// | |
// Copyright (c) 2000-2009 | |
// Joerg Walter, Mathias Koch, Gunter Winkler | |
// | |
// Distributed under the Boost Software License, Version 1.0. (See | |
// accompanying file LICENSE_1_0.txt or copy at | |
// http://www.boost.org/LICENSE_1_0.txt) | |
// | |
// The authors gratefully acknowledge the support of | |
// GeNeSys mbH & Co. KG in producing this work. | |
// | |
#ifndef _BOOST_UBLAS_FUNCTIONAL_ | |
#define _BOOST_UBLAS_FUNCTIONAL_ | |
#include <functional> | |
#include <boost/numeric/ublas/traits.hpp> | |
#ifdef BOOST_UBLAS_USE_DUFF_DEVICE | |
#include <boost/numeric/ublas/detail/duff.hpp> | |
#endif | |
#ifdef BOOST_UBLAS_USE_SIMD | |
#include <boost/numeric/ublas/detail/raw.hpp> | |
#else | |
namespace boost { namespace numeric { namespace ublas { namespace raw { | |
}}}} | |
#endif | |
#ifdef BOOST_UBLAS_HAVE_BINDINGS | |
#include <boost/numeric/bindings/traits/std_vector.hpp> | |
#include <boost/numeric/bindings/traits/ublas_vector.hpp> | |
#include <boost/numeric/bindings/traits/ublas_matrix.hpp> | |
#include <boost/numeric/bindings/atlas/cblas.hpp> | |
#endif | |
#include <boost/numeric/ublas/detail/definitions.hpp> | |
namespace boost { namespace numeric { namespace ublas { | |
// Scalar functors | |
// Unary | |
template<class T> | |
struct scalar_unary_functor { | |
typedef T value_type; | |
typedef typename type_traits<T>::const_reference argument_type; | |
typedef typename type_traits<T>::value_type result_type; | |
}; | |
template<class T> | |
struct scalar_identity: | |
public scalar_unary_functor<T> { | |
typedef typename scalar_unary_functor<T>::argument_type argument_type; | |
typedef typename scalar_unary_functor<T>::result_type result_type; | |
static BOOST_UBLAS_INLINE | |
result_type apply (argument_type t) { | |
return t; | |
} | |
}; | |
template<class T> | |
struct scalar_negate: | |
public scalar_unary_functor<T> { | |
typedef typename scalar_unary_functor<T>::argument_type argument_type; | |
typedef typename scalar_unary_functor<T>::result_type result_type; | |
static BOOST_UBLAS_INLINE | |
result_type apply (argument_type t) { | |
return - t; | |
} | |
}; | |
template<class T> | |
struct scalar_conj: | |
public scalar_unary_functor<T> { | |
typedef typename scalar_unary_functor<T>::value_type value_type; | |
typedef typename scalar_unary_functor<T>::argument_type argument_type; | |
typedef typename scalar_unary_functor<T>::result_type result_type; | |
static BOOST_UBLAS_INLINE | |
result_type apply (argument_type t) { | |
return type_traits<value_type>::conj (t); | |
} | |
}; | |
// Unary returning real | |
template<class T> | |
struct scalar_real_unary_functor { | |
typedef T value_type; | |
typedef typename type_traits<T>::const_reference argument_type; | |
typedef typename type_traits<T>::real_type result_type; | |
}; | |
template<class T> | |
struct scalar_real: | |
public scalar_real_unary_functor<T> { | |
typedef typename scalar_real_unary_functor<T>::value_type value_type; | |
typedef typename scalar_real_unary_functor<T>::argument_type argument_type; | |
typedef typename scalar_real_unary_functor<T>::result_type result_type; | |
static BOOST_UBLAS_INLINE | |
result_type apply (argument_type t) { | |
return type_traits<value_type>::real (t); | |
} | |
}; | |
template<class T> | |
struct scalar_imag: | |
public scalar_real_unary_functor<T> { | |
typedef typename scalar_real_unary_functor<T>::value_type value_type; | |
typedef typename scalar_real_unary_functor<T>::argument_type argument_type; | |
typedef typename scalar_real_unary_functor<T>::result_type result_type; | |
static BOOST_UBLAS_INLINE | |
result_type apply (argument_type t) { | |
return type_traits<value_type>::imag (t); | |
} | |
}; | |
// Binary | |
template<class T1, class T2> | |
struct scalar_binary_functor { | |
typedef typename type_traits<T1>::const_reference argument1_type; | |
typedef typename type_traits<T2>::const_reference argument2_type; | |
typedef typename promote_traits<T1, T2>::promote_type result_type; | |
}; | |
template<class T1, class T2> | |
struct scalar_plus: | |
public scalar_binary_functor<T1, T2> { | |
typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type; | |
typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type; | |
typedef typename scalar_binary_functor<T1, T2>::result_type result_type; | |
static BOOST_UBLAS_INLINE | |
result_type apply (argument1_type t1, argument2_type t2) { | |
return t1 + t2; | |
} | |
}; | |
template<class T1, class T2> | |
struct scalar_minus: | |
public scalar_binary_functor<T1, T2> { | |
typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type; | |
typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type; | |
typedef typename scalar_binary_functor<T1, T2>::result_type result_type; | |
static BOOST_UBLAS_INLINE | |
result_type apply (argument1_type t1, argument2_type t2) { | |
return t1 - t2; | |
} | |
}; | |
template<class T1, class T2> | |
struct scalar_multiplies: | |
public scalar_binary_functor<T1, T2> { | |
typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type; | |
typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type; | |
typedef typename scalar_binary_functor<T1, T2>::result_type result_type; | |
static BOOST_UBLAS_INLINE | |
result_type apply (argument1_type t1, argument2_type t2) { | |
return t1 * t2; | |
} | |
}; | |
template<class T1, class T2> | |
struct scalar_divides: | |
public scalar_binary_functor<T1, T2> { | |
typedef typename scalar_binary_functor<T1, T2>::argument1_type argument1_type; | |
typedef typename scalar_binary_functor<T1, T2>::argument2_type argument2_type; | |
typedef typename scalar_binary_functor<T1, T2>::result_type result_type; | |
static BOOST_UBLAS_INLINE | |
result_type apply (argument1_type t1, argument2_type t2) { | |
return t1 / t2; | |
} | |
}; | |
template<class T1, class T2> | |
struct scalar_binary_assign_functor { | |
// ISSUE Remove reference to avoid reference to reference problems | |
typedef typename type_traits<typename boost::remove_reference<T1>::type>::reference argument1_type; | |
typedef typename type_traits<T2>::const_reference argument2_type; | |
}; | |
struct assign_tag {}; | |
struct computed_assign_tag {}; | |
template<class T1, class T2> | |
struct scalar_assign: | |
public scalar_binary_assign_functor<T1, T2> { | |
typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type; | |
typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type; | |
#if BOOST_WORKAROUND( __IBMCPP__, <=600 ) | |
static const bool computed ; | |
#else | |
static const bool computed = false ; | |
#endif | |
static BOOST_UBLAS_INLINE | |
void apply (argument1_type t1, argument2_type t2) { | |
t1 = t2; | |
} | |
template<class U1, class U2> | |
struct rebind { | |
typedef scalar_assign<U1, U2> other; | |
}; | |
}; | |
#if BOOST_WORKAROUND( __IBMCPP__, <=600 ) | |
template<class T1, class T2> | |
const bool scalar_assign<T1,T2>::computed = false; | |
#endif | |
template<class T1, class T2> | |
struct scalar_plus_assign: | |
public scalar_binary_assign_functor<T1, T2> { | |
typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type; | |
typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type; | |
#if BOOST_WORKAROUND( __IBMCPP__, <=600 ) | |
static const bool computed ; | |
#else | |
static const bool computed = true ; | |
#endif | |
static BOOST_UBLAS_INLINE | |
void apply (argument1_type t1, argument2_type t2) { | |
t1 += t2; | |
} | |
template<class U1, class U2> | |
struct rebind { | |
typedef scalar_plus_assign<U1, U2> other; | |
}; | |
}; | |
#if BOOST_WORKAROUND( __IBMCPP__, <=600 ) | |
template<class T1, class T2> | |
const bool scalar_plus_assign<T1,T2>::computed = true; | |
#endif | |
template<class T1, class T2> | |
struct scalar_minus_assign: | |
public scalar_binary_assign_functor<T1, T2> { | |
typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type; | |
typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type; | |
#if BOOST_WORKAROUND( __IBMCPP__, <=600 ) | |
static const bool computed ; | |
#else | |
static const bool computed = true ; | |
#endif | |
static BOOST_UBLAS_INLINE | |
void apply (argument1_type t1, argument2_type t2) { | |
