cosmhology.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cosmology.jl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Jupyter Notebook for cosmology.jl: Change the kernel to Julia Kernel. Select it from the Kernel Menu."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Run this section inside Julia kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m    Status\u001b[22m\u001b[39m `/srv/julia/pkg/environments/v0.7/Project.toml`\n",
      " \u001b[90m [7073ff75]\u001b[39m\u001b[37m IJulia v1.20.2\u001b[39m\n",
      " \u001b[90m [1fd47b50]\u001b[39m\u001b[37m QuadGK v2.3.1\u001b[39m\n",
      " \u001b[90m [1986cc42]\u001b[39m\u001b[37m Unitful v0.12.0\u001b[39m\n",
      " \u001b[90m [6112ee07]\u001b[39m\u001b[37m UnitfulAstro v0.2.0\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "# Check if package is installed\n",
    "import Pkg; Pkg.status()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Clone the Cosmology.jl package\n",
    "import Pkg; Pkg.clone(\"https://github.com/LaGuer/Cosmology.jl.git\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Pkg; Pkg.instantiate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Pkg; Pkg.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pkg.add(\"Cosmology\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling Cosmology [76746363-e552-5dba-9a5a-cef6fa9cc5ab]\n",
      "└ @ Base loading.jl:1187\n"
     ]
    }
   ],
   "source": [
    "using Cosmology "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cosmology.FlatLCDM{Float64}(0.7079, 0.6999165470916852, 0.3, 8.345290831484895e-5)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = cosmology()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.311876832294882 Gyr"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age(C, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cosmology.OpenLCDM{Float64}(0.7079, 0.1, 0.5999165470916853, 0.3, 8.345290831484895e-5)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = cosmology(OmegaK=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.911439353675439 Gyr"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age(C, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cosmology.ClosedWCDM{Float64}(0.7079, -0.1, 0.7999165470916852, 0.3, 8.345290831484895e-5, -0.9, 0.0)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = cosmology(w0=-0.9, OmegaK=-0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.484804131094544 Gyr"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age(C, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cosmology.FlatLCDM{Float64}(0.7079, 0.7299165470916852, 0.27, 8.345290831484895e-5)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = cosmology(OmegaM=0.27)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.705983172937254 Gyr"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age(C, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1663.4663847718539 Mpc"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "angular_diameter_dist(C, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3326.9327695437078 Mpc"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "comoving_radial_dist(C, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "154.24840559055747 Gpc^3"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "comoving_volume(C, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6653.8655390874155 Mpc"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "luminosity_dist(C, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cosmology.FlatLCDM{Float64}(0.7079, 0.7299165470916852, 0.27, 8.345290831484895e-5)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = cosmology(OmegaM=0.27)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.705983172937254 Gyr"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age(C, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6653.8655390874155 Mpc"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "luminosity_dist(C, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "44.1153701021242"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distmod(C, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cosmology.OpenLCDM{Float64}(0.7079, 0.1, 0.5999165470916853, 0.3, 8.345290831484895e-5)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = cosmology(OmegaK=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.911439353675439 Gyr"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age(C, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cosmology.FlatWCDM{Float64}(0.7079, 0.0, 0.7, 0.3, 0.0, -0.9, 0.1)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#C = cosmology(w0=-0.9, OmegaK=-0.1)\n",
