Line data    Source code

       1           0 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : #pragma once
       5             : 
       6             : #include <blaze/math/DynamicMatrix.h>
       7             : #include <blaze/math/DynamicVector.h>
       8             : #include <cstddef>
       9             : #include <tuple>
      10             : #include <utility>
      11             : 
      12             : #include "DataStructures/DataBox/DataBox.hpp"
      13             : #include "DataStructures/DataBox/PrefixHelpers.hpp"
      14             : #include "IO/Logging/Tags.hpp"
      15             : #include "IO/Logging/Verbosity.hpp"
      16             : #include "NumericalAlgorithms/Convergence/Tags.hpp"
      17             : #include "NumericalAlgorithms/LinearSolver/InnerProduct.hpp"
      18             : #include "Parallel/GlobalCache.hpp"
      19             : #include "Parallel/Invoke.hpp"
      20             : #include "Parallel/Printf/Printf.hpp"
      21             : #include "ParallelAlgorithms/LinearSolver/Gmres/Tags/InboxTags.hpp"
      22             : #include "ParallelAlgorithms/LinearSolver/Observe.hpp"
      23             : #include "ParallelAlgorithms/LinearSolver/Tags.hpp"
      24             : #include "Utilities/EqualWithinRoundoff.hpp"
      25             : #include "Utilities/Gsl.hpp"
      26             : #include "Utilities/PrettyType.hpp"
      27             : #include "Utilities/Requires.hpp"
      28             : 
      29             : /// \cond
      30             : namespace tuples {
      31             : template <typename...>
      32             : class TaggedTuple;
      33             : }  // namespace tuples
      34             : /// \endcond
      35             : 
      36             : namespace LinearSolver::gmres::detail {
      37             : 
      38             : template <typename FieldsTag, typename OptionsGroup, typename BroadcastTarget>
      39             : struct InitializeResidualMagnitude {
      40             :  private:
      41             :   using fields_tag = FieldsTag;
      42             :   using residual_magnitude_tag = LinearSolver::Tags::Magnitude<
      43             :       db::add_tag_prefix<LinearSolver::Tags::Residual, fields_tag>>;
      44             :   using initial_residual_magnitude_tag =
      45             :       ::Tags::Initial<residual_magnitude_tag>;
      46             :   using previous_residual_magnitude_tag =
      47             :       ::Tags::Previous<residual_magnitude_tag>;
      48             :   using orthogonalization_history_tag =
      49             :       LinearSolver::Tags::OrthogonalizationHistory<fields_tag>;
      50             : 
      51             :  public:
      52             :   template <typename ParallelComponent, typename DbTagsList,
      53             :             typename Metavariables, typename ArrayIndex,
      54             :             typename DataBox = db::DataBox<DbTagsList>>
      55             :   static void apply(db::DataBox<DbTagsList>& box,
      56             :                     Parallel::GlobalCache<Metavariables>& cache,
      57             :                     const ArrayIndex& /*array_index*/,
      58             :                     const double residual_magnitude) {
      59             :     constexpr size_t iteration_id = 0;
      60             : 
      61             :     db::mutate<initial_residual_magnitude_tag, previous_residual_magnitude_tag>(
      62             :         [residual_magnitude](
      63             :             const gsl::not_null<double*> initial_residual_magnitude,
      64             :             const gsl::not_null<double*> previous_residual_magnitude) {
      65             :           *initial_residual_magnitude = residual_magnitude;
      66             :           *previous_residual_magnitude = residual_magnitude;
      67             :         },
      68             :         make_not_null(&box));
      69             : 
      70             :     LinearSolver::observe_detail::contribute_to_reduction_observer<
      71             :         OptionsGroup, ParallelComponent>(iteration_id, residual_magnitude,
      72             :                                          cache);
      73             : 
      74             :     // Determine whether the linear solver has already converged
      75             :     Convergence::HasConverged has_converged{
      76             :         get<Convergence::Tags::Criteria<OptionsGroup>>(box), iteration_id,
      77             :         residual_magnitude, residual_magnitude};
      78             : 
      79             :     // Do some logging
      80             :     if (UNLIKELY(get<logging::Tags::Verbosity<OptionsGroup>>(cache) >=
      81             :                  ::Verbosity::Quiet)) {
      82             :       Parallel::printf("%s initialized with residual: %e\n",
      83             :                        pretty_type::name<OptionsGroup>(), residual_magnitude);
