FTDistributions2D.cpp

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//  ************************************************************************************************
//
//  BornAgain: simulate and fit reflection and scattering
//
//! @file      Sample/Correlations/FTDistributions2D.cpp
//! @brief     Implements interface class IFTDistribution2D and children thereof.
//!
//! @homepage  http://www.bornagainproject.org
//! @license   GNU General Public License v3 or higher (see COPYING)
//! @copyright Forschungszentrum Jülich GmbH 2018
//! @authors   Scientific Computing Group at MLZ (see CITATION, AUTHORS)
//
//  ************************************************************************************************
 
#include "Sample/Correlations/FTDistributions2D.h"
#include "Base/Math/Bessel.h"
#include "Base/Math/IntegratorGK.h"
#include <limits>
 
//  ************************************************************************************************
//  interface IFTDistribution1D
//  ************************************************************************************************
 
IFTDistribution2D::IFTDistribution2D(const NodeMeta& meta, const std::vector<double>& PValues)
    : INode(nodeMetaUnion({{"OmegaX", "nm", "Half-width along x axis", 0, INF, 1.},
                           {"OmegaY", "nm", "Half-width along y axis", 0, INF, 1.},
                           {"Gamma", "rad",
                            "direct-space orientation with respect to the first lattice vector",
                            -M_PI_2, +M_PI_2, 0}},
                          meta),
            PValues)
    , m_omega_x(m_P[0])
    , m_omega_y(m_P[1])
    , m_gamma(m_P[2])
{
}
 
double IFTDistribution2D::sumsq(double qx, double qy) const
{
    return qx * qx * m_omega_x * m_omega_x + qy * qy * m_omega_y * m_omega_y;
}
 
//  ************************************************************************************************
//  class FTDistribution2DCauchy
//  ************************************************************************************************
 
FTDistribution2DCauchy::FTDistribution2DCauchy(const std::vector<double> P)
    : IFTDistribution2D({"FTDistribution2DCauchy", "class_tooltip", {}}, P)
{
}
 
FTDistribution2DCauchy::FTDistribution2DCauchy(double omega_x, double omega_y, double gamma)
    : FTDistribution2DCauchy(std::vector<double>{omega_x, omega_y, gamma})
{
}
 
FTDistribution2DCauchy* FTDistribution2DCauchy::clone() const
{
    return new FTDistribution2DCauchy(m_omega_x, m_omega_y, m_gamma);
}
 
double FTDistribution2DCauchy::evaluate(double qx, double qy) const
{
    return std::pow(1.0 + sumsq(qx, qy), -1.5);
}
 
std::unique_ptr<IDistribution2DSampler> FTDistribution2DCauchy::createSampler() const
{
    return std::make_unique<Distribution2DCauchySampler>(m_omega_x, m_omega_y);
}
 
//  ************************************************************************************************
//  class FTDistribution2DGauss
//  ************************************************************************************************
 
FTDistribution2DGauss::FTDistribution2DGauss(const std::vector<double> P)
    : IFTDistribution2D({"FTDistribution2DGauss", "class_tooltip", {}}, P)
{
}
 
FTDistribution2DGauss::FTDistribution2DGauss(double omega_x, double omega_y, double gamma)
    : FTDistribution2DGauss(std::vector<double>{omega_x, omega_y, gamma})
{
}
 
FTDistribution2DGauss* FTDistribution2DGauss::clone() const
{
    return new FTDistribution2DGauss(m_omega_x, m_omega_y, m_gamma);
}
 
double FTDistribution2DGauss::evaluate(double qx, double qy) const
{
    return std::exp(-sumsq(qx, qy) / 2);
}
 
std::unique_ptr<IDistribution2DSampler> FTDistribution2DGauss::createSampler() const
{
    return std::make_unique<Distribution2DGaussSampler>(m_omega_x, m_omega_y);
}
 
//  ************************************************************************************************
//  class FTDistribution2DGate
//  ************************************************************************************************
 
FTDistribution2DGate::FTDistribution2DGate(const std::vector<double> P)
    : IFTDistribution2D({"FTDistribution2DGate", "class_tooltip", {}}, P)
{
}
 
