examples.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Import modules</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math ; pi=math.pi\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "matplotlib.rcParams['mathtext.fontset'] = 'stix'\n",
    "matplotlib.rcParams['font.family'] = 'STIXGeneral'\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import PySSC module\n",
    "import PySSC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>I Compute a Sij matrix : turbo mode</h1>\n",
    "<h3>Sharp / top-hat redshift bins</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Define boundaries (stakes) of the redshift bins</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#zstakes = np.linspace(0.2,1.5,num=14)\n",
    "zstakes = np.array([0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,1.1,1.2,1.3,1.4,1.5]) #Explicitely\n",
    "zmin = np.min(zstakes) ; zmax = np.max(zstakes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Compute the matrix</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.041803\n"
     ]
    }
   ],
   "source": [
    "t0 = time.clock()\n",
    "Sij = PySSC.turboSij(zstakes=zstakes)  #Uses the default cosmology of the article (arXiv:1809.05437) : Planck 2013 LCDM\n",
    "t1 = time.clock()\n",
    "print(t1-t0)\n",
    "#The computation takes ~4 seconds on an i7 laptop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# If you want to change cosmology, specify the parameters with a dictionnary in the format of CLASS :\n",
    "params = {'omega_b':0.022,'omega_cdm':0.12,'H0':67.,'n_s':0.96,'sigma8':0.81}\n",
    "Sijbis = PySSC.turboSij(zstakes=zstakes,cosmo_params=params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Applications</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Example 1: Plot the Sij matrix</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sij can be negative (anti-correlation between bins), and varies by some order of magnitude due to redshift evolution.\n",
    "# Let's first plot ln|Sij|\n",
    "fig = plt.figure(figsize=(5.5,5))\n",
    "P = plt.imshow(np.log(abs(Sij)),interpolation='none',cmap='bwr',extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "ax1 = fig.add_axes([0.89, 0.1, 0.035, 0.8])\n",
    "cbar = plt.colorbar(P,ax1)\n",
    "cbar.ax.tick_params(labelsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 396x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's now plot the correlation matrix : Sij/sqrt(Sii*Sjj)\n",
    "#Compute the correlation matrix\n",
    "nzbins = len(zstakes) - 1\n",
    "correl = np.zeros((nzbins,nzbins))\n",
    "for i in range(nzbins):\n",
    "    for j in range(nzbins):\n",
    "        correl[i,j] = Sij[i,j] / np.sqrt(Sij[i,i]*Sij[j,j])\n",
    "#Plot it\n",
    "fig = plt.figure(figsize=(5.5,5))\n",
    "P = plt.imshow(correl,interpolation='none',cmap='bwr',vmin=-1,vmax=1,extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "ax1 = fig.add_axes([0.89, 0.1, 0.035, 0.8])\n",
    "cbar = plt.colorbar(P,ax1)\n",
    "cbar.ax.tick_params(labelsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Example 2: Find the characteristic multipole ell_SSC depending on redshift</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The multipole where the SSC decreases the S/N by a factor 2 compared to the Gaussian cosmic variance-limited case\n",
    "# Defined in Eq.46 of the article (arXiv:1809.05437)\n",
    "#Compute it\n",
    "fsky    = 1.\n",
    "Nprobes = 1.\n",
    "Resp    = 5.\n",
    "ell_SSC = np.zeros(nzbins)\n",
    "for i in range(nzbins):\n",
    "    ell_SSC[i] = np.sqrt(2./(Nprobes*Resp**2*fsky*Sij[i,i]))"
   ]
  },
  {
   "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": [
    "# Plot it as a function of redshift\n",
    "zcenter = (zstakes[1:]+zstakes[:-1])/2.\n",
    "plt.plot(zcenter,ell_SSC,lw=3)\n",
    "plt.xlabel('z',fontsize=20) ; plt.ylabel(r'$\\ell_\\mathrm{SSC}$',fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "so SSC starts to dominate for multipoles above a few hundred, i.e. sub-degree scale in real space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Example 3: Find the critical density of clusters where SSC/sample variance surpasses shot-noise/Poisson</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# If Ncl is the cluster count (per steradian), then the shot-noise/Poisson variance is Cov_shot(Ncl)=Ncl/4pi\n",
    "# and the SSC/sample variance is Cov_SSC = b^2 Ncl^2 * Sij\n",
    "# the latter dominates shot-noise when Ncl >= Ncrit = 1./(4pi*b^2*Sij)\n",
    "\n",
    "#Compute Ncrit\n",
    "bcl = 5.                                  # Average cluster bias\n",
    "Ncrit = np.zeros(nzbins)                  # Number density per sterad\n",
    "for i in range(nzbins):\n",
    "    Ncrit[i] = 1./(4.*pi*bcl**2*Sij[i,i])\n",
