abacus_Pk_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we downloaded is Planck catalogs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1297520]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "halos = np.fromfile(fp,dtype=halo_type)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ (      0, 105835, [-0.37403375,  0.06187559,  0.32598749], [-0.0030261 ,  0.00091194,  0.00050777], [ 0.01571805,  0.01938944,  0.01615746],   9.87340813e-04,   1.57746335e-03,  0.00215333,  0.00261515,        0, 10580)\n",
      " (      1,  85752, [-0.25992078, -0.41617808,  0.12623017], [ 0.00087401,  0.00065161, -0.0041647 ], [ 0.01437996,  0.01328415,  0.01738182],   1.07903010e-03,   1.70135486e-03,  0.0023814 ,  0.00289032,    10580,  8530)\n",
      " (      2,  79582, [-0.22334227, -0.46090865,  0.20009035], [-0.00287477,  0.00541451, -0.0001645 ], [ 0.02000825,  0.01585446,  0.01493386],   6.27144822e-04,   1.21005834e-03,  0.0019134 ,  0.00257296,    19110,  7873)\n",
      " ...,\n",
      " (1340616,     30, [-0.16719955,  0.44681725,  0.47114328], [-0.00473511, -0.00026293,  0.00814649], [ 0.00065897,  0.0005725 ,  0.00076932],   1.07802072e-04,   1.53549830e-04,  0.00019062,  0.00024076, 26137540,     5)\n",
      " (1340618,     30, [-0.1686196 ,  0.49417335,  0.49076039], [-0.00586702, -0.00398773,  0.00464996], [ 0.00062504,  0.00072351,  0.00073854],   6.94499977e-05,   1.14446295e-04,  0.00015007,  0.00018304, 26137545,     0)\n",
      " (1340619,     30, [-0.17053288,  0.49405596,  0.49229601], [-0.00512373, -0.0032624 ,  0.0016612 ], [ 0.00085245,  0.00059173,  0.00094295],   6.18001723e-05,   9.51115071e-05,  0.00015052,  0.00018342, 26137545,     6)]\n"
     ]
    }
   ],
   "source": [
    "print(halos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('gid', '<i4'), ('N', '<i4'), ('Position', '<f4', (3,)), ('Velocity', '<f4', (3,)), ('sigma_v', '<f4', (3,)), ('r25', '<f4'), ('r50', '<f4'), ('r75', '<f4'), ('r90', '<f4'), ('pf_start', '<i8'), ('pf_np', '<i4')]\n"
     ]
    }
   ],
   "source": [
    "print(halos.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<memory at 0x111b22c48>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "halos.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import nbodykit.lab as nlab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "cat = nlab.ArrayCatalog(halos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['N',\n",
       " 'Position',\n",
       " 'Selection',\n",
       " 'Velocity',\n",
       " 'Weight',\n",
       " 'gid',\n",
       " 'pf_np',\n",
       " 'pf_start',\n",
       " 'r25',\n",
       " 'r50',\n",
       " 'r75',\n",
       " 'r90',\n",
       " 'sigma_v']"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cat.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cat.attrs['BoxSize']=720.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'BoxSize': 720.0}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cat.attrs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on class FFTPower in module nbodykit.algorithms.fftpower:\n",
      "\n",
      "class FFTPower(FFTPowerBase)\n",
      " |  Algorithm to compute the 1d or 2d power spectrum and/or multipoles\n",
      " |  in a periodic box, using a Fast Fourier Transform (FFT)\n",
      " |  \n",
      " |  Notes\n",
      " |  -----\n",
      " |  The algorithm saves the power spectrum results to a plaintext file, \n",
      " |  as well as the meta-data associted with the algorithm. The names of the\n",
      " |  columns saved to file are:\n",
      " |  \n",
      " |      - k : \n",
      " |          the mean value for each `k` bin\n",
      " |      - mu : 2D power only\n",
      " |          the mean value for each `mu` bin\n",
      " |      - power.real, power.imag : 1D/2D power only\n",
      " |          the real and imaginary components of 1D power\n",
      " |      - power_X.real, power_X.imag : multipoles only\n",
      " |          the real and imaginary components for the `X` multipole\n",
      " |      - modes : \n",
      " |          the number of Fourier modes averaged together in each bin\n",
      " |  \n",
      " |  The plaintext files also include meta-data associated with the algorithm:\n",
      " |  \n",
      " |      - Lx, Ly, Lz : \n",
      " |          the length of each side of the box used when computing FFTs\n",
      " |      - volumne : \n",
      " |          the volume of the box; equal to ``Lx*Ly*Lz``\n",
      " |      - N1 : \n",
      " |          the number of objects in the 1st catalog\n",
      " |      - N2 : \n",
      " |          the number of objects in the 2nd catalog; equal to `N1`\n",
      " |          if the power spectrum is an auto spectrum\n",
      " |  \n",
      " |  See :func:`nbodykit.files.Read1DPlainText`, :func:`nbodykit.files.Read2DPlainText`\n",
      " |  and :func:`nbodykit.dataset.Power1dDataSet.from_nbkit`\n",
      " |  :func:`nbodykit.dataset.Power2dDataSet.from_nbkit` for examples on how to read the\n",
      " |  the plaintext file.\n",
