//
// Copyright (c) 2000-2002
// Joerg Walter, Mathias Koch
//
// Permission to use, copy, modify, distribute and sell this software
// and its documentation for any purpose is hereby granted without fee,
// provided that the above copyright notice appear in all copies and
// that both that copyright notice and this permission notice appear
// in supporting documentation. The authors make no representations
// about the suitability of this software for any purpose.
// It is provided "as is" without express or implied warranty.
//
// 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
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 T>
struct vector_scalar_unary_functor {
typedef std::size_t size_type;
typedef std::ptrdiff_t difference_type;
typedef T value_type;
typedef T result_type;
};
template<class T>
struct vector_sum:
public vector_scalar_unary_functor<T> {
typedef typename vector_scalar_unary_functor<T>::size_type size_type;
typedef typename vector_scalar_unary_functor<T>::difference_type difference_type;
typedef typename vector_scalar_unary_functor<T>::value_type value_type;
typedef typename vector_scalar_unary_functor<T>::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);
size_type size (e ().size ());
for (size_type i = 0; i < size; ++ i)
t += e () (i);
return t;
}
// Dense case
template<class I>
static BOOST_UBLAS_INLINE
result_type apply (difference_type 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 T>
struct vector_scalar_real_unary_functor {
typedef std::size_t size_type;
typedef std::ptrdiff_t difference_type;
typedef T value_type;
typedef typename type_traits<T>::real_type real_type;
typedef real_type result_type;
};
template<class T>
struct vector_norm_1:
public vector_scalar_real_unary_functor<T> {
typedef typename vector_scalar_real_unary_functor<T>::size_type size_type;
typedef typename vector_scalar_real_unary_functor<T>::difference_type difference_type;
typedef typename vector_scalar_real_unary_functor<T>::value_type value_type;
typedef typename vector_scalar_real_unary_functor<T>::real_type real_type;
typedef typename vector_scalar_real_unary_functor<T>::result_type result_type;
template<class E>
static BOOST_UBLAS_INLINE
result_type apply (const vector_expression<E> &e) {
real_type t = real_type ();
size_type size (e ().size ());
for (size_type i = 0; i < size; ++ i) {
real_type u (type_traits<value_type>::norm_1 (e () (i)));
t += u;
}
return t;
}
// Dense case
template<class I>
static BOOST_UBLAS_INLINE
result_type apply (difference_type 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 T>
struct vector_norm_2:
public vector_scalar_real_unary_functor<T> {
typedef typename vector_scalar_real_unary_functor<T>::size_type size_type;
typedef typename vector_scalar_real_unary_functor<T>::difference_type difference_type;
typedef typename vector_scalar_real_unary_functor<T>::value_type value_type;
typedef typename vector_scalar_real_unary_functor<T>::real_type real_type;
typedef typename vector_scalar_real_unary_functor<T>::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 ();
size_type size (e ().size ());
for (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>::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 (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>::sqrt (sum_squares);
#endif
}
// Dense case
template<class I>
static BOOST_UBLAS_INLINE
result_type apply (difference_type 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>::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>::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>::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>::sqrt (sum_squares);
#endif
}
};
template<class T>
struct vector_norm_inf:
public vector_scalar_real_unary_functor<T> {
typedef typename vector_scalar_real_unary_functor<T>::size_type size_type;
typedef typename vector_scalar_real_unary_functor<T>::difference_type difference_type;
typedef typename vector_scalar_real_unary_functor<T>::value_type value_type;
typedef typename vector_scalar_real_unary_functor<T>::real_type real_type;
typedef typename vector_scalar_real_unary_functor<T>::result_type result_type;
template<class E>
static BOOST_UBLAS_INLINE
result_type apply (const vector_expression<E> &e) {
real_type t = real_type ();
size_type size (e ().size ());
for (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 I>
static BOOST_UBLAS_INLINE
result_type apply (difference_type 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 T>
