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cottrell/gibbs.ipynb

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Created February 25, 2014 05:40
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gibbs.ipynb
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{
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"source": [
"## Playing around with timings of Darren Wilkinson's Gibbs sampler example\n",
"\n",
"http://darrenjw.wordpress.com/2011/07/16/gibbs-sampler-in-various-languages-revisited/"
]
},
{
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"input": [
"import random, math, time\n",
"import scipy.stats.distributions as ssd\n",
"import numpy.random as nr\n",
"import numpy\n",
" \n",
"def gibbs(N=5000, thin=100):\n",
" x=0\n",
" y=0\n",
"\n",
" out = []\n",
" for i in range(N):\n",
" for j in range(thin):\n",
" x=random.gammavariate(3,1.0/(y*y+4))\n",
" y=random.gauss(1.0/(x+1),1.0/math.sqrt(2*x+2))\n",
" out += [[x, y]]\n",
" out = numpy.array(out)\n",
" return(out)\n",
"\n",
"def gibbs1(N=5000, thin=100):\n",
" x=0\n",
" y=0\n",
" out = []\n",
" for i in range(N):\n",
" for j in range(thin):\n",
" x = nr.gamma(3, 1.0 / (y * y + 4))\n",
" y = nr.normal(1.0 / (x + 1), 1.0 / math.sqrt(2 * x + 2)) \n",
" out += [[x, y]]\n",
" out = numpy.array(out)\n",
" return(out)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 147
},
{
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"input": [
"%load_ext cythonmagic"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The cythonmagic extension is already loaded. To reload it, use:\n",
" %reload_ext cythonmagic\n"
]
}
],
"prompt_number": 136
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{
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"input": [
"%%cython -a\n",
"# non-optimize cython hack, probably some way to reach down to numpy c libraries\n",
"cimport cython\n",
"import numpy\n",
"cimport numpy\n",
"from libc.math cimport sqrt\n",
"@cython.cdivision(True)\n",
"def gibbs_cython(int N=5000, int thin=100):\n",
" cdef double x = 0, y = 0\n",
" out = []\n",
" for i in range(N):\n",
" for j in range(thin):\n",
" x = numpy.random.gamma(3, 1.0 / (y * y + 4))\n",
" y = numpy.random.normal(1.0 / (x + 1), 1.0 / sqrt(2 * x + 2)) \n",
" out += [[x, y]]\n",
" out = numpy.array(out)\n",
" return(out)"
],
"language": "python",
"metadata": {},
"outputs": [
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"input": [
"def gibbs1(N=5000, thin=100):\n",
" x=0\n",
" y=0\n",
" out = []\n",
" for i in range(N):\n",
" for j in range(thin):\n",
" x = nr.gamma(3, 1.0 / (y * y + 4))\n",
" y = nr.normal(1.0 / (x + 1), 1.0 / math.sqrt(2 * x + 2)) \n",
" out += [[x, y]]\n",
" out = numpy.array(out)\n",
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],
"language": "python",
"metadata": {},
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},
{
"cell_type": "code",
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"input": [
"t = time.time()\n",
"out = gibbs()\n",
"print(time.time() - t)\n",
"\n",
"%timeit gibbs1()\n",
"\n",
"t = time.time()\n",
"out1 = gibbs1()\n",
"print(time.time() - t)\n",
"\n",
"%timeit gibbs_cython()\n",
"\n",
"t = time.time()\n",
"out2 = gibbs_cython()\n",
"print(time.time() - t)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2.900670051574707\n",
"1 loops, best of 3: 659 ms per loop"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
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},
{
"output_type": "stream",
"stream": "stdout",
"text": [
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},
{
"output_type": "stream",
"stream": "stdout",
"text": [
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},
{
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"stream": "stdout",
"text": [
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]
}
],
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},
{
"cell_type": "code",
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"input": [
"from pylab import *\n",
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"df = numpy.hstack([out, out1, out2])\n",
"df = pandas.DataFrame(df)\n",
"p = df.plot(ax=ax, kind='density', alpha=0.5, linewidth=3, style=['-', '--', 'x'] * 2)"
],
"language": "python",
"metadata": {},
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{
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0tvpg9ephmzAm5boT+gz6JrB06VKWLl3KBx98wF133XUlyyQII1NrK/uuX05W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\n8S5TMlcSMiRh1RoJqkFKK55FCIHNNo3Gxo0RNEB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w0Nzau/8LyIuz9q8ho0kGEDJCfNkz\n+vqTqoGkeBEhA2ggNAmhChCgqn19Mdwfw4QdVvibyKX6fV8bNM1HKHQGRUnodwBmc+bln3cxTOzZ\ns0csWbKk//O6devEiy++eI7M6tWrxebNm/s/T5kyRTQ3N5+3r7y8vL47nL7oi77oi74McsnLy7vk\nvXrY0kFz5syhsrKSmpoasrOzeeedd9i8efM5MsuWLWP9+vXcfffd7N27l6SkpAFTQVVVVcOlpo6O\njs6oZticgKIorF+/niVLlqCqKg899BCFhYW8/vrrAKxevZrbbruNbdu2kZ+fj81mY9OmTcOljo6O\njo7OAFwRxWI6Ojo6OsPDFTN30KuvvkphYSHTpk1jzZo1kVZnWHjppZeQZZnOzs5IqzKk/OAHP6Cw\nsJCZM2eyfPlynE5npFUaEgZTDHmlcubMGW644Qauuuoqpk2bxs9//vNIqzTkqKpKcXExd955Z6RV\nGXIcDgcrVqygsLCQoqKii9dfXfbI7wiyc+dOcfPNN4tAICCEEKK1tTXCGg09dXV1YsmSJSI3N1d0\ndHREWp0hZfv27UJVVSGEEGvWrBFr1qyJsEZfn1AoJPLy8kR1dbUIBAJi5syZ4vjx45FWa8hoamoS\nZWVlQgghuru7RUFBQUzZJ4QQL730krjnnnvEnXfeGWlVhpz77rtPbNy4UQghRDAYFA6H44KyV0Qk\n8Itf/IKnn34ao9EIQHp6eoQ1Gnq+//3v85Of/CTSagwLixcvRu4tupo/fz719fUR1ujrc3YxpNFo\n7C+GjBUyMzOZNWsWAHa7ncLCQhobGyOs1dBRX1/Ptm3bePjhh2NuXjKn08nu3btZtWoVEB6fTUxM\nvKD8FeEEKisr2bVrF9dccw2LFi2itLQ00ioNKe+99x45OTnMmDEj0qoMO7/85S+57bbbIq3G12ag\nQseGhoYIajR81NTUUFZWxvz58yOtypDx5JNP8tOf/rT/y0ksUV1dTXp6Og8++CCzZ8/mkUcewePx\nXFB+2J4O+ltZvHgxzc3N561fu3YtoVCIrq4u9u7dy4EDB1i5ciWnT5+OgJaXz8Xse+GFF9i+fXv/\nuivxm8mF7Fu3bl1/znXt2rWYTCbