Eigen/src/Core/Solve.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 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/.
// SPDX-License-Identifier: MPL-2.0

#ifndef EIGEN_SOLVE_H
#define EIGEN_SOLVE_H

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

namespace Eigen {

template <typename Decomposition, typename RhsType, typename StorageKind>
class SolveImpl;

/** \class Solve
 * \ingroup Core_Module
 *
 * \brief Pseudo expression representing a solving operation
 *
 * \tparam Decomposition the type of the matrix or decomposition object
 * \tparam RhsType the type of the right-hand side
 *
 * This class represents an expression of A.solve(B)
 * and most of the time this is the only way it is used.
 *
 */
namespace internal {

// this solve_traits class permits to determine the evaluation type with respect to storage kind (Dense vs Sparse)
template <typename Decomposition, typename RhsType, typename StorageKind>
struct solve_traits;

template <typename Decomposition, typename RhsType>
struct solve_traits<Decomposition, RhsType, Dense> {
  using PlainObject =
      typename make_proper_matrix_type<typename RhsType::Scalar, Decomposition::ColsAtCompileTime,
                                       RhsType::ColsAtCompileTime, RhsType::PlainObject::Options,
                                       Decomposition::MaxColsAtCompileTime, RhsType::MaxColsAtCompileTime>::type;
};

template <typename Decomposition, typename RhsType>
struct traits<Solve<Decomposition, RhsType> >
    : traits<
          typename solve_traits<Decomposition, RhsType, typename internal::traits<RhsType>::StorageKind>::PlainObject> {
  using PlainObject =
      typename solve_traits<Decomposition, RhsType, typename internal::traits<RhsType>::StorageKind>::PlainObject;
  using StorageIndex =
      typename promote_index_type<typename Decomposition::StorageIndex, typename RhsType::StorageIndex>::type;
  using BaseTraits = traits<PlainObject>;
  enum { Flags = BaseTraits::Flags & RowMajorBit, CoeffReadCost = HugeCost };
};

}  // namespace internal

template <typename Decomposition, typename RhsType>
class Solve : public SolveImpl<Decomposition, RhsType, typename internal::traits<RhsType>::StorageKind> {
 public:
  using PlainObject = typename internal::traits<Solve>::PlainObject;
  using StorageIndex = typename internal::traits<Solve>::StorageIndex;

  Solve(const Decomposition &dec, const RhsType &rhs) : m_dec(dec), m_rhs(rhs) {}

  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_dec.cols(); }
  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_rhs.cols(); }

  EIGEN_DEVICE_FUNC constexpr const Decomposition &dec() const { return m_dec; }
  EIGEN_DEVICE_FUNC constexpr const RhsType &rhs() const { return m_rhs; }

 protected:
  const Decomposition &m_dec;
  const typename internal::ref_selector<RhsType>::type m_rhs;
};

// Specialization of the Solve expression for dense results
template <typename Decomposition, typename RhsType>
class SolveImpl<Decomposition, RhsType, Dense> : public MatrixBase<Solve<Decomposition, RhsType> > {
  using Derived = Solve<Decomposition, RhsType>;

 public:
  using Base = MatrixBase<Solve<Decomposition, RhsType>>;
  EIGEN_DENSE_PUBLIC_INTERFACE(Derived)

 private:
  Scalar coeff(Index row, Index col) const;
  Scalar coeff(Index i) const;
};

// Generic API dispatcher
template <typename Decomposition, typename RhsType, typename StorageKind>
class SolveImpl : public internal::generic_xpr_base<Solve<Decomposition, RhsType>, MatrixXpr, StorageKind>::type {
 public:
  using Base = typename internal::generic_xpr_base<Solve<Decomposition, RhsType>, MatrixXpr, StorageKind>::type;
};

namespace internal {

// Evaluator of Solve -> eval into a temporary
template <typename Decomposition, typename RhsType>
struct evaluator<Solve<Decomposition, RhsType> >
    : public evaluator<typename Solve<Decomposition, RhsType>::PlainObject> {
  using SolveType = Solve<Decomposition, RhsType>;
  using PlainObject = typename SolveType::PlainObject;
  using Base = evaluator<PlainObject>;

  enum { Flags = Base::Flags | EvalBeforeNestingBit };

  EIGEN_DEVICE_FUNC explicit evaluator(const SolveType &solve) : m_result(solve.rows(), solve.cols()) {
    internal::construct_at<Base>(this, m_result);
    solve.dec()._solve_impl(solve.rhs(), m_result);
  }

 protected:
  PlainObject m_result;
};

// Specialization for "dst = dec.solve(rhs)"
// NOTE we need to specialize it for Dense2Dense to avoid ambiguous specialization error and a Sparse2Sparse
// specialization must exist somewhere
template <typename DstXprType, typename DecType, typename RhsType, typename Scalar>
struct Assignment<DstXprType, Solve<DecType, RhsType>, internal::assign_op<Scalar, Scalar>, Dense2Dense> {
  using SrcXprType = Solve<DecType, RhsType>;
  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar, Scalar> &func) {
    resize_if_allowed(dst, src, func);

    src.dec()._solve_impl(src.rhs(), dst);
  }
};

// Specialization for "dst = dec.transpose().solve(rhs)"
template <typename DstXprType, typename DecType, typename RhsType, typename Scalar>
struct Assignment<DstXprType, Solve<Transpose<const DecType>, RhsType>, internal::assign_op<Scalar, Scalar>,
                  Dense2Dense> {
  using SrcXprType = Solve<Transpose<const DecType>, RhsType>;
  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar, Scalar> &func) {
    resize_if_allowed(dst, src, func);

    src.dec().nestedExpression().template _solve_impl_transposed<false>(src.rhs(), dst);
  }
};

// Specialization for "dst = dec.adjoint().solve(rhs)"
template <typename DstXprType, typename DecType, typename RhsType, typename Scalar>
struct Assignment<
    DstXprType,
    Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,
          RhsType>,
    internal::assign_op<Scalar, Scalar>, Dense2Dense> {
  using SrcXprType =
      Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType>>,
            RhsType>;
  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar, Scalar> &func) {
    resize_if_allowed(dst, src, func);

    src.dec().nestedExpression().nestedExpression().template _solve_impl_transposed<true>(src.rhs(), dst);
  }
};

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_SOLVE_H