scalar cnoidalFirst::ddxPd
(
const point & x,
const scalar & time,
const vector & unitVector
) const
{
scalar Z(returnZ(x));
scalar arg(argument(x,time));
scalar snn(0.0), cnn(0.0), dnn(0.0);
gsl_sf_elljac_e( arg, m_, &snn, &cnn, &dnn);
scalar ddxPd(0);
ddxPd = rhoWater_ * Foam::mag(g_)
* (
eta_x(snn, cnn, dnn) + 1.0 / 2.0 * Foam::pow(h_, 2.0) * (1 - Foam::pow((Z + h_) / h_, 2.0)) * eta_xxx(snn, cnn, dnn)
);
ddxPd *= factor(time);
// Info << "ddxPd still isn't implemented. Need to think about the gradient on arbitrary directed mesh with arbitrary wave number vector! and arbitrary g-direction!!!" << endl;
return ddxPd;
}
static VALUE rb_gsl_sf_elljac_e(VALUE obj, VALUE n, VALUE m)
{
double sn, cn, dn;
// local variable "status" declared and set, but never used
//int status;
Need_Float(n); Need_Float(m);
/*status =*/ gsl_sf_elljac_e(NUM2DBL(n), NUM2DBL(m), &sn, &cn, &dn);
return rb_ary_new3(3, rb_float_new(sn),
rb_float_new(cn), rb_float_new(dn));
}
/// Jacobian elliptic integrals dn.
double
jacobi_dn(double k, double u)
{
double m = k * k;
double sn, cn, dn;
int stat = gsl_sf_elljac_e(u, m, &sn, &cn, &dn);
if (stat != GSL_SUCCESS)
{
std::ostringstream msg("Error in jacobi_dn:");
msg << " u=" << u << " k=" << k;
throw std::runtime_error(msg.str());
}
else
return dn;
}
scalar cnoidalFirst::eta
(
const point & x,
const scalar & time
) const
{
scalar arg(argument(x,time));
scalar snn(0.0), cnn(0.0), dnn(0.0);
gsl_sf_elljac_e( arg, m_, &snn, &cnn, &dnn);
scalar eta = ( etaMin_ + H_ * Foam::pow(cnn,2.0) ) * factor(time) + seaLevel_;
return eta;
}
const vector<double> getOmega(int Ns,double lambda_min,double lambda_max){
double u, m;
double sn, cn, dn;
double kprime = sqrt(1.0-(lambda_min/lambda_max)*(lambda_min/lambda_max));
vector<double> omegas(Ns);
for(int ii=0; ii<Ns; ++ii){
int is = 2*ii + 1;
m = kprime*kprime;
double vs = set_vs( is, Ns*2, kprime );
gsl_sf_elljac_e( vs, m, &sn, &cn, &dn );
double sn2 = sn * sn;
double kappaprime2 = kprime * kprime;
omegas[ii] = (1.0/lambda_min)* sqrt(1.0-kappaprime2*sn2);
}
#if VERBOSITY>2
for( int ii=0; ii<Ns; ++ii) printf("%24.16E\n", omegas[ii] );
#endif
return omegas;
}
vector cnoidalFirst::U
(
const point & x,
const scalar & time
) const
{
scalar Z(returnZ(x));
scalar arg(argument(x, time));
scalar snn(0.0), cnn(0.0), dnn(0.0);
gsl_sf_elljac_e( arg, m_, &snn, &cnn, &dnn);
scalar etaVal = eta(x,time);
scalar Uhorz = celerity_
* (
etaVal / h_
- Foam::pow(etaVal / h_, 2.0)
+ 1.0 / 2.0 *
(
1.0 / 3.0
- Foam::pow((Z + h_) / h_, 2.0)
)
* h_ * eta_xx(snn, cnn, dnn)
);
Uhorz *= factor(time);
scalar Uvert = - celerity_ * (Z + h_)
* (
eta_x(snn, cnn, dnn) / h_ * (1 - 2.0 * etaVal / h_)
+ 1.0 / 6.0 * h_ * eta_xxx(snn, cnn, dnn)
* (1 - Foam::pow((Z + h_) / h_, 2.0))
);
Uvert *= factor(time);
return Uhorz * propagationDirection_ - Uvert * direction_; // Note "-" because of "g" working in the opposite direction
}
int main()
{
#include "jacobi_elliptic.ipp"
#include "jacobi_elliptic_small.ipp"
#include "jacobi_near_1.ipp"
#include "jacobi_large_phi.ipp"
add_data(data1);
add_data(jacobi_elliptic);
add_data(jacobi_elliptic_small);
add_data(jacobi_near_1);
add_data(jacobi_large_phi);
unsigned data_total = data.size();
std::cout << "Screening Boost data:\n";
screen_data([](const std::vector<double>& v) {
return boost::math::jacobi_dn(v[1], v[0]);
}, [](const std::vector<double>& v) {
return v[4];
});
#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES)
std::cout << "Screening GSL data:\n";
screen_data([](const std::vector<double>& v)
{
double s, c, d;
gsl_sf_elljac_e(v[0], v[1] * v[1], &s, &c, &d);
return d;
}, [](const std::vector<double>& v) {
return v[4];
});
#endif
unsigned data_used = data.size();
std::string function = "jacobi_dn[br](" + boost::lexical_cast<std::string>(data_used) + "/" + boost::lexical_cast<std::string>(data_total) + " tests selected)";
std::string function_short = "jacobi_dn";
double time;
time = exec_timed_test([](const std::vector<double>& v) {
return boost::math::jacobi_dn(v[1], v[2]);
});
std::cout << time << std::endl;
#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH))
report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name());
#endif
report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name());
//
// Boost again, but with promotion to long double turned off:
//
#if !defined(COMPILER_COMPARISON_TABLES)
if(sizeof(long double) != sizeof(double))
{
time = exec_timed_test([](const std::vector<double>& v) {
return boost::math::jacobi_dn(v[1], v[0], boost::math::policies::make_policy(boost::math::policies::promote_double<false>()));
});
std::cout << time << std::endl;
#if !defined(COMPILER_COMPARISON_TABLES) && (defined(TEST_GSL) || defined(TEST_RMATH))
report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, boost_name() + "[br]promote_double<false>");
#endif
report_execution_time(time, std::string("Compiler Comparison on ") + std::string(platform_name()), function_short, compiler_name() + std::string("[br]") + boost_name() + "[br]promote_double<false>");
}
#endif
#if defined(TEST_GSL) && !defined(COMPILER_COMPARISON_TABLES)
time = exec_timed_test([](const std::vector<double>& v)
{
double s, c, d;
gsl_sf_elljac_e(v[0], v[1] * v[1], &s, &c, &d);
return d;
});
std::cout << time << std::endl;
report_execution_time(time, std::string("Library Comparison with ") + std::string(compiler_name()) + std::string(" on ") + platform_name(), function, "GSL " GSL_VERSION);
#endif
return 0;
}
