/******************************************************************************* * * TRIQS: a Toolbox for Research in Interacting Quantum Systems * * Copyright (C) 2011-2013 by O. Parcollet * * TRIQS is free software: you can redistribute it and/or modify it under the * terms of the GNU General Public License as published by the Free Software * Foundation, either version 3 of the License, or (at your option) any later * version. * * TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along with * TRIQS. If not, see <http://www.gnu.org/licenses/>. * ******************************************************************************/ #ifndef TRIQS_ARRAYS_EXPRESSION_MATRIX_ALGEBRA_H #define TRIQS_ARRAYS_EXPRESSION_MATRIX_ALGEBRA_H #include "./vector_algebra.hpp" #include "../matrix.hpp" #include "../linalg/det_and_inverse.hpp" #include "../blas_lapack/gemv.hpp" #include "../blas_lapack/gemm.hpp" namespace triqs { namespace arrays { // matrix * matrix template<typename A, typename B, typename Enable = void> struct _matmul_rvalue {}; template<typename A, typename B> struct _matmul_rvalue<A,B, ENABLE_IFC(ImmutableMatrix<A>::value && ImmutableMatrix<B>::value)> { typedef typename std::remove_const<typename A::value_type>::type V1; typedef typename std::remove_const<typename B::value_type>::type V2; typedef matrix<typename std::decay<decltype( V1{} * V2{})>::type> type; }; template<typename A, typename B> typename _matmul_rvalue<A,B>::type operator * (A const & a, B const & b) { if (second_dim(a) != first_dim(b)) TRIQS_RUNTIME_ERROR<< "Matrix product : dimension mismatch in A*B "<< a<<" "<< b; auto R = typename _matmul_rvalue<A,B>::type( first_dim(a), second_dim(b)); blas::gemm(1.0,a, b, 0.0, R); return R; } // matrix * vector template<typename M, typename V, typename Enable = void> struct _mat_vec_mul_rvalue {}; template<typename M, typename V> struct _mat_vec_mul_rvalue<M,V, ENABLE_IFC(ImmutableMatrix<M>::value && ImmutableVector<V>::value)> { typedef typename std::remove_const<typename M::value_type>::type V1; typedef typename std::remove_const<typename V::value_type>::type V2; typedef vector<typename std::decay<decltype(V1{} * V2{})>::type> type; }; template<typename M, typename V> typename _mat_vec_mul_rvalue<M,V>::type operator * (M const & m, V const & v) { if (second_dim(m) != v.size()) TRIQS_RUNTIME_ERROR<< "Matrix product : dimension mismatch in Matrix*Vector "<< m<<" "<< v; auto R = typename _mat_vec_mul_rvalue<M,V>::type(first_dim(m)); blas::gemv(1.0,m,v,0.0,R); return R; } // expression template template<typename Tag, typename L, typename R> struct matrix_expr : TRIQS_CONCEPT_TAG_NAME(ImmutableMatrix) { typedef typename std::remove_reference<L>::type L_t; typedef typename std::remove_reference<R>::type R_t; static_assert( get_rank<R_t>::value==0 || get_rank<L_t>::value==0 || get_rank<L_t>::value == get_rank<R_t>::value, "rank mismatch in matrix operations"); typedef typename std::result_of<utility::operation<Tag>(typename L_t::value_type,typename R_t::value_type)>::type value_type; typedef typename std::remove_cv< typename std::remove_reference<typename std::result_of<combine_domain(L_t,R_t)>::type>::type>::type domain_type; L l; R r; template<typename LL, typename RR> matrix_expr(LL && l_, RR && r_) : l(std::forward<LL>(l_)), r(std::forward<RR>(r_)) {} domain_type domain() const { return combine_domain()(l,r); } template<typename ... Args> value_type operator()(Args && ... args) const { return utility::operation<Tag>()(l(std::forward<Args>(args)...) , r(std::forward<Args>(args)...));} friend std::ostream &operator <<(std::ostream &sout, matrix_expr const &expr){return sout << "("<<expr.l << " "<<utility::operation<Tag>::name << " "<<expr.r<<")" ; } }; template<typename L> // a special case : the unary operator ! struct matrix_unary_m_expr : TRIQS_CONCEPT_TAG_NAME(ImmutableMatrix) { typedef typename std::remove_reference<L>::type L_t; typedef typename L_t::value_type value_type; typedef typename L_t::domain_type domain_type; L l; template<typename LL> matrix_unary_m_expr(LL && l_) : l(std::forward<LL>(l_)) {} domain_type domain() const { return l.domain(); } template<typename ... Args> value_type operator()(Args && ... args) const { return -l(std::forward<Args>(args)...);} friend std::ostream &operator <<(std::ostream &sout, matrix_unary_m_expr const &expr){return sout << '-'<<expr.l; } }; // Now we can define all the C++ operators ... #define DEFINE_OPERATOR(TAG, OP, TRAIT1, TRAIT2) \ template<typename A1, typename A2>\ typename std::enable_if<TRAIT1<A1>::value && TRAIT2 <A2>::value, \ matrix_expr<utility::tags::TAG, typename node_t<A1,false>::type, typename node_t<A2,false>::type>>::type\ operator OP (A1 && a1, A2 && a2) { return {std::forward<A1>(a1),std::forward<A2>(a2)};} DEFINE_OPERATOR(plus, +, ImmutableMatrix,ImmutableMatrix); DEFINE_OPERATOR(minus, -, ImmutableMatrix,ImmutableMatrix); DEFINE_OPERATOR(minus, -, ImmutableMatrix,is_in_ZRC); DEFINE_OPERATOR(minus, -, is_in_ZRC,ImmutableMatrix); DEFINE_OPERATOR(multiplies, *, is_in_ZRC,ImmutableMatrix); DEFINE_OPERATOR(multiplies, *, ImmutableMatrix,is_in_ZRC); DEFINE_OPERATOR(divides, /, ImmutableMatrix,is_in_ZRC); #undef DEFINE_OPERATOR // the addition/substraction of diagonal matrix is special : all scalar are diagonal matrices here... #define DEFINE_OPERATOR(TAG, OP, TRAIT1, TRAIT2) \ template<typename A1, typename A2>\ typename std::enable_if<TRAIT1<A1>::value && TRAIT2 <A2>::value, \ matrix_expr<utility::tags::TAG, typename node_t<A1,true>::type, typename node_t<A2,true>::type>>::type\ operator OP (A1 && a1, A2 && a2) { return {std::forward<A1>(a1),std::forward<A2>(a2)};} DEFINE_OPERATOR(plus, +, ImmutableMatrix,is_in_ZRC); DEFINE_OPERATOR(plus, +, is_in_ZRC,ImmutableMatrix); DEFINE_OPERATOR(minus, -, ImmutableMatrix,is_in_ZRC); DEFINE_OPERATOR(minus, -, is_in_ZRC,ImmutableMatrix); #undef DEFINE_OPERATOR // the unary is special template<typename A1> typename std::enable_if< ImmutableMatrix<A1>::value, matrix_unary_m_expr<typename node_t<A1,true>::type > >::type operator - (A1 && a1) { return {std::forward<A1>(a1)};} template<typename M1, typename Enable = typename std::enable_if<ImmutableMatrix<M1>::value>::type > struct _a_div_matrix { template<typename A, typename M> auto operator() (A && a, M && m) DECL_AND_RETURN ( std::forward<A>(a) * inverse(std::forward<M>(m))); }; //typedef decltype ( std::declval<typename std::remove_reference<A>::type>() * inverse(std::declval<typename std::remove_reference<M>::type>() )) type; template<typename A, typename M> // anything / matrix ---> anything * inverse(matrix) //typename boost::lazy_enable_if< ImmutableMatrix<M>, std::result_of<_a_div_matrix(A,M)__type_of_mult_expr_matrix<A,M> >::type //typename std::result_of<_a_div_matrix(A,M)>::type //operator/ (A && a, M && m) {return _a_div_matrix<M>()( std::forward<A>(a), std::forward<M>(m));} auto operator/ (A && a, M && m) DECL_AND_RETURN( _a_div_matrix<M>()( std::forward<A>(a), std::forward<M>(m))); // -> typename std::enable_if< ImmutableMatrix<M>::value, decltype(std::forward<A>(a) * inverse(std::forward<M>(m)))>::type //{ return std::forward<A>(a) * inverse(std::forward<M>(m));} }}//namespace triqs::arrays #endif