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{
"cells": [
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The autoreload extension is already loaded. To reload it, use:\n",
" %reload_ext autoreload\n"
]
}
],
"source": [
"# automatically reflect changes in imported modules\n",
"%load_ext autoreload\n",
"%autoreload 2\n",
"\n",
"from pathlib import Path\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import astropy.units as u\n",
"\n",
"import utils\n",
"import utils.logging_config\n",
"import logging\n",
"logger = logging.getLogger(\"task1\")"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"DATA_ROOT = Path('data')\n",
"DATA_NAME = 'data.txt'\n",
"NBINS = 30\n",
"CACHE_ROOT = Path('.cache')"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"12:58:01 - utils.load - Loaded 50010 rows and 10 columns from data/data.txt\n",
"12:58:01 - task1 - Fetched 50010 points, columns: ['ID', 'MASS', 'X', 'Y', 'Z', 'VX', 'VY', 'VZ', 'SOFTENING', '?']\n"
]
}
],
"source": [
"points, columns = utils.load_data(DATA_ROOT / DATA_NAME)\n",
"logger.debug(f\"Fetched {points.shape[0]} points, columns: {columns}\")\n",
"# reorder the columns to match the expected order (x, y, z, mass)\n",
"particles = points[:, [2, 3, 4, 1]]\n",
"\n",
"# particles = particles[::10, ...]\n",
"# particles = particles[:5000, ...]\n",
"# particles = utils.remove_outliers(particles)\n",
"# logger.warning(f\"Reduced selection to {particles.shape[0]} particles\")\n",
"# TODO: make sure this is not executed in the final version"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot the distribution of the particles\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(particles[:,0], particles[:,1], particles[:,2], cmap='viridis', c=particles[:,3])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Choice of units\n",
"Recap of the particle properties:\n",
"- $\\sim 10^4$ particles\n",
"- spherical distribution\n",
"\n",
"$\\implies$ this seems to be a **globular cluster**"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"12:58:03 - utils.units - Set scales: M_SCALE = 0.021634629254180957 solMass, R_SCALE = 0.02759802045521005 pc\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"4622219.258999999\n"
]
}
],
"source": [
"# Set G = 1\n",
"G = 1\n",
"\n",
"\n",
"# Since we have a globular cluster, we can use typical values\n",
"M_TOT = 1e5 * u.M_sun\n",
"R_TOT = 20 * u.pc\n",
"\n",
"# Rescale the units of the particles\n",
"M_particles = particles[:,3].sum()\n",
"print(M_particles.sum())\n",
"R_particles = np.max(np.linalg.norm(particles[:, :3], axis=1))\n",
"m_scale = M_TOT / M_particles\n",
"r_scale = R_TOT / R_particles\n",
"utils.seed_scales(r_scale, m_scale)\n",
"\n",
"\n",
"\n",
"# ### Plot again with scales\n",
"# positions = utils.apply_units(particles[:, :3], \"position\")\n",
"# masses = utils.apply_units(particles[:, 3], \"mass\")\n",
"# fig = plt.figure()\n",
"# ax = fig.add_subplot(111, projection='3d')\n",
"# sc = ax.scatter(positions[:,0], positions[:,1], positions[:,2], cmap='viridis', c=masses)\n",
"#\n",
"# ax.set_xlabel(f'x [{positions.unit}]')\n",
"# ax.set_ylabel(f'y [{positions.unit}]')\n",
"# ax.set_zlabel(f'z [{positions.unit}]')\n",
"# cbar = plt.colorbar(sc, ax=ax, pad=0.1)\n",
"# cbar.set_label(f'Mass [{masses.unit}]')\n",
"#\n",
"# plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"12:58:03 - utils.particles - Half mass radius: 0.1887071270700712 for 25004th particle of 50010\n",
"12:58:03 - task1 - Scale length: a=0.078, total mass: m=4.6e+06\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"all_r = utils.r_distribution(particles)\n",
"rbins = np.logspace(np.log10(np.min(all_r)), np.log10(np.max(all_r)), NBINS, endpoint=True)\n",
"\n",
"## Using the Hernquist model with parameters M and a\n",
"m = M_particles\n",
"a = utils.half_mass_radius(particles) / (1 + np.sqrt(2))\n",
"logger.debug(f\"Scale length: {a=:.2g}, total mass: {m=:.2g}\")\n",
"rho_t = utils.model_density_distribution(rbins, m, a)\n",
"\n",
"## Numerical density distribution\n",
