blob: 75127937c77dc3b28a0bcc937951eff43d4eb11a [file]
// 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;
};
// Type trait to detect if a sparse type supports direct compressed storage access
// (i.e., has valuePtr(), innerIndexPtr(), outerIndexPtr(), isCompressed()).
// All types deriving from SparseCompressedBase provide these methods.
template <typename T>
struct has_compressed_storage : std::is_base_of<SparseCompressedBase<T>, T> {};
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;
// RowMajor, single column (ColPerCol=true): CSR SpMV
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;
typedef typename Res::Scalar ResScalar;
static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res,
const typename Res::Scalar& alpha) {
LhsEval lhsEval(lhs);
Index n = lhs.outerSize();
for (Index c = 0; c < rhs.cols(); ++c) {
runCol(lhsEval, lhs, rhs, res, alpha, n, c, std::integral_constant<bool, has_compressed_storage<Lhs>::value>());
}
}
// Direct pointer path: works for both compressed and non-compressed storage.
static void runCol(const LhsEval& /*lhsEval*/, const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res,
const ResScalar& alpha, Index n, Index c, std::true_type /* has_compressed_storage */) {
runColImpl(lhs, rhs, res, alpha, n, c, std::integral_constant<bool, bool(DenseRhsType::Flags & DirectAccessBit)>());
}
template <typename RhsT>
static void runColImpl(const SparseLhsType& lhs, const RhsT& rhs, DenseResType& res, const ResScalar& alpha, Index n,
Index c, std::true_type) {
const Lhs& mat = lhs;
const auto* vals = mat.valuePtr();
const auto* inds = mat.innerIndexPtr();
// Sparse vectors don't store outer indices.
const auto* outer = mat.outerIndexPtr();
const auto* innerNnz = mat.innerNonZeroPtr();
// The fast rhs pointer path requires unit inner stride (common case: VectorXd, contiguous matrix column).
if (rhs.innerStride() == 1) {
const auto* x = rhs.data() + c * rhs.outerStride();
#ifdef EIGEN_HAS_OPENMP
Index threads = Eigen::nbThreads();
if (threads > 1 && mat.nonZeros() > 20000) {
#pragma omp parallel for schedule(dynamic, (n + threads * 4 - 1) / (threads * 4)) num_threads(threads)
for (Index i = 0; i < n; ++i) {
Index k = outer ? outer[i] : 0;
const Index end = innerNnz ? (outer ? outer[i] : 0) + innerNnz[i]
: (outer ? outer[i + 1] : mat.nonZeros());
ResScalar sum0(0), sum1(0);
for (; k < end; ++k) {
sum0 += vals[k] * x[inds[k]];
++k;
if (k < end) {
sum1 += vals[k] * x[inds[k]];
}
}
res.coeffRef(i, c) += alpha * (sum0 + sum1);
}
} else
#endif
{
for (Index i = 0; i < n; ++i) {
Index k = outer ? outer[i] : 0;
const Index end = innerNnz ? (outer ? outer[i] : 0) + innerNnz[i]
: (outer ? outer[i + 1] : mat.nonZeros());
// Two independent accumulators to break the dependency chain
ResScalar sum0(0), sum1(0);
for (; k < end; ++k) {
sum0 += vals[k] * x[inds[k]];
++k;
if (k < end) {
sum1 += vals[k] * x[inds[k]];
}
}
res.coeffRef(i, c) += alpha * (sum0 + sum1);
}
}
} else {
runColImpl(lhs, rhs, res, alpha, n, c, std::false_type());
}
}
// Use fall-back path without direct access to rhs.
template <typename RhsT>
static void runColImpl(const SparseLhsType& lhs, const RhsT& rhs, DenseResType& res, const ResScalar& alpha, Index n,
Index c, std::false_type) {
const Lhs& mat = lhs;
const auto* vals = mat.valuePtr();
const auto* inds = mat.innerIndexPtr();
const auto* outer = mat.outerIndexPtr();
const auto* innerNnz = mat.innerNonZeroPtr();
// Non-unit rhs stride (or no direct access): use direct pointers for sparse side, coeff() for rhs
for (Index i = 0; i < n; ++i) {
Index k = outer ? outer[i] : 0;
const Index end = innerNnz ? (outer ? outer[i] : 0) + innerNnz[i]
: (outer ? outer[i + 1] : mat.nonZeros());
ResScalar sum0(0), sum1(0);
for (; k < end; ++k) {
sum0 += vals[k] * rhs.coeff(inds[k], c);
++k;
if (k < end) {
sum1 += vals[k] * rhs.coeff(inds[k], c);
}
}
res.coeffRef(i, c) += alpha * (sum0 + sum1);
}
}
// Iterator fallback path
static void runCol(const LhsEval& lhsEval, const SparseLhsType& /*lhs*/, const DenseRhsType& rhs, DenseResType& res,
const ResScalar& alpha, Index n, Index c, std::false_type /* has_compressed_storage */) {
#ifdef EIGEN_HAS_OPENMP
Index threads = Eigen::nbThreads();
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 ResScalar& alpha,
Index i, Index col) {
ResScalar tmp_a(0);
ResScalar 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);
}
};
// ColMajor, single column (ColPerCol=true): CSC SpMV
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) {
runImpl(lhs, rhs, res, alpha, std::integral_constant<bool, has_compressed_storage<Lhs>::value>());
}
// Direct pointer path: works for both compressed and non-compressed storage.
static void runImpl(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const AlphaType& alpha,
std::true_type /* has_compressed_storage */) {
typedef typename Lhs::Scalar LhsScalar;
typedef typename Lhs::StorageIndex StorageIndex;
const Lhs& mat = lhs;
const LhsScalar* vals = mat.valuePtr();
const StorageIndex* inds = mat.innerIndexPtr();
// Sparse vectors don't store outer indices.
const auto* outer = mat.outerIndexPtr();
const auto* innerNnz = mat.innerNonZeroPtr();
// The fast result pointer path requires contiguous ColMajor result layout.