    "Ncrit_deg2 = Ncrit * (pi/180.)**2         # Number density per deg^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": [
    "# Plot it as a function of redshift\n",
    "plt.plot(zcenter,Ncrit_deg2,lw=3)\n",
    "plt.xlabel('z',fontsize=20) ; plt.ylabel(r'$N_\\mathrm{crit}$ [deg$^{-2}$]',fontsize=20)\n",
    "#plt.savefig(\"Ncrit-halos-vs-z.png\",bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "so SSC dominates when we detect more than a few clusters per square degree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<h1>II Compute a Sij matrix : general mode</h1>\n",
    "<h2>With window functions</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define redshift range\n",
    "nz       = 500\n",
    "z_arr    = np.linspace(0,2,num=nz+1)[1:] # Redshifts must be > 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Top-hat window functions, for comparison with turbo mode</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "nbins_T   = len(zstakes)-1\n",
    "windows_T = np.zeros((nbins_T,nz))\n",
    "for i in range(nbins_T):\n",
    "    zminbin = zstakes[i] ; zmaxbin = zstakes[i+1] ; Dz = zmaxbin-zminbin\n",
    "    for iz in range(nz):\n",
    "        z = z_arr[iz]\n",
    "        if ((z>zminbin) and (z<=zmaxbin)):\n",
    "            windows_T[i,iz] = 1/Dz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zn1bCGGSicxNxdQbVRfjxZVNQ4thLdZ4pkUIloZ50liBWMvRJZ+EmGi1hDDLRNqojvS0G/sQyyacrfEe9/aLTo/OSZgnaG/EGkK1AThAsodBaWOst0sMYjI8wBpmQAshNzICOKyrupfpnsTOQebQ2dUOP2kmzLayVuz0j+uzVbKKwBeMjjEEm9K6l6rGX7LgCrQFk3nyKsrMy5oC+RMljL9kUYouupdNKGIPMKG4iPpsogeeBOc+gLTqjB2UFk0DVGSzwavGyzacsGDH6pDO+hTUj1UlHAHqshDHIRLfy4SeYJPUCfeWkrqXNNcjBBayQ732OArxgiZgByM+53RloSsfOYHyEMcgEW+3fyQhdSy1BYim14uTNmMG13kCKt6WdF4fO/BJz9gX43kRRgTythDHIDLmJL7+ZllozJNZlcaMXGjhBBXKJM5CVrqXCZiayicZLGIORop1nUCaA3H69iYskCR8XnV8KZF8JHzRdaZ6iCCYYJWEMMtG5iTjXg9Q7hpacEzOg8+Y5Dco5TObWhAhuIgKrc/bZIItSp8cHvsXDbWJnMFrCGGSinWAI2W5KLZGzwRfLdZkmw0/qpnb30zWgZIqZwK6gpKecmE0UdQajJYxBJrQAsjadKhXISoc9l10I6rRYrt8OHxAtdNKZuPOMmMH0EcYgE1rX0hHEDBT/BzsxSrOishdSzp5Qzn9oWjsMn0SsuYn0rK/IJhofYQxGir5yK5jHRF2Cb7/RXqHg/MI1JCwYQBYqkIPpJIxBJpqVD9u1tEqUHD5moOwMXPQnKxONFiXRA8isIfI5f/Yemxuyli1UZxBuotESxiATSppl+4WRJkdSTvBvtRNyiSW6aVk5ScanRhb3Yqry0cI6qAljkAn12EvFbVIqgKwtVcullko7kjZmTp6yNoEB5EqelIsK5NESxiAbSlCyCSCzI+s7Ci6UKqQNyl1eTXDVJAggS6mlBSqQF3i1OEFLUoEcjI/ixsDMXmVmbzOz00vrMiYMoFesxdbYyrxYEulAn4YCAWRq1EZOyYIKppGlJQc3s98AsNbdP1JSjxyobiKDw0l/T3VgCiWqpZa2AWR2a1CmzkBqVCeN3NQQS9FneuT5rwYYNmIGI6aYMTCzcwFcA+CiUjrkRHK9N35VJZ2bTjkULiCuMrXsmLIrXG58g9tMmQAyW4EMMc4RdQajpaSb6CoAjwP4oJndambnFNQlOd3OgFttKsdeVgqIctQk0bwgBm8WyRIlun/WIxeZ3Pj1tdIpNbKJppOSxuBMANe7+78D8CkAH5j/C2a2ycy2mtnW7du3D65gCqSTzorEDFqfCSHZyDLjim4iU+xfuQBy9SfrZBLqSYSdQTU2O27EKMZKSWOwA9036bsADgggu/tmd9/g7hvWrFkzqHIq6kpxxrR2FCxJslIVYZIUbqLhjYEKb0DlrrhytXjsDMZGSWPwvwD8XP36JADfLqhLcrT1YrOVZh3/wopRC3ZUP4+kL7qw0u2ekSSR4N7M8r0sIrV0CilmDNz9qwCWmdk7ALwawMdL6ZIDF6xB1+WXLWTSUbbzlN5y0ZmQlVMIWVvJhkTMINifoqml7v6+kuPnpDvPgPC9N5ZESS1l/dDSqr72gRcpOitjCpQC5GbnV6rojHdDKhXbUYE8VooXnQULUbcvkwLIvIuJRenHJCOMyUdnKml6/ILBVKXCPZhOwhjkQirwbHpZ6m0less5MCsmkZepmxb2Btb+QSD4A9udX4mdAX+/05QHhikaG2EMMpEigKwgB5ClQck6A4kyq2zlGEeXjGejAC9a5vCkiBmMlTAGmeiOvSRiBqZ0uW++5EKAUC8vJQaF5DZR3rFW2yemaEKYz8skIWnGIGIGoyWMQSa6Qqb+sqakIkFsY8GL6l4emeH7vCqOHjWArN1uwYxFaulUEsZglGgxg2JdS2u4MIm6UuRLkNMsUoUcYiWFmN5NKWHzmNCnkTAGmZC6ljbXYMcmxwWqmIG6vhY65pByYgzYlBWrkkJMDtnIi7JFYgbhJhotizYGZnaOmX3CzO4ys++b2V+Z2XvM7OicCk4qUiFvew1hchQSa9SYQal1Y4mgZDe59ZdNUoFMYvxGKom2EUAeH4syBmb2ZgC/COC/AngtgPMAXAHgWwA+YGanZdNwQnHB798EkIt8X6QxS4Ul67GLzC8TGkCOrqXBPA5rDMzsVAD3uvsfAHg7gOfd/QV33wHgEQBfRdWBNJiDtDNoC5BLpP4JOwOlHFdEqd9KMTGVCCArmOBXcwg7z3ATjZbDGgN33+bu36//92IAv2hmZ9X//wMAp7r7llwKHpmI2UTpFOk3boJCOx4tnbZIzEAMIAMu1MqpJjAm82mjbwB5pbv/GYCVZnYZgN8H8FR6taYAIYDcZROxQ2tdS5WUw0qBMhPFpE1P7LGm3QV4URObcISbaProawzeaWYnu/vdAO4EsAZA7AoWQDkwpStqZfsLlakXUHPIS+ag89kx1U+tUd3wVAFkxQ3JyUadwXg5bNdSMzOvHXzu/kDz9+7+NIBfmf87QYWWWqoFkKWOEkpqqXSegbZWrCaZWUrW2z+GxRd4NQloZ3NHzGCsLGZncKKZ/dLB/tHMzgBwZTqVpgsptbTEsZeWoB1FoZ2FntejyPIVJWV2carxjcl82jjszsDdd5jZHWb231DFBx4GsAfV6WTnA7gLwH/MquUEoi18tJgBoBWdsfgBL4ZGqOQt4b5ohyyQTQSnYxZKrKG7RhiTsbGow23c/UEAv25mrwDwCgDHArgPwCdrd1Ewj269yFem8l/WMrnrDdyqUS3HVeMVLPzOwFXrKW5oogI5mMtii84MANz9m+7+XwD8GMBzAF5iZmdn1G9iaR525ShhUQFKTKtAbgcn5YbPblFRJje56ExAq8uIbKJpZLHZRJ8ys5Oa/3H3GwB8B8BZAN6ZQ7FJJ4WLp0i7ACm1VKxAFp3nZSaYFDGD4R2Cqs9fNQbB+FjsGci3AHhz3Yfoi+6+w91/COCHAG7Ipt0UwAWQ9aIzqYhYCiArQYcyefdaxn3DJAaQC/S+KnjUZ3BoFhsz+BIAmNkyAFeZ2bEAbqhbUgQLkCSATH5v1C4/KpOZaaJVIFOWSK5AVuCNgZ7eEDGDMbIoY2Bm1wL4EYC1AE4DsA7A75nZte7+2/nUm2T4NgWNJSkRQFbW9l08lKnAUt0WvOZppiUlgEwiXCDJ50yNGzGDsbJYN9H59c8LAVwP4AEAj7j7E1m0mgKUPj3yTlqKDrrQqK4JpjKyKLudIenq7EoEkPk9mBjdkT+qMAbjY7HG4O11vcEKAG8CcBGqeEFwENovulJ0JoxPH6UopSuqPnC16ExbKXNj8ldw+ZNWvP6Cm0hodxKppeNlscbgA2b2AIAX1/+dBeA/mdnH3f13sml3pNK4iQr0jpEzgljJopND2QpkseMcTYqweTA9LNYYbATwPKr6gq8BeAjAQ+7+bC7FJp2uNxFRdGa6MWAnmBTHXhqxvZA9Y4LLRKlATpEJRGsu2RC1HQUrFzGDsbJYY/CP3X1nVk2mjK5raX/Zbr1YwOEixQy6a2gXYBneTaRcQWlmqFIFkMtVIAfjY1FFZ2EI+qN1LRXHbv/gxpanVLJrqYaVydBMEECW3GuknJL+6xDqDJqdQcQMRkff8wyCnihFZyVWbrUCGsUWfyVSS3VnS6m6jDK2M3YGYyWMQSa0mjO9rEf19Cgwq0bVh2zSxkBwyLUrXCWbiB2bGhaAVoGcpOgsYgajI4xBJlyYJFIEkPnJTQ8g8190ZXIss53pTqUbbswUmCvGQFjfC261IC9hDDLDuYmaSXV4DEqLIGlm1FACJYVokwxK6C2lpEY20TRS3BiY2cvN7PrSeqRGyxTx/X5Q0uzKqxmakZdSJcVIh+AmSjItUa6xBI3qhJTYSC0N5lLUGJjZiQD+AYDlJfXICZVKp/SyQILeRDahX1axVw85qHAFNYCsFcuVSF2O1NLxUnpncCWAPyqsQxa0yVQL0SXpHcOkSnad6pgBkzRAY2hGHtyPLXYt9ZIBZPVeTeBaY9opZgzM7EoAN+IQj4WZbTKzrWa2dfv27cMplwDJTVQLz7JdS4XeMU0AmZqaTVvp6mmHys6A9DM1wX7K/jVCBeoMBHdgCqM9kTvPKafkzuBqAJ8CsBnA68zsvfN/wd03u/sGd9+wZs2awRVUED09xTD3FNuKJLr0HrbIqDwJyuxkYcqICWO3jeom7tOafhbbjiI57n45AJjZegD/xt3/fSldctB5kpmvTYo6A221qewM+Ni14sNOYHX5mHmRz0oa0x3uZKhf2Xk214jU0tFROmYw9VA7gyRdSzkMVqWWCt9Vbjek99BkJxhXiitqFGNkYuYXNaaVaVRXyU7YdvkIodjOoMHdfwTgVwurkRxt5aMbA3FoameQwAVejK6yo+89VyqQE8DOq149X85GocWVfbiJxkfsDDKRph2FsDMgFejcHlQ0dY4GfZEbUpDjNlJaozsp+0o6UYijySbqO3LzPqWdgVm4iUZIGINcJAkg67uL/mIJWlgXaUcxeSgVCsl06PlRKa3ZG8JNNE7CGGSGK7JJETPQyqiUlRsZMpD9JiWOvewEleD35MUMpLHDGIySMAaZ6PrOMMLamrEyBmyuf3ON4d1EYjcKmva9UrdMqDNoxy1QgdzEDHpeI4WbCJNa4T7lhDHIRAqX6KwgqxSdAWIxEisr3TNLcNNJIwZQfpMU0yHr0mtjBqSbSNU+YgbjI4xBJtq1vZBaKnkPhAAy37W0UYCdVLWB6enF+dV9FybhA8iSm4j+nIU0XOippbEzGB9hDDLRfdEV330JP3QKz7uYyjQ0lsKPLewMlGwiUe3eNqx9rnnCGIyTMAaZYQuwuj9ZaRYTfLrqzFSmN1HpaUmrQFZaWCuFcrRodC4dKWEMMpEigFymApnPJtLS5lUTlmC1OXgAuYKuQN7vKv3lqAByIjdRcQscHEAYg0xo8THVGOhn+koTK59NqyFspboKZHZQxk2kGy8nV9mNGSgWQA5rMDrCGGSi8wcr19BSB1m5MgHkEUB5xprmfEoAmUTsIQVCPEUWUFQgj5MwBrlo87H5vi8uzMpl6gwa4VLZREqGjNDkBxDk515jGDFgbmrp8G6iudcJxkMYg8woAeQSx14C1c6AOwPZ5v4YGG2ZLHfgkJD9W70pGkCOCuRREsYgE1rIQA8gsyhf8rY8ggo+yzlQ+gKbCgLzestrYzEuxZQppDidrRs9GBNhDDKh+YP5DJVGWnVaSL2JJu6ks/qO0e4tQKkzKHG4TXOAMvtRRdfS6SOMQSbaHi6CzyTF7qIv0rGXzXulFS9TZ6DQnulLBZD1VTYraV1wqOd4iVJLg9ERxiATUlixdRPxY8s7A2L0bj5k/C3qRK6dZ2C0CuV2BhIOrs6gTYxQ4jNRgTxGwhhkRgogFyg6A+oAMvNllRd8YjbRhM4vUm8iqVGdgBSYUgYOchHGIBNaUWklrHUtZd1EjQpUNFUYu9yZvHAlr4aP7ygbKR21a6k4+qRa7ikmjEEmurX98OW42he2cVFRFVj7XYMcmoavM2heKAFkQZJO4eI/aWs/Z27EcBNNH2EMMuFaOhEAYLZEHrgLFcitLSB3JQW7lvL+liaA3F80wSMiwWSNxRnI00sYg8xI5xmUqDMQ5BVnC1yxQkCaw20YUoxJ7mikwi+x6IwfOrKJRkoYg8xodQbDH3sJoJ5XdVfTMFJz5dlxXSpaq5isbKK2HQUrL52RHW6iMRLGIBMpAsjsQlnKJmoCyFw57v4/e4kWnBwKpdXoZyBD+qCdGDrcO9NLGINMtIE2zk+03w9WA06smSSIOoM51xiaKkaiBpAl6aEHrmsFtMHZ8wyUkSNmME7CGGQiRXBwVlkwkrJSuzdrfvA5Ljyas8XId95VIPcfU4sMaVjzJ5laqvr9w000PsIYZEbZGJTqWgr12Eup0E6AXm0mcPUIFOlNBDWArMUMgvERxiATKeoMlOxzpehMnt7oZbK62hQhLmALvOo/3PDldta4A3vKtamlyq7VIoA8RsIYZCJJBbKQTaQiVSALxVulspi0zkZiBTKLO1wqWIsK5KAjjEEmugAyJ62NrQg73ZtRNN6iAAAO8ElEQVSoDS1KwefeonMuwgfN2bGl8wwSnQ3A0FUgszvIcBNNG2EMMpFi4VOiAlnZ/islxDbnT1ZeC3yrAWTeAEqhb0mU2BmkqECOOoNREsYgM6UqkIt0LVXGFOMkc6/RWy5JCu/wwVglzKIdEioSG4NRUswYmNkJZvZ5M/uBmX3GlFNgRowSQC7RtbQZnTuspV7f0416lJYS2uNDVyDbAS8WTWtGhCPt+IwgLs0gWaO6iBmMjpI7gzcAeCeA8wG8HMArC+qSHOlhF3zYlZhLjeqaa/DCaikUKyy/aXpMKU5SImbgTQC539ipJvFwE42PksbgZnd/3t33APgOgCfn/4KZbTKzrWa2dfv27cNrKNAWnSm92zQNKCnl2MtOrMwXfdKmF9EbWF2DfdfNCaVkNlF0LZ0+ihmD2gjAzJYDeNjdH1jgdza7+wZ337BmzZrBdUyBlBwqFJ3RNEWpVGZNgqKzJP77/lJ0hovgJtpfAxLaS6RNxpFNNH2MIYD8VgAfLa1EatpFHzOht3UG/NhKozo1gMzFDFAZP3qhmyBDRTiUgHvLvP/dRVdi6RbW4SYaH0WNgZldDuAWd3/GzM4sqUtqUmSosF/WyhhoOffD1xloee/7KdBXLEGhG2P0ldqKzsUkBJCdTy2d2AOng4NSMpvobQCuB3Cbmf0tgMtL6ZIDybcqrDbnKEDRHVaWIABOyTLDtWaIH5cVb33vittECT5rY7JdSyNmMH0sLTWwu38BwBdKjZ+bJAFkqYhLSFekh01ROkag2gJL1JOpJ11n2zLZV47+djtZO4pwE42OMcQMphrlPAMu01FfuXkJn67z77m9hGAAhUhsAo+JEDMgaU46U+R52Qggj5EwBplIkS8vBSXZQ+nr6DMdM/BZrXCsSDZRc+wlr/fQdQYpTLUT10nSjiK6lo6SMAa5SODwZ1Zuui9WyFJRIqLNexbafxZxQycpsGN2BqxkdwGq6CzRzY6YwfgIY5CJJlOSE1YmGNGB7s2KcdgAcpr+QPzOgBY33ogpn5W6su4CyL0HruWVsWNnMEbCGGRCKORt0XoTsTgfQLb6a87M7Cb4kpPMK8Id07J45aaCtKxwnoHqJgpbMD7CGGSE773XJpETkvqXFWBXuuC/5LLfQwsgJ2hzJ0gPvZMC9DTcCCBPG2EMMiHlaignnTWrTSGArLmJnJwoEmQTke+5C3UMG+tQYgYqXQUyFzOQzmCA8nwFuQhjkIk0FciMpLgzaBfobCDX1RmdHFdBSbJMEEAWYixadEmoQBYJYzA+whhkQgsg7/ejp6ia7VEfeykdXclM6FVOK6e29p6lJKhGdPDUUjGATNZ1JDnPICqQR0kYg4yU9I2WGrmkN1jNr6HHVaK40sgayv1Ss4mC8RHGIBPNwV2kNAAuZiBXprqWoQLnYgaKc8tTLO0L0BVwCQFkuvM26SZqPinhVkdq6TgJY5CJFAFkquhM3cZLAeS2zR03MCvaXoF3jRlYL5MeQDYiibitUKDvV3PsZW9rACBBamkwOsIY5CJFAJlyvasrLn5yk2YoOXAN+p67NLOWWeEmC+SSO4OoQJ4+whhkQgsg68sv/pB113oTsUVnqP1qA6/O06D2JhJ2BpKbiDAGidqFh5tofIQxyIgaKCsT4BPyRKxsAFlj+Ark0mhdSwXZcBONkjAGmXB34SwDIYAs1hmYsDOoFODqDLzeSmmeGja1tOlaykmrgW+qybnsDaxTedmiM7ECOdxE4yOMQSak3kRKANn1L6u3f/Qdu65oLeR7L+N6UALIjeEmulCJ8XbaTZSiziCyiUZJGINMqB5VQJtg+KFbz798jZ5CtWiJAHKaoGjvcQ940Uc2TaJAb6moQJ5awhhkwl33jSo+Xb6Vplhn0FxkSBIYsGKN/ea94q/RF6PqDDppnuhaOk7CGGREdhMRxkSOGYgHvCv1DQmmZEFWOfZyeL1TFZ2xxLGX00cYg0w4pKBB9adQZyAVnUkBZGgxg6G9U3OHLLOh4SqQEwzu6P85J6sziK3B6AhjkAnt1Ms6m6jEyk1wuXgdeVZcJnSPu/2u0n90tWvp4I3qyEZzc0ePrqXBXMIYZERui0y1NtYDyK5eh9oYNCmawvTGdi1tb/ewWVCdp2f4nQF77GWS1NLoWjpKwhhkoqozKBdAVr6sfMAB4FNLBYpOLAa+AllMgxJhjH6SYy8jtXSUhDHIiNqOQmlUp0A7W1wJDVY7gxSHAjFyvOaewoHfXyLBmBFADuYSxiATjdODlya9LWJRUNPCmjMq9a5AOLlLQXeRcUK88ax+cm4iLWZgTo7c6KxsPC12BmMkjEEmUgSQOde7mJXTjC0dP8n73rVxOdS8GKBEjIUXnStJdy0te9ODDIQxyIRDiRnU2UTUvKjtDOZfp59M84Jer4qppVoGFd96m+xNVP9UzjPg4fYWKdqdRMxgnIQxyIjuGVV8ujx8DZWWDaSjTFBDCya9BIVU4a4QIYNREsYgE1U7CkEYXNfSBuU8AyW11FjZBG4WrehMCSBr5xnwNR284ZaPveSGrWUjtXSMhDHIhP6V0WIGeoMEweVCT4xsNlHj8FCyiUBvLPjwTPOuGTeRFkDuKpC5cSO1dPooZgzMbKmZfczMrjCzD5nZVBmmYgFkObCnhiTBWjFeWBpYG1oJuCsxlkQHjsVJZ0GLldqumdk1ANzdrzezdwHY4e5fPNjvb9iwwbdu3dp7nC9/+Yv44aPfEzTleHjHLjy9ay9e9uKT+gs/vx3Yfj++e9QFOPu0Nb1E987uwb0/vRvn7d6Hk190Se+h99x9D548ei+WXnAeVi5d2Ut257ZZ7N2xG2uO3gaceVov2Uf/9j7YzBqccs6pWLK03zNps4ZjHl2Gnzz3faw495ResgDwyPYdOP6FY7D2xBOwb3m/Vfrs0fdgNx7H09tei9XHHtdL9r5lK3DbsSfhn+29ASc9c3Ev2WdemMGnH1qFF84+Du9e+uNesgCw8eHP4I695+LetW/Gi5bvW7Tc49iGW3Az/sPjz+KxVf+i97gA8LmZP4cDeNPsayn5I5GXnb8Rr3r1GylZM7vL3Tcc9vcKGoP/AeA6d99iZq8CcI27v+Ngv88ag01/8Hp8/fjHBU2DIJjPH/5kG16xazcl+2trT8GdK5Yn1mi6ufSps/HJf3kTJbtYY7CUunoa1gLYWb/eCeDU+b9gZpsAbAKAdevWUYOc/sJ5eO1Tx5IqHqHozf35gdmouzscs7TzYYngMfXZJZidXcKNa3txnD/LjWsz8OUzYBysDuC+F16Mp63/d+OE2b3YMrMb3ziG+6zWP/s8lu/ZefhfDFrWHXVu9jFKGoMnATT76uMAPDH/F9x9M4DNQLUzYAb56LuvY/ULgiA4YigZtP0KgMZRehGAWwvqEgRBcERT0hh8FsA6M7sKwBkAPldQlyAIgiOaYm4id58F8OH6f28opUcQBEEQRWdBEAQBwhgEQRAECGMQBEEQIIxBEARBgDAGQRAEAQq2o+iLmW0H0L8JS8VqLFDUNgJCr36EXv0IvfozVt0Uvc5098M2OZsYY6BgZlsX05tjaEKvfoRe/Qi9+jNW3YbQK9xEQRAEQRiDIAiC4MgxBptLK3AQQq9+hF79CL36M1bdsut1RMQMgiAIgkNzpOwMgiAIgkMQxmCEmNkJoUM/cutrZheaGXeCTWYY3Yb4fA+nV6lnbKz3qzQlD7dJgpktBfBRAP8XwAUAfrfuiAozex2Al6I6u2uLu9+50N8V0OuXAPwmqtPd3uHud5jZKgB3AFgC4AsAPlJArwN0GOp+HUo3MzMAW9Gdwr7S3c8d8J5dAuAvAawC8MKcvy/2fC1Ct2LP2GH0Kv2MHaDXCJ6vEwBcD+ASALcDuNpr//2gz5i7T/R/AK4B8K769bsAvLV+vQTVB2z1f3+50N8V0GsFgLfUr38ZwF/Ur98H4PxS92shHYa8X4e5Z2cAWF2/Ph7AtUPes3qsHwFYfqh7M/T9OoRuRZ+xg+k1hmfsIPer6PMF4Mr6M1sG4F4AG0s8Y9PgJroEwN3163sAXF6/XgfgCa8BsA/A+vl/Z2ZnD6zXXgB/VL/+FqrjPwFgDYA/M7O/qlckuTiYXgvpcMA9zHi/Dqqbuz/k7k315T8E8OWD6DskpZ+vQ1H6GTsUpZ+xAxjB83Wzuz/v7nsAfAfd5zXoMzYNxmAtgOZ07Z2otsXz/775t1MW+LtTkYcF9XL3fV67ZQD8fQAfr//+/QBegmoy/LeZdDqoXgfRYaF7mOt+HVK3ObwOwG3AoPdsIUo/XwdlBM/YoXQr/YwdjsGfr9oIwMyWA3jY3R+o/2nQZ2wajMGTAI6rXx+Hrn/H3L9v/u2nC/xdrj4kB9MLAFBb8wfd/dvN37n7CwB+G8DfyaTTYfWap8NC9zBn35bD3bOjax33HkTfISn9fB2Wgs/YISn8jB2UETxfb0UVM2sY9BmbBmPwFQAX168vAnCrmZ3i7vcBON5qABzn7t9b4O/uH1IvAKh/nu/uf2Fmy83slOZBRGX5t2TS6XB67afDQe5hrvt1SN1qXg/gfzf/M+A9azGzmZE8XwfVrX5d8hk7lF6ln7EF9aop9nyZ2eUAbnH3Z8zszBLP2MQXnZnZDCrL/W0AFwL4EwDvd/erzOw1ADbWv3qnu/+fhf5uSL0A/CqqQNDx9a86gH8C4EZUVYZ7AHza3XcPrNf7AfzpfB2Gul+H0s3dr6r//T8D+KC7P21mZy2kbya9NgD4awBvA/AggA+Vfr4OpRsKP2OH0GsMz9iCn2X9b6Wer7ehcuU9hSpA/FkALxv6GZt4YxAEQRDoTIObKAiCIBAJYxAEQRCEMQiCIAjCGARBEAQIYxAEQRAgjEEQBEGAMAZBEAQBpqCFdRCUxMzeCeBpAD8H4PXuvvEwIkEwSqLoLAgEzOx4AM+galfwz939rsIqBQFFuImCQMDddwK4GsC3whAEk0zsDIJAoD6l6usAXoPqHIGl7r6jrFZB0J/YGQSBxkcA/A2qjpe/h+oAkiCYOGJnEARBEMTOIAiCIAhjEARBECCMQRAEQYAwBkEQBAHCGARBEAQIYxAEQRAgjEEQBEGAMAZBEAQBgP8Pqcq90e6C9PMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(nbins_T):   \n",
    "    plt.plot(z_arr,windows_T[i,:])\n",
    "plt.xlabel('z') ; plt.ylabel('$W_i(z)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Compute the matrices</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5.22481, 13.449793)\n"
     ]
    }
   ],
   "source": [
    "# There are two different routines, which perform the k and z integrals in different orders\n",
    "# We compute both of them for speed test and further comparison\n",
    "t0 = time.clock()\n",
    "Sijw_T = PySSC.Sij(z_arr,windows_T)\n",
    "t1 = time.clock()\n",
    "Sijw_T_alt = PySSC.Sij_alt(z_arr,windows_T)\n",
    "t2 = time.clock()\n",
    "print(t1-t0,t2-t1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Comparison with turbo mode\n",
    "# Let's first plot ln|Sij| with a common range of color\n",
    "lnSij = np.log(abs(Sij)) ; lnSijw_T = np.log(abs(Sijw_T))\n",
    "vmin = min(lnSij.min(),lnSijw_T.min()) ; vmax = max(lnSij.max(),lnSijw_T.max()) #common range of color\n",
    "# Turbo mode\n",
    "fig = plt.figure(figsize=(18,5))\n",
    "plt.subplot(1,3,1)\n",
    "plt.imshow(np.log(abs(Sij)),interpolation='none',cmap='bwr',vmin=vmin,vmax=vmax,extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "# General mode\n",
    "plt.subplot(1,3,2)\n",
    "plt.imshow(np.log(abs(Sijw_T)),interpolation='none',cmap='bwr',vmin=vmin,vmax=vmax,extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "# General mode : alt\n",
    "plt.subplot(1,3,3)\n",
    "P = plt.imshow(np.log(abs(Sijw_T_alt)),interpolation='none',cmap='bwr',vmin=vmin,vmax=vmax,extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "ax1 = fig.add_axes([0.9, 0.1, 0.02, 0.8])\n",
    "cbar = plt.colorbar(P,ax1)\n",
