{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Angular Pair Counting\n",
    "\n",
    "In this notebook, we explore the functionality of the ``AngularPairCount`` algorithm, which computes the number of pairs in angular separation bins for survey-like input data, assumed to be angular sky coordinates (i.e., right ascension and declination). \n",
    "\n",
    "**Note**\n",
    "\n",
    "The data used in this notebook is not realistic -- rather, we choose the simplicity of generating mock data to help users get up and running quickly. Although the end results are not cosmologically interesting, we use the mock data to help illustrate the various steps necessary to use the ``AngularPairCount`` algorithm properly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from nbodykit.lab import *\n",
    "from nbodykit import setup_logging, style\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use(style.notebook)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "setup_logging()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initalizing Mock Data\n",
    "\n",
    "In this notebook, we construct our fake \"data\" catalog simply by generating 10,000 objects that have uniformly distributed right ascension and declination values within a region of the sky."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NDATA = 10000\n",
    "\n",
    "# randomly distributed RA/DEC on the sky\n",
    "data = RandomCatalog(NDATA, seed=42)\n",
    "data['RA']  = data.rng.uniform(low=110, high=260)\n",
    "data['DEC'] = data.rng.uniform(low=-3.6, high=60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adding Weights\n",
    "\n",
    "\n",
    "The ``AngularPairCount`` algorithm also supports computing weighted pair counts. The total weight for a pair of objects is the product of the individual weights. Users can specify the name of column they would like to treat as a weight by passing the ``weight`` keyword to the algorithm constructor. \n",
    "\n",
    "Here, we choose randomly distributed weights between 0 and 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data['Weight'] = numpy.random.random(size=len(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Auto-correlation Pair Counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute the pair counts, we simply specify the edges of the angular separation bins (in degrees), as well as the names of the columns holding the sky coordinates and weight values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000000.06 ]   0: 10-30 20:54  AngularPairCount INFO     using cpu grid decomposition: (1, 1, 1)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000000.08 ]   0: 10-30 20:54  AngularPairCount INFO     correlating 10000 x 10000 objects in total\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000000.08 ]   0: 10-30 20:54  AngularPairCount INFO     correlating A x B = 10000 x 10000 objects (median) per rank\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000000.08 ]   0: 10-30 20:54  AngularPairCount INFO     min A load per rank = 10000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000000.08 ]   0: 10-30 20:54  AngularPairCount INFO     max A load per rank = 10000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000000.08 ]   0: 10-30 20:54  AngularPairCount INFO     (even distribution would result in 10000 x 10000)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000000.08 ]   0: 10-30 20:54  AngularPairCount INFO     calling function 'Corrfunc.mocks.DDtheta_mocks.DDtheta_mocks'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000000.38 ]   0: 10-30 20:54  AngularPairCount INFO     10% done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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      "[ 000000.70 ]   0: 10-30 20:54  AngularPairCount INFO     20% done\n"
     ]
    },
    {
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     "output_type": "stream",
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      "[ 000000.98 ]   0: 10-30 20:54  AngularPairCount INFO     30% done\n"
     ]
    },
    {
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     "output_type": "stream",
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      "[ 000001.26 ]   0: 10-30 20:54  AngularPairCount INFO     40% done\n"
     ]
    },
    {
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     "output_type": "stream",
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      "[ 000001.58 ]   0: 10-30 20:54  AngularPairCount INFO     50% done\n"
     ]
    },
    {
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     "output_type": "stream",
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      "[ 000001.94 ]   0: 10-30 20:54  AngularPairCount INFO     60% done\n"
     ]
    },
    {
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     "output_type": "stream",
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      "[ 000002.22 ]   0: 10-30 20:54  AngularPairCount INFO     70% done\n"
     ]
    },
    {
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      "[ 000002.52 ]   0: 10-30 20:54  AngularPairCount INFO     80% done\n"
     ]
    },
    {
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      "[ 000002.83 ]   0: 10-30 20:54  AngularPairCount INFO     90% done\n"
     ]
    },
    {
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     "output_type": "stream",
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      "[ 000003.13 ]   0: 10-30 20:54  AngularPairCount INFO     100% done\n"
     ]
    }
   ],
   "source": [
    "# the angular bin edges in degrees\n",