// Transpose<ColMajor> reports innerStride()==1 but is actually RowMajor, so check both.
if (!(Res::Flags & RowMajorBit) && res.innerStride() == 1) {
for (Index c = 0; c < rhs.cols(); ++c) {
typename Res::Scalar* y = res.data() + c * res.outerStride();
for (Index j = 0; j < lhs.outerSize(); ++j) {
typename ScalarBinaryOpTraits<AlphaType, typename Rhs::Scalar>::ReturnType rhs_j(alpha * rhs.coeff(j, c));
const Index start = outer ? outer[j] : 0;
const Index end = innerNnz ? start + innerNnz[j] : (outer ? outer[j + 1] : mat.nonZeros());
Index k = start;
// 4-way unrolled scatter-add (no SIMD: writes are scattered)
for (; k + 3 < end; k += 4) {
y[inds[k]] += vals[k] * rhs_j;
y[inds[k + 1]] += vals[k + 1] * rhs_j;
y[inds[k + 2]] += vals[k + 2] * rhs_j;
y[inds[k + 3]] += vals[k + 3] * rhs_j;
}
for (; k < end; ++k) y[inds[k]] += vals[k] * rhs_j;
}
}
} else {
// Non-unit result stride: use coeffRef() for result access
for (Index c = 0; c < rhs.cols(); ++c) {
for (Index j = 0; j < lhs.outerSize(); ++j) {
typename ScalarBinaryOpTraits<AlphaType, typename Rhs::Scalar>::ReturnType rhs_j(alpha * rhs.coeff(j, c));
const Index start = outer ? outer[j] : 0;
const Index end = innerNnz ? start + innerNnz[j] : (outer ? outer[j + 1] : mat.nonZeros());
for (Index k = start; k < end; ++k) res.coeffRef(inds[k], c) += vals[k] * rhs_j;
}
}
}
}
// Iterator-based fallback
static void runImpl(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const AlphaType& alpha,
std::false_type /* has_compressed_storage */) {
LhsEval lhsEval(lhs);
for (Index c = 0; c < rhs.cols(); ++c) {
for (Index j = 0; j < lhs.outerSize(); ++j) {
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;
}
}
}
};
// RowMajor, multiple columns (ColPerCol=false): sparse * dense_matrix
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 constexpr bool IsCompressedLhs = has_compressed_storage<Lhs>::value;
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, lhs, rhs, res, alpha, i, std::integral_constant<bool, IsCompressedLhs>());
} else
#endif
{
for (Index i = 0; i < n; ++i)
processRow(lhsEval, lhs, rhs, res, alpha, i, std::integral_constant<bool, IsCompressedLhs>());
}
}
// Direct pointer path: works for both compressed and non-compressed storage.
static void processRow(const LhsEval& /*lhsEval*/, const SparseLhsType& lhs, const DenseRhsType& rhs, Res& res,
const typename Res::Scalar& alpha, Index i, std::true_type /* has_compressed_storage */) {
typedef typename Lhs::Scalar LhsScalar;
typedef typename Lhs::StorageIndex StorageIndex;
const Lhs& mat = lhs;
const LhsScalar* vals = mat.valuePtr();
const StorageIndex* inds = mat.innerIndexPtr();
// Sparse vectors don't store outer indices.
const Index start = mat.outerIndexPtr() ? mat.outerIndexPtr()[i] : 0;
const auto* innerNnz = mat.innerNonZeroPtr();
const Index end = innerNnz
? start + innerNnz[i]
: (mat.outerIndexPtr() ? mat.outerIndexPtr()[i + 1]
: mat.nonZeros());
typename Res::RowXpr res_i(res.row(i));
for (Index k = start; k < end; ++k) res_i += (alpha * vals[k]) * rhs.row(inds[k]);
}
static void processRow(const LhsEval& lhsEval, const SparseLhsType& /*lhs*/, const DenseRhsType& rhs, Res& res,
const typename Res::Scalar& alpha, Index i, std::false_type /* has_compressed_storage */) {
typename Res::RowXpr res_i(res.row(i));
for (LhsInnerIterator it(lhsEval, i); it; ++it) res_i += (alpha * it.value()) * rhs.row(it.index());
}
};
// ColMajor, multiple columns (ColPerCol=false): sparse * dense_matrix
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) {
runImpl(lhs, rhs, res, alpha, std::integral_constant<bool, has_compressed_storage<Lhs>::value>());
}
// Direct pointer path: works for both compressed and non-compressed storage.
static void runImpl(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res,
const typename Res::Scalar& alpha, std::true_type /* has_compressed_storage */) {
typedef typename Lhs::Scalar LhsScalar;
typedef typename Lhs::StorageIndex StorageIndex;
const Lhs& mat = lhs;
const LhsScalar* vals = mat.valuePtr();
const StorageIndex* inds = mat.innerIndexPtr();
// Sparse vectors don't store outer indices.
const auto* outer = mat.outerIndexPtr();
const auto* innerNnz = mat.innerNonZeroPtr();
for (Index j = 0; j < lhs.outerSize(); ++j) {
typename Rhs::ConstRowXpr rhs_j(rhs.row(j));
const Index start = outer ? outer[j] : 0;
const Index end = innerNnz ? start + innerNnz[j] : (outer ? outer[j + 1] : mat.nonZeros());
for (Index k = start; k < end; ++k) res.row(inds[k]) += (alpha * vals[k]) * rhs_j;
}
}
static void runImpl(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res,
const typename Res::Scalar& alpha, std::false_type /* has_compressed_storage */) {
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