Cython_CodeCorner.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimizing numerical Python code using Cython\n",
    "\n",
    "### Code Corner, Institute of Astronomy, 07/11/2017\n",
    "\n",
    "#### by Bjoern Soergel\n",
    "\n",
    "NB: This is based on a longer workshop about Python optimization that I gave for the other students earlier this year. \n",
    "There I was also talking about other Python optimization tools (e.g. numba) and some simple ways of parallel programming in Python.\n",
    "The Jupyter notebooks from this workshop are available here: http://www.ast.cam.ac.uk/~bs538/programming.html. \n",
    "\n",
    "After testing various options for making numerical Python code fast, Cython is my clear favourite. For my current main project, all numerically expensive parts are written as Cython extensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some general points about Cython:\n",
    "- Cython is a superset of the Python language. The most notable new feature are static type definitions.\n",
    "- Cython can be used to created compiled C extensions from Python-like code.\n",
    "- It integrates seamlessly with numpy arrays, making it a great tool for speeding up the performance critical parts of our Python code.\n",
    "- It can also be used for wrapping existing C/C++ libraries in Python. (But I am not going to talk about this in more detail today.)\n",
    "- It is a mature project and a well-established part of the scientific Python stack.\n",
    "- Do not confuse it with CPython (the standard Python implementation written in C we all use)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Installation\n",
    "Cython is included in the Anaconda Python distribution. It can also be installed via pip."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cython compilation workflow:\n",
    "- Step 1: Cythonize: Translate Cython source file (.pyx) into C source code.\n",
    "- Step 2: Compile .c source code\n",
    "- Step 3: Import extension into Python\n",
    "\n",
    "\n",
    "Fortunately we can automate these steps, and they also integrate with Jupyter notebooks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Cython to optimize numerical Python code:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some general remarks about optimizing code:\n",
    "\n",
    "Here is the procedure I would recommend for optimizing a piece of numerical code.\n",
    "\n",
    "- Remember the 80/20 principle: For a typical code, 80% of the runtime will be spent in at most 20% of the code. Don't waste your time optimizing anything but the critical 20%. \n",
    "- Profile your code to find out what the bottleneck is. In Jupyter notebooks, we can e.g. use the %timeit and %%time magic for that.\n",
    "- Before you start coding, think/research if there is a better algorithm of doing the same thing. Again, we don't want to waste our time optimizing a bad algorithm.\n",
    "- Don't parallelize blindly, first optimize on a single CPU.\n",
    "- Check carefully that the optimized version still gives the same result.\n",
    "\n",
    "For the sake of this tutorial we focus exclusively on optimizing a given piece of code, but profiling and the algorithm are equally important!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Worked example: Contaminant removal on the sphere\n",
    "\n",
    "#### Setup:\n",
    "- one catalogue with coordinates of objects of interest\n",
    "- second catalogue with coordinates of contaminants\n",
    "- want to flag all objects of interest that are closer than a certain angular distance to a contaminant object\n",
    "\n",
    "NB: There are built-in functions in scipy and astropy to do exactly this computation, but that's not the point here. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup: generate random points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#helper function to generate points\n",
    "def gen_points_sphere(n):\n",
    "    \"\"\"\n",
    "    generate random points on sphere\n",
    "    \"\"\"\n",
    "    #angles\n",
    "    costheta = 2*np.random.rand(n)-1\n",
    "    theta = np.arccos(costheta)\n",
    "    phi = 2*np.pi*np.random.rand(n)\n",
    "    #unit vectors on the sphere\n",
    "    x = np.sin(theta)*np.cos(phi)\n",
    "    y = np.sin(theta)*np.sin(phi)\n",
    "    z = np.cos(theta)\n",
    "    vec = np.array([x,y,z]).T\n",
    "    return vec,theta,phi\n",
    "\n",
    "n = 100000\n",
    "vec,theta,phi = gen_points_sphere(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next cell is just for visualization and can be commented if you do not have healpy installed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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187PRtdzgzj40FLQ/yge4GZOrlqVO/ioMxiha1JfQ4zmMkRpb06kKULzXBnG0XWgBUNdy\nUSBUX0DWG8ibeT1BCYhrEz3hJJZizhI3e3VXWOHEi7i19fW0hAsDlSCobj9Va1pmrO1a92baYRV0\nVdixY1LfvQqFOoa07p4Qx89eW6mZHD00GRUKY8EqXgSy1jPGXekJtTZqW+ul92nZNugGKPr2psCW\nhGsESTBMSPhRIeYjyI3CChXeJm43IstDx2u858RoVmKmwzINob1WEdPOvVrfOKVksUEwtsxmJsnN\nEGFvpk9iQnbs+c0Ejpg/ZAwqoMc0r7G6x+rIfn7nJ1/MaSStVhbwx23MVK+I+aIqYtlvYvfG2ux9\nX6aJ9PBaOSNjhwo95Kn52QbdEElITHgDkQTDhIQfJsgZCGxus/F+p/CgGkE1a2kZqn1RihUbtamb\nmmrhCG+jtQJHWfSrhaVBse32AiSm9l8tcM/ZemjdVcMW40/0AiZsnWLle4hp+LzneUJgzIyrApia\nI1WbpponD0rVEtNoss6vfOa9eOcnXwzXxJ5jo5vL4I2PmJCtbbAR5loWEBcCdUxbqhlbnnd4KTN/\nNzN7ayrGzQisSgFExLTNyT8x4UeMJBgmJLxe0GARIrZhWOimRFOVR44cM0nyMzfHscfvwvZTtabB\nFfSRUy5A9ZOy5Vv+Omqbek63FjKlKF+iPlu1ZRQC+g8+H/IG73zsBYw9flfB2d/Tfll+QSu82k3c\nEk8DyPWT5XW8cmBfaR5nfRf6ri2tjtLnqIBnhfSYhs8Tvj2CcEv1YwV4RYw70ZrP9Z1d2FPF5V2r\nOYHdE37Z99b07/n0KY2RXmO13bFUhpaUXfvX60/rSqD9o3OOoO8s+31tbDwEEin9EsvT52mdvMOg\njkce+mIHOm1LinpO+CEiCYYJCX8XxCKHic2mkQN88mjAN5/FfAhV82Lz5wJ1syE39WYm55imjUEA\nQD7rhmqlmlHlxAJiCBUMYzQ4GlXKZ8SEDy/SVH3VYtyE2oZm5l/PhKsCqEe7sxnzdTM/OAU1W5d3\nrQbz+2ZSEjZLpUdUjp4MfI1KY1OWpxqovyP1yyM24+qgQUdeEEksclyxWV9TFfZjLhEKL83fq6Ey\nitE0qWDaTDObhMSE1xlJMExIeC14+2//GwAIgRFAMRUbEPe/8gSCmLbI8yNs5jO3GV89Tb9GeIJO\njCA6FlFso1XtM8qeBTRMoNqfnmlVn+EFQShibfQQ29g9beOr2cA9QSMmIKswrcIH0SyaWYX3GA+h\nh2ZR2jENIxHrW82sQ8R8F71Ic9VYepluvACaV+OzGeOT9Oql9DwrO9bC3zTFx4Rr75DQzNUAaH7g\nZBlJQEx4nZAEw4SEZqBW0KNBUeimpVlCCKVzUTQjklZNnPLlqU+b3eBiNBveM6x5l1DTmWeGViin\nnc27CzSyrlhtIhHzy/P8AD2/MaVyUXgUNzHTM9EsYKOZdkzfTWycqAmSwlLn9HqpoKtayxg/oic0\neWTeMb9Er+3aXgo3ekjR90GoBg0Axp/uAgB0f7Y71COWd5tjRH1NNSWj+jkSHqm2Hmg8dwCbZtHe\nbyPctY6EpyVslrlGfShj9EF0CfAOiIxG1wwsSh9EU3rv8ankn5jwWpAEw4QED2oibhbF6OUM9sxb\nzUyFMfNwM3O0p+FSs5Ru4p7WIkb94QVTaAQrQd9ARSxbiefn5bXPE75ipr1mQliZBipWvidge9q9\nZpHJXiALgBzlC9HMjNsseOm1jh/PnO4dGjyBPGYK93gAdU54/esdGDTNoGca99rhmaeVhsl7p160\ntb2W0Lm187EXwt8cC9OPrITvKAjbejcLxmpmRfAI4cvqDKQgloRNIwmGCQlAPXq4jJ6FGkDr72b9\n+6wJSLU84/d3hAhRDXI4//DdBXJoL8hEBQDVFijUB9EKDBpsYLkTgXzGk5Fnl0LwQCzjB7Ol2Mhf\nK2guDFQKFCVWo6XBKjaQA8gTb1eOngxkytYUZ7nsrIClEabsc43eZV97dDo6FmwQDgBXkI5FKnvC\n3OJge0hFp+Zfz1Qbe6deIIYn5FmNow1YsZlstB0rw32YfmQFA0+15frV9lvX4WNBm8kAIhXO1N/V\nE2R1vnmcitpO5QPUOcf3bbVvm9Xma3CUFbi8YB4bpGIPK+yfuY/NBaHR5inXqHCCZVq3kgt7qrl3\nx/JiPI7aB0lQTIggCYYJ1zdIJ9NMG9OM105NSh7Js1eel73D094QsZy3r4bXzzM5exucCk9l9Wim\nMfPKUUFZzX6EmuIIz1crxt1YlhrOC+ppluYvRv9jEetzwtPobSbHc1lmEjXJlr2zsw8NlZKfN+Mi\n5HVjj99VSHvXTGuo5asASG2gap89/z7PTNws6GezQR88vCmaBUbF3B6IWB7u2LvWegPxYDIgT/qt\nGYrs4UXh+SvqYS4JiAkGSTBMuP7g0coAxQ3Y8zFqlm2jDDFaES+LiCfAqB9ULD1bmUBo/fGsEEuB\nUIVGakBU06RaoLK2Wu2GFb4pGJYJ2l7mEWpeAX8j3CwJs0eBY98vNWYqdDVLV0dYocNmAQFQoLQB\n/IwmdvPnIcJq4HpOt0YFQ8APeqgcPYmpP70DADD40y8V7lXQbSAWCEXY3NsEM49olLzyJ/Jey/N4\ncXcWAn28Q43H47ky3IezD7bijifPl85jakRVU+cd0tbGxjH2+F0587F3sFJ4Qp4XWa8R10Axj/eV\nA/vC/Gc/LN1YC3XRsm0blTbIy7CkdUzE2glIgmHC9YD99z4RFZg8jcHZh4bCgttMoxPzP7RmaQoX\nGpigXGh2E/J42mI+ZLrAK48en1+mFfIoZtSka4U7qw0p07bEyIf1fj6b8DJ72A0z5tDPvvZ8BWOZ\nNPRZlmKGYyDms2V977ygE8vVSOjvZdHhnpAU0xCXBfXYsaPE5s0y23gaQcs9qNfFfAmtAEWhzdaP\niAV8aLANkH93GthTJuQpPFM8x/3KjjX0nG4t3KP5kAlr0tXneQdKGzDCOlO484ReD2XvScu27hlA\nQwNJ1xFbXtImXpdIgmHCWxeemVhhhUJuBjsfe8GNXGxGUE2oUGifzcVZN1brv6VlsBzApyBRrZ+a\nFJtRpwANLVcsEKQsYpcCTYyj0PaV9rU6znuCC9t+eVeDI1G5F+1mq/3NPlLfNbv5Wl9R2zZFLIqb\nn60fZkyjzD7QSFsgTx+kfeu5GXimYvqxeeOMiGlLibJMI54WWt0gvCAUjwLGo7ZRf0o71mLE1DY6\nnu9SNWXNglw8cO5TG6d9rCTuViAcOjIRfid1ldUoEjFNM5D3T/YOiWVclmWuBkBe0PMOaCocAo3g\nmYGn2pK5+frEaxYMK80vSUh4Y7D/3icKQqEuymtj4zlBZfKB4bDQjzy7hPV77sTiYHtBKFwZ7gvl\nBL64h4bCptI2cSmnPdJT/9rYOGb3DuaEQi2PQuGFPdVgbus/+Dx2nFgM373zky/inZ98EXc8eT60\ngYJPy84RnH1oCCvDfTmBVDWL1ISxPN20WnaOBFMa/3FDWRio5MyzQFGIYltWhvvCb7phaXQpUSaw\nqJBCU2Pl6El0HT6G8ae7Av0J28n+BpDT8PAZKqiWCYXab+w7tovf8TODRSjAqkBihcKzDw0VtLmW\nX5DPrk4tB4HG2/z598pwX6ABIjiWW3aOlPoNan94mlY+Q79TYZN9aE35a2Pjpan6dNxQeNe5SXOp\nR9PC9px9sDUIY6yHXt85vY4dJxax48Qizj98N8YevyvMv5gQ1TFTN1Uv3VjDjhOLoR9Xhvtwx5Pn\nMfrMKi7vWsVLj/Zjdu8gho5MhOt6Tm+Yq3esYeTZpVyUvvZZ28SlgpC9fs+dWL/nTnQdPlYQCGf3\nDmLygeHcPb3Hp3K/8xDGfq1OLYe/qYnmWrYy3Jejt+Hv/QefR8dMFt71wFNtGHiqLRdd/aFbH8nl\nek9I8JA0hgnXDCgE2ghiwDeTWSFH4WVXUB+vskjfMkHH8ykkbFo3fqd1sijLjOERJXtRqqqtYHkx\nraTtD34uo93wsqV4gQakxvHMmxR8Y7QuHhl2WWS212Z+RxOlZulQeh/VBBEUAlTTZP35yCNJgV+f\n5XEqWv9BoDG2LuypusEHRFnwRSxSXc2X+hu1wmpiteXFoJpabz5pNG0MnhZSXSOU/xHwXRfKspGo\n5tOjPyqLQva0k54p2UZL6z2qZbbuHp5G1wvg0jlYFkxVNkZigXWEl2c7kWq/pZE0hglvXnyg8pGC\nUAg0iKi5CVeOngwmyN7jUxg6MhEWWd2cho5MhFzBumjStEcNYMyvy2oE9Jnc0LwNW33TgMaiO3Rk\nIpAeU0joOnws0FHo87i5q98ezcQUMroOHwvCAZ3PdSM6+2ArRp9ZxR1Png8O+16Us9cGbh4qWBLU\nRKhQSFSnlrEy3IeWnSNhY9d3wvp5QjfbaqNk2R+2nvzcsnOksAGq35rdnHc+9kLB55T9O3poMgiA\nl3etFnwyV4b7wt/W3zFG4cON+sqBfUG4UnO5DTxSLRHrTI2y1369Tj+z7hSGe49PoWXnCPoPPp/T\nUtryvAAgovf4lHtQIH0N79UyPC5OoixiXbXW7GPWm3NF53B1ahmd0+vonF7H5APD4Xl27mi9OHdW\nhvuwNjYe1pLO6fWwbvB9cJ6O39+B9XvuDGXxegp0bROXgtBFrXR1ajmsHZ3T6xg6MlGg2GGbVbvc\ne3yqYO1gH3F+6fugxpFWAV1TWIb2h10P9t/7RDSYL+H6Q9IYJvzIsfuXngZQ32DLImPVJ4m+Oza6\n1l4L5DUlhBfhaDdc1UpYTjvA1w4Rqgmh47wXBAL4aeOAIoWHlz1C22GdzD0KEfV94/02eMbrA4/f\nT33OqP1T0znbT9j62TpqFpWYD5zn9E+U+Qiq9oWaTE/rSgSXAgmk0N+s4G61LzEico3eVe2hfZ+2\njZ72mHPAanetuRvIj1sbgezlEaZLhOf7qfBI4K2/nPfe7Ltim4DydJOWUzF2nydo2mAhZhaK5Wom\nPN9KwmqgVcOtfWD9Zjln7HVexDvbY31OPc09zfg2Ep/P5vi371ZRxuKQNIlvarxmjeGWT3/6069j\nPX6k+PQbXYGEVw8KhQCw8L6bMXRkAt1n5jB/+zasbm1B6/waLuypYtuLdU3X/O3bsLJrGNWpZczf\nvg0AUMmK2qwtc0uYfGAY87d1o/Pcam7zqS7UN4iXHu3HpfdsKRUK18bG0Vppw+zeQSwPbUXb6Qlc\nObAPP9g/gs7pddz4pUlMPjCM7jNzAOqL9fR9N4RyFm9qrZswZy/Xhbp334K2iUvYMrcUymd7zr2/\nFSPPLqHn7BpaF1tydQWASm8PZvcOhus7X57BynAfrnZ3BEGo95UGWfT5h+/GwvtuxtQ/GcAdT55H\n60pPro3cFOZv60b3mTmsz17O/b5+z53YMrcU6ggArfNroe7zt3Vjx4lF1EYGMPuONiy872Z0n5nL\ntb/zXGOjWh7aWifFPtcIPsnGp0O/XNhTzZXBPiXaJ+dDH1tUjp5Epbcn5x7QeW4VW+aWMLt3EKtd\n9TXxxi9Nhr4E8psgyweAq90dqBw9if5vtcBiy9wSzj40hErLVgDA2z7/jVx/AcCVB2u4eqE+5nrO\nNvLuLt7UioX33YzqF76F6kIF5z6+C11f/x5atm1H6/wa5m/fhuWhrWifnMfV7o7cM4H6WF/d2hLe\nx/LQVvS+soTFm1pDv77t899A2+kJzH3wXaFNcx98F9pOb0T1/tTNAIDWxfr8ap3P1w8AJn6mA32n\n1rG6taVQnwt7quFZnedWsXhTK9Z7usKzlofq/VKdWsaWuSX3vc3fvi2Uubq13sfVhQrWZy+jNjJQ\n6HP2Qe3UGbSdnsDKruG6JuxKLdyXjU+Hf+v33InWShtavnYa1YVK6KfOc6uY+fCt6D2fYW1sHF1f\n/x5+sH8k9N/V7g7UTp1BpbenHhQzexm95zN0n5nDuY/vAt4+FNaAlV3DeNvnv4HayAB6zq6h5+wa\nzr2/FYv9GaobZwkKxqtbW9D58gzaF1pCHW780mS9Xsen0D45j9m9g2jZth21U2ewPnsZld4ebJlb\nqtdpZCAIe1e7O3C1uyOsI1e7OzDwFxdx4Se60HdqPYzfxcH23LvtPLca3ue597di+zeXcbW7ozDX\n+P66Dh8COnByAAAgAElEQVQL42j2HW3oPLeK3//3f4Wf/bl73feTcM3j117rjUljmPBDRywtnaWj\nUB+cMo2g5w+nPGJAXqtgtQLNogpjUKJez+xZRowc819UmhM1g8YImD1/wGZaHKJMW2C1jjHCay/a\nms+2PlfN0oV5WSsAn2aoLFeuwvqfqh+f1Tw1IwwmlPIEqGthrcaJQTQAQiYR1cxZf7oyPzYPZT6w\nnu/YZqJe1UeXgTfUMHscfV691fTt+SCWtTF2nRd962nrm+Xq1rK958VodGxZm8mL7j1HtYHeM706\nAuU0OWX3e64AapEglEfSYxgA8muRzt+kQXxTIdHVJFxbuOujTxU2Omq56KenFCs2tRzgU2gARZPK\n6DOrUZML7+d304+shBRWU/uvBoqNhYGKS4nB+zRLBwmdaXLR3yi42brTHEx/JRskwP6IZb3Q6GJN\nd6apzpTcWoVrBhDEcrxS22gFODXj2WCSGP0P/UIZET61/2ru/Sjxtudfxr6d2n81+DIyaIImXUvV\nwfdgSbttYIS3iVuw3dp+9rGSNFuCaeXd86hu9D0x8pzjxcuna+tM8yznB3377DtQqiYABVO/+kPS\nLG2J0LW8MhO8V26z7D2eaZj3xYJFPNokLYv3MhWkzs2ydYHQd24pcsoOH7G5rL6V20/VXJ7PZtBx\npYddW4YlbLdk72qS1rVVA1xi2Xs81x1tZxISr3kkwTDh2oBSIVhNhRfR621kZVBfMKAYcavQTYEa\nHQqFltjaOz0rbFCACjKa7xTIb74xPyoVVj2BxXM6j2m8yrQJKkTZ9+FlZ7G+nmXaizLfNgqG3nPK\nBEMvDVlMC6Q+U834/oByTj8PHu2I5mNWeGTbNm8xkE9JByAXgGIjrj1SdjueYsKhnU824rUs8lfb\nvhmfSC+7DxFjBlCU1aWM0Los97SnfbT1LhsDMcL7ZvDmtZ1vr5ZT1c4bhafZjx009FDV7PBry7P1\n1LUqCYjXLFJUcsIbD/oPMnJWefSqU8tRoZALUbM8rwwciQmFjOLjNYzoHH+6CwNPtRWEQgU1K1bA\nXBioRIVCrTuAEEHNqEIGDHjt0s3DPlcFnljuVJ7mGbWr2g7Lj8dNXXketQ3ccKxpum3iUmiL7TOt\nD+vO57bsHIlGEqsmlEJHLBBAo3m9aFqrJWPU5fj9HTmuRwv7nX3nGgms5lY+j0KX9oFGyFM44nM0\nopcYeXYJI88u5Z7F67lp6z1eVhUL9hFNhVcO7AvfqYaoOrXscgGyH7Q/WBeNtJ7dO1iITGYfWKhA\nSA0j+7QsyCWGlx7tD9yHOkdse3TekPtP59yFPdVc9LPeT35D+x61PQTL10hpXs/naZQxI5UJL+pc\nI7CBev92Tq/j/MN3h39kItDoY32e1o1YGe4L99s2AI1xzbnDvqFGdm1sPKwhWjYZJRLeOkgaw4TX\njLf/9r8B0IiMA/ycoZ7/EVDuB2VzzNJkzPKA/GZZnVp2r/H48XSz93j21KxapoVTeNG8ijIfLKJM\ni9gshZ3WS3nnlIeO92p9FTSLd8xkhWwv1l9QeQFtZKbNBQwUDwGsF2mFgKLPaZk2BagLCW0XWoLW\nrey+sr4uS89HWN9VgpuzPpvvwUYDq+aHv7Hv1LdLo5iB5r6HrPPF3Rm2n6qFfMTWtO2ZcDdTNgUx\nL2uN9b/UiG7rH6gHj1gaPs9XT7E2No5XPvPe8BzbRzZaWDXtdv5plhS+X8s1yGu2n6q5WWKsi8dm\nsyoBxWw+NPV6PIe8HshzYbI+VltoI7K9/M6xaG+9vuvwsdzzlEnCOwjw+S/8UaK+uQaQNIYJP1q8\n41/+WwCNjYCncGrN6HejacFi4KKo2kWCwgr91NomLgWurlc+81688pn3hutjQqFq9XRxp39d5ehJ\njD1+V1gYd5xYzGmdVCOm6byAhpaKWgeg6GBPTjTvdK+giVO1iOxDIJ/lgNeXaVusqdd7D5a/cfup\nGjqn17E42B7a4/HQEdRO2SwN+lw+QwVIq0Xlxuy1h/er1vClR/sx+sxqeLdlQhTvZ9+rZqeMu08z\nbyhU0GaZXpYYCqz63gEE3kSvzP6Dz+OVz7wXa2PjpUKbbRuv7T0+hdFDk1i6sVZodxlhMoUOTxOs\nc9yWw/dvaZE8qAZMx27l6MlQV+99WE2ml/OYIFflxd1Zwf2CGjs+e/TQJLafqoUAJaAxDnkQGj00\nGcrj2kaew5XhvhwXKbk8bb1ZFuvCjEXr99wZ5iSz3DCIi9ladOzwMMF3pYK2mv67Dh8LdeX61HX4\nWIEb0a61qqGf+9hc+E77Rg/Nmi3KHspSdpU3N5LGMOFVgQIhgMLmZv1XYoEUQDmfmRXs9Fksk1GU\nqq0kXk32AevjCPi8b0C5dsXjFNyMs3lMY2I1AECxnyi4jh6azGk2LKw/pWpJgfK8ylbjSvM44Ofm\ntdHd1gRaJpx4fIzEq7nf88kqc9q3iJkkFWXuBV6UeOyZnj8rcw97Y5vQoCagyJXp5c1WoSUWxe/1\ns9Xc2WhyG9Ciz9pMFK6+b4+vU6FmXU/rGPPT9HxXvd/02QprJVCf3TKtp6231UyWwbNaWM27wovc\nB8r9tsu0yRQORz51JXzXTEPrRcAn7eEbhhR8kvDDg+dDYqNVbTYIoLjBK5GxJVn2gjOAfLorGzWs\nUaI7H3sh9701G+nCboUW+71HyGwjYG1EsYLk0ox4plaBUaCxdH1KjK20Kd5mYB3YGV3KE72a1b1g\nBouYoAEg5FodeKotR0hNqh1G2Wod1czWNnEJZx8aKhwkCPanvcaS//JaW+fYxqw5Yrm5qXCm9bPv\nlP3GSHEKIRpdrs9U8mr14VKzsGpQPUHOzh0N4AF8M2BMgFJTv5rvgbxApOPZo5Jin2n7lZicbWf9\nNPpV7/GEk9ghpCwQTd81+1TrR7cTAGi70OCktAEVHGsa5e0dlFimjnWv7p4gzfqV0QQR2ldaB2+8\nM5Bu5FNXcoKdHtq8Q5bmd/dgD0Tax80i+e39Wgcdi3/9q78cLSfhdUcSDBNef1Ag9E6sPCFamhd1\nvrYnXk8otP4yVpuiQqFS2gANzZ4VChW8vyxPsV3YPF+bWFRejHqD5cWEQs9fyAqF9BtrFmHqbTRl\nvHTaZiC/GTGilZtl28SlELwT6yvet/1UrUDdAeQ1m9p/quHxrqFAoVQtXj8ARS2o3SDLNE2Ep6m0\n/lSeD6yn1fU4KbVdhD2kcDyUpYyLadq1jfYQxf7WORfTtNo6W8FQYX0hvchXLxLW0jd54DyijyNN\nyDHBhu1UWI2lpZOxwqHtBz7PEw5ZBuBHl9tnWx9gbaOttw2w0/vtmLTCoV5jI5k94dA+21IsNYtK\n5iHBrr1ewBS/+4/rn0PCDx1JMEx4fcDI4rKFgwueFVCAYnBDzHwJxFPFeQESMRqLstRWnpkOKPLu\nefUrI6aNaai8zdy2xbbR0+LZOnjBLtaca53MXw0NhvpYxYilyzTDMRPaZjSVtnyPwNgKS2XaJ9vu\nmN+nwiPijtXTakHUBYHgO6AGzLpBeCbusoMGYfuobA7ENDxlGvTYXCozjW7GLcFqAu1zy6ho7G96\nGLAHI428tohplz1YAUxJ0u29m1mHLHgPXQYo8Ho8qs0Csco06Far7K2H1lVkM/RPlqzdcyWIUfR4\nh9hTv/4pt20Jf2ek4JOEvzuoIeRiTydtS3vA3/Raj9KE4EbGMujkzMAPoLEQeRvB5APDOcdoS8ug\ndVoZ7sP4010Yf7orVycbgMFrbRAK66fP4emd39HZXK+xVCMLA5WgXYgJhXyOCsskabaE3+cfvjtc\nHxMK1++5MyzE1mFfqWxYf74XbgoUYPhsFYb4nrkZsP36/ipHT+aCdiztiv2/DKx3yEW88Q5opveu\n5UZrv7eCglKeEOxDqy1ioIA3vlWI5j+gMdaUBHtluK8QEMC6AI0+YfCA0gSxPJtRJiYEK9hvVhva\njBoKaMxJpS/S/xmk1DZxqXCIsQLNyLNLhWfagB0NLqpOLbvrCYUQPUB0Tq9j6MhE6KtgchUTJteR\ntolLIQDFtjP2LAbYcGyvDPcV3gHnihd8Qtg+oasHqY64xmlgTsyvWamnbPmE7T8dS1yDOEbtuqjr\nrQbNAPko8x0nFnNBcay3ddMhOqfXQ79yzmlmrIRrA0kwTMCHbn3EFQoVXFDU/KdCod5DE+/a2HjO\nDAP4/n00Gaq5EChqJBn11zZxqeD3Yv3K1GGaZtyFgQo6p9dz9WGkIvn+aN6i7+DZB1tzEZeMsibv\nGQWHoSMTOaGQAgAX2pXhPlzcneHi7iw8p+vwsfBsoL7wWo4xS/Vhfy+DJxRasG9jQqEHXmOFeqJj\nJgvjRP1KgaJwQQGAm/va2HhBKCTYT7xGr92sUOghJhSWwWpWbR2tcOghJhx6eDXC4drYeC6aPQaO\n+erUMhYGKjnhkWNFhUNyZq4M92HoyERB+xPTcJf1QUw4LMNmAjisMMP5w37TtjIDk7VKdB0+FgSZ\n7adq4d/4/R3oP/g8Jh8YDmZWjfjVA7UKeRd3ZznhsG3iEkafWQ3XeOWQ5squxxwHdszy4AcglGmh\nwuHa2DhGD02G98ny+F5UOGQ2ocu7VnPrkPYXn8vPHNOWl9UTDlMk87WDZEq+jsGTWow7kH97OPvQ\nUOC7I5iOqizbB+CbYq0zO4U4SzmjQQ02bZPWDfD59WLRpSybPljWDKNC6tT+q+g53RoEGbshWjNr\nGV+jti/W11YryXRo5Bhj6jf2P9AQlO548nzOn4/XxupFGhj1V1KTP98VBVvLRUh4+a7ZBusbRS1p\n/8HnXZ86QtusPIgsA2hwWqo/WMwpXk1immLOzgPrhK/CvJrLYyZ129cc2/qe2i60hFRuWoY1D+uz\nbbmE59vFPrH+hGy3BuGwr/U+nWesh+frpnNIA2i8dmmQGGH929S3z5Zl0zoCeZcNHZeahaZZ1LHn\nRmEDaSybgfUbLDPVaySv52NoTdXa92VuD+x79SPUQ7CuPeriwsA13kc/aO13O7bVB5LPsPPDC5Cy\n/ua817oDpEjm1wXJxzDh1WH/vU/kNgIiJrzZgA+gSJnAhaSMANWL/tTnxIJHPJ9H6xhtfYOsz1EZ\nDY4tW9uk8IRCbzP17vU2Abt4EjE6FevPqO2lL9TooUm89Gh/znFdy6Rg6D2D2itqSa2PpEfbwQ2Y\nHGyx4I4YRYq2waZsi/WtJxjarCBWCLfmrViAiI5RC3uI0e+JGKGyJR/unF53ibW99seixm10um76\nsSwpsYCHV+M7p3PNEwwVMR/GmB+k1ifmv2vb4Pk4xvw27bjYDO1MjIKozI+5WT/YuV8WnGIRq6tG\nhQN5ATJGaO35CtrrYtQ+mm9e26aIzQfCBm+RCujz304axL8jko9hwuZAszFTQhH0saOJtG2iSMbM\nBWvnYy9g5NmlnHDCyW8XJPrjkLCV13kLqtX8WaFQzTIxoZDX0+cotgiPPLsUIhJt2bzeM8WpUEh/\nIJrtvOcRZQumpbRQ4cr2jy3XLupBsypUHQolr+Y91mxI36eyABmCJkiahFimJVcmyvK92o3JlsH6\nLA62F/yf7KZrfS31MADk+43uBbzWEpuzHpMPDEf5Kb2xYttuzWj8TJ9HS2Du9QWfzTpawaE6tRz8\nHS3puL12Mz6ftl0cK3xnnOf0MbV+b2Vl2XqwTZx7LNODJcTm+/SETRI565iYfGA4JyByHuu66PWL\nto/rj5KL83mzewdDH+n70HXAmtGVjNqaZb0+o+CsaxD9A/sPPo+hIxM5Tb59/0zX2X/w+XBIsT6I\nvcencOXAvtx+oGXxANl7fAoXd2dYHGwPz+S747X8zD2G5nvrv8t0qh+69ZHkf/gGIWkMrwNopLHl\n7YqZfNQUo7x7hGpsYnxXNDcpZ5yaKHWDpTCkWpVYlKHWM0bhoL8BjaAFZlCx2j6rnfBO7Vbjo1rD\nGA8dywbyGoyYwMp600TMBVvNNV67bV+N39+BlR1rGH1m1dWmAT5FCvtENTQe/56+W4+nTr/T8vTg\noCZMHR9qBtfybBusj5mWSbRN1PkRR55dwoU9VSzdWAvp4lS7Row9flcQrsfv78DOx14oUHyo4M5x\nb90XYmkL1TRtx7USc6uGlmOh/+DzBX5LpWoqM1+qQEuXAmBzmlLVrKlmyCMS13no8QyqJtsTwFRr\nZjWf1qR7/uG7w9pEjXVMkOJ8VHcI9uvSjbWc24mnUeQYoqad70Kpg/TdeG4ldONQKMODp0FWbR3n\n0Njjd7n0OJbzspmLgLpBqBuK9oGlz9K1SK9jG5ZurIW5FkszqO46rAefwfFh1zsiaRFfFZLGMMEH\nHXpVy8XFSU+0QJF/zzoiE9TYaASgTmBG/jHFk5bh0dlwoV0bGw/p7nhfmfO0CkdMND+7dzCXqglo\nbCx3PHk+1NczBbLebJueZK1QyPqyHhqBq5uwt9GqULgwUMm1RwWgMvqUZmDuWruAU3Pm9autsxXE\nrKDLd+QJQFcO7MsFQliwXhqEAvhZP8q0UF6ZhH0u68v/PYJzbmrUXrEPbNAHYfuR/Rsz4+p8iWnQ\nYgFGVitG4cDjCST0GQyWAIrBGESZeVcDemKaPAX7xo7jlx7tj7qUEBwP3oFDv/fyF1tYDRb/p6A2\n8uxSCAxT4dfO/fH7O3D2oSEMHZkIB2o9XGlqPxugpXWhRpTR0bN7BwsURHz+lQP7CuNk52MvhDVO\nhWu7TlutuX539sHWoMlsm7iE0UOToQ+0HnqYoCZUn6X1HToygY6ZLPQrr7FjrWXnCC7sqYbfua6w\nni892o+zD7bm2sPneMkWEl5/+PamhLcEPKFQJ1vhxL+h+cLGJPR8TipHTwJSjtUUeoJXbhPgCVoW\n8KEjE8DG9VYTYzWQWkZlYxHWwAGgQS/BzXlq/9UgaKi2hG1UYl7VkPF6oLGgXtxd1yJ52kBPE+mB\np29LNKv8dyNTNBc17lkcbNB5VDbqqu9I3+2P3/EdnPvNUQCNd2HNqfxtBXFzYsz/yvPl0t89eMEK\nK8P1XNjqr1qWCm5hoCLR8A1tC8fAwkAFVZHVeEBgvUaeXQpjoP/gePCZ9VIJtu26DJzqDs8gPMLq\nkWcbZmgKF9SU2b7zCIOBYu7b+vuqa6oYEcpNl2VQW01wXKqWxvObJQXRhT3VUE/PxzDm4wYU1wc+\nu8y3+I4nzwc/VhUqFgfr7Rl7/K4C3yH7U90UWsx6oZHAAHKaKIVq+Nn+Ourvn6TXtv29x/PtaZu4\nhBURDq8c2IeqWdsY2MH36pGwdx0+huo9d+bWO32fXRvzfHGwHdWN5yl0TdQ1QuvJ/iGqU8sYfK4d\nZx+sfx58rn7PyLNLOYofz4+RwmH9YFO/z/NVVuGQEc16LWE1/Jz7Zx9szQV/cQxUp5ax/94n8Nxf\n/gsk/PCQTMlvMVAYtFFn1kxhc6mujY3nzGgqaDXLd2ud62O/x/wDgWJgBK+398aIdbnBUyiMaRDU\nZE3BjP1DKCEvTR6agaQsW4ttp24MXjYDjboMnH0bWUTs+/Iidq1ZMubYreYw7TerkfEyOWibPNJq\nG5kbCxiwJiW+c5qfeI/NVQ3kA1e8Td8bY4yc12fGAgIIjonxp7vQ/dnuQlQ866gC2djjdwXBUqN4\ntb+1joCfj9kzt2vbFV4UtYVGgHuma9aJY1QDR5rllramyVhAC6/h4asMPCTwnREUbu39nuDiRUDz\nGuveYO9lf1E49A6lPDjadtp54Y19jYwm1B1CXW60ztZdRLWk9lCl8FxYgGJebxvwZfvSC8KJmcRj\nAT0eywNTeNKUr33ktcXuL1xPv/tP/yf3noRkSk5Ag36GCweFwqUba64QRmfnleG+XLSxh1hkYUwo\nVHONgoEPujhxY7KaP3WuprYE8LMtjB6aDMJMmVmJG9vCQAVLN9ZyQiEdqLefqgUhkJtaM6FQN/rK\n0ZNBE2MXOmY5ABq+d9Yfjc/iosr3ZYMIeLrn96yT5YRjX3sbCB3vY6CgoJoEhXX+t0EB7C/WwQaf\nkCOOJvgy7DixiN7jU655TsH3bgUMIkYUDjSEkO7PdhfuY4DWlQP7ClH61md0du8gOmayaBCTdbgH\nGsKY7SNrArdge20/7Dix6G7qipXhOich56UVlHm/rZN9BzxQxN4hn1021hYH290xaoOALPE2f6eg\nYIU+Oxa9wLe2iUuhv6gx1IAL3svACDUHq+uICojqJ9k5ve6uR53T66FvGYih16k7jqV0ubCnGvwe\nGTjj9ZsGb3UdPpYbj+QvZLv0AK6mYyK2tpYFyQD1+aEWC7aJbb+4OwvBMqyf1tOL+mfgSzIvv/5I\nGsO3ACgQeip9dZqmlsxq5YA8Zxc5raiZ0Tyi1lyq2gAbEMHnWBOPLire8/ksCiMdM1nUZMo6qbBp\nna71f5roRp5dKgQ/eOXT6V+1qaoN8BziVRikRkbfi2o/YpojK4DqO+Oz6IRug1UUlpOPgg2De6gR\nOPtgazDjqAO95k8GkDOTezxv9l0TnmYpNibYLxpIw/elXGk8+NigEA3K4MGI/aRtJ7USDyQxTklq\nN9Qv1qYgtH3N/iM0UCu2iaqGz2rwdd6pRsuOYc1drs9kvQEEflAVwpSr0L47Ox60beqewmAdAMEk\nbAPMlCOP75JzTA+fnuZPg+XULYHziRyc2h57L3/z2hjTQAK+RlTXDbWq2GAx5WW1nH76DB4QVWur\n7giqQeR37HMNfNF3bdd6jyKnLKe1Hpw92hrS8midvMCUhmtEwxqhY80LbrEBNDp+tA76LpOJOYfE\nY3g9Yv+9T7jRrwqdqIDPJeaZjVUwUUEnlv82ZgazsHX0oveAhlDombY9gcMTFr1TZux+BX9nxKLW\nA8i3tXN63Y2O1bZaQcATCvW5sT62Akcsz67643j3se4aKUpY4dDep89UgZtgXZiBxmre1JQENNdA\nKBmw9pHnIgDkuRwBFIiI2Xab81mf4wlTetiyWmag3DRM2Gfp4QQoaqHpUmDL80ztAHICBlDk/PMy\nCSmamWotyrjrxu/vcDOeNOunGIefnUMUJmN8kh7vJVAMoPKEQe9zDHyOCj0x1w4dSzGTO9ttD9lA\n3lJCQVCD7GwuZ89iYZ+jbeS43KwbiR1vNvWn1YhTkPUEQ61bzDUCyO9HnkmeB8O//tVfjpZxHSGZ\nkq83UCgkuBiQE428gYRGnAENLimCpi2al9WMAjS4xTQnLCcmF6pm+VdpXuUC2WzRtQsdecBiGxX7\nwxNY9H4LLmD1wIXGJm1zCY/f3xE0VSoUkjdx6MhEoAHiCZf1qDuGt4eTMakorEmx58kJbP2r7bn2\nWMTIphWa3soKoCoUAg2TjCXEts/TqFhPGCRCoIekJQSKUZJ2gWc9Y0Ih+8kK1vx/6MgERg9NhnHD\ncmxgCZ/LdrGf9D1713PsWq3s7N5BzH1sDnMfm8t937JzJDcv7Hi0JjPrlmAPRawvv7emQxvJa4XW\ny7tWc9fZHMh2PMX8Ve3zOE51o465LbBeajK17Ag0edrn8frx+zvCAUChQl3v8SlM7b+ay3PuvQdv\nHFvtId0cdH1hu6tT9ZSOOx97IUQLM+JcXWGA/PtV1wmPK5Jjp//g8wXhjlpTmr3pMsFy1Px/YU+1\n8BwKcpa9QXN7839q573+s3uGzXevbdf77PfqJsR66j/7O/9Wvkedk6OHJvGOf/lvkfDakTSGbzJ8\n6NZHcmZRXfyn9l/F4HNbgv8czWca6adaBMuDplBeOSBP7WGjmwHfKZkLo2bF8CLzWB9eq+YPK7za\nemleYqBhTrS8gmpKJW8XgOD0bKNH1VR2cXeW474DGoz/GsVIU5BqBjTSWc1OZRkabvrFs5j/iYt4\n5TPvDbyLQJHjzead1udYvzn2pZp9qSl85ydfBNAwE6tQrO/AmshiKQBj98UCRux1npuD5yNLWDO7\npzXSoBbVWLA/dC7p/Rxr6uJg661m2elHVrDly72uSd/TQtlUfm0TlzD+dBcGnmrLtUHLiGWXKePH\n5PpAjTA1ulu+3FsIPGF9eL93yNJ370X/sg767mPl6u88fChPYEwjSZJ9NaNabZUNpqLbhOVSVOHH\nrkE6h9WNgc+z81m5/xRWG8m1THlkrfbMzh1rwVFztHK/6lz1NHpqAmbwl9ZXXZC0HLZL3Yl0TGpd\nNMgPKAYuaV8A+cBAXceo3Ve3D3WJsm4NrDPHyHVsXk4aw+sB9CXUExvQWAyp+WGUFyeMJxSujY0X\naCEITkhPKGzZOVIqFKqWS0/Ks3sHQxSdt0lMPjAczEMxUys/W982nlYpMOgGxxP/7N7B8Fz65TDy\n15p2uBFwoaGPoycUjjy7lOP80jZz8VShZmr/1dx1ntZ06cFqKQ8iEOe6U+2Zh9j3vLeZCS2mXSJi\n36vmxl6vmlzbXnWCB4rm0JjLAt81y7XBVayn5cvUbCt6AIm5B1ALz+dRoFMtNBDnWGS9bKaLZoE4\nsfejcwPIzyE9ZBBX/6vZ8De1VArb7xZ8r7FxGnMV0XZ4bbWHHgsbDGbhBZhoPZXTUaFa3JXheoYU\nFahoNWH/k2uQeOnR/mBx8TTpLJf3ahuUH5Ljj3+37BwJGYa8YKuLu7NCIgK2lRlOrEavZecIdpxY\nDEFStr48PFMDy3ZqMJC2k2OEdbBzlZ9jY8XORf6vhwWWr1ld+H7sHOJhLQWnvHokwfBNgv33PlEw\n/wKNU2d1atlNqXX+4buDqh/w/YFIrMy/CZar9wMN1T+FLkYUx6AEsdRQUmBSocnzGVJYU7AN+qA5\nV83hfD5P9S07R0I2ixhHmzrBKx9XdWq5IBTy9LowUMlp26ip1T7gvdwMrQAL1Dd0LqA28weAXKoz\nhTXD2T5aGe5z28vDhBVg/66YfGA41EV9GBWeEMnISPalB08o5BjWNGpWe0ZzH59bnVouHAiA4sZF\nISsmNFMbxefaDY73W02mFQ5pfqQJPhZ97WlevPSU1veVaJu4hIGn2jDwVFvB3A/UxxLrbtkDrBnQ\nlr8B4OgAACAASURBVBt7Zyw3Vqcy0DXDQiO+WSctf3bvoMtPqcwANqoeQEinuThY599j+jzO88Ad\nKAIe+0V5Gj3hkOVaUzWhZmJritaodZq2uSeQoJpaR97HdYsCraYn5TN2nFjMjVGaqEcPTeZMzc04\nLRl57e0JXJt1rwGQcyvSf4SNhrcHLJZHlw3rBsIxkoTDV4dkSr7GcddHn3JTyKl5xwYjxJzCld5F\nTa264WlqKS+6TM3B1gxkqS7U3Ok5umsAgnUWjznSEzxdl/GSqRklZu7kfTb1nzWNe0KBNevYRYvm\neqam0/s08lvbSnOJmnBsu2OgWUVTdXnk40DDxObxJdr+UngmStV0EGpiPPtgay6nqjdm7FhR06+t\np0bXA/loVfV1Uv43NUl5496aBy28PvIOFx6RPNAYK7HAIqYk84K/AERdMfQ6jexVAUnNb4SmLmPZ\nXtQ80HA56DndmktB5wUOqUBvBVgbUOZZBmyEu17njWMbyap+ngx8sn7Jyh6gUa9aF1pVdKywj9TP\n1AvmA/wAD89n04vStxHDXqCWd732s5rZvTlrxwfQWAO1P/U+r94WPITbCHOWY91p7NwjrEBtDxyx\n4DHNBqRt1/d0HaXVS6bktxp2/9LTgawayAtG3oldfeyAuGM4r7Mbk3WQji0KlraGk1rrR14sm2pP\n68JF1pqfFVb7yTZZJ3suNnZx1k3Wiz5WobD/4PM5oZAnXp6A7Um2cvRkgXdRn1mdWg5aRTXh2fcQ\ngzXd2Q3IBi4QtlzbNx6amSVf7X0UyFgXCoWWb9FGzcaieTWQwW5qWlevT8nTFiPkJex8iAngFJKs\naVrdCbR8blg24MW2kRsa+85qPl56tB9DRyaicyWmsb+8azVHDq7gM6xbg+0bHmoYvGI1nhbctK2A\nHSNiJqpTy9F2xEzDVpu75cu9AIomfQs+x44lugZ4faF8knZN63gmT0Zu1y67hlgNPgNZ1G1Cs7uo\n6ZRlcIzaOc5+5mHJjuXe41M5/kSCByi6lLBvbLAg6+hp/BmMwn7UNYQ8jUBj7lvlRkxrb3kPrSuN\n1QxfObAPlaMn3ff/oVsfCW5ZCT6SYPgmQCzvKtXoVigkrFDYzB9HNyOPgBcomj40Zyn/6bOshkgj\nMGP+RTbYAMifPK0ZpTq1jPH7O3LmEfrltOwcaSrgqKM7zUdsq/YPEXMWD6mxNupK4mbrwK197EFP\nxxpJbq+PtYs+QfrZgy6mKuSdf/juqODpXa/wfB/p5gDkydV1jOnYvHJgXyjHCoVE5/R6LlJUQbOS\n9ae0LgYxbFYoZJu4mZVF0QLFQ4Gtu/WpipGKKwuAbQvN9ypg9R98vhC9SR9ba5anX51dS0afWcU7\nP/liU4FHn+n1ib5PPqP3+FSuz2PBCdZs7JUDNIRDrwwVZnSeaZn24OmZhPk8CiBAXTgc/cgruLCn\nivV77iz0lRXsVob7whpGH0I+33MbsinnLuyphjVXBSq7PseEwysH9pUKhwBywqH2A8tbGxt33//O\nx17I5Z/W9Uj3CaAx3vlM7mvNhEO7L24/Vcv1mz14AsVI7AQfyZR8DcGeYihMeOYKjQRUE7E1s/E+\n9VnxEBOCYvQwLE85u1gXbljW+RhAzqRHsB2MFoyZhb0ABS99nGe2iWlDWEc1TbBdbD/vUyGcUP9F\n23c2oMEj/vbMcBRUgTjBtY3WfunR/ijdDOsw9ad3hM8DT7WFPlUBJZZCkfUDGtGvlk6Gi7018wAI\nxNoKjq2XHu1H24V62nYGFZAOyJrJ7Bywrgo2SlX7KyaI61jWspSjbmXHWvBN0yhva/ptFkVLWE2J\nV2c+g/NZ35Oa0JR8XMu0nKI2SrvMfKcHAmr/PeJ1m67Ocl7GTIJqvtaxrJYGDVgafWa1YBaMlWnN\n7do3AApCTxmvoE2JaNdJLYPmSxXolYA+Zl72glS8Z5CiR7k2Y36mnom1jF+xmctMjDhfxx/QcK+w\npPiEtzbbLEJesCT3ACvkWU2hDciMWSFs3va3qHk5mZLf7LDOsbGBbX3AOMkYdaYnMdVW6WRkWVaL\n5wWeeHXiouFp0q4c2Jd7FhccOm9TaOBiEfIDm3RW4/d3hNMo62NPw9a5nIELsQhYT/tFp2lG7rEc\ntp9BNjzV29M+TSeqtVgYqBSEQpbNBdZG8tn+aqbVUlhToAWfMfjTLwFomNns++XCTPOrhcebaYmn\nWX8u6jGNY1kQwvo9d4bMJAq7aVlzLgUELzVY7HnNNme+RwqFqllT2IAXW04zM2pM8wY00qnFSOWt\nny37hWPNi4jWyFqvvrF2WNM4wbJYRzUVxgReCjoxTTj7XINFvPboO7ECDOC7bfCZFAwsp2PsvWnA\nCZAPjqB1YuTZpRyXZsvOEYzf3xE051yn7LNiz2AdWSaDTGjy1T2A9WDAjg0iWRxsD8EtihjnKYAQ\nfKd1IkaeXYq6VcTSrGoAjF7HtcSLSFdhWetIjaQ1q1vOU+tCZf1YP1D5iFvX6xVbPv3pT7/RdXit\n+PQbXYHXA3d99Cl89uCXCwLPxd0Zes6uoXL0JLLx6SB8LLzvZmTZFnS+PIMtc/WFYu3dtwQNwHpP\nF+ZuBXZ8ZQYrw3242t3R8Afs7UHt1Bm07BxB7dQZAMDCvp31U/rs5WAGbZ1fA1BfRFa3tmB5aCta\nvnYa1YW6iaHz5Rl850AfBv9sCi1fO43ayADaJi5h7oPvAgAsD23F8tBWtF2pYXVrC7oOH0Oltwfd\nZ+ZQ6e3B3AffhfbJeay9+xZc7a5vNFdb2nHzF/4W4/d3oOfsGrb93jdw5cA+rG5tCW1dGe7Dlrk6\nPczy0FYA9QWgfXIeK8N9+O6HM1x6zxYMPrcF3//x+vPWxsYx98F3oXV+DZ0vz+T63moqsvFp1EYG\n0Dq/Vs/ZeVPd2b6StaJ1fi3Udf72beh8eQYtXzuNcx/fhfnbujF0ZALLQ1vx/R/vqWv8Zi+j0tuD\nSm8P1mcvozYygG0vnsfy0NbQv20TlzB/Wze6z8yFclvn15CNT6PS24Mtc0tY7+lC7yv198w+uNrd\ngdWtLaHurfNraL/Yhtb5NXznQB+WhntQ/cK3UOntqZ+0b2pFtfUGLOzbiW1fzJ+wx+/vQPfKdnz3\nE7cAAPpOzNfrcls3Zn5ia/hMh/3Oc6vhOQBQPd8QIjrPrYYxBSDU8W2f/wZado5geWgrFgYqWO2q\nc0LyXd70r4+jZfsw1n5qDp2TQ+He6kIjUtIKhQzWABrR40NHJnDu47twedcqesbehqvdHWH8z9/W\nHfpkbWwc67OXsfbuW3BhTxXtCy31+bNtO1rn18JBgJqKHV+Zwfxt3cGntJK11jfXXcPhX8u27WGu\nLuzbidl3tKHz3Cq2zC1hy9xSqAf/nr7vhjAfKr09YV6xzrVTZ7A+exk/2D+CG79U9z+82t2B2sgA\naiMD9Qjm0xPo/dJEKGP+9m2oZK3oObuG737iFtz4m8eAt0t/bsxtjmOWuWVuCWtj46iNDDT66/Zt\nqE4tY3VrC1Z2DdfnQKUNl/Z04/Jo/RlsH8cty22ttKF9ch6TDwyHsc1+aF9oQee5VaxubcHgn9U1\nS30n5tE+OY/loa34wf6RsG6sdmVov7AFQ0cm8J0Dfaier8/TlV3D6Hx5BrVTZ1AbGQAAbP3ci6iN\nDNTv2/hXXaig0tsDi0rWii1zS6FunCNsT3g32cZh4CszmL7vBmTZFrTOr4VxCwAru4bR97svYH32\nMuY++C70Hp/C/O3bQvv4PnvO1teUi//NMG78zfpac+7ju9C+0JJ7HwTn+rn3t2JpuCdYDCotW7H9\nm8s49/5WDP7ZVFgLO1+u13HhfTejfaEFrZW2XHl9J+r923t8KuwDXH+3vXge3WfmcLW7I7zHxcH2\nMB65D1SnlsM1QGN/2P7NZdRGBpCNT2Nl1zCqU8vY9nvfQMv2YbSdnghzbcvcEmqnzqDr699DtfUG\nXNhTxfxt3VjrBGZ/6mYs9mfB+jP3wXehulBBy9dOh/3i+z/eg7Yr9QCtuQ++C4N/NoVLe7qxNNyD\nbS+eD79z/wmuBXNL9cjy81mYQ/O3b8ONX5rE9H03oH2hBbWRAfzBz/8m/u/n/ho/+3P3Ft7HmxS/\n9lpvTBrDNxAMLrEnRpov1E+O8E7EQONEFHOetho6oEHeTM4+C6XBARqCFE+f6tcSCwqwWh+rdeSJ\nl6d+RtOdf/junG+KasVYL/vb4HNbAsE362fzxdp6sCybuaX/4PO5gBSCfoKqXSXH4cXdGZZurBXe\nGdDQ7tiTrPWDi/lcajsV2r/U5lATw+tt5DT7XE1eI88u5UxCLIPvOsab2HX4WKHO+m5IdwQUNSBW\nO9H92e4cBQnhUaBQe8L3Y/uRbWQ/e+4LVsPI6229qHFVH1d9thf57tXb842zAQlaP8Cf7z1PTuCm\nXzxb+F7ryHfZdfgYpvZfda+N1ctG1rKdK8N9uXzh1v/PZqhgGz3ErBFAI3it/+DzuffKtS3W3/qb\nrYOth22z1QRPPjCca6O+BwaO0DrAuWGztSgvKNExk19vvbFtNYlLN9aCDzXpboD63FR6KtV+clxZ\nLbTn00jo3Ivxiiq4dlqNpcd/y37TtnuBRuxD5VpkvYGGpYFlM2jLG2exeWx/5ztg/RO1TRIM3zBQ\nKFThZmW4r8DUDyCQN9vNjfdxYqpTrbfB2sivi7uzXLoxal4UVjhVn5srB/blgk8suLhYYlQtG6g7\n9XNTplBIWLOL3Zwt6XXX4WMhis9y/sUiG9lmlmmJUwntT/aJXdzYnzaSj31w9qGhQh9rEI2iLOUd\nUPSFI0YPTRbqTiHQksAynZZ1jNeyYkEVHKN2g27Go2cXaHXUZ5tUuPfAiEO7cfUffL5gemSbbGo/\nvcer19rYeF1zMr3uBrJoPW1gib1ehXv7vmJRvhwztv/Pfu6diIGpED1/ToU1nXpClt34CWtetQK/\npVdR2LKsKwIFMLtm2GfO7h101yotywYZxOZ/WXBazOTK7z3fOxtswUOYutV49bYYf7orl+KRz+09\nPhVMxATnie1zFf5skA8DsRiQwXp5rkVall2L+V3bxKXQfm9N0Ov1746Zug8vUDcrdx0+FvpXI5l1\nbFw5sC9co0EpmtZU6XGGjkygc3o9vD8db53T64UxoIwg1yNS8MmPGOQl9LjUYguEl/KH0OCHsw8N\nhSwdXsog5Xi7cmBfznFa07hpeiNqUPSUrnxXQGMBVo2T5ZBSIVDBgAk+Q1Mu2fbyJKkpp7g42GAc\nDYDRNFEAcsEVkw8MY+nGWhCQ2Afav7xX+5HP1fRxbMP5h+8OASQaoMMABC/Qx2o/yeNH0woDU+zC\nz2AHdcy2bdb3Y7n9CA1QUC45raeabAm7cXoaB743FRhijvOWl4/w/I6s8KtBFxqsYx3XdXzz2eqM\nrt/b7Dy2XzjPqEnWNGG8hhuUCvIx/jp1xOe7V7O2BlrYFHZKt6QCiw3M0f61Y5lBLnZjt0FSMQ08\n0BCWvfRltgzrJuAdKuyY14Asy5nIuigXps5t5enTtnk+oxrYpOsgA6M4H7Sv7WFb28s0hEoq7nEi\namDQ+NNdIW0hkB87GgzH9VLry7711kuWo2VoIJ8NNOPfyqkb4/v0/HZV8OJ6xRSNXoAdqb5sf8S0\n2UCeC7QsTacNKATynKRa/8XBdrzwR29aapvXHHySBMMfIdTBVaMQYxGzhBchq99bgcBu7Dr5dRMA\nimY9XdSBolkgtoF6sBs3hUIbPavt8yLrYs7ZOrFtBKw1QWgfabspNHHziEX/6ulTFyPdGKzpxPY5\n0SywRLOmWFNJWYYZ1gcoajJUMLO/a3s8qqDY2LDwIhpZZrN7rWBIDaeNUPTI3i28+eRFJcfeix3X\nVsOoc8aLeoxFGJdFf9p5Zt8/77d1YD2AolbQbp5ePmLWF2iMHY2KV+hmH6s/EYsO9caI9hV9WS3s\nQQaIB2opibK2l/DSQsaCiSzliQoSQFErznSkhL4TTzDU+tr3ZGnIbHstS8L4010A6sFl3viLCWqa\n6zmmVbXWCft+CXvAVdjxyCBBJf/X9nl7ldcGu37Z77TMWF/afcLW/02abzlFJb+ZoNo09dPzohK5\nofUenwoRsvye/iWzewfDpqNUNS892u/yHPLZ1q+GC2n/wedzqn8VeKxZjfXhQmnJjQk+m4uAbafd\ntMtyq9q/+UxG3PFe/q6cW15ZOx97IZrWz4vOBuqL2tkHWwvmIY0MBIrmrMXB9kJaKF4Xi0qd3Tvo\nmjOtHx0XWl5nfeAIak08+pbqVD2dlmfC1TpwsW7GEcky7UJ8YU8V4/d3RLn6NLKTsH1sffPsRqLm\nKKDoGws03qPXDutzChQFW8sRyrFon61BM96m3XX4WPB1JShgqDlM62I3M2sejvEx8j16wvWOE4sh\nW42WqW1Q8Do+i/+rEOvVQ31dY7B9bV1pKEDxvdr+0HJi8zs256wwGePGszyQo4cmCzx9QL293Z/t\nRvdnuwtzi3ORc8Gu13bOsb1kouBnsg1ou7zDD02+XvusKwfXDs/f1LveQtcoPRy0TVwqCIRad14H\nNN47NXm2Lsq5yvVa5zOjsFeG+0JfqmZSzejN8jlfL0hRyT9k3PXRp3Dw6Nfxfz17LESGMqKV0YTf\nOdCHrpl8MnpGnzKSlj6Ga+++BV3/7vvAr7wCoKECb1+oR4Bu/dyLIap1x9EFVHp7MPnAcIgGrBw9\nibbTE+j6+vdCFGLl6En8YP8IFt53My7vWsXbqiOoTi3jbZ//BtpO1yfS+j13YmHfzqA5YyTc7N5B\nVBcqaJ+cx7mP76qbWBYqof7813luFX2n6osoo/AYVc2o4gt7qqi23oBsfDr8a620YXbvICpZa7hv\ncbA9RMbNfPjWnMmq2noDph9ZQcfprrrPYtYa+rTS2xMiiLn4tC7Woy7Pvb81RFuyXqwjoxAZAX3m\nF7ox+NwWbP1OBZ0vz4QITEba9Z6vH9TI5cXISS5crZW2EC25NjaOb//KHRg9NBmetfbuW7DjKzPo\nOzGf2+xUk8Wow7MPDYWxM/AXF0OkJdvdPjmPSm8PXnq0Hz/2O+fqUc5qitq2PbSVEeEAwhhaGe5D\n58szIaK4+8wczvxCN37sd85hy9xSLsr6andHiMjkd0TbxCV0n5nLmUPXOuvCz+rWFkx97GZs/3Yl\nRJq2TVyqR0BW2nDu47vQ97sv1COK312PnmYkLK9ntO/V7g4s3tQaIkivdncgG5/G1MdurvdLy1a0\nbNseom8v/ERdy7L1O5UQzfi2z38jvLNsfBp4+xDaTk+g2npDbty2fO00VnYNh7bWRgZyz94ytxQi\nMoF61Pbl0dYQ6T27dzDcy4h4ltNzdg2t82uYvu+GEGnZPjmP9Z4urOwaDlG87ZPz4X0v3tSKbS+e\nz80xRpa2TVzC+uxlrN9zJ1a3toTI3HMf34XOc6vh/bAfL71nCy69Zwt+7HfOoXbqTK5+7IPZvYNh\nDmi06urWFrRdqRX6h4dfjhvWnd8xcrR9oSW0pX2hBVm2EVD29iGsdjWUIF1f/x6y8Wl0r2zH9H03\nYLUrw3pPF9on58O4Z3T/dw70hUhqRqKSXUAjx1nP9oUWzHz4VvS+soTVrS1h3SOJPZ/BdzL7jjbs\nOLGYi7xmZDqFlKn9VzF/aw3bZm8MkecaJf+37x7B4k2tIVq9faElREjz3/R9N2D4yRfw7V+5Azu+\nMoO1d9+CnrN1loBtv/eNENUPbFgzzq025sVgexjjrfNr4R/byTnVOr9W7/uNNb3vd18I6wTb8rbP\nfwNr774lrGm8npHo0/fdgM5zq5i/fRvaJ+dD1L2+87aJS9j2By/ju5+4Jay9nPeMygbqLAdtV2rh\nmbq2sL60dGgbLuyp4vvvaQnrSmulrW4e3ujj2qkz2P7tCrr/5DS+/St3YPs36+1YGe7D9H03YNuL\n58PY+MPf+CL+8De+iH/3wrfw0H/nB+Jdg0hRydcqrAnNRlupRqnMx7D/4PPY+lfb0fNkQ2ukye4Z\nuAEUGeGbmR95OmbKK+vHqFlMbNSdgn43MTOCp5Wh9swGgMSeYfvIpraiucb6LxExMlugERFtYa9n\nijeCp0zrDK8+l0BRc0LNgZoLWXcgry1W0PHaY/An96NtNwmkrUmM7bWaO5vajf1rfUS9qGTeZzWa\nBLU3lpzWtof3xQI5rDM8Yc3oLTtHMHposvA8oO7W8M5PvpjLMMOy2yYa3IExDbZ9p1Yzau+zWkAi\nlt0IaETpepom79kWti5Wg14YKxvaHOvywT65sKdaCNRhgIUdRzEuymZmfduPXtu86H8gn0FDQW0t\ny4qZG1kXex3rbNtkNba2Dbzfasio8YvB8ynmXODawjqrP54i5ubjRf57ml1qlr29qXL0JLoOHyuU\npethdaqR4k/HPCOntS0cO3yW1XxfObAvF/mudbq4O8tp/oiOmQyTDwwX1jPWkf3POth3bxEjyX+r\nIQmGP0Tsv/eJnAmjbaKe5eGlR/tDJGrHTBaS2QN504b69HBRP/ebo5j/iYvBj8max6hB5H06GdX3\nLua/R6FnbWwcr3zmvXjlM+8tpB6jul5NJvY53oKkQqzn8M1Fj5uk3cjoAE7YBYkCgZpUCM+sokTY\n1mxJgZX3WIFKy/XaYH0fWVebnzaWs9qLkPWgGRn0GqUF0jHilVM5ejInxLKOvN5msKHAYKN91fVg\nbWw85I+1FEXWRYFjqGMmy/WHvmv7DAt9D3aDo2lcN/RY5CWvuXJgX+75nCf2/fEgwvLKiIIJrYvO\nP5032k41+3p0LMxZbuEJfPZ7Nc/GqGXsmkEqJxvhbg84luDYzpVmwiCh1EeeSV+vtxs3x7Cd37a/\nOA6aHVDX77lzU/6thA2miZlPgUZO5GZsBLZONiKe6D/4PM4/fHeBXsnmMbb+5CzbjmH93VKcqbvD\n0JGJMEY0CphC4