pointer; };
template <typename R> struct const_reference;
template <typename R> struct const_reference<R &>
{ typedef const R &reference; };
template <typename R> struct const_reference<const R &>
{ typedef const R &reference; };
inline bool is_sparse(abstract_sparse) { return true; }
inline bool is_sparse(abstract_dense) { return false; }
inline bool is_sparse(abstract_skyline) { return true; }
inline bool is_sparse(abstract_indirect) { return false; }
template <typename L> inline bool is_sparse(const L &)
{ return is_sparse(typename linalg_traits<L>::storage_type()); }
inline bool is_row_matrix_(row_major) { return true; }
inline bool is_row_matrix_(col_major) { return false; }
inline bool is_row_matrix_(row_and_col) { return true; }
inline bool is_row_matrix_(col_and_row) { return true; }
template <typename L> inline bool is_row_matrix(const L &)
{ return is_row_matrix_(typename linalg_traits<L>::sub_orientation()); }
inline bool is_col_matrix_(row_major) { return false; }
inline bool is_col_matrix_(col_major) { return true; }
inline bool is_col_matrix_(row_and_col) { return true; }
inline bool is_col_matrix_(col_and_row) { return true; }
template <typename L> inline bool is_col_matrix(const L &)
{ return is_col_matrix_(typename linalg_traits<L>::sub_orientation()); }
inline bool is_col_matrix(row_major) { return false; }
inline bool is_col_matrix(col_major) { return true; }
inline bool is_row_matrix(row_major) { return true; }
inline bool is_row_matrix(col_major) { return false; }
template <typename L> inline bool is_const_reference(L) { return false; }
inline bool is_const_reference(linalg_const) { return true; }
template <typename T> struct is_gmm_interfaced_ { typedef linalg_true result;
};
template<> struct is_gmm_interfaced_<abstract_null_type> {
typedef linalg_false result;
};
template <typename T> struct is_gmm_interfaced {
typedef typename is_gmm_interfaced_<typename gmm::linalg_traits<T>::this_type >::result result;
};
/* ******************************************************************** */
/* types to deal with const object representing a modifiable reference */
/* ******************************************************************** */
template <typename PT, typename R> struct mref_type_
{ typedef abstract_null_type return_type; };
template <typename L, typename R> struct mref_type_<L *, R>
{ typedef L & return_type; };
template <typename L, typename R> struct mref_type_<const L *, R>
{ typedef const L & return_type; };
template <typename L> struct mref_type_<L *, linalg_const>
{ typedef const L & return_type; };
template <typename L> struct mref_type_<const L *, linalg_const>
{ typedef const L & return_type; };
template <typename L> struct mref_type_<const L *, linalg_modifiable>
{ typedef L & return_type; };
template <typename L> struct mref_type_<L *, linalg_modifiable>
{ typedef L & return_type; };
template <typename PT> struct mref_type {
typedef typename std::iterator_traits<PT>::value_type L;
typedef typename mref_type_<PT,
typename linalg_traits<L>::is_reference>::return_type return_type;
};
template <typename L> typename mref_type<const L *>::return_type
linalg_cast(const L &l)
{ return const_cast<typename mref_type<const L *>::return_type>(l); }
template <typename L> typename mref_type<L *>::return_type linalg_cast(L &l)
{ return const_cast<typename mref_type<L *>::return_type>(l); }
template <typename L, typename R> struct cref_type_
{ typedef abstract_null_type return_type; };
template <typename L> struct cref_type_<L, linalg_modifiable>
{ typedef L & return_type; };
template <typename L> struct cref_type {
typedef typename cref_type_<L,
typename linalg_traits<L>::is_reference>::return_type return_type;
};
template <typename L> typename cref_type<L>::return_type
linalg_const_cast(const L &l)
{ return const_cast<typename cref_type<L>::return_type>(l); }
// To be used to select between a reference or a const refercence for
// the return type of a function
// select_return<C1, C2, L *> return C1 if L is a const reference,
// C2 otherwise.
// select_return<C1, C2, const L *> return C2 if L is a modifiable reference
// C1 otherwise.
template <typename C1, typename C2, typename REF> struct select_return_ {
typedef abstract_null_type return_type;
};
template <typename C1, typename C2, typename L>
struct select_return_<C1, C2, const L &> { typedef C1 return_type; };
template <typename C1, typename C2, typename L>
struct select_return_<C1, C2, L &> { typedef C2 return_type; }; template <typename C1, typename C2, typename PT> struct select_return {
typedef typename std::iterator_traits<PT>::value_type L;
typedef typename select_return_<C1, C2,
typename mref_type<PT>::return_type>::return_type return_type;
};
// To be used to select between a reference or a const refercence inside
// a structure or a linagl_traits
// select_ref<C1, C2, L *> return C1 if L is a const reference,
// C2 otherwise.