"rho, err = utils.density_distribution(rbins, particles, ret_error=True)\n",
"\n",
"## Add the units\n",
"rho = utils.apply_units(rho, \"density\")\n",
"err = utils.apply_units(err, \"density\")\n",
"rho_t = utils.apply_units(rho_t, \"density\")\n",
"rbins = utils.apply_units(rbins, \"position\")\n",
"\n",
"\n",
"plt.figure()\n",
"plt.title('Density distribution')\n",
"plt.xscale('log')\n",
"plt.yscale('log')\n",
"plt.xlabel(f'r [{rbins.unit}]')\n",
"plt.ylabel(f'$\\\\rho$ [{rho.unit}]')\n",
"plt.errorbar(rbins.value, rho.value, yerr=err.value, fmt='o', label=\"Particle data\")\n",
"plt.plot(rbins.value, rho_t.value, 'o', label=\"Analytic model\")\n",
"plt.legend()\n",
"plt.show()\n",
"\n",
"## Note that by construction, the first shell contains no particles\n",
"## => the numerical density is zero there\n",
"## Having more bins means to have shells that are nearly empty\n",
"## => the error is large, NBINS = 30 is a good compromise"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"13:14:03 - utils.particles - Half mass radius: 0.1887071270700712 for 25004th particle of 50010\n",
"13:14:03 - utils.particles - Number of particles within half mass radius: 25004 of 50010\n",
"13:14:03 - utils.particles - Found mean interparticle distance: 0.010402746349924056\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"13:14:03 - utils.forces_basic - Computing forces for 50010 particles using spherical approximation\n",
"13:14:03 - utils.forces_basic - Particle 0 done\n",
"13:14:07 - utils.forces_basic - Particle 5000 done\n",
"13:14:11 - utils.forces_basic - Particle 10000 done\n",
"13:14:15 - utils.forces_basic - Particle 15000 done\n",
"13:14:18 - utils.forces_basic - Particle 20000 done\n",
"13:14:22 - utils.forces_basic - Particle 25000 done\n",
"13:14:26 - utils.forces_basic - Particle 30000 done\n",
"13:14:30 - utils.forces_basic - Particle 35000 done\n",
"13:14:34 - utils.forces_basic - Particle 40000 done\n",
"13:14:38 - utils.forces_basic - Particle 45000 done\n",
"13:14:41 - utils.forces_basic - Particle 50000 done\n"
]
}
],
"source": [
"### Direct N body force computation and comparison with analytical model\n",
"epsilon = utils.mean_interparticle_distance(particles)\n",
"\n",
"\n",
"# TODO: compute this in a threaded way\n",
"epsilon_range = np.logspace(-3, 3, 7)\n",
"n_squared_forces = []\n",
"for e in epsilon_range:\n",
" n_particles = particles.shape[0]\n",
" cache_file = CACHE_ROOT / f\"n_squared_forces__n_{n_particles}__softening_multiplier_{e:.0f}.npy\"\n",
" try:\n",
" f = np.load(cache_file)\n",
" except FileNotFoundError:\n",
" f = utils.n_body_forces(particles, G, e * epsilon)\n",
" np.save(cache_file, f)\n",
" logger.debug(f\"Saved forces to {cache_file}\")\n",
" n_squared_forces.append(f)\n",
"\n",
"analytical_force = utils.analytical_forces(particles)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\"## compare the two force calculations\\n# since the forces were computed for each particle, rather than comparing them directly we compare the relative error in the magnitude and direction of the forces\\n\\n\\n# f_diff = f_nsquare_1e - f_analytical\\nf_diff = f_nsquare_2e - f_analytical\\ndiff_mag = np.linalg.norm(f_diff, axis=1)\\n\\n\\n# plot the distribution of the error\\n# create 4 stacked histograms, sharing the same x axis\\nfig, ax = plt.subplots(4, sharex=True)\\nax[0].hist(diff_mag, bins=NBINS)\\nax[0].set_title('Magnitude of the force difference')\\nax[0].set_yscale('log')\\n\\nax[1].hist(f_diff[:,0], bins=NBINS)\\nax[1].set_title('X component of the force difference')\\nax[1].set_yscale('log')\\n\\nax[2].hist(f_diff[:,1], bins=NBINS)\\nax[2].set_title('Y component of the force difference')\\nax[2].set_yscale('log')\\n\\nax[3].hist(f_diff[:,2], bins=NBINS)\\nax[3].set_title('Z component of the force difference')\\nax[3].set_yscale('log')\\n\\nplt.title('Error in forces')\\nplt.show()\\n\""
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"## compare the two force calculations\n",