uzewcJa3zGT5YKEAjWacVXgGmQP/hx7+t2OE4sFH3oNIFOKMvZT5ejJIHza9ZK0\nR9cDnU0yJf8Q8IHKR/DMr30umF7aJi6hduoMvv0rd2DLYgX9x+o5JGtZPUiEpJ80e1DtT4JVmlUv\nLewGALRs247x+zvQNVNXv5Os+vzDd9dJYRdawv2t83mS7JXhvmCqC6bcDdNH36l1dL48g/nbt2Hs\n4Ztwx5PnsePoAib+/RCy2o+F8nhv9QvfQu/5DGtj44GIt3bqTF2jtUFCqyYtjfZS81bLzpFgZiQ5\ncsu27TlTsJLKAgjE2bWRgfrCt0HkSwLnq90d9ZylPV1YHtoaTMVdM/XyzvxCN3pOt6L3laVgiiCZ\nb8vXTtd5vjZIg1e3tqDla6exPnsZQJ3Ulmbl6fvq5sUdJxaDGaJ26gzW77kz18/tk/P4zoE+jB6a\nDP3A901wU6HpvfPlmbqJ+gvfwtjjdwVTS/vkPLbMLaFrpjUQ0QIIJOXsm7V334K2iUu4tKcbo4cm\nc2TKLdu2Ixufxvo9d4ax0XdiHrVTZzD7Uzeja6Y1fE8z1vLQVtz8H6ZDXdmGtbHxHLltNj6N8w/f\njS1/0BHIuNXk/LbPfwPZ+HTYFFa7Muz87CTmb+sOpjclqCXUrN4+OY+5D74rkC8DCOP8u5+4BYv9\nGVoX6ybt8fs70PuliTA/aPZaGe4LdV3rRCDqba20YXloa9iMaBbeMreES3u60f0npwPR9JW7r+JS\nT1cgLV54381Y7cqC+ZcmLbpxrOwaRnWhgvXZy5j62M3BDYCEzOuzl7Gwb2eONDyQUL/7FmTj04H4\nm32ysqtOJJyNT+dJ4zfum907GEx40/fdgPnbupFlW8J9SoSu8+XSnm50zdRNzhyrXD9IaPyD/SM5\nc+WFuzLM31pD/9dWcHm0Fdu/XQnuKnRPAOASapM4ve/EPOZv34aJD9Wfz2tITrz1cy/iu5+4BV0z\nrcEcO39bN4A6MfuNX6pn+uhe2R7qubBvJ7Z/czmYCM99fBe+/54WXNrTjb4T9bHU8rXTwNuH0Pny\nDCq9PZi+74ZAfH3u/a2otGzF6taW0JecByTLnviZugn+akt7uI/rb9fXv4eZD98avidmPnwrqq03\nBHcIALm6zL6jDdUvfCsQ5gMIpPkt27Zj/vZtYfxw3eIewr46//Dd2Pq5F8O4al1swcXdGQb/bCpc\ny7oqmfXsO9rCeGifnA+uAZx/nINAXXCj2ZjzCqib+zlGOJda59eCGf/7P96Damvd7Nx5bjUQu1cX\n6vmf31YdwXc/nGHgLy7W3QOy1mCinn1HW3ChIok4hUJNRtB2pRbIuc/9PWClbxuGjkyEsVDprScE\nAOrCdfUL38LC+27GwvtuDm5BK8N92Pbi+eA2cOR//GP84W98Ef/4n/99XMNIpuRrDUqdQu0bUNfw\nXNydYfTQpHs6nHxgOPhLqHmY5ZGnzObutKShSl0B1E/vm0kezs2XWiFGusWiChlFaE+AMVORjSgu\ni9xVglgVCkm6rQnsFTz1WXPA6KHJIJharjugro3xnKjZFprcbduUHwsoamOtRkWjCvV/rb/eR82L\nvc9qVmykpD1NW9hAGZbLsWU1ECxXaUUUHCMxMmzAJ/Tl2Lm8a9Utl1yW+gyLZkEwMS0P6xrrI9vH\n9jqrnY7NP6/dCo6pMpMyEDdpx9png18s9F155rPFwfbovTaaWdE2cSmMo9i7seNciZuBohbfmsRt\nmlDCBi9YrT3XEpr1NZjDg+W+8zSfs3sHC9pAS5zskdnTP9qC46Bzet2dTy07R1zzL4NRbNs1QK86\ntey6VbCNGryhFqHzD98dNaOz3GZcsfocwI8QZzuA+pqsLg3WvBwLgrPXcawMPrcFl3et4qVH+3N5\nutnf3JNsyjzuG9WpZXROr0fnxFsFia7mdcSHbn0EK8N9OWGFAiH5mqypEWhwA1L1D+SpJJRzytJY\nkEtt6MhELnG5pZVRrigg7s+oizQXBaWKsPeTIkcFR6rrSeehZmM1eSqHmlJp9B98PscrpfViR1Mr\nPgAAIABJREFUGcoNCNR9RK4c2FfgkrPPZX96NCPkedTcx0raq/6JHt2D5eljvZXigfXS928FM6BI\nZ8S2KJWFpWCx75muBtRSap1ZFx1bhKWG0SwhHmej8mCqWUrpQvi90vvc9Itnc2TNHDNKn6FtIw8k\nkE+Jp+CBQbnM6ELB/rtyYB+m9l/N5T9W05R9Z8qLt37PnaU8f94B56VH+/HOT75Y6Fed66yfRlxq\n0MIdT54vzAFtj+XZ5DhWlwalo+FvrIMKKJbHznIuXtydBT5OWycAuWcrA4PluNOy+E45jz0KEq2H\nnbcc+0NHJvDSo/0YfWY1t0Zx7nIslNGs2MOo8hVqvTiPWV+uKzpHvf7x6HTUL9b2N59v88yzzaTI\n0bVA571VLhAs0wralotTuTU7ZrLcWNGkCOwfe58+V9der5+5f+heqJyslkuUUHcXSznD9zT2+F1h\nfGn/czwsDFTQOb0eMgVZlxm7Z+q7vUbpbF4zXU1L80sSNoP99z6BNhT52HiKtL5HvRv3cXBZKobA\nK2VpbXZdzpVD2NRldvKob4aHIjVC3q8slorPfu85pQPKS+drxwgvu4uWUzitbzDmxzQtQasQ+T7m\na8l2WaoQIuZzSPD7xcgJ2uOpIzyOS0WMXFbrHXvPMa0Hn+tRFBGqUfJ+j3EjEpWjJ9E5WHxPFFRi\n5QLF4BiFClE6DlSQ9Hw6VaC1Gm0grxnmeNHxquUrVGBisM4rn3kvBp8r1p3jfW1sHBhu0Eaxntyk\nKOwApHpBrr2zewfRi+J4pIBWOXoSQxMjhfnJDVgFDAWDyZr5K9rxpMFNVRlXev/i4CC2n6q5/sYq\nkC4OFsc6BfQYzj7YijueLH6/fs+dwMSl3MHI1kv9ij0/u7IAhMXBdvRGtLcst5Har/HbwkAlpKEE\niryUO04sRtd2llmd8gUYJb62UGvPZKR8nTONOtZh+88bm5oty6tDrF6WZ5PwuDF1LhcDFvMa9bB2\nyzW9x6ew8MAwFgYqGH3Gt0p4hwm+0/33PnGtCoevCcmU/Dpg/71P5LRAsRRhVojiQONEttpCggN5\n6k/vANAwX9H0yYlM512bmcJGltrnE1YYsqYlDR7R6+wJcMeJRZdQWFOo2dM0kN/UvcV38oHhcKK0\nXFWsh552bfvWnQ1KYbWFMcQilxlo5AllMW2h4vzDd0fNWUzPFsv2EQtA4EYfExQtN6AFv49F6fH7\n2O/WjEdwzPA+2yfB+dzJqgM0xrodJ83SjbGPKGQ1iz60Y5T970VGep9tBDtBS0Kz1HX2/phJjoi9\nRzVNAsXocq4ZlreOsNd7/JxAPOjGpluziGm1gPq6RQGZri0KapNj6Jxej8656tSyKwDaenvjZHbv\nYGlQFF1hYgJs7F0Rql2L/b7jxKIbOMdUlt6853exVJC8j9+z/pxzrBf7xo4dBp2x7py7DCSxhwnl\nIdT5ZvuH2sKYmxJ5fC34bkcPTWLs8btc87G2w+5v/Bz24Y2xaMfMWykoJZmS/46466NP5VjgPYZ4\nL+2OQs2pHKxzH5vDyKeu5AQ7Xkf/OTuAPXMI0Jj41MzYlGl2gNMHkmXbVGL6vZoj+Wybbsm2QU1x\ndkHtOnwMY4/fFcwgBM1EJPJmSiVunGrSoCma3xOev6I+l1ATnH5HaJ9YwcGmjCP03an/ivaLvtfZ\nvYOY2n8V7/zkiwDyAoQ1V9GcpSZY+15Y74WBSi5dn22D1kHNfmcfbA3m0N7jUzkNFuCnrSJoMgSK\nfmOEZ3rnPTRfaR0BFMYioSZVoJFxRP1atY6anguoawJHD00W7qN2Rd03WGc16ep9NI1resSuw8fw\nymfei9FnVgumfGt2IzhPNY2lPpvtta4ZehiiqQxAzlym64fN7KFjra713JJ7N2rC1HnFccb1RseU\njku+D7rBeGZHvu/Lu+oUOuNPd2HkU1cKB1NNOalpL63pVq0EHONMB6d9zXtsOjk9dKoJ2RIv20Og\nPdjzGiCfGk8RIwe3Fgudzzr+7TsB8mkBNW2gZoNiajmOeZpimXKVfaPru77DnicnsPRgNbxv9j3H\nvb5f3fcU7HsVkO36SXgWIF1LbMYkdbux6V091xutE9t89sHWnMsCUJ8D11AKvZQS740AE21bIcH6\nxDSDd9/4011hAfFSc6lg6G0qOlh1cbJ+GxZc8K0PI2GFHrsply3CXl3t5LMCBE+Z6oDMSanf66nX\nEwzt5NU6WljhCoDbRjUlAEWBxfrdNfudsIuZXTTtIhdL52S1BXpAKBMMtY5AXltEwUAFKevvZeuk\n2iUbNGXr6gnaQLGPyg5Feh+hvr1WyAeKOVet9t2mE4zNeQA54a3Ml9SmzrMCbUyLxTlitahlgrnW\nq1k6MMIKmbbO3n38zgrOFio0Ka2NHhysQAD46w9QFKBiKT/tukRQ42hN6Z5Awbp5z7WHMes3zLZ7\nc1TruJmDrfUN9nwFdQxZAV4FaqCx5lstveXcZR95a7zmOI4FDmpfaTksq2z9o29wjI/W85P1fqcg\nb+cE+8IGTlmf9JhVkLhGhMOUEu9HjQ/dWn/xdrJVjp50SYm9FGgerFBoo8ti5spmZgmSwZJnKubr\nMXpoMhqh2Tm97vJbETZyNGb2JNgGai/YZ3ZxVm5FmlQBFKIA2baYv+HKcJ3L0Hs/BDUcFARsP9GM\nbRdVtsVuXDTXcEEhibjWWXFhTzXHD6nR6EB8YyNoUl4cbI++p/MP311qYrJ1otaSwRq9x6dwx//P\n3rvHxnlleWK/KlaVyGKx+BAlUsUSTRly+0FHLchovdo98LQzXnWAEdwBRugG1g4SONsJgtV2bw+C\neNdBZrGeNTbYHgceIEBjDWMCJ+gZGejJ2oPYnoWdzo5syZKhFhTLjjxcm02TFElJbL6qyC5Sxfzx\n8XfrfOc791bJHvd02zqAQJFV33df55577nn8zjOzCd7Upbw4xxSy/KlL1pG4J3KTNjA253rmhzXT\npSiflVhqkuS8McvQIu3i5py4A2Srfe1m0tmWvIiRJzk3PiWu/uD+WIyb7l9+es2VC6w/uN/MWB17\nLBvDRFz67lLscz3/+oKklRb2Ve9n9k3Lsvz0mgsnAew4tIWDJTcnWt4QDN+3NhPPFjDxbCGBTSmJ\nsoDE/SNdv5LHdB+aZb+zXb3/dX9Cmc4S5FkTZYyFCdtzbtphhfpAvgF/3KcOCdLylnOh9zMVRZ1B\n79vPPCso3/XYKef0HBF1YvbkUcyePBqTt0AkQzfGJ1w5SyAZg0wrJsfIPsqx56fXErJOX7ZIei9o\n+aRd2NQPflvpNo7hpyBmHxPniZhOxPuSuGEb4xMOb+3GAxHe1tw3ujD82qrDBctNRlh3xMrrnBpy\nfwOAjfv3RArnbMrhqbH0UK3c57D8JG4i2yZOYK3c50qWEaes9Mp0hH3V2+9KQ5H4/c4P5lDvLmDn\nm1MOR4q4blPHy+j5cBWbl640yn5tvYel+IjfVl9YxIc//hq2/9U0Zk8eRe/52cg9cXIX9r647rD4\n0pkIv47YZ9vywzG3dLqnG5PfKqKtmkbvn73rsL2KV5awcLDk8Oeyyxuxclfyps/yetl0LsIM6+13\n+HUAXNk84kkCUfmzq4+Pur+nT1+MlbJbOFjCzjcjFwTnBgBwxxC2vfouAGD6vxrEV753vlFqbguP\niyXk6CYpXllyuFrZdA7tU8sOn41YhSz3tnxPLyqDafS9EJXJ6nlzEuNPH0F+NhKwxHnjHC3fXcTA\nc287PmVpQ84RS6pJHph79E60X4uUczlG4hfKEn+cP5awA6LyaX0XlhslDXdlkX/9Pcev6dMXsfTI\nvagOpFxJQu4hYmxS8HePbWDl6E0M/2AFANze436QVF9YdIrT8t1Fh5NIPr9Z7MDYY1ks37mJ9us5\ntw47fhbhb6ZSbchdnsTSI/c6/DQgwoz71X/yK2z+sj9amy38NuIpcg43xidQObQb+ex2V94OAPLZ\n7bESbMRuIwYl9xf7yFJilDES16+6K4vKod3AHUNOftz4/SFs/6tpxz+Lx3IYeOEG5r7RhY1OIFtJ\nJcr2ZXr73byTt7h3AODq46NYvrsY4w/2bf5AEavlSLb1fNiQIcSrA4CFu3IxbL/1rghLL9Mf4VCy\nBCS/z3nmvhh47m2HKddxuYCVozfROTXk8DN/8WgKfZfqqJbaY3uDuHrVXRFmKfH9WE6xvrDo9n1h\nLutw9gC4fQvA8TJLJgJA7vIkMv1ROc2+Cw35T7lL7MeN+/egcngE610Z/OLRFLrHt6G6K+v2Qnsl\n47BO14a6HAasxK6UGJDsj9zD+UralS6sP7jfYSb2vXAGucuTET5rb7+TB7JM3Y0HutHzHzdj5ep2\n/KxR7rR4ZcmVKyz+9DI27t/jnqsc2h3HBMx0Ofxa8m22FvV7+uGbaL+ew843p2Jl/rgmxH1dvqfX\ntVu8suRkZH56DX2X6mi/nkNttIxd//ocehd2YuyxLArjbbjx1QxKr0w7mUY51ba06vAHi1eW3Dil\nnGb5u43796D3zxolMckPsozrR394nytXut6VwXpXxp2PNx7oRt8LZ7Bx/x78+b/8d3/fOIe3cQx/\nXcSbgL6BkLSVRmPLDb086UqvbYxPJKwiuvyQlVSgoVNC2XlA0gKg41N8sXfp0xfNJBL2YceFqjc+\nRAYuZ0aGXbA9D2pXDk5Z/XzJBPpWLF3dVt9JtXKfC6bWlgv5jJxz3iK1dYB/53zrmzbnWVcKyYwM\nY/bkUTdWn2stRBonUhPdcfyprbY6+72Z1ddnyWiGiyfbaPVz9pEWRV8b/JzWdAsDVFq0Q5aUZtVC\nrCxn+Tn7wLYS2fJbv/tw2kLzx8+njpdNjEAZrN85U0+EhTC8gpaY0rffj33OzFK9H8i3/HuzPvqs\nbUBDPl7flzITAsifoeQK2RftXuf8uzF6knx8iXSSZIUji3TpOsoyEuUA36FlnN7bsuISEM2Vbz+y\n/dmTR4PemoWDJdQf3O/2v+YJn6dBuv4lcSwSlaFW7vNausnnDB2x5FnpjbZY/KYv5MWH+KDdus7i\nvCVXZUKalUkv58Q3j7nJ+dgcyb0m++zz+Okz4rfVcnhbMbwF4iL7hA2ZRm8yHTBOIgOOPTGEsSeG\nEgcZmW/86SMum8pS3kjSvK1dVlop5CHLPvjeS4HCUn6Wiw+Aq5Mq+6iFEzdw50wdKycOe+MPOY8W\nll2t3OcOIn1o00VMV1Szg027KOQ8TG1BF+Sn11B/cH/iMLAUNHnQyuQeiziPVh+47roN7apne0Mv\nT2Lv81MYeeqM+8c25HO1cp+b88Kps0GXuiZLAQEah6BWyNiOFO5UzuW42EcLV5LU7OLDNlimTY9J\nl1G7diCP2ZNHkRkZxn3PzGLvi+uxLEvpouTfdElIkm5Lx+PpcVqKIktzSV5In76Igefejn1f7lEZ\nJxYCFpd7QLv05XvYbxnGIJ/X/Zbryox8wM7OtVz6vouQbp9uaUlsg3uo59w0ru9LOauyD+y4GfF9\nvpKeQGO9KQ8qg2kTb1UrhxzL3hfXsffFdW82P/mO+8nKtraUGjlnfKZzph4r+6Zlt84qlooa51X+\nnSR5mXG0oTJ+1/elErXIfcoh38PPfe/leCnr2RdfiIklZ32ky1LqnzrGUgN7U75xbL+NyuHt5JMW\