      84             :     }
      85             :     if (UNLIKELY(has_converged and get<logging::Tags::Verbosity<OptionsGroup>>(
      86             :                                        cache) >= ::Verbosity::Quiet)) {
      87             :       Parallel::printf("%s has converged without any iterations: %s\n",
      88             :                        pretty_type::name<OptionsGroup>(), has_converged);
      89             :     }
      90             : 
      91             :     Parallel::receive_data<Tags::InitialOrthogonalization<OptionsGroup>>(
      92             :         Parallel::get_parallel_component<BroadcastTarget>(cache), iteration_id,
      93             :         // NOLINTNEXTLINE(performance-move-const-arg)
      94             :         std::make_tuple(residual_magnitude, std::move(has_converged)));
      95             :   }
      96             : };
      97             : 
      98             : template <typename FieldsTag, typename OptionsGroup, typename BroadcastTarget>
      99             : struct StoreOrthogonalization {
     100             :  private:
     101             :   using fields_tag = FieldsTag;
     102             :   using residual_magnitude_tag = LinearSolver::Tags::Magnitude<
     103             :       db::add_tag_prefix<LinearSolver::Tags::Residual, fields_tag>>;
     104             :   using initial_residual_magnitude_tag =
     105             :       ::Tags::Initial<residual_magnitude_tag>;
     106             :   using previous_residual_magnitude_tag =
     107             :       ::Tags::Previous<residual_magnitude_tag>;
     108             :   using orthogonalization_history_tag =
     109             :       LinearSolver::Tags::OrthogonalizationHistory<fields_tag>;
     110             :   using ValueType =
     111             :       tt::get_complex_or_fundamental_type_t<typename fields_tag::type>;
     112             : 
     113             :  public:
     114             :   template <typename ParallelComponent, typename DbTagsList,
     115             :             typename Metavariables, typename ArrayIndex,
     116             :             typename DataBox = db::DataBox<DbTagsList>>
     117             :   static void apply(db::DataBox<DbTagsList>& box,
     118             :                     Parallel::GlobalCache<Metavariables>& cache,
     119             :                     const ArrayIndex& /*array_index*/,
     120             :                     const size_t iteration_id,
     121             :                     const size_t orthogonalization_iteration_id,
     122             :                     const ValueType orthogonalization) {
     123             :     if (UNLIKELY(orthogonalization_iteration_id == 0)) {
     124             :       // Append a row and a column to the orthogonalization history. Zero the
     125             :       // entries that won't be set during the orthogonalization procedure below.
     126             :       db::mutate<orthogonalization_history_tag>(
     127             :           [iteration_id](const auto orthogonalization_history) {
     128             :             orthogonalization_history->resize(iteration_id + 1, iteration_id);
     129             :             for (size_t j = 0; j < orthogonalization_history->columns() - 1;
     130             :                  ++j) {
     131             :               (*orthogonalization_history)(
     132             :                   orthogonalization_history->rows() - 1, j) = 0.;
     133             :             }
     134             :           },
     135             :           make_not_null(&box));
     136             :     }
     137             : 
     138             :     // While the orthogonalization procedure is not complete, store the
     139             :     // orthogonalization, broadcast it back to all elements and return early
     140             :     if (orthogonalization_iteration_id < iteration_id) {
     141             :       db::mutate<orthogonalization_history_tag>(
     142             :           [orthogonalization, iteration_id, orthogonalization_iteration_id](
     143             :               const auto orthogonalization_history) {
     144             :             (*orthogonalization_history)(orthogonalization_iteration_id,
     145             :                                          iteration_id - 1) = orthogonalization;
     146             :           },
     147             :           make_not_null(&box));
     148             : 
     149             :       Parallel::receive_data<Tags::Orthogonalization<OptionsGroup, ValueType>>(
     150             :           Parallel::get_parallel_component<BroadcastTarget>(cache),
     151             :           iteration_id, orthogonalization);
     152             :       return;
     153             :     }
     154             : 
     155             :     // At this point, the orthogonalization procedure is complete.