// select_ref<C1, C2, const L *> return C2 in any case.
template <typename C1, typename C2, typename REF> struct select_ref_
{ typedef abstract_null_type ref_type; };
template <typename C1, typename C2, typename L>
struct select_ref_<C1, C2, const L &> { typedef C1 ref_type; };
template <typename C1, typename C2, typename L>
struct select_ref_<C1, C2, L &> { typedef C2 ref_type; };
template <typename C1, typename C2, typename PT> struct select_ref {
typedef typename std::iterator_traits<PT>::value_type L;
typedef typename select_ref_<C1, C2,
typename mref_type<PT>::return_type>::ref_type ref_type;
};
template <typename C1, typename C2, typename L>
struct select_ref<C1, C2, const L *>
{ typedef C1 ref_type; };
template<typename R> struct is_a_reference_
{ typedef linalg_true reference; };
template<> struct is_a_reference_<linalg_false>
{ typedef linalg_false reference; };
template<typename L> struct is_a_reference {
typedef typename is_a_reference_<typename linalg_traits<L>::is_reference>
::reference reference;
};
template <typename L> inline bool is_original_linalg(const L &)
{ return is_original_linalg(typename is_a_reference<L>::reference()); }
inline bool is_original_linalg(linalg_false) { return true; }
inline bool is_original_linalg(linalg_true) { return false; }
template <typename PT> struct which_reference
{ typedef abstract_null_type is_reference; };
template <typename PT> struct which_reference<PT *>
{ typedef linalg_modifiable is_reference; };
template <typename PT> struct which_reference<const PT *>
{ typedef linalg_const is_reference; };
template <typename C1, typename C2, typename R> struct select_orientation_
{ typedef abstract_null_type return_type; };
template <typename C1, typename C2>
struct select_orientation_<C1, C2, row_major>
{ typedef C1 return_type; };
template <typename C1, typename C2>
struct select_orientation_<C1, C2, col_major>
{ typedef C2 return_type; };
template <typename C1, typename C2, typename L> struct select_orientation {
typedef typename select_orientation_<C1, C2,
typename principal_orientation_type<typename
linalg_traits<L>::sub_orientation>::potype>::return_type return_type;
};
/* ******************************************************************** */
/* Operations on scalars */
/* ******************************************************************** */
template <typename T> inline T sqr(T a) { return a * a; }
template <typename T> inline T abs(T a) { return (a < T(0)) ? T(-a) : a; }
template <typename T> inline T abs(std::complex<T> a)
{ T x = a.real(), y = a.imag(); return ::sqrt(x*x+y*y); }
template <typename T> inline T abs_sqr(T a) { return a*a; }
template <typename T> inline T abs_sqr(std::complex<T> a)
{ return gmm::sqr(a.real()) + gmm::sqr(a.imag()); }
template <typename T> inline T pos(T a) { return (a < T(0)) ? T(0) : a; }
template <typename T> inline T neg(T a) { return (a < T(0)) ? T(-a) : T(0); }
template <typename T> inline T sgn(T a) { return (a < T(0)) ? T(-1) : T(1); }
inline double random() { return double(rand())/(RAND_MAX+0.5); }
template <typename T> inline T random(T)
{ return T(rand()*2.0)/(T(RAND_MAX)+T(1)/T(2)) - T(1); }
template <typename T> inline std::complex<T> random(std::complex<T>)
{ return std::complex<T>(gmm::random(T()), gmm::random(T())); }
template <typename T> inline T irandom(T max)
{ return T(gmm::random() * max); }
template <typename T> inline T conj(T a) { return a; }
template <typename T> inline std::complex<T> conj(std::complex<T> a)
{ return std::conj(a); }
template <typename T> inline T real(T a) { return a; }
template <typename T> inline T real(std::complex<T> a) { return a.real(); }
template <typename T> inline T imag(T ) { return T(0); }
template <typename T> inline T imag(std::complex<T> a) { return a.imag(); }
template <typename T> inline T sqrt(T a) { return ::sqrt(a); }
template <typename T> inline std::complex<T> sqrt(std::complex<T> a) {
T x = a.real(), y = a.imag();
if (x == T(0)) {
T t = ::sqrt(gmm::abs(y) / T(2));
return std::complex<T>(t, y < T(0) ? -t : t);
}
T t = ::sqrt(T(2) * (gmm::abs(a) + gmm::abs(x))), u = t / T(2);
return x > T(0) ? std::complex<T>(u, y / t)
: std::complex<T>(gmm::abs(y) / t, y < T(0) ? -u : u);
}
using std::swap;
template <typename T> struct number_traits {
typedef T magnitude_type;
};
template <typename T> struct number_traits<std::complex<T> > {
typedef T magnitude_type;
};
template <typename T> inline T conj_product(T a, T b) { return a * b; }
template <typename T> inline
std::complex<T> conj_product(std::complex<T> a, std::complex<T> b)
{ return std::conj(a) * b; } // to be optimized ?