    "edges = numpy.linspace(0.1, 10., 20+1) # 20 total bins\n",
    "\n",
    "# run the algorithm\n",
    "r_auto = AngularPairCount(data, edges, ra='RA', dec='DEC', weight='Weight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The measured paircounts are stored in the ``result`` attribute. The number of pairs in a given angular bin is stored as the ``npairs`` field. Below, we plot the number of pairs $DD(\\theta)$ as a function of angular separation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x112e080b8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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rGc8TUMDw9XWFhYjV7Dyp9NUVGR1wE20rlfw5CQEEVHR0vy72t46s8mPz9fHo/Ha/u5XsPqfr99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\nJMQv+wQAXBiyGQDMq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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112d88b00>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 640,
       "width": 1022
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pc = r_auto.result\n",
    "plt.plot(pc['theta'], pc['npairs'])\n",
    "\n",
    "# format the axes\n",
    "plt.xlabel(r\"$\\theta$ [$\\mathrm{degrees}$]\")\n",
    "plt.ylabel(r\"$DD(\\theta)$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The total weight for a given pair is the product of their individual weights, and the average total weight is computed in each angular bin. This value is stored in the ``weightavg`` field of the ``result`` attribute. Below, we plot the average weight as a function of angular separation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1.0)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11743cb38>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 629,
       "width": 1023
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r_auto.result['theta'], r_auto.result['weightavg'])\n",
    "\n",
    "# format the axes\n",
    "plt.xlabel(r\"$\\theta$ [$\\mathrm{degrees}$]\")\n",
    "plt.ylabel(r\"$\\mathrm{average \\ weight}$\")\n",
    "plt.ylim(0, 1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we chose to weight our objects with random values ranging from 0 to 1. Thus, on average, the expectation value of the square of those weights will be 0.25, which we see reproduced in the figure above. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross-correlation Pair Counts\n",
    "\n",
    "We can also compute the cross-correlation of pair counts between two sources. Below, we initialize a second randomly distributed catalog, and compute the pair counts between the two catalogs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# randomly distributed RA/DEC on the sky\n",
    "data2 = RandomCatalog(NDATA, seed=84)\n",
    "data2['RA']  = data2.rng.uniform(low=110, high=260, size=len(data2))\n",
