From f8eae117dda2cb7ed06f1f348dff907be5e50947 Mon Sep 17 00:00:00 2001 From: Yohai Meiron Date: Sun, 26 Apr 2020 22:51:52 -0400 Subject: [PATCH] Processed subhalo data and modified integrator to read and use new data structure --- loadtxt.cpp | 2 +- main.cpp | 103 +++++++++++++------ plot.py | 51 ++++++---- plot_subhalo_parameters.ipynb | 187 ++++++++++++++++++++++++++++++++-- 4 files changed, 281 insertions(+), 62 deletions(-) diff --git a/loadtxt.cpp b/loadtxt.cpp index 4b60ce5..6cc1ccb 100644 --- a/loadtxt.cpp +++ b/loadtxt.cpp @@ -62,7 +62,7 @@ void Loadtxt::line_to_buf(std::vector cols, std::string line, double *buffe if (col++ == cols[idx]) buffer[idx++] = std::stod(num_as_string); } if (col++ == cols[idx]) buffer[idx++] = std::stod(line); - if (idx < n_cols) throw; + if (idx < n_cols) throw std::runtime_error("Read fewer columns than expected"); } // Below is a deomonstration. The file has multiple columns but we are only diff --git a/main.cpp b/main.cpp index 48401f4..31ef955 100644 --- a/main.cpp +++ b/main.cpp @@ -1,6 +1,7 @@ #include #include #include +#include #include #include #include @@ -11,7 +12,7 @@ #include "loadtxt.h" - +using double3 = Eigen::Vector3d; // Our units are {kiloparsec, solar mass, gigayear} constexpr double G = 4.498317481097514e-06; @@ -41,52 +42,78 @@ private: gsl_spline *spline; }; -class Plummer { -public: - Plummer(double M, double b) - : M(M), b(b) {} - void calc_acceleration(const double *pos, double *acc) - { - double r2 = (pos[0]*pos[0] + pos[1]*pos[1] + pos[2]*pos[2] + b*b); - double r = sqrt(r2); - double r3_inv = 1/(r*r2); - acc[0] = -G*M*pos[0]*r3_inv; - acc[1] = -G*M*pos[1]*r3_inv; - acc[2] = -G*M*pos[2]*r3_inv; - } +void plummer(double M, double b, const double3& pos, double3& acc) +{ + double r2 = (pos[0]*pos[0] + pos[1]*pos[1] + pos[2]*pos[2] + b*b); + double r = sqrt(r2); + double r3_inv = 1/(r*r2); + acc = -G*M*pos*r3_inv; +} -private: - double M, b; -}; +void miyamoto_nagai(double M, double a, double b, double phi, double theta, const double3& pos, double3& acc) +{ + // 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::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 + acc = rot.inverse() * acc_in_rotated_frame; +} class Galaxy { public: Galaxy(std::string file_name) { - auto data = Loadtxt("file.dat", {1, 2, 3}).get_cols(); - auto& t_data = data[0]; - auto& halo_m_data = data[1]; - auto& halo_b_data = data[2]; + auto data = Loadtxt(file_name, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}).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; }); - std::transform(halo_b_data.begin(), halo_b_data.end(), halo_b_data.begin(), [](const double& x){ return x*0.7664209365408798; }); - interp_halo_m = Interp(t_data, halo_m_data); - interp_halo_b = Interp(t_data, halo_b_data); + for (int i=0; i<10; i++) interp[i] = Interp(t_data, data[i+1]); } void func(const std::array &y, std::array &f, const double t) { - double halo_m = interp_halo_m(t); - double halo_b = interp_halo_b(t); - Plummer plummer(halo_m, halo_b); f[0] = y[3]; // vx -> x' f[1] = y[4]; // vy -> y' f[2] = y[5]; // vz -> z' - plummer.calc_acceleration(y.data(), f.data()+3); // a -> v' + double m_disk = interp[0](t); + double phi = interp[1](t); + double theta = interp[2](t); + double a_disk = interp[3](t); + double b_disk = interp[4](t); + double m_halo = interp[5](t); + double b_halo = interp[6](t); + double3 dalembert; + // for (int i=0; i<3; i++) dalembert[i] = interp[7+i](t); + dalembert = {0,0,0}; + + double3 acc_disk, acc_halo; + const double3 pos(y.data()); + miyamoto_nagai(m_disk, a_disk, b_disk, phi, theta, pos, acc_disk); + plummer(m_halo, b_halo, pos, acc_halo); + for (int i=0; i<3; i++) f[3+i] = acc_disk[i] + acc_halo[i] + dalembert[i]; } private: - Interp interp_halo_m; - Interp interp_halo_b; -} galaxy("file.dat"); + Interp interp[10]; +} galaxy("subhalo_411321_parameters_processed.dat"); extern "C" int integrate(const double y0[], const double t_max, const double stride_size, double y[]) @@ -113,14 +140,24 @@ int integrate(const double y0[], const double t_max, const double stride_size, d } + + + int main() { std::cout << "Hi" << 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); + 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]; diff --git a/plot.py b/plot.py index d805035..7fe779c 100644 --- a/plot.py +++ b/plot.py @@ -4,7 +4,7 @@ import numpy as np import ctypes, subprocess -recompile = True +recompile = False if recompile: p = subprocess.Popen('g++ -I/home/meiron/boost_1_72_0 -shared -o libmain.so -fPIC loadtxt.cpp main.cpp -lgsl'.split()) @@ -21,28 +21,43 @@ def integrate(y0, t_max, step_size=None): y = np.array(y).reshape(size,6) return np.array(y), status -def integrate_boost(y0, t_max, step_size=None): - y0 = (ctypes.c_double*6)(*y0) - if step_size is None: step_size = t_max - size = int(t_max // step_size) + 1 - y = (ctypes.c_double*size*6)() - libmain.integrate_boost(y0, ctypes.c_double(t_max), ctypes.c_double(step_size), y) - y = np.array(y).reshape(size,6) - return np.array(y), 0 - -#gsl_success = libmain.gsl_success() - from pylab import * t_max = 10 +x_max = 85 ic = [80,0,0,0,80,0] res = integrate(ic, t_max, step_size=32/4096) x, y, z, vx, vy, vz = res[0].T -zzz = x[-1] -plot(x,y) -res = integrate(ic, t_max) -x, y, z, vx, vy, vz = res[0].T -plot(x,y,'o') -print(zzz - x[-1]) + +figure(figsize=(8,8)) +subplot(221) +plot(x, y) +plot(x[0], y[0], 'x') gca().set_aspect('equal') +xlabel('x') +ylabel('y') +xlim(-x_max,x_max) +ylim(-x_max,x_max) + +subplot(223) +plot(x, z) +plot(x[0], z[0], 'x') +gca().set_aspect('equal') +xlabel('x') +ylabel('z') +xlim(-x_max,x_max) +ylim(-x_max,x_max) + +subplot(224) +plot(y, z) +plot(y[0], z[0], 'x') +gca().set_aspect('equal') +xlabel('z') +ylabel('y') +xlim(-x_max,x_max) +ylim(-x_max,x_max) + +subplots_adjust(wspace=0.25) + +savefig('test_orbit.png') show() \ No newline at end of file diff --git a/plot_subhalo_parameters.ipynb b/plot_subhalo_parameters.ipynb index 2bd93b8..08d3224 100644 --- a/plot_subhalo_parameters.ipynb +++ b/plot_subhalo_parameters.ipynb @@ -17,7 +17,8 @@ "source": [ "from pylab import *\n", "import matplotlib\n", - "matplotlib.rcParams['figure.dpi'] = 120" + "matplotlib.rcParams['figure.dpi'] = 120\n", + "import scipy.interpolate" ] }, { @@ -26,7 +27,8 @@ "metadata": {}, "outputs": [], "source": [ - "data = loadtxt('subhalo_411321_parameters.dat')\n", + "file_name = 'subhalo_411321_parameters.dat'\n", + "data = loadtxt(file_name)\n", "snapshot = data[:,0]\n", "t = data[:,1]\n", "M_disk = data[:,2]\n", @@ -220,7 +222,7 @@ { "data": { "text/plain": [ - "Text(0, 0.5, '$\\\\mathbf{r}_\\\\mathrm{corrected}$ [kpc]')" + "Text(0, 0.5, '$\\\\phi$ [deg]')" ] }, "execution_count": 8, @@ -229,7 +231,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -238,6 +240,74 @@ "needs_background": "light" }, "output_type": "display_data" + } + ], + "source": [ + "# Make sure we don't have these weird jumps between -180 to +180\n", + "def fix_continuity(input_array, threshold_factor=0.95):\n", + " arr = input_array.copy()\n", + " threshold = threshold_factor*2*pi\n", + " for i in range(1, len(arr)):\n", + " if arr[i] - arr[i-1] > threshold: arr[i] -= 2*pi\n", + " if arr[i] - arr[i-1] < -threshold: arr[i] += 2*pi\n", + " return arr\n", + "phi_inertia_fixed = fix_continuity(phi_inertia)\n", + "plot(t, rad2deg(phi_inertia_fixed))\n", + "xlabel(r'$t$ [Gyr]')\n", + "ylabel(r'$\\phi$ [deg]')" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Inspecting the coordinates of the centre as a function of time\n", + "# Hopefully they look kinda like straight lines\n", + "plot(t, X_center_stars)\n", + "xlabel('$t$ [Gyr]')\n", + "ylabel('$\\mathbf{r}$ [kpc]')\n", + "legend(('$x$', '$y$', '$z$'))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, '$\\\\mathbf{r}_\\\\mathrm{corrected}$ [kpc]')" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" }, { "data": { @@ -253,23 +323,120 @@ } ], "source": [ - "# Average velocity throughout cosmic time\n", - "plot(t, X_center_stars)\n", - "xlabel('$t$ [Gyr]')\n", - "ylabel('$\\mathbf{r}$ [kpc]')\n", + "# Calculate the average velocity throughout cosmic time and subtract such that we only see the residual motion\n", + "\n", "Vx, _ = polyfit(t, X_center_stars[:,0], 1)\n", "Vy, _ = polyfit(t, X_center_stars[:,1], 1)\n", "Vz, _ = polyfit(t, X_center_stars[:,2], 1)\n", "V = array([Vx, Vy, Vz])\n", - "legend(('x', 'y', 'z'))\n", + "legend(('$x$', '$y$', '$z$'))\n", "\n", - "figure()\n", "plot(t, X_center_stars-V*(t-t[-1])[:,None])\n", "legend(('x', 'y', 'z'))\n", "xlabel('$t$ [Gyr]')\n", "ylabel('$\\mathbf{r}_\\mathrm{corrected}$ [kpc]')" ] }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, '$\\\\mathbf{r}_\\\\mathrm{corrected}$ [kpc]')" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Fit a relatively low order B-spline to each\n", + "k = 6 # Spline order\n", + "midpoint = 0.5*(t[0]+t[-1])\n", + "knots = r_[[t[0]]*(k+1), midpoint, midpoint, midpoint, [t[-1]]*(k+1)]\n", + "spline = scipy.interpolate.make_lsq_spline(t, X_center_stars-V*(t-t[-1])[:,None], knots, k)\n", + "plot(t, X_center_stars-V*(t-t[-1])[:,None])\n", + "plot(t, spline(t), c='k', alpha=0.4, ls='--')\n", + "legend(('$x$', '$y$', '$z$', 'splines'))\n", + "xlabel('$t$ [Gyr]')\n", + "ylabel('$\\mathbf{r}_\\mathrm{corrected}$ [kpc]')" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'acceleration [kpc/Gyr${}^2$]')" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Calculate acceleration from the splines\n", + "acc = spline(t, 2)\n", + "plot(t, acc)\n", + "legend(('$a_x$', '$a_y$', '$a_z$', 'splines'))\n", + "xlabel('$t$ [Gyr]')\n", + "ylabel('acceleration [kpc/Gyr${}^2$]')" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "output_file_name = file_name[:-4] + '_processed.dat'\n", + "with open(output_file_name, 'w') as f:\n", + " for i in range(len(snapshot)):\n", + " output_string = '%d %.8E %.8E %15.8E %15.8E %.8E %.8E %.8E %.8E %15.8E %15.8E %15.8E\\n' % (\n", + " snapshot[i],\n", + " t[i],\n", + " M_disk[i],\n", + " phi_inertia_fixed[i], theta_inertia[i],\n", + " a_mn[i], b_mn[i],\n", + " M_halo[i],\n", + " b_halo[i],\n", + " -acc[i,0], -acc[i,1], -acc[i,2]\n", + " )\n", + " f.write(output_string)" + ] + }, { "cell_type": "code", "execution_count": null,