/usr/include/dune/localfunctions/dualmortarbasis/dualq1/dualq1localbasis.hh is in libdune-localfunctions-dev 2.5.0-2.
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// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_DUAL_Q1_LOCALBASIS_HH
#define DUNE_DUAL_Q1_LOCALBASIS_HH
#include <array>
#include <numeric>
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
#include <dune/localfunctions/common/localbasis.hh>
namespace Dune
{
/**@ingroup LocalBasisImplementation
\brief Dual Lagrange shape functions of order 1 on the reference cube.
\tparam D Type to represent the field in the domain.
\tparam R Type to represent the field in the range.
\tparam dim Dimension of the cube
\nosubgrouping
*/
template<class D, class R, int dim>
class DualQ1LocalBasis
{
public:
typedef LocalBasisTraits<D,dim,Dune::FieldVector<D,dim>,R,1,Dune::FieldVector<R,1>,
Dune::FieldMatrix<R,1,dim> > Traits;
void setCoefficients(const std::array<Dune::FieldVector<R, (1<<dim)> ,(1<<dim)>& coefficients)
{
coefficients_ = coefficients;
}
//! \brief number of shape functions
unsigned int size () const
{
return 1<<dim;
}
//! \brief Evaluate all shape functions
inline void evaluateFunction (const typename Traits::DomainType& in,
std::vector<typename Traits::RangeType>& out) const
{
// compute q1 values
std::vector<typename Traits::RangeType> q1Values(size());
for (size_t i=0; i<size(); i++) {
q1Values[i] = 1;
for (int j=0; j<dim; j++)
// if j-th bit of i is set multiply with in[j], else with 1-in[j]
q1Values[i] *= (i & (1<<j)) ? in[j] : 1-in[j];
}
// compute the dual values by using that they are linear combinations of q1 functions
out.resize(size());
for (size_t i=0; i<size(); i++)
out[i] = 0;
for (size_t i=0; i<size(); i++)
for (size_t j=0; j<size(); j++)
out[i] += coefficients_[i][j]*q1Values[j];
}
//! \brief Evaluate Jacobian of all shape functions
inline void
evaluateJacobian (const typename Traits::DomainType& in, // position
std::vector<typename Traits::JacobianType>& out) const // return value
{
// compute q1 jacobians
std::vector<typename Traits::JacobianType> q1Jacs(size());
// Loop over all shape functions
for (size_t i=0; i<size(); i++) {
// Loop over all coordinate directions
for (int j=0; j<dim; j++) {
// Initialize: the overall expression is a product
// if j-th bit of i is set to -1, else 1
q1Jacs[i][0][j] = (i & (1<<j)) ? 1 : -1;
for (int k=0; k<dim; k++) {
if (j!=k)
// if k-th bit of i is set multiply with in[j], else with 1-in[j]
q1Jacs[i][0][j] *= (i & (1<<k)) ? in[k] : 1-in[k];
}
}
}
// compute the dual jacobians by using that they are linear combinations of q1 functions
out.resize(size());
for (size_t i=0; i<size(); i++)
out[i] = 0;
for (size_t i=0; i<size(); i++)
for (size_t j=0; j<size(); j++)
out[i].axpy(coefficients_[i][j],q1Jacs[j]);
}
//! \brief Evaluate partial derivatives of all shape functions
void partial (const std::array<unsigned int, dim>& order,
const typename Traits::DomainType& in, // position
std::vector<typename Traits::RangeType>& out) const // return value
{
auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
if (totalOrder == 0) {
evaluateFunction(in, out);
} else {
DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
}
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return 1;
}
private:
std::array<Dune::FieldVector<R, (1<<dim)> ,(1<<dim)> coefficients_;
};
}
#endif
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