Eigen/src/Core/GeneralProduct.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008-2011 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_GENERAL_PRODUCT_H
#define EIGEN_GENERAL_PRODUCT_H

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

namespace Eigen {

enum { Large = 2, Small = 3 };

// Define the threshold value to fallback from the generic matrix-matrix product
// implementation (heavy) to the lightweight coeff-based product one.
// See generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct>
// in products/GeneralMatrixMatrix.h for more details.
// TODO This threshold should also be used in the compile-time selector below.
#ifndef EIGEN_GEMM_TO_COEFFBASED_THRESHOLD
// This default value has been obtained on a Haswell architecture.
#define EIGEN_GEMM_TO_COEFFBASED_THRESHOLD 20
#endif

namespace internal {

template <int Rows, int Cols, int Depth>
struct product_type_selector;

template <int Size, int MaxSize>
struct product_size_category {
  enum {
#ifndef EIGEN_GPU_COMPILE_PHASE
    is_large = MaxSize == Dynamic || Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ||
               (Size == Dynamic && MaxSize >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD),
#else
    is_large = 0,
#endif
    value = is_large    ? Large
            : Size == 1 ? 1
                        : Small
  };
};

template <typename Lhs, typename Rhs>
struct product_type {
  typedef remove_all_t<Lhs> Lhs_;
  typedef remove_all_t<Rhs> Rhs_;
  enum {
    MaxRows = traits<Lhs_>::MaxRowsAtCompileTime,
    Rows = traits<Lhs_>::RowsAtCompileTime,
    MaxCols = traits<Rhs_>::MaxColsAtCompileTime,
    Cols = traits<Rhs_>::ColsAtCompileTime,
    MaxDepth = min_size_prefer_fixed(traits<Lhs_>::MaxColsAtCompileTime, traits<Rhs_>::MaxRowsAtCompileTime),
    Depth = min_size_prefer_fixed(traits<Lhs_>::ColsAtCompileTime, traits<Rhs_>::RowsAtCompileTime)
  };

  // the splitting into different lines of code here, introducing the _select enums and the typedef below,
  // is to work around an internal compiler error with gcc 4.1 and 4.2.
 private:
  enum {
    rows_select = product_size_category<Rows, MaxRows>::value,
    cols_select = product_size_category<Cols, MaxCols>::value,
    depth_select = product_size_category<Depth, MaxDepth>::value
  };
  typedef product_type_selector<rows_select, cols_select, depth_select> selector;

 public:
  enum { value = selector::ret, ret = selector::ret };
#ifdef EIGEN_DEBUG_PRODUCT
  static void debug() {
    EIGEN_DEBUG_VAR(Rows);
    EIGEN_DEBUG_VAR(Cols);
    EIGEN_DEBUG_VAR(Depth);
    EIGEN_DEBUG_VAR(rows_select);
    EIGEN_DEBUG_VAR(cols_select);
    EIGEN_DEBUG_VAR(depth_select);
    EIGEN_DEBUG_VAR(value);
  }
#endif
};

/* The following allows to select the kind of product at compile time
 * based on the three dimensions of the product.
 * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
// FIXME: the current compile-time product-type mapping may not be optimal.
template <int M, int N>
struct product_type_selector<M, N, 1> {
  enum { ret = OuterProduct };
};
template <int M>
struct product_type_selector<M, 1, 1> {
  enum { ret = LazyCoeffBasedProductMode };
};
template <int N>
struct product_type_selector<1, N, 1> {
  enum { ret = LazyCoeffBasedProductMode };
};
template <int Depth>
struct product_type_selector<1, 1, Depth> {
  enum { ret = InnerProduct };
};
template <>
struct product_type_selector<1, 1, 1> {
  enum { ret = InnerProduct };
};
template <>
struct product_type_selector<Small, 1, Small> {
  enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<1, Small, Small> {
  enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Small, Small, Small> {
  enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Small, Small, 1> {
  enum { ret = LazyCoeffBasedProductMode };
};
template <>
struct product_type_selector<Small, Large, 1> {
  enum { ret = LazyCoeffBasedProductMode };
};
template <>
struct product_type_selector<Large, Small, 1> {
  enum { ret = LazyCoeffBasedProductMode };
};
template <>
struct product_type_selector<1, Large, Small> {
  enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<1, Large, Large> {
  enum { ret = GemvProduct };
};
template <>
struct product_type_selector<1, Small, Large> {
  enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Large, 1, Small> {
  enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Large, 1, Large> {
  enum { ret = GemvProduct };
};
template <>
struct product_type_selector<Small, 1, Large> {
  enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Small, Small, Large> {
  enum { ret = GemmProduct };
};
template <>
struct product_type_selector<Large, Small, Large> {
  enum { ret = GemmProduct };
};
template <>
struct product_type_selector<Small, Large, Large> {
  enum { ret = GemmProduct };
};
template <>
struct product_type_selector<Large, Large, Large> {
  enum { ret = GemmProduct };
};
template <>
struct product_type_selector<Large, Small, Small> {
  enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Small, Large, Small> {
  enum { ret = CoeffBasedProductMode };
};
template <>
struct product_type_selector<Large, Large, Small> {
  enum { ret = GemmProduct };
};

