lognormal.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from classy import Class\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.interpolate import interp1d\n",
    "from nbodykit.lab import LinearMesh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "z = 0.  # which redshift"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Get power spectrum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# You can change the cosmo parameters here\n",
    "class_parameters = {'output': 'mTk,mPk',\n",
    "                    'H0': 67.66,\n",
    "                    'Omega_b': 0.04897,\n",
    "                    'N_ur': 3.046,\n",
    "                    'Omega_cdm': 0.2607,\n",
    "                    'YHe': 0.245,\n",
    "                    'z_reio': 7.82,\n",
    "                    'n_s': 0.9665,\n",
    "                    'A_s': 2.105e-9,\n",
    "                    'P_k_max_1/Mpc': 100.0,\n",
    "                    'perturbed recombination': 'n',\n",
    "                    'non linear': 'halofit'\n",
    "                    }\n",
    "\n",
    "M = Class()\n",
    "M.set(class_parameters)\n",
    "M.set({'z_pk': z})\n",
    "M.compute()\n",
    "\n",
    "h = M.h()  # get reduced Hubble for conversions to 1/Mpc\n",
    "\n",
    "one_time = M.get_transfer(z)\n",
    "\n",
    "# Convert to units of Mpc^{-1}\n",
    "k_ary = one_time['k (h/Mpc)'] * h\n",
    "\n",
    "Pk_tot_nonlin_ary = [M.pk(k, z) * h ** 3 for k in k_ary]  # Get non-linear matter PS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(k_ary / h, Pk_tot_nonlin_ary)\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate Gaussian random field with nbodykit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed = 42\n",
    "\n",
    "k_max = ... # scales up to which to use power spectrun in Mpc^-1 h\n",
    "delta_d_comoving = ... # box size in Mpc h^-1 (?)\n",
    "pk_interp = interp1d(k_ary / h, Pk_tot_nonlin_ary) # This is the power spectrum interpolation function P(k)\n",
    "\n",
    "n_points = np.ceil(k_max * delta_d_comoving_ary / (2 * np.pi))  # Number of points in simulation mesh\n",
    "\n",
    "mesh = LinearMesh(pk_interp, Nmesh=n_points, BoxSize=delta_d_comoving, seed=seed)\n",
    "field = mesh_smooth.preview()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Do log-normal transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lognormal_transform(delta, sigma):\n",
    "    t = 1 + sigma ** 2\n",
    "    delta /= sigma\n",
    "    delta *= np.sqrt(np.log(t))\n",
    "    delta = np.exp(delta, out=delta)\n",
    "    delta /= np.sqrt(t)\n",
    "    return delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma = np.std(field)\n",
    "delta = field - 1\n",
    "\n",
    "lognormal_field = lognormal_transform(delta, sigma)"
   ]
  }
 ],
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