{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a3461285-3f18-4ba7-9619-4ead5fa207c5",
   "metadata": {},
   "source": [
    "# Intialize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f764a698-d3ad-4991-8ca4-f8ba72b05734",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from classy_sz import Class as Class_sz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ebd21063-d1ca-4721-a3f4-e66c00e0aae9",
   "metadata": {},
   "outputs": [],
   "source": [
    "cosmo_params = {\n",
    "'omega_b': 0.02242,\n",
    "'omega_cdm':  0.11933,\n",
    "'H0': 67.66, # use H0 because this is what is used by the emulators and to avoid any ambiguity when comparing with camb. \n",
    "'tau_reio': 0.0561,\n",
    "'ln10^{10}A_s': 3.047,\n",
    "'n_s': 0.9665   \n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73965ac7-574c-475e-8975-3549dbd1d1bd",
   "metadata": {},
   "source": [
    "# Compute $\\rho_c(z)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f669b4ae-a304-4a1d-9995-51bb329fb0fa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 187 μs, sys: 1.24 ms, total: 1.43 ms\n",
      "Wall time: 3.1 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time \n",
    "classy_sz = Class_sz()\n",
    "classy_sz.set(cosmo_params)\n",
    "classy_sz.set({\n",
    "'output':' ',\n",
    "'skip_background_and_thermo': 0,\n",
    "'cosmo_model': 0,\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "588083b0-3056-43f8-bd87-54ef25c8e626",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 290 ms, sys: 48.5 ms, total: 338 ms\n",
      "Wall time: 120 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "classy_sz.compute_class_szfast()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b78455e9-874d-4176-b213-ff195df86e69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "277517901355.0651"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classy_sz.get_rho_crit_at_z(0.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35da13be-547f-4f3d-81c3-a59aecb10915",
   "metadata": {},
   "source": [
    "# Conversion to standard units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d1355fcb-7a74-452a-a740-689c53a0bb38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.598840023056267e-30"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_light = 2.997924581e8 # s \n",
    "G = 6.674*1e-11 # m3 kg-1 s-2\n",
    "solar = 1.98855*1e30 ## kg \n",
    "mpc = 3.08567758149137*1e22 # m \n",
    "gamma =  G/c_light**2*solar/mpc\n",
    "\n",
    "conv_fac = 1./(1000.*mpc**3/solar)\n",
    "\n",
    "classy_sz.get_rho_crit_at_z(0.)*conv_fac*classy_sz.h()**2 # g/m^3 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03d4c115-0b63-4319-8a0c-6c04ccd9a5c6",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Plot $\\rho(z)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "22c1ebe3-bde8-4389-a66d-1ffda3b4f913",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x3221aa600>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "label_size = 15\n",
    "title_size = 20\n",
    "legend_size = 13\n",
    "handle_length = 1.5\n",
    "fig, (ax1) = plt.subplots(1,1,figsize=(18,5))\n",
    "\n",
    "ax = ax1\n",
    "ax.tick_params(axis = 'x',which='both',length=5,direction='in', pad=10)\n",
    "ax.tick_params(axis = 'y',which='both',length=5,direction='in', pad=5)\n",
    "ax.xaxis.set_ticks_position('both')\n",
    "ax.yaxis.set_ticks_position('both')\n",
    "plt.setp(ax.get_yticklabels(), rotation='horizontal', fontsize=label_size)\n",
    "plt.setp(ax.get_xticklabels(), fontsize=label_size)\n",
    "ax.grid( visible=True, which=\"both\", alpha=0.2, linestyle='--')\n",
    "\n",
    "\n",
    "z = np.linspace(0.,20,100)\n",
    "\n",
    "ax.plot(z,np.vectorize(classy_sz.get_rho_crit_at_z)(z),ls='-',label='class_szfast')\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "ax.set_ylabel(r\"$\\rho_c(z)$\",size=title_size)\n",