"# since the forces were computed for each particle, rather than comparing them directly we compare the relative error in the magnitude and direction of the forces\n",
"\n",
"\n",
"# f_diff = f_nsquare_1e - f_analytical\n",
"f_diff = f_nsquare_2e - f_analytical\n",
"diff_mag = np.linalg.norm(f_diff, axis=1)\n",
"\n",
"\n",
"# plot the distribution of the error\n",
"# create 4 stacked histograms, sharing the same x axis\n",
"fig, ax = plt.subplots(4, sharex=True)\n",
"ax[0].hist(diff_mag, bins=NBINS)\n",
"ax[0].set_title('Magnitude of the force difference')\n",
"ax[0].set_yscale('log')\n",
"\n",
"ax[1].hist(f_diff[:,0], bins=NBINS)\n",
"ax[1].set_title('X component of the force difference')\n",
"ax[1].set_yscale('log')\n",
"\n",
"ax[2].hist(f_diff[:,1], bins=NBINS)\n",
"ax[2].set_title('Y component of the force difference')\n",
"ax[2].set_yscale('log')\n",
"\n",
"ax[3].hist(f_diff[:,2], bins=NBINS)\n",
"ax[3].set_title('Z component of the force difference')\n",
"ax[3].set_yscale('log')\n",
"\n",
"plt.title('Error in forces')\n",
"plt.show()\n",
"\"\"\""
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"SKIP_N = 20\n",
"## Plot the radial force behaviour\n",
"r = np.linalg.norm(particles[:,:3], axis=1)\n",
"\n",
"plt.figure()\n",
"plt.title('Radial force')\n",
"plt.xscale('log')\n",
"plt.yscale('log')\n",
"plt.xlabel('$r$')\n",
"plt.ylabel('$F_r(r)$')\n",
"\n",
"plt.plot(r[::SKIP_N], np.linalg.norm(analytical_force[::SKIP_N], axis=1), '.', label=\"Analytical\", zorder=10, alpha=0.5)\n",
"\n",
"for e, f in zip(epsilon_range, n_squared_forces):\n",
" r_red = r[::SKIP_N]\n",
" f_red = f[::SKIP_N]\n",
" plt.plot(r, np.linalg.norm(f, axis=1), '.', label=f\"$N^2$ - {e:.1g} * $\\\\epsilon$\")\n",
"\n",
"\n",
"plt.legend()\n",
"plt.show()\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Discussion\n",
"- basic $N^2$ matches analytical solution without dropoff. but: noisy data from \"bad\" samples\n",
"- $N^2$ with softening matches analytical solution but has a dropoff. No noisy data.\n",
" - softening $\\approx 1 \\varepsilon$ is a sweet spot since the dropoff is \"late\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Relaxation time\n",
"\n",
"For an estimate of the crossing time we use the half mass radius and the circular velocity at the half mass radius.\n",
"\n",
"$\\implies$ the crossing time is of order radius / velocity"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"13:10:27 - utils.particles - Half mass radius: 0.1887071270700712 for 25004th particle of 50010\n",
"13:10:27 - task1 - Crossing time for half mass system: 5.392276839004401e-05\n",
"13:10:27 - task1 - Direct estimate of the relaxation timescale: 0.025\n"
]
}
],
"source": [
"## Computes the relaxation timescale of a set of particles using the velocity at the half mass radius.\n",
"\n",
"# enclosed mass at half mass radius\n",
"m_half = np.sum(particles[:, 3]) / 2\n",
"r_half = utils.half_mass_radius(particles)\n",
"\n",
"v_c = np.sqrt(G * m_half / r_half)\n",
"\n",
"t_c = r_half / v_c\n",
"# TODO: what is the unit of the crossing time?\n",
"# we expressed the mass in solar masses, the radius in pc and set G = 1\n",
"# => ???\n",
"logger.info(f\"Crossing time for half mass system: {t_c}\")\n",
"\n",
"\n",
"## Using the derived formula for the relaxation timescale\n",
"# We can directly compute the relaxation timescale through the estimate\n",
"# t_relax = t_c * N / (10 * log(N))\n",
"n = particles.shape[0]\n",
"t_rel = t_c * n / (10 * np.log(n))\n",
"logger.info(f\"Direct estimate of the relaxation timescale: {t_rel:.2g}\")\n",
"\n",
"\n",
"## Manual computation of the relaxation timescale by summing up 2 body interactions\n",
"# From the crossing time, we can estimate the number of interactions per crossing time\n",
"# We then multiply by the number of particles to get the relaxation timescale\n",
"n_interactions = n * np.log(n)\n",
"# TODO\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Discussion\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "projects-X-9bmgL6",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}