template <typename T> inline bool is_complex(T) { return false; }
template <typename T> inline bool is_complex(std::complex<T> )
{ return true; }
# define magnitude_of_linalg(M) typename number_traits<typename \
linalg_traits<M>::value_type>::magnitude_type
template<typename T> inline std::complex<T> operator*(const std::complex<T>& a, int b) {
return a*T(b);
}
template<typename T> inline std::complex<T> operator*(int b, const std::complex<T>& a) {
return a*T(b);
}
/* ******************************************************************** */
/* types promotion */
/* ******************************************************************** */
/* should be completed for more specific cases <unsigned int, float> etc */
template <typename T1, typename T2, bool c>
struct strongest_numeric_type_aux {
typedef T1 T;
};
template <typename T1, typename T2>
struct strongest_numeric_type_aux<T1,T2,false> {
typedef T2 T;
};
template <typename T1, typename T2>
struct strongest_numeric_type {
typedef typename
strongest_numeric_type_aux<T1,T2,(sizeof(T1)>sizeof(T2))>::T T;
};
template <typename T1, typename T2>
struct strongest_numeric_type<T1,std::complex<T2> > {
typedef typename number_traits<T1>::magnitude_type R1;
typedef std::complex<typename strongest_numeric_type<R1,T2>::T > T;
};
template <typename T1, typename T2>
struct strongest_numeric_type<std::complex<T1>,T2 > {
typedef typename number_traits<T2>::magnitude_type R2;
typedef std::complex<typename strongest_numeric_type<T1,R2>::T > T;
};
template <typename T1, typename T2>
struct strongest_numeric_type<std::complex<T1>,std::complex<T2> > {
typedef std::complex<typename strongest_numeric_type<T1,T2>::T > T;
};
template<> struct strongest_numeric_type<int,float> { typedef float T; };
template<> struct strongest_numeric_type<float,int> { typedef float T; };
template<> struct strongest_numeric_type<long,float> { typedef float T; };
template<> struct strongest_numeric_type<float,long> { typedef float T; };
template<> struct strongest_numeric_type<long,double> { typedef double T; };
template<> struct strongest_numeric_type<double,long> { typedef double T; };
template <typename V1, typename V2>
struct strongest_value_type {
typedef typename
strongest_numeric_type<typename linalg_traits<V1>::value_type,
typename linalg_traits<V2>::value_type>::T
value_type;
};
template <typename V1, typename V2, typename V3>
struct strongest_value_type3 {
typedef typename
strongest_value_type<V1, typename
strongest_value_type<V2,V3>::value_type>::value_type
value_type;
};
/* ******************************************************************** */
/* Basic vectors used */
/* ******************************************************************** */
template<typename T> struct dense_vector_type
{ typedef std::vector<T> vector_type; };
template <typename T> class wsvector;
template <typename T> class rsvector;
template<typename T> struct sparse_vector_type
{ typedef wsvector<T> vector_type; };
template <typename T> class slvector;
template <typename T> class dense_matrix;
template <typename VECT> class row_matrix;
template <typename VECT> class col_matrix;
/* ******************************************************************** */
/* Selects a temporary vector type */
/* V if V is a valid vector type, */
/* wsvector if V is a reference on a sparse vector, */
/* std::vector if V is a reference on a dense vector. */
/* ******************************************************************** */
template <typename R, typename S, typename L, typename V>
struct temporary_vector_ {
typedef abstract_null_type vector_type;
};
template <typename V, typename L>
struct temporary_vector_<linalg_true, abstract_sparse, L, V>
{ typedef wsvector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V, typename L>
struct temporary_vector_<linalg_true, abstract_skyline, L, V>
{ typedef slvector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V, typename L>
struct temporary_vector_<linalg_true, abstract_dense, L, V>
{ typedef std::vector<typename linalg_traits<V>::value_type> vector_type; };
template <typename S, typename V>
struct temporary_vector_<linalg_false, S, abstract_vector, V>
{ typedef V vector_type; };
template <typename V>