    "# c = cosmology(h=0.7, OmegaK=-0.1, OmegaM=0.3, OmegaR=0, w0=-0.9, wa=0.1)\n",
    "C = cosmology(h=0.7079, OmegaM=0.3, OmegaR=0, w0=-0.9, wa=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.042271462027319 Gyr"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age(C, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cosmology.FlatWCDM{BigFloat}(7.07899999999999973709918776876293122768402099609375e-01, 0.0, 6.999999999999999555910790149937383830547332763671875e-01, 2.99999999999999988897769753748434595763683319091796875e-01, 0.0, -9.0000000000000002220446049250313080847263336181640625e-01, 1.000000000000000055511151231257827021181583404541015625e-01)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = cosmology(h=big(0.7079), OmegaM=0.3, OmegaR=0, w0=-0.9, wa=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.304227146202732023586112767332675257612795424515085289479484034823174898083907e+01 Gyr"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age(c, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "70.78999999999999 km Mpc^-1 s^-1"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H(c,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cosmology.FlatWCDM{Float64}(0.7079, 0.0, 0.75, 0.25, 0.0, -0.9, 0.1)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = cosmology(h=0.7079, OmegaM=0.25, OmegaR=0, w0=-0.9, wa=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.662816076764386 Gyr"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age(c, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cosmology.jl with nbodykit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Run this section inside a Python Kernel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## nbodykit\n",
    "\n",
    "https://github.com/bccp/nbodykit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Python mode run:\n",
    "\n",
    "conda install -c bccp nbodykit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install xelatex\n",
    "!pip install matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "conda install -c bccp nbodykit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "conda list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "nbsphinx": "hidden"
   },
   "outputs": [],
   "source": [
    "# this cell is hidden by metadata\n",
    "from nbodykit import style\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use(style.notebook)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. _cosmology:\n",
    "\n",
    "Cosmological Calculations\n",
    "=========================\n",
    "\n",
    "The :mod:`nbodykit.cosmology` module includes functionality for\n",
    "representing cosmological parameter sets and computing various\n",
    "theoretical quantities prevalent in large-scale structure that depend\n",
    "on the background cosmological model. The module relies on the\n",
    "`CLASS CMB Boltzmann code <http://class-code.net>`_ as the underlying\n",
    "engine for its cosmological calculations via the Python wrapper\n",
    "provided by the :mod:`classylss` package. For consistency, the cosmology\n",
    "syntax used in nbodykit largely follows that of the CLASS code. A useful\n",
    "set of links for reference material on CLASS is available\n",
    "`here <http://classylss.readthedocs.io/en/stable/class-docs.html>`_.\n",
    "\n",
    ".. currentmodule:: nbodykit.cosmology\n",
    "\n",
    "\n",
    "The :class:`Cosmology` class\n",
    "----------------------------\n",
    "\n",
    "nbodykit provides the :class:`~cosmology.Cosmology`\n",
    "class for representing cosmological parameter sets. Given an input set of\n",
    "parameters, this class uses the CLASS code to evaluate various quantities\n",
    "relevant to large-scale structure. The class can compute background quantities,\n",
    "such as distances, as a function of redshift, as well as linear and nonlinear\n",
    "power spectra and transfer functions.\n",
    "\n",
    "..  note::\n",
    "\n",
    "  For a full list of the attributes and\n",
    "  functions available, please see the :ref:`API docs <api-cosmology>`.\n",
    "  \n",
    "The CLASS code supports multiple sets of input parameters, e.g., the user\n",
    "can specify ``H0`` or ``h``. For simplicity, we use the following parameters\n",
