void operator()(LinPdeSysT const & pde_system,
SegmentT const & segment,
StorageType & storage,
MatrixT & system_matrix,
VectorT & load_vector)
{
typedef viennamath::equation equ_type;
typedef viennamath::expr expr_type;
typedef typename expr_type::interface_type interface_type;
typedef typename expr_type::numeric_type numeric_type;
typedef typename viennagrid::result_of::cell_tag<SegmentT>::type CellTag;
std::size_t map_index = viennafvm::create_mapping(pde_system, segment, storage);
system_matrix.clear();
system_matrix.resize(map_index, map_index, false);
load_vector.clear();
load_vector.resize(map_index);
for (std::size_t pde_index = 0; pde_index < pde_system.size(); ++pde_index)
{
#ifdef VIENNAFVM_DEBUG
std::cout << std::endl;
std::cout << "//" << std::endl;
std::cout << "// Equation " << pde_index << std::endl;
std::cout << "//" << std::endl;
#endif
assemble(pde_system, pde_index,
segment, storage,
system_matrix, load_vector);
} // for pde_index
} // functor
void make_rotation_matrix(MatrixT & mat,
vcl_size_t new_size,
vcl_size_t off_diagonal_distance = 4)
{
mat.resize(new_size, new_size, false);
mat.clear();
double val = 1.0 / std::sqrt(2.0);
for (vcl_size_t i=0; i<new_size; ++i)
mat(i,i) = val;
for (vcl_size_t i=off_diagonal_distance; i<new_size; ++i)
{
mat(i-off_diagonal_distance, i) = val;
mat(i, i-off_diagonal_distance) = -val;
}
}
void operator()(SystemType pde_system,
DomainType & domain,
MatrixT & system_matrix,
VectorT & load_vector
) const
{
typedef typename viennagrid::result_of::cell_tag<DomainType>::type CellTag;
typedef typename viennagrid::result_of::point<DomainType>::type PointType;
typedef typename viennagrid::result_of::element<DomainType, CellTag>::type CellType;
typedef typename viennagrid::result_of::element_range<DomainType, CellTag>::type CellContainer;
typedef typename viennagrid::result_of::iterator<CellContainer>::type CellIterator;
typedef typename SystemType::equation_type EquationType;
#ifdef VIENNAFEM_DEBUG
std::cout << "Strong form: " << pde_system.pde(0) << std::endl;
#endif
log_strong_form(pde_system);
EquationType weak_form_general = viennafem::make_weak_form(pde_system.pde(0));
#ifdef VIENNAFEM_DEBUG
std::cout << "* pde_solver::operator(): Using weak form general: " << weak_form_general << std::endl;
#endif
std::vector<EquationType> temp(1); temp[0] = weak_form_general;
log_weak_form(temp, pde_system);
EquationType weak_form = viennamath::apply_coordinate_system(viennamath::cartesian< PointType::dim >(), weak_form_general);
//EquationType weak_form = viennamath::apply_coordinate_system(viennamath::cartesian<Config::coordinate_system_tag::dim>(), weak_form_general);
temp[0] = weak_form;
log_coordinated_weak_form(temp, pde_system);
#ifdef VIENNAFEM_DEBUG
std::cout << "* pde_solver::operator(): Using weak form " << weak_form << std::endl;
std::cout << "* pde_solver::operator(): Write dt_dx coefficients" << std::endl;
#endif
typedef typename reference_cell_for_basis<CellTag, viennafem::lagrange_tag<1> >::type ReferenceCell;
//
// Create accessors for performance in the subsequent dt_dx_handler step
//
//viennafem::dtdx_assigner<DomainType, StorageType, ReferenceCell>::apply(domain, storage);
viennafem::dt_dx_handler<DomainType, StorageType, ReferenceCell> dt_dx_handler(domain, storage);
//fill with cell quantities
CellContainer cells = viennagrid::elements<CellType>(domain);
for (CellIterator cell_iter = cells.begin();
cell_iter != cells.end();
++cell_iter)
{
//cell_iter->print_short();
//viennadata::access<example_key, double>()(*cell_iter) = i;
//viennafem::dt_dx_handler<ReferenceCell>::apply(storage, *cell_iter);
dt_dx_handler(*cell_iter);
}
#ifdef VIENNAFEM_DEBUG
std::cout << "* pde_solver::operator(): Create Mapping:" << std::endl;
#endif
std::size_t map_index = create_mapping(storage, pde_system, domain);
#ifdef VIENNAFEM_DEBUG
std::cout << "* pde_solver::operator(): Assigned degrees of freedom in domain so far: " << map_index << std::endl;
#endif
// resize global system matrix and load vector if needed:
// TODO: This can be a performance bottleneck for large numbers of segments! (lots of resize operations...)
