eigen/Eigen/src/SparseCore/SparseDenseProduct.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_SPARSEDENSEPRODUCT_H
#define EIGEN_SPARSEDENSEPRODUCT_H

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

namespace Eigen {

namespace internal {

template <>
struct product_promote_storage_type<Sparse, Dense, OuterProduct> {
  typedef Sparse ret;
};
template <>
struct product_promote_storage_type<Dense, Sparse, OuterProduct> {
  typedef Sparse ret;
};

template <typename SparseLhsType, typename DenseRhsType, typename DenseResType, typename AlphaType,
          int LhsStorageOrder = ((SparseLhsType::Flags & RowMajorBit) == RowMajorBit) ? RowMajor : ColMajor,
          bool ColPerCol = ((DenseRhsType::Flags & RowMajorBit) == 0) || DenseRhsType::ColsAtCompileTime == 1>
struct sparse_time_dense_product_impl;

template <typename SparseLhsType, typename DenseRhsType, typename DenseResType>
struct sparse_time_dense_product_impl<SparseLhsType, DenseRhsType, DenseResType, typename DenseResType::Scalar,
                                      RowMajor, true> {
  typedef internal::remove_all_t<SparseLhsType> Lhs;
  typedef internal::remove_all_t<DenseRhsType> Rhs;
  typedef internal::remove_all_t<DenseResType> Res;
  typedef typename evaluator<Lhs>::InnerIterator LhsInnerIterator;
  typedef evaluator<Lhs> LhsEval;
  static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res,
                  const typename Res::Scalar& alpha) {
    LhsEval lhsEval(lhs);

    Index n = lhs.outerSize();
#ifdef EIGEN_HAS_OPENMP
    Index threads = Eigen::nbThreads();
#endif

    for (Index c = 0; c < rhs.cols(); ++c) {
#ifdef EIGEN_HAS_OPENMP
      // This 20000 threshold has been found experimentally on 2D and 3D Poisson problems.
      // It basically represents the minimal amount of work to be done to be worth it.
      if (threads > 1 && lhsEval.nonZerosEstimate() > 20000) {
#pragma omp parallel for schedule(dynamic, (n + threads * 4 - 1) / (threads * 4)) num_threads(threads)
        for (Index i = 0; i < n; ++i) processRow(lhsEval, rhs, res, alpha, i, c);
      } else
#endif
      {
        for (Index i = 0; i < n; ++i) processRow(lhsEval, rhs, res, alpha, i, c);
      }
    }
  }

  static void processRow(const LhsEval& lhsEval, const DenseRhsType& rhs, DenseResType& res,
                         const typename Res::Scalar& alpha, Index i, Index col) {
    // Two accumulators, which breaks the dependency chain on the accumulator
    // and allows more instruction-level parallelism in the following loop
    typename Res::Scalar tmp_a(0);
    typename Res::Scalar tmp_b(0);
    for (LhsInnerIterator it(lhsEval, i); it; ++it) {
      tmp_a += it.value() * rhs.coeff(it.index(), col);
      ++it;
      if (it) {
        tmp_b += it.value() * rhs.coeff(it.index(), col);
      }
    }
    res.coeffRef(i, col) += alpha * (tmp_a + tmp_b);
  }
};

// FIXME: what is the purpose of the following specialization? Is it for the BlockedSparse format?
// -> let's disable it for now as it is conflicting with generic scalar*matrix and matrix*scalar operators
// template<typename T1, typename T2/*, int Options_, typename StrideType_*/>
// struct ScalarBinaryOpTraits<T1, Ref<T2/*, Options_, StrideType_*/> >
// {
//   enum {
//     Defined = 1
//   };
//   typedef typename CwiseUnaryOp<scalar_multiple2_op<T1, typename T2::Scalar>, T2>::PlainObject ReturnType;
// };

template <typename SparseLhsType, typename DenseRhsType, typename DenseResType, typename AlphaType>
struct sparse_time_dense_product_impl<SparseLhsType, DenseRhsType, DenseResType, AlphaType, ColMajor, true> {
  typedef internal::remove_all_t<SparseLhsType> Lhs;
  typedef internal::remove_all_t<DenseRhsType> Rhs;
  typedef internal::remove_all_t<DenseResType> Res;
  typedef evaluator<Lhs> LhsEval;
  typedef typename LhsEval::InnerIterator LhsInnerIterator;
  static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const AlphaType& alpha) {
    LhsEval lhsEval(lhs);
    for (Index c = 0; c < rhs.cols(); ++c) {
      for (Index j = 0; j < lhs.outerSize(); ++j) {
        //        typename Res::Scalar rhs_j = alpha * rhs.coeff(j,c);
        typename ScalarBinaryOpTraits<AlphaType, typename Rhs::Scalar>::ReturnType rhs_j(alpha * rhs.coeff(j, c));
        for (LhsInnerIterator it(lhsEval, j); it; ++it) res.coeffRef(it.index(), c) += it.value() * rhs_j;
      }
    }
  }
};

template <typename SparseLhsType, typename DenseRhsType, typename DenseResType>
struct sparse_time_dense_product_impl<SparseLhsType, DenseRhsType, DenseResType, typename DenseResType::Scalar,
                                      RowMajor, false> {
  typedef internal::remove_all_t<SparseLhsType> Lhs;
  typedef internal::remove_all_t<DenseRhsType> Rhs;
  typedef internal::remove_all_t<DenseResType> Res;
  typedef evaluator<Lhs> LhsEval;
  typedef typename LhsEval::InnerIterator LhsInnerIterator;
  static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res,
                  const typename Res::Scalar& alpha) {
    Index n = lhs.rows();
    LhsEval lhsEval(lhs);