    "to initialize a :class:`~cosmology.Cosmology` object:\n",
    "\n",
    "* ``h`` : the dimensionless Hubble parameter\n",
    "* ``T0_cmb`` : the temperature of the CMB in Kelvins\n",
    "* ``Omega0_b`` : the current baryon density parameter, :math:`\\Omega_{b,0}`\n",
    "* ``Omega0_cdm`` : the current cold dark matter density parameter, :math:`\\Omega_{cdm,0}`\n",
    "* ``N_ur`` : the number of ultra-relativistic (massless neutrino) species\n",
    "* ``m_ncdm`` : the masses (in eV) for all massive neutrino species\n",
    "* ``P_k_max`` : the maximum wavenumber to compute power spectrum results to, in units\n",
    "  of :math:`h \\mathrm{Mpc}^{-1}`\n",
    "* ``P_z_max`` : the maximum redshift to compute power spectrum results to\n",
    "* ``gauge`` : the General Relativity gauge, either \"synchronous\" or \"newtonian\"\n",
    "* ``n_s`` : the tilt of the primordial power spectrum\n",
    "* ``nonlinear`` : whether to compute nonlinear power spectrum results via `HaloFit`_\n",
    "\n",
    "Any valid CLASS parameters can be additionally specified as keywords to the\n",
    ":class:`~cosmology.Cosmology` constructor. If these additional parameters\n",
    "conflict with the base set of parameters above, an exception will be raised.\n",
    "For a guide to the valid input CLASS parameters, the \"`explanatory.ini`_\"\n",
    "parameter file in the CLASS GitHub is a good place to start.\n",
    "\n",
    "**Notes and Caveats**\n",
    "\n",
    "* The default configuration assumes a flat cosmology, :math:`\\Omega_{k,0}=0`.\n",
    "  Pass ``Omega0_k`` as a keyword to specify the desired non-flat curvature.\n",
    "* By default, the value for ``N_ur`` is inferred from the number of massive\n",
    "  neutrinos using the following logic: if you have respectively 1,2,3 massive\n",
    "  neutrinos and use the default ``T_ncdm`` value (0.71611 K), which is\n",
    "  designed to give m/omega of 93.14 eV, and you wish to have ``N_eff=3.046`` in\n",
    "  the early universe, then ``N_ur`` is set to 2.0328, 1.0196, 0.00641,\n",
    "  respectively.\n",
    "* For consistency of variable names, the present day values can be passed\n",
    "  with or without the \"0\" postfix, e.g., ``Omega0_cdm`` is translated to\n",
    "  ``Omega_cdm`` as CLASS always uses the names without \"0\" as input\n",
    "  parameters.\n",
    "* By default, a cosmological constant (``Omega0_lambda``) is assumed, with\n",
    "  its density value inferred by the curvature condition.\n",
    "* Non-cosmological constant dark energy can be used by specifying the\n",
    "  ``w0_fld``, ``wa_fld``, and/or ``Omega0_fld`` values.\n",
    "* To pass in CLASS parameters that are not valid Python argument names, use\n",
    "  the dictionary/keyword arguments trick, e.g.,\n",
    "  ``Cosmology(..., **{'temperature contributions': 'y'})``\n",
    "\n",
    "Builtin Cosmologies\n",
    "^^^^^^^^^^^^^^^^^^^\n",
    "\n",
    "We include several builtin cosmologies for users, accessible from the :mod:`nbodykit.cosmology` module:\n",
    "\n",
    ".. include:: ../api/builtin-cosmos.rst\n",
    "\n",
    "Updating cosmological parameters\n",
    "^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
    "\n",
    "The :class:`Cosmology` class is immutable. To update cosmological parameters,\n",
    "we provide the following functions:\n",
    "\n",
    "* :func:`~cosmology.Cosmology.clone`: provides a new :class:`Cosmology` object\n",
    "  with only the specified parameters changed; this function accepts any keyword\n",
    "  parameters that can be passed to the :class:`Cosmology` constructor\n",
    "* :func:`~cosmology.Cosmology.match`: provides a new :class:`Cosmology` object\n",
    "  that has matched a specific, derived parameter value. The derived parameters\n",
    "  that can be matched include:\n",
    "\n",
    "  - ``sigma8``: re-scale the scalar amplitude ``A_s`` to match ``sigma8``\n",
    "  - ``Omega0_cb``: match the total sum of cdm and baryons density, :math:`\\Omega_{cdm,0}+\\Omega_{b,0}`\n",
    "  - ``Omega0_m``: match the total density of matter-like components,\n",
    "    :math:`\\Omega_{cdm,0}+\\Omega_{b,0}+\\Omega_{ncdm,0}-\\Omega_{pncdm,0}+\\Omega_{dcdm,0}`\n",
    "    \n",
    "For example, we can match a specific ``sigma8`` value using:"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/latex"
   },
   "source": [