struct temporary_vector_<linalg_false, abstract_dense, abstract_matrix, V>
{ typedef std::vector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V>
struct temporary_vector_<linalg_false, abstract_sparse, abstract_matrix, V>
{ typedef wsvector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V> struct temporary_vector {
typedef typename temporary_vector_<typename is_a_reference<V>::reference,
typename linalg_traits<V>::storage_type,
typename linalg_traits<V>::linalg_type,
V>::vector_type vector_type;
};
/* ******************************************************************** */
/* Selects a temporary matrix type */
/* M if M is a valid matrix type, */
/* row_matrix<wsvector> if M is a reference on a sparse matrix, */
/* dense_matrix if M is a reference on a dense matrix. */
/* ******************************************************************** */
template <typename R, typename S, typename L, typename V>
struct temporary_matrix_ { typedef abstract_null_type matrix_type; };
template <typename V, typename L>
struct temporary_matrix_<linalg_true, abstract_sparse, L, V> {
typedef typename linalg_traits<V>::value_type T;
typedef row_matrix<wsvector<T> > matrix_type;
};
template <typename V, typename L>
struct temporary_matrix_<linalg_true, abstract_skyline, L, V> {
typedef typename linalg_traits<V>::value_type T;
typedef row_matrix<slvector<T> > matrix_type;
};
template <typename V, typename L>
struct temporary_matrix_<linalg_true, abstract_dense, L, V>
{ typedef dense_matrix<typename linalg_traits<V>::value_type> matrix_type; };
template <typename S, typename V>
struct temporary_matrix_<linalg_false, S, abstract_matrix, V>
{ typedef V matrix_type; };
template <typename V> struct temporary_matrix {
typedef typename temporary_matrix_<typename is_a_reference<V>::reference,
typename linalg_traits<V>::storage_type, typename linalg_traits<V>::linalg_type,
V>::matrix_type matrix_type;
};
template <typename S, typename L, typename V>
struct temporary_col_matrix_ { typedef abstract_null_type matrix_type; };
template <typename V, typename L>
struct temporary_col_matrix_<abstract_sparse, L, V> {
typedef typename linalg_traits<V>::value_type T;
typedef col_matrix<wsvector<T> > matrix_type;
};
template <typename V, typename L>
struct temporary_col_matrix_<abstract_skyline, L, V> {
typedef typename linalg_traits<V>::value_type T;
typedef col_matrix<slvector<T> > matrix_type;
};
template <typename V, typename L>
struct temporary_col_matrix_<abstract_dense, L, V>
{ typedef dense_matrix<typename linalg_traits<V>::value_type> matrix_type; };
template <typename V> struct temporary_col_matrix {
typedef typename temporary_col_matrix_<
typename linalg_traits<V>::storage_type,
typename linalg_traits<V>::linalg_type,
V>::matrix_type matrix_type;
};
template <typename S, typename L, typename V>
struct temporary_row_matrix_ { typedef abstract_null_type matrix_type; };
template <typename V, typename L>
struct temporary_row_matrix_<abstract_sparse, L, V> {
typedef typename linalg_traits<V>::value_type T;
typedef row_matrix<wsvector<T> > matrix_type;
};
template <typename V, typename L>
struct temporary_row_matrix_<abstract_skyline, L, V> {
typedef typename linalg_traits<V>::value_type T;
typedef row_matrix<slvector<T> > matrix_type;
};
template <typename V, typename L>
struct temporary_row_matrix_<abstract_dense, L, V>
{ typedef dense_matrix<typename linalg_traits<V>::value_type> matrix_type; };
template <typename V> struct temporary_row_matrix {
typedef typename temporary_row_matrix_<
typename linalg_traits<V>::storage_type,
typename linalg_traits<V>::linalg_type,
V>::matrix_type matrix_type;
};
/* ******************************************************************** */
/* Selects a temporary dense vector type */
/* V if V is a valid dense vector type, */
/* std::vector if V is a reference or another type of vector */
/* ******************************************************************** */
template <typename R, typename S, typename V>
struct temporary_dense_vector_ { typedef abstract_null_type vector_type; };
template <typename S, typename V>
struct temporary_dense_vector_<linalg_true, S, V>
{ typedef std::vector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V>
struct temporary_dense_vector_<linalg_false, abstract_sparse, V>
