LocalLinearLeastSquaresExtrapolator.cpp

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#include "LocalLinearLeastSquaresExtrapolator.h"
 
#include <Eigen/SVD>
 
#include "BaseLib/Logging.h"
#include "ExtrapolatableElementCollection.h"
#include "MathLib/LinAlg/Eigen/EigenMapTools.h"
#include "MathLib/LinAlg/LinAlg.h"
#include "MathLib/LinAlg/MatrixVectorTraits.h"
#include "NumLib/Assembler/SerialExecutor.h"
#include "NumLib/Function/Interpolation.h"
 
namespace NumLib
{
LocalLinearLeastSquaresExtrapolator::LocalLinearLeastSquaresExtrapolator(
    NumLib::LocalToGlobalIndexMap const& dof_table)
    : _dof_table_single_component(dof_table)
{
    /* Note in case the following assertion fails:
     * If you copied the extrapolation code, for your processes from
     * somewhere, note that the code from the groundwater flow process might
     * not suit your needs: It is a special case and is therefore most
     * likely too simplistic. You better adapt the extrapolation code from
     * some more advanced process, like the TES process.
     */
    if (dof_table.getNumberOfGlobalComponents() != 1)
    {
        OGS_FATAL(
            "The d.o.f. table passed must be for one variable that has only "
            "one component!");
    }
}
 
void LocalLinearLeastSquaresExtrapolator::extrapolate(
    const unsigned num_components,
    ExtrapolatableElementCollection const& extrapolatables,
    const double t,
    std::vector<GlobalVector*> const& x,
    std::vector<NumLib::LocalToGlobalIndexMap const*> const& dof_table)
{
    auto const num_nodal_dof_result =
        _dof_table_single_component.dofSizeWithoutGhosts() * num_components;
 
    std::vector<GlobalIndexType> ghost_indices;
    {  // Create num_components times version of ghost_indices arranged by
       // location. For example for 3 components and ghost_indices {5,6,10} we
       // compute {15, 16, 17,  18, 19, 20,  30, 31, 32}.
        auto const& single_component_ghost_indices =
            _dof_table_single_component.getGhostIndices();
        auto const single_component_ghost_indices_size =
            single_component_ghost_indices.size();
        ghost_indices.reserve(single_component_ghost_indices_size *
                              num_components);
        for (unsigned i = 0; i < single_component_ghost_indices_size; ++i)
        {
            for (unsigned c = 0; c < num_components; ++c)
            {
                ghost_indices.push_back(
                    single_component_ghost_indices[i] * num_components + c);
            }
        }
    }
 
    if (!_nodal_values ||
#ifdef USE_PETSC
        _nodal_values->getLocalSize() + _nodal_values->getGhostSize()
#else
        _nodal_values->size()
#endif
            != static_cast<GlobalIndexType>(num_nodal_dof_result))
    {
        _nodal_values = MathLib::MatrixVectorTraits<GlobalVector>::newInstance(
            {num_nodal_dof_result, num_nodal_dof_result, &ghost_indices,
             nullptr});
    }
    _nodal_values->setZero();
 
    // counts the writes to each nodal value, i.e., the summands in order to
    // compute the average afterwards
    auto counts =
        MathLib::MatrixVectorTraits<GlobalVector>::newInstance(*_nodal_values);
    counts->setZero();
 
    auto const size = extrapolatables.size();
    for (std::size_t i = 0; i < size; ++i)
    {
        extrapolateElement(i, num_components, extrapolatables, t, x, dof_table,
                           *counts);
    }
    MathLib::LinAlg::finalizeAssembly(*_nodal_values);
 