niYkmFjgt0AjK1gHkOpONWXZWnKDEEmR2lAzm1QJPK5xsW2JTyWw7+YwMQJdWQTK43Mi1HRsJPEZm\nBvsUi2YJGrIPQCMj28ru80FcyD77kkNIzNxlf7TAteYI8Ae7k3SAtOxzSBDlJucTmb2aH7TQ1ADa\nFq6WfFa2obP0ZD/lLV7HTjZLFpFZ4vJ5vlv3LWQZ8SXPMCNYZghrIq6d3HfycKclZeSpM7F3afIl\nbsgkJu5jZnQCcauZXFfZhk5ckFmisg3ATujRmdRAHPPQ128LBcCXPLPrH48BAFYfi8eNyYQJIJnc\nIxVDzUMWNqLVV4l+AMTnRcoaOf8kuf80T1tt6zZ5GZOg0ONPHzFlL7PK73tm1oExy0QP3/hIUgZL\nntW0cLAUS8azEpw4Rz7jgy8hkgllBE737W+gscf1uWUlXrENneUNwGUtW4D+QCNZRmb+Asm9wORD\nJqHIvpB0kgh/l5W5fOgSsthE50w9Bprve6dVLUavxasf/Qi/ZrqdfPJ5EjV+fTOnMKRSyM3Gw0Lf\n8FnODrBvsdIqw4OGgkne6GVf9I2TCSa1cl/C3E0hM/TyZOz2qE332qroyuNtCfqhlycTEDWaes5N\nozKYNk36HCuQPGB8WWAhJcuXgUaSwfxyHBRc/Mm59blCQ0qN7K+lFIbc2HzO+txnuWhmDQX8rhgd\nfO7DbSQPhsq5kf900L3ut8+aTqultJRokqXXLKVQJ0fwHXyO+5HrHHJ106rpu4zohApfolYruH5D\nL08mAIOBxnzrbFD9btln+VN/16d4AI11otXt//1/7jI/1/ym5Y4uG2eRVhg1cW2ZoOXDPmxm+eHn\nlgtbyzxnudoRh8DXnhbN30zI8uFwhp7Vn5M4x1oOk8d0Eock8lEIr1F+zouLxqf0hRGw8kuzhBkg\nmtO9z08lxq3B5jnHGk9w5cThWKiHVWXoK987j8XR9YTs0gqg7x3SYmmdUTzjK4NpZEaGY1BgMusb\ngPNSkTSSAcf122Q5vJ180oR+L/0H2Lh/D7LLUYHudE+3C4ivltpRGy1jvSuDjx7Po/tyFtd/v4zh\n11ajAFohCDdTaRdA7ZJGtgKBZaIHg6UZGM3A45UThx0OWX56DWOPZbH79V/F4gPzlTQWDpaQTkVZ\nicVaP7rHNnD161n0/3wN3WMbqO7KYvnuItorGVf4Xga/M9GjWOtH+vRF9H+Udha24ddW0Xs+uiUz\nCYFBuR+f6HMF6UkscM6g6M3hwSigf6uoOW+g0lq47dV3kentBxDHdWQQcHZ5A9tefRe5y5MuGJuC\nhgHzLPbOJJNqqR35SuOQ6LuwjHSmK9rs/VGW8cJdOQy9PBklEfREgfQAXEKDtELeeKAb64UUciub\nLnFl4lgHdv5pZL1Z78pg4a6cC/CXimK1FBWp7zk3jR2nK5h5aDu6XooOGY6HbWWXN7A5POjW6cZX\nMyj9zapLPOB8/OLRFAbeqrnxc87rD+5H36W645F0KuuSfPg9JrasF1LY+eYUNi9dwebwIBb3NgLq\nl+8uOp5lcP/yPb0u2YIWKe4RJjTkK2mXDMQ2ZVtrQ10uCD53eRL1hUXURqNg/h0/m4tcVFtJTQzW\nL7zzCVZOHEZttIxfPjyMyqHdLkCdQeVrQ10ucSGbzmH+QBEjT51BbbSMfCWN+sIi5h69043p4xN9\nMb5dG+oCABfwzjVc74r4OT+9Fn22xVPFn152+7htaRU7TldckkJttIy1oS73e2piJsaL8weKqA6k\n0P/ztVhCCRMtmJRTmMs6/gEiZYMJBUxIaVtadYH6hVNnXdKBTFphUhb3jUxs6LuwjPkDRdRf6UM6\nlcXyPb3IXZ50e1dT7/nZKJh/Sx5eO5B3CToAsONncyj+9DJylycx/d3d6B7bwMJdOWx0Rp+R9zO9\n/Vjvyrg9fe0bBfxqZx07Tldc0g3ncPJbRSzuzaJ7bAOpiRkAET5g719vYuGuHHrPzzpeaK9E+3C9\nkELPh6uJJALKibWhLizfuYmbnXUs3tODHT+bc3KC3033dCPzVjQWJsEBwMxD26PkonTOfZ5N59z+\n4hxyLQCg58NVlwS1cf+eWKIPkwmZ0Fcr5tBeyUQW275eXD+0geU7N3HH//gOemZTSKeyuPr1iDdK\nf7MaJZ8sLLpkIa5HbnLeybaN8Qlk0zl0j29D+/Wc4wfKiGqp3SVvkB8pG+vdBax3Zdzez03Ou4RE\n+X8mkGTeupyYq2sH8i7hJt3TjXQqi8rhEdRGyyicOot8JY10T7c7/5iYsjk8iJmHtmP57iIK73yC\n7X81jcI7n+Dq46Poeuk8NocHUTk84s4QvnPbq++icngEmd5+l/hE4p5ceuRerHdl0PnBHJbvLmLH\nhao7qzJvXW4ohT3dLhl04/49yKZzzvLIsd8sdri9sXCwFO3TrcSw/+2Nv8V/8V/+TmIvfU50O/nk\n86DfS/8BACRiTiyLAqE8eCvSt2NZ+krehqwUfyC68ch/QMPKphHkdQIG301YAB+oMMci25ClrGT/\n+A7egvRNrf9SspyWJsataGunvt2RdIydZYUKQTJYCSckGR8CJM3+Qy9PumLp3Pjaba7XWEPLaOuu\nD9+SFU/YlnyGpGExNJEnyF8+mAzOmXXrZ9vaoqMrAuiYG6staaUiNIgkXYqORKs2rWTp0xcd/MzQ\ny5Om9SsUSA40LC4+TDq5P0IQNpK0lV0n7bQau7n3+amEJYX7guPyhZJwPKGEofz0WiJ2TH5Xx4Jy\nrnTyTbM4TyCST7KPGqeQfGVVaJJt3ffMLLovZ4MViPguvluXHNVx4NrqzfFzDktvtCF3LVwh1md5\n1RZebbWjfGXMMnna6o8FTyY/776cddZK+X2SjCnk55pvtDVU7x8ZNjFxrCNoYa+V+9w5Y/VHzxm/\n56vg40uuI2kYIiAJCabDevi79EYREke3x7m4diAfk/l6TTXouZ5Dyli+Q8IKUa/4TabbimETokmZ\nm00mAJC5KFy0eyV9+mIsGYDv0thmFNghV6VsE0gW+CYD68NPZthWS+0OB9EiPjv+9JEYI3MTWy4s\nS/AQB5AKNZNnLNKZvzohhRvLirnS7/AR50wqRZYy41OY+BnHBjQOQd12yO3aDDNPu56kgjb82qrp\ntqyW2nHfM7O475nZRCISkDzQ2WeNPSYzqPc+P4X+S5uxRBygIRy1Uk2yFHfyrJXFKJ/nevBywT0j\ncf0kycB5rbRrN6G8bEnSLlhmATfjJyIKyH6T5JpZigS/zz0iM4/ZrlbM9WGr45ylwsc51XFQzLzV\nCohWRIBGGIiklROHY/MicTJ9SiP7R8WW/LvjQjWxD7Wrc+jlSfc9+bkOsQGA2uUGjIuFmQcklVZJ\nHCvf3SwjX5JWUohA4MNBle8KJWxYJEOXZD+1XLAujwsHS7E2dWjH+08OxHhRu5iZDKOTg2TfNG/p\n84wKnFbufOuilVzZb+5lfq75SIYg+eKeSfSU6WQc9p987HM7y9Ac+c9HzTCHfxPodvKJQYwFYNCt\nJB3ET8pPr8UC4/Xiy5JuLKvFZ7SVSCpLVtCrvKlExeJnY0G7QNz1KTeorprADcYgdln1QRKDcBm4\nz34A8WoTHKOsPkKSMYlaIfT1m4KecBT8O2/edEFL0v0iWaj2XAM9BvaD7dMirDNz2fa1A3ms7tyM\nzZ1vnhifqYOrpcVh5cRhXN+XCpaQ00k38qDR65qbnI/xs4y9YfyQvB3TwiHH3Axcmy5lOV7Ora7e\no/th/V1fEuT7OI9AOGmFc0G+kRU5ZOxe/6VNVAbTLpFG7xPJnwy3kLwXqg7i43GGhrB8nK4VLvv7\n/pMDKL3RFru8SdLKgaxewbKJTKbQsaX6IJR9kO/qv7TpeFLuPV8SCNeCyQIAYiUsucZyH1qVPHxJ\nD/ydSQ2UTUxMkLJbV8SoltpjiTv6c7arE/tIshScVhZ0EqD8Xc63tOynT19037cUU86fhvcK7QHy\nj96/XDfNBzKRRfJcSA7p/lklE3kuaU+GPLuAeHlBwK56JOWCFT/I5yeOdWDkqTMJuDid6GUlzsjq\nSHqvyndJWSUvgTphi3xtJZG98R/+eWBWPzPdTj75u6aN8QlvGS69GQunzsYOLCtYlsoGhYIM1JXv\nImkLIIVK+vTFmFIo3+ErpaVveNrlK9HntVKoYVf0nEh3D8fmcz2w31TQfCXftFIoiUKW7/AphboA\nvHWDo/DiO7U7ikTXjRYMkuSYO2fq3rJjmixri8T1s/otMeKs5yRR8aOyrskXIO+zdFAhsfrlc7Xp\n7/rce5KkNQxIwliQQkkrJI6lWWa0lR3sI+2OI1meBR/5MA5J5P9W3uVzaYUyXn2kXdSauPc4n6Gs\naF/ymc+iYr1r4Lm3g7wiLZFAQzmxniGmqa8t3T+t1JFYecM370CDn9iOZV20vm/NjSwJCiQz29m+\nVp4tiKnCqbMxhYjzppUnthkKEeJ75MUdaFyoKKN8vCQtk/KC4Ou7bNMX5lAttWP4tdUI6N+zZ3wJ\nTRomh5ZEeXEm6Xr1PHO4P3SIx8b4RIz/fpPptmKo6Mh3fmSa+GXMnTQ7ayFqKYWaeAPXcQwkKwZN\n9kESN+/1fSkT51C6NPLTa03jAIFGfB03JgWaHlsoBkia9qU5n2MnPqDPqiiJihnnmsKG7i26rH1K\noSTefLl5JWZV50wdi6PrMYVUK4WStLVo7/NTCXBsGTcYGqOv3BgQ8RDjeHjY+QBWfe8gyVs22wzF\nEFlZxzLekfiVocxYkqWkzJ48ipUTh9E5U48qspy+GMzct4j7Vc453ZShw9/C9eM7hl9bRcdcyuEd\nAmFlyhqblAl0iRMfkzygMfv030i0FHHP9F/adGEq7L/sny9bWvarc6YeU1ZkdrjknZC1SCpZmZFh\nk7dr5T7X/1DspZwvubeBuFWzmaufYwMiGTv2WDZxyWw1BhSIK4dcS41ryr75yKccaiVVK3ihPSCV\nw8pgGlPHyzEFTO//UHa6VA5l6IfMDJexwpZstZRDlm6UYyRRtlpyyqccaguvjI9n/zXdinKYn14L\nxjkSTUADWevygZSLoThsoAGD95tGt13JgrhIWmj4XFRAMpBdxrTod1nmZMsFod+t+yHbkYe6Bahr\nuQmAuIDSrrlmOGMEEWX1AXkz53v5HZYu02OUbiLZPzlfErcvRL5Abh2jJ7/rc9+TpAvWRxrzUUML\nAclYrw9//LWYO0i7QzgflgtL84O2Nuvffa50IKk4+J71uR3lu5sF0ssDkxn1QNwK4ptL9tmK/7Jc\nTb52JWkXKYAE5pqeO75T877+vBXS75a8QdIWIgvbD7CxInUbvtAKX0IQEFfE5KXAx4POnpd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g8gyUupDnEgSW+R7pt8FvjM+Iaf2pX8pVcMSb64Mh0XCNwaELUvJsgXqyXb9GWAAc0tRBrQlbA4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ON/voJKg6b51K15+NAohd+2y/Y+KiA8BDrRzLkvHuWd4l8RDUbrU7gdbclPB5FMc0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n+ubLzq9jFnfZY2saBSXiQ9uyfeclyV91mKJc6e2ey821qRJdzEsDUIQ4AlTCRmAlHaZPbF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f59f2d62358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import healpy as hp\n",
    "def skymap(theta,phi,nside): \n",
    "    \"\"\"\n",
    "    creates healpix map of density on the sky\n",
    "    \"\"\"\n",
    "    ipix = hp.ang2pix(nside,theta,phi)\n",
    "    testmap = np.bincount(ipix,minlength=hp.nside2npix(nside))\n",
    "    return testmap\n",
    "        \n",
    "testmap = skymap(theta,phi,64)\n",
    "hp.mollview(testmap)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate the populations for the example. We begin with a small number of objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5000, 3) (500, 3)\n"
     ]
    }
   ],
   "source": [
    "# objects (obj)\n",
    "vec_obj,theta_obj,phi_obj = gen_points_sphere(5000) # ~500,000 in my real use case\n",
    "# contaminants (ps)\n",
    "vec_ps,theta_ps,phi_ps = gen_points_sphere(500) # ~50,000 in my real use case\n",
    "print(vec_obj.shape,vec_ps.shape)\n",
    "# maximum separation: \n",
    "maxsep_deg = 1.\n",
    "cos_maxsep = np.cos(np.deg2rad(maxsep_deg))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm:\n",
    "\n",
    "If we represent our points by 3D unit vectors, then $ \\cos (\\Delta \\sigma) = \\bf{n}_1 \\dot \\bf{n}_2$. We therefore only need compute one dot product per pair, which is faster then computing the great-circle distance.\n",
    "\n",
    "NB: For large N a k-d tree is more efficient (this is what the astropy version uses internally. But for the sake of having an example that is easy to implement, let's stick with the dot product (2)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1) Naive Python\n",
    "(we all know that for loops in Python are slow)\n",
    "\n",
    "NB: For convenience we are still using numpy arrays as input and output (we could do the same with lists though). The core of the computation is however in pure Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def angdistcut_python_naive(vec_obj,vec_ps,cos_maxsep):\n",
