/usr/include/dune/localfunctions/orthonormal/orthonormalcompute.hh is in libdune-localfunctions-dev 2.4.1-1.
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_ORTHONORMALCOMPUTE_HH
#define DUNE_ORTHONORMALCOMPUTE_HH
#include <cassert>
#include <iostream>
#include <fstream>
#include <iomanip>
#include <map>
#include <dune/common/fmatrix.hh>
#include <dune/geometry/genericgeometry/topologytypes.hh>
#include <dune/localfunctions/utility/field.hh>
#include <dune/localfunctions/utility/lfematrix.hh>
#include <dune/localfunctions/utility/monomialbasis.hh>
#include <dune/localfunctions/utility/multiindex.hh>
namespace ONBCompute
{
template< class scalar_t >
scalar_t factorial( int start, int end )
{
scalar_t ret( 1 );
for( int j = start; j <= end; ++j )
ret *= scalar_t( j );
return ret;
}
// Integral
// --------
template< class Topology >
struct Integral;
template< class Base >
struct Integral< Dune::GenericGeometry::Pyramid< Base > >
{
template< int dim, class scalar_t >
static int compute ( const Dune::MultiIndex< dim, scalar_t > &alpha,
scalar_t &p, scalar_t &q )
{
const int dimension = Base::dimension+1;
int i = alpha.z( Base::dimension );
int ord = Integral< Base >::compute( alpha, p, q );
p *= factorial< scalar_t >( 1, i );
q *= factorial< scalar_t >( dimension + ord, dimension + ord + i );
return ord + i;
}
};
template< class Base >
struct Integral< Dune::GenericGeometry::Prism< Base > >
{
template< int dim, class scalar_t >
static int compute ( const Dune::MultiIndex< dim, scalar_t > &alpha,
scalar_t &p, scalar_t &q )
{
int i = alpha.z( Base::dimension );
int ord = Integral< Base >::compute( alpha, p, q );
//Integral< Base >::compute( alpha, p, q );
//p *= scalar_t( 1 );
q *= scalar_t( i+1 );
return ord + i;
}
};
template<>
struct Integral< Dune::GenericGeometry::Point >
{
template< int dim, class scalar_t >
static int compute ( const Dune::MultiIndex< dim, scalar_t > &alpha,
scalar_t &p, scalar_t &q )
{
p = scalar_t( 1 );
q = scalar_t( 1 );
return 0;
}
};
// ONBMatrix
// ---------
template< class Topology, class scalar_t >
class ONBMatrix
: public Dune::LFEMatrix< scalar_t >
{
typedef ONBMatrix< Topology, scalar_t > This;
typedef Dune::LFEMatrix< scalar_t > Base;
public:
typedef std::vector< scalar_t > vec_t;
typedef Dune::LFEMatrix< scalar_t > mat_t;
explicit ONBMatrix ( unsigned int order )
{
// get all multiindecies for monomial basis
const unsigned int dim = Topology::dimension;
typedef Dune::MultiIndex< dim, scalar_t > MI;
Dune::StandardMonomialBasis< dim, MI > basis( order );
const std::size_t size = basis.size();
std::vector< Dune::FieldVector< MI, 1 > > y( size );
Dune::FieldVector< MI, dim > x;
for( unsigned int i = 0; i < dim; ++i )
x[ i ].set( i );
basis.evaluate( x, y );
// set bounds of data
Base::resize( size, size );
S.resize( size, size );
d.resize( size );
// setup matrix for bilinear form x^T S y: S_ij = int_A x^(i+j)
scalar_t p, q;
for( std::size_t i = 0; i < size; ++i )
{
for( std::size_t j = 0; j < size; ++j )
{
Integral< Topology >::compute( y[ i ][ 0 ] * y[ j ][ 0 ], p, q );
S( i, j ) = p;
S( i, j ) /= q;
}
}
// orthonormalize
gramSchmidt();
}
template< class Vector >
void row ( unsigned int row, Vector &vec ) const
{
// transposed matrix is required
assert( row < Base::cols() );
for( std::size_t i = 0; i < Base::rows(); ++i )
Dune::field_cast( Base::operator()( i, row ), vec[ i ] );
}
private:
void sprod ( int col1, int col2, scalar_t &ret )
{
ret = 0;
for( int k = 0; k <= col1; ++k )
{
for( int l = 0; l <=col2; ++l )
ret += Base::operator()( l, col2 ) * S( l, k ) * Base::operator()( k, col1 );
}
}
void vmul ( std::size_t col, std::size_t rowEnd, const scalar_t &s )
{
for( std::size_t i = 0; i <= rowEnd; ++i )
Base::operator()( i, col ) *= s;
}
void vsub ( std::size_t coldest, std::size_t colsrc, std::size_t rowEnd, const scalar_t &s )
{
for( std::size_t i = 0; i <= rowEnd; ++i )
Base::operator()( i, coldest ) -= s * Base::operator()( i, colsrc );
}
void gramSchmidt ()
{
// setup identity
const std::size_t N = Base::rows();
for( std::size_t i = 0; i < N; ++i )
{
for( std::size_t j = 0; j < N; ++j )
Base::operator()( i, j ) = scalar_t( i == j ? 1 : 0 );
}
// perform Gram-Schmidt procedure
scalar_t s;
sprod( 0, 0, s );
vmul( 0, 0, scalar_t( 1 ) / sqrt( s ) );
for( std::size_t i = 1; i < N; ++i )
{
for( std::size_t k = 0; k < i; ++k )
{
sprod( i, k, s );
vsub( i, k, i, s );
}
sprod( i, i, s );
vmul( i, i, scalar_t( 1 ) / sqrt( s ) );
}
}
vec_t d;
mat_t S;
};
} // namespace ONBCompute
#endif // #ifndef DUNE_ORTHONORMALCOMPUTE_HH
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