if (map_index > system_matrix.size1())
{
MatrixT temp = system_matrix;
////std::cout << "Resizing system matrix..." << std::endl;
system_matrix.resize(map_index, map_index, false);
system_matrix.clear();
system_matrix.resize(map_index, map_index, false);
for (typename MatrixT::iterator1 row_it = temp.begin1();
row_it != temp.end1();
++row_it)
{
for (typename MatrixT::iterator2 col_it = row_it.begin();
col_it != row_it.end();
++col_it)
system_matrix(col_it.index1(), col_it.index2()) = *col_it;
}
}
if (map_index > load_vector.size())
{
VectorT temp = load_vector;
#ifdef VIENNAFEM_DEBUG
std::cout << "Resizing load vector..." << std::endl;
#endif
load_vector.resize(map_index, false);
load_vector.clear();
load_vector.resize(map_index, false);
for (std::size_t i=0; i<temp.size(); ++i)
load_vector(i) = temp(i);
}
#ifdef VIENNAFEM_DEBUG
std::cout << "* pde_solver::operator(): Transform to reference element" << std::endl;
#endif
EquationType transformed_weak_form = viennafem::transform_to_reference_cell<CellType>(storage, weak_form, pde_system);
temp[0] = transformed_weak_form;
log_transformed_weak_form<CellType, StorageType>(temp, pde_system);
std::cout << "* pde_solver::operator(): Transformed weak form:" << std::endl;
std::cout << transformed_weak_form << std::endl;
//std::cout << std::endl;
#ifdef VIENNAFEM_DEBUG
std::cout << "* pde_solver::operator(): Assemble system" << std::endl;
#endif
typedef detail::equation_wrapper<MatrixT, VectorT> wrapper_type;
wrapper_type wrapper(system_matrix, load_vector);
detail::pde_assembler_internal()(storage, transformed_weak_form, pde_system, domain, wrapper);
// pde_assembler_internal()(transformed_weak_form, pde_system, domain, system_matrix, load_vector);
}
void RowEchelon<T>::getNullspace(MatrixT& N) const
{
if(R.isEmpty()) {
N.clear();
return;
}
Assert((int)firstEntry.size() == R.m+1);
int nullspace_dims=getNull();
N.resize(R.n,nullspace_dims);
//first get nullspace vectors from 0 to firstEntry[0]
int i,j,numVecs=0;
int m=R.m,n=R.n;
for(j=0;j<firstEntry[0];j++) {
N.setCol(numVecs,0); N(j,numVecs)=1;
numVecs++;
}
for(i=0;i<m;i++) {
//cancel out the i'th entry
for(j=firstEntry[i]+1;j<firstEntry[i+1];j++) {
if(numVecs >= N.n) {
LOG4CXX_INFO(KrisLibrary::logger(),"Num nullspace vectors "<<numVecs);
LOG4CXX_INFO(KrisLibrary::logger(),"Found more nullspace vectors than found dims, row "<<i);
LOG4CXX_INFO(KrisLibrary::logger(),MatrixPrinter(R));
}
Assert(numVecs < N.n);
VectorT xn; N.getColRef(numVecs,xn);
xn.setZero();
xn[firstEntry[i]] = R(i,j);
xn[j] = -R(i,firstEntry[i]);
//cancel out all the entries prior to i
int isave=i;
i--;
for(;i>=0;i--) {
VectorT ri; R.getRowRef(i,ri);
//calculate alpha
int ji=firstEntry[i];
Assert(ji != n);
int ji2=firstEntry[i+1]; //(i+1==m?n:firstEntry[i+1]);
T alpha;
if(ji2 == n) alpha = Zero;
else {
VectorT rji2; rji2.setRef(ri,ji2,1,R.n-ji2);
VectorT xji2; xji2.setRef(xn,ji2,1,R.n-ji2);
alpha = xji2.dot(rji2);
}
xn[ji] = -alpha/ri[ji];
}
i=isave;
numVecs++;
}
}
if(numVecs != nullspace_dims) {
LOG4CXX_ERROR(KrisLibrary::logger(),"Error in counting rank in row-eschelon decomposition");
LOG4CXX_INFO(KrisLibrary::logger(),"Num nullspace vectors "<<numVecs);
LOG4CXX_INFO(KrisLibrary::logger(),MatrixPrinter(R));
}
Assert(numVecs == nullspace_dims);
/*
VectorT temp;
for(int i=0;i<numVecs;i++) {
VectorT xi; N.getColRef(i,xi);
xi.print();
R.mul(xi,temp);
if(temp.maxAbsElement() > 1e-4) {
LOG4CXX_INFO(KrisLibrary::logger(),"Nullspace vector "<<i<<" not in null space!");
xi.print();
LOG4CXX_INFO(KrisLibrary::logger(),"Result = "); temp.print();
KrisLibrary::loggerWait();
}
}
*/
VectorT* N0 = new VectorT[nullspace_dims];
for(int i=0;i<nullspace_dims;i++) N.getColRef(i,N0[i]);
int num=OrthonormalBasis(N0,N0,nullspace_dims);
Assert(num == nullspace_dims);
delete [] N0;
}