    "    nobj = vec_obj.shape[0]\n",
    "    nps = vec_ps.shape[0]\n",
    "    dim = vec_obj.shape[1]\n",
    "    #objects to be deleted\n",
    "    out = []\n",
    "    for i in range(nobj):\n",
    "        for j in range(nps):\n",
    "            cos = 0.\n",
    "            #compute dot product\n",
    "            for k in range(dim):\n",
    "                cos += vec_obj[i,k] * vec_ps[j,k]\n",
    "            #stop once we have found one contaminant\n",
    "            if cos > cos_maxsep:\n",
    "                out.append(i)\n",
    "                break   \n",
    "    return np.array(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4.19 s, sys: 8 ms, total: 4.2 s\n",
      "Wall time: 4.21 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result_python_naive = angdistcut_python_naive(vec_obj,vec_ps,cos_maxsep)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### NB: All timing-related statements may vary depending on your machine."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2) Numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a more sensible solution making use of the numpy-builtins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def angdistcut_numpy(vec_obj,vec_ps,cos_maxsep):\n",
    "    nobj = vec_obj.shape[0]\n",
    "    nps = vec_ps.shape[0]\n",
    "    # fast vectorized way to compute dot product\n",
    "    # (looses the advantage of stopping once one contaminant is found)\n",
    "    # (but the numpy speed gains easily outweigh that)\n",
    "    cos_arr = np.einsum('ik,jk->ij',vec_obj,vec_ps)\n",
    "    # number of contaminants per object\n",
    "    temp = (cos_arr > cos_maxsep).sum(axis=1)\n",
    "    #indices of objects that should be removed\n",
    "    out = np.flatnonzero(temp)\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 16 ms, sys: 4 ms, total: 20 ms\n",
      "Wall time: 17.1 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result_numpy = angdistcut_numpy(vec_obj,vec_ps,cos_maxsep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# check that results agree\n",
    "assert np.array_equal(result_python_naive,result_numpy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using numpy has given us a speed-up of a factor of ~200. This is quite typical for computations that can be vectorized efficiently."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05555555555555555"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# expected runtime for full sample (100 times as many objects and contaminants)\n",
    "20e-3*100*100/3600. #hours"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In terms of runtime, our problem is solved. However, we have not considered memory usage so far. For its vectorized computation to be efficient, numpy has to store everything in large arrays that are contiguous in memory. Simply to store the intermediate array *cos_arr* we need at least:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# double precision (64 bit = 8 byte per element)\n",
    "# Nobj*Nps*8 \n",
    "5e5*5e4*8/1e9 #in GB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our work desktops have 16 GB, so suddenly memory becomes the bottleneck. As soon as things need to be swapped from memory to the hard drive, things become *really* slow."
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "# only try this if you want to freeze your computer :)\n",
    "%%time\n",
    "vec_obj_new,_,_ = gen_points_sphere(500000)\n",
    "vec_ps_new,_,_ = gen_points_sphere(50000)\n",
    "test = angdistcut_numpy(vec_obj_new,vec_ps_new,cos_maxsep)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On top, some numpy functions allocate larger temporary arrays \"behind the scenes\", making this problem even worse. \n",
    "\n",
    "## Enter: python optimization tools\n",
    "- *numba* (numpy-aware just-in-time compiler)\n",
    "- *Cython* (Python/C hybrid language, creates compiled C extension)\n",
    "\n",
    "From my experience, the two above are the most mature and useful ones, but there are certainly other options, such as:\n",
    "- other JIT compilers (Hope, Pythran, PyPy,...)\n",
    "- scipy weave (importing C code into python). Deprecated!\n",
    "- ctypes (Python/C API for C extensions)\n",
    "- f2py (Fortran --> Python modules)\n",
    "- ...\n",
    "\n",
    "NB: The latter three require you to write C/C++ or Fortran code. If you are proficient in either of these, you might not run into the issue of having to optimize numerical Python code so frequently. It might still be worth learning, as Python (and also Cython) are much nicer to write than C/C++ or Fortran.\n",
    "\n",
    "#### Today I am only showing Cython, but it is worth knowing about the others."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Cython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cython is a super-set of Python. It allows static type definitions, translates our Python code into C code, which we can then compile and then import as an external library (.so on linux) back into Python. In Jupyter notebooks, all this can be done automatically behind the scenes. \n",
    "\n",
    "Outside of Jupyter notebooks, we need to write a very short Python Makefile that handles the compilation for us, see e.g. here:\n",
    "http://cython.readthedocs.io/en/latest/src/tutorial/cython_tutorial.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%load_ext Cython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Start: a cythonized version of the naive pure-Python implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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   "source": [
    "%%cython -a\n",
    "# -a provides annotation\n",
    "# yellow annotations: calls to Python --> slow\n",
    "# want to remove all yellow from our loops\n",
    "\n",
    "#Python functions,attributes from numpy\n",
    "import numpy as np\n",
    "# C functions,attributes\n",
    "cimport numpy as np\n",
    "# Cython handles the namespace ambiguity internally in this case\n",
    "\n",
    "def angdistcut_cython_naive(vec_obj, vec_ps, cos_maxsep):\n",
    "    nobj = vec_obj.shape[0]\n",
    "    nps = vec_ps.shape[0]\n",
    "    dim = vec_obj.shape[1]\n",
    "    #objects to be deleted\n",
    "    out = []\n",
    "    for i in range(nobj):\n",
    "        for j in range(nps):\n",
    "            cos = 0.\n",
    "            #compute dot product\n",
    "            for k in range(dim):\n",
    "                cos += vec_obj[i,k] * vec_ps[j,k]\n",
    "            #stop once we have found one contaminant\n",
    "            if cos > cos_maxsep:\n",
    "                out.append(i)\n",
    "                break   \n",
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   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.67 s, sys: 8 ms, total: 3.68 s\n",
      "Wall time: 3.66 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result_cython_naive = angdistcut_cython_naive(vec_obj,vec_ps,cos_maxsep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
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   "outputs": [],
   "source": [
    "assert np.array_equal(result_cython_naive,result_numpy)"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Essentially all Python code is valid Cython code. But without adding type definitions we get only a very small speed-up.\n",
    "\n",
    "### Adding static type definitions\n",
    "\n",
    "#### Here we make use of Cython's *typed memorview*. This is a container that provides fast access to numpy-like arrays in Cython.\n",
    "\n",
    "NB: I have also made one small change to the algorithm: instead of appending to a list I use an array to store which objects are flagged as contaminated, and at the end return the nonzero elements of that array (similar to the numpy case above.)"