    "data2['DEC'] = data2.rng.uniform(low=-3.6, high=60., size=len(data2))\n",
    "data2['Weight'] = numpy.random.random(size=len(data2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000006.07 ]   0: 10-30 20:54  AngularPairCount INFO     using cpu grid decomposition: (1, 1, 1)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000006.12 ]   0: 10-30 20:54  AngularPairCount INFO     correlating 10000 x 10000 objects in total\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000006.12 ]   0: 10-30 20:54  AngularPairCount INFO     correlating A x B = 10000 x 10000 objects (median) per rank\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000006.12 ]   0: 10-30 20:54  AngularPairCount INFO     min A load per rank = 10000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000006.13 ]   0: 10-30 20:54  AngularPairCount INFO     max A load per rank = 10000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000006.13 ]   0: 10-30 20:54  AngularPairCount INFO     (even distribution would result in 10000 x 10000)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000006.14 ]   0: 10-30 20:54  AngularPairCount INFO     calling function 'Corrfunc.mocks.DDtheta_mocks.DDtheta_mocks'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000006.44 ]   0: 10-30 20:54  AngularPairCount INFO     10% done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000006.72 ]   0: 10-30 20:54  AngularPairCount INFO     20% done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000007.00 ]   0: 10-30 20:54  AngularPairCount INFO     30% done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000007.29 ]   0: 10-30 20:54  AngularPairCount INFO     40% done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000007.59 ]   0: 10-30 20:54  AngularPairCount INFO     50% done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000007.88 ]   0: 10-30 20:54  AngularPairCount INFO     60% done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000008.16 ]   0: 10-30 20:54  AngularPairCount INFO     70% done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000008.45 ]   0: 10-30 20:54  AngularPairCount INFO     80% done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000008.74 ]   0: 10-30 20:54  AngularPairCount INFO     90% done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[ 000009.03 ]   0: 10-30 20:54  AngularPairCount INFO     100% done\n"
     ]
    }
   ],
   "source": [
    "# compute the cross correlation pair counts\n",
