//-----------------------------------------------------------------------------
SubSpace::SubSpace(const FunctionSpace& V,
const std::vector<std::size_t>& component)
: FunctionSpace(V.mesh(), V.element(), V.dofmap())
{
// Extract subspace and assign
std::shared_ptr<FunctionSpace> _function_space(V.extract_sub_space(component));
*static_cast<FunctionSpace*>(this) = *_function_space;
}
Probe::Probe(const Array<double>& x, const FunctionSpace& V) :
_element(V.element()), _num_evals(0)
{
const Mesh& mesh = *V.mesh();
std::size_t gdim = mesh.geometry().dim();
// Find the cell that contains probe
const Point point(gdim, x.data());
unsigned int cell_id = mesh.bounding_box_tree()->compute_first_entity_collision(point);
// If the cell is on this process, then create an instance
// of the Probe class. Otherwise raise a dolfin_error.
if (cell_id != std::numeric_limits<unsigned int>::max())
{
// Store position of probe
for (std::size_t i = 0; i < 3; i++)
_x[i] = (i < gdim ? x[i] : 0.0);
// Compute in tensor (one for scalar function, . . .)
_value_size_loc = 1;
for (std::size_t i = 0; i < _element->value_rank(); i++)
_value_size_loc *= _element->value_dimension(i);
_probes.resize(_value_size_loc);
// Create cell that contains point
dolfin_cell.reset(new Cell(mesh, cell_id));
dolfin_cell->get_cell_data(ufc_cell);
coefficients.resize(_element->space_dimension());
// Cell vertices
dolfin_cell->get_vertex_coordinates(vertex_coordinates);
// Create work vector for basis
basis_matrix.resize(_value_size_loc);
for (std::size_t i = 0; i < _value_size_loc; ++i)
basis_matrix[i].resize(_element->space_dimension());
std::vector<double> basis(_value_size_loc);
const int cell_orientation = 0;
for (std::size_t i = 0; i < _element->space_dimension(); ++i)
{
_element->evaluate_basis(i, &basis[0], &x[0],
vertex_coordinates.data(),
cell_orientation);
for (std::size_t j = 0; j < _value_size_loc; ++j)
basis_matrix[j][i] = basis[j];
}
}
else
{
dolfin_error("Probe.cpp","set probe","Probe is not found on processor");
}
}
//-----------------------------------------------------------------------------
SubSpace::SubSpace(const FunctionSpace& V,
std::size_t component,
std::size_t sub_component)
: FunctionSpace(V.mesh(), V.element(), V.dofmap())
{
// Create array
std::vector<std::size_t> c = {{component, sub_component}};
// Extract subspace and assign
std::shared_ptr<FunctionSpace> _function_space(V.extract_sub_space(c));
*static_cast<FunctionSpace*>(this) = *_function_space;
}
StatisticsProbes::StatisticsProbes(const Array<double>& x, const FunctionSpace& V, bool segregated)
{
const std::size_t Nd = V.mesh()->geometry().dim();
const std::size_t N = x.size() / Nd;
Array<double> _x(Nd);
total_number_probes = N;
_num_evals = 0;
_value_size = 1;
for (std::size_t i = 0; i < V.element()->value_rank(); i++)
_value_size *= V.element()->value_dimension(i);
if (segregated)
{
assert(V.element()->value_rank() == 0);
_value_size *= V.element()->geometric_dimension();
}
// Symmetric statistics. Velocity: u, v, w, uu, vv, ww, uv, uw, vw
_value_size = _value_size*(_value_size+3)/2.;
for (std::size_t i=0; i<N; i++)
{
for (std::size_t j=0; j<Nd; j++)
_x[j] = x[i*Nd + j];
try
{
StatisticsProbe* probe = new StatisticsProbe(_x, V, segregated);
std::pair<std::size_t, StatisticsProbe*> newprobe = std::make_pair(i, &(*probe));
_allprobes.push_back(newprobe);
}
catch (std::exception &e)
{ // do-nothing
}
}
//cout << local_size() << " of " << N << " probes found on processor " << MPI::process_number() << endl;
}
void extract_dof_component_map(std::map<std::size_t, std::size_t>& dof_component_map,
const FunctionSpace& VV, int* component)
{ // Extract sub dofmaps recursively and store dof to component map
boost::unordered_map<std::size_t, std::size_t> collapsed_map;
boost::unordered_map<std::size_t, std::size_t>::iterator map_it;