t1 -= t2; | |
} | |
template<class U1, class U2> | |
struct rebind { | |
typedef scalar_minus_assign<U1, U2> other; | |
}; | |
}; | |
#if BOOST_WORKAROUND( __IBMCPP__, <=600 ) | |
template<class T1, class T2> | |
const bool scalar_minus_assign<T1,T2>::computed = true; | |
#endif | |
template<class T1, class T2> | |
struct scalar_multiplies_assign: | |
public scalar_binary_assign_functor<T1, T2> { | |
typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type; | |
typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type; | |
static const bool computed = true; | |
static BOOST_UBLAS_INLINE | |
void apply (argument1_type t1, argument2_type t2) { | |
t1 *= t2; | |
} | |
template<class U1, class U2> | |
struct rebind { | |
typedef scalar_multiplies_assign<U1, U2> other; | |
}; | |
}; | |
template<class T1, class T2> | |
struct scalar_divides_assign: | |
public scalar_binary_assign_functor<T1, T2> { | |
typedef typename scalar_binary_assign_functor<T1, T2>::argument1_type argument1_type; | |
typedef typename scalar_binary_assign_functor<T1, T2>::argument2_type argument2_type; | |
static const bool computed ; | |
static BOOST_UBLAS_INLINE | |
void apply (argument1_type t1, argument2_type t2) { | |
t1 /= t2; | |
} | |
template<class U1, class U2> | |
struct rebind { | |
typedef scalar_divides_assign<U1, U2> other; | |
}; | |
}; | |
template<class T1, class T2> | |
const bool scalar_divides_assign<T1,T2>::computed = true; | |
template<class T1, class T2> | |
struct scalar_binary_swap_functor { | |
typedef typename type_traits<typename boost::remove_reference<T1>::type>::reference argument1_type; | |
typedef typename type_traits<typename boost::remove_reference<T2>::type>::reference argument2_type; | |
}; | |
template<class T1, class T2> | |
struct scalar_swap: | |
public scalar_binary_swap_functor<T1, T2> { | |
typedef typename scalar_binary_swap_functor<T1, T2>::argument1_type argument1_type; | |
typedef typename scalar_binary_swap_functor<T1, T2>::argument2_type argument2_type; | |
static BOOST_UBLAS_INLINE | |
void apply (argument1_type t1, argument2_type t2) { | |
std::swap (t1, t2); | |
} | |
template<class U1, class U2> | |
struct rebind { | |
typedef scalar_swap<U1, U2> other; | |
}; | |
}; | |
// Vector functors | |
// Unary returning scalar | |
template<class V> | |
struct vector_scalar_unary_functor { | |
typedef typename V::value_type value_type; | |
typedef typename V::value_type result_type; | |
}; | |
template<class V> | |
struct vector_sum: | |
public vector_scalar_unary_functor<V> { | |
typedef typename vector_scalar_unary_functor<V>::value_type value_type; | |
typedef typename vector_scalar_unary_functor<V>::result_type result_type; | |
template<class E> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const vector_expression<E> &e) { | |
result_type t = result_type (0); | |
typedef typename E::size_type vector_size_type; | |
vector_size_type size (e ().size ()); | |
for (vector_size_type i = 0; i < size; ++ i) | |
t += e () (i); | |
return t; | |
} | |
// Dense case | |
template<class D, class I> | |
static BOOST_UBLAS_INLINE | |
result_type apply (D size, I it) { | |
result_type t = result_type (0); | |
while (-- size >= 0) | |
t += *it, ++ it; | |
return t; | |
} | |
// Sparse case | |
template<class I> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I it, const I &it_end) { | |
result_type t = result_type (0); | |
while (it != it_end) | |
t += *it, ++ it; | |
return t; | |
} | |
}; | |
// Unary returning real scalar | |
template<class V> | |
struct vector_scalar_real_unary_functor { | |
typedef typename V::value_type value_type; | |
typedef typename type_traits<value_type>::real_type real_type; | |
typedef real_type result_type; | |
}; | |
template<class V> | |
struct vector_norm_1: | |
public vector_scalar_real_unary_functor<V> { | |
typedef typename vector_scalar_real_unary_functor<V>::value_type value_type; | |
typedef typename vector_scalar_real_unary_functor<V>::real_type real_type; | |
typedef typename vector_scalar_real_unary_functor<V>::result_type result_type; | |
template<class E> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const vector_expression<E> &e) { | |
real_type t = real_type (); | |
typedef typename E::size_type vector_size_type; | |
vector_size_type size (e ().size ()); | |
for (vector_size_type i = 0; i < size; ++ i) { | |
real_type u (type_traits<value_type>::type_abs (e () (i))); | |
t += u; | |
} | |
return t; | |
} | |
// Dense case | |
template<class D, class I> | |
static BOOST_UBLAS_INLINE | |
result_type apply (D size, I it) { | |
real_type t = real_type (); | |
while (-- size >= 0) { | |
real_type u (type_traits<value_type>::norm_1 (*it)); | |
t += u; | |
++ it; | |
} | |
return t; | |
} | |
// Sparse case | |
template<class I> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I it, const I &it_end) { | |
real_type t = real_type (); | |
while (it != it_end) { | |
real_type u (type_traits<value_type>::norm_1 (*it)); | |
t += u; | |
++ it; | |
} | |
return t; | |
} | |
}; | |
template<class V> | |
struct vector_norm_2: | |
public vector_scalar_real_unary_functor<V> { | |
typedef typename vector_scalar_real_unary_functor<V>::value_type value_type; | |
typedef typename vector_scalar_real_unary_functor<V>::real_type real_type; | |
typedef typename vector_scalar_real_unary_functor<V>::result_type result_type; | |
template<class E> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const vector_expression<E> &e) { | |
#ifndef BOOST_UBLAS_SCALED_NORM | |
real_type t = real_type (); | |
typedef typename E::size_type vector_size_type; | |
vector_size_type size (e ().size ()); | |
for (vector_size_type i = 0; i < size; ++ i) { | |
real_type u (type_traits<value_type>::norm_2 (e () (i))); | |
t += u * u; | |
} | |
return type_traits<real_type>::type_sqrt (t); | |
#else | |
real_type scale = real_type (); | |
real_type sum_squares (1); | |
size_type size (e ().size ()); | |
for (size_type i = 0; i < size; ++ i) { | |
real_type u (type_traits<value_type>::norm_2 (e () (i))); | |
if ( real_type () /* zero */ == u ) continue; | |
if (scale < u) { | |
real_type v (scale / u); | |
sum_squares = sum_squares * v * v + real_type (1); | |
scale = u; | |
} else { | |
real_type v (u / scale); | |
sum_squares += v * v; | |
} | |
} | |
return scale * type_traits<real_type>::type_sqrt (sum_squares); | |
#endif | |
} | |
// Dense case | |
template<class D, class I> | |
static BOOST_UBLAS_INLINE | |
result_type apply (D size, I it) { | |
#ifndef BOOST_UBLAS_SCALED_NORM | |
real_type t = real_type (); | |
while (-- size >= 0) { | |
real_type u (type_traits<value_type>::norm_2 (*it)); | |
t += u * u; | |
++ it; | |
} | |
return type_traits<real_type>::type_sqrt (t); | |
#else | |
real_type scale = real_type (); | |
real_type sum_squares (1); | |
while (-- size >= 0) { | |
real_type u (type_traits<value_type>::norm_2 (*it)); | |
if (scale < u) { | |
real_type v (scale / u); | |
sum_squares = sum_squares * v * v + real_type (1); | |
scale = u; | |
} else { | |
real_type v (u / scale); | |
sum_squares += v * v; | |
} | |
++ it; | |
} | |
return scale * type_traits<real_type>::type_sqrt (sum_squares); | |
#endif | |
} | |
// Sparse case | |
template<class I> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I it, const I &it_end) { | |
#ifndef BOOST_UBLAS_SCALED_NORM | |
real_type t = real_type (); | |
while (it != it_end) { | |
real_type u (type_traits<value_type>::norm_2 (*it)); | |
t += u * u; | |
++ it; | |
} | |
return type_traits<real_type>::type_sqrt (t); | |
#else | |
real_type scale = real_type (); | |
real_type sum_squares (1); | |
while (it != it_end) { | |
real_type u (type_traits<value_type>::norm_2 (*it)); | |
if (scale < u) { | |
real_type v (scale / u); | |
sum_squares = sum_squares * v * v + real_type (1); | |
scale = u; | |
} else { | |
real_type v (u / scale); | |
sum_squares += v * v; | |
} | |
++ it; | |
} | |
return scale * type_traits<real_type>::type_sqrt (sum_squares); | |
#endif | |
} | |
}; | |
template<class V> | |
struct vector_norm_inf: | |
public vector_scalar_real_unary_functor<V> { | |
typedef typename vector_scalar_real_unary_functor<V>::value_type value_type; | |