    "r_cross = AngularPairCount(data, edges, ra='RA', dec='DEC', weight='Weight', second=data2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1198cff28>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SrVu3BjJWSLh+/Xqu7e1x9uxZIGOr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vNZkoLHbJakYDKfK3PBXwmhqKiI2bNnk5mZ6X/YkhQg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\nenB7jmpbdnY2eXl5lV7LysoiNze3liqSJEnSXss3FvDbtxcyY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nyL344cXY6FoeOg+ygI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\nm4bx2diefDkujm7N65z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XX365jh8/runTp1freIcPH9Z9992nr776yqXZ/1s3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\n61GTv7Tg4OCSj8+cOVPpYzqdTs2bN0+SdNttt1W43mq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hduWgAnfx+S0mpW3Mb58PzF8OCpsOgfNv4l6SA8d45nw18tQnl5ORs3\nbqS8vLypS5Ek7cd8lqTgMZslKZjMZ0lqXOkpiTx+2SiG925b5X6rt5Vw4UO5bCqsxu394yboBOPv\nijX+T70ZkjNqNn7TQnjhu/DHk2DBixCprNl4SWrBPHeOZ8NfLUJJSQkzZ86kpKSkqUuRJO3HfJak\n4DGbJSmYzGdJanwZqUk8fvlohvaquum/alsJkx7KY3NNm/4AaR3gjJ/CTfNhzI8gJbNm47d8DC9d\nAQ+cCPOeh8qKmtcgSS2M587xbPhLkiRJkiRJkqQjUpvUJJ64YjRZh2n6r9hazIUP57G5qBZNf4DW\n7WHcT2KN/7E/gdQaNv63fQp/vxoeGAVzn4ZKr2qVJMXY8JckSZIkSZIkSUesNqlJPHH5aIb0rLoJ\nv2JLMZMeymNL0e7aT9aqLYz9Edy0EE6/DVq1q9n4/BXw8vfg/pEw5wmoKKt9LZKkFsGGvyRJkiRJ\nkiRJOqJltkriyctP5IQebarcb/mWYi56OI+tO+vQ9AdIbQOn/SfctADOvBNad6zZ+O2r4J+T4b4R\nMOtRqKhjPZKkZsuGv1qEcDhMRkYG4bA/0pIUJOazJAWP2SxJwWQ+S1LTy2ydxFNXnMig7lU3/T/d\nvJOLHs5jW12b/gApGXDKTbFb/Z/1v5DWuWbjC9bAKz+A3w+DGQ9DeS0fOSBJzYjnzvFC0Wg02tRF\nqOXLyckhLy8v7r3s7Gxyc3ObqCJJkiRJkiRJkg60vbiMi/48nY83FFa538CuGTxzVTbt05Lrb/Ly\nXTD7LzDtd1C0oebj07vGFhAM/y4kt66/uiRJh9VU/VCXPUiSJEmSJEmSJH2uXVoyT195IgO7ZlS5\n35KNRVz0cB7bi8vqb/KkVpB9Ldz4EZzza2jTo2bjd26E134M92bBh/dBWXH91SZJCiQb/moRCgsL\n+fe//01hYdUrLiVJjct8lqTgMZslKZjMZ0kKlvZpyTx44SB6pFW935KNRVz85+n12/QHSEqF0VfB\njXPhS7+DzN41G1+8Gd74b/jdYHj9VljwImz9FCKR+q1TkpqA587xEpu6AKk+RKNRKioq8AkVkhQs\n5rMkBY/ZLEnBZD5LUvC0bZXI9YMiPLIineVbSw653+INhXz7kek8feWJtG1dj7f3B0hMgZGXwbBv\nw7zn4INfw/ZV1R9fsg1y79/3dVIadB0M3YZAtyzoOgQ6DYTEeq5bkhqQ587xbPhLkiRJkiRJkiQd\nREYSPHzRCVzz3GI+3bzzkPstWv950/+KbDJbJ9V/IQlJMPwSyJoEC16A938F+ctrfpzyYvgsL/ba\ne+xk6HzcvgUA3bKgyyBIPsztDSRJgWDDX5IkSZIkSZIk6RA6pCXzzFXZTHo4j2VVNP0Xrivkkken\n8+QVJ5LZqgGa/gAJiTB0Egz5Jiz8G7x/D2z9pG7HrCyDDfNirz1CYehwTKz5v/duAIOhVbu6zSVJ\nqnc2/CVJkiRJkiRJkqrQKSOFZ646kUkP5bF8S/Eh95u/toDvPDKdJ688kTapDdT0BwgnwJBvwAlf\ng8Uvx67437y4/o4fjcDWpbHXgr/ue79tn9gCgK5Z+xYDZHStv3klSTUWivpwAzWCnJwc8vLy4t7L\nzs4mNze3Xo5fWVnJzp07SU9PJyEhoV6OKUmqO/NZkoLHbJakYDKfJSl4DpbNmwtLufChPFZsPXTT\nH2Bor7Y8ecVoMhqy6b+/SASWvALv3QObFjTOnHukd9n3KIA9dwNo2wdCocatQ9IRI6jnzg3dDz0U\nr/BXi5CQkEBmZmZTlyFJ+gLzWZKCx2yWpGAynyUpeA6WzZ3bpPLs1dlc+FAeK6to+n/02Q6+++gM\n/nJ5IzX9w2E4/itw3Jdh6b9jV/yvn9Pw8wLs3ATL3oy99kjN3LcIYM+fHY+J3ZlAkurIc+d4NvzV\nIuzatYtly5bRv39/WrVq1dTlSJI+Zz5LUvCYzZIUTOazJAXPobK5S5tUnr0qmwsfymXVtpJDjp+z\nZgeXPjaTv1w+mvSURmrHhEIw8JzYK38FrJsDG+fDhnmwYT7sym+cOkoLYNUHsdceia2g6wnxdwPo\nfDwkpjROTZJaDM+d49nwV4tQVlbGqlWr6N27t/+xJSlAzGdJCh6zWZKCyXyWpOCpKpu7Zsau9P/W\ng3msyT9003/26u1c9tgMHr9sNGmN1fTfo/1RsdfgC2JfR6NQsDZ+AcDG+VC4rnHqqdgFa2fGXnuE\nE6HTcfseBdB1SGxRQEpG49QkqVny3DmeDX9JkiRJkiRJkqQa6pbZ6vPb++fyWf6uQ+43c9V2Lnts\nJo9dNqrxm/77C4Wgba/Ya+C5+94v3vr5AoB5+xYD5K9onJoiFbBpQez10dN7CoUOR8ffCaBrFqR1\naJyaJKmZseEvSZIkSZIkSZJUCz3atvr89v55rN1+6Kb/jFX5XP54rOnfOjlgrZm0jtD/jNhrj9JC\n2LRw350ANsyDLUsgWtkIBUVh27LYa9Hf9r3dpue+BQB77gbQpntsIYMkHcEC9ltFkiRJkiRJkiSp\n+ejZrvXepv+6HYdu+k9fmc8Vj8/i0UtH0So5oRErrIXUNtDnpNhrj/JS2Lxo36MANsyDTYugorRx\naipcG3st/de+91p32Nf875YVe7XrB+Fw49QkSQFgw18tQkpKCkcddRQpKSlNXYokaT/msyQFj9ks\nScFkPktS8NQkm3u1b81zV2fzrQdzWV9w6AZ47optXPGXmTzy3WbQ9P+ipFToMSL22qOyArZ+sm8B\nwJ7FALsLG6emkm2w/J3Ya4/kDOg6eL/HAQyBTgMgIalxapLU4Dx3jheKRqPRpi5CLV9OTg55eXlx\n72VnZ5Obm9tEFUmSJEmSJEmSVL/WbCvhWw/lsqGKpj/AKf078ufvjiQ1qZk1/asjEoEdq/Y9CmDP\nYoDiLU1XU0IKdDl+v7sBDI19ndSq6WqS1OI0VT/UK/zVIlRUVFBUVERGRgaJif5YS1JQmM+SFDxm\nsyQFk/ksScFTm2zu3WHPlf55bCw8dNN/6rKtXPXELB7+Tgts+ofD0P6o2GvQebH3olEo2hi/AGDD\nfChY0zg1Ve6G9XNjrz1CCbEr//c+DmBI7M4AqZmNU5OkWvPcOZ4PMVGLUFxczNSpUykuLm7qUiRJ\n+zGfJSl4zGZJCibzWZKCp7bZ3KdDGs9enU2XNlXfavqDT7dy9ZOzKS2vrEuZzUMoBG26wYCzYcwP\n4cKn4QcL4Icr4Tsvw/ifwQkXQMdjgVDj1BSthM2LYf5z8Pp/wePnwt294d6h8NfvwAf/B5++BTs3\nN049kqrNc+d4LnmQJEmSJEmSJEmqR/06pvHsVdlc+FAem4t2H3K/9z/ZwrVPzebBS0aQktjCrvSv\njtbt4aixsdceu3fCpkWf3wngo9idADZ/DJHyxqlp+8rYa/HL+97L6Lbf4wA+vyNAZq/YQgZJamI2\n/CVJkiRJkiRJkurZUZ3SefbqWNN/SxVN/3eXbuG6p+bwx28PPzKb/l+Ukg69T4y99qgogy0fx5r/\nex4LsHEBlJc0Tk1FG2KvT17b916rdvseBzBgIvTOcQGApCZhw1+SJEmSJEmSJKkBHN0pfe+V/lt3\nHrrp/86SzVz/9Bz+cPEIkhN9GvMBEpNjjfVuWcAlsfcilbBt+ecLAObF/twwH0p3NE5Nu7bDyvdi\nrw9/D31OhrN/8XmNktR4bPirRQiFQiQnJxNy9ZwkBYr5LEnBYzZLUjCZz5IUPPWVzf07p/PsVScy\n6eE8tu4sO+R+b328meufmcMDFw236V8d4QTodGzsNeQbsfeiUSj4bF/zf8/dAIo2NHw9q6fBg2Ng\n2MVw+k8ho0vDzykdoTx3jheKRqPRpi5CLV9OTg55eXlx72VnZ5Obm9tEFUmSJEmSJEmS1Hg+2VTE\npIfy2FZ86KY/wFnHd+GBi4eTlGDTv97s3BxbALD/nQC2r2y4+ZLT4dT/gOzrISm14eaRFChN1Q/1\nCn9JkiRJkiRJkqQGdmyXDJ65KptJD+eRX0XT/43Fm5j8zFzuu2iYTf/6kt4Zjjkz9tqjtAA2Loi/\nG8DWpRCN1H2+sp3w9l0w+3EY/zM4/qvglciSGoi/KdQiFBUV8c4771BUVNTUpUiS9mM+S1LwmM2S\nFEzmsyQFT0Nk84CuGTx95Ym0a51U5X6vLdrI95+bS3llPTSfdXCpmdD3FMi5Hr72IFyfBz9ZD1e+\nA+f+BkZcCt2HQUJK7efYsQZe+C48dg6s/6jeSpeOdJ47x/MKf7UIkUiE4uJiIhFPfiQpSMxnSQoe\ns1mSgsl8lqTgaahsPq5bG56+MpuL/pzHjpLyQ+736oKNhEIfce+3hpLolf6NI6kV9BwRe+1RWQ5b\nlsLG+fvuBLBxAZTVoNG45kN4aCwMvRjOuA0yutZ76dKRxHPneDb8JUmSJEmSJEmSGtHx3dvw9JUn\nctHD0ynYdeim/7/mbyAcCvHbb2bZ9G8qCUnQ9YTYa+hFsfciEdi+EuY8AXl/gMpDP6Jhnyh89BQs\n+juc+h+QcwMkpTZo6ZKODP52kCRJkiRJkiRJamSDumfy9JUn0ia16msz/9+89dz8wjwqI9FGqkyH\nFQ5Dh6Nh/J1w/Qw47ivVH1teDO/8DO4fFWv+R/2+SqobG/6SJEmSJEmSJElN4IQemTx9ZfZhm/4v\nf7Se/7TpH0zt+8G3noRL/wVdB1d/XMEaeOFSeGwirJ/bYOVJavls+KtFSEtLIzs7m7S0tKYuRZK0\nH/NZkoLHbJakYDKfJSl4GiubB/fM5MkrTiTjME3/v89dxy0v2vQPrL6nwNXvwVfuh7TO1R+3Jhce\nGgf/+B4Ubmi4+qQWxHPneDb81SIkJibSqVMnEhOrPiGSJDUu81mSgsdslqRgMp8lKXgaM5uzerXl\nictHk5FS9Vx/m7OOH700n4hN/2AKJ8DwS+DGOXDKDyAhuZoDo/DR03DfCHj/V1C+q0HLlJo7z53j\n2fBXi1