std::vector<std::size_t> comp(1);
if (VV.element()->num_sub_elements() == 0)
{
boost::shared_ptr<GenericDofMap> dummy = VV.dofmap()->collapse(collapsed_map, *VV.mesh());
(*component)++;
for (map_it =collapsed_map.begin(); map_it!=collapsed_map.end(); ++map_it)
dof_component_map[map_it->second] = (*component);
}
else
{
for (std::size_t i=0; i<VV.element()->num_sub_elements(); i++)
{
comp[0] = i;
boost::shared_ptr<FunctionSpace> Vs = VV.extract_sub_space(comp);
extract_dof_component_map(dof_component_map, *Vs, component);
}
}
}
//-----------------------------------------------------------------------------
void
Extrapolation::add_cell_equations(Eigen::MatrixXd& A,
Eigen::VectorXd& b,
const Cell& cell0,
const Cell& cell1,
const std::vector<double>& coordinate_dofs0,
const std::vector<double>& coordinate_dofs1,
const ufc::cell& c0,
const ufc::cell& c1,
const FunctionSpace& V,
const FunctionSpace& W,
const Function& v,
std::map<std::size_t, std::size_t>& dof2row)
{
// Extract coefficients for v on patch cell
dolfin_assert(V.element());
std::vector<double> dof_values(V.element()->space_dimension());
v.restrict(&dof_values[0], *V.element(), cell1, coordinate_dofs1.data(),
c1);
// Create basis function
dolfin_assert(W.element());
BasisFunction phi(0, W.element(), coordinate_dofs0);
// Iterate over given local dofs for V on patch cell
for (auto const &it : dof2row)
{
const std::size_t i = it.first;
const std::size_t row = it.second;
// Iterate over basis functions for W on center cell
for (std::size_t j = 0; j < W.element()->space_dimension(); ++j)
{
// Create basis function
phi.update_index(j);
// Evaluate dof on basis function
const double dof_value
= V.element()->evaluate_dof(i, phi, coordinate_dofs1.data(),
c1.orientation, c1);
// Insert dof_value into matrix
A(row, j) = dof_value;
}
// Insert coefficient into vector
b[row] = dof_values[i];
}
}
//-----------------------------------------------------------------------------
void Extrapolation::add_cell_equations(arma::Mat<double>& A,
arma::Col<double>& b,
const Cell& cell0,
const Cell& cell1,
const ufc::cell& c0,
const ufc::cell& c1,
const FunctionSpace& V,
const FunctionSpace& W,
const Function& v,
std::map<std::size_t, std::size_t>& dof2row)
{
// Extract coefficents for v on patch cell
dolfin_assert(V.element());
std::vector<double> dof_values(V.element()->space_dimension());
v.restrict(&dof_values[0], *V.element(), cell1, c1);
// Iterate over given local dofs for V on patch cell
dolfin_assert(W.element());
for (std::map<std::size_t, std::size_t>::iterator it = dof2row.begin(); it!= dof2row.end(); it++)
{
const std::size_t i = it->first;
const std::size_t row = it->second;
// Iterate over basis functions for W on center cell
for (std::size_t j = 0; j < W.element()->space_dimension(); ++j)
{
// Create basis function
const BasisFunction phi(j, *W.element(), c0);
// Evaluate dof on basis function
const int cell_orientation = 0;
const double dof_value = V.element()->evaluate_dof(i,
phi,
&c1.vertex_coordinates[0],
cell_orientation,
c1);
// Insert dof_value into matrix
A(row, j) = dof_value;
}
// Insert coefficient into vector
b[row] = dof_values[i];
}
}
//-----------------------------------------------------------------------------
void Extrapolation::compute_coefficients(
std::vector<std::vector<double>>& coefficients,
const Function& v,
const FunctionSpace& V,
const FunctionSpace& W,
const Cell& cell0,
const std::vector<double>& coordinate_dofs0,
const ufc::cell& c0,
const ArrayView<const dolfin::la_index>& dofs,
std::size_t& offset)
{
// Call recursively for mixed elements
dolfin_assert(V.element());
const std::size_t num_sub_spaces = V.element()->num_sub_elements();
if (num_sub_spaces > 0)
{
for (std::size_t k = 0; k < num_sub_spaces; k++)
{
compute_coefficients(coefficients, v[k], *V[k], *W[k], cell0,