typedef typename vector_scalar_real_unary_functor<V>::real_type real_type; | |
typedef typename vector_scalar_real_unary_functor<V>::result_type result_type; | |
template<class E> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const vector_expression<E> &e) { | |
real_type t = real_type (); | |
typedef typename E::size_type vector_size_type; | |
vector_size_type size (e ().size ()); | |
for (vector_size_type i = 0; i < size; ++ i) { | |
real_type u (type_traits<value_type>::norm_inf (e () (i))); | |
if (u > t) | |
t = u; | |
} | |
return t; | |
} | |
// Dense case | |
template<class D, class I> | |
static BOOST_UBLAS_INLINE | |
result_type apply (D size, I it) { | |
real_type t = real_type (); | |
while (-- size >= 0) { | |
real_type u (type_traits<value_type>::norm_inf (*it)); | |
if (u > t) | |
t = u; | |
++ it; | |
} | |
return t; | |
} | |
// Sparse case | |
template<class I> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I it, const I &it_end) { | |
real_type t = real_type (); | |
while (it != it_end) { | |
real_type u (type_traits<value_type>::norm_inf (*it)); | |
if (u > t) | |
t = u; | |
++ it; | |
} | |
return t; | |
} | |
}; | |
// Unary returning index | |
template<class V> | |
struct vector_scalar_index_unary_functor { | |
typedef typename V::value_type value_type; | |
typedef typename type_traits<value_type>::real_type real_type; | |
typedef typename V::size_type result_type; | |
}; | |
template<class V> | |
struct vector_index_norm_inf: | |
public vector_scalar_index_unary_functor<V> { | |
typedef typename vector_scalar_index_unary_functor<V>::value_type value_type; | |
typedef typename vector_scalar_index_unary_functor<V>::real_type real_type; | |
typedef typename vector_scalar_index_unary_functor<V>::result_type result_type; | |
template<class E> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const vector_expression<E> &e) { | |
// ISSUE For CBLAS compatibility return 0 index in empty case | |
result_type i_norm_inf (0); | |
real_type t = real_type (); | |
typedef typename E::size_type vector_size_type; | |
vector_size_type size (e ().size ()); | |
for (vector_size_type i = 0; i < size; ++ i) { | |
real_type u (type_traits<value_type>::norm_inf (e () (i))); | |
if (u > t) { | |
i_norm_inf = i; | |
t = u; | |
} | |
} | |
return i_norm_inf; | |
} | |
// Dense case | |
template<class D, class I> | |
static BOOST_UBLAS_INLINE | |
result_type apply (D size, I it) { | |
// ISSUE For CBLAS compatibility return 0 index in empty case | |
result_type i_norm_inf (0); | |
real_type t = real_type (); | |
while (-- size >= 0) { | |
real_type u (type_traits<value_type>::norm_inf (*it)); | |
if (u > t) { | |
i_norm_inf = it.index (); | |
t = u; | |
} | |
++ it; | |
} | |
return i_norm_inf; | |
} | |
// Sparse case | |
template<class I> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I it, const I &it_end) { | |
// ISSUE For CBLAS compatibility return 0 index in empty case | |
result_type i_norm_inf (0); | |
real_type t = real_type (); | |
while (it != it_end) { | |
real_type u (type_traits<value_type>::norm_inf (*it)); | |
if (u > t) { | |
i_norm_inf = it.index (); | |
t = u; | |
} | |
++ it; | |
} | |
return i_norm_inf; | |
} | |
}; | |
// Binary returning scalar | |
template<class V1, class V2, class TV> | |
struct vector_scalar_binary_functor { | |
typedef TV value_type; | |
typedef TV result_type; | |
}; | |
template<class V1, class V2, class TV> | |
struct vector_inner_prod: | |
public vector_scalar_binary_functor<V1, V2, TV> { | |
typedef typename vector_scalar_binary_functor<V1, V2, TV>::value_type value_type; | |
typedef typename vector_scalar_binary_functor<V1, V2, TV>::result_type result_type; | |
template<class C1, class C2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const vector_container<C1> &c1, | |
const vector_container<C2> &c2) { | |
#ifdef BOOST_UBLAS_USE_SIMD | |
using namespace raw; | |
typedef typename C1::size_type vector_size_type; | |
vector_size_type size (BOOST_UBLAS_SAME (c1 ().size (), c2 ().size ())); | |
const typename V1::value_type *data1 = data_const (c1 ()); | |
const typename V1::value_type *data2 = data_const (c2 ()); | |
vector_size_type s1 = stride (c1 ()); | |
vector_size_type s2 = stride (c2 ()); | |
result_type t = result_type (0); | |
if (s1 == 1 && s2 == 1) { | |
for (vector_size_type i = 0; i < size; ++ i) | |
t += data1 [i] * data2 [i]; | |
} else if (s2 == 1) { | |
for (vector_size_type i = 0, i1 = 0; i < size; ++ i, i1 += s1) | |
t += data1 [i1] * data2 [i]; | |
} else if (s1 == 1) { | |
for (vector_size_type i = 0, i2 = 0; i < size; ++ i, i2 += s2) | |
t += data1 [i] * data2 [i2]; | |
} else { | |
for (vector_size_type i = 0, i1 = 0, i2 = 0; i < size; ++ i, i1 += s1, i2 += s2) | |
t += data1 [i1] * data2 [i2]; | |
} | |
return t; | |
#elif defined(BOOST_UBLAS_HAVE_BINDINGS) | |
return boost::numeric::bindings::atlas::dot (c1 (), c2 ()); | |
#else | |
return apply (static_cast<const vector_expression<C1> > (c1), static_cast<const vector_expression<C2> > (c2)); | |
#endif | |
} | |
template<class E1, class E2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const vector_expression<E1> &e1, | |
const vector_expression<E2> &e2) { | |
typedef typename E1::size_type vector_size_type; | |
vector_size_type size (BOOST_UBLAS_SAME (e1 ().size (), e2 ().size ())); | |
result_type t = result_type (0); | |
#ifndef BOOST_UBLAS_USE_DUFF_DEVICE | |
for (vector_size_type i = 0; i < size; ++ i) | |
t += e1 () (i) * e2 () (i); | |
#else | |
vector_size_type i (0); | |
DD (size, 4, r, (t += e1 () (i) * e2 () (i), ++ i)); | |
#endif | |
return t; | |
} | |
// Dense case | |
template<class D, class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (D size, I1 it1, I2 it2) { | |
result_type t = result_type (0); | |
#ifndef BOOST_UBLAS_USE_DUFF_DEVICE | |
while (-- size >= 0) | |
t += *it1 * *it2, ++ it1, ++ it2; | |
#else | |
DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2)); | |
#endif | |
return t; | |
} | |
// Packed case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end) { | |
result_type t = result_type (0); | |
typedef typename I1::difference_type vector_difference_type; | |
vector_difference_type it1_size (it1_end - it1); | |
vector_difference_type it2_size (it2_end - it2); | |
vector_difference_type diff (0); | |
if (it1_size > 0 && it2_size > 0) | |
diff = it2.index () - it1.index (); | |
if (diff != 0) { | |
vector_difference_type size = (std::min) (diff, it1_size); | |
if (size > 0) { | |
it1 += size; | |
it1_size -= size; | |
diff -= size; | |
} | |
size = (std::min) (- diff, it2_size); | |
if (size > 0) { | |
it2 += size; | |
it2_size -= size; | |
diff += size; | |
} | |
} | |
vector_difference_type size ((std::min) (it1_size, it2_size)); | |
while (-- size >= 0) | |
t += *it1 * *it2, ++ it1, ++ it2; | |
return t; | |
} | |
// Sparse case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, sparse_bidirectional_iterator_tag) { | |
result_type t = result_type (0); | |
if (it1 != it1_end && it2 != it2_end) { | |
while (true) { | |
if (it1.index () == it2.index ()) { | |
t += *it1 * *it2, ++ it1, ++ it2; | |
if (it1 == it1_end || it2 == it2_end) | |
break; | |
} else if (it1.index () < it2.index ()) { | |
increment (it1, it1_end, it2.index () - it1.index ()); | |
if (it1 == it1_end) | |
break; | |
} else if (it1.index () > it2.index ()) { | |
increment (it2, it2_end, it1.index () - it2.index ()); | |
if (it2 == it2_end) | |
break; | |
} | |
} | |
} | |
return t; | |
} | |
}; | |
// Matrix functors | |
// Binary returning vector | |
template<class M1, class M2, class TV> | |
struct matrix_vector_binary_functor { | |
typedef typename M1::size_type size_type; | |
typedef typename M1::difference_type difference_type; | |
typedef TV value_type; | |
typedef TV result_type; | |
}; | |
template<class M1, class M2, class TV> | |
struct matrix_vector_prod1: | |
public matrix_vector_binary_functor<M1, M2, TV> { | |
typedef typename matrix_vector_binary_functor<M1, M2, TV>::size_type size_type; | |
typedef typename matrix_vector_binary_functor<M1, M2, TV>::difference_type difference_type; | |