struct vector_scalar_index_unary_functor {
typedef std::size_t size_type;
typedef std::ptrdiff_t difference_type;
typedef T value_type;
typedef typename type_traits<T>::real_type real_type;
typedef size_type result_type;
};
template<class T>
struct vector_index_norm_inf:
public vector_scalar_index_unary_functor<T> {
typedef typename vector_scalar_index_unary_functor<T>::size_type size_type;
typedef typename vector_scalar_index_unary_functor<T>::difference_type difference_type;
typedef typename vector_scalar_index_unary_functor<T>::value_type value_type;
typedef typename vector_scalar_index_unary_functor<T>::real_type real_type;
typedef typename vector_scalar_index_unary_functor<T>::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 ();
size_type size (e ().size ());
for (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 I>
static BOOST_UBLAS_INLINE
result_type apply (difference_type 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 T1, class T2, class TR>
struct vector_scalar_binary_functor {
typedef std::size_t size_type;
typedef std::ptrdiff_t difference_type;
typedef TR value_type;
typedef TR result_type;
};
template<class T1, class T2, class TR>
struct vector_inner_prod:
public vector_scalar_binary_functor<T1, T2, TR> {
typedef typename vector_scalar_binary_functor<T1, T2, TR>::size_type size_type ;
typedef typename vector_scalar_binary_functor<T1, T2, TR>::difference_type difference_type;
typedef typename vector_scalar_binary_functor<T1, T2, TR>::value_type value_type;
typedef typename vector_scalar_binary_functor<T1, T2, TR>::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;
size_type size (BOOST_UBLAS_SAME (c1 ().size (), c2 ().size ()));
const T1 *data1 = data_const (c1 ());
const T2 *data2 = data_const (c2 ());
size_type s1 = stride (c1 ());
size_type s2 = stride (c2 ());
result_type t = result_type (0);
if (s1 == 1 && s2 == 1) {
for (size_type i = 0; i < size; ++ i)
t += data1 [i] * data2 [i];
} else if (s2 == 1) {
for (size_type i = 0, i1 = 0; i < size; ++ i, i1 += s1)
t += data1 [i1] * data2 [i];
} else if (s1 == 1) {
for (size_type i = 0, i2 = 0; i < size; ++ i, i2 += s2)
t += data1 [i] * data2 [i2];
} else {
for (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) {
size_type size (BOOST_UBLAS_SAME (e1 ().size (), e2 ().size ()));
result_type t = result_type (0);
#ifndef BOOST_UBLAS_USE_DUFF_DEVICE
for (size_type i = 0; i < size; ++ i)
t += e1 () (i) * e2 () (i);
#else
size_type i (0);
DD (size, 4, r, (t += e1 () (i) * e2 () (i), ++ i));
#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.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) {
result_type t = result_type (0);
if (it1 != it1_end && it2 != it2_end) {
size_type it1_index = it1.index (), 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.index ();
it2_index = it2.index ();
} 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.index ();
else
break;
}
}
}
return t;
}
};
// Matrix functors
// Binary returning vector
template<class T1, class T2, class TR>
struct matrix_vector_binary_functor {
typedef std::size_t size_type;
typedef std::ptrdiff_t difference_type;
typedef TR value_type;
typedef TR result_type;
};
template<class T1, class T2, class TR>
struct matrix_vector_prod1:
public matrix_vector_binary_functor<T1, T2, TR> {
typedef typename matrix_vector_binary_functor<T1, T2, TR>::size_type size_type;
typedef typename matrix_vector_binary_functor<T1, T2, TR>::difference_type difference_type;
typedef typename matrix_vector_binary_functor<T1, T2, TR>::value_type value_type;
typedef typename matrix_vector_binary_functor<T1, T2, TR>::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 T1 *data1 = data_const (c1 ()) + i * stride1 (c1 ());
const T2 *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 T1, class T2, class TR>
struct matrix_vector_prod2:
public matrix_vector_binary_functor<T1, T2, TR> {
typedef typename matrix_vector_binary_functor<T1, T2, TR>::size_type size_type;
typedef typename matrix_vector_binary_functor<T1, T2, TR>::difference_type difference_type;
typedef typename matrix_vector_binary_functor<T1, T2, TR>::value_type value_type;
typedef typename matrix_vector_binary_functor<T1, T2, TR>::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 T1 *data1 = data_const (c1 ());
const T2 *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 T1, class T2, class TR>
struct matrix_matrix_binary_functor {
typedef std::size_t size_type;