{ typedef std::vector<typename linalg_traits<V>::value_type> vector_type; }; template <typename V>
struct temporary_dense_vector_<linalg_false, abstract_skyline, V>
{ typedef std::vector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V>
struct temporary_dense_vector_<linalg_false, abstract_dense, V>
{ typedef V vector_type; };
template <typename V> struct temporary_dense_vector {
typedef typename temporary_dense_vector_<typename
is_a_reference<V>::reference,
typename linalg_traits<V>::storage_type, V>::vector_type vector_type;
};
/* ******************************************************************** */
/* Selects a temporary sparse vector type */
/* V if V is a valid sparse vector type, */
/* wsvector if V is a reference or another type of vector */
/* ******************************************************************** */
template <typename R, typename S, typename V>
struct temporary_sparse_vector_ { typedef abstract_null_type vector_type; };
template <typename S, typename V>
struct temporary_sparse_vector_<linalg_true, S, V>
{ typedef wsvector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V>
struct temporary_sparse_vector_<linalg_false, abstract_sparse, V>
{ typedef V vector_type; };
template <typename V>
struct temporary_sparse_vector_<linalg_false, abstract_dense, V>
{ typedef wsvector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V>
struct temporary_sparse_vector_<linalg_false, abstract_skyline, V>
{ typedef wsvector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V> struct temporary_sparse_vector {
typedef typename temporary_sparse_vector_<typename
is_a_reference<V>::reference,
typename linalg_traits<V>::storage_type, V>::vector_type vector_type;
};
/* ******************************************************************** */
/* Selects a temporary sky-line vector type */
/* V if V is a valid sky-line vector type, */
/* slvector if V is a reference or another type of vector */
/* ******************************************************************** */
template <typename R, typename S, typename V>
struct temporary_skyline_vector_
{ typedef abstract_null_type vector_type; };
template <typename S, typename V>
struct temporary_skyline_vector_<linalg_true, S, V>
{ typedef slvector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V>
struct temporary_skyline_vector_<linalg_false, abstract_skyline, V>
{ typedef V vector_type; };
template <typename V>
struct temporary_skyline_vector_<linalg_false, abstract_dense, V>
{ typedef slvector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V>
struct temporary_skyline_vector_<linalg_false, abstract_sparse, V>
{ typedef slvector<typename linalg_traits<V>::value_type> vector_type; };
template <typename V> struct temporary_skylines_vector {
typedef typename temporary_skyline_vector_<typename
is_a_reference<V>::reference,
typename linalg_traits<V>::storage_type, V>::vector_type vector_type;
};
/* ********************************************************************* */
/* Definition & Comparison of origins. */ /* ********************************************************************* */
template <typename L>
typename select_return<const typename linalg_traits<L>::origin_type *,
typename linalg_traits<L>::origin_type *,
L *>::return_type
linalg_origin(L &l)
{ return linalg_traits<L>::origin(linalg_cast(l)); }
template <typename L>
typename select_return<const typename linalg_traits<L>::origin_type *,
typename linalg_traits<L>::origin_type *,
const L *>::return_type
linalg_origin(const L &l)
{ return linalg_traits<L>::origin(linalg_cast(l)); }
template <typename PT1, typename PT2>
bool same_porigin(PT1, PT2) { return false; }
template <typename PT>
bool same_porigin(PT pt1, PT pt2) { return (pt1 == pt2); }
template <typename L1, typename L2>
bool same_origin(const L1 &l1, const L2 &l2)
{ return same_porigin(linalg_origin(l1), linalg_origin(l2)); }
/* ******************************************************************** */
/* Miscellaneous */
/* ******************************************************************** */
template <typename V> inline size_type vect_size(const V &v)
{ return linalg_traits<V>::size(v); }
template <typename MAT> inline size_type mat_nrows(const MAT &m)
