ClassDemo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a copy of the code in Class's Python wiki at https://github.com/lesgourg/class_public/wiki/Python-wrapper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from classy import Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'pp': array([  0.00000000e+00,   0.00000000e+00,   9.59855233e-09, ...,\n",
      "         5.30793102e-22,   5.29036706e-22,   5.27286711e-22]), 'ell': array([   0,    1,    2, ..., 1998, 1999, 2000]), 'bb': array([  0.00000000e+00,   0.00000000e+00,   2.71574126e-19, ...,\n",
      "         1.00585903e-20,   1.00369386e-20,   1.00153492e-20]), 'ee': array([  0.00000000e+00,   0.00000000e+00,   7.90999980e-15, ...,\n",
      "         1.88034961e-18,   1.86769054e-18,   1.85502334e-18]), 'tt': array([  0.00000000e+00,   0.00000000e+00,   1.61157384e-10, ...,\n",
      "         4.89578624e-17,   4.89084328e-17,   4.88588893e-17]), 'tp': array([  0.00000000e+00,   0.00000000e+00,   5.20501127e-10, ...,\n",
      "         1.72573628e-22,   1.72365841e-22,   1.72148094e-22]), 'te': array([  0.00000000e+00,   0.00000000e+00,   5.24381240e-13, ...,\n",
      "        -3.78705478e-18,  -3.78169608e-18,  -3.77580522e-18])}\n"
     ]
    }
   ],
   "source": [
    "from classy import Class\n",
    "\n",
    "# Define your cosmology (what is not specified will be set to CLASS default parameters)\n",
    "params = {\n",
    "    'output': 'tCl pCl lCl',\n",
    "    'l_max_scalars': 2000,\n",
    "    'lensing': 'yes',\n",
    "    'A_s': 2.3e-9,\n",
    "    'n_s': 0.9624, \n",
    "    'h': 0.6711,\n",
    "    'omega_b': 0.022068,\n",
    "    'omega_cdm': 0.12029}\n",
    "\n",
    "# Create an instance of the CLASS wrapper\n",
    "cosmo = Class()\n",
    "\n",
    "# Set the parameters to the cosmological code\n",
    "cosmo.set(params)\n",
    "\n",
    "# Run the whole code. Depending on your output, it will call the\n",
    "# CLASS modules more or less fast. For instance, without any\n",
    "# output asked, CLASS will only compute background quantities,\n",
    "# thus running almost instantaneously.\n",
    "# This is equivalent to the beginning of the `main` routine of CLASS,\n",
    "# with all the struct_init() methods called.\n",
    "cosmo.compute()\n",
    "\n",
    "# Access the lensed cl until l=2000\n",
    "cls = cosmo.lensed_cl(2000)\n",
    "\n",
    "# Print on screen to see the output\n",
    "print(cls)\n",
    "# It is a dictionnary that contains the fields: tt, te, ee, bb, pp, tp\n",
    "\n",
    "# plot something with matplotlib...\n",
    "\n",
    "# Clean CLASS (the equivalent of the struct_free() in the `main`\n",
    "# of CLASS. This step is primordial when running in a loop over different\n",
    "# cosmologies, as you will saturate your memory very fast if you ommit\n",
    "# it.\n",
    "cosmo.struct_cleanup()\n",
    "\n",
    "# If you want to change completely the cosmology, you should also\n",
    "# clean the arguments, otherwise, if you are simply running on a loop\n",
    "# of different values for the same parameters, this step is not needed\n",
    "cosmo.empty()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fc7caeb5590>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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Lp0F1GdzzX7j1fZizCcY9Cd8vhS//t+FjKwpgy8vQ7yboNdXYNvxBiO8Nn/yp/lCqroC1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\n5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc7cb420f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "llp1 = cls['ell']*(cls['ell']+1.0) / (2*np.pi)\n",
    "plt.loglog(cls['ell'], llp1*cls['tt'])\n",
    "plt.loglog(cls['ell'], llp1*cls['ee'])\n",
    "plt.loglog(cls['ell'], llp1*cls['bb'])\n",
    "plt.xlabel(r'$\\ell$')\n",
    "plt.ylabel(r'$\\ell (\\ell+1) C_{\\ell} / 2\\pi$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}