    "ax.set_xlabel(r\"$z$\",size=title_size)\n",
    "ax.set_xscale('linear')\n",
    "ax.set_yscale('log')\n",
    "ax.set_xlim(0,20)\n",
    "ax.legend(fontsize=legend_size)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15356e9f-d3d1-46f5-a558-0ca8fe81cbf2",
   "metadata": {},
   "source": [
    "# Compute with Jax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f2af2bbb-2e5a-4606-8a22-0c271ceb4361",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from classy_sz import Class as Class_sz\n",
    "import jax.numpy as jnp\n",
    "from jax import jacfwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "37ff5cfa-4baf-4b77-bc3e-17f36e4254dd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 648 ms, sys: 212 ms, total: 860 ms\n",
      "Wall time: 1.12 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "cosmo_params = {\n",
    "'omega_b': 0.02242,\n",
    "'omega_cdm':  0.11933,\n",
    "'H0': 67.66, # use H0 because this is what is used by the emulators.\n",
    "'tau_reio': 0.0561,\n",
    "'ln10^{10}A_s': 3.047,\n",
    "'n_s': 0.9665,\n",
    "}\n",
    "\n",
    "# initialize computation\n",
    "classy_sz = Class_sz()\n",
    "classy_sz.set(cosmo_params)\n",
    "classy_sz.set({\n",
    "'output':' ',\n",
    "'jax': 1,\n",
    "})\n",
    "classy_sz.compute_class_szfast()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6e7b1fd9-9cb5-49c5-b16e-59d16fd04d36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(3.06136466e+11, dtype=float64)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zp = 0.1\n",
    "classy_sz.get_rho_crit_at_z(zp,params_values_dict=cosmo_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1af45be2-91ab-49ee-b076-255c4c8941b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "Omega_c = 0.26\n",
    "z = jnp.linspace(0.1,20.,200)\n",
    "\n",
    "def rhoc_allzs(Omega_c):\n",
    "    omega_cdm = Omega_c*(cosmo_params['H0']/100.)**2\n",
    "    cosmo_params.update({'omega_cdm':omega_cdm})\n",
    "    rhoc = classy_sz.get_rho_crit_at_z(z,params_values_dict=cosmo_params)\n",
    "    return rhoc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2d566732-84f7-4250-8474-b70778311d68",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 37 μs, sys: 4 μs, total: 41 μs\n",
      "Wall time: 53.2 μs\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "drhoc_allzs = jacfwd(rhoc_allzs,argnums=(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "59cd43f5-d35a-4d82-b694-b78bd2165831",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x341667b90>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "label_size = 15\n",
    "title_size = 20\n",
    "legend_size = 13\n",
    "handle_length = 1.5\n",
    "fig, (ax1) = plt.subplots(1,1,figsize=(18,5))\n",
    "\n",
    "ax = ax1\n",
    "ax.tick_params(axis = 'x',which='both',length=5,direction='in', pad=10)\n",
    "ax.tick_params(axis = 'y',which='both',length=5,direction='in', pad=5)\n",
    "ax.xaxis.set_ticks_position('both')\n",
    "ax.yaxis.set_ticks_position('both')\n",
    "plt.setp(ax.get_yticklabels(), rotation='horizontal', fontsize=label_size)\n",
    "plt.setp(ax.get_xticklabels(), fontsize=label_size)\n",
    "ax.grid( visible=True, which=\"both\", alpha=0.2, linestyle='--')\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "ax.plot(z,drhoc_allzs(Omega_c),ls='-',label='class_szfast')\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "ax.set_ylabel(r\"$d\\rho_c(z)/d\\Omega_c$\",size=title_size)\n",
    "ax.set_xlabel(r\"$z$\",size=title_size)\n",
    "ax.set_xscale('linear')\n",
    "ax.set_yscale('log')\n",
    "ax.set_xlim(0,20)\n",
    "ax.legend(fontsize=legend_size)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (venv_class_sz)",
   "language": "python",
   "name": "venv_class_sz312"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.8"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}