opm-simulators/opm/simulators/linalg/DILU.hpp

/*
  Copyright 2022-2023 SINTEF AS
  This file is part of the Open Porous Media project (OPM).
  OPM is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 3 of the License, or
  (at your option) any later version.
  OPM is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.
  You should have received a copy of the GNU General Public License
  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
*/

#ifndef OPM_DILU_HEADER_INCLUDED
#define OPM_DILU_HEADER_INCLUDED

#include <opm/common/ErrorMacros.hpp>
#include <opm/common/TimingMacros.hpp>
#include <opm/simulators/linalg/PreconditionerWithUpdate.hpp>

#include <dune/common/fmatrix.hh>
#include <dune/common/unused.hh>
#include <dune/common/version.hh>
#include <dune/istl/bcrsmatrix.hh>

#include <opm/simulators/linalg/GraphColoring.hpp>

#include <cstddef>
#include <optional>
#include <vector>

#if HAVE_OPENMP
#include <omp.h>
#endif

// TODO: rewrite factory and constructor to keep track of a number of threads variable
namespace Dune
{

/*! \brief The OpenMP thread parallelized DILU preconditioner.
 *  \details Safe to run serially without OpenMP. When run in parallel
             the matrix is assumed to be symmetric.

   \tparam M The matrix type to operate on
   \tparam X Type of the update
   \tparam Y Type of the defect
*/
template <class M, class X, class Y>
class MultithreadDILU : public PreconditionerWithUpdate<X, Y>
{
public:
    //! \brief The matrix type the preconditioner is for.
    using matrix_type = M;
    //! \brief The domain type of the preconditioner.
    using domain_type = X;
    //! \brief The range type of the preconditioner.
    using range_type = Y;
    //! \brief The field type of the preconditioner.
    using field_type = typename X::field_type;
    //! \brief scalar type underlying the field_type

    /*! \brief Constructor gets all parameters to operate the prec.
       \param A The matrix to operate on.
    */
    MultithreadDILU(const M& A)
        : A_(A)
    {
        OPM_TIMEBLOCK(prec_construct);
        // TODO: rewrite so this value is set by an argument to the constructor
#if HAVE_OPENMP
        use_multithreading = omp_get_max_threads() > 1;
#endif

        if (use_multithreading) {
            A_reordered_.emplace(A_.N(), A_.N(), A_.nonzeroes(), M::row_wise);

            //! Assuming symmetric matrices using a lower triangular coloring to construct
            //! the levels is sufficient
            level_sets_ = Opm::getMatrixRowColoring(A_, Opm::ColoringType::LOWER);
            reordered_to_natural_ = std::vector<std::size_t>(A_.N());
            natural_to_reorder_ = std::vector<std::size_t>(A_.N());
            int globCnt = 0;
            for (const auto& level_set : level_sets_) {
                for (const auto j : level_set) {
                    reordered_to_natural_[globCnt] = j;
                    natural_to_reorder_[j] = globCnt++;
                }
            }

            for (auto dst_row_it = A_reordered_->createbegin(); dst_row_it != A_reordered_->createend(); ++dst_row_it) {
                auto src_row = A_.begin() + reordered_to_natural_[dst_row_it.index()];
                // For elements in A
                for (auto elem = src_row->begin(); elem != src_row->end(); elem++) {
                    dst_row_it.insert(elem.index());
                }
            }
        }

        Dinv_.resize(A_.N());
        update();
    }

    /*!
       \brief Update the preconditioner.
       \copydoc Preconditioner::update()
    */
    void update() override
    {
        OPM_TIMEBLOCK(prec_update);
        if (use_multithreading) {
            parallelUpdate();
        } else {
            serialUpdate();
        }
    }

    /*!
       \brief Prepare the preconditioner.
       \copydoc Preconditioner::pre(X&,Y&)
    */
    void pre(X& v, Y& d) override
    {
        DUNE_UNUSED_PARAMETER(v);
        DUNE_UNUSED_PARAMETER(d);
    }


    /*!
       \brief Apply the preconditioner.
       \copydoc Preconditioner::apply(X&,const Y&)
    */
    void apply(X& v, const Y& d) override
    {
        OPM_TIMEBLOCK(prec_apply);
        if (use_multithreading) {
            parallelApply(v, d);
        } else {
            serialApply(v, d);
        }
    }

