eigen/Eigen/src/SparseCore/SparseProduct.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_SPARSEPRODUCT_H
#define EIGEN_SPARSEPRODUCT_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

/** \returns an expression of the product of two sparse matrices.
 * By default a conservative product preserving the symbolic non zeros is performed.
 * The automatic pruning of the small values can be achieved by calling the pruned() function
 * in which case a totally different product algorithm is employed:
 * \code
 * C = (A*B).pruned();             // suppress numerical zeros (exact)
 * C = (A*B).pruned(ref);
 * C = (A*B).pruned(ref,epsilon);
 * \endcode
 * where \c ref is a meaningful non zero reference value.
 * */
template <typename Derived>
template <typename OtherDerived>
inline const Product<Derived, OtherDerived, AliasFreeProduct> SparseMatrixBase<Derived>::operator*(
    const SparseMatrixBase<OtherDerived>& other) const {
  return Product<Derived, OtherDerived, AliasFreeProduct>(derived(), other.derived());
}

namespace internal {

// sparse * sparse
template <typename Lhs, typename Rhs, int ProductType>
struct generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType> {
  template <typename Dest>
  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs) {
    evalTo(dst, lhs, rhs, typename evaluator_traits<Dest>::Shape());
  }

  // dense += sparse * sparse
  template <typename Dest, typename ActualLhs>
  static void addTo(Dest& dst, const ActualLhs& lhs, const Rhs& rhs,
                    std::enable_if_t<is_same<typename evaluator_traits<Dest>::Shape, DenseShape>::value, int*>* = 0) {
    typedef typename nested_eval<ActualLhs, Dynamic>::type LhsNested;
    typedef typename nested_eval<Rhs, Dynamic>::type RhsNested;
    LhsNested lhsNested(lhs);
    RhsNested rhsNested(rhs);
    internal::sparse_sparse_to_dense_product_selector<remove_all_t<LhsNested>, remove_all_t<RhsNested>, Dest>::run(
        lhsNested, rhsNested, dst);
  }

  // dense -= sparse * sparse
  template <typename Dest>
  static void subTo(Dest& dst, const Lhs& lhs, const Rhs& rhs,
                    std::enable_if_t<is_same<typename evaluator_traits<Dest>::Shape, DenseShape>::value, int*>* = 0) {
    addTo(dst, -lhs, rhs);
  }

 protected:
  // sparse = sparse * sparse
  template <typename Dest>
  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, SparseShape) {
    typedef typename nested_eval<Lhs, Dynamic>::type LhsNested;
    typedef typename nested_eval<Rhs, Dynamic>::type RhsNested;
    LhsNested lhsNested(lhs);
    RhsNested rhsNested(rhs);
    internal::conservative_sparse_sparse_product_selector<remove_all_t<LhsNested>, remove_all_t<RhsNested>, Dest>::run(
        lhsNested, rhsNested, dst);
  }

  // dense = sparse * sparse
  template <typename Dest>
  static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, DenseShape) {
    dst.setZero();
    addTo(dst, lhs, rhs);
  }
};

// sparse * sparse-triangular
template <typename Lhs, typename Rhs, int ProductType>
struct generic_product_impl<Lhs, Rhs, SparseShape, SparseTriangularShape, ProductType>
    : public generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType> {};

// sparse-triangular * sparse
template <typename Lhs, typename Rhs, int ProductType>
struct generic_product_impl<Lhs, Rhs, SparseTriangularShape, SparseShape, ProductType>
    : public generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType> {};

// dense = sparse-product (can be sparse*sparse, sparse*perm, etc.)
template <typename DstXprType, typename Lhs, typename Rhs>
struct Assignment<
    DstXprType, Product<Lhs, Rhs, AliasFreeProduct>,
    internal::assign_op<typename DstXprType::Scalar, typename Product<Lhs, Rhs, AliasFreeProduct>::Scalar>,
    Sparse2Dense> {
  typedef Product<Lhs, Rhs, AliasFreeProduct> SrcXprType;
  static void run(DstXprType& dst, const SrcXprType& src,
                  const internal::assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>&) {
    Index dstRows = src.rows();
    Index dstCols = src.cols();
    if ((dst.rows() != dstRows) || (dst.cols() != dstCols)) dst.resize(dstRows, dstCols);

    generic_product_impl<Lhs, Rhs>::evalTo(dst, src.lhs(), src.rhs());
  }
};