typedef typename matrix_vector_binary_functor<M1, M2, TV>::value_type value_type; | |
typedef typename matrix_vector_binary_functor<M1, M2, TV>::result_type result_type; | |
template<class C1, class C2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const matrix_container<C1> &c1, | |
const vector_container<C2> &c2, | |
size_type i) { | |
#ifdef BOOST_UBLAS_USE_SIMD | |
using namespace raw; | |
size_type size = BOOST_UBLAS_SAME (c1 ().size2 (), c2 ().size ()); | |
const typename M1::value_type *data1 = data_const (c1 ()) + i * stride1 (c1 ()); | |
const typename M2::value_type *data2 = data_const (c2 ()); | |
size_type s1 = stride2 (c1 ()); | |
size_type s2 = stride (c2 ()); | |
result_type t = result_type (0); | |
if (s1 == 1 && s2 == 1) { | |
for (size_type j = 0; j < size; ++ j) | |
t += data1 [j] * data2 [j]; | |
} else if (s2 == 1) { | |
for (size_type j = 0, j1 = 0; j < size; ++ j, j1 += s1) | |
t += data1 [j1] * data2 [j]; | |
} else if (s1 == 1) { | |
for (size_type j = 0, j2 = 0; j < size; ++ j, j2 += s2) | |
t += data1 [j] * data2 [j2]; | |
} else { | |
for (size_type j = 0, j1 = 0, j2 = 0; j < size; ++ j, j1 += s1, j2 += s2) | |
t += data1 [j1] * data2 [j2]; | |
} | |
return t; | |
#elif defined(BOOST_UBLAS_HAVE_BINDINGS) | |
return boost::numeric::bindings::atlas::dot (c1 ().row (i), c2 ()); | |
#else | |
return apply (static_cast<const matrix_expression<C1> > (c1), static_cast<const vector_expression<C2> > (c2, i)); | |
#endif | |
} | |
template<class E1, class E2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const matrix_expression<E1> &e1, | |
const vector_expression<E2> &e2, | |
size_type i) { | |
size_type size = BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size ()); | |
result_type t = result_type (0); | |
#ifndef BOOST_UBLAS_USE_DUFF_DEVICE | |
for (size_type j = 0; j < size; ++ j) | |
t += e1 () (i, j) * e2 () (j); | |
#else | |
size_type j (0); | |
DD (size, 4, r, (t += e1 () (i, j) * e2 () (j), ++ j)); | |
#endif | |
return t; | |
} | |
// Dense case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (difference_type size, I1 it1, I2 it2) { | |
result_type t = result_type (0); | |
#ifndef BOOST_UBLAS_USE_DUFF_DEVICE | |
while (-- size >= 0) | |
t += *it1 * *it2, ++ it1, ++ it2; | |
#else | |
DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2)); | |
#endif | |
return t; | |
} | |
// Packed case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end) { | |
result_type t = result_type (0); | |
difference_type it1_size (it1_end - it1); | |
difference_type it2_size (it2_end - it2); | |
difference_type diff (0); | |
if (it1_size > 0 && it2_size > 0) | |
diff = it2.index () - it1.index2 (); | |
if (diff != 0) { | |
difference_type size = (std::min) (diff, it1_size); | |
if (size > 0) { | |
it1 += size; | |
it1_size -= size; | |
diff -= size; | |
} | |
size = (std::min) (- diff, it2_size); | |
if (size > 0) { | |
it2 += size; | |
it2_size -= size; | |
diff += size; | |
} | |
} | |
difference_type size ((std::min) (it1_size, it2_size)); | |
while (-- size >= 0) | |
t += *it1 * *it2, ++ it1, ++ it2; | |
return t; | |
} | |
// Sparse case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, | |
sparse_bidirectional_iterator_tag, sparse_bidirectional_iterator_tag) { | |
result_type t = result_type (0); | |
if (it1 != it1_end && it2 != it2_end) { | |
size_type it1_index = it1.index2 (), it2_index = it2.index (); | |
while (true) { | |
difference_type compare = it1_index - it2_index; | |
if (compare == 0) { | |
t += *it1 * *it2, ++ it1, ++ it2; | |
if (it1 != it1_end && it2 != it2_end) { | |
it1_index = it1.index2 (); | |
it2_index = it2.index (); | |
} else | |
break; | |
} else if (compare < 0) { | |
increment (it1, it1_end, - compare); | |
if (it1 != it1_end) | |
it1_index = it1.index2 (); | |
else | |
break; | |
} else if (compare > 0) { | |
increment (it2, it2_end, compare); | |
if (it2 != it2_end) | |
it2_index = it2.index (); | |
else | |
break; | |
} | |
} | |
} | |
return t; | |
} | |
// Sparse packed case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &/* it2_end */, | |
sparse_bidirectional_iterator_tag, packed_random_access_iterator_tag) { | |
result_type t = result_type (0); | |
while (it1 != it1_end) { | |
t += *it1 * it2 () (it1.index2 ()); | |
++ it1; | |
} | |
return t; | |
} | |
// Packed sparse case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &/* it1_end */, I2 it2, const I2 &it2_end, | |
packed_random_access_iterator_tag, sparse_bidirectional_iterator_tag) { | |
result_type t = result_type (0); | |
while (it2 != it2_end) { | |
t += it1 () (it1.index1 (), it2.index ()) * *it2; | |
++ it2; | |
} | |
return t; | |
} | |
// Another dispatcher | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, | |
sparse_bidirectional_iterator_tag) { | |
typedef typename I1::iterator_category iterator1_category; | |
typedef typename I2::iterator_category iterator2_category; | |
return apply (it1, it1_end, it2, it2_end, iterator1_category (), iterator2_category ()); | |
} | |
}; | |
template<class M1, class M2, class TV> | |
struct matrix_vector_prod2: | |
public matrix_vector_binary_functor<M1, M2, TV> { | |
typedef typename matrix_vector_binary_functor<M1, M2, TV>::size_type size_type; | |
typedef typename matrix_vector_binary_functor<M1, M2, TV>::difference_type difference_type; | |
typedef typename matrix_vector_binary_functor<M1, M2, TV>::value_type value_type; | |
typedef typename matrix_vector_binary_functor<M1, M2, TV>::result_type result_type; | |
template<class C1, class C2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const vector_container<C1> &c1, | |
const matrix_container<C2> &c2, | |
size_type i) { | |
#ifdef BOOST_UBLAS_USE_SIMD | |
using namespace raw; | |
size_type size = BOOST_UBLAS_SAME (c1 ().size (), c2 ().size1 ()); | |
const typename M1::value_type *data1 = data_const (c1 ()); | |
const typename M2::value_type *data2 = data_const (c2 ()) + i * stride2 (c2 ()); | |
size_type s1 = stride (c1 ()); | |
size_type s2 = stride1 (c2 ()); | |
result_type t = result_type (0); | |
if (s1 == 1 && s2 == 1) { | |
for (size_type j = 0; j < size; ++ j) | |
t += data1 [j] * data2 [j]; | |
} else if (s2 == 1) { | |
for (size_type j = 0, j1 = 0; j < size; ++ j, j1 += s1) | |
t += data1 [j1] * data2 [j]; | |
} else if (s1 == 1) { | |
for (size_type j = 0, j2 = 0; j < size; ++ j, j2 += s2) | |
t += data1 [j] * data2 [j2]; | |
} else { | |
for (size_type j = 0, j1 = 0, j2 = 0; j < size; ++ j, j1 += s1, j2 += s2) | |
t += data1 [j1] * data2 [j2]; | |
} | |
return t; | |
#elif defined(BOOST_UBLAS_HAVE_BINDINGS) | |
return boost::numeric::bindings::atlas::dot (c1 (), c2 ().column (i)); | |
#else | |
return apply (static_cast<const vector_expression<C1> > (c1), static_cast<const matrix_expression<C2> > (c2, i)); | |
#endif | |
} | |
template<class E1, class E2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const vector_expression<E1> &e1, | |
const matrix_expression<E2> &e2, | |
size_type i) { | |
size_type size = BOOST_UBLAS_SAME (e1 ().size (), e2 ().size1 ()); | |
result_type t = result_type (0); | |
#ifndef BOOST_UBLAS_USE_DUFF_DEVICE | |
for (size_type j = 0; j < size; ++ j) | |
t += e1 () (j) * e2 () (j, i); | |
#else | |
size_type j (0); | |
DD (size, 4, r, (t += e1 () (j) * e2 () (j, i), ++ j)); | |
#endif | |
return t; | |
} | |
// Dense case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (difference_type size, I1 it1, I2 it2) { | |
result_type t = result_type (0); | |
#ifndef BOOST_UBLAS_USE_DUFF_DEVICE | |
while (-- size >= 0) | |
t += *it1 * *it2, ++ it1, ++ it2; | |
#else | |
DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2)); | |
#endif | |
return t; | |
} | |
// Packed case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end) { | |
result_type t = result_type (0); | |
difference_type it1_size (it1_end - it1); | |
difference_type it2_size (it2_end - it2); | |
difference_type diff (0); | |
if (it1_size > 0 && it2_size > 0) | |
diff = it2.index1 () - it1.index (); | |
if (diff != 0) { | |
difference_type size = (std::min) (diff, it1_size); | |
if (size > 0) { | |
it1 += size; | |
it1_size -= size; | |
diff -= size; | |
} | |
size = (std::min) (- diff, it2_size); | |
