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// ************************************************************************************************
//
// BornAgain: simulate and fit reflection and scattering
//
//! @file Sample/Correlation/IDistribution2DSampler.cpp
//! @brief Defines class interface IProfile1D, 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/Correlation/IDistribution2DSampler.h"
#include <numbers>
#include <random>
using std::numbers::pi;
namespace {
const double sigma_scale = 3.0;
const size_t n_boxes = 256; // number of boxes for Ziggurat sampling
struct ZigguratBox {
ZigguratBox(double x_min, double x_max, double y_max, double y_lower)
: m_x_min(x_min)
, m_x_max(x_max)
, m_y_max(y_max)
, m_y_lower(y_lower)
{
}
double m_x_min; // left edge of the box
double m_x_max; // right edge of the box
// m_y_min is inherently 0 for every box and hence has not been defined
double m_y_max; // height of box
double m_y_lower; // minimum height of the box for which points below that height
// are located below the density function curve in the box
};
std::pair<double, double> samplingZiggurat(double r, double x_func_max, double (*func_phi)(double),
int seed)
{
// This sampling is based on vertical boxes instead of the conventional
// Ziggurat sampling that is done with horizontal boxes
std::random_device rd; // random device class instance
std::mt19937 gen(seed < 0 ? rd() : seed); // Standard mersenne_twister_engine seeded with rd()
std::uniform_real_distribution<double> uniformDist(0.0, 1.0);
double box_width = (x_func_max + r) / n_boxes; // r = rightmost box's right-edge from x_func_max
std::vector<ZigguratBox> boxes;
std::vector<double> cum_area_vector;
double x_min = 0, x_max = 0, y_max = 0, y_lower = 0, cum_area_box = 0;
// Establising vectors of boxes and cumulative area (probability of each box) for Ziggurat
// sampling
for (size_t i = 0; i < n_boxes; ++i) {
if (i != 0)
x_min = x_max;
x_max += box_width;
if (x_func_max >= x_max) {
y_max = func_phi(x_max);
y_lower = func_phi(x_min);
} else if (x_func_max > x_min && x_func_max <= x_max) {
y_max = func_phi(x_func_max);
y_lower = std::min(func_phi(x_min), func_phi(x_max));
} else {
y_max = func_phi(x_min);
y_lower = func_phi(x_max);
}
boxes.emplace_back(x_min, x_max, y_max, y_lower);
cum_area_box += box_width * y_max;
cum_area_vector.emplace_back(cum_area_box);
}
// Normalizing the cumulative area to 1
for (size_t i = 0; i < n_boxes; ++i)
cum_area_vector[i] = cum_area_vector[i] / cum_area_vector.back();
// Sampling a phi value
double phi = 0;
bool solnFound(false);
while (!solnFound) {
double random_cum_area = uniformDist(gen);
for (size_t i = 0; i < n_boxes; ++i) {
if (random_cum_area <= cum_area_vector[i]) {
double random_y = uniformDist(gen) * boxes[i].m_y_max;
std::uniform_real_distribution<double> uniformDistAB(boxes[i].m_x_min,
boxes[i].m_x_max);
double phi_attempt = uniformDistAB(gen);
if (random_y <= boxes[i].m_y_lower) {
phi = phi_attempt;
solnFound = true;
} else {
if (random_y <= func_phi(phi_attempt)) {
phi = phi_attempt;
solnFound = true;
}
}
break;
}
}
}
// Sampling an alpha value
double alpha = (2 * pi) * uniformDist(gen);
return std::make_pair(phi, alpha);
}
double func_phi_Cauchy(double phi)
{
// The independent "phi" density function of the 2D Cauchy distribution
return phi * std::exp(-phi);
}
double func_phi_Cone(double phi)
{
// The independent "phi" density function of the 2D Cone distribution
return 6 * (1 - phi) * phi;
}
} // namespace
IDistribution2DSampler::~IDistribution2DSampler() = default;
std::pair<double, double> Distribution2DCauchySampler::randomSample(int seed) const
{
// Use Ziggurat sampling instead of Inverse Transform Sampling (ITS requires numerical solver)
double phi_max_Cauchy = 1.0;
// rightmost box's right-edge from phi_max_Cauchy for Ziggurat Sampling
double r = sigma_scale * std::sqrt(2); // standard dev of func_phi_Cauchy is sqrt(2)
std::pair<double, double> samples = samplingZiggurat(r, phi_max_Cauchy, func_phi_Cauchy, seed);
return std::make_pair(m_omega_x * samples.first * std::cos(samples.second),
m_omega_y * samples.first * std::sin(samples.second));
}
std::pair<double, double> Distribution2DGaussSampler::randomSample(int seed) const
{
std::random_device rd; // random device class instance
std::mt19937 gen(seed < 0 ? rd() : seed); // Standard mersenne_twister_engine seeded with rd()
std::uniform_real_distribution<double> uniformDist(0.0, 1.0);
double cdf_value_phi = uniformDist(gen);
// Use ITS and solve for phi from the cdf of radial (phi) distribution
double phi = std::sqrt(-2 * std::log(1 - cdf_value_phi));
double alpha = (2 * pi) * uniformDist(gen);
return std::make_pair(m_omega_x * phi * std::cos(alpha), m_omega_y * phi * std::sin(alpha));
}
std::pair<double, double> Distribution2DGateSampler::randomSample(int seed) const
{
std::random_device rd; // random device class instance
std::mt19937 gen(seed < 0 ? rd() : seed); // Standard mersenne_twister_engine seeded with rd()
std::uniform_real_distribution<double> uniformDist(0.0, 1.0);
double cdf_value_phi = uniformDist(gen);
// Use ITS and solve for phi from the cdf of radial (phi) distribution
double phi = std::sqrt(cdf_value_phi);
double alpha = (2 * pi) * uniformDist(gen);
return std::make_pair(m_omega_x * phi * std::cos(alpha), m_omega_y * phi * std::sin(alpha));
}
std::pair<double, double> Distribution2DConeSampler::randomSample(int seed) const
{
// Use Ziggurat sampling instead of Inverse Transform Sampling (ITS requires numerical solver)
double phi_max_Cone = 0.5;
// rightmost box's right-edge from phi_max_Cone for Ziggurat Sampling
double r = 0.5;
std::pair<double, double> samples = samplingZiggurat(r, phi_max_Cone, func_phi_Cone, seed);
return std::make_pair(m_omega_x * samples.first * std::cos(samples.second),
m_omega_y * samples.first * std::sin(samples.second));
}
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