#ifdef EIGEN_HAS_OPENMP
    Index threads = Eigen::nbThreads();
    // This 20000 threshold has been found experimentally on 2D and 3D Poisson problems.
    // It basically represents the minimal amount of work to be done to be worth it.
    if (threads > 1 && lhsEval.nonZerosEstimate() * rhs.cols() > 20000) {
#pragma omp parallel for schedule(dynamic, (n + threads * 4 - 1) / (threads * 4)) num_threads(threads)
      for (Index i = 0; i < n; ++i) processRow(lhsEval, rhs, res, alpha, i);
    } else
#endif
    {
      for (Index i = 0; i < n; ++i) processRow(lhsEval, rhs, res, alpha, i);
    }
  }

  static void processRow(const LhsEval& lhsEval, const DenseRhsType& rhs, Res& res, const typename Res::Scalar& alpha,
                         Index i) {
    typename Res::RowXpr res_i(res.row(i));
    for (LhsInnerIterator it(lhsEval, i); it; ++it) res_i += (alpha * it.value()) * rhs.row(it.index());
  }
};

template <typename SparseLhsType, typename DenseRhsType, typename DenseResType>
struct sparse_time_dense_product_impl<SparseLhsType, DenseRhsType, DenseResType, typename DenseResType::Scalar,
                                      ColMajor, false> {
  typedef internal::remove_all_t<SparseLhsType> Lhs;
  typedef internal::remove_all_t<DenseRhsType> Rhs;
  typedef internal::remove_all_t<DenseResType> Res;
  typedef typename evaluator<Lhs>::InnerIterator LhsInnerIterator;
  static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res,
                  const typename Res::Scalar& alpha) {
    evaluator<Lhs> lhsEval(lhs);
    for (Index j = 0; j < lhs.outerSize(); ++j) {
      typename Rhs::ConstRowXpr rhs_j(rhs.row(j));
      for (LhsInnerIterator it(lhsEval, j); it; ++it) res.row(it.index()) += (alpha * it.value()) * rhs_j;
    }
  }
};

template <typename SparseLhsType, typename DenseRhsType, typename DenseResType, typename AlphaType>
inline void sparse_time_dense_product(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res,
                                      const AlphaType& alpha) {
  sparse_time_dense_product_impl<SparseLhsType, DenseRhsType, DenseResType, AlphaType>::run(lhs, rhs, res, alpha);
}

}  // end namespace internal

namespace internal {

template <typename Lhs, typename Rhs, int ProductType>
struct generic_product_impl<Lhs, Rhs, SparseShape, DenseShape, ProductType>
    : generic_product_impl_base<Lhs, Rhs, generic_product_impl<Lhs, Rhs, SparseShape, DenseShape, ProductType> > {
  typedef typename Product<Lhs, Rhs>::Scalar Scalar;

  template <typename Dest>
  static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha) {
    typedef typename nested_eval<Lhs, ((Rhs::Flags & RowMajorBit) == 0) ? 1 : Rhs::ColsAtCompileTime>::type LhsNested;
    typedef typename nested_eval<Rhs, ((Lhs::Flags & RowMajorBit) == 0) ? 1 : Dynamic>::type RhsNested;
    LhsNested lhsNested(lhs);
    RhsNested rhsNested(rhs);
    internal::sparse_time_dense_product(lhsNested, rhsNested, dst, alpha);
  }
};

template <typename Lhs, typename Rhs, int ProductType>
struct generic_product_impl<Lhs, Rhs, SparseTriangularShape, DenseShape, ProductType>
    : generic_product_impl<Lhs, Rhs, SparseShape, DenseShape, ProductType> {};

template <typename Lhs, typename Rhs, int ProductType>
struct generic_product_impl<Lhs, Rhs, DenseShape, SparseShape, ProductType>
    : generic_product_impl_base<Lhs, Rhs, generic_product_impl<Lhs, Rhs, DenseShape, SparseShape, ProductType> > {
  typedef typename Product<Lhs, Rhs>::Scalar Scalar;

  template <typename Dst>
  static void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha) {
    typedef typename nested_eval<Lhs, ((Rhs::Flags & RowMajorBit) == 0) ? Dynamic : 1>::type LhsNested;
    typedef typename nested_eval<Rhs, ((Lhs::Flags & RowMajorBit) == RowMajorBit) ? 1 : Lhs::RowsAtCompileTime>::type
        RhsNested;
    LhsNested lhsNested(lhs);
    RhsNested rhsNested(rhs);