     156             :     ASSERT(equal_within_roundoff(imag(orthogonalization), 0.0),
     157             :            "Normalization is not real: " << orthogonalization);
     158             :     const double normalization = sqrt(real(orthogonalization));
     159             :     db::mutate<orthogonalization_history_tag>(
     160             :         [normalization, iteration_id,
     161             :          orthogonalization_iteration_id](const auto orthogonalization_history) {
     162             :           (*orthogonalization_history)(orthogonalization_iteration_id,
     163             :                                        iteration_id - 1) = normalization;
     164             :         },
     165             :         make_not_null(&box));
     166             : 
     167             :     // Perform a QR decomposition of the Hessenberg matrix that was built during
     168             :     // the orthogonalization
     169             :     const auto& orthogonalization_history =
     170             :         get<orthogonalization_history_tag>(box);
     171             :     const auto num_rows = orthogonalization_iteration_id + 1;
     172             :     blaze::DynamicMatrix<ValueType> qr_Q;
     173             :     blaze::DynamicMatrix<ValueType> qr_R;
     174             :     blaze::qr(orthogonalization_history, qr_Q, qr_R);
     175             :     // Compute the residual vector from the QR decomposition
     176             :     blaze::DynamicVector<double> beta(num_rows, 0.);
     177             :     const double initial_residual_magnitude =
     178             :         get<initial_residual_magnitude_tag>(box);
     179             :     beta[0] = initial_residual_magnitude;
     180             :     blaze::DynamicVector<ValueType> minres =
     181             :         blaze::inv(qr_R) * blaze::ctrans(qr_Q) * beta;
     182             :     blaze::DynamicVector<ValueType> res =
     183             :         beta - orthogonalization_history * minres;
     184             :     const double residual_magnitude = sqrt(magnitude_square(res));
     185             : 
     186             :     // At this point, the iteration is complete. We proceed with observing,
     187             :     // logging and checking convergence before broadcasting back to the
     188             :     // elements.
     189             : 
     190             :     LinearSolver::observe_detail::contribute_to_reduction_observer<
     191             :         OptionsGroup, ParallelComponent>(iteration_id, residual_magnitude,
     192             :                                          cache);
     193             : 
     194             :     // Determine whether the linear solver has converged.
     195             :     // GMRES is guaranteed to decrease the residual monotonically, so an
     196             :     // increase in the residual is an error.
     197             :     const auto& convergence_criteria =
     198             :         get<Convergence::Tags::Criteria<OptionsGroup>>(box);
     199             :     const double previous_residual_magnitude =
     200             :         get<previous_residual_magnitude_tag>(box);
     201             :     auto has_converged =
     202             :         residual_magnitude < previous_residual_magnitude
     203             :             ? Convergence::HasConverged{convergence_criteria, iteration_id,
     204             :                                         residual_magnitude,
     205             :                                         initial_residual_magnitude}
     206             :             : Convergence::HasConverged{
     207             :                   Convergence::Reason::Error,
     208             :                   MakeString{} << std::scientific
     209             :                                << "Residual should decrease monotonically, but "
     210             :                                   "increased from "
     211             :                                << previous_residual_magnitude << " to "
     212             :                                << residual_magnitude << ".",
     213             :                   iteration_id};
     214             : 
     215             :     db::mutate<previous_residual_magnitude_tag>(
     216             :         [residual_magnitude](
     217             :             const gsl::not_null<double*> stored_previous_residual_magnitude) {
     218             :           *stored_previous_residual_magnitude = residual_magnitude;
     219             :         },
     220             :         make_not_null(&box));
     221             : 
     222             :     // Do some logging
     223             :     if (UNLIKELY(get<logging::Tags::Verbosity<OptionsGroup>>(cache) >=
     224             :                  ::Verbosity::Quiet)) {
     225             :       Parallel::printf("%s(%zu) iteration complete. Remaining residual: %e\n",
     226             :                        pretty_type::name<OptionsGroup>(), iteration_id,
     227             :                        residual_magnitude);
     228             :     }
     229             :     if (UNLIKELY(has_converged and get<logging::Tags::Verbosity<OptionsGroup>>(
     230             :                                        cache) >= ::Verbosity::Quiet)) {
     231             :       if (has_converged.reason() == Convergence::Reason::Error) {
     232             :         Parallel::printf("%s has encountered an error in iteration %zu: %s\n",
     233             :                          pretty_type::name<OptionsGroup>(), iteration_id,
     234             :                          has_converged.error_message());
     235             :       } else {
     236             :         Parallel::printf("%s has converged in %zu iterations: %s\n",
     237             :                          pretty_type::name<OptionsGroup>(), iteration_id,
     238             :                          has_converged);
     239             :       }
     240             :     }
     241             : 
     242             :     Parallel::receive_data<
     243             :         Tags::FinalOrthogonalization<OptionsGroup, ValueType>>(
     244             :         Parallel::get_parallel_component<BroadcastTarget>(cache), iteration_id,
     245             :         std::make_tuple(normalization, std::move(minres),
     246             :                         // NOLINTNEXTLINE(performance-move-const-arg)
     247             :                         std::move(has_converged)));
     248             :   }
     249             : };
     250             : 
     251             : }  // namespace LinearSolver::gmres::detail