| // |
| // 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 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 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 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 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 |