    "$\\Omega_{cdm,0}+\\Omega_{b,0}+\\Omega_{ncdm,0}-\\Omega_{pncdm,0}+\\Omega_{dcdm,0}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original sigma8 = 0.8380\n",
      "new sigma8 = 0.8200\n"
     ]
    }
   ],
   "source": [
    "from nbodykit.lab import cosmology\n",
    "\n",
    "cosmo = cosmology.Cosmology()\n",
    "print(\"original sigma8 = %.4f\" % cosmo.sigma8)\n",
    "\n",
    "new_cosmo = cosmo.match(sigma8=0.82)\n",
    "print(\"new sigma8 = %.4f\" % new_cosmo.sigma8)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "And we can clone a :class:`Cosmology` using h=0.7079, T0_cmb=2.725820831 from `Back to Cosmos, 2019`_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can clone a :class:`Cosmology` using h=0.7079, T0_cmb=2.725820831 values taken from [Back to Cosmos, 2019](http://rxiv.org/abs/1904.0218) as described by [Kritov](https://books.google.com/books?id=6TI7DwAAQBAJ) and J.Maruani in [The Dirac Electron and Elementary Interactions: The Gyromagnetic Factor, Fine-Structure Constant, and Gravitational Invariant: Deviations from Whole Numbers](https://link.springer.com/chapter/10.1007/978-3-319-74582-4_19)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's set h=0.7079, T_cmb=2.725820831 as in http://rxiv.org/abs/1904.0218\n",
    "cosmo = cosmo.clone(h=0.7079, T_cmb=2.725820831, nonlinear=True)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "Converting to a dictionary\n",
    "^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
    "\n",
    "The keyword parameters passed to the constructor of a :class:`Cosmology` object are not passed directly to the underlying CLASS engine, but must be edited first to be compatible with CLASS. Users can access the full set of parameters passed directly to CLASS by converting the :class:`Cosmology` object to a dict. This can be accomplished simply using:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'output': 'vTk dTk mPk', 'extra metric transfer functions': 'y', 'N_ur': 2.0328, 'gauge': 'synchronous', 'n_s': 0.9667, 'Omega_cdm': 0.26377065934278865, 'Omega_b': 0.0482754208891869, 'N_ncdm': 1, 'P_k_max_h/Mpc': 10.0, 'z_max_pk': 100.0, 'h': 0.7079, 'T_cmb': 2.725820831, 'm_ncdm': [0.06], 'non linear': 'halofit'}\n"
     ]
    }
   ],
   "source": [
    "cosmo_dict = dict(cosmo)\n",
    "print(cosmo_dict)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "Each of the parameters in this dictionary are valid CLASS parameters. For example, we see that the CLASS parameter \"non linear\" has been set to \"halofit\", since we have set the ``nonlinear`` parameter to be ``True``. \n",
    "\n",
    ".. note::\n",
    "    To create a new :class:`Cosmology` object from a dictionary, users should use \n",
    "    ``Cosmology.from_dict(dict(c))``. Because of the differences in syntax between the :class:`Cosmology` constructor\n",
    "    and CLASS, the following will not work: ``Cosmology(**dict(c))``.\n",
    "    \n",
    "Interfacing with :mod:`astropy`\n",
    "^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
    "\n",
    "We provide some comptability for interfacing with the :mod:`astropy.cosmology` module. The following functions\n",
    "of the :func:`~cosmology.Cosmology` class allow users to convert between the nbodykit and :mod:`astropy` cosmology\n",
    "implementations:\n",
    "\n",
    ".. autosummary::\n",
    "\n",
    "    ~cosmology.Cosmology.to_astropy\n",
    "    ~cosmology.Cosmology.from_astropy\n",
    "    \n",
    "We also provide support for some of the syntax used by :mod:`astropy` for attributes in its cosmology classes by aliasing the :mod:`astropy` names to the appropriate nbodykit attributes. For example, \n",
    "\n",
    ".. autosummary::\n",
    "    \n",
    "   ~classylss.astropy_compat.AstropyCompat.Om0\n",
    "   ~classylss.astropy_compat.AstropyCompat.Odm0\n",
    "   ~classylss.astropy_compat.AstropyCompat.Ode0\n",
    "   ~classylss.astropy_compat.AstropyCompat.Ob0\n",
    "\n",
    ".. warning::\n",
    "\n",
    "    The conversion between :mod:`astropy` and nbodykit cosmology objects is not one-to-one, as the classes are\n",
    "    implemented using different underlying engines. For example, the neutrino calculations performed in nbodykit \n",
    "    using CLASS differ from those in :mod:`astropy`. We have attempted to provide as  much compatibility as possible, \n",
    "    but these differences will always remain when converting between the two implementations."