// dense += sparse-product (can be sparse*sparse, sparse*perm, etc.)
template <typename DstXprType, typename Lhs, typename Rhs>
struct Assignment<
    DstXprType, Product<Lhs, Rhs, AliasFreeProduct>,
    internal::add_assign_op<typename DstXprType::Scalar, typename Product<Lhs, Rhs, AliasFreeProduct>::Scalar>,
    Sparse2Dense> {
  typedef Product<Lhs, Rhs, AliasFreeProduct> SrcXprType;
  static void run(DstXprType& dst, const SrcXprType& src,
                  const internal::add_assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>&) {
    generic_product_impl<Lhs, Rhs>::addTo(dst, src.lhs(), src.rhs());
  }
};

// dense -= sparse-product (can be sparse*sparse, sparse*perm, etc.)
template <typename DstXprType, typename Lhs, typename Rhs>
struct Assignment<
    DstXprType, Product<Lhs, Rhs, AliasFreeProduct>,
    internal::sub_assign_op<typename DstXprType::Scalar, typename Product<Lhs, Rhs, AliasFreeProduct>::Scalar>,
    Sparse2Dense> {
  typedef Product<Lhs, Rhs, AliasFreeProduct> SrcXprType;
  static void run(DstXprType& dst, const SrcXprType& src,
                  const internal::sub_assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>&) {
    generic_product_impl<Lhs, Rhs>::subTo(dst, src.lhs(), src.rhs());
  }
};

template <typename Lhs, typename Rhs, int Options>
struct unary_evaluator<SparseView<Product<Lhs, Rhs, Options> >, IteratorBased>
    : public evaluator<typename Product<Lhs, Rhs, DefaultProduct>::PlainObject> {
  typedef SparseView<Product<Lhs, Rhs, Options> > XprType;
  typedef typename XprType::PlainObject PlainObject;
  typedef evaluator<PlainObject> Base;

  explicit unary_evaluator(const XprType& xpr) : m_result(xpr.rows(), xpr.cols()) {
    using std::abs;
    internal::construct_at<Base>(this, m_result);
    typedef typename nested_eval<Lhs, Dynamic>::type LhsNested;
    typedef typename nested_eval<Rhs, Dynamic>::type RhsNested;
    LhsNested lhsNested(xpr.nestedExpression().lhs());
    RhsNested rhsNested(xpr.nestedExpression().rhs());

    internal::sparse_sparse_product_with_pruning_selector<remove_all_t<LhsNested>, remove_all_t<RhsNested>,
                                                          PlainObject>::run(lhsNested, rhsNested, m_result,
                                                                            abs(xpr.reference()) * xpr.epsilon());
  }

 protected:
  PlainObject m_result;
};

}  // end namespace internal

// sparse matrix = sparse-product (can be sparse*sparse, sparse*perm, etc.)
template <typename Scalar, int Options_, typename StorageIndex_>
template <typename Lhs, typename Rhs>
SparseMatrix<Scalar, Options_, StorageIndex_>& SparseMatrix<Scalar, Options_, StorageIndex_>::operator=(
    const Product<Lhs, Rhs, AliasFreeProduct>& src) {
  // std::cout << "in Assignment : " << DstOptions << "\n";
  SparseMatrix dst(src.rows(), src.cols());
  internal::generic_product_impl<Lhs, Rhs>::evalTo(dst, src.lhs(), src.rhs());
  this->swap(dst);
  return *this;
}

}  // end namespace Eigen

#endif  // EIGEN_SPARSEPRODUCT_H