BaWsrSpUspLS1t6lIkSfsxnyUpeMxmSQom81mSgqexs3lY73b85YrRpB+m6f/i7LX8+G82\n/QMtJQPOvANumAnHf7X648qL4Z3/gftHwcKXIOr3WDoYz53j2fBXi7B7924++eQTdu/e3dSlSJL2\nYz5LUvCYzZIUTOazJAVPU2Tz8N7t+Mvlo0hLTqhyv7/OWstP/r7Apn/QtesL33wCLn0Vug6p/riC\nz+DFy+HRs2HdnAYrT2quPHeOZ8NfkiRJkiRJkiQpIEb0ac9fLh9N68M0/Z+b+Rm3/mOhTf/moO/J\ncPW78NUHIL1L9cd9lgcPj4O/XweFGxqqOknNnA1/SZIkSZIkSZKkABnZtz2PX3b4pv+zM9Zw28sL\niXrr9+ALJ8Cwb8Pk2XDqzZCQUv2x856B+4bDe7+C8l0NV6OkZsmGvyRJkiRJkiRJUsCM7teexy4d\nRaukqpv+T09fw09fXmTTv7lIyYAzfgo3zIRB51d/XHkJTPkfuH8ULHgR/H5L+pwNf7UISUlJ9OjR\ng6SkpKYuRZK0H/NZkoLHbJakYDKfJSl4gpDNJx7VgUcvHUVqUtXtnCfzVnPHP236Nyvt+sA3HofL\n/g3dsqo/ruAzeOkKeHQCrJvdYOVJQRaEfA6SUNT0VyPIyckhLy8v7r3s7Gxyc3ObqCJJkiRJkiRJ\nkpqHD5dt5fK/zKS0PFLlfped3Jefful4QqFQI1WmehGJwLxn4e07Yeemmo3NmhS7Y0Cb7g1Tm6Rq\na6p+qFf4q0WIRCIUFxcTiVR9siNJalzmsyQFj9ksScFkPktS8AQpm0/q35FHvjuKlMSq2zqPTVvF\nz1752Cv9m5twGIZdDJPnwKn/CQkp1R8771m4bwS8dw+UlTRcjVKABCmfg8CGv1qEoqIi3nnnHYqK\nipq6FEnSfsxnSQoes1mSgsl8lqTgCVo2n9y/I3/+7kiSD9P0f3TaSn7+qk3/ZiklHc64DW6YCYPO\nr/648hKY8r9w/yhY8CL4vVcLF7R8bmo2/CVJkiRJkiRJkpqBU4/pxMPfOXzT/+EPVnL3v5fY9G+u\n2vWBbzwOl70G3YZWf1zhWnjpCnjkLFg7q8HKkxQsNvwlSZIkSZIkSZKaiTHHduKhS0aQnFB1i+fB\n91fwy9eW2vRvzvrkwFVT4Lw/QnrX6o9bOwP+fAb87WooWNdw9UkKBBv+kiRJkiRJkiRJzcjYAZ15\nsBpN/z+9t5xfv2HTv1kLh2HoRTB5Npx2CySmVn/s/Ofh/pHw7t1QVtJwNUpqUjb8JUmSJEmSJEmS\nmplxAzvzx28PJykhVOV+D0xZzuifv831T8/hsWkrWbiugMqICwCanZR0OP2/4YaZMOhr1R9XXgLv\n/iLW+J//Arj4Q2pxQlGXdakR5OTkkJeXF/dednY2ubm5TVSRJEmSJEmSJEnN31uLN3Hd07Mpr6x+\nuycjJZHhfdoxul97RvVtz5CemaQmJTRglap3a/LgtR/D+rk1G9dzFEz4BfQa1TB1SUewpuqHJjbo\n0SVJkiRJkiRJktRgzjy+Cw9cNJzvPT2HimpeuV+0u4L3PtnCe59sASA5IcyQnpmM6tee0X3bM7xP\nOzJbJTVk2aqr3tlw5Tux2/a/dQfs3Fi9cWtnwiNnwuBvwpm3Q2bPBi1TUsPzlv5qEXbu3MnUqVPZ\nuXNnU5ciSdqP+SxJwWM2S1Iwmc+SFDzNKZvPGtSV+y8aTmK46tv7H0pZZYRZq7fzx3eXc9njMxl6\n1xtMvPcDfvryQv7fvPVsKiyt54pVL8JhGDoJJs+G034IianVH7vgr3DfSJjyCygrbrgapQbQnPK5\nMXiFv1qEyspKtm/fTmVlZVOXIknaj/ksScFjNktSMJnPkhQ8zS2bzz6hK/dNGsYNz86lsppX+h9K\nNAofbyjk4w2FPJG7GoDe7Vszqm97Rvdrx6i+7enXMY1QqHYLDFTPUtLh9Fth+Hfgrdth4UvVG1ex\nC967G+Y8AePvhBMuiC0ikAKuueVzQ7PhX89WrVrFY489xltvvcXq1atJT09n8ODBXHnllUyYMKFB\n5iwoKODZZ5/lb3/7G8uWLaOyspJBgwZx7rnncu2115KQ4HN3JEmSJEmSJElq6SYO7sb9wA/++hGl\n5ZF6Pfaa/BLW5Jfw0py1AHRMT2Zkn/Z7HwNwXLcMEhNsFjeptr3ggkdh9DXw2o9h/ZzqjStaD3+7\nCqY/CGffDb1GNWydkuqVDf96snv3bu644w7uueceJk6cyG233UZ2djaVlZVMmzaNH/zgB3zpS1/i\nnnvuqbc5o9EozzzzDDfccAPdu3fn1ltv5dRTT6Vjx47MmTOHu+++m+eff5433niD1NQa3MZFkiRJ\nkiRJkiQ1SxMHd+P47m14cfZa8lZsY95nBZRV1m/zH2DrzjJeW7SR1xbFnh2flpzA8D6xq/9H9W3P\nsN5tSU3ygsQm0ftEuPLt2G3737oDijZUb9y6WfDImTD4G3DmHZDZswGLlFRfbPjXgx07dnDWWWcx\nc+ZM7rnnHm655Za47V/5ylfIzs4mKyuLiRMnMm7cuDrPGYlE+N73vseDDz7I+eefz3PPPUdycvLe\n7SeffDIvv/wyEyZM4O677+aOO+6o85ySJEmSJEmSJCn4+nRI4+azBgBQWl7J/LUFzFyVz4yV+cxZ\nvZ2i3RX1PmdxWSUffLqVDz7dCkBSQojBPTIZ1a89o/q0Z2TfdrRtnXyYo6jehMOQdSEc92WYdm/s\nVVFavbELXoCPX4GTb4STvw/JaQ1bq6Q6CUWj0bo9yOUIV1xczJlnnkleXh6TJ0/m97///QH7zJgx\ng8svv5yPP/6YSZMm8dRTT9V53htvvJH77ruPYcOGMX36dJKSkuK2b926lQsvvJAPP/yQ9u3bs3bt\n2jrPWRc5OTnk5eXFvZednU1ubm69HL+8vJxNmzbRpUuXAz4LSVLTMZ8lKXjMZkkKJvNZkoKnpWZz\nZSTKko2FzFyZz8xV25mxKp8tRbsbZe4BXTIY1S92F4DR/drTLbNVo8wrYMdn8PadsWZ+TWR0i13t\nP/ibsUUEUgAENZ8buh96KDb862jy5Mncf//99OjRg48//piMjIwD9rnooot49tlnARg6dChz586t\n05wvvfQSF1xwAaFQiFmzZjF8+PAD9nnooYe45ppr9n69fft22rZtW6d566KpfsAlSZIkSZIkSdKh\nRaNRVm8rYeaq/M9f21m5tbhR5u7RthWj+7X/fAFAO47ulE4oFGqUuY9Yn82A134M62bXbFyPEXD2\n3dBrdMPUdRKNCQAAIABJREFUJbUATdUP9Zb+dTB16lTuv/9+AK677rqDNvshdvv9PdLT0+s0Z35+\nPt/73vcAOOOMMw7a7P/inImJiaSmptZp3qArKytj/fr1dO/ePe7RBpKkpmU+S1LwmM2SFEzmsyQF\nz5GSzaFQiL4d0+jbMY1vjOwFwOaiUmat2s6MlfnMWp3P4vWFRBrg8tF1O3bx97nr+PvcdQC0T0tm\nZJ/YHQBG9WvPoO5tSErwqvJ61Ws0XPFW7Er/t+6AovXVG7duNjwyHk64IHbFf9teDVikVLUjJZ+r\ny4Z/Hdx5551A7JfhJZdccsj9fvKTnzBr1iwSExO566676jTnH//4RzZv3gzApZdeesj9Lr74Yp5/\n/nk+/vhjbr311hbf8N+1axcLFiygXbt2/seWpAAxnyUpeMxmSQom81mSgudIzubOGamcM7gb5wzu\nBkBRaTlz1uxg5sp8ZqzK56PPdlBWETnMUWouv7iMNxZv4o3FmwBonZzAsN5tY3cA6Nueob3b0jrZ\n1ladhcOQ9S047ksw7fcw7V6o2FW9sQtfhCWvwEk3wsnfh5S6Xegq1caRnM8HYyrW0pIlS3jrrbcA\nGDx4ML179z7kvkOGDGHZsmV1nrOiooI//elPe7+eOHHiIffNyMhgypQpdZ5TkiRJkiRJkiQd2TJS\nkxhzbCfGHNsJgN0VlSxcV8CMlduZuSqfWavyKSytqPd5S8oqmbZsG9OWbQMgMRxiUI9MRvf9/C4A\nfdvTLs1mX60lp8G4/4Lhl8Bbd8KCv1ZvXEUpvH8PzH0SzrgdhnwrtohAUpOw4V9LTzzxxN6/H+q2\n+vXtnXfeYe3atQD07duX9u3bN8q8kiRJkiRJkiRJe6QkJjCiT3tG9GnPdRxNJBJl6aYiZq3KZ8aq\n7cxcmc/GwtJ6n7ciEmXeZzuY99kOHv5gJQDHdE5nZN/2jO4XWwTQs13rep+3xcvsCV9/GEZfDa/9\nGNbNqt64og3wj2thxoNw9t3QO7th65R0UDb8a+m9997b+/dhw4a12DklSZIkSZIkSZKqEg6HOK5b\nG47r1oZLcvoSjUZZu30XM1bmM2t1PjNW5rN8S3GDzP3p5p18unknz85YA0D3zFRG9WsfWwTQtz3H\ndE4nHA41yNwtTq9RcMWbsdv2v3k7FK2v3rj1c+HRCTDoazD+Tmh76LtiS6p/NvxrYdeuXcycOXPv\n1/369WuUeT/44INGnTMnJ6fejrVw4cJ6O9bBJCYm0qlTJxIT/ZGWpCAxnyUpeMxmSQom81mSgsds\nrr1QKESv9q3p1b41Xx/RE4BtO3czc1XsEQAzV+WzaH0hlZFovc+9vqCUlz9az8sfxZrVbVsnMbLP\n548A6NeeE7pnkpzo7ecPKRyGId+EgefCh/fB1N9Bxa7qjV30N1j6Kpw0GU6+CVLSG7ZWHbHM53ih\naDRa/2nawi1YsIAhQ4bs/frdd99lzJgxTJ8+n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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1180bb668>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 640,
       "width": 1022
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the auto and cross pair counts\n",
    "pc_auto = r_auto.result\n",
    "pc_cross = r_cross.result\n",
    "plt.plot(pc_auto['theta'], pc_auto['npairs'], label='auto correlation')\n",
    "plt.plot(pc_cross['theta'], pc_cross['npairs'], label='cross correlation')\n",
    "\n",
    "# format the axes\n",
    "plt.legend(loc=0)\n",
    "plt.xlabel(r\"$\\theta$ [$\\mathrm{degrees}$]\")\n",
    "plt.ylabel(r\"$DD(\\theta)$\")"
   ]
  }
 ],
 "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}