/usr/include/dune/localfunctions/lagrange/pk1d/pk1dlocalbasis.hh is in libdune-localfunctions-dev 2.3.1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_Pk1DLOCALBASIS_HH
#define DUNE_Pk1DLOCALBASIS_HH
#include <dune/common/fmatrix.hh>
#include <dune/localfunctions/common/localbasis.hh>
namespace Dune
{
/**@ingroup LocalBasisImplementation
\brief Lagrange shape functions of arbitrary order on the 1D reference triangle.
Lagrange shape functions of arbitrary order have the property that
\f$\hat\phi^i(x_j) = \delta_{i,j}\f$ for certain points \f$x_j\f$.
\tparam D Type to represent the field in the domain.
\tparam R Type to represent the field in the range.
\tparam k Polynomial order.
\nosubgrouping
*/
template<class D, class R, unsigned int k>
class Pk1DLocalBasis
{
public:
/** \brief Export the number of degrees of freedom */
enum {N = k+1};
/** \brief Export the element order */
enum {O = k};
typedef LocalBasisTraits<D,
1,
Dune::FieldVector<D,1>,
R,
1,
Dune::FieldVector<R,1>,
Dune::FieldMatrix<R,1,1>
> Traits;
//! \brief Standard constructor
Pk1DLocalBasis ()
{
for (unsigned int i=0; i<=k; i++)
pos[i] = (1.0*i)/std::max(k,(unsigned int)1);
}
//! \brief number of shape functions
unsigned int size () const
{
return N;
}
//! \brief Evaluate all shape functions
inline void evaluateFunction (const typename Traits::DomainType& x,
std::vector<typename Traits::RangeType>& out) const
{
out.resize(N);
for (unsigned int i=0; i<N; i++)
{
out[i] = 1.0;
for (unsigned int alpha=0; alpha<i; alpha++)
out[i] *= (x[0]-pos[alpha])/(pos[i]-pos[alpha]);
for (unsigned int gamma=i+1; gamma<=k; gamma++)
out[i] *= (x[0]-pos[gamma])/(pos[i]-pos[gamma]);
}
}
//! \brief Evaluate Jacobian of all shape functions
inline void
evaluateJacobian (const typename Traits::DomainType& x, // position
std::vector<typename Traits::JacobianType>& out) const // return value
{
out.resize(N);
for (unsigned int i=0; i<=k; i++) {
// x_0 derivative
out[i][0][0] = 0.0;
R factor=1.0;
for (unsigned int a=0; a<i; a++)
{
R product=factor;
for (unsigned int alpha=0; alpha<i; alpha++)
product *= (alpha==a) ? 1.0/(pos[i]-pos[alpha])
: (x[0]-pos[alpha])/(pos[i]-pos[alpha]);
for (unsigned int gamma=i+1; gamma<=k; gamma++)
product *= (pos[gamma]-x[0])/(pos[gamma]-pos[i]);
out[i][0][0] += product;
}
for (unsigned int c=i+1; c<=k; c++)
{
R product=factor;
for (unsigned int alpha=0; alpha<i; alpha++)
product *= (x[0]-pos[alpha])/(pos[i]-pos[alpha]);
for (unsigned int gamma=i+1; gamma<=k; gamma++)
product *= (gamma==c) ? -1.0/(pos[gamma]-pos[i])
: (pos[gamma]-x[0])/(pos[gamma]-pos[i]);
out[i][0][0] += product;
}
}
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return k;
}
private:
R pos[k+1]; // positions on the interval
};
}
#endif
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