{ return linalg_traits<MAT>::nrows(m); }
template <typename MAT> inline size_type mat_ncols(const MAT &m)
{ return linalg_traits<MAT>::ncols(m); }
template <typename V> inline
typename select_return<typename linalg_traits<V>::const_iterator,
typename linalg_traits<V>::iterator, V *>::return_type
vect_begin(V &v)
{ return linalg_traits<V>::begin(linalg_cast(v)); }
template <typename V> inline
typename select_return<typename linalg_traits<V>::const_iterator,
typename linalg_traits<V>::iterator, const V *>::return_type
vect_begin(const V &v)
{ return linalg_traits<V>::begin(linalg_cast(v)); }
template <typename V> inline
typename linalg_traits<V>::const_iterator
vect_const_begin(const V &v)
{ return linalg_traits<V>::begin(v); }
template <typename V> inline
typename select_return<typename linalg_traits<V>::const_iterator,
typename linalg_traits<V>::iterator, V *>::return_type
vect_end(V &v)
{ return linalg_traits<V>::end(linalg_cast(v)); }
template <typename V> inline
typename select_return<typename linalg_traits<V>::const_iterator,
typename linalg_traits<V>::iterator, const V *>::return_type
vect_end(const V &v)
{ return linalg_traits<V>::end(linalg_cast(v)); }
template <typename V> inline
typename linalg_traits<V>::const_iterator
vect_const_end(const V &v)
{ return linalg_traits<V>::end(v); }
template <typename M> inline
typename select_return<typename linalg_traits<M>::const_row_iterator,
typename linalg_traits<M>::row_iterator, M *>::return_type
mat_row_begin(M &m) { return linalg_traits<M>::row_begin(linalg_cast(m)); }
template <typename M> inline
typename select_return<typename linalg_traits<M>::const_row_iterator,
typename linalg_traits<M>::row_iterator, const M *>::return_type
mat_row_begin(const M &m)
{ return linalg_traits<M>::row_begin(linalg_cast(m)); }
template <typename M> inline typename linalg_traits<M>::const_row_iterator
mat_row_const_begin(const M &m)
{ return linalg_traits<M>::row_begin(m); }
template <typename M> inline
typename select_return<typename linalg_traits<M>::const_row_iterator,
typename linalg_traits<M>::row_iterator, M *>::return_type
mat_row_end(M &v) {
return linalg_traits<M>::row_end(linalg_cast(v));
}
template <typename M> inline
typename select_return<typename linalg_traits<M>::const_row_iterator,
typename linalg_traits<M>::row_iterator, const M *>::return_type
mat_row_end(const M &v) {
return linalg_traits<M>::row_end(linalg_cast(v));
}
template <typename M> inline
typename linalg_traits<M>::const_row_iterator
mat_row_const_end(const M &v)
{ return linalg_traits<M>::row_end(v); }
template <typename M> inline
typename select_return<typename linalg_traits<M>::const_col_iterator,
typename linalg_traits<M>::col_iterator, M *>::return_type
mat_col_begin(M &v) {
return linalg_traits<M>::col_begin(linalg_cast(v));
}
template <typename M> inline
typename select_return<typename linalg_traits<M>::const_col_iterator,
typename linalg_traits<M>::col_iterator, const M *>::return_type
mat_col_begin(const M &v) {
return linalg_traits<M>::col_begin(linalg_cast(v));
}
template <typename M> inline
typename linalg_traits<M>::const_col_iterator
mat_col_const_begin(const M &v)
{ return linalg_traits<M>::col_begin(v); }
template <typename M> inline
typename linalg_traits<M>::const_col_iterator
mat_col_const_end(const M &v)
{ return linalg_traits<M>::col_end(v); }
template <typename M> inline
typename select_return<typename linalg_traits<M>::const_col_iterator,
typename linalg_traits<M>::col_iterator,
M *>::return_type
mat_col_end(M &m)
{ return linalg_traits<M>::col_end(linalg_cast(m)); }
template <typename M> inline
typename select_return<typename linalg_traits<M>::const_col_iterator,
typename linalg_traits<M>::col_iterator,
const M *>::return_type
mat_col_end(const M &m)
{ return linalg_traits<M>::col_end(linalg_cast(m)); }
template <typename MAT> inline
typename select_return<typename linalg_traits<MAT>::const_sub_row_type,
typename linalg_traits<MAT>::sub_row_type,
const MAT *>::return_type
mat_row(const MAT &m, size_type i)
{ return linalg_traits<MAT>::row(mat_row_begin(m) + i); }
template <typename MAT> inline
typename select_return<typename linalg_traits<MAT>::const_sub_row_type,
typename linalg_traits<MAT>::sub_row_type,