    // transpose everything
    Transpose<Dst> dstT(dst);
    internal::sparse_time_dense_product(rhsNested.transpose(), lhsNested.transpose(), dstT, alpha);
  }
};

template <typename Lhs, typename Rhs, int ProductType>
struct generic_product_impl<Lhs, Rhs, DenseShape, SparseTriangularShape, ProductType>
    : generic_product_impl<Lhs, Rhs, DenseShape, SparseShape, ProductType> {};

template <typename LhsT, typename RhsT, bool NeedToTranspose>
struct sparse_dense_outer_product_evaluator {
 protected:
  typedef std::conditional_t<NeedToTranspose, RhsT, LhsT> Lhs1;
  typedef std::conditional_t<NeedToTranspose, LhsT, RhsT> ActualRhs;
  typedef Product<LhsT, RhsT, DefaultProduct> ProdXprType;

  // if the actual left-hand side is a dense vector,
  // then build a sparse-view so that we can seamlessly iterate over it.
  typedef std::conditional_t<is_same<typename internal::traits<Lhs1>::StorageKind, Sparse>::value, Lhs1,
                             SparseView<Lhs1> >
      ActualLhs;
  typedef std::conditional_t<is_same<typename internal::traits<Lhs1>::StorageKind, Sparse>::value, Lhs1 const&,
                             SparseView<Lhs1> >
      LhsArg;

  typedef evaluator<ActualLhs> LhsEval;
  typedef evaluator<ActualRhs> RhsEval;
  typedef typename evaluator<ActualLhs>::InnerIterator LhsIterator;
  typedef typename ProdXprType::Scalar Scalar;

 public:
  enum { Flags = NeedToTranspose ? RowMajorBit : 0, CoeffReadCost = HugeCost };

  class InnerIterator : public LhsIterator {
   public:
    InnerIterator(const sparse_dense_outer_product_evaluator& xprEval, Index outer)
        : LhsIterator(xprEval.m_lhsXprImpl, 0),
          m_outer(outer),
          m_empty(false),
          m_factor(get(xprEval.m_rhsXprImpl, outer, typename internal::traits<ActualRhs>::StorageKind())) {}

    EIGEN_STRONG_INLINE Index outer() const { return m_outer; }
    EIGEN_STRONG_INLINE Index row() const { return NeedToTranspose ? m_outer : LhsIterator::index(); }
    EIGEN_STRONG_INLINE Index col() const { return NeedToTranspose ? LhsIterator::index() : m_outer; }

    EIGEN_STRONG_INLINE Scalar value() const { return LhsIterator::value() * m_factor; }
    EIGEN_STRONG_INLINE operator bool() const { return LhsIterator::operator bool() && (!m_empty); }

   protected:
    Scalar get(const RhsEval& rhs, Index outer, Dense = Dense()) const { return rhs.coeff(outer); }

    Scalar get(const RhsEval& rhs, Index outer, Sparse = Sparse()) {
      typename RhsEval::InnerIterator it(rhs, outer);
      if (it && it.index() == 0 && it.value() != Scalar(0)) return it.value();
      m_empty = true;
      return Scalar(0);
    }

    Index m_outer;
    bool m_empty;
    Scalar m_factor;
  };

  sparse_dense_outer_product_evaluator(const Lhs1& lhs, const ActualRhs& rhs)
      : m_lhs(lhs), m_lhsXprImpl(m_lhs), m_rhsXprImpl(rhs) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }

  // transpose case
  sparse_dense_outer_product_evaluator(const ActualRhs& rhs, const Lhs1& lhs)
      : m_lhs(lhs), m_lhsXprImpl(m_lhs), m_rhsXprImpl(rhs) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }

 protected:
  const LhsArg m_lhs;
  evaluator<ActualLhs> m_lhsXprImpl;
  evaluator<ActualRhs> m_rhsXprImpl;
};

// sparse * dense outer product
template <typename Lhs, typename Rhs>
struct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, OuterProduct, SparseShape, DenseShape>
    : sparse_dense_outer_product_evaluator<Lhs, Rhs, Lhs::IsRowMajor> {
  typedef sparse_dense_outer_product_evaluator<Lhs, Rhs, Lhs::IsRowMajor> Base;

  typedef Product<Lhs, Rhs> XprType;
  typedef typename XprType::PlainObject PlainObject;

  explicit product_evaluator(const XprType& xpr) : Base(xpr.lhs(), xpr.rhs()) {}
};

template <typename Lhs, typename Rhs>
struct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, OuterProduct, DenseShape, SparseShape>
    : sparse_dense_outer_product_evaluator<Lhs, Rhs, Rhs::IsRowMajor> {
  typedef sparse_dense_outer_product_evaluator<Lhs, Rhs, Rhs::IsRowMajor> Base;

  typedef Product<Lhs, Rhs> XprType;
  typedef typename XprType::PlainObject PlainObject;

  explicit product_evaluator(const XprType& xpr) : Base(xpr.lhs(), xpr.rhs()) {}
};

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_SPARSEDENSEPRODUCT_H