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       "</pre><pre class=\"cython line score-4\" onclick='toggleDiv(this)'>+<span class=\"\">23</span>:             <span class=\"n\">cos</span> <span class=\"o\">=</span> <span class=\"p\">(</span><span class=\"n\">vec_obj</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span><span class=\"mf\">0</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">vec_ps</span><span class=\"p\">[</span><span class=\"n\">j</span><span class=\"p\">,</span><span class=\"mf\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span></pre>\n",
       "<pre class='cython code score-4 '>      __pyx_t_12 = __pyx_v_i;\n",
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       "      __pyx_t_14 = -1;\n",
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       "        if (unlikely(__pyx_t_12 &lt; 0)) __pyx_t_14 = 0;\n",
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       "      if (__pyx_t_13 &lt; 0) {\n",
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       "      __pyx_t_14 = -1;\n",
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       "</pre><pre class=\"cython line score-4\" onclick='toggleDiv(this)'>+<span class=\"\">24</span>:                    <span class=\"n\">vec_obj</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span><span class=\"mf\">1</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">vec_ps</span><span class=\"p\">[</span><span class=\"n\">j</span><span class=\"p\">,</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"o\">+</span></pre>\n",
       "<pre class='cython code score-4 '>      __pyx_t_17 = __pyx_v_i;\n",
       "      __pyx_t_18 = 1;\n",
       "      __pyx_t_14 = -1;\n",
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       "      } else if (unlikely(__pyx_t_17 &gt;= __pyx_v_vec_obj.shape[0])) __pyx_t_14 = 0;\n",
       "      if (__pyx_t_18 &lt; 0) {\n",
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       "      __pyx_t_14 = -1;\n",
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       "</pre><pre class=\"cython line score-4\" onclick='toggleDiv(this)'>+<span class=\"\">25</span>:                    <span class=\"n\">vec_obj</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span><span class=\"mf\">2</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">vec_ps</span><span class=\"p\">[</span><span class=\"n\">j</span><span class=\"p\">,</span><span class=\"mf\">2</span><span class=\"p\">])</span></pre>\n",
       "<pre class='cython code score-4 '>      __pyx_t_21 = __pyx_v_i;\n",
       "      __pyx_t_22 = 2;\n",
       "      __pyx_t_14 = -1;\n",
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       "      } else if (unlikely(__pyx_t_22 &gt;= __pyx_v_vec_obj.shape[1])) __pyx_t_14 = 1;\n",
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       "<pre class='cython code score-0 '>      __pyx_t_25 = ((__pyx_v_cos &gt; __pyx_v_cos_maxsep) != 0);\n",
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   "source": [
    "%%cython -a\n",
    "\n",
    "import numpy as np\n",
    "cimport numpy as np\n",
    "\n",
    "def angdistcut_cython_typed(double[:,::1] vec_obj, double[:,::1] vec_ps, double cos_maxsep):\n",
    "    \"\"\"\n",
    "    NB: double[:] --> \"typed memoryview\": gives fast access to numpy-like arrays in Cython\n",
    "    double[:,::1] --> 2D typed memoryview, with last index varying fastest\n",
    "    for this it needs to be C contigous\n",
    "    \"\"\"\n",
    "    \n",
    "    cdef:\n",
    "        int nps = vec_ps.shape[0]\n",
    "        int nobj = vec_obj.shape[0]\n",
    "        int dim = vec_obj.shape[1]\n",
    "        #use int array instead of list\n",
    "        int[:] found = np.zeros(nobj, np.int32)\n",
    "        int i,j\n",
    "        double cos\n",
    "\n",
    "    for i in range(nobj):\n",
    "        for j in range(nps):\n",
    "            cos = (vec_obj[i,0]*vec_ps[j,0] + \n",
    "                   vec_obj[i,1]*vec_ps[j,1] + \n",
    "                   vec_obj[i,2]*vec_ps[j,2])\n",
    "            if cos > cos_maxsep:\n",
    "                found[i] = 1\n",
    "                break\n",
    "    #convert result from typed memory view into array before returning \n",
    "    return np.flatnonzero(np.asarray(found))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the way we have created the input arrays, they are not C-contiguous (row-major ordering) in memory, but Fortran-contiguous (column-major ordering). If we simply input them into the Cython function, we would get an error.\n",
    "Of course we could have anticipated this when creating them, but is an instructive to do this here. (For Python this is never an issue.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#change memory ordering\n",
    "vec_obj_c = np.ascontiguousarray(vec_obj)\n",
    "vec_ps_c = np.ascontiguousarray(vec_ps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 12 ms, sys: 0 ns, total: 12 ms\n",
      "Wall time: 10.5 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result_cython_typed = angdistcut_cython_typed(vec_obj_c,vec_ps_c,cos_maxsep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "assert np.array_equal(result_cython_typed,result_numpy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a little typing effort, we are already at roughly the same speed as the (internally highly optimized!) numpy version.\n",
    "\n",
    "NB: again, this statement is somewhat platform dependent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's add some compiler directives to optimize our Cython function for even more speed-up.\n",
    "\n",
    "full overview of available directives:\n",
    "http://cython.readthedocs.io/en/latest/src/reference/compilation.html#compiler-directives"
   ]
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       "<div class=\"cython\"><pre class=\"cython line score-0\">&#xA0;<span class=\"\">01</span>: </pre>\n",
       "<pre class=\"cython line score-19\" onclick='toggleDiv(this)'>+<span class=\"\">02</span>: <span class=\"k\">import</span> <span class=\"nn\">numpy</span> <span class=\"k\">as</span> <span class=\"nn\">np</span></pre>\n",
       "<pre class='cython code score-19 '>  __pyx_t_1 = <span class='pyx_c_api'>__Pyx_Import</span>(__pyx_n_s_numpy, 0, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 2, __pyx_L1_error)\n",
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       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">03</span>: <span class=\"k\">cimport</span> <span class=\"nn\">numpy</span> <span class=\"k\">as</span> <span class=\"nn\">np</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">04</span>: <span class=\"k\">cimport</span> <span class=\"nn\">cython</span></pre>\n",
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       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">08</span>: <span class=\"nd\">@cython</span><span class=\"o\">.</span><span class=\"n\">nonecheck</span><span class=\"p\">(</span><span class=\"bp\">False</span><span class=\"p\">)</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">09</span>: <span class=\"nd\">@cython</span><span class=\"o\">.</span><span class=\"n\">cdivision</span><span class=\"p\">(</span><span class=\"bp\">True</span><span class=\"p\">)</span></pre>\n",
       "<pre class=\"cython line score-75\" onclick='toggleDiv(this)'>+<span class=\"\">10</span>: <span class=\"k\">def</span> <span class=\"nf\">angdistcut_cython_opt</span><span class=\"p\">(</span><span class=\"n\">double</span><span class=\"p\">[:,::</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"n\">vec_obj</span><span class=\"p\">,</span> <span class=\"n\">double</span><span class=\"p\">[:,::</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"n\">vec_ps</span><span class=\"p\">,</span> <span class=\"n\">double</span> <span class=\"n\">cos_maxsep</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-75 '>/* Python wrapper */\n",
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       "static char __pyx_doc_46_cython_magic_b93a464e795d8c6062607c0172b204b3_angdistcut_cython_opt[] = \"\\n    disabled some of the run-time checks, and also enabled C division\\n    the latter is pointless here, but can make large differences when divisions are involved\\n    \";\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_b93a464e795d8c6062607c0172b204b3_1angdistcut_cython_opt = {\"angdistcut_cython_opt\", (PyCFunction)__pyx_pw_46_cython_magic_b93a464e795d8c6062607c0172b204b3_1angdistcut_cython_opt, METH_VARARGS|METH_KEYWORDS, __pyx_doc_46_cython_magic_b93a464e795d8c6062607c0172b204b3_angdistcut_cython_opt};\n",
       "static PyObject *__pyx_pw_46_cython_magic_b93a464e795d8c6062607c0172b204b3_1angdistcut_cython_opt(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
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       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">17</span>:         <span class=\"nb\">int</span> <span class=\"n\">nps</span> <span class=\"o\">=</span> <span class=\"n\">vec_ps</span><span class=\"o\">.</span><span class=\"n\">shape</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
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       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">23</span>:         <span class=\"n\">double</span> <span class=\"n\">cos</span></pre>\n",
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       "<pre class='cython code score-0 '>      __pyx_t_12 = __pyx_v_i;\n",
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       "<pre class='cython code score-0 '>      __pyx_t_16 = __pyx_v_i;\n",
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   "source": [
    "%%cython -a\n",
    "\n",
    "import numpy as np\n",
    "cimport numpy as np\n",
    "cimport cython\n",
    "\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "@cython.nonecheck(False)\n",
    "@cython.cdivision(True)\n",
    "def angdistcut_cython_opt(double[:,::1] vec_obj, double[:,::1] vec_ps, double cos_maxsep):\n",
    "    \"\"\"\n",
    "    disabled some of the run-time checks, and also enabled C division\n",
    "    the latter is pointless here, but can make large differences when divisions are involved\n",
    "    \"\"\"\n",
    "    \n",
    "    cdef:\n",
    "        int nps = vec_ps.shape[0]\n",
    "        int nobj = vec_obj.shape[0]\n",
    "        int dim = vec_obj.shape[1]\n",
    "        #use int array instead of list\n",
    "        int[:] found = np.zeros(nobj, np.int32)\n",
    "        int i,j\n",
    "        double cos\n",
    "\n",
    "    for i in range(nobj):\n",
    "        for j in range(nps):\n",
    "            cos = (vec_obj[i,0]*vec_ps[j,0] + \n",
    "                   vec_obj[i,1]*vec_ps[j,1] + \n",
    "                   vec_obj[i,2]*vec_ps[j,2])\n",
    "            if cos > cos_maxsep:\n",
    "                found[i] = 1\n",
    "                break\n",
    "                \n",
    "    return np.flatnonzero(np.asarray(found))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n",
      "Wall time: 4.05 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result_cython_opt = angdistcut_cython_opt(vec_obj_c,vec_ps_c,cos_maxsep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "assert np.array_equal(result_cython_opt,result_numpy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By adding the decorators Cython now runs significantly faster than numpy. (NB: Part of this is because our Cython implementation does not calculate any further dot products once one contaminant is found for a certain object.)\n",
    "\n",
    "### But we can do even better by adding parallelization.\n",
    "Cython has an easy integration of *OMP-parallel loops* (very similar to C,C++, Fortran). This circumvents the *Global Interpreter Lock (GIL)*, which normally prohibits the execution of parallel code in Python (for reasons related to Python's internal memory management).\n",
    "More infos here: https://wiki.python.org/moin/GlobalInterpreterLock\n",
    "\n",
    "NB: The different threads share access to the same memory. Therefore we need to make sure that our implementation is thread-safe, i.e. that different threads do not write to the same memory location.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Now with OMP-parallelization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%cython --compile-args=-fopenmp --link-args=-fopenmp\n",
    "\n",
    "import numpy as np\n",
    "cimport numpy as np\n",
    "cimport cython\n",
    "from cython.parallel import prange, parallel\n",
    "\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "@cython.nonecheck(False)\n",
    "@cython.cdivision(True)\n",
    "def angdistcut_cython_par(double[:,::1] vec_obj, double[:,::1] vec_ps, double cos_maxsep, int num_threads):\n",
    "    \"\"\"\n",
    "    added extra compiler flags\n",
    "    also added a new argument for the number of threads\n",
    "    \"\"\"\n",
    "    \n",
    "    cdef:\n",
    "        int nps = vec_ps.shape[0]\n",
    "        int nobj = vec_obj.shape[0]\n",
    "        int dim = vec_obj.shape[1]\n",
    "        #use int array instead of list\n",
    "        int[:] found = np.zeros(nobj, np.int32)\n",
    "        int i,j\n",
    "        double cos\n",
    "\n",
    "    #every object is independent, so can parallelize the outer loop easily\n",
    "    # need to release the GIL for that (see above)\n",
    "    with nogil, parallel(num_threads=num_threads):\n",
    "        #extra keyword arguments of prange control OMP settings (can fine-tune this based on our problem)\n",
    "        for i in prange(nobj): #,schedule='static',chunksize=1):\n",
    "            for j in range(nps):\n",
    "                cos = (vec_obj[i,0]*vec_ps[j,0] + \n",
    "                       vec_obj[i,1]*vec_ps[j,1] + \n",
    "                       vec_obj[i,2]*vec_ps[j,2])\n",
    "                if cos > cos_maxsep:\n",
    "                    found[i] = 1\n",
    "                    break\n",
    "                \n",
    "    return np.flatnonzero(np.asarray(found))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 8 ms, sys: 0 ns, total: 8 ms\n",
      "Wall time: 13.4 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result_cython_par = angdistcut_cython_par(vec_obj_c,vec_ps_c,cos_maxsep, num_threads=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "assert np.array_equal(result_cython_par,result_numpy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For such a small computation overhead becomes significant, therefore there is no further speedup (NB: slightly different on my work desktop). Let's repeat the benchmark with larger arrays."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Timings with larger arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# similar to real use case\n",
    "vec_obj_large,theta_obj_large,phi_obj_large = gen_points_sphere(500000)\n",
    "vec_ps_large,theta_ps_large,phi_ps_large = gen_points_sphere(50000)\n",
    "#make them C contiguous again\n",
    "vec_obj_large_c = np.ascontiguousarray(vec_obj_large)\n",
    "vec_ps_large_c = np.ascontiguousarray(vec_ps_large)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 22.1 s, sys: 52 ms, total: 22.1 s\n",
      "Wall time: 22.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result_cython_typed = angdistcut_cython_typed(vec_obj_large_c,vec_ps_large_c,cos_maxsep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 9.46 s, sys: 16 ms, total: 9.48 s\n",
      "Wall time: 9.44 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result_cython_opt = angdistcut_cython_opt(vec_obj_large_c,vec_ps_large_c,cos_maxsep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 10.9 s, sys: 8 ms, total: 10.9 s\n",
      "Wall time: 5.47 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result_cython_par_large = angdistcut_cython_par(vec_obj_large_c,vec_ps_large_c,cos_maxsep,num_threads=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 18.4 s, sys: 8 ms, total: 18.5 s\n",
      "Wall time: 4.67 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "result_cython_par_large = angdistcut_cython_par(vec_obj_large_c,vec_ps_large_c,cos_maxsep,num_threads=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### On this laptop, I get almost linear speed-up up to 2 cores, and then no further improvement.  On the work desktop: Until 4 cores, I get a roughly linear speed-up. When using all 8 cores, there is no further speed-up.\n",
    "\n",
    "How much speed-up OMP parallelization brings, depends both on the system and the problem. In purely CPU-bound problems (almost no memory I/O needed), one can get quasi-linear speed-up to a large number of cores.\n",
    "\n",
    "NB: Sometimes we can squeeze out some extra speed-up by fine-tuning the 'schedule' and 'chunksize' arguments of prange. See e.g. http://cython.readthedocs.io/en/latest/src/userguide/parallelism.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimization summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Python/Numpy\n",
    "- The naive *pure-Python* implementation of this problem would have run for 8 hours for the full data set.\n",
    "- A vectorized *numpy* version is >100 times faster, but has prohibitively large memory requirements.\n",
    "\n",
    "#### Cython\n",
    "- A statically typed *Cython* version with the appropriate decorators is faster than the numpy version and solves the memory issues.\n",
    "- With a few easy modifications, we have made our *Cython* code *OMP-parallel* and gained another factor of 3.5 in speed when run on 4 cores (on my work desktop). This makes our final version several thousand times faster than the first pure-Python version. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Compilation outside of Jupyter notebooks:\n",
    "You need the following files:\n",
    "- Cython source code (.pyx). See the included example angdist.pyx.\n",
    "- A simple setup.py file (Example included in this repository.)\n",
    "- Then run *$ python setup.py build_ext --inplace* or put this command into a Makefile."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Final remarks:\n",
    "\n",
    "- Today I have only covered a small fraction of what is possible with Cython.\n",
    "- There is a lot of great material on Cython on the web, e.g. here http://cython.readthedocs.io/en/latest/index.html\n",
    "- I would also highly recommend the book \"Cython: A Guide for Python Programmers\" by Kurt Smith."
   ]
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