if (size > 0) { | |
it2 += size; | |
it2_size -= size; | |
diff += size; | |
} | |
} | |
difference_type size ((std::min) (it1_size, it2_size)); | |
while (-- size >= 0) | |
t += *it1 * *it2, ++ it1, ++ it2; | |
return t; | |
} | |
// Sparse case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, | |
sparse_bidirectional_iterator_tag, sparse_bidirectional_iterator_tag) { | |
result_type t = result_type (0); | |
if (it1 != it1_end && it2 != it2_end) { | |
size_type it1_index = it1.index (), it2_index = it2.index1 (); | |
while (true) { | |
difference_type compare = it1_index - it2_index; | |
if (compare == 0) { | |
t += *it1 * *it2, ++ it1, ++ it2; | |
if (it1 != it1_end && it2 != it2_end) { | |
it1_index = it1.index (); | |
it2_index = it2.index1 (); | |
} else | |
break; | |
} else if (compare < 0) { | |
increment (it1, it1_end, - compare); | |
if (it1 != it1_end) | |
it1_index = it1.index (); | |
else | |
break; | |
} else if (compare > 0) { | |
increment (it2, it2_end, compare); | |
if (it2 != it2_end) | |
it2_index = it2.index1 (); | |
else | |
break; | |
} | |
} | |
} | |
return t; | |
} | |
// Packed sparse case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &/* it1_end */, I2 it2, const I2 &it2_end, | |
packed_random_access_iterator_tag, sparse_bidirectional_iterator_tag) { | |
result_type t = result_type (0); | |
while (it2 != it2_end) { | |
t += it1 () (it2.index1 ()) * *it2; | |
++ it2; | |
} | |
return t; | |
} | |
// Sparse packed case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &/* it2_end */, | |
sparse_bidirectional_iterator_tag, packed_random_access_iterator_tag) { | |
result_type t = result_type (0); | |
while (it1 != it1_end) { | |
t += *it1 * it2 () (it1.index (), it2.index2 ()); | |
++ it1; | |
} | |
return t; | |
} | |
// Another dispatcher | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, | |
sparse_bidirectional_iterator_tag) { | |
typedef typename I1::iterator_category iterator1_category; | |
typedef typename I2::iterator_category iterator2_category; | |
return apply (it1, it1_end, it2, it2_end, iterator1_category (), iterator2_category ()); | |
} | |
}; | |
// Binary returning matrix | |
template<class M1, class M2, class TV> | |
struct matrix_matrix_binary_functor { | |
typedef typename M1::size_type size_type; | |
typedef typename M1::difference_type difference_type; | |
typedef TV value_type; | |
typedef TV result_type; | |
}; | |
template<class M1, class M2, class TV> | |
struct matrix_matrix_prod: | |
public matrix_matrix_binary_functor<M1, M2, TV> { | |
typedef typename matrix_matrix_binary_functor<M1, M2, TV>::size_type size_type; | |
typedef typename matrix_matrix_binary_functor<M1, M2, TV>::difference_type difference_type; | |
typedef typename matrix_matrix_binary_functor<M1, M2, TV>::value_type value_type; | |
typedef typename matrix_matrix_binary_functor<M1, M2, TV>::result_type result_type; | |
template<class C1, class C2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const matrix_container<C1> &c1, | |
const matrix_container<C2> &c2, | |
size_type i, size_type j) { | |
#ifdef BOOST_UBLAS_USE_SIMD | |
using namespace raw; | |
size_type size = BOOST_UBLAS_SAME (c1 ().size2 (), c2 ().sizc1 ()); | |
const typename M1::value_type *data1 = data_const (c1 ()) + i * stride1 (c1 ()); | |
const typename M2::value_type *data2 = data_const (c2 ()) + j * stride2 (c2 ()); | |
size_type s1 = stride2 (c1 ()); | |
size_type s2 = stride1 (c2 ()); | |
result_type t = result_type (0); | |
if (s1 == 1 && s2 == 1) { | |
for (size_type k = 0; k < size; ++ k) | |
t += data1 [k] * data2 [k]; | |
} else if (s2 == 1) { | |
for (size_type k = 0, k1 = 0; k < size; ++ k, k1 += s1) | |
t += data1 [k1] * data2 [k]; | |
} else if (s1 == 1) { | |
for (size_type k = 0, k2 = 0; k < size; ++ k, k2 += s2) | |
t += data1 [k] * data2 [k2]; | |
} else { | |
for (size_type k = 0, k1 = 0, k2 = 0; k < size; ++ k, k1 += s1, k2 += s2) | |
t += data1 [k1] * data2 [k2]; | |
} | |
return t; | |
#elif defined(BOOST_UBLAS_HAVE_BINDINGS) | |
return boost::numeric::bindings::atlas::dot (c1 ().row (i), c2 ().column (j)); | |
#else | |
return apply (static_cast<const matrix_expression<C1> > (c1), static_cast<const matrix_expression<C2> > (c2, i)); | |
#endif | |
} | |
template<class E1, class E2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const matrix_expression<E1> &e1, | |
const matrix_expression<E2> &e2, | |
size_type i, size_type j) { | |
size_type size = BOOST_UBLAS_SAME (e1 ().size2 (), e2 ().size1 ()); | |
result_type t = result_type (0); | |
#ifndef BOOST_UBLAS_USE_DUFF_DEVICE | |
for (size_type k = 0; k < size; ++ k) | |
t += e1 () (i, k) * e2 () (k, j); | |
#else | |
size_type k (0); | |
DD (size, 4, r, (t += e1 () (i, k) * e2 () (k, j), ++ k)); | |
#endif | |
return t; | |
} | |
// Dense case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (difference_type size, I1 it1, I2 it2) { | |
result_type t = result_type (0); | |
#ifndef BOOST_UBLAS_USE_DUFF_DEVICE | |
while (-- size >= 0) | |
t += *it1 * *it2, ++ it1, ++ it2; | |
#else | |
DD (size, 4, r, (t += *it1 * *it2, ++ it1, ++ it2)); | |
#endif | |
return t; | |
} | |
// Packed case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, packed_random_access_iterator_tag) { | |
result_type t = result_type (0); | |
difference_type it1_size (it1_end - it1); | |
difference_type it2_size (it2_end - it2); | |
difference_type diff (0); | |
if (it1_size > 0 && it2_size > 0) | |
diff = it2.index1 () - it1.index2 (); | |
if (diff != 0) { | |
difference_type size = (std::min) (diff, it1_size); | |
if (size > 0) { | |
it1 += size; | |
it1_size -= size; | |
diff -= size; | |
} | |
size = (std::min) (- diff, it2_size); | |
if (size > 0) { | |
it2 += size; | |
it2_size -= size; | |
diff += size; | |
} | |
} | |
difference_type size ((std::min) (it1_size, it2_size)); | |
while (-- size >= 0) | |
t += *it1 * *it2, ++ it1, ++ it2; | |
return t; | |
} | |
// Sparse case | |
template<class I1, class I2> | |
static BOOST_UBLAS_INLINE | |
result_type apply (I1 it1, const I1 &it1_end, I2 it2, const I2 &it2_end, sparse_bidirectional_iterator_tag) { | |
result_type t = result_type (0); | |
if (it1 != it1_end && it2 != it2_end) { | |
size_type it1_index = it1.index2 (), it2_index = it2.index1 (); | |
while (true) { | |
difference_type compare = difference_type (it1_index - it2_index); | |
if (compare == 0) { | |
t += *it1 * *it2, ++ it1, ++ it2; | |
if (it1 != it1_end && it2 != it2_end) { | |
it1_index = it1.index2 (); | |
it2_index = it2.index1 (); | |
} else | |
break; | |
} else if (compare < 0) { | |
increment (it1, it1_end, - compare); | |
if (it1 != it1_end) | |
it1_index = it1.index2 (); | |
else | |
break; | |
} else if (compare > 0) { | |
increment (it2, it2_end, compare); | |
if (it2 != it2_end) | |
it2_index = it2.index1 (); | |
else | |
break; | |
} | |
} | |
} | |
return t; | |
} | |
}; | |
// Unary returning scalar norm | |
template<class M> | |
struct matrix_scalar_real_unary_functor { | |
typedef typename M::value_type value_type; | |
typedef typename type_traits<value_type>::real_type real_type; | |
typedef real_type result_type; | |
}; | |
template<class M> | |
struct matrix_norm_1: | |
public matrix_scalar_real_unary_functor<M> { | |
typedef typename matrix_scalar_real_unary_functor<M>::value_type value_type; | |
typedef typename matrix_scalar_real_unary_functor<M>::real_type real_type; | |
typedef typename matrix_scalar_real_unary_functor<M>::result_type result_type; | |
template<class E> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const matrix_expression<E> &e) { | |
real_type t = real_type (); | |
typedef typename E::size_type matrix_size_type; | |
matrix_size_type size2 (e ().size2 ()); | |
for (matrix_size_type j = 0; j < size2; ++ j) { | |
real_type u = real_type (); | |
matrix_size_type size1 (e ().size1 ()); | |
for (matrix_size_type i = 0; i < size1; ++ i) { | |
real_type v (type_traits<value_type>::norm_1 (e () (i, j))); | |
u += v; | |
} | |
if (u > t) | |
t = u; | |
} | |
return t; | |
} | |
}; | |
template<class M> | |
struct matrix_norm_frobenius: | |
public matrix_scalar_real_unary_functor<M> { | |