MAT *>::return_type
mat_row(MAT &m, size_type i)
{ return linalg_traits<MAT>::row(mat_row_begin(m) + i); }
template <typename MAT> inline
typename linalg_traits<MAT>::const_sub_row_type
mat_const_row(const MAT &m, size_type i)
{ return linalg_traits<MAT>::row(mat_row_const_begin(m) + i); }
template <typename MAT> inline
typename select_return<typename linalg_traits<MAT>::const_sub_col_type,
typename linalg_traits<MAT>::sub_col_type,
const MAT *>::return_type
mat_col(const MAT &m, size_type i)
{ return linalg_traits<MAT>::col(mat_col_begin(m) + i); }
template <typename MAT> inline
typename select_return<typename linalg_traits<MAT>::const_sub_col_type,
typename linalg_traits<MAT>::sub_col_type,
MAT *>::return_type
mat_col(MAT &m, size_type i)
{ return linalg_traits<MAT>::col(mat_col_begin(m) + i); }
template <typename MAT> inline
typename linalg_traits<MAT>::const_sub_col_type
mat_const_col(const MAT &m, size_type i)
{ return linalg_traits<MAT>::col(mat_col_const_begin(m) + i); }
/* ********************************************************************* */
/* Set to begin end set to end for iterators on non-const sparse vectors.*/
/* ********************************************************************* */
template <typename IT, typename ORG, typename VECT> inline
void set_to_begin(IT &it, ORG o, VECT *, linalg_false)
{ it = vect_begin(*o); }
template <typename IT, typename ORG, typename VECT> inline
void set_to_begin(IT &it, ORG o, const VECT *, linalg_false)
{ it = vect_const_begin(*o); }
template <typename IT, typename ORG, typename VECT> inline
void set_to_end(IT &it, ORG o, VECT *, linalg_false)
{ it = vect_end(*o); }
template <typename IT, typename ORG, typename VECT> inline
void set_to_end(IT &it, ORG o, const VECT *, linalg_false)
{ it = vect_const_end(*o); }
template <typename IT, typename ORG, typename VECT> inline
void set_to_begin(IT &, ORG, VECT *, linalg_const) { }
template <typename IT, typename ORG, typename VECT> inline
void set_to_begin(IT &, ORG, const VECT *, linalg_const) { }
template <typename IT, typename ORG, typename VECT> inline
void set_to_end(IT &, ORG, VECT *, linalg_const) { }
template <typename IT, typename ORG, typename VECT> inline
void set_to_end(IT &, ORG, const VECT *, linalg_const) { }
template <typename IT, typename ORG, typename VECT> inline
void set_to_begin(IT &, ORG, VECT *v, linalg_modifiable)
{ GMM_ASSERT3(!is_sparse(*v), "internal_error"); v = 0; }
template <typename IT, typename ORG, typename VECT> inline
void set_to_begin(IT &, ORG, const VECT *v, linalg_modifiable)
{ GMM_ASSERT3(!is_sparse(*v), "internal_error"); v = 0; }
template <typename IT, typename ORG, typename VECT> inline
void set_to_end(IT &, ORG, VECT *v, linalg_modifiable)
{ GMM_ASSERT3(!is_sparse(*v), "internal_error"); v = 0; }
template <typename IT, typename ORG, typename VECT> inline
void set_to_end(IT &, ORG, const VECT *v, linalg_modifiable)
{ GMM_ASSERT3(!is_sparse(*v), "internal_error"); v = 0; }
/* ******************************************************************** */
/* General index for certain algorithms. */
/* ******************************************************************** */
template<class IT>
size_type index_of_it(const IT &it, size_type, abstract_sparse)
{ return it.index(); }
template<class IT>
size_type index_of_it(const IT &it, size_type, abstract_skyline)
{ return it.index(); }
template<class IT>
size_type index_of_it(const IT &, size_type k, abstract_dense)
{ return k; }
/* ********************************************************************* */
/* Numeric limits. */
/* ********************************************************************* */
template<typename T> inline T default_tol(T) {
using namespace std;
static T tol(10);
if (tol == T(10)) {
if (numeric_limits<T>::is_specialized)
tol = numeric_limits<T>::epsilon();
else {
int i=sizeof(T)/4; while(i-- > 0) tol*=T(1E-8);
GMM_WARNING1("The numeric type " << typeid(T).name()
<< " has no numeric_limits defined !!\n"
<< "Taking " << tol << " as default tolerance");
}
}
return tol;
}
template<typename T> inline T default_tol(std::complex<T>)
{ return default_tol(T()); }
template<typename T> inline T default_min(T) {
using namespace std;
static T mi(10);
if (mi == T(10)) {
