Andrea-sample-stream-ICs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0973ffc0",
   "metadata": {},
   "source": [
    "This demonstrates a ~~smooth brain~~ simple / brute force way of generating initial conditions in a gravitational potential that have a given density profile, pericenter distribution, and eccentricity distribution. The idea is to generate positions from a density profile, then generate velocities using a heuristic, then integrate orbits and do importance sampling to get the desired distributions. This is not a very efficient way to do this, but it works!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "96dd4642",
   "metadata": {},
   "outputs": [],
   "source": [
    "import astropy.units as u\n",
    "import gala.dynamics as gd\n",
    "import gala.potential as gp\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.special import logit\n",
    "from scipy.stats import beta\n",
    "from scipy.stats import gaussian_kde, norm\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eecbcc08",
   "metadata": {},
   "source": [
    "First define the background potential and the target density profile that we want the initial conditions to follow.\n",
    "\n",
    "Here we'll use a Milky Way potential from gala as the background potential, but you could use a single snapshot of the EXP reconstruction. \n",
    "\n",
    "The target density profile is somewhat arbitrary, so we might want to pick a power law or something. I'll use a Gaussian here for simplicity. If we used a power law, we would use inverse transform sampling to generate positions, but for a Gaussian we can just use `numpy.random.normal`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8a3c12d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "pot = gp.MilkyWayPotential(\"v2\")\n",
    "\n",
    "# target density profile - only used for sampling positions for the ICs\n",
    "# - 50_000 is an arbitrary number and might blow up your RAM! You also could do fewer\n",
    "#   and do an outer loop over batches to build up a larger sample of ICs\n",
    "rng = np.random.default_rng(123)\n",
    "pos = rng.normal(scale=25.0, size=(3, 50_000)) * u.kpc\n",
    "r = np.linalg.norm(pos, axis=0).value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "89c0271d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/67/2zgxpmyd2z183j4k6r33nf740000gr/T/ipykernel_5550/3743204703.py:9: UserWarning: The figure layout has changed to tight\n",
      "  fig.tight_layout()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 351,
       "width": 570
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Quick check: histogram of radii vs analytic density\n",
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "\n",
    "r_bins = np.logspace(-1, 2.5, 64)\n",
    "ax.hist(r, bins=r_bins, density=True, alpha=0.5, label=\"Sampled radii\")\n",
    "\n",
    "ax.set(xscale=\"log\", xlabel=\"r [kpc]\", ylabel=\"PDF\", title=\"Radial distribution\")\n",
    "ax.legend()\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32df0508",
   "metadata": {},
   "source": [
    "At each sampled position, we assign a total velocity as a fraction of the local circular velocity. This is arbitrary since later we will do importance sampling to get the desired distributions, but it gives us a reasonable starting point:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "eb5ad068",
   "metadata": {},
   "outputs": [],
   "source": [
    "v_circ = pot.circular_velocity(pos)\n",
    "\n",
    "# Speed as a fraction of v_circ: draw from a broad distribution to explore a range of\n",
    "# eccentricities, but we want it to be in the range (0, 1), so we'll use a beta\n",
    "# distribution:\n",
    "eta = rng.beta(3, 2, size=pos.shape[1])\n",
    "v_tot = eta * v_circ\n",
    "\n",
    "# Isotropic velocity directions\n",
    "X = rng.normal(size=pos.shape)\n",
    "X /= np.linalg.norm(X, axis=0)\n",
    "vel = (X * v_tot).to(u.km / u.s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "ef3b2902",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'v / v_circ')"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 440
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(eta, bins=np.linspace(0, 1, 32))\n",
    "plt.xlabel(\"v / v_circ\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "9b10666d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'total velocity [km/s]')"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 440,
       "width": 440
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(v_tot.to_value(u.km / u.s), bins=32)\n",
    "plt.xlabel(\"total velocity [km/s]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a980dbc",
   "metadata": {},
   "source": [
    "Now we have to integrate orbits and measure orbital properties\n",
    "\n",
    "We integrate each particle for a few Gyr in the host potential, then measure pericenter, apocenter, and eccentricity from each orbit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "e0663e1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4000, 50000)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w0 = gd.PhaseSpacePosition(pos=pos, vel=vel)\n",
    "orbits = pot.integrate_orbit(w0, dt=2.0 * u.Myr, t1=0, t2=8 * u.Gyr)\n",
    "orbits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "d5c710e6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/aprice-whelan/projects/scratch/.venv/lib/python3.12/site-packages/numpy/_core/fromnumeric.py:3860: RuntimeWarning: Mean of empty slice.\n",
      "  return _methods._mean(a, axis=axis, dtype=dtype,\n",
      "/Users/aprice-whelan/projects/scratch/.venv/lib/python3.12/site-packages/numpy/_core/_methods.py:145: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  ret = ret.dtype.type(ret / rcount)\n"
     ]
    }
   ],
   "source": [
    "peris = orbits.pericenter(approximate=True)\n",
    "eccs = orbits.eccentricity(approximate=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "64873134",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/67/2zgxpmyd2z183j4k6r33nf740000gr/T/ipykernel_5550/1894632977.py:8: UserWarning: The figure layout has changed to tight\n",
      "  fig.tight_layout()\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 351,
       "width": 857
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(12, 5))\n",
    "axes[0].hist(peris.value, bins=np.logspace(-1, 2, 32))\n",
    "axes[0].set_xscale(\"log\")\n",
    "axes[0].set_xlabel(\"pericenter [kpc]\")\n",
    "\n",
    "axes[1].hist(eccs, bins=np.linspace(0, 1, 32))\n",
    "axes[1].set_xlabel(\"eccentricity\")\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8b6f4c9",
   "metadata": {},
   "source": [
    "## Importance sampling to match target distributions\n",
    "\n",
    "We now reweight the sample to match desired pericenter and eccentricity distributions. The general idea is:\n",
    "\n",
    "1. Define a target pericenter distribution $p(r_\\mathrm{peri})$ and eccentricity distribution $p(e)$.\n",
    "2. Compute importance weights $w_i = p_\\mathrm{target}(r_{\\mathrm{peri},i}, e_i) \\,/\\, p_\\mathrm{proposal}(r_{\\mathrm{peri},i}, e_i)$.\n",
    "3. Resample using the normalized weights.\n",
    "\n",
    "For the proposal distribution, we use a KDE of the raw sample, but with a coordinate transform to deal with the fact that eccentricity is bounded between 0 and 1. We can use a logit transform for eccentricity and a log transform for pericenter to make the KDE more effective:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "7b8c3e91",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valid samples: 49993 / 50000\n"
     ]
    }
   ],
   "source": [
    "# Filter out invalid values (NaN, eccentricity out of bounds, non-positive pericenter)\n",
    "peri_vals = peris.value\n",
    "ecc_vals = eccs.value\n",
    "\n",
    "valid = (\n",
    "    np.isfinite(peri_vals)\n",
    "    & np.isfinite(ecc_vals)\n",
    "    & (peri_vals > 0)\n",
    "    & (ecc_vals > 0)\n",
    "    & (ecc_vals < 1)\n",
    ")\n",
    "peri_clean = peri_vals[valid]\n",
    "ecc_clean = ecc_vals[valid]\n",
    "print(f\"Valid samples: {valid.sum()} / {len(valid)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "e6efdd48",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fit KDE in transformed space: log(r_peri) and logit(ecc)\n",