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "collapsed": true,
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "Theoretical Power Spectra\n",
    "-------------------------\n",
    "\n",
    "Linear power\n",
    "^^^^^^^^^^^^\n",
    "\n",
    "The linear power spectrum can be computed for a given :class:`Cosmology` and redshift using the :class:`~power.linear.LinearPower` class. This object can compute the linear power spectrum using one of \n",
    "several transfer functions: \n",
    "\n",
    "- \"CLASS\": calls CLASS to evaluate the total density transfer function at the specified redshift\n",
    "- \"EisensteinHu\": uses the analytic transfer function from `Eisenstein & Hu, 1998`_\n",
    "- \"NoWiggleEisensteinHu\": uses the no-BAO analytic transfer function from `Eisenstein & Hu, 1998`_\n",
    "\n",
    "The :class:`~power.linear.LinearPower` object is a callable function, taking wavenumber in units of :math:`h \\mathrm{Mpc}^{-1}` as input:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "c = cosmology.Planck15\n",
    "Plin = cosmology.LinearPower(c, redshift=0., transfer='CLASS')\n",
    "\n",
    "k = np.logspace(-3, 0, 100)\n",
    "plt.loglog(k, Plin(k), c='k')\n",
    "\n",
    "plt.xlabel(r\"$k$ $[h \\mathrm{Mpc}^{-1}]$\")\n",
    "plt.ylabel(r\"$P$ $[h^{-3} \\mathrm{Mpc}^{3}]$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "The redshift and power spectrum normalization can easily be updated by adjusting the ``redshift`` and ``sigma8`` attributes of the :class:`~power.linear.LinearPower` instance. For example,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# original power\n",
    "plt.loglog(k, Plin(k), label=r\"$z=0, \\sigma_8=%.2f$\" % Plin.sigma8)\n",
    "\n",
    "# update the redshift and sigma8\n",
    "Plin.redshift = 0.55\n",
    "Plin.sigma8 = 0.80\n",
    "plt.loglog(k, Plin(k), label=r\"$z=0.55, \\sigma_8=0.8$\")\n",
    "\n",
    "# format the axes\n",
    "plt.legend()\n",
    "plt.xlabel(r\"$k$ $[h \\mathrm{Mpc}^{-1}]$\")\n",
    "plt.ylabel(r\"$P$ $[h^{-3} \\mathrm{Mpc}^{3}]$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "Nonlinear and Zel'dovich power\n",
    "^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
    "\n",
    "We also provide the :class:`~power.halofit.HalofitPower` and :class:`~power.zeldovich.ZeldovichPower` classes to compute the nonlinear and Zel'dovich power spectra, respectively. The nonlinear power uses the `HaloFit`_ prescription that is available in CLASS. These objects behavior very similarly to the :class:`~power.linear.LinearPower` class. \n",
    "For example, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/srv/conda/envs/notebook/lib/python3.7/site-packages/mcfit/mcfit.py:125: UserWarning: The default value of lowring has been changed to False, set it to True if you cannot reproduce previous results\n",
      "  warnings.warn(\"The default value of lowring has been changed to False, \"\n",
      "/srv/conda/envs/notebook/lib/python3.7/site-packages/mcfit/mcfit.py:219: UserWarning: The default value of extrap has been changed to False, set it to True if you cannot reproduce previous results\n",
