/usr/include/dune/localfunctions/lagrange/qk/qklocalbasis.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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 | // -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_LOCALFUNCTIONS_QKLOCALBASIS_HH
#define DUNE_LOCALFUNCTIONS_QKLOCALBASIS_HH
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
#include <dune/common/power.hh>
#include <dune/geometry/type.hh>
#include <dune/localfunctions/common/localbasis.hh>
#include <dune/localfunctions/common/localfiniteelementtraits.hh>
namespace Dune
{
/**@ingroup LocalBasisImplementation
\brief Lagrange shape functions of order k on the reference cube.
Also known as \f$Q^k\f$.
\tparam D Type to represent the field in the domain.
\tparam R Type to represent the field in the range.
\tparam k Polynomial degree
\tparam d Dimension of the cube
\nosubgrouping
*/
template<class D, class R, int k, int d>
class QkLocalBasis
{
enum { n = StaticPower<k+1,d>::power };
// ith Lagrange polynomial of degree k in one dimension
static R p (int i, D x)
{
R result(1.0);
for (int j=0; j<=k; j++)
if (j!=i) result *= (k*x-j)/(i-j);
return result;
}
// derivative of ith Lagrange polynomial of degree k in one dimension
static R dp (int i, D x)
{
R result(0.0);
for (int j=0; j<=k; j++)
if (j!=i)
{
R prod( (k*1.0)/(i-j) );
for (int l=0; l<=k; l++)
if (l!=i && l!=j)
prod *= (k*x-l)/(i-l);
result += prod;
}
return result;
}
// Return i as a d-digit number in the (k+1)-nary system
static Dune::FieldVector<int,d> multiindex (int i)
{
Dune::FieldVector<int,d> alpha;
for (int j=0; j<d; j++)
{
alpha[j] = i % (k+1);
i = i/(k+1);
}
return alpha;
}
public:
typedef LocalBasisTraits<D,d,Dune::FieldVector<D,d>,R,1,Dune::FieldVector<R,1>,Dune::FieldMatrix<R,1,d> > Traits;
//! \brief number of shape functions
unsigned int size () const
{
return StaticPower<k+1,d>::power;
}
//! \brief Evaluate all shape functions
inline void evaluateFunction (const typename Traits::DomainType& in,
std::vector<typename Traits::RangeType>& out) const
{
out.resize(size());
for (size_t i=0; i<size(); i++)
{
// convert index i to multiindex
Dune::FieldVector<int,d> alpha(multiindex(i));
// initialize product
out[i] = 1.0;
// dimension by dimension
for (int j=0; j<d; j++)
out[i] *= p(alpha[j],in[j]);
}
}
/** \brief Evaluate Jacobian of all shape functions
* \param in position where to evaluate
* \param out The return value
*/
inline void
evaluateJacobian (const typename Traits::DomainType& in,
std::vector<typename Traits::JacobianType>& out) const
{
out.resize(size());
// Loop over all shape functions
for (size_t i=0; i<size(); i++)
{
// convert index i to multiindex
Dune::FieldVector<int,d> alpha(multiindex(i));
// Loop over all coordinate directions
for (int j=0; j<d; j++)
{
// Initialize: the overall expression is a product
// if j-th bit of i is set to -1, else 1
out[i][0][j] = dp(alpha[j],in[j]);
// rest of the product
for (int l=0; l<d; l++)
if (l!=j)
out[i][0][j] *= p(alpha[l],in[l]);
}
}
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return k;
}
};
}
#endif
|