void QK_find_N_opt_3D()
{
using namespace Feel;
typedef T value_type;
Gauss<Hypercube<3,1>, N ,value_type > im;
ublas::vector<value_type> x_i( ublas::row( im.points(),0 ) );
ublas::vector<value_type> y_i( ublas::row( im.points(),1 ) );
ublas::vector<value_type> z_i( ublas::row( im.points(),2 ) );
const value_type tol = value_type( 2.5 )*type_traits<value_type>::epsilon();
/* 1D number of Nodes */
//@{
uint16_type Q = ( uint16_type )pow( im.nPoints(),double( 1 )/3 );
//@}
value_type error = 0.0;
value_type res;
uint16_type i=1;
value_type sum=0.0;
ost << "Nbre of Points on the Hexaedra : " << Q << "^3 = "<< im.nPoints() << std::endl;
do
{
if ( i%2 == 0 )
res = value_type( 8.0 )/value_type( i+1.0 )/value_type( i+1.0 )/value_type( i+1.0 );
else
res = 0.0;
sum = 0.0;
for ( uint16_type l=0; l< x_i.size(); ++l )
{
sum += pow( x_i( l ), i )*pow( y_i( l ),i )*pow( z_i( l ),i )*im.weight( l );
}
error = math::abs( sum - res );
ost << "i = " << i <<" Error = "<< error << "\n";
++i;
}
while ( error <= tol );
if ( i-2 < 2*Q-1 )
QK_log_3D << "Q = " << Q << " ; i = " << i << " ; Error" << error << std::endl;
BOOST_CHECK( i-2 >= 2*Q-1 );
}
void PK_find_N_opt()
//@}
{
using namespace Feel;
typedef T value_type;
Gauss<Simplex<2,1> , N, value_type> im;
ublas::vector<value_type> x_i( ublas::row( im.points(),0 ) );
ublas::vector<value_type> y_i( ublas::row( im.points(),1 ) );
const value_type tol = value_type( 7.0 )*type_traits<value_type>::epsilon();
ost << "Tolerance = " << tol << "\n";
uint16_type Q = ( uint16_type )sqrt( im.nPoints() );
value_type error;
value_type res;
uint16_type i=1;
value_type sum;
ost << "Nbre of Points on the triangle : " << Q << "^2 = "<< im.nPoints() << std::endl;
do
{
if ( i%2 == 0 )
res = value_type( 2.0 )/value_type( double( i )+1.0 )/value_type( double( i )+1.0 );
else
res = value_type( 0.0 );
sum = value_type( 0.0 );
for ( uint16_type l=0; l< x_i.size(); ++l )
{
value_type p = pow( x_i( l ),i )*pow( y_i( l ),i )*im.weight( l );
// std::cout << "Contrib = " << p << "\n";
sum += p;
}
#if 0
std::cout << "i = " << i << "\n";
std::cout << "res = " << res << "\n";
std::cout << "sum = " << sum << "\n";
#endif
error = math::abs( sum - res );
ost << "i = " << i <<" Error = "<< error << "\n";
++i;
}
while ( error <= tol );
if ( i-2 < Q-1 )
PK_log << "Q = " << Q << " ; i = " << i << " ; Error = " << error << std::endl;
BOOST_CHECK( i-2 >= Q-1 );
}