    MathLib::LinAlg::componentwiseDivide(*_nodal_values, *_nodal_values,
                                         *counts);
}
 
void LocalLinearLeastSquaresExtrapolator::calculateResiduals(
    const unsigned num_components,
    ExtrapolatableElementCollection const& extrapolatables,
    const double t,
    std::vector<GlobalVector*> const& x,
    std::vector<NumLib::LocalToGlobalIndexMap const*> const& dof_table)
{
    auto const num_element_dof_result = static_cast<GlobalIndexType>(
        _dof_table_single_component.size() * num_components);
 
    if (!_residuals || _residuals->size() != num_element_dof_result)
    {
#ifndef USE_PETSC
        _residuals.reset(new GlobalVector{num_element_dof_result});
#else
        _residuals.reset(new GlobalVector{num_element_dof_result, false});
#endif
    }
 
    if (static_cast<std::size_t>(num_element_dof_result) !=
        extrapolatables.size() * num_components)
    {
        OGS_FATAL("mismatch in number of D.o.F.");
    }
 
    auto const size = extrapolatables.size();
    for (std::size_t i = 0; i < size; ++i)
    {
        calculateResidualElement(i, num_components, extrapolatables, t, x,
                                 dof_table);
    }
    MathLib::LinAlg::finalizeAssembly(*_residuals);
}
 
void LocalLinearLeastSquaresExtrapolator::extrapolateElement(
    std::size_t const element_index,
    const unsigned num_components,
    ExtrapolatableElementCollection const& extrapolatables,
    const double t,
    std::vector<GlobalVector*> const& x,
    std::vector<NumLib::LocalToGlobalIndexMap const*> const& dof_table,
    GlobalVector& counts)
{
    auto const& integration_point_values =
        extrapolatables.getIntegrationPointValues(
            element_index, t, x, dof_table, _integration_point_values_cache);
 
    // Empty vector means to ignore the values and not to change the counts.
    if (integration_point_values.empty())
    {
        return;
    }
 
    auto const& N_0 = extrapolatables.getShapeMatrix(element_index, 0);
    auto const num_nodes = static_cast<unsigned>(N_0.cols());
    auto const num_values =
        static_cast<unsigned>(integration_point_values.size());
 
    if (num_values % num_components != 0)
    {
        OGS_FATAL(
            "The number of computed integration point values is not divisible "
            "by the number of num_components. Maybe the computed property is "
            "not a {:d}-component vector for each integration point.",
            num_components);
    }
 
    // number of integration points in the element
    const auto num_int_pts = num_values / num_components;
 
    if (num_int_pts < num_nodes)
    {
        OGS_FATAL(
            "Least squares is not possible if there are more nodes than "
            "integration points.");
    }
 
    auto const pair_it_inserted = _qr_decomposition_cache.emplace(
        std::make_pair(num_nodes, num_int_pts), CachedData{});
 
    auto& cached_data = pair_it_inserted.first->second;
    if (pair_it_inserted.second)
    {
        DBUG("Computing new singular value decomposition");
 
        // interpolation_matrix * nodal_values = integration_point_values
        // We are going to pseudo-invert this relation now using singular value
        // decomposition.
        auto& interpolation_matrix = cached_data.A;
        interpolation_matrix.resize(num_int_pts, num_nodes);
 
        interpolation_matrix.row(0) = N_0;
        for (unsigned int_pt = 1; int_pt < num_int_pts; ++int_pt)
        {
            auto const& shp_mat =
                extrapolatables.getShapeMatrix(element_index, int_pt);
            assert(shp_mat.cols() == num_nodes);
 
            // copy shape matrix to extrapolation matrix row-wise
            interpolation_matrix.row(int_pt) = shp_mat;
        }
 
        // JacobiSVD is extremely reliable, but fast only for small matrices.
        // But we usually have small matrices and we don't compute very often.
        // Cf.
        // http://eigen.tuxfamily.org/dox/group__TopicLinearAlgebraDecompositions.html
        //
        // Decomposes interpolation_matrix = U S V^T.
        Eigen::JacobiSVD<Eigen::MatrixXd> svd(
            interpolation_matrix, Eigen::ComputeThinU | Eigen::ComputeThinV);
 
        auto const& S = svd.singularValues();
        auto const& U = svd.matrixU();
        auto const& V = svd.matrixV();
 
        // Compute and save the pseudo inverse V * S^{-1} * U^T.
        auto const rank = svd.rank();
        assert(rank == num_nodes);
 