    "cbar.ax.tick_params(labelsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LU233JHntdKfu/nB3/9XU428l+S9JvjJpunDy+LeS3F9VH5gEHoOwLQUAAADG6MhsS9leVTunHl/f3ddPPT4zyaNrnvNIklOqalt3r72WJKmqc5J8PaurPNLddya5tKqOz+oKjn86qfvLQ3wRwg0AAAAYm/3bUhZvd3dfssH1J5M8taZtZc39eq5J8ve6e+90Y3c/keS6qqqsnssxSLhhWwoAAACM0Ti2pTyYZOuattOSPN7d31jvCZNPU/nj7v7zDep+aJ26h0y4AQAAAGMzkgNFk9yS5NSqet5U245J+zrDrtcl+VZ3f2Sq7bh1um5Osmv2N2Rj821LWVlJjj9+qNf+Ts2h7dkzeMlzzjlx8Jr33D3IJ958l/N31OA1v7Br2HE+//mbBq2XJCefPHzN2vf04DWzb9/wNTmmLGJ14uYFbFA86aTha5577vA1//Qzw8/Dr7x0+Hl46HGec86g5ZIkWwf7/y6LtYh/diyipr8uxs1cPCxz8XAWMRdv2TJ8zUUwFy9Od99RVbcmuSLJb1fVlqweJvrGqrooyc8l+YXufrqqXpPkB5LcWFU7khyX5O8k+a2q+p+SfL27PzYpfU2SXx1qnM7cAAAAgDE6MmduzOKKJO+tqhOSnJ/k3d39iar6iSSvT/L2qrowyYeTfE+S/3XquR/s7seq6uVJrq6qm5PckeTj3f2JoQYo3AAAAIAxGkm40d0PJblqnfabktw0efgfkxxwzVh3vzXJWxcywAg3AAAAYHyO3KelPCsINwAAAGCMhBszE24AAADA2Fi5MRfhBgAAAIyRcGNmwg0AAAAYI+HGzIQbAAAAMDa2pczFOwUAAAAsNSs3AAAAYIys3JiZcAMAAADGxraUuQg3AAAAYIyEGzMTbgAAAMAYCTdmJtwAAACAsbEtZS7CDQAAABgj4cbMhBsAAAAwNlZuzEW4AQAAAGMk3JiZdwoAAABYalZuAAAAwBhZuTGz+cONzQPnIUvyzao93x685tlnnzh4zS/s6sFrXvDSGrTe5z83/BjPOmvwkjn11E2D19y0eQE/7/v2DV+TUVuGafP444evuW3b8DVf9KLha/7pZ4af41556bDz8K1/NvwYe/iSC/meb9kyfM1FWIbf82PdMnyPzMXDWoa5eBG2bh2+prl4Rs7cmIuVGwAAADBGwo2ZCTcAAABgbKzcmItwAwAAAMZIuDEz4QYAAACMjZUbcxFuAAAAwBgJN2Ym3AAAAIAxEm7MzDsFAAAALDUrNwAAAGBsRnTmRlVtT/LrSe5KcnGST3f3763T78Qk70ny5STfl+T+7v5nU9dfneTKJF9I8jeT/OPu/soQYxRuAAAAwBiNJNxIclOSD3X3dVV1QpJ7q+q+7r51Tb/rk3y1u/95VVWS26rqge7+N1V1YZIbk5zX3bur6v4kf1hVL+vuPtwBjuadAgAAACb2r9xY9O2gw6jLklya5KNJ0t17knw8ydvW9Ds3yU9P9eushiK/POny1iR3dffuyeOPJTkvyesP961KhBsAAAAwTiMIN5JclmRPd395qu2eJK9d0+/SJJVk15p+r6iq0yd1/vpadz+V5L516hwS21IAAABghDp1JF5me1XtnHp8fXdfP/X4zCSPrnnOI0lOqapt3f3oVL+s6fvI5P7sDeqcfcgjnyLcAAAAgBHat++IvMzu7r5kg+tPJnlqTdvKmvv9/bKm73S/A9UZZEeJcAMAAABGpvuIhRsH82CSrWvaTkvyeHd/Y02/TPo+MtUvSR7YoM7tQwzSmRsAAAAwQvv2Lf42g1uSnFpVz5tq2zFpn/bJJE9n9ZDQ6X53dPfDk/5/fW3yqSvnrFPnkAg3AAAAgHV19x1Jbk1yRZJU1ZasHgL6/qq6qKreV1WbJgHGv9nfb+INSd4/+fMNSX5kcrhokvxYkoeS3DzEOG1LAQAAgJEZ0baUZDWweO9ktcX5Sd7d3Z+oqp/I6ke5vj3JN5P8wyS/WVVvS/K9Wf0o2N9Jku7+XFVdNalzZ5IfTfLjk09NOWzCDQAAABihsYQb3f1QkqvWab8pqwHG/sf7A44D1flIko9MHr5vyDEKNwAAAGCExhJuLAPhBgAAAIzMyLaljN584UZVsjLwGaRD11uUBfxUnXjC04PXfP7zNw1e8/Of60HrXXhRDVovGX6MSbJ37+Als23b8F/75s3Df88rw7+fHFsWMbUfd9zwNU85Zfia55wzfM1b/2zY38kf+uHh56I//0/LMW9s2zZ8zS1bhq8JQzAXD2sZ5uLbdg4/F/cCpvdjdS4+lPdSuDE7KzcAAABgZKzcmI9wAwAAAEZIuDE74QYAAACMjJUb81mSAy8AAAAA1mflBgAAAIyQlRuzE24AAADACAk3ZifcAAAAgJFx5sZ8hBsAAAAwQsKN2Qk3AAAAYGSs3JiPcAMAAABGSLgxO+EGAAAAjJBwY3bCDQAAABgZ21Lms3K0BwAAAABwOKzcAAAAgBGycmN2wg0AAAAYGdtS5iPcAAAAgBESbsxOuAEAAAAjJNyYnXADAAAARsa2lPkINwAAAGCEhBuzE24AAADAyFi5MZ/5wo2qZPPAecjKyrD1FlVzEfbuHbzkySdvGrzmWWcNW+/zn+thCya58KIavOYXdg0/zkVMTtu2DV9z8+bh30/GaxFT5iJ+1of+62dRtm4dvmYPPB39+X8afn77wf9m+HnjjtuXYx4+/fThay7LzzvDMRcPaxFz8dBu2zn8HPeKS8zFQxr65/1Q/j4XbsxuSVIAAAAA4FhUVZur6oyN+ixJ9goAAADHlmVauVFVK0muTfJ4kpOTbEryju5+xldRVacl+RdJfjzJk0k+mORXpvtW1c1JLp88fDrJuRu9vnADAAAARmYJz9y4NskF3X1lklTVHyS5JslvrNP3nyT5v5O8J8mVSX41yYNJrps892VJ/iLJOyf9H+3uBzZ6cdtSAAAAYIT27Vv8bQhVdVKStyT56FTzjUmuqarj1vT93iSf7u4/7O6/6O5rk/xpkldNdfvFJN9M8kR37+zuew82BuEGAAAAjMz+lRvLEG4keUWSk5Lsmmq7J8kZSS767q+rv9rd/3rN8x9K8pUkqarjkzwnydVJ7qqqTx/svI1EuAEAAACjdITCje1VtXPqdvUhDPXMyf2jU22PTO7P3uiJVVVJLkzygSTp7ie6+/LuPivJ65K8MMlNBxuAMzcAAABghI7QmRu7u/uSw6zx5OT+qam2lTX3B/LTSd6/3taT7v54Vb0hye1VtaO77z5QEeEGAAAAjMxYDhStqj5Il6uSfGny561T7adN7u/foPaFSV7Q3f/bgfp092er6p41tZ9BuAEAAAAjNIZwo7vrYH2qanOSryc5L8kdk+YdSR5OcucBnvPCJK+bDjaqakt3P7lO9853ApR1OXMDAAAAOGTdvTfJDUmumGp+Q5Lru3tvVZ1UVb9TVS9Iksn9Lyb5SFXtmNyuSvJDVfXKqrp6/6esVNXfTvLR7v7GRmOwcgMAAABGZizbUubwziTvqap3ZXUhxf1Jrp1cOz3J5Uk+WFXfTvInWV3l8XNTz78vyYuT/FSSX0vypqq6McnuJL90sBcXbgAAAMAILVO40d1PJXnrAa49kOSsqaaXbFDq9ye3uQg3AAAAYISWKdw42oQbAAAAMDJLuC3lqBJuAAAAwAgJN2Yn3AAAAICRsXJjPsINAAAAGCHhxuyEGwAAADBCwo3ZrRztAQAAAAAcDis3AAAAYGScuTGf+cONlYEXewxd7xhX+54evOapp24atN7evYOWS5J8YVcPXvOCl9bgNe+5e/hxLmLC27Zt+JocWxYxtS/iZ33zkkT8y/A7ecftw89v3/8Dw8/Dn71z+HEuwjJ8zxm/ZZmLFzHOLVuGr7l167D1egHT0bLMxZ+769iciw/ley7cmN2S/LMOAAAAjh1WbsxHuAEAAAAjJNyYnXADAAAARsbKjfkINwAAAGCEhBuzE24AAADACAk3ZifcAAAAgJGxLWU+PocVAAAAWGpWbgAAAMAIWbkxO+EGAAAAjIxtKfMRbgAAAMAICTdmJ9wAAACAERJuzE64AQAAACNjW8p8hBsAAAAwQsKN2Qk3AAAAYGSs3JiPcAMAAABGSLgxu5WjPQAAAADg2FZVZx/O863cAAAAgBFappUbVbWS5Nokjyc5OcmmJO/o7nW/iqr6oSR/NtV0fZKfm1w7N8k7ktyW5IeT/J/d/YmNXl+4AQAAACOzhGduXJvkgu6+Mkmq6g+SXJPkNw7Q/+okfzPJ3snjXZPnnZDkliRv6e5/W1U3JvlCVf1Ad//VgV7cthQAAAAYoX37Fn8bQlWdlOQtST461Xxjkmuq6rh1+p+f5OVJzkhyd3fv7O5vTS7/VJIXJPlEknT315LckeTNG41BuAEAAAAjs3/lxjKEG0lekeSkTFZfTNyT1fDionX6/1CSfUn+dZKHqurqqWuXJflyd+9ZU+u1Gw1g/m0pKwPnIUPXW1TNZbGAdUubNg/7fm7bVoPWSxazXOueu3vwmufvGP5r/9IXhx/n008PXhIO2yKm9kXMHYsY55Ytw9bbtm3Yesli3svP3jn8/Paylw8/D39h1/Dj3Lv34H3g2WJZ/ul+rM7Fn7tr+DnuoouXYy4e+v08lLn9CG1L2V5VO6ceX9/d189Z48zJ/aNTbY9M7s9Ocvt05+7+3SS/W1Xbk/xakt+uqge6++ZJrek6+2tteOCoMzcAAABghI5QuLG7uy85zBpPTu6fmmpbWXP/DN29O8k/qqrnJnljkpsntZ5a03VlozqJcAMAAABGZywHilbVwZbFXJXkS5M/b51qP21yf/8ML/OhJP9g8ucHk3zfmuunHayOcAMAAABGaAzhRncfdB9RVW1O8vUk52X18M8k2ZHk4SR3zvAym/Od8zpuSfIzVbUy9TGyOybtB7QkO9wAAACAMeruvUluSHLFVPMbsnp+x96qOqmqfqeqXlBVm6rqF6vqoiSpquOT/M9J/vnkeTdnNSh5zeT69qweWHrDRmOwcgMAAABGZizbUubwziTvqap3ZXUhxf1Jrp1cOz3J5Uk+mORrSV6X5J1V9S+T7E7ylu5+IEm6e09VXT65fl5Wg42f6e5d2YBwAwAAAEZomcKN7n4qyVsPcO2BJGdNNb3qILXuTvLT87y+cAMAAABGaJnCjaNNuAEAAAAjs4TbUo4q4QYAAACMkHBjdsINAAAAGBkrN+Yj3AAAAIAREm7MTrgBAAAAIyTcmN3K0R4AAAAAwOGwcgMAAABGxpkb8xFuAAAAwAgJN2Yn3AAAAICRsXJjPsINAAAAGCHhxuyEGwAAADBCwo3ZCTcAAABgZGxLmY9wAwAAAEZIuDG7+cKNqmRlZUFDYbQG/o3avHnToPWSZNu2wUsuZCL50hd78JrnvaQGr/mX9w4/TjhWLMNfk1u2DF/z9NOHr7kIX9g1/Px2wUuHn4fvuds8zDgtYo5bxL+5zMXjdqzOxT1nOSs35rMEv/YAAAAAB2ZbCgAAAIyQlRuzE24AAADACAk3ZifcAAAAgJFx5sZ8hBsAAAAwQsKN2Qk3AAAAYGSs3JiPcAMAAABGSLgxO+EGAAAAjIyVG/MRbgAAAMAICTdmt3K0BwAAAABwIFW1uarO2KiPlRsAAAAwQsu0cqOqVpJcm+TxJCcn2ZTkHd39jK+iqm5I8rNrmp9Ksr27H5v0uTnJ5ZNrTyc5d6PXF24AAADAyCzhmRvXJrmgu69Mkqr6gyTXJPmN6U5VtTXJE0l2TO6T5OIk/2gq2HhZkr9I8s7J9Ue7+4GNXly4AQAAACO0LOFGVZ2U5C1J3jzVfGOS91bVb3X3U1PtxyW5prufmHr+1ZP++/1iki8meaK7PzfLGJy5AQAAACOzf+XGom8DeUWSk5Lsmmq7J8kZSS767q+rd08HGxNXJPlwklTV8Umek+TqJHdV1acPdt5GItwAAACAUTpC4cb2qto5dbv6EIZ65uT+0am2Ryb3Z2/0xKr6/iT/X3fvTpLufqK7L+/us5K8LskLk9x0sAHYlgIAAAAjdIS2pezu7ksOs8aTk/vp7Scra+4P5Cfz3VtS/lp3f7yq3pDk9qra0d13H6iIcAMAAABGZiwHilZVH6TL0HVzAAAE6UlEQVTLVUm+NPnz1qn20yb39x/k+f9jkssOdLG7P1tV96yp/QzCDQAAABihMYQb3V0H61NVm5N8Pcl5Se6YNO9I8nCSOzd43g8k+Wp3P3SwYeQ7Acq6nLkBAAAAHLLu3pvkhqweDLrfG5Jc3917q+qkqvqdqnrBmqc+Y0tKVb2yqq6uquMmj/92ko929zc2GoOVGwAAADAyY9mWMod3JnlPVb0rqwsp7k9y7eTa6UkuT/LBJA9MPefKJK9eU+f5SX4tyZuq6sYku5P80sFefP5wY2XgxR5D11uUZRnnEqgcbMvW/DZvPuhKqblt2zZ4yTz99PA1//Le4d/PF714+PcTxmgRU/si/hGyDH8FbV7A/y5ZxDy8d+/wNe+5e/h5+Pwd5mGOHebi4SzLXLyI788yzMUnHMJzlinc6O6nkrz1ANceSHLWOu0vXqft95P8/ryvb+UGAAAAjNAyhRtHm3ADAAAARmYJt6UcVcINAAAAGCHhxuyEGwAAADAyVm7MR7gBAAAAIyTcmJ1wAwAAAEZIuDG7JfhAIwAAAIADs3IDAAAARsaZG/MRbgAAAMAICTdmJ9wAAACAkbFyYz7CDQAAABgh4cbshBsAAAAwQsKN2Qk3AAAAYGRsS5mPcAMAAABGSLgxO+EGAAAAjIyVG/NZOdoDAAAAADgcVm4AAADACFm5MTvhBgAAAIyQcGN2wg0AAAAYGWduzEe4AQAAACMk3JhddffsnaseTvJXixsO8Cy1O0m6+/KjPZBlZx4GDsP3dfdzj/Ygng3MxcAhmmse3rTpkj755J2LHE+S5LHH6rbuvmThL7Rgc63c8BciwNFlHgY4+szFwJFi5cbsbEsBAACAERJuzE64AQAAACPjQNH5rBztAQAAAADPHlV1xpF+TSs3AAAAYISWbeVGVZ2f5N1JXpbkbxyk708m+eEkDya5OMlbuvsbk2vbk/x6krsm1z7d3b+3UT3hBgAAAIzMsm1LqapKsjfJI0k2HaTva5L8ZpIXdveTVfULSX43yf8w6XJTkg9193VVdUKSe6vqvu6+9UA1bUsBAACAEdq3b/G3ofSqv0zy8Azd/3GSP+nuJyePb0zy+qq6sKouS3Jpko9O6u5J8vEkb9uooJUbAAAAMELLtHJjVlV1XJIfyWpgkSTp7v+3qh5P8tokJyfZ091fnnraPUneuVFd4QYAAACMzm1/lNT2I/BCJ1TVzqnH13f39Qt8veck2ZLk0TXtjyY5O8kJ61x7JMkpVbWtu9deSyLcAAAAgNHp7suP9hgWZP9WlKfWtK9Mbk8e4Nr0/TM4cwMAAABYV1X1QW4/M0+9ySeifDvJ1jWXTktyf1Y/PWW9a4/v/zSV9Vi5AQAAAKyru2sBZf84yXn7H1TV92V1O8otWf2klfdU1fO6+2uTLjsm1w7Iyg0AAABgKM/4GNhadV1VvWzS9H9k9dNRjps8fkOS/6e77+ruO5LcmuSKyXO3ZPWg0fdv9KLV3UN9AQAAAMAxqqr++yT/e1ZXZfzDJB/r7m9U1YlJdiX5pe7+0KTvzyb5/iT3Jrkkydu6+6HJtTOSvDfJziTnJ7m9u2/Y8LWFGwAAAMAysy0FAAAAWGrCDQAAAGCpCTcAAACApSbcAAAAAJaacAMAAABYasINAAAAYKkJNwAAAIClJtwAAAAAltr/DwT0iA0Y3CILAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1296x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.1378016729371035, -0.25790565242174196, -0.25519574753879104)\n"
     ]
    }
   ],
   "source": [
    "# Let's now plot the correlation matrix : Sij/sqrt(Sii*Sjj)\n",
    "#Compute the correlation matrix\n",
    "correl_T = np.zeros((nbins_T,nbins_T)) ; correl_T_alt = np.zeros((nbins_T,nbins_T))\n",
    "for i in range(nbins_T):\n",
    "    for j in range(nbins_T):\n",
    "        correl_T[i,j] = Sijw_T[i,j] / np.sqrt(Sijw_T[i,i]*Sijw_T[j,j])\n",
    "        correl_T_alt[i,j] = Sijw_T_alt[i,j] / np.sqrt(Sijw_T_alt[i,i]*Sijw_T_alt[j,j])\n",
    "#Plot correlation matrices\n",
    "#Turbo mode\n",
    "fig = plt.figure(figsize=(18,5))\n",
    "plt.subplot(1,3,1)\n",
    "plt.imshow(correl,interpolation='none',cmap='bwr',vmin=-1,vmax=1,extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "#General mode\n",
    "plt.subplot(1,3,2)\n",
    "plt.imshow(correl_T,interpolation='none',cmap='bwr',vmin=-1,vmax=1,extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "#General mode : alt\n",
    "plt.subplot(1,3,3)\n",
    "P = plt.imshow(correl_T_alt,interpolation='none',cmap='bwr',vmin=-1,vmax=1,extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "ax1 = fig.add_axes([0.9, 0.1, 0.02, 0.8])\n",
    "cbar = plt.colorbar(P,ax1)\n",
    "cbar.ax.tick_params(labelsize=15)\n",
    "plt.show()\n",
    "print(correl[0,1],correl_T[0,1],correl_T_alt[0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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"
    },
    {
     "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": [
    "#Now focus on the diagonal Sii\n",
    "indices = range(nbins_T)\n",
    "plt.semilogy(zcenter,np.sqrt(Sij[indices,indices]),linewidth=3,label='Turbo')\n",
    "plt.semilogy(zcenter,np.sqrt(Sijw_T[indices,indices]),linewidth=4,label='General')\n",