typedef std::ptrdiff_t difference_type;
typedef TR value_type;
typedef TR result_type;
};
template<class T1, class T2, class TR>
struct matrix_matrix_prod:
public matrix_matrix_binary_functor<T1, T2, TR> {
typedef typename matrix_matrix_binary_functor<T1, T2, TR>::size_type size_type;
typedef typename matrix_matrix_binary_functor<T1, T2, TR>::difference_type difference_type;
typedef typename matrix_matrix_binary_functor<T1, T2, TR>::value_type value_type;
typedef typename matrix_matrix_binary_functor<T1, T2, TR>::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 T1 *data1 = data_const (c1 ()) + i * stride1 (c1 ());
const T2 *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 = 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 T>
struct matrix_scalar_real_unary_functor {
typedef std::size_t size_type;
typedef std::ptrdiff_t difference_type;
typedef T value_type;
typedef typename type_traits<T>::real_type real_type;
typedef real_type result_type;
};
template<class T>
struct matrix_norm_1:
public matrix_scalar_real_unary_functor<T> {
typedef typename matrix_scalar_real_unary_functor<T>::size_type size_type;
typedef typename matrix_scalar_real_unary_functor<T>::difference_type difference_type;
typedef typename matrix_scalar_real_unary_functor<T>::value_type value_type;
typedef typename matrix_scalar_real_unary_functor<T>::real_type real_type;
typedef typename matrix_scalar_real_unary_functor<T>::result_type result_type;
template<class E>
static BOOST_UBLAS_INLINE
result_type apply (const matrix_expression<E> &e) {
real_type t = real_type ();
size_type size2 (e ().size2 ());
for (size_type j = 0; j < size2; ++ j) {
real_type u = real_type ();
size_type size1 (e ().size1 ());
for (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 T>
struct matrix_norm_frobenius:
public matrix_scalar_real_unary_functor<T> {
typedef typename matrix_scalar_real_unary_functor<T>::size_type size_type;
typedef typename matrix_scalar_real_unary_functor<T>::difference_type difference_type;
typedef typename matrix_scalar_real_unary_functor<T>::value_type value_type;
typedef typename matrix_scalar_real_unary_functor<T>::real_type real_type;
typedef typename matrix_scalar_real_unary_functor<T>::result_type result_type;
template<class E>
static BOOST_UBLAS_INLINE
result_type apply (const matrix_expression<E> &e) {
real_type t = real_type ();
size_type size1 (e ().size1 ());
for (size_type i = 0; i < size1; ++ i) {
size_type size2 (e ().size2 ());
for (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>::sqrt (t);
}
};
template<class T>
struct matrix_norm_inf:
public matrix_scalar_real_unary_functor<T> {
typedef typename matrix_scalar_real_unary_functor<T>::size_type size_type;
typedef typename matrix_scalar_real_unary_functor<T>::difference_type difference_type;
typedef typename matrix_scalar_real_unary_functor<T>::value_type value_type;
typedef typename matrix_scalar_real_unary_functor<T>::real_type real_type;
typedef typename matrix_scalar_real_unary_functor<T>::result_type result_type;
template<class E>
static BOOST_UBLAS_INLINE
result_type apply (const matrix_expression<E> &e) {
real_type t = real_type ();
size_type size1 (e ().size1 ());
for (size_type i = 0; i < size1; ++ i) {
real_type u = real_type ();
size_type size2 (e ().size2 ());
for (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;
}
};
// This functor computes the address translation
// matrix [i] [j] -> storage [i * size2 + j]
template <class Z, class D>
struct basic_row_major {
typedef Z size_type;
typedef D difference_type;
typedef row_major_tag orientation_category;
static
BOOST_UBLAS_INLINE
size_type storage_size (size_type size1, size_type size2) {
// Guard against size_type overflow
BOOST_UBLAS_CHECK (size2 == 0 || size1 <= (std::numeric_limits<size_type>::max) () / size2, bad_size ());
return size1 * size2;
}
// Indexing
static
BOOST_UBLAS_INLINE
size_type element (size_type i, size_type size1, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (i < size1, bad_index ());
BOOST_UBLAS_CHECK (j < size2, bad_index ());
// Guard against size_type overflow
BOOST_UBLAS_CHECK (i <= ((std::numeric_limits<size_type>::max) () - j) / size2, bad_index ());
return i * size2 + j;
}
static
BOOST_UBLAS_INLINE
size_type address (size_type i, size_type size1, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (i <= size1, bad_index ());
BOOST_UBLAS_CHECK (j <= size2, bad_index ());
// Guard against size_type overflow - address may be size2 past end of storage