typedef typename matrix_scalar_real_unary_functor<M>::value_type value_type; | |
typedef typename matrix_scalar_real_unary_functor<M>::real_type real_type; | |
typedef typename matrix_scalar_real_unary_functor<M>::result_type result_type; | |
template<class E> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const matrix_expression<E> &e) { | |
real_type t = real_type (); | |
typedef typename E::size_type matrix_size_type; | |
matrix_size_type size1 (e ().size1 ()); | |
for (matrix_size_type i = 0; i < size1; ++ i) { | |
matrix_size_type size2 (e ().size2 ()); | |
for (matrix_size_type j = 0; j < size2; ++ j) { | |
real_type u (type_traits<value_type>::norm_2 (e () (i, j))); | |
t += u * u; | |
} | |
} | |
return type_traits<real_type>::type_sqrt (t); | |
} | |
}; | |
template<class M> | |
struct matrix_norm_inf: | |
public matrix_scalar_real_unary_functor<M> { | |
typedef typename matrix_scalar_real_unary_functor<M>::value_type value_type; | |
typedef typename matrix_scalar_real_unary_functor<M>::real_type real_type; | |
typedef typename matrix_scalar_real_unary_functor<M>::result_type result_type; | |
template<class E> | |
static BOOST_UBLAS_INLINE | |
result_type apply (const matrix_expression<E> &e) { | |
real_type t = real_type (); | |
typedef typename E::size_type matrix_size_type; | |
matrix_size_type size1 (e ().size1 ()); | |
for (matrix_size_type i = 0; i < size1; ++ i) { | |
real_type u = real_type (); | |
matrix_size_type size2 (e ().size2 ()); | |
for (matrix_size_type j = 0; j < size2; ++ j) { | |
real_type v (type_traits<value_type>::norm_inf (e () (i, j))); | |
u += v; | |
} | |
if (u > t) | |
t = u; | |
} | |
return t; | |
} | |
}; | |
// forward declaration | |
template <class Z, class D> struct basic_column_major; | |
// This functor defines storage layout and it's properties | |
// matrix (i,j) -> storage [i * size_i + j] | |
template <class Z, class D> | |
struct basic_row_major { | |
typedef Z size_type; | |
typedef D difference_type; | |
typedef row_major_tag orientation_category; | |
typedef basic_column_major<Z,D> transposed_layout; | |
static | |
BOOST_UBLAS_INLINE | |
size_type storage_size (size_type size_i, size_type size_j) { | |
// Guard against size_type overflow | |
BOOST_UBLAS_CHECK (size_j == 0 || size_i <= (std::numeric_limits<size_type>::max) () / size_j, bad_size ()); | |
return size_i * size_j; | |
} | |
// Indexing conversion to storage element | |
static | |
BOOST_UBLAS_INLINE | |
size_type element (size_type i, size_type size_i, size_type j, size_type size_j) { | |
BOOST_UBLAS_CHECK (i < size_i, bad_index ()); | |
BOOST_UBLAS_CHECK (j < size_j, bad_index ()); | |
detail::ignore_unused_variable_warning(size_i); | |
// Guard against size_type overflow | |
BOOST_UBLAS_CHECK (i <= ((std::numeric_limits<size_type>::max) () - j) / size_j, bad_index ()); | |
return i * size_j + j; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type address (size_type i, size_type size_i, size_type j, size_type size_j) { | |
BOOST_UBLAS_CHECK (i <= size_i, bad_index ()); | |
BOOST_UBLAS_CHECK (j <= size_j, bad_index ()); | |
// Guard against size_type overflow - address may be size_j past end of storage | |
BOOST_UBLAS_CHECK (size_j == 0 || i <= ((std::numeric_limits<size_type>::max) () - j) / size_j, bad_index ()); | |
detail::ignore_unused_variable_warning(size_i); | |
return i * size_j + j; | |
} | |
// Storage element to index conversion | |
static | |
BOOST_UBLAS_INLINE | |
difference_type distance_i (difference_type k, size_type /* size_i */, size_type size_j) { | |
return size_j != 0 ? k / size_j : 0; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
difference_type distance_j (difference_type k, size_type /* size_i */, size_type /* size_j */) { | |
return k; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type index_i (difference_type k, size_type /* size_i */, size_type size_j) { | |
return size_j != 0 ? k / size_j : 0; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type index_j (difference_type k, size_type /* size_i */, size_type size_j) { | |
return size_j != 0 ? k % size_j : 0; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool fast_i () { | |
return false; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool fast_j () { | |
return true; | |
} | |
// Iterating storage elements | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void increment_i (I &it, size_type /* size_i */, size_type size_j) { | |
it += size_j; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void increment_i (I &it, difference_type n, size_type /* size_i */, size_type size_j) { | |
it += n * size_j; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void decrement_i (I &it, size_type /* size_i */, size_type size_j) { | |
it -= size_j; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void decrement_i (I &it, difference_type n, size_type /* size_i */, size_type size_j) { | |
it -= n * size_j; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void increment_j (I &it, size_type /* size_i */, size_type /* size_j */) { | |
++ it; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void increment_j (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) { | |
it += n; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void decrement_j (I &it, size_type /* size_i */, size_type /* size_j */) { | |
-- it; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void decrement_j (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) { | |
it -= n; | |
} | |
// Triangular access | |
static | |
BOOST_UBLAS_INLINE | |
size_type triangular_size (size_type size_i, size_type size_j) { | |
size_type size = (std::max) (size_i, size_j); | |
// Guard against size_type overflow - simplified | |
BOOST_UBLAS_CHECK (size == 0 || size / 2 < (std::numeric_limits<size_type>::max) () / size /* +1/2 */, bad_size ()); | |
return ((size + 1) * size) / 2; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type lower_element (size_type i, size_type size_i, size_type j, size_type size_j) { | |
BOOST_UBLAS_CHECK (i < size_i, bad_index ()); | |
BOOST_UBLAS_CHECK (j < size_j, bad_index ()); | |
BOOST_UBLAS_CHECK (i >= j, bad_index ()); | |
detail::ignore_unused_variable_warning(size_i); | |
detail::ignore_unused_variable_warning(size_j); | |
// FIXME size_type overflow | |
// sigma_i (i + 1) = (i + 1) * i / 2 | |
// i = 0 1 2 3, sigma = 0 1 3 6 | |
return ((i + 1) * i) / 2 + j; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type upper_element (size_type i, size_type size_i, size_type j, size_type size_j) { | |
BOOST_UBLAS_CHECK (i < size_i, bad_index ()); | |
BOOST_UBLAS_CHECK (j < size_j, bad_index ()); | |
BOOST_UBLAS_CHECK (i <= j, bad_index ()); | |
// FIXME size_type overflow | |
// sigma_i (size - i) = size * i - i * (i - 1) / 2 | |
// i = 0 1 2 3, sigma = 0 4 7 9 | |
return (i * (2 * (std::max) (size_i, size_j) - i + 1)) / 2 + j - i; | |
} | |
// Major and minor indices | |
static | |
BOOST_UBLAS_INLINE | |
size_type index_M (size_type index1, size_type /* index2 */) { | |
return index1; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type index_m (size_type /* index1 */, size_type index2) { | |
return index2; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type size_M (size_type size_i, size_type /* size_j */) { | |
return size_i; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type size_m (size_type /* size_i */, size_type size_j) { | |
return size_j; | |
} | |
}; | |
// This functor defines storage layout and it's properties | |
// matrix (i,j) -> storage [i + j * size_i] | |
template <class Z, class D> | |
struct basic_column_major { | |
typedef Z size_type; | |
typedef D difference_type; | |
typedef column_major_tag orientation_category; | |
typedef basic_row_major<Z,D> transposed_layout; | |
static | |
BOOST_UBLAS_INLINE | |
size_type storage_size (size_type size_i, size_type size_j) { | |
// Guard against size_type overflow | |
BOOST_UBLAS_CHECK (size_i == 0 || size_j <= (std::numeric_limits<size_type>::max) () / size_i, bad_size ()); | |
return size_i * size_j; | |
} | |
// Indexing conversion to storage element | |
static | |
BOOST_UBLAS_INLINE | |
