swh:1:snp:f521c49ab17ef7db6ec70b2430e1ed203f50383f
Tip revision: efb2971310de2f1b0365d79d340b2b3c6dd37305 authored by Dmitry Yu. Naumov on 17 March 2021, 19:35:52 UTC
Merge branch 'BaseLibInterfaces' into 'master'
Merge branch 'BaseLibInterfaces' into 'master'
Tip revision: efb2971
LocalLinearLeastSquaresExtrapolator.cpp
/**
* \file
* \copyright
* Copyright (c) 2012-2021, OpenGeoSys Community (http://www.opengeosys.org)
* Distributed under a Modified BSD License.
* See accompanying file LICENSE.txt or
* http://www.opengeosys.org/project/license
*
*/
#include "LocalLinearLeastSquaresExtrapolator.h"
#include <Eigen/SVD>
#include "BaseLib/Logging.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"
#include "ExtrapolatableElementCollection.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