BOOST_UBLAS_CHECK (size2 == 0 || i <= ((std::numeric_limits<size_type>::max) () - j) / size2, bad_index ());
return i * size2 + j;
}
static
BOOST_UBLAS_INLINE
difference_type distance1 (difference_type k, size_type /* size1 */, size_type size2) {
return size2 != 0 ? k / size2 : 0;
}
static
BOOST_UBLAS_INLINE
difference_type distance2 (difference_type k, size_type /* size1 */, size_type /* size2 */) {
return k;
}
static
BOOST_UBLAS_INLINE
size_type index1 (difference_type k, size_type /* size1 */, size_type size2) {
return size2 != 0 ? k / size2 : 0;
}
static
BOOST_UBLAS_INLINE
size_type index2 (difference_type k, size_type /* size1 */, size_type size2) {
return size2 != 0 ? k % size2 : 0;
}
static
BOOST_UBLAS_INLINE
bool fast1 () {
return false;
}
static
BOOST_UBLAS_INLINE
size_type one1 (size_type /* size1 */, size_type size2) {
return size2;
}
static
BOOST_UBLAS_INLINE
bool fast2 () {
return true;
}
static
BOOST_UBLAS_INLINE
size_type one2 (size_type /* size1 */, size_type /* size2 */) {
return 1;
}
static
BOOST_UBLAS_INLINE
size_type triangular_size (size_type size1, size_type size2) {
size_type size = (std::max) (size1, size2);
// 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 size1, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (i < size1, bad_index ());
BOOST_UBLAS_CHECK (j < size2, bad_index ());
BOOST_UBLAS_CHECK (i >= j, bad_index ());
// 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 size1, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (i < size1, bad_index ());
BOOST_UBLAS_CHECK (j < size2, 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) (size1, size2) - i + 1)) / 2 + j - i;
}
static
BOOST_UBLAS_INLINE
size_type element1 (size_type i, size_type size1, size_type /* j */, size_type /* size2 */) {
BOOST_UBLAS_CHECK (i < size1, bad_index ());
return i;
}
static
BOOST_UBLAS_INLINE
size_type element2 (size_type /* i */, size_type /* size1 */, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (j < size2, bad_index ());
return j;
}
static
BOOST_UBLAS_INLINE
size_type address1 (size_type i, size_type size1, size_type /* j */, size_type /* size2 */) {
BOOST_UBLAS_CHECK (i <= size1, bad_index ());
return i;
}
static
BOOST_UBLAS_INLINE
size_type address2 (size_type /* i */, size_type /* size1 */, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (j <= size2, bad_index ());
return j;
}
static
BOOST_UBLAS_INLINE
size_type index1 (size_type index1, size_type /* index2 */) {
return index1;
}
static
BOOST_UBLAS_INLINE
size_type index2 (size_type /* index1 */, size_type index2) {
return index2;
}
static
BOOST_UBLAS_INLINE
size_type size1 (size_type size1, size_type /* size2 */) {
return size1;
}
static
BOOST_UBLAS_INLINE
size_type size2 (size_type /* size1 */, size_type size2) {
return size2;
}
// Iterating
template<class I>
static
BOOST_UBLAS_INLINE
void increment1 (I &it, size_type /* size1 */, size_type size2) {
it += size2;
}
template<class I>
static
BOOST_UBLAS_INLINE
void decrement1 (I &it, size_type /* size1 */, size_type size2) {
it -= size2;
}
template<class I>
static
BOOST_UBLAS_INLINE
void increment2 (I &it, size_type /* size1 */, size_type /* size2 */) {
++ it;
}
template<class I>
static
BOOST_UBLAS_INLINE
void decrement2 (I &it, size_type /* size1 */, size_type /* size2 */) {
-- it;
}
};
// This functor computes the address translation
// matrix [i] [j] -> storage [i + j * size1]
template <class Z, class D>
struct basic_column_major {
typedef Z size_type;
typedef D difference_type;
typedef column_major_tag orientation_category;
static
BOOST_UBLAS_INLINE
size_type storage_size (size_type size1, size_type size2) {
// Guard against size_type overflow
BOOST_UBLAS_CHECK (size1 == 0 || size2 <= (std::numeric_limits<size_type>::max) () / size1, bad_size ());
return size1 * size2;
}
// Indexing
static
BOOST_UBLAS_INLINE
size_type element (size_type i, size_type size1, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (i < size1, bad_index ());
BOOST_UBLAS_CHECK (j < size2, bad_index ());
// Guard against size_type overflow
BOOST_UBLAS_CHECK (j <= ((std::numeric_limits<size_type>::max) () - i) / size1, bad_index ());
return i + j * size1;
}
static
BOOST_UBLAS_INLINE
size_type address (size_type i, size_type size1, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (i <= size1, bad_index ());
BOOST_UBLAS_CHECK (j <= size2, bad_index ());
// Guard against size_type overflow - address may be size1 past end of storage
