tpmv.hpp

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//===========================================================================
/*!
 *
 * \brief       Implements the triangular packed matrix-vector multiplication
 *
 * \author      O. Krause
 * \date        2010
 *
 *
 * \par Copyright 1995-2015 Shark Development Team
 * 
 * <BR><HR>
 * This file is part of Shark.
 * <http://image.diku.dk/shark/>
 * 
 * Shark is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published 
 * by the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * Shark is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with Shark.  If not, see <http://www.gnu.org/licenses/>.
 *
 */
//===========================================================================
#ifndef REMORA_KERNELS_DEFAULT_tpmv_HPP
#define REMORA_KERNELS_DEFAULT_tpmv_HPP
 
#include "../../expression_types.hpp" //matrix/vector_expression
#include "../../detail/traits.hpp" //orientations and triangular types
#include <type_traits> //std::false_type marker for unoptimized
 
 
namespace remora{ namespace bindings{
    
//Lower triangular(row-major) - vector product
// computes the row-wise inner product of the matrix
// starting with row 0 and stores the result in b(i)
//this does not interfere with the next products as 
// the element b(i) is not needed for iterations j > i
template<class MatA, class V>
void tpmv_impl(
    matrix_expression<MatA, cpu_tag> const& A,
    vector_expression<V, cpu_tag>& b,
    row_major,
    upper
){
    typedef typename V::value_type value_type;
    typedef typename V::size_type size_type;
    size_type size = A().size1();
    
    for(size_type i = 0; i != size; ++i){
        value_type sum(0);
        auto end = A().major_end(i);
        for(auto pos = A().major_begin(i); pos != end; ++pos){
            sum += *pos * b()(pos.index());
        }
        b()(i) = sum;
    }
}
 
//Upper triangular(row-major) - vector product
// computes the row-wise inner product of the matrix
// starting with the last row and stores the result in b(i)
// this does not interfere with the next products as 
// the element b(i) is not needed for row products j < i
template<class MatA, class V>
void tpmv_impl(
    matrix_expression<MatA, cpu_tag> const& A,
    vector_expression<V, cpu_tag>& b,
    row_major,
    lower
){
    typedef typename V::value_type value_type;
    typedef typename V::size_type size_type;
    size_type size = A().size1();
    
    for(size_type irev = size; irev != 0; --irev){
        size_type i= irev-1;
        value_type sum(0);
        auto end = A().major_end(i);
        for(auto pos = A().major_begin(i); pos != end; ++pos){
            sum += *pos * b()(pos.index());
        }
        b()(i) = sum;
    }
}
 
//Upper triangular(column-major) - vector product
//computes the product as a series of vector-additions
//on b starting with the last column of A.
template<class MatA, class V>
void tpmv_impl(
    matrix_expression<MatA, cpu_tag> const& A,
    vector_expression<V, cpu_tag>& b,
    column_major,
    upper
){
    typedef typename V::size_type size_type;
    typedef typename V::value_type value_type;
    size_type size = A().size1();
    for(size_type i = 0; i != size; ++i){
        value_type bi = b()(i);
        b()(i)= value_type/*zero*/();
        auto end = A().major_end(i);
        for(auto pos = A().major_begin(i); pos != end; ++pos){
            b()(pos.index()) += *pos*bi;
        }
    }
    
}
 
//Lower triangular(column-major) - vector product
// computes the product as a series of vector-additions
// on b starting with the first column of A.
template<class MatA, class V>
void tpmv_impl(
    matrix_expression<MatA, cpu_tag> const& A,
    vector_expression<V, cpu_tag>& b,
    column_major,
    lower
){
    typedef typename V::size_type size_type;
    typedef typename V::value_type value_type;
    size_type size = A().size1();
    
    for(size_type irev = size; irev != 0; --irev){
        size_type i= irev-1;
        value_type bi = b()(i);
        b()(i)= value_type/*zero*/();
        auto end = A().major_end(i);
        for(auto pos = A().major_begin(i); pos != end; ++pos){
            b()(pos.index()) += *pos*bi;
        }
    }
}
 
//dispatcher
template <typename MatA, typename V>
void tpmv(
    matrix_expression<MatA, cpu_tag> const& A, 
    vector_expression<V, cpu_tag>& b,
    std::false_type//unoptimized
){
    REMORA_SIZE_CHECK(A().size1() == A().size2());
    REMORA_SIZE_CHECK(A().size2() == b().size());   
    tpmv_impl(
        A, b,
        typename MatA::orientation::orientation(),
        typename MatA::orientation::triangular_type()
    );
}
 
}}
#endif