      " |  \n",
      " |  Method resolution order:\n",
      " |      FFTPower\n",
      " |      FFTPowerBase\n",
      " |      builtins.object\n",
      " |  \n",
      " |  Methods defined here:\n",
      " |  \n",
      " |  __getstate__(self)\n",
      " |  \n",
      " |  __init__(self, first, mode, Nmesh=None, BoxSize=None, second=None, los=[0, 0, 1], Nmu=5, dk=None, kmin=0.0, poles=[])\n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      comm : \n",
      " |          the MPI communicator\n",
      " |      first : CatalogSource, MeshSource\n",
      " |          the source for the first field. CatalogSource is automatically converted to MeshSource\n",
      " |      mode : {'1d', '2d'}\n",
      " |          compute either 1d or 2d power spectra\n",
      " |      Nmesh : int\n",
      " |          the number of cells per side in the particle mesh used to paint the source\n",
      " |      second : CatalogSource, MeshSource; optional\n",
      " |          the second source for cross-correlations\n",
      " |      los : array_like ; optional\n",
      " |          the direction to use as the line-of-sight\n",
      " |      Nmu : int; optional\n",
      " |          the number of mu bins to use from mu=[0,1]; if `mode = 1d`, then `Nmu` is set to 1\n",
      " |      dk : float; optional\n",
      " |          the spacing of k bins to use; if not provided, the fundamental mode of the box is used\n",
      " |      kmin : float, optional\n",
      " |          the lower edge of the first ``k`` bin to use\n",
      " |      poles : list of int; optional\n",
      " |          a list of multipole numbers ``ell`` to compute :math:`P_\\ell(k)` from :math:`P(k,\\mu)`\n",
      " |  \n",
      " |  __setstate__(self, state)\n",
      " |  \n",
      " |  run(self)\n",
      " |      Compute the power spectrum in a periodic box, using FFTs. This\n",
      " |      function returns nothing, but attaches several attributes\n",
      " |      to the class (see below).\n",
      " |      \n",
      " |      Attributes\n",
      " |      ----------\n",
      " |      edges : array_like\n",
      " |          the edges of the wavenumber bins\n",
      " |      power : :class:`~nbodykit.dataset.DataSet`\n",
      " |          a DataSet object that behaves similar to a structured array, with\n",
      " |          fancy slicing and re-indexing; it holds the measured :math:`P(k)` or \n",
      " |          :math:`P(k,\\mu)`\n",
      " |      poles : :class:`~nbodykit.dataset.DataSet` or ``None``\n",
      " |          a DataSet object to hold the multipole results :math:`P_\\ell(k)`;\n",
      " |          if no multipoles were requested by the user, this is ``None``\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data and other attributes defined here:\n",
      " |  \n",
      " |  logger = <Logger FFTPower (WARNING)>\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from FFTPowerBase:\n",
      " |  \n",
      " |  save(self, output)\n",
      " |      Save the FFTPower result to disk.\n",
      " |      \n",
      " |      The format is currently JSON.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Class methods inherited from FFTPowerBase:\n",
      " |  \n",
      " |  load(output, comm=None) from builtins.type\n",
      " |      Load a saved FFTPower result.\n",
      " |      \n",
      " |      The result has been saved to disk with :func:`FFTPower.save`.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors inherited from FFTPowerBase:\n",
      " |  \n",
      " |  __dict__\n",
      " |      dictionary for instance variables (if defined)\n",
      " |  \n",
      " |  __weakref__\n",
      " |      list of weak references to the object (if defined)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(nlab.FFTPower)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = nlab.FFTPower(cat, mode='1d', Nmesh=128, los=[0,0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'BoxSize': array([ 720.,  720.,  720.]),\n",
       " 'Lx': 720.0,\n",
       " 'Ly': 720.0,\n",
       " 'Lz': 720.0,\n",
       " 'N1': 1297520,\n",
       " 'N2': 1297520,\n",
       " 'Nmesh': array([128, 128, 128]),\n",
       " 'Nmu': 1,\n",
       " 'dk': 0.0087266462599716477,\n",
       " 'kmin': 0.0,\n",
       " 'los': [0, 0, 1],\n",
       " 'mode': '1d',\n",
       " 'poles': [],\n",
       " 'shotnoise': 287.66261791725753,\n",
       " 'volume': 373248000.0}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.attrs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(64,)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.power['k'].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEACAYAAABCl1qQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d307b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(r.power['k'], abs(r.power['power']))\n",
    "xscale(\"log\")\n",
    "yscale(\"log\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": 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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}