BOOST_UBLAS_CHECK (size1 == 0 || j <= ((std::numeric_limits<size_type>::max) () - i) / size1, bad_index ());
return i + j * size1;
}
static
BOOST_UBLAS_INLINE
difference_type distance1 (difference_type k, size_type /* size1 */, size_type /* size2 */) {
return k;
}
static
BOOST_UBLAS_INLINE
difference_type distance2 (difference_type k, size_type size1, size_type /* size2 */) {
return size1 != 0 ? k / size1 : 0;
}
static
BOOST_UBLAS_INLINE
size_type index1 (difference_type k, size_type size1, size_type /* size2 */) {
return size1 != 0 ? k % size1 : 0;
}
static
BOOST_UBLAS_INLINE
size_type index2 (difference_type k, size_type size1, size_type /* size2 */) {
return size1 != 0 ? k / size1 : 0;
}
static
BOOST_UBLAS_INLINE
bool fast1 () {
return true;
}
static
BOOST_UBLAS_INLINE
size_type one1 (size_type /* size1 */, size_type /* size2 */) {
return 1;
}
static
BOOST_UBLAS_INLINE
bool fast2 () {
return false;
}
static
BOOST_UBLAS_INLINE
size_type one2 (size_type size1, size_type /* size2 */) {
return size1;
}
static
BOOST_UBLAS_INLINE
size_type triangular_size (size_type size1, size_type size2) {
size_type size = (std::max) (size1, size2);
// 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 size1, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (i < size1, bad_index ());
BOOST_UBLAS_CHECK (j < size2, 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) (size1, size2) - j + 1)) / 2;
}
static
BOOST_UBLAS_INLINE
size_type upper_element (size_type i, size_type size1, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (i < size1, bad_index ());
BOOST_UBLAS_CHECK (j < size2, 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;
}
static
BOOST_UBLAS_INLINE
size_type element1 (size_type /* i */, size_type /* size1 */, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (j < size2, bad_index ());
return j;
}
static
BOOST_UBLAS_INLINE
size_type element2 (size_type i, size_type size1, size_type /* j */, size_type /* size2 */) {
BOOST_UBLAS_CHECK (i < size1, bad_index ());
return i;
}
static
BOOST_UBLAS_INLINE
size_type address1 (size_type /* i */, size_type /* size1 */, size_type j, size_type size2) {
BOOST_UBLAS_CHECK (j <= size2, bad_index ());
return j;
}
static
BOOST_UBLAS_INLINE
size_type address2 (size_type i, size_type size1, size_type /* j */, size_type /* size2 */) {
BOOST_UBLAS_CHECK (i <= size1, bad_index ());
return i;
}
static
BOOST_UBLAS_INLINE
size_type index1 (size_type /* index1 */, size_type index2) {
return index2;
}
static
BOOST_UBLAS_INLINE
size_type index2 (size_type index1, size_type /* index2 */) {
return index1;
}
static
BOOST_UBLAS_INLINE
size_type size1 (size_type /* size1 */, size_type size2) {
return size2;
}
static
BOOST_UBLAS_INLINE
size_type size2 (size_type size1, size_type /* size2 */) {
return size1;
}
// Iterating
template<class I>
static
BOOST_UBLAS_INLINE
void increment1 (I &it, size_type /* size1 */, size_type /* size2 */) {
++ it;
}
template<class I>
static
BOOST_UBLAS_INLINE
void decrement1 (I &it, size_type /* size1 */, size_type /* size2 */) {
-- it;
}
template<class I>
static
BOOST_UBLAS_INLINE
void increment2 (I &it, size_type size1, size_type /* size2 */) {
it += size1;
}
template<class I>
static
BOOST_UBLAS_INLINE
void decrement2 (I &it, size_type size1, size_type /* size2 */) {
it -= size1;
}
};
template <class Z>
struct basic_full {
typedef Z size_type;
template<class L>
static
BOOST_UBLAS_INLINE
size_type packed_size (size_type size1, size_type size2) {
return L::storage_size (size1, size2);
}
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;
}
};
template <class Z>
struct basic_lower {
typedef Z size_type;
template<class L>
static
BOOST_UBLAS_INLINE
size_type packed_size (L, size_type size1, size_type size2) {
return L::triangular_size (size1, size2);
}
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 size1, size_type j, size_type size2) {
return L::lower_element (i, size1, j, size2);
}
static
BOOST_UBLAS_INLINE
size_type restrict1 (size_type i, size_type j) {
return (std::max) (i, j);
}
static
BOOST_UBLAS_INLINE
size_type restrict2 (size_type i, size_type j) {
return (std::min) (i + 1, j);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict1 (size_type i, size_type j) {
return (std::max) (i, j);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict2 (size_type i, size_type j) {
return (std::min) (i + 1, j);
}
};
template <class Z>
struct basic_upper {
typedef Z size_type;
template<class L>
static
BOOST_UBLAS_INLINE