    /*!
       \brief Clean up.
       \copydoc Preconditioner::post(X&)
    */
    void post(X& x) override
    {
        DUNE_UNUSED_PARAMETER(x);
    }

    std::vector<typename M::block_type> getDiagonal()
    {
        return Dinv_;
    }

    //! Category of the preconditioner (see SolverCategory::Category)
    virtual SolverCategory::Category category() const override
    {
        return SolverCategory::sequential;
    }

private:
    //! \brief The matrix we operate on.
    const M& A_;
    //! \brief Copy of A_ that is reordered to store rows that can be computed simultaneously next to each other to
    //! increase cache usage when multithreading
    std::optional<M> A_reordered_;
    //! \brief The inverse of the diagnal matrix
    std::vector<typename M::block_type> Dinv_;
    //! \brief SparseTable storing each row by level
    Opm::SparseTable<std::size_t> level_sets_;
    //! \brief converts from index in reordered structure to index natural ordered structure
    std::vector<std::size_t> reordered_to_natural_;
    //! \brief converts from index in natural ordered structure to index reordered strucutre
    std::vector<std::size_t> natural_to_reorder_;
    //! \brief Boolean value describing whether or not to use multithreaded version of functions
    bool use_multithreading{false};

    void serialUpdate()
    {
        for (std::size_t row = 0; row < A_.N(); ++row) {
            Dinv_[row] = A_[row][row];
        }
        for (auto row = A_.begin(); row != A_.end(); ++row) {
            const auto row_i = row.index();
            auto Dinv_temp = Dinv_[row_i];
            for (auto a_ij = row->begin(); a_ij.index() < row_i; ++a_ij) {
                const auto col_j = a_ij.index();
                const auto a_ji = A_[col_j].find(row_i);
                // if A[i, j] != 0 and A[j, i] != 0
                if (a_ji != A_[col_j].end()) {
                    // Dinv_temp -= A[i, j] * d[j] * A[j, i]
                    Dinv_temp -= (*a_ij) * Dune::FieldMatrix(Dinv_[col_j]) * (*a_ji);
                }
            }
            Dinv_temp.invert();
            Dinv_[row_i] = Dinv_temp;
        }
    }

    void parallelUpdate()
    {
#ifdef _OPENMP
#pragma omp parallel for
#endif
        for (std::size_t row = 0; row != A_.N(); ++row) {
            Dinv_[natural_to_reorder_[row]] = A_[row][row];
        }

        // TODO: is there a better/faster way of copying all values?
        for (auto dst_row_it = A_reordered_->begin(); dst_row_it != A_reordered_->end(); ++dst_row_it) {
            auto src_row = A_.begin() + reordered_to_natural_[dst_row_it.index()];
            for (auto elem = src_row->begin(); elem != src_row->end(); elem++) {
                (*A_reordered_)[dst_row_it.index()][elem.index()] = *elem;
            }
        }

        int level_start_idx = 0;
        for (int level = 0; level < level_sets_.size(); ++level) {
            const int num_of_rows_in_level = level_sets_[level].size();

#ifdef _OPENMP
#pragma omp parallel for
#endif
            for (int row_idx_in_level = 0; row_idx_in_level < num_of_rows_in_level; ++row_idx_in_level) {
                auto row = A_reordered_->begin() + level_start_idx + row_idx_in_level;
                const auto row_i = reordered_to_natural_[row.index()];
                // auto Dinv_temp = Dinv_[row_i];
                auto Dinv_temp = Dinv_[level_start_idx + row_idx_in_level];
                for (auto a_ij = row->begin(); a_ij.index() < row_i; ++a_ij) {
                    const auto col_j = natural_to_reorder_[a_ij.index()];
                    const auto a_ji = (*A_reordered_)[col_j].find(row_i);
                    if (a_ji != (*A_reordered_)[col_j].end()) {
                        // Dinv_temp -= A[i, j] * d[j] * A[j, i]
                        Dinv_temp -= (*a_ij) * Dune::FieldMatrix(Dinv_[col_j]) * (*a_ji);
                    }
                }
                Dinv_temp.invert();
                Dinv_[level_start_idx + row_idx_in_level] = Dinv_temp;
            }

