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   "source": [
    "# Halo Occupation Distribution from extragalactic catalogs\n",
    "\n",
    "> Notebook owner: Yao-Yuan Mao [@yymao](https://github.com/LSSTDESC/DC2-analysis/issues/new?body=@yymao). Last run: Nov 30, 2018\n",
    "\n",
    "In this notebook we demostrate how to plot the halo occupation distribution of the protoDC2/cosmoDC2 galaxy catalog.\n",
    "\n",
    "## Learning objectives\n",
    "- Use `GCRCatalogs` to access the protoDC2 or cosmoDC2 catalogs. \n",
    "- Access cosmology in the extragalactic catalogs.\n",
    "- Use `CCL` to predict Halo Mass Function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import GCRCatalogs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyccl as ccl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "gc = GCRCatalogs.load_catalog('cosmoDC2_v1.1.4_small')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "zmax = 0.25\n",
    "mass_bins = np.logspace(10, 15, 21)\n",
    "mass_center = np.sqrt(mass_bins[1:] * mass_bins[:-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = gc.get_quantities(['halo_mass', 'Mag_true_r_lsst_z0', 'redshift'], filters=['redshift < {}'.format(zmax)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cosmo = ccl.Cosmology(\n",
    "    Omega_c=gc.cosmology.Om0-gc.cosmology.Ob0, \n",
    "    Omega_b=gc.cosmology.Ob0, \n",
    "    h=gc.cosmology.h, \n",
    "    sigma8=gc.cosmology.sigma8, \n",
    "    n_s=gc.cosmology.n_s, \n",
    "    transfer_function='bbks',\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# approximate hmf using mean redshift\n",
    "mean_scale_factor = 1.0/(1.0+data['redshift'].mean())\n",
    "hmf_dn_dlogm = ccl.massfunc(cosmo, mass_center, mean_scale_factor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = gc.cosmology.comoving_distance(zmax).to('Mpc').value\n",
    "volume = np.deg2rad(np.deg2rad(gc.sky_area)) * d**3 / 3.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dlogm = np.ediff1d(np.log10(mass_bins))\n",
    "nhalo_expected = hmf_dn_dlogm * volume * dlogm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for Mr_thres, color in zip((-21.5, -21, -20.5, -20), plt.cm.tab20c.colors):\n",
    "    plt.loglog(\n",
    "        mass_center, \n",
    "        np.histogram(data['halo_mass'][data['Mag_true_r_lsst_z0'] < Mr_thres], mass_bins)[0] / nhalo_expected,\n",
    "        label=r'$M_r < {}$'.format(Mr_thres),\n",
    "        c=color,\n",
    "    );\n",
    "\n",
    "plt.xlabel(r'${\\rm M}_h \\,/\\, {\\rm M}_\\odot$');\n",
    "plt.ylabel(r'$\\langle N_{\\rm gal} \\,|\\, {\\rm M}_h \\rangle$');\n",
    "plt.title(r'HOD $(z < 0.25)$');\n",
    "plt.ylim(0.01, None)\n",
    "plt.axhline(1, lw=0.5, c='k');\n",
    "plt.legend();"
   ]
  }
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