      "  warnings.warn(\"The default value of extrap has been changed to False, \"\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# initialize the power objects\n",
    "Plin = cosmology.LinearPower(c, redshift=0, transfer='CLASS')\n",
    "Pnl = cosmology.HalofitPower(c, redshift=0)\n",
    "Pzel = cosmology.ZeldovichPower(c, redshift=0)\n",
    "\n",
    "# plot each kind\n",
    "plt.loglog(k, Plin(k), label='linear')\n",
    "plt.loglog(k, Pnl(k), label='nonlinear')\n",
    "plt.loglog(k, Pzel(k), label=\"Zel'dovich\")\n",
    "\n",
    "# format the axes\n",
    "plt.legend()\n",
    "plt.xlabel(r\"$k$ $[h \\mathrm{Mpc}^{-1}]$\")\n",
    "plt.ylabel(r\"$P$ $[h^{-3} \\mathrm{Mpc}^{3}]$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "Correlation functions\n",
    "---------------------\n",
    "\n",
    "nbodykit also includes functionality for computing theoretical correlation functions by computing the Fourier transform of a power spectrum. We use the `mcfit`_ package, which provides a Python version of the `FFTLog`_ algorithm. The main class to compute correlation functions is :class:`~correlation.CorrelationFunction`. This class\n",
    "takes a power spectrum instance (one of :class:`~power.linear.LinearPower`, :class:`~power.halofit.HalofitPower`, \n",
    "or :class:`~power.zeldovich.ZeldovichPower`) as input. Below, we show the correlation function for each of these classes: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# initialize the correlation objects\n",
    "cf_lin = cosmology.CorrelationFunction(Plin)\n",
    "cf_nl = cosmology.CorrelationFunction(Pnl)\n",
    "cf_zel = cosmology.CorrelationFunction(Pzel)\n",
    "\n",
    "# plot each kind\n",
    "r = np.logspace(-1, np.log10(150), 1000)\n",
    "plt.plot(r, r**2 * cf_lin(r), label='linear')\n",
    "plt.plot(r, r**2 * cf_nl(r), label='nonlinear')\n",
    "plt.plot(r, r**2 * cf_zel(r), label=\"Zel'dovich\")\n",
    "\n",
    "# format the axes\n",
    "plt.legend()\n",
    "plt.xlabel(r\"$r$ $[h^{-1} \\mathrm{Mpc}]$\")\n",
    "plt.ylabel(r\"$r^2 \\xi \\ [h^{-2} \\mathrm{Mpc}^2]$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "We also include utility functions for performing the $P(k) \\leftrightarrow \\xi(r)$ transformation: \n",
    "\n",
    ".. autosummary::\n",
    "\n",
    "    ~correlation.xi_to_pk\n",
    "    ~correlation.pk_to_xi\n",
    "    \n",
    "These functions take discretely evaluated :math:`(r, \\xi(r))` or :math:`(k, P(k))` arrays and return a function that evaluates the appropriate transformed quantity. "
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. _Halofit: https://arxiv.org/abs/1208.2701\n",
    ".. _explanatory.ini: https://cdn.rawgit.com/lesgourg/class_public/master/explanatory.ini\n",
    ".. _Eisenstein & Hu, 1998: https://arxiv.org/abs/astro-ph/9709112\n",
    ".. _FFTLog: http://casa.colorado.edu/~ajsh/FFTLog/\n",
    ".. _DiracElectron: https://link.springer.com/chapter/10.1007/978-3-319-74582-4_19\n",
    ".. _Back to Cosmos, 2019: http://rxiv.org/abs/1904.0218\n",
    ".. _Kritov: https://books.google.com/books?id=6TI7DwAAQBAJ\n",
    ".. _mcfit: https://github.com/eelregit/mcfit"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}