unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>
// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>
// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
//
// 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 KRONECKER_TENSOR_PRODUCT_H
#define KRONECKER_TENSOR_PRODUCT_H

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

namespace Eigen {

/*!
 * \ingroup KroneckerProduct_Module
 *
 * \brief The base class of dense and sparse Kronecker product.
 *
 * \tparam Derived is the derived type.
 */
template <typename Derived>
class KroneckerProductBase : public ReturnByValue<Derived> {
 private:
  typedef typename internal::traits<Derived> Traits;
  typedef typename Traits::Scalar Scalar;

 protected:
  typedef typename Traits::Lhs Lhs;
  typedef typename Traits::Rhs Rhs;

 public:
  /*! \brief Constructor. */
  KroneckerProductBase(const Lhs& A, const Rhs& B) : m_A(A), m_B(B) {}

  inline Index rows() const { return m_A.rows() * m_B.rows(); }
  inline Index cols() const { return m_A.cols() * m_B.cols(); }

  /*!
   * This overrides ReturnByValue::coeff because this function is
   * efficient enough.
   */
  Scalar coeff(Index row, Index col) const {
    return m_A.coeff(row / m_B.rows(), col / m_B.cols()) * m_B.coeff(row % m_B.rows(), col % m_B.cols());
  }

  /*!
   * This overrides ReturnByValue::coeff because this function is
   * efficient enough.
   */
  Scalar coeff(Index i) const {
    EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
    return m_A.coeff(i / m_A.size()) * m_B.coeff(i % m_A.size());
  }

 protected:
  typename Lhs::Nested m_A;
  typename Rhs::Nested m_B;
};

/*!
 * \ingroup KroneckerProduct_Module
 *
 * \brief Kronecker tensor product helper class for dense matrices
 *
 * This class is the return value of kroneckerProduct(MatrixBase,
 * MatrixBase). Use the function rather than construct this class
 * directly to avoid specifying template prarameters.
 *
 * \tparam Lhs  Type of the left-hand side, a matrix expression.
 * \tparam Rhs  Type of the rignt-hand side, a matrix expression.
 */
template <typename Lhs, typename Rhs>
class KroneckerProduct : public KroneckerProductBase<KroneckerProduct<Lhs, Rhs> > {
 private:
  typedef KroneckerProductBase<KroneckerProduct> Base;
  using Base::m_A;
  using Base::m_B;

 public:
  /*! \brief Constructor. */
  KroneckerProduct(const Lhs& A, const Rhs& B) : Base(A, B) {}

  /*! \brief Evaluate the Kronecker tensor product. */
  template <typename Dest>
  void evalTo(Dest& dst) const;
};

/*!
 * \ingroup KroneckerProduct_Module
 *
 * \brief Kronecker tensor product helper class for sparse matrices
 *
 * If at least one of the operands is a sparse matrix expression,
 * then this class is returned and evaluates into a sparse matrix.
 *
 * This class is the return value of kroneckerProduct(EigenBase,
 * EigenBase). Use the function rather than construct this class
 * directly to avoid specifying template prarameters.
 *
 * \tparam Lhs  Type of the left-hand side, a matrix expression.
 * \tparam Rhs  Type of the rignt-hand side, a matrix expression.
 */
template <typename Lhs, typename Rhs>
class KroneckerProductSparse : public KroneckerProductBase<KroneckerProductSparse<Lhs, Rhs> > {
 private:
  typedef KroneckerProductBase<KroneckerProductSparse> Base;
  using Base::m_A;
  using Base::m_B;

 public:
  /*! \brief Constructor. */
  KroneckerProductSparse(const Lhs& A, const Rhs& B) : Base(A, B) {}

  /*! \brief Evaluate the Kronecker tensor product. */
  template <typename Dest>
  void evalTo(Dest& dst) const;
};

template <typename Lhs, typename Rhs>
template <typename Dest>
void KroneckerProduct<Lhs, Rhs>::evalTo(Dest& dst) const {
  const int BlockRows = Rhs::RowsAtCompileTime, BlockCols = Rhs::ColsAtCompileTime;
  const Index Br = m_B.rows(), Bc = m_B.cols();
  for (Index i = 0; i < m_A.rows(); ++i)
    for (Index j = 0; j < m_A.cols(); ++j)
      Block<Dest, BlockRows, BlockCols>(dst, i * Br, j * Bc, Br, Bc) = m_A.coeff(i, j) * m_B;
}

template <typename Lhs, typename Rhs>
template <typename Dest>
void KroneckerProductSparse<Lhs, Rhs>::evalTo(Dest& dst) const {
  Index Br = m_B.rows(), Bc = m_B.cols();
  dst.resize(this->rows(), this->cols());
  dst.resizeNonZeros(0);

  // 1 - evaluate the operands if needed:
  typedef typename internal::nested_eval<Lhs, Dynamic>::type Lhs1;
  typedef internal::remove_all_t<Lhs1> Lhs1Cleaned;
  const Lhs1 lhs1(m_A);
  typedef typename internal::nested_eval<Rhs, Dynamic>::type Rhs1;
  typedef internal::remove_all_t<Rhs1> Rhs1Cleaned;
  const Rhs1 rhs1(m_B);