}  // end namespace internal

/***********************************************************************
 *  Implementation of Inner Vector Vector Product
 ***********************************************************************/

// FIXME: consider returning a Scalar instead of a 1x1 matrix for inner products.
// Pro: more natural for the user.
// Con: in a meta-unrolled algorithm a matrix-matrix product may reduce to a
// row-vector times column-vector product. To handle this, we could specialize
// Block<MatrixType,1,1> with operator=(Scalar x).

/***********************************************************************
 *  Implementation of Outer Vector Vector Product
 ***********************************************************************/

/***********************************************************************
 *  Implementation of General Matrix Vector Product
 ***********************************************************************/

/*  According to the shape/flags of the matrix we have to distinguish 3 different cases:
 *   1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
 *   2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
 *   3 - all other cases are handled using a simple loop along the outer-storage direction.
 *  Therefore we need a lower level meta selector.
 *  Furthermore, if the matrix is the rhs, then the product has to be transposed.
 */
namespace internal {

template <int Side, int StorageOrder, bool BlasCompatible>
struct gemv_dense_selector;

}  // end namespace internal

namespace internal {

template <typename Scalar, int Size, int MaxSize, bool Cond>
struct gemv_static_vector_if;

template <typename Scalar, int Size, int MaxSize>
struct gemv_static_vector_if<Scalar, Size, MaxSize, false> {
  EIGEN_DEVICE_FUNC constexpr Scalar* data() {
    eigen_internal_assert(false && "should never be called");
    return 0;
  }
};

template <typename Scalar, int Size>
struct gemv_static_vector_if<Scalar, Size, Dynamic, true> {
  EIGEN_DEVICE_FUNC constexpr Scalar* data() { return 0; }
};

template <typename Scalar, int Size, int MaxSize>
struct gemv_static_vector_if<Scalar, Size, MaxSize, true> {
#if EIGEN_MAX_STATIC_ALIGN_BYTES != 0
  internal::plain_array<Scalar, internal::min_size_prefer_fixed(Size, MaxSize), 0, AlignedMax> m_data;
  constexpr Scalar* data() { return m_data.array; }
#else
  // Some architectures cannot align on the stack,
  // => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
  internal::plain_array<Scalar, internal::min_size_prefer_fixed(Size, MaxSize) + EIGEN_MAX_ALIGN_BYTES, 0> m_data;
  constexpr Scalar* data() {
    return reinterpret_cast<Scalar*>((std::uintptr_t(m_data.array) & ~(std::size_t(EIGEN_MAX_ALIGN_BYTES - 1))) +
                                     EIGEN_MAX_ALIGN_BYTES);
  }
#endif
};

// The vector is on the left => transposition
template <int StorageOrder, bool BlasCompatible>
struct gemv_dense_selector<OnTheLeft, StorageOrder, BlasCompatible> {
  template <typename Lhs, typename Rhs, typename Dest>
  static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
    Transpose<Dest> destT(dest);
    enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
    gemv_dense_selector<OnTheRight, OtherStorageOrder, BlasCompatible>::run(rhs.transpose(), lhs.transpose(), destT,
                                                                            alpha);
  }
};

template <>
struct gemv_dense_selector<OnTheRight, ColMajor, true> {
  template <typename Lhs, typename Rhs, typename Dest>
  static inline void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
    typedef typename Lhs::Scalar LhsScalar;
    typedef typename Rhs::Scalar RhsScalar;
    typedef typename Dest::Scalar ResScalar;

    typedef internal::blas_traits<Lhs> LhsBlasTraits;
    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
    typedef internal::blas_traits<Rhs> RhsBlasTraits;
    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;

    typedef Map<Matrix<ResScalar, Dynamic, 1>, plain_enum_min(AlignedMax, internal::packet_traits<ResScalar>::size)>
        MappedDest;

    ActualLhsType actualLhs = LhsBlasTraits::extract(lhs);
    ActualRhsType actualRhs = RhsBlasTraits::extract(rhs);

    ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);

