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Added scattering experiment

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Yohai Meiron 2020-05-06 11:58:53 -04:00
parent 8cb62ac88c
commit b67c2cf2cb
4 changed files with 222 additions and 11 deletions
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main.cpp
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#include <algorithm>
#include <array>
#include <boost/numeric/odeint.hpp>
#include <Eigen/Geometry>
#include <fstream>
#include <gsl/gsl_spline.h>
#include <iostream>
#include <numeric>
#include <string>
#include <stdexcept>
#include <vector>
#include "loadtxt.h"
using double3 = Eigen::Vector3d;
// Our units are {kiloparsec, solar mass, gigayear}
constexpr double G = 4.498317481097514e-06;
class Interp {
// This is a wrapper around GSL spline interpolation. I tried to use
// boost::math::interpolators but as of version 1.72 none were suitable:
// barycentric_rational is the one suitalbe for non-uniform sampling but it
// is very slow. I also tried to resample the data uniformly using
// barycentric rational interpolation and then using cardinal_cubic_b_spline
// on the result, but was still slower than GSL.
public:
Interp(std::vector<double>& x, std::vector<double>& y)
{
acc = gsl_interp_accel_alloc();
spline = gsl_spline_alloc(gsl_interp_cspline, x.size());
gsl_spline_init(spline, x.data(), y.data(), x.size());
}
Interp() {}
inline double operator()(double x) const
{
return gsl_spline_eval(spline, x, acc);
}
private:
gsl_interp_accel *acc;
gsl_spline *spline;
};
double3 plummer(const double M, const double b, const double3& pos)
{
double r2 = pos.squaredNorm() + b*b;
double r = sqrt(r2);
double r3_inv = 1/(r*r2);
return -G*M*pos*r3_inv;
}
double3 nfw(const double rho_0, const double b, const double3& pos)
{
double r2 = pos.squaredNorm();
double r = sqrt(r2);
double tmp = -4*M_PI*G*rho_0*b*b*b*(log(1+r/b) - r/(b+r))/(r2*r);
return pos*tmp;
}
double3 miyamoto_nagai(const double M, const double a, const double b, const double phi, const double theta, const double3& pos)
{
// Construct new z-axis from the angles
double cos_theta = cos(theta);
double sin_theta = sqrt(1-cos_theta*cos_theta);
double cos_phi = cos(phi);
double sin_phi = sqrt(1-cos_phi*cos_phi);
Eigen::Vector3d old_z_axis = {cos_phi*sin_theta, sin_phi*sin_theta, cos_theta};
// Construct rotation
auto rot = Eigen::Quaternion<double>::FromTwoVectors(old_z_axis, Eigen::Vector3d::UnitZ());
// Rotate the position vector
auto new_pos = rot * pos;
// Calculate acceleration in new frame
Eigen::Vector3d acc_in_rotated_frame;
auto z_tmp = sqrt(new_pos[2]*new_pos[2] + b*b);
auto r2_tmp = new_pos[0]*new_pos[0] + new_pos[1]*new_pos[1] + (z_tmp + a)*(z_tmp + a);
auto r_tmp = sqrt(r2_tmp);
auto tmp = G*M / (r2_tmp*r_tmp);
acc_in_rotated_frame[0] = - tmp * new_pos[0];
acc_in_rotated_frame[1] = - tmp * new_pos[1];
acc_in_rotated_frame[2] = - tmp * new_pos[2] * (z_tmp + a)/z_tmp;
// Return to original frame
return rot.inverse() * acc_in_rotated_frame;
}
class Galaxy {
public:
Galaxy(std::string file_name)
{
auto data = Loadtxt(file_name, {1, 2, 3, 4, 5, 6, 7, 8}).get_cols();
auto& t_data = data[0];
std::transform(begin(t_data), end(t_data), begin(t_data), [t0=t_data[0]](const double& x){ return x-t0; });
for (int i=0; i<7; i++) interp[i] = Interp(t_data, data[i+1]);
}
void func(const std::array<double, 6> &y, std::array<double, 6> &f, const double t)
{
f[0] = y[3]; // vx -> x'
f[1] = y[4]; // vy -> y'
f[2] = y[5]; // vz -> z'
double phi = interp[0](t);
double theta = interp[1](t);
double m_disk = interp[2](t);
double a_disk = interp[3](t);
double b_disk = interp[4](t);
double rho_0_nfw = interp[5](t);
double b_nfw = interp[6](t);
double3 pos(y.data());
double3 acc_disk = miyamoto_nagai(m_disk, a_disk, b_disk, phi, theta, pos);
double3 acc_halo = nfw(rho_0_nfw, b_nfw, pos);
for (int i=0; i<3; i++) f[3+i] = acc_disk[i] + acc_halo[i];
}
private:
Interp interp[10];
} galaxy("subhalo_411321_parameters_processed.dat");
extern "C"
void integrate(const double y0[], const double t_max, const double stride_size, double y[])
{
using namespace boost::numeric::odeint;
using Coordinates = std::array<double, 6>;
auto stepper = bulirsch_stoer<Coordinates>(1E-7, 0);
auto function_wrapper = [](const Coordinates &x, Coordinates &dxdt, const double t) { return galaxy.func(x, dxdt, t); };
const int stride_count = t_max / stride_size;
Coordinates y_current;
std::copy(y0, y0+6, begin(y_current));
std::copy(y0, y0+6, y);
double t = 0;
const double h = std::min(1./4096., stride_size);
for (int i=0; i<stride_count; i++) {
integrate_adaptive(stepper, function_wrapper, y_current, t, t+stride_size, h);
// NOTE h here is just a recommended initial step size for the stepper,
// the actual step is adapted as needed. Since the integration is
// interrupted here in order for the data to be saved, the result
// somewhat depends on stride_size.
std::copy(begin(y_current), end(y_current), y+(i+1)*6);
t += stride_size;
}
}
int main()
{
std::cout << "Hi" << std::endl;
double y[12];
double y0[] = {80,0,0,0,80,0};
integrate(y0, 10, 10, y);
for (int i=0; i<12; i++) std::cout << y[i] << std::endl;
// double y[12];
// double y0[] = {80,0,0,0,80,0};
// for (int i=0; i<8000; i++)
// integrate(y0, 10, 10, y);
/*double y0[] = {80,0,0,0,80,0};
double y[12];
integrate(y0, 10, 10, y);
for (int i=0; i<12; i++) std::cout << y[i] << std::endl;*/
//std::vector<double> w = {8, 0.12, 0.04, -0.08, 200, -0.001};
std::cout << "Bye" << std::endl;
return 0;
}