size_type element (size_type i, size_type size_i, size_type j, size_type size_j) { | |
BOOST_UBLAS_CHECK (i < size_i, bad_index ()); | |
BOOST_UBLAS_CHECK (j < size_j, bad_index ()); | |
detail::ignore_unused_variable_warning(size_j); | |
// Guard against size_type overflow | |
BOOST_UBLAS_CHECK (j <= ((std::numeric_limits<size_type>::max) () - i) / size_i, bad_index ()); | |
return i + j * size_i; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type address (size_type i, size_type size_i, size_type j, size_type size_j) { | |
BOOST_UBLAS_CHECK (i <= size_i, bad_index ()); | |
BOOST_UBLAS_CHECK (j <= size_j, bad_index ()); | |
detail::ignore_unused_variable_warning(size_j); | |
// Guard against size_type overflow - address may be size_i past end of storage | |
BOOST_UBLAS_CHECK (size_i == 0 || j <= ((std::numeric_limits<size_type>::max) () - i) / size_i, bad_index ()); | |
return i + j * size_i; | |
} | |
// Storage element to index conversion | |
static | |
BOOST_UBLAS_INLINE | |
difference_type distance_i (difference_type k, size_type /* size_i */, size_type /* size_j */) { | |
return k; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
difference_type distance_j (difference_type k, size_type size_i, size_type /* size_j */) { | |
return size_i != 0 ? k / size_i : 0; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type index_i (difference_type k, size_type size_i, size_type /* size_j */) { | |
return size_i != 0 ? k % size_i : 0; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type index_j (difference_type k, size_type size_i, size_type /* size_j */) { | |
return size_i != 0 ? k / size_i : 0; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool fast_i () { | |
return true; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool fast_j () { | |
return false; | |
} | |
// Iterating | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void increment_i (I &it, size_type /* size_i */, size_type /* size_j */) { | |
++ it; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void increment_i (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) { | |
it += n; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void decrement_i (I &it, size_type /* size_i */, size_type /* size_j */) { | |
-- it; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void decrement_i (I &it, difference_type n, size_type /* size_i */, size_type /* size_j */) { | |
it -= n; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void increment_j (I &it, size_type size_i, size_type /* size_j */) { | |
it += size_i; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void increment_j (I &it, difference_type n, size_type size_i, size_type /* size_j */) { | |
it += n * size_i; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void decrement_j (I &it, size_type size_i, size_type /* size_j */) { | |
it -= size_i; | |
} | |
template<class I> | |
static | |
BOOST_UBLAS_INLINE | |
void decrement_j (I &it, difference_type n, size_type size_i, size_type /* size_j */) { | |
it -= n* size_i; | |
} | |
// Triangular access | |
static | |
BOOST_UBLAS_INLINE | |
size_type triangular_size (size_type size_i, size_type size_j) { | |
size_type size = (std::max) (size_i, size_j); | |
// Guard against size_type overflow - simplified | |
BOOST_UBLAS_CHECK (size == 0 || size / 2 < (std::numeric_limits<size_type>::max) () / size /* +1/2 */, bad_size ()); | |
return ((size + 1) * size) / 2; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type lower_element (size_type i, size_type size_i, size_type j, size_type size_j) { | |
BOOST_UBLAS_CHECK (i < size_i, bad_index ()); | |
BOOST_UBLAS_CHECK (j < size_j, bad_index ()); | |
BOOST_UBLAS_CHECK (i >= j, bad_index ()); | |
// FIXME size_type overflow | |
// sigma_j (size - j) = size * j - j * (j - 1) / 2 | |
// j = 0 1 2 3, sigma = 0 4 7 9 | |
return i - j + (j * (2 * (std::max) (size_i, size_j) - j + 1)) / 2; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type upper_element (size_type i, size_type size_i, size_type j, size_type size_j) { | |
BOOST_UBLAS_CHECK (i < size_i, bad_index ()); | |
BOOST_UBLAS_CHECK (j < size_j, bad_index ()); | |
BOOST_UBLAS_CHECK (i <= j, bad_index ()); | |
// FIXME size_type overflow | |
// sigma_j (j + 1) = (j + 1) * j / 2 | |
// j = 0 1 2 3, sigma = 0 1 3 6 | |
return i + ((j + 1) * j) / 2; | |
} | |
// Major and minor indices | |
static | |
BOOST_UBLAS_INLINE | |
size_type index_M (size_type /* index1 */, size_type index2) { | |
return index2; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type index_m (size_type index1, size_type /* index2 */) { | |
return index1; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type size_M (size_type /* size_i */, size_type size_j) { | |
return size_j; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type size_m (size_type size_i, size_type /* size_j */) { | |
return size_i; | |
} | |
}; | |
template <class Z> | |
struct basic_full { | |
typedef Z size_type; | |
template<class L> | |
static | |
BOOST_UBLAS_INLINE | |
size_type packed_size (L, size_type size_i, size_type size_j) { | |
return L::storage_size (size_i, size_j); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool zero (size_type /* i */, size_type /* j */) { | |
return false; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool one (size_type /* i */, size_type /* j */) { | |
return false; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool other (size_type /* i */, size_type /* j */) { | |
return true; | |
} | |
// FIXME: this should not be used at all | |
static | |
BOOST_UBLAS_INLINE | |
size_type restrict1 (size_type i, size_type /* j */) { | |
return i; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type restrict2 (size_type /* i */, size_type j) { | |
return j; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type mutable_restrict1 (size_type i, size_type /* j */) { | |
return i; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type mutable_restrict2 (size_type /* i */, size_type j) { | |
return j; | |
} | |
}; | |
namespace detail { | |
template < class L > | |
struct transposed_structure { | |
typedef typename L::size_type size_type; | |
template<class LAYOUT> | |
static | |
BOOST_UBLAS_INLINE | |
size_type packed_size (LAYOUT l, size_type size_i, size_type size_j) { | |
return L::packed_size(l, size_j, size_i); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool zero (size_type i, size_type j) { | |
return L::zero(j, i); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool one (size_type i, size_type j) { | |
return L::one(j, i); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool other (size_type i, size_type j) { | |
return L::other(j, i); | |
} | |
template<class LAYOUT> | |
static | |
BOOST_UBLAS_INLINE | |
size_type element (LAYOUT /* l */, size_type i, size_type size_i, size_type j, size_type size_j) { | |
return L::element(typename LAYOUT::transposed_layout(), j, size_j, i, size_i); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type restrict1 (size_type i, size_type j, size_type size1, size_type size2) { | |
return L::restrict2(j, i, size2, size1); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type restrict2 (size_type i, size_type j, size_type size1, size_type size2) { | |
return L::restrict1(j, i, size2, size1); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type mutable_restrict1 (size_type i, size_type j, size_type size1, size_type size2) { | |
return L::mutable_restrict2(j, i, size2, size1); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type mutable_restrict2 (size_type i, size_type j, size_type size1, size_type size2) { | |
return L::mutable_restrict1(j, i, size2, size1); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_restrict1 (size_type index1, size_type size1, size_type index2, size_type size2) { | |
return L::global_restrict2(index2, size2, index1, size1); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_restrict2 (size_type index1, size_type size1, size_type index2, size_type size2) { | |
return L::global_restrict1(index2, size2, index1, size1); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_mutable_restrict1 (size_type index1, size_type size1, size_type index2, size_type size2) { | |