    "log_peri = np.log(peri_clean)\n",
    "logit_ecc = logit(ecc_clean)\n",
    "kde = gaussian_kde(np.vstack([log_peri, logit_ecc]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "baf02ec9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def log_proposal_density(peri, e):\n",
    "    \"\"\"Proposal log-density in original (peri, e) via KDE in transformed space.\"\"\"\n",
    "    log_kde = np.log(kde(np.vstack([np.log(peri), logit(e)])))\n",
    "    log_jac = -np.log(peri) - np.log(e) - np.log(1.0 - e)  # jacobian\n",
    "    return log_kde + log_jac"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76ae6e09",
   "metadata": {},
   "source": [
    "target distributions - let's say we want a Gaussian in pericenter and a Beta distribution in eccentricity (though we should figure out exactly what we want here...):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "993bcd57",
   "metadata": {},
   "outputs": [],
   "source": [
    "def log_target_density(peri, e):\n",
    "    log_p_r = norm.logpdf(\n",
    "        peri, loc=15.0, scale=5.0\n",
    "    )\n",
    "    log_p_e = beta.logpdf(e, a=2.0, b=5.0)  # weighted towards low eccentricity\n",
    "    return log_p_r + log_p_e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "8cfcef86",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute (log) importance weights w_i = p_target / p_proposal\n",
    "log_w = log_target_density(peri_clean, ecc_clean) - log_proposal_density(\n",
    "    peri_clean, ecc_clean\n",
    ")\n",
    "\n",
    "# shift by max before exp for numerical stability\n",
    "log_w -= log_w.max()\n",
    "w = np.exp(log_w)\n",
    "w /= w.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "59f4d7df",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Effective sample size: 2396 / 49993\n"
     ]
    }
   ],
   "source": [
    "# Effective sample size as a diagnostic (high = weights are well spread)\n",
    "n_eff = 1.0 / np.sum(w**2)\n",
    "print(f\"Effective sample size: {n_eff:.0f} / {len(w)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "3bd81763",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resampled 2396 initial conditions.\n"
     ]
    }
   ],
   "source": [
    "# Resample without replacement up to n_eff\n",
    "idx_resampled = rng.choice(len(peri_clean), size=int(n_eff), p=w, replace=False)\n",
    "\n",
    "# Map back to indices in the original pos/vel arrays\n",
    "valid_indices = np.where(valid)[0]\n",
    "original_idx = valid_indices[idx_resampled]\n",
    "\n",
    "# Resampled phase-space positions\n",
    "w0_resampled = gd.PhaseSpacePosition(pos=pos[:, original_idx], vel=vel[:, original_idx])\n",
    "print(f\"Resampled {n_eff:.0f} initial conditions.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "31e9e1f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/67/2zgxpmyd2z183j4k6r33nf740000gr/T/ipykernel_5550/830174253.py:23: UserWarning: The figure layout has changed to tight\n",
      "  fig.tight_layout()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 352,
       "width": 857
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(12, 5))\n",
    "\n",
    "# --- Pericenter ---\n",
    "r_bins = np.linspace(0, 100, 64)\n",
    "axes[0].hist(peri_clean, bins=r_bins, density=True, alpha=0.5, label=\"initial\")\n",
    "axes[0].hist(\n",
    "    peri_clean[idx_resampled], bins=r_bins, density=True, alpha=0.5, label=\"resampled\"\n",
    ")\n",
    "\n",
    "axes[0].set(xlabel=\"pericenter [kpc]\")\n",
    "axes[0].legend()\n",
    "\n",
    "# --- Eccentricity ---\n",
    "e_bins = np.linspace(0, 1, 32)\n",
    "axes[1].hist(ecc_clean, bins=e_bins, density=True, alpha=0.5, label=\"initial\")\n",
    "axes[1].hist(\n",
    "    ecc_clean[idx_resampled], bins=e_bins, density=True, alpha=0.5, label=\"resampled\"\n",
    ")\n",
    "\n",
    "axes[1].set(xlabel=\"eccentricity\")\n",
    "# axes[1].legend()\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ddbaabd4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "scratch (3.12.10)",
   "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": "3.12.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}