if (numeric_limits<T>::is_specialized)
mi = std::numeric_limits<T>::min();
else {
mi = T(0); GMM_WARNING1("The numeric type " << typeid(T).name()
<< " has no numeric_limits defined !!\n"
<< "Taking 0 as default minimum");
}
}
return mi;
}
template<typename T> inline T default_min(std::complex<T>)
{ return default_min(T()); }
template<typename T> inline T default_max(T) {
using namespace std;
static T mi(10);
if (mi == T(10)) {
if (numeric_limits<T>::is_specialized)
mi = std::numeric_limits<T>::max();
else {
mi = T(1);
GMM_WARNING1("The numeric type " << typeid(T).name()
<< " has no numeric_limits defined !!\n"
<< "Taking 1 as default maximum !");
}
}
return mi;
}
template<typename T> inline T default_max(std::complex<T>)
{ return default_max(T()); }
/*
use safe_divide to avoid NaNs when dividing very small complex
numbers, for example
std::complex<float>(1e-23,1e-30)/std::complex<float>(1e-23,1e-30)
*/
template<typename T> inline T safe_divide(T a, T b) { return a/b; }
template<typename T> inline std::complex<T>
safe_divide(std::complex<T> a, std::complex<T> b) {
T m = std::max(gmm::abs(b.real()), gmm::abs(b.imag()));
a = std::complex<T>(a.real()/m, a.imag()/m);
b = std::complex<T>(b.real()/m, b.imag()/m);
return a / b;
}
/* ******************************************************************** */
/* Write */
/* ******************************************************************** */
template <typename T> struct cast_char_type { typedef T return_type; };
template <> struct cast_char_type<signed char> { typedef int return_type; };
template <> struct cast_char_type<unsigned char>
{ typedef unsigned int return_type; };
template <typename T> inline typename cast_char_type<T>::return_type
cast_char(const T &c) { return typename cast_char_type<T>::return_type(c); }
template <typename L> inline void write(std::ostream &o, const L &l)
{ write(o, l, typename linalg_traits<L>::linalg_type()); }
template <typename L> void write(std::ostream &o, const L &l,
abstract_vector) {
o << "vector(" << vect_size(l) << ") [";
write(o, l, typename linalg_traits<L>::storage_type());
o << " ]";
}
template <typename L> void write(std::ostream &o, const L &l,
abstract_sparse) {
typename linalg_traits<L>::const_iterator it = vect_const_begin(l),
ite = vect_const_end(l); for (; it != ite; ++it)
o << " (r" << it.index() << "," << cast_char(*it) << ")";
}
template <typename L> void write(std::ostream &o, const L &l,
abstract_dense) {
typename linalg_traits<L>::const_iterator it = vect_const_begin(l),
ite = vect_const_end(l);
if (it != ite) o << " " << cast_char(*it++);
for (; it != ite; ++it) o << ", " << cast_char(*it);
}
template <typename L> void write(std::ostream &o, const L &l,
abstract_skyline) {
typedef typename linalg_traits<L>::const_iterator const_iterator;
const_iterator it = vect_const_begin(l), ite = vect_const_end(l);
if (it != ite) {
o << "<r+" << it.index() << ">";
if (it != ite) o << " " << cast_char(*it++);
for (; it != ite; ++it) { o << ", " << cast_char(*it); }
}
}
template <typename L> inline void write(std::ostream &o, const L &l,
abstract_matrix) {
write(o, l, typename linalg_traits<L>::sub_orientation());
}
template <typename L> void write(std::ostream &o, const L &l,
row_major) {
o << "matrix(" << mat_nrows(l) << ", " << mat_ncols(l) << ")" << endl;
for (size_type i = 0; i < mat_nrows(l); ++i) {
o << "(";
write(o, mat_const_row(l, i), typename linalg_traits<L>::storage_type());
o << " )\n";
}
}
template <typename L> inline
void write(std::ostream &o, const L &l, row_and_col)
{ write(o, l, row_major()); }
template <typename L> inline
void write(std::ostream &o, const L &l, col_and_row)
{ write(o, l, row_major()); }
template <typename L> void write(std::ostream &o, const L &l, col_major) {
o << "matrix(" << mat_nrows(l) << ", " << mat_ncols(l) << ")" << endl;
for (size_type i = 0; i < mat_nrows(l); ++i) {
o << "(";
if (is_sparse(l)) { // not optimized ...
for (size_type j = 0; j < mat_ncols(l); ++j)
if (l(i,j) != typename linalg_traits<L>::value_type(0))
o << " (r" << j << ", " << l(i,j) << ")";
}
else {
if (mat_ncols(l) != 0) o << ' ' << l(i, 0);
for (size_type j = 1; j < mat_ncols(l); ++j) o << ", " << l(i, j);
}
o << " )\n";
}
}
}
#endif // GMM_DEF_H__