return L::global_mutable_restrict2(index2, size2, index1, size1); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_mutable_restrict2 (size_type index1, size_type size1, size_type index2, size_type size2) { | |
return L::global_mutable_restrict1(index2, size2, index1, size1); | |
} | |
}; | |
} | |
template <class Z> | |
struct basic_lower { | |
typedef Z size_type; | |
typedef lower_tag triangular_type; | |
template<class L> | |
static | |
BOOST_UBLAS_INLINE | |
size_type packed_size (L, size_type size_i, size_type size_j) { | |
return L::triangular_size (size_i, size_j); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool zero (size_type i, size_type j) { | |
return j > i; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool one (size_type /* i */, size_type /* j */) { | |
return false; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool other (size_type i, size_type j) { | |
return j <= i; | |
} | |
template<class L> | |
static | |
BOOST_UBLAS_INLINE | |
size_type element (L, size_type i, size_type size_i, size_type j, size_type size_j) { | |
return L::lower_element (i, size_i, j, size_j); | |
} | |
// return nearest valid index in column j | |
static | |
BOOST_UBLAS_INLINE | |
size_type restrict1 (size_type i, size_type j, size_type size1, size_type /* size2 */) { | |
return (std::max)(j, (std::min) (size1, i)); | |
} | |
// return nearest valid index in row i | |
static | |
BOOST_UBLAS_INLINE | |
size_type restrict2 (size_type i, size_type j, size_type /* size1 */, size_type /* size2 */) { | |
return (std::max)(size_type(0), (std::min) (i+1, j)); | |
} | |
// return nearest valid mutable index in column j | |
static | |
BOOST_UBLAS_INLINE | |
size_type mutable_restrict1 (size_type i, size_type j, size_type size1, size_type /* size2 */) { | |
return (std::max)(j, (std::min) (size1, i)); | |
} | |
// return nearest valid mutable index in row i | |
static | |
BOOST_UBLAS_INLINE | |
size_type mutable_restrict2 (size_type i, size_type j, size_type /* size1 */, size_type /* size2 */) { | |
return (std::max)(size_type(0), (std::min) (i+1, j)); | |
} | |
// return an index between the first and (1+last) filled row | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_restrict1 (size_type index1, size_type size1, size_type /* index2 */, size_type /* size2 */) { | |
return (std::max)(size_type(0), (std::min)(size1, index1) ); | |
} | |
// return an index between the first and (1+last) filled column | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_restrict2 (size_type /* index1 */, size_type /* size1 */, size_type index2, size_type size2) { | |
return (std::max)(size_type(0), (std::min)(size2, index2) ); | |
} | |
// return an index between the first and (1+last) filled mutable row | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_mutable_restrict1 (size_type index1, size_type size1, size_type /* index2 */, size_type /* size2 */) { | |
return (std::max)(size_type(0), (std::min)(size1, index1) ); | |
} | |
// return an index between the first and (1+last) filled mutable column | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_mutable_restrict2 (size_type /* index1 */, size_type /* size1 */, size_type index2, size_type size2) { | |
return (std::max)(size_type(0), (std::min)(size2, index2) ); | |
} | |
}; | |
// the first row only contains a single 1. Thus it is not stored. | |
template <class Z> | |
struct basic_unit_lower : public basic_lower<Z> { | |
typedef Z size_type; | |
typedef unit_lower_tag triangular_type; | |
template<class L> | |
static | |
BOOST_UBLAS_INLINE | |
size_type packed_size (L, size_type size_i, size_type size_j) { | |
// Zero size strict triangles are bad at this point | |
BOOST_UBLAS_CHECK (size_i != 0 && size_j != 0, bad_index ()); | |
return L::triangular_size (size_i - 1, size_j - 1); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool one (size_type i, size_type j) { | |
return j == i; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool other (size_type i, size_type j) { | |
return j < i; | |
} | |
template<class L> | |
static | |
BOOST_UBLAS_INLINE | |
size_type element (L, size_type i, size_type size_i, size_type j, size_type size_j) { | |
// Zero size strict triangles are bad at this point | |
BOOST_UBLAS_CHECK (size_i != 0 && size_j != 0 && i != 0, bad_index ()); | |
return L::lower_element (i-1, size_i - 1, j, size_j - 1); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type mutable_restrict1 (size_type i, size_type j, size_type size1, size_type /* size2 */) { | |
return (std::max)(j+1, (std::min) (size1, i)); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type mutable_restrict2 (size_type i, size_type j, size_type /* size1 */, size_type /* size2 */) { | |
return (std::max)(size_type(0), (std::min) (i, j)); | |
} | |
// return an index between the first and (1+last) filled mutable row | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_mutable_restrict1 (size_type index1, size_type size1, size_type /* index2 */, size_type /* size2 */) { | |
return (std::max)(size_type(1), (std::min)(size1, index1) ); | |
} | |
// return an index between the first and (1+last) filled mutable column | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_mutable_restrict2 (size_type /* index1 */, size_type /* size1 */, size_type index2, size_type size2) { | |
BOOST_UBLAS_CHECK( size2 >= 1 , external_logic() ); | |
return (std::max)(size_type(0), (std::min)(size2-1, index2) ); | |
} | |
}; | |
// the first row only contains no element. Thus it is not stored. | |
template <class Z> | |
struct basic_strict_lower : public basic_unit_lower<Z> { | |
typedef Z size_type; | |
typedef strict_lower_tag triangular_type; | |
template<class L> | |
static | |
BOOST_UBLAS_INLINE | |
size_type packed_size (L, size_type size_i, size_type size_j) { | |
// Zero size strict triangles are bad at this point | |
BOOST_UBLAS_CHECK (size_i != 0 && size_j != 0, bad_index ()); | |
return L::triangular_size (size_i - 1, size_j - 1); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool zero (size_type i, size_type j) { | |
return j >= i; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool one (size_type /*i*/, size_type /*j*/) { | |
return false; | |
} | |
static | |
BOOST_UBLAS_INLINE | |
bool other (size_type i, size_type j) { | |
return j < i; | |
} | |
template<class L> | |
static | |
BOOST_UBLAS_INLINE | |
size_type element (L, size_type i, size_type size_i, size_type j, size_type size_j) { | |
// Zero size strict triangles are bad at this point | |
BOOST_UBLAS_CHECK (size_i != 0 && size_j != 0 && i != 0, bad_index ()); | |
return L::lower_element (i-1, size_i - 1, j, size_j - 1); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type restrict1 (size_type i, size_type j, size_type size1, size_type size2) { | |
return basic_unit_lower<Z>::mutable_restrict1(i, j, size1, size2); | |
} | |
static | |
BOOST_UBLAS_INLINE | |
size_type restrict2 (size_type i, size_type j, size_type size1, size_type size2) { | |
return basic_unit_lower<Z>::mutable_restrict2(i, j, size1, size2); | |
} | |
// return an index between the first and (1+last) filled row | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_restrict1 (size_type index1, size_type size1, size_type index2, size_type size2) { | |
return basic_unit_lower<Z>::global_mutable_restrict1(index1, size1, index2, size2); | |
} | |
// return an index between the first and (1+last) filled column | |
static | |
BOOST_UBLAS_INLINE | |
size_type global_restrict2 (size_type index1, size_type size1, size_type index2, size_type size2) { | |
return basic_unit_lower<Z>::global_mutable_restrict2(index1, size1, index2, size2); | |
} | |
}; | |
template <class Z> | |
struct basic_upper : public detail::transposed_structure<basic_lower<Z> > | |
{ | |
typedef upper_tag triangular_type; | |
}; | |
template <class Z> | |
struct basic_unit_upper : public detail::transposed_structure<basic_unit_lower<Z> > | |
{ | |
typedef unit_upper_tag triangular_type; | |
}; | |
template <class Z> | |
struct basic_strict_upper : public detail::transposed_structure<basic_strict_lower<Z> > | |
{ | |
typedef strict_upper_tag triangular_type; | |
}; | |
}}} | |
#endif |