FTDistribution2DGate::FTDistribution2DGate(double omega_x, double omega_y, double gamma)
    : FTDistribution2DGate(std::vector<double>{omega_x, omega_y, gamma})
{
}
 
FTDistribution2DGate* FTDistribution2DGate::clone() const
{
    return new FTDistribution2DGate(m_omega_x, m_omega_y, m_gamma);
}
 
double FTDistribution2DGate::evaluate(double qx, double qy) const
{
    double scaled_q = std::sqrt(sumsq(qx, qy));
    return Math::Bessel::J1c(scaled_q) * 2.0;
}
 
std::unique_ptr<IDistribution2DSampler> FTDistribution2DGate::createSampler() const
{
    return std::make_unique<Distribution2DGateSampler>(m_omega_x, m_omega_y);
}
 
//  ************************************************************************************************
//  class FTDistribution2DCone
//  ************************************************************************************************
 
FTDistribution2DCone::FTDistribution2DCone(const std::vector<double> P)
    : IFTDistribution2D({"FTDistribution2DCone", "class_tooltip", {}}, P)
{
}
 
FTDistribution2DCone::FTDistribution2DCone(double omega_x, double omega_y, double gamma)
    : FTDistribution2DCone(std::vector<double>{omega_x, omega_y, gamma})
{
}
 
FTDistribution2DCone* FTDistribution2DCone::clone() const
{
    return new FTDistribution2DCone(m_omega_x, m_omega_y, m_gamma);
}
 
double FTDistribution2DCone::evaluate(double qx, double qy) const
{
    double scaled_q = std::sqrt(sumsq(qx, qy));
    if (scaled_q < std::numeric_limits<double>::epsilon())
        return 1.0 - 3.0 * scaled_q * scaled_q / 40.0;
    // second part of the integrand: \f$u^2\cdot J_0(u)\f$
    double integral = RealIntegrator().integrate(
        [](double x) -> double { return x * x * Math::Bessel::J0(x); }, 0.0, scaled_q);
    return 6.0 * (Math::Bessel::J1c(scaled_q) - integral / scaled_q / scaled_q / scaled_q);
}
 
std::unique_ptr<IDistribution2DSampler> FTDistribution2DCone::createSampler() const
{
    return std::make_unique<Distribution2DConeSampler>(m_omega_x, m_omega_y);
}
 
//  ************************************************************************************************
//  class FTDistribution2DVoigt
//  ************************************************************************************************
 
FTDistribution2DVoigt::FTDistribution2DVoigt(const std::vector<double> P)
    : IFTDistribution2D(
        {"FTDistribution2DVoigt",
         "class_tooltip",
         {{"Eta", "", "balances between Gauss (eta=0) and Cauchy (eta=1) limiting cases", -INF,
           +INF, 0}}},
        P)
    , m_eta(m_P[3])
{
}
 
FTDistribution2DVoigt::FTDistribution2DVoigt(double omega_x, double omega_y, double gamma,
                                             double eta)
    : FTDistribution2DVoigt(std::vector<double>{omega_x, omega_y, gamma, eta})
{
}
 
FTDistribution2DVoigt* FTDistribution2DVoigt::clone() const
{
    return new FTDistribution2DVoigt(m_omega_x, m_omega_y, m_gamma, m_eta);
}
 
double FTDistribution2DVoigt::evaluate(double qx, double qy) const
{
    double sum_sq = sumsq(qx, qy);
    return m_eta * std::exp(-sum_sq / 2) + (1.0 - m_eta) * std::pow(1.0 + sum_sq, -1.5);
}
 
std::unique_ptr<IDistribution2DSampler> FTDistribution2DVoigt::createSampler() const
{
    // TODO Need to implement 2D Voigt
 
    std::ostringstream ostr;
    ostr << "FTDistribution2DVoigt::createSampler() -> Error in class initialization";
    ostr << "\n\n Has not been implemented yet...stay tuned!";
    throw std::runtime_error(ostr.str());
}