SolveTriangular.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 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_SOLVETRIANGULAR_H
#define EIGEN_SOLVETRIANGULAR_H

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

namespace Eigen {

namespace internal {

// Forward declarations:
// The following two routines are implemented in the products/TriangularSolver*.h files
template <typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
struct triangular_solve_vector;

template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder,
          int OtherStorageOrder, int OtherInnerStride>
struct triangular_solve_matrix;

// small helper struct extracting some traits on the underlying solver operation
template <typename Lhs, typename Rhs, int Side>
class trsolve_traits {
 private:
  enum { RhsIsVectorAtCompileTime = (Side == OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime) == 1 };

 public:
  enum {
    Unrolling = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime != Dynamic && Rhs::SizeAtCompileTime <= 8)
                    ? CompleteUnrolling
                    : NoUnrolling,
    RhsVectors = RhsIsVectorAtCompileTime ? 1 : Dynamic
  };
};

template <typename Lhs, typename Rhs,
          int Side,  // can be OnTheLeft/OnTheRight
          int Mode,  // can be Upper/Lower | UnitDiag
          int Unrolling = trsolve_traits<Lhs, Rhs, Side>::Unrolling,
          int RhsVectors = trsolve_traits<Lhs, Rhs, Side>::RhsVectors>
struct triangular_solver_selector;

template <typename Lhs, typename Rhs, int Side, int Mode>
struct triangular_solver_selector<Lhs, Rhs, Side, Mode, NoUnrolling, 1> {
  typedef typename Lhs::Scalar LhsScalar;
  typedef typename Rhs::Scalar RhsScalar;
  typedef blas_traits<Lhs> LhsProductTraits;
  typedef typename LhsProductTraits::ExtractType ActualLhsType;
  typedef Map<Matrix<RhsScalar, Dynamic, 1>, Aligned> MappedRhs;
  static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs) {
    ActualLhsType actualLhs = LhsProductTraits::extract(lhs);

    // FIXME find a way to allow an inner stride if packet_traits<Scalar>::size==1

    bool useRhsDirectly = Rhs::InnerStrideAtCompileTime == 1 || rhs.innerStride() == 1;

    ei_declare_aligned_stack_constructed_variable(RhsScalar, actualRhs, rhs.size(), (useRhsDirectly ? rhs.data() : 0));

    if (!useRhsDirectly) MappedRhs(actualRhs, rhs.size()) = rhs;

    triangular_solve_vector<LhsScalar, RhsScalar, Index, Side, Mode, LhsProductTraits::NeedToConjugate,
                            (int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor>::run(actualLhs.cols(),
                                                                                        actualLhs.data(),
                                                                                        actualLhs.outerStride(),
                                                                                        actualRhs);

    if (!useRhsDirectly) rhs = MappedRhs(actualRhs, rhs.size());
  }
};

// the rhs is a matrix
template <typename Lhs, typename Rhs, int Side, int Mode>
struct triangular_solver_selector<Lhs, Rhs, Side, Mode, NoUnrolling, Dynamic> {
  typedef typename Rhs::Scalar Scalar;
  typedef blas_traits<Lhs> LhsProductTraits;
  typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;

  static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs) {
    add_const_on_value_type_t<ActualLhsType> actualLhs = LhsProductTraits::extract(lhs);

    const Index size = lhs.rows();
    const Index othersize = Side == OnTheLeft ? rhs.cols() : rhs.rows();

    typedef internal::gemm_blocking_space<(Rhs::Flags & RowMajorBit) ? RowMajor : ColMajor, Scalar, Scalar,
                                          Rhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime,
                                          Lhs::MaxRowsAtCompileTime, 4>
        BlockingType;

    // Nothing to solve.
    if (actualLhs.size() == 0 || rhs.size() == 0) {
      return;
    }

    BlockingType blocking(rhs.rows(), rhs.cols(), size, 1, false);

    triangular_solve_matrix<Scalar, Index, Side, Mode, LhsProductTraits::NeedToConjugate,
                            (int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
                            (Rhs::Flags & RowMajorBit) ? RowMajor : ColMajor,
                            Rhs::InnerStrideAtCompileTime>::run(size, othersize, &actualLhs.coeffRef(0, 0),
                                                                actualLhs.outerStride(), &rhs.coeffRef(0, 0),
                                                                rhs.innerStride(), rhs.outerStride(), blocking);
  }
};