coordinate_dofs0, c0, dofs, offset);
}
return;
}
// Build data structures for keeping track of unique dofs
std::map<std::size_t, std::map<std::size_t, std::size_t>> cell2dof2row;
std::set<std::size_t> unique_dofs;
build_unique_dofs(unique_dofs, cell2dof2row, cell0, V);
// Compute size of linear system
dolfin_assert(W.element());
const std::size_t N = W.element()->space_dimension();
const std::size_t M = unique_dofs.size();
// Check size of system
if (M < N)
{
dolfin_error("Extrapolation.cpp",
"compute extrapolation",
"Not enough degrees of freedom on local patch to build extrapolation");
}
// Create matrix and vector for linear system
Eigen::MatrixXd A(M, N);
Eigen::VectorXd b(M);
// Add equations on cell and neighboring cells
dolfin_assert(V.mesh());
ufc::cell c1;
std::vector<double> coordinate_dofs1;
// Get unique set of surrounding cells (including cell0)
std::set<std::size_t> cell_set;
for (VertexIterator vtx(cell0); !vtx.end(); ++vtx)
{
for (CellIterator cell1(*vtx); !cell1.end(); ++cell1)
cell_set.insert(cell1->index());
}
for (auto cell_it : cell_set)
{
if (cell2dof2row[cell_it].empty())
continue;
Cell cell1(cell0.mesh(), cell_it);
cell1.get_coordinate_dofs(coordinate_dofs1);
cell1.get_cell_data(c1);
add_cell_equations(A, b, cell0, cell1,
coordinate_dofs0, coordinate_dofs1,
c0, c1, V, W, v,
cell2dof2row[cell_it]);
}
// Solve least squares system
const Eigen::VectorXd x
= A.jacobiSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(b);
// Insert resulting coefficients into global coefficient vector
dolfin_assert(W.dofmap());
for (std::size_t i = 0; i < W.dofmap()->num_element_dofs(cell0.index()); ++i)
coefficients[dofs[i + offset]].push_back(x[i]);
// Increase offset
offset += W.dofmap()->num_element_dofs(cell0.index());
}
//-----------------------------------------------------------------------------
void Extrapolation::compute_coefficients(std::vector<std::vector<double> >& coefficients,
const Function& v,
const FunctionSpace& V,
const FunctionSpace& W,
const Cell& cell0,
const ufc::cell& c0,
const std::vector<dolfin::la_index>& dofs,
std::size_t& offset)
{
// Call recursively for mixed elements
dolfin_assert(V.element());
const std::size_t num_sub_spaces = V.element()->num_sub_elements();
if (num_sub_spaces > 0)
{
for (std::size_t k = 0; k < num_sub_spaces; k++)
{
compute_coefficients(coefficients, v[k], *V[k], *W[k], cell0, c0,
dofs, offset);
}
return;
}
// Build data structures for keeping track of unique dofs
std::map<std::size_t, std::map<std::size_t, std::size_t> > cell2dof2row;
std::set<std::size_t> unique_dofs;
build_unique_dofs(unique_dofs, cell2dof2row, cell0, c0, V);
// Compute size of linear system
dolfin_assert(W.element());
const std::size_t N = W.element()->space_dimension();
const std::size_t M = unique_dofs.size();
// Check size of system
if (M < N)
{
dolfin_error("Extrapolation.cpp",
"compute extrapolation",
"Not enough degrees of freedom on local patch to build extrapolation");
}
// Create matrix and vector for linear system
arma::mat A(M, N);
arma::vec b(M);
// Add equations on cell and neighboring cells
add_cell_equations(A, b, cell0, cell0, c0, c0, V, W, v, cell2dof2row[cell0.index()]);
dolfin_assert(V.mesh());
UFCCell c1(*V.mesh());
for (CellIterator cell1(cell0); !cell1.end(); ++cell1)
{
if (cell2dof2row[cell1->index()].empty())
continue;
c1.update(*cell1);
add_cell_equations(A, b, cell0, *cell1, c0, c1, V, W, v, cell2dof2row[cell1->index()]);
}
// Solve least squares system
arma::Col<double> x = arma::solve(A, b);
// Insert resulting coefficients into global coefficient vector
dolfin_assert(W.dofmap());
for (std::size_t i = 0; i < W.dofmap()->cell_dimension(cell0.index()); ++i)
coefficients[dofs[i + offset]].push_back(x[i]);
// Increase offset
offset += W.dofmap()->cell_dimension(cell0.index());
}