            level_start_idx += num_of_rows_in_level;
        }
    }

    void serialApply(X& v, const Y& d)
    {
        // M = (D + L_A) D^-1 (D + U_A)   (a LU decomposition of M)
        // where L_A and U_A are the strictly lower and upper parts of A and M has the properties:
        // diag(A) = diag(M)
        // Working with defect d = b - Ax and update v = x_{n+1} - x_n
        // solving the product M^-1(d) using upper and lower triangular solve
        // v = M^{-1}*d = (D + U_A)^{-1} D (D + L_A)^{-1} * d
        // lower triangular solve: (D + L_A) y = d
        using Xblock = typename X::block_type;
        using Yblock = typename Y::block_type;
        {
            OPM_TIMEBLOCK(lower_solve);
            auto endi = A_.end();
            for (auto row = A_.begin(); row != endi; ++row) {
                const auto row_i = row.index();
                Yblock rhs = d[row_i];
                for (auto a_ij = (*row).begin(); a_ij.index() < row_i; ++a_ij) {
                    // if  A[i][j] != 0
                    // rhs -= A[i][j]* y[j], where v_j stores y_j
                    const auto col_j = a_ij.index();
                    a_ij->mmv(v[col_j], rhs);
                }
                // y_i = Dinv_i * rhs
                // storing y_i in v_i
                Dinv_[row_i].mv(rhs, v[row_i]); // (D + L_A)_ii = D_i
            }
        }

        {
            OPM_TIMEBLOCK(upper_solve);

            // upper triangular solve: (D + U_A) v = Dy
            auto rendi = A_.beforeBegin();
            for (auto row = A_.beforeEnd(); row != rendi; --row) {
                const auto row_i = row.index();
                // rhs = 0
                Xblock rhs(0.0);
                for (auto a_ij = (*row).beforeEnd(); a_ij.index() > row_i; --a_ij) {
                    // if A[i][j] != 0
                    // rhs += A[i][j]*v[j]
                    const auto col_j = a_ij.index();
                    a_ij->umv(v[col_j], rhs);
                }
                // calculate update v = M^-1*d
                // v_i = y_i - Dinv_i*rhs
                // before update v_i is y_i
                Dinv_[row_i].mmv(rhs, v[row_i]);
            }
        }
    }

    void parallelApply(X& v, const Y& d)
    {
        using Xblock = typename X::block_type;
        using Yblock = typename Y::block_type;
        {
            OPM_TIMEBLOCK(lower_solve);
            int level_start_idx = 0;
            for (int level = 0; level < level_sets_.size(); ++level) {
                const int num_of_rows_in_level = level_sets_[level].size();

#ifdef _OPENMP
#pragma omp parallel for
#endif
                for (int row_idx_in_level = 0; row_idx_in_level < num_of_rows_in_level; ++row_idx_in_level) {
                    auto row = A_reordered_->begin() + level_start_idx + row_idx_in_level;
                    const auto row_i = reordered_to_natural_[row.index()];
                    Yblock rhs = d[row_i];
                    for (auto a_ij = (*row).begin(); a_ij.index() < row_i; ++a_ij) {
                        // if  A[i][j] != 0
                        // rhs -= A[i][j]* y[j], where v_j stores y_j
                        const auto col_j = a_ij.index();
                        a_ij->mmv(v[col_j], rhs);
                    }
                    // y_i = Dinv_i * rhs
                    // storing y_i in v_i
                    Dinv_[level_start_idx + row_idx_in_level].mv(rhs, v[row_i]); // (D + L_A)_ii = D_i
                }
                level_start_idx += num_of_rows_in_level;
            }
        }

        {
            int level_start_idx = A_.N();
            //  upper triangular solve: (D + U_A) v = Dy
            for (int level = level_sets_.size() - 1; level >= 0; --level) {
                const int num_of_rows_in_level = level_sets_[level].size();
                level_start_idx -= num_of_rows_in_level;
#ifdef _OPENMP
#pragma omp parallel for
#endif
                for (int row_idx_in_level = num_of_rows_in_level - 1; row_idx_in_level >= 0; --row_idx_in_level) {
                    auto row = A_reordered_->begin() + level_start_idx + row_idx_in_level;
                    const auto row_i = reordered_to_natural_[row.index()];
                    Xblock rhs(0.0);
                    for (auto a_ij = (*row).beforeEnd(); a_ij.index() > row_i; --a_ij) {
                        // rhs += A[i][j]*v[j]
                        const auto col_j = a_ij.index();
                        a_ij->umv(v[col_j], rhs);
                    }
                    // calculate update v = M^-1*d
                    // v_i = y_i - Dinv_i*rhs
                    // before update v_i is y_i
                    Dinv_[level_start_idx + row_idx_in_level].mmv(rhs, v[row_i]);
                }
            }
        }
    }
};

} // namespace Dune

#endif