    // make sure Dest is a compile-time vector type (bug 1166)
    typedef std::conditional_t<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr> ActualDest;

    enum {
      // FIXME: find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
      // on, the other hand it is good for the cache to pack the vector anyways...
      EvalToDestAtCompileTime = (ActualDest::InnerStrideAtCompileTime == 1),
      ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
      MightCannotUseDest = ((!EvalToDestAtCompileTime) || ComplexByReal) && (ActualDest::MaxSizeAtCompileTime != 0)
    };

    typedef const_blas_data_mapper<LhsScalar, Index, ColMajor> LhsMapper;
    typedef const_blas_data_mapper<RhsScalar, Index, RowMajor> RhsMapper;
    RhsScalar compatibleAlpha = get_factor<ResScalar, RhsScalar>::run(actualAlpha);

    if (!MightCannotUseDest) {
      // shortcut if we are sure to be able to use dest directly,
      // this ease the compiler to generate cleaner and more optimzized code for most common cases
      general_matrix_vector_product<Index, LhsScalar, LhsMapper, ColMajor, LhsBlasTraits::NeedToConjugate, RhsScalar,
                                    RhsMapper, RhsBlasTraits::NeedToConjugate>::run(actualLhs.rows(), actualLhs.cols(),
                                                                                    LhsMapper(actualLhs.data(),
                                                                                              actualLhs.outerStride()),
                                                                                    RhsMapper(actualRhs.data(),
                                                                                              actualRhs.innerStride()),
                                                                                    dest.data(), 1, compatibleAlpha);
    } else {
      gemv_static_vector_if<ResScalar, ActualDest::SizeAtCompileTime, ActualDest::MaxSizeAtCompileTime,
                            MightCannotUseDest>
          static_dest;

      const bool alphaIsCompatible = (!ComplexByReal) || (numext::is_exactly_zero(numext::imag(actualAlpha)));
      const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;

      ei_declare_aligned_stack_constructed_variable(ResScalar, actualDestPtr, dest.size(),
                                                    evalToDest ? dest.data() : static_dest.data());

      if (!evalToDest) {
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
        constexpr int Size = Dest::SizeAtCompileTime;
        Index size = dest.size();
        EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#endif
        if (!alphaIsCompatible) {
          MappedDest(actualDestPtr, dest.size()).setZero();
          compatibleAlpha = RhsScalar(1);
        } else
          MappedDest(actualDestPtr, dest.size()) = dest;
      }

      general_matrix_vector_product<Index, LhsScalar, LhsMapper, ColMajor, LhsBlasTraits::NeedToConjugate, RhsScalar,
                                    RhsMapper, RhsBlasTraits::NeedToConjugate>::run(actualLhs.rows(), actualLhs.cols(),
                                                                                    LhsMapper(actualLhs.data(),
                                                                                              actualLhs.outerStride()),
                                                                                    RhsMapper(actualRhs.data(),
                                                                                              actualRhs.innerStride()),
                                                                                    actualDestPtr, 1, compatibleAlpha);

      if (!evalToDest) {
        if (!alphaIsCompatible)
          dest.matrix() += actualAlpha * MappedDest(actualDestPtr, dest.size());
        else
          dest = MappedDest(actualDestPtr, dest.size());
      }
    }
  }
};

template <>
struct gemv_dense_selector<OnTheRight, RowMajor, true> {
  template <typename Lhs, typename Rhs, typename Dest>
  static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
    typedef typename Lhs::Scalar LhsScalar;
    typedef typename Rhs::Scalar RhsScalar;
    typedef typename Dest::Scalar ResScalar;

    typedef internal::blas_traits<Lhs> LhsBlasTraits;
    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
    typedef internal::blas_traits<Rhs> RhsBlasTraits;
    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
    typedef internal::remove_all_t<ActualRhsType> ActualRhsTypeCleaned;

    std::add_const_t<ActualLhsType> actualLhs = LhsBlasTraits::extract(lhs);
    std::add_const_t<ActualRhsType> actualRhs = RhsBlasTraits::extract(rhs);

    ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);

    enum {
      // FIXME: find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
      // on, the other hand it is good for the cache to pack the vector anyways...
      DirectlyUseRhs =
          ActualRhsTypeCleaned::InnerStrideAtCompileTime == 1 || ActualRhsTypeCleaned::MaxSizeAtCompileTime == 0
    };

    gemv_static_vector_if<RhsScalar, ActualRhsTypeCleaned::SizeAtCompileTime,
                          ActualRhsTypeCleaned::MaxSizeAtCompileTime, !DirectlyUseRhs>
        static_rhs;

    ei_declare_aligned_stack_constructed_variable(
        RhsScalar, actualRhsPtr, actualRhs.size(),
        DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());

    if (!DirectlyUseRhs) {
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
      constexpr int Size = ActualRhsTypeCleaned::SizeAtCompileTime;
      Index size = actualRhs.size();
      EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#endif
      Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
    }