    "plt.semilogy(zcenter,np.sqrt(Sijw_T_alt[indices,indices]),linewidth=1,label='General alt')\n",
    "plt.legend(labelspacing=0.0,fontsize=15,loc='upper right')\n",
    "plt.xlabel('z',fontsize=15)\n",
    "plt.ylabel('$S_{i,i}^{1/2}$',fontsize=15)\n",
    "plt.show()\n",
    "#Ratios\n",
    "plt.plot(zcenter,np.sqrt(Sijw_T[indices,indices]/Sij[indices,indices]),linewidth=2,label='General/Turbo')\n",
    "plt.plot(zcenter,np.sqrt(Sijw_T_alt[indices,indices]/Sij[indices,indices]),linewidth=2,label='General alt/Turbo')\n",
    "plt.plot(zcenter,np.sqrt(Sijw_T_alt[indices,indices]/Sijw_T[indices,indices]),linewidth=2,label='General alt/General')\n",
    "plt.legend(labelspacing=0.0,fontsize=15,loc='lower right')\n",
    "plt.xlabel('z',fontsize=15)\n",
    "plt.ylabel('ratio of $S_{i,i}^{1/2}$',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5> turbo mode is ok for the diagonal Sii at z>0.5, but precision decreases at lower redshifts, and it gradually fails for off-diagonal terms when the bin separation increases.\n",
    "<br>This happens because turboSij assumes that the growth function varies slowly with redshift within the bin, which fails at low z."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Gaussian window functions</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigmaz    = 0.05\n",
    "zcenter_G = [0.4,0.55,0.7,0.85,1.,1.15,1.3,1.45,1.6]\n",
    "nbins_G   = len(zcenter_G)\n",
    "windows_G = np.zeros((nbins_G,nz))\n",
    "for i in range(nbins_G):\n",
    "    windows_G[i,:] = np.exp(-(z_arr-zcenter_G[i])**2/(2*sigmaz**2)) / np.sqrt(2*pi*sigmaz**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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": [
    "# Plot window functions\n",
    "for i in range(nbins_G):\n",
    "    plt.plot(z_arr,windows_G[i,:])\n",
    "plt.xlabel('z') ; plt.ylabel('$W_i(z)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Compute the matrix</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.143056\n"
     ]
    }
   ],
   "source": [
    "t0 = time.clock()\n",
    "Sijw_G = PySSC.Sij(z_arr,windows_G)\n",
    "t1 = time.clock()\n",
    "print(t1-t0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 396x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.20604273786722885\n"
     ]
    }
   ],
   "source": [
    "#First plot ln|Sij|\n",
    "fig = plt.figure(figsize=(5.5,5))\n",
    "P = plt.imshow(np.log(abs(Sijw_G)),interpolation='none',cmap='bwr',extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "P.axes.tick_params(labelsize=15)\n",
    "ax1 = fig.add_axes([0.89, 0.1, 0.035, 0.8])\n",
    "cbar = plt.colorbar(P,ax1)\n",
    "cbar.ax.tick_params(labelsize=15)\n",
    "plt.show()\n",
    "#Second plot the correlation matrix\n",
    "correl_G = np.zeros((nbins_G,nbins_G))\n",
    "for i in range(nbins_G):\n",
    "    for j in range(nbins_G):\n",
    "        correl_G[i,j] = Sijw_G[i,j] / np.sqrt(Sijw_G[i,i]*Sijw_G[j,j])\n",
    "fig = plt.figure(figsize=(5.5,5))\n",
    "P = plt.imshow(correl_G,interpolation='none',cmap='bwr',vmin=-1,vmax=1,extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "P.axes.tick_params(labelsize=15)\n",
    "ax1 = fig.add_axes([0.89, 0.1, 0.035, 0.8])\n",
    "cbar = plt.colorbar(P,ax1)\n",
    "cbar.ax.tick_params(labelsize=15)\n",
    "plt.show()\n",
    "print correl_G[0,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though the bins overlap, there is still a significant (20%) anticorrelation between neighbouring bins"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Most general case with cross-spectra : Sijkl</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.783268\n"
     ]
    }
   ],
   "source": [
    "#Top-hat window functions have no interest here, since the cross-spectra would be basically zero\n",
    "#So we go for Gaussian window functions\n",
    "t0 = time.clock()\n",
    "Sijkl_G = PySSC.Sijkl(z_arr,windows_G)\n",
    "t1 = time.clock()\n",
    "print(t1-t0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Build indexing of pairs of redshift bins\n",
    "npairs_G = (nbins_G*(nbins_G+1))//2\n",
    "pairs_G  = np.zeros((2,npairs_G),dtype=int)\n",
    "count       = 0\n",
    "for ibin in range(nbins_G):\n",
    "    for jbin in range(ibin,nbins_G):\n",
    "        pairs_G[0,count] = ibin\n",
    "        pairs_G[1,count] = jbin\n",
    "        count +=1\n",
    "#Recast Sijkl as a matrix of pairs, for later visualisation\n",
    "Sijkl_G_recast = np.zeros((npairs_G,npairs_G))\n",
    "for ipair in range(npairs_G):\n",
    "    ibin = pairs_G[0,ipair]\n",
    "    jbin = pairs_G[1,ipair]\n",
    "    for jpair in range(npairs_G):\n",
    "        kbin = pairs_G[0,jpair]\n",
    "        lbin = pairs_G[1,jpair]\n",
    "        Sijkl_G_recast[ipair,jpair] = Sijkl_G[ibin,jbin,kbin,lbin]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot |Sijkl|\n",