  // 2 - construct respective iterators
  typedef Eigen::InnerIterator<Lhs1Cleaned> LhsInnerIterator;
  typedef Eigen::InnerIterator<Rhs1Cleaned> RhsInnerIterator;

  // compute number of non-zeros per innervectors of dst
  {
    // TODO VectorXi is not necessarily big enough!
    VectorXi nnzA = VectorXi::Zero(Dest::IsRowMajor ? m_A.rows() : m_A.cols());
    for (Index kA = 0; kA < m_A.outerSize(); ++kA)
      for (LhsInnerIterator itA(lhs1, kA); itA; ++itA) nnzA(Dest::IsRowMajor ? itA.row() : itA.col())++;

    VectorXi nnzB = VectorXi::Zero(Dest::IsRowMajor ? m_B.rows() : m_B.cols());
    for (Index kB = 0; kB < m_B.outerSize(); ++kB)
      for (RhsInnerIterator itB(rhs1, kB); itB; ++itB) nnzB(Dest::IsRowMajor ? itB.row() : itB.col())++;

    Matrix<int, Dynamic, Dynamic, ColMajor> nnzAB = nnzB * nnzA.transpose();
    dst.reserve(VectorXi::Map(nnzAB.data(), nnzAB.size()));
  }

  for (Index kA = 0; kA < m_A.outerSize(); ++kA) {
    for (Index kB = 0; kB < m_B.outerSize(); ++kB) {
      for (LhsInnerIterator itA(lhs1, kA); itA; ++itA) {
        for (RhsInnerIterator itB(rhs1, kB); itB; ++itB) {
          Index i = itA.row() * Br + itB.row(), j = itA.col() * Bc + itB.col();
          dst.insert(i, j) = itA.value() * itB.value();
        }
      }
    }
  }
}

namespace internal {

template <typename Lhs_, typename Rhs_>
struct traits<KroneckerProduct<Lhs_, Rhs_> > {
  typedef remove_all_t<Lhs_> Lhs;
  typedef remove_all_t<Rhs_> Rhs;
  typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
  typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;

  enum {
    Rows = size_at_compile_time(traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime),
    Cols = size_at_compile_time(traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime),
    MaxRows = size_at_compile_time(traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime),
    MaxCols = size_at_compile_time(traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime)
  };

  typedef Matrix<Scalar, Rows, Cols> ReturnType;
};

template <typename Lhs_, typename Rhs_>
struct traits<KroneckerProductSparse<Lhs_, Rhs_> > {
  typedef MatrixXpr XprKind;
  typedef remove_all_t<Lhs_> Lhs;
  typedef remove_all_t<Rhs_> Rhs;
  typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
  typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind,
                                              scalar_product_op<typename Lhs::Scalar, typename Rhs::Scalar> >::ret
      StorageKind;
  typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;

  enum {
    LhsFlags = Lhs::Flags,
    RhsFlags = Rhs::Flags,

    RowsAtCompileTime = size_at_compile_time(traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime),
    ColsAtCompileTime = size_at_compile_time(traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime),
    MaxRowsAtCompileTime = size_at_compile_time(traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime),
    MaxColsAtCompileTime = size_at_compile_time(traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime),

    EvalToRowMajor = (int(LhsFlags) & int(RhsFlags) & RowMajorBit),
    RemovedBits = ~(EvalToRowMajor ? 0 : RowMajorBit),

    Flags = ((int(LhsFlags) | int(RhsFlags)) & HereditaryBits & RemovedBits) | EvalBeforeNestingBit,
    CoeffReadCost = HugeCost
  };

  typedef SparseMatrix<Scalar, 0, StorageIndex> ReturnType;
};

}  // end namespace internal

/*!
 * \ingroup KroneckerProduct_Module
 *
 * Computes Kronecker tensor product of two dense matrices
 *
 * \warning If you want to replace a matrix by its Kronecker product
 *          with some matrix, do \b NOT do this:
 * \code
 * A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
 * \endcode
 * instead, use eval() to work around this:
 * \code
 * A = kroneckerProduct(A,B).eval();
 * \endcode
 *
 * \param a  Dense matrix a
 * \param b  Dense matrix b
 * \return   Kronecker tensor product of a and b
 */
template <typename A, typename B>
KroneckerProduct<A, B> kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b) {
  return KroneckerProduct<A, B>(a.derived(), b.derived());
}

/*!
 * \ingroup KroneckerProduct_Module
 *
 * Computes Kronecker tensor product of two matrices, at least one of
 * which is sparse
 *
 * \warning If you want to replace a matrix by its Kronecker product
 *          with some matrix, do \b NOT do this:
 * \code
 * A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
 * \endcode
 * instead, use eval() to work around this:
 * \code
 * A = kroneckerProduct(A,B).eval();
 * \endcode
 *
 * \param a  Dense/sparse matrix a
 * \param b  Dense/sparse matrix b
 * \return   Kronecker tensor product of a and b, stored in a sparse
 *           matrix
 */
template <typename A, typename B>
KroneckerProductSparse<A, B> kroneckerProduct(const EigenBase<A>& a, const EigenBase<B>& b) {
  return KroneckerProductSparse<A, B>(a.derived(), b.derived());
}

}  // end namespace Eigen

#endif  // KRONECKER_TENSOR_PRODUCT_H