/***************************************************************************
 * meta-unrolling implementation
 ***************************************************************************/

template <typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size, bool Stop = LoopIndex == Size>
struct triangular_solver_unroller;

template <typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>
struct triangular_solver_unroller<Lhs, Rhs, Mode, LoopIndex, Size, false> {
  enum {
    IsLower = ((Mode & Lower) == Lower),
    DiagIndex = IsLower ? LoopIndex : Size - LoopIndex - 1,
    StartIndex = IsLower ? 0 : DiagIndex + 1
  };
  static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs) {
    if (LoopIndex > 0)
      rhs.coeffRef(DiagIndex) -= lhs.row(DiagIndex)
                                     .template segment<LoopIndex>(StartIndex)
                                     .transpose()
                                     .cwiseProduct(rhs.template segment<LoopIndex>(StartIndex))
                                     .sum();

    if (!(Mode & UnitDiag)) rhs.coeffRef(DiagIndex) /= lhs.coeff(DiagIndex, DiagIndex);

    triangular_solver_unroller<Lhs, Rhs, Mode, LoopIndex + 1, Size>::run(lhs, rhs);
  }
};

template <typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>
struct triangular_solver_unroller<Lhs, Rhs, Mode, LoopIndex, Size, true> {
  static EIGEN_DEVICE_FUNC void run(const Lhs&, Rhs&) {}
};

template <typename Lhs, typename Rhs, int Mode>
struct triangular_solver_selector<Lhs, Rhs, OnTheLeft, Mode, CompleteUnrolling, 1> {
  static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs) {
    triangular_solver_unroller<Lhs, Rhs, Mode, 0, Rhs::SizeAtCompileTime>::run(lhs, rhs);
  }
};

template <typename Lhs, typename Rhs, int Mode>
struct triangular_solver_selector<Lhs, Rhs, OnTheRight, Mode, CompleteUnrolling, 1> {
  static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs) {
    Transpose<const Lhs> trLhs(lhs);
    Transpose<Rhs> trRhs(rhs);

    triangular_solver_unroller<Transpose<const Lhs>, Transpose<Rhs>,
                               ((Mode & Upper) == Upper ? Lower : Upper) | (Mode & UnitDiag), 0,
                               Rhs::SizeAtCompileTime>::run(trLhs, trRhs);
  }
};

}  // end namespace internal

/***************************************************************************
 * TriangularView methods
 ***************************************************************************/

#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename MatrixType, unsigned int Mode>
template <int Side, typename OtherDerived>
EIGEN_DEVICE_FUNC void TriangularViewImpl<MatrixType, Mode, Dense>::solveInPlace(
    const MatrixBase<OtherDerived>& _other) const {
  OtherDerived& other = _other.const_cast_derived();
  eigen_assert(derived().cols() == derived().rows() && ((Side == OnTheLeft && derived().cols() == other.rows()) ||
                                                        (Side == OnTheRight && derived().cols() == other.cols())));
  eigen_assert((!(int(Mode) & int(ZeroDiag))) && bool(int(Mode) & (int(Upper) | int(Lower))));
  // If solving for a 0x0 matrix, nothing to do, simply return.
  if (derived().cols() == 0) return;

  enum {
    copy = (internal::traits<OtherDerived>::Flags & RowMajorBit) && OtherDerived::IsVectorAtCompileTime &&
           OtherDerived::SizeAtCompileTime != 1
  };
  typedef std::conditional_t<copy, typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>
      OtherCopy;
  OtherCopy otherCopy(other);

  internal::triangular_solver_selector<MatrixType, std::remove_reference_t<OtherCopy>, Side, Mode>::run(
      derived().nestedExpression(), otherCopy);

  if (copy) other = otherCopy;
}

template <typename Derived, unsigned int Mode>
template <int Side, typename Other>
const internal::triangular_solve_retval<Side, TriangularView<Derived, Mode>, Other>
TriangularViewImpl<Derived, Mode, Dense>::solve(const MatrixBase<Other>& other) const {
  return internal::triangular_solve_retval<Side, TriangularViewType, Other>(derived(), other.derived());
}
#endif

namespace internal {

template <int Side, typename TriangularType, typename Rhs>
struct traits<triangular_solve_retval<Side, TriangularType, Rhs> > {
  typedef typename internal::plain_matrix_type_column_major<Rhs>::type ReturnType;
};

template <int Side, typename TriangularType, typename Rhs>
struct triangular_solve_retval : public ReturnByValue<triangular_solve_retval<Side, TriangularType, Rhs> > {
  typedef remove_all_t<typename Rhs::Nested> RhsNestedCleaned;
  typedef ReturnByValue<triangular_solve_retval> Base;

  triangular_solve_retval(const TriangularType& tri, const Rhs& rhs) : m_triangularMatrix(tri), m_rhs(rhs) {}

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

  template <typename Dest>
  inline void evalTo(Dest& dst) const {
    if (!is_same_dense(dst, m_rhs)) dst = m_rhs;
    m_triangularMatrix.template solveInPlace<Side>(dst);
  }

 protected:
  const TriangularType& m_triangularMatrix;
  typename Rhs::Nested m_rhs;
};

}  // namespace internal

}  // end namespace Eigen

#endif  // EIGEN_SOLVETRIANGULAR_H