    typedef const_blas_data_mapper<LhsScalar, Index, RowMajor> LhsMapper;
    typedef const_blas_data_mapper<RhsScalar, Index, ColMajor> RhsMapper;
    general_matrix_vector_product<Index, LhsScalar, LhsMapper, RowMajor, LhsBlasTraits::NeedToConjugate, RhsScalar,
                                  RhsMapper, RhsBlasTraits::NeedToConjugate>::
        run(actualLhs.rows(), actualLhs.cols(), LhsMapper(actualLhs.data(), actualLhs.outerStride()),
            RhsMapper(actualRhsPtr, 1), dest.data(),
            dest.col(0).innerStride(),  // NOTE  if dest is not a vector at compile-time, then dest.innerStride() might
                                        // be wrong. (bug 1166)
            actualAlpha);
  }
};

template <>
struct gemv_dense_selector<OnTheRight, ColMajor, false> {
  template <typename Lhs, typename Rhs, typename Dest>
  static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
    EIGEN_STATIC_ASSERT((!nested_eval<Lhs, 1>::Evaluate),
                        EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
    // TODO: if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory,
    // otherwise use a temp
    typename nested_eval<Rhs, 1>::type actual_rhs(rhs);
    const Index size = rhs.rows();
    for (Index k = 0; k < size; ++k) dest += (alpha * actual_rhs.coeff(k)) * lhs.col(k);
  }
};

template <>
struct gemv_dense_selector<OnTheRight, RowMajor, false> {
  template <typename Lhs, typename Rhs, typename Dest>
  static void run(const Lhs& lhs, const Rhs& rhs, Dest& dest, const typename Dest::Scalar& alpha) {
    EIGEN_STATIC_ASSERT((!nested_eval<Lhs, 1>::Evaluate),
                        EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
    typename nested_eval<Rhs, Lhs::RowsAtCompileTime>::type actual_rhs(rhs);
    const Index rows = dest.rows();
    for (Index i = 0; i < rows; ++i)
      dest.coeffRef(i) += alpha * (lhs.row(i).cwiseProduct(actual_rhs.transpose())).sum();
  }
};

}  // end namespace internal

/***************************************************************************
 * Implementation of matrix base methods
 ***************************************************************************/

/** \returns the matrix product of \c *this and \a other.
 *
 * \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
 *
 * \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
 */
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Product<Derived, OtherDerived> MatrixBase<Derived>::operator*(
    const MatrixBase<OtherDerived>& other) const {
  // A note regarding the function declaration: In MSVC, this function will sometimes
  // not be inlined since DenseStorage is an unwindable object for dynamic
  // matrices and product types are holding a member to store the result.
  // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
  enum {
    ProductIsValid = Derived::ColsAtCompileTime == Dynamic || OtherDerived::RowsAtCompileTime == Dynamic ||
                     int(Derived::ColsAtCompileTime) == int(OtherDerived::RowsAtCompileTime),
    AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
    SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived, OtherDerived)
  };
  // note to the lost user:
  //    * for a dot product use: v1.dot(v2)
  //    * for a coeff-wise product use: v1.cwiseProduct(v2)
  EIGEN_STATIC_ASSERT(
      ProductIsValid || !(AreVectors && SameSizes),
      INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
                      INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
#ifdef EIGEN_DEBUG_PRODUCT
  internal::product_type<Derived, OtherDerived>::debug();
#endif

  return Product<Derived, OtherDerived>(derived(), other.derived());
}

/** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
 *
 * The returned product will behave like any other expressions: the coefficients of the product will be
 * computed once at a time as requested. This might be useful in some extremely rare cases when only
 * a small and no coherent fraction of the result's coefficients have to be computed.
 *
 * \warning This version of the matrix product can be much much slower. So use it only if you know
 * what you are doing and that you measured a true speed improvement.
 *
 * \sa operator*(const MatrixBase&)
 */
template <typename Derived>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Product<Derived, OtherDerived, LazyProduct>
MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived>& other) const {
  enum {
    ProductIsValid = Derived::ColsAtCompileTime == Dynamic || OtherDerived::RowsAtCompileTime == Dynamic ||
                     int(Derived::ColsAtCompileTime) == int(OtherDerived::RowsAtCompileTime),
    AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
    SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived, OtherDerived)
  };
  // note to the lost user:
  //    * for a dot product use: v1.dot(v2)
  //    * for a coeff-wise product use: v1.cwiseProduct(v2)
  EIGEN_STATIC_ASSERT(
      ProductIsValid || !(AreVectors && SameSizes),
      INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
                      INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)

  return Product<Derived, OtherDerived, LazyProduct>(derived(), other.derived());
}

}  // end namespace Eigen

#endif  // EIGEN_PRODUCT_H