    "fig = plt.figure(figsize=(5.5,5))\n",
    "P = plt.imshow(abs(Sijkl_G_recast),interpolation='none',cmap='bwr',extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "P.axes.tick_params(labelsize=15)\n",
    "ax1 = fig.add_axes([0.89, 0.1, 0.035, 0.8])\n",
    "cbar = plt.colorbar(P,ax1)\n",
    "cbar.ax.tick_params(labelsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many elements are zero : indeed bins far enough apart have basically no overlap so the cross-spectra is zero\n",
    "<br>If the overlap is small enough (&lt;0.1% by default), the code sets Sijkl to zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Remove pairs of bins with zero covariance\n",
    "invalid_list         = np.where(np.diag(Sijkl_G_recast)==0)[0]\n",
    "Sijkl_G_recast_valid = np.delete(np.delete(Sijkl_G_recast,invalid_list,0),invalid_list,1)\n",
    "nvalid               = Sijkl_G_recast_valid.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.21448680112044952\n"
     ]
    }
   ],
   "source": [
    "#Plot ln|Sijkl|\n",
    "fig = plt.figure(figsize=(5.5,5))\n",
    "P = plt.imshow(np.log(abs(Sijkl_G_recast_valid)),interpolation='none',cmap='bwr',extent=[zmin,zmax,zmax,zmin])\n",
    "P.axes.tick_params(labelsize=15)\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "ax1 = fig.add_axes([0.89, 0.1, 0.035, 0.8])\n",
    "cbar = plt.colorbar(P,ax1)\n",
    "cbar.ax.tick_params(labelsize=15)\n",
    "plt.show()\n",
    "#Second plot the correlation matrix\n",
    "correl_ijkl_G = np.zeros((nvalid,nvalid))\n",
    "for i in range(nvalid):\n",
    "    for j in range(nvalid):\n",
    "        correl_ijkl_G[i,j] = Sijkl_G_recast_valid[i,j] / np.sqrt(Sijkl_G_recast_valid[i,i]*Sijkl_G_recast_valid[j,j])\n",
    "fig = plt.figure(figsize=(5.5,5))\n",
    "P = plt.imshow(correl_ijkl_G,interpolation='none',cmap='bwr',vmin=-1,vmax=1,extent=[zmin,zmax,zmax,zmin])\n",
    "plt.xticks([]) ; plt.yticks([])\n",
    "P.axes.tick_params(labelsize=15)\n",
    "ax1 = fig.add_axes([0.89, 0.1, 0.035, 0.8])\n",
    "cbar = plt.colorbar(P,ax1)\n",
    "cbar.ax.tick_params(labelsize=15)\n",
    "plt.show()\n",
    "print(correl_ijkl_G.min())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The off-diagonal structure is quite important, there is positive correlation between closest cross-spectra, but also non-negligible anti-correlation with the second-closest cross-spectrum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Advanced: use your own cosmology</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Say you do not want PySSC to recompute (with CLASS) the cosmology : comoving distances, P(k) etc.\n",
    "<br>For instance because you have already computed it, or you study a non-standard model that is not supported by CLASS.\n",
    "<br>Then you can input this cosmology to PySSC by creating an object with the same keys as the CLASS objects, and pass it to PySSC routines.\n",
    "<br>In detail, if the object is called cosmo, the necessary keys are:\n",
    "<ul><li>cosmo.h giving the hubble factor</li>\n",
    "    <li>cosmo.z_of_r giving the comoving distance (in Mpc) and its derivative w.r.t. redshift</li>\n",
    "    <li>cosmo.pk(k,z) giving the (linear) matter power spectrum in Mpc^3</li>\n",
    "    <li>cosmo.scale_independent_growth_factor(z) giving the linear growth factor</li>\n",
    "</ul>\n",
    "The format of these objects should be identical to the one of CLASS."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Example:\n",
    "<br>let's precompute the cosmo with CLASS ourselves and feed it to PySSC</h5>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from classy import Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Precompute the cosmo\n",
    "cosmo = Class()\n",
    "dico4Class = params\n",
    "dico4Class['output'] = 'mPk'\n",
    "cosmo.set(dico4Class)\n",
    "cosmo.compute()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.955822\n"
     ]
    }
   ],
   "source": [
    "#Feed it to PySSC: use the optional parameter cosmo_Class\n",
    "t0 = time.clock()\n",
    "Sij_precomp = PySSC.Sij(z_arr,windows_G,cosmo_Class=cosmo)\n",
    "t1 = time.clock()\n",
    "print(t1-t0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.027398\n"
     ]
    }
   ],
   "source": [
    "#Compute the same matrix the standard way\n",
    "t0 = time.clock()\n",
    "Sij_std = PySSC.Sij(z_arr,windows_G,cosmo_params=params)\n",
    "t1 = time.clock()\n",
    "print(t1-t0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.0, 0.0)\n"
     ]
    }
   ],
   "source": [
    "#Check the difference\n",
    "diff = Sij_precomp - Sij_std\n",
    "print(diff.min(),diff.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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