        // cf. http://eigen.tuxfamily.org/dox/JacobiSVD_8h_source.html
        cached_data.A_pinv.noalias() = V.leftCols(rank) *
                                       S.head(rank).asDiagonal().inverse() *
                                       U.leftCols(rank).transpose();
    }
    else if (cached_data.A.row(0) != N_0)
    {
        OGS_FATAL("The cached and the passed shapematrices differ.");
    }
 
    auto const& global_indices =
        _dof_table_single_component(element_index, 0).rows;
 
    if (num_components == 1)
    {
        auto const integration_point_values_vec =
            MathLib::toVector(integration_point_values);
 
        // Apply the pre-computed pseudo-inverse.
        Eigen::VectorXd const nodal_values =
            cached_data.A_pinv * integration_point_values_vec;
 
        // TODO does that give rise to PETSc problems? E.g., writing to ghost
        // nodes? Furthermore: Is ghost nodes communication necessary for PETSc?
        _nodal_values->add(global_indices, nodal_values);
        counts.add(global_indices,
                   std::vector<double>(global_indices.size(), 1.0));
    }
    else
    {
        auto const integration_point_values_mat = MathLib::toMatrix(
            integration_point_values, num_components, num_int_pts);
 
        // Apply the pre-computed pseudo-inverse.
        Eigen::MatrixXd const nodal_values =
            cached_data.A_pinv * integration_point_values_mat.transpose();
 
        std::vector<GlobalIndexType> indices;
        indices.reserve(num_components * global_indices.size());
 
        // _nodal_values is ordered location-wise
        for (unsigned comp = 0; comp < num_components; ++comp)
        {
            transform(cbegin(global_indices), cend(global_indices),
                      back_inserter(indices),
                      [&](auto const i) { return num_components * i + comp; });
        }
 
        // Nodal_values are passed as a raw pointer, because PETScVector and
        // EigenVector implementations differ slightly.
        _nodal_values->add(indices, nodal_values.data());
        counts.add(indices, std::vector<double>(indices.size(), 1.0));
    }
}
 
void LocalLinearLeastSquaresExtrapolator::calculateResidualElement(
    std::size_t const element_index,
    const unsigned num_components,
    ExtrapolatableElementCollection const& extrapolatables,
    const double t,
    std::vector<GlobalVector*> const& x,
    std::vector<NumLib::LocalToGlobalIndexMap const*> const& dof_table)
{
    auto const& int_pt_vals = extrapolatables.getIntegrationPointValues(
        element_index, t, x, dof_table, _integration_point_values_cache);
 
    auto const num_values = static_cast<unsigned>(int_pt_vals.size());
    if (num_values % num_components != 0)
    {
        OGS_FATAL(
            "The number of computed integration point values is not divisible "
            "by the number of num_components. Maybe the computed property is "
            "not a {:d}-component vector for each integration point.",
            num_components);
    }
 
    // number of integration points in the element
    const auto num_int_pts = num_values / num_components;
 
    const auto& global_indices =
        _dof_table_single_component(element_index, 0).rows;
    const auto num_nodes = static_cast<unsigned>(global_indices.size());
 
    auto const& interpolation_matrix =
        _qr_decomposition_cache.find({num_nodes, num_int_pts})->second.A;
 
    Eigen::VectorXd nodal_vals_element(num_nodes);
    auto const int_pt_vals_mat =
        MathLib::toMatrix(int_pt_vals, num_components, num_int_pts);
 
    MathLib::LinAlg::setLocalAccessibleVector(
        *_nodal_values);  // For access in the for-loop.
    for (unsigned comp = 0; comp < num_components; ++comp)
    {
        // filter nodal values of the current element
        for (unsigned i = 0; i < num_nodes; ++i)
        {
            // TODO PETSc negative indices?
            auto const idx = num_components * global_indices[i] + comp;
            nodal_vals_element[i] = _nodal_values->get(idx);
        }
 
        double const residual = (interpolation_matrix * nodal_vals_element -
                                 int_pt_vals_mat.row(comp).transpose())
                                    .squaredNorm();
 
        auto const eidx =
            static_cast<GlobalIndexType>(num_components * element_index + comp);
        // The residual is set to the root mean square value.
        auto const root_mean_square = std::sqrt(residual / num_int_pts);
        _residuals->set(eidx, root_mean_square);
    }
}
 
}  // namespace NumLib