size_type packed_size (L, size_type size1, size_type size2) {
return L::triangular_size (size1, size2);
}
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 size1, size_type j, size_type size2) {
return L::upper_element (i, size1, j, size2);
}
static
BOOST_UBLAS_INLINE
size_type restrict1 (size_type i, size_type j) {
return (std::min) (i, j + 1);
}
static
BOOST_UBLAS_INLINE
size_type restrict2 (size_type i, size_type j) {
return (std::max) (i, j);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict1 (size_type i, size_type j) {
return (std::min) (i, j + 1);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict2 (size_type i, size_type j) {
return (std::max) (i, j);
}
};
template <class Z>
struct basic_unit_lower : public basic_lower<Z> {
typedef Z size_type;
template<class L>
static
BOOST_UBLAS_INLINE
size_type packed_size (L, size_type size1, size_type size2) {
// Zero size strict triangles are bad at this point
BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
return L::triangular_size (size1 - 1, size2 - 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 size1, size_type j, size_type size2) {
// Zero size strict triangles are bad at this point
BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
return L::lower_element (i, size1 - 1, j, size2 - 1);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict1 (size_type i, size_type j) {
return (std::max) (i, j);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict2 (size_type i, size_type j) {
return (std::min) (i, j);
}
};
template <class Z>
struct basic_unit_upper : public basic_upper<Z> {
typedef Z size_type;
template<class L>
static
BOOST_UBLAS_INLINE
size_type packed_size (L, size_type size1, size_type size2) {
// Zero size strict triangles are bad at this point
BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
return L::triangular_size (size1 - 1, size2 - 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 size1, size_type j, size_type size2) {
// Zero size strict triangles are bad at this point
BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
return L::upper_element (i, size1 - 1, j, size2 - 1);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict1 (size_type i, size_type j) {
return (std::min) (i, j);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict2 (size_type i, size_type j) {
return (std::max) (i, j);
}
};
template <class Z>
struct basic_strict_lower : public basic_lower<Z> {
typedef Z size_type;
template<class L>
static
BOOST_UBLAS_INLINE
size_type packed_size (L, size_type size1, size_type size2) {
// Zero size strict triangles are bad at this point
BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
return L::triangular_size (size1 - 1, size2 - 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 size1, size_type j, size_type size2) {
// Zero size strict triangles are bad at this point
BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
return L::lower_element (i, size1 - 1, j, size2 - 1);
}
static
BOOST_UBLAS_INLINE
size_type restrict1 (size_type i, size_type j) {
return (std::max) (i, j);
}
static
BOOST_UBLAS_INLINE
size_type restrict2 (size_type i, size_type j) {
return (std::min) (i, j);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict1 (size_type i, size_type j) {
return (std::max) (i, j);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict2 (size_type i, size_type j) {
return (std::min) (i, j);
}
};
template <class Z>
struct basic_strict_upper : public basic_upper<Z> {
typedef Z size_type;
template<class L>
static
BOOST_UBLAS_INLINE
size_type packed_size (L, size_type size1, size_type size2) {
// Zero size strict triangles are bad at this point
BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
return L::triangular_size (size1 - 1, size2 - 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 size1, size_type j, size_type size2) {
// Zero size strict triangles are bad at this point
BOOST_UBLAS_CHECK (size1 != 0 && size2 != 0, bad_index ());
return L::upper_element (i, size1 - 1, j, size2 - 1);
}
static
BOOST_UBLAS_INLINE
size_type restrict1 (size_type i, size_type j) {
return (std::min) (i, j);
}
static
BOOST_UBLAS_INLINE
size_type restrict2 (size_type i, size_type j) {
return (std::max) (i, j);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict1 (size_type i, size_type j) {
return (std::min) (i, j);
}
static
BOOST_UBLAS_INLINE
size_type mutable_restrict2 (size_type i, size_type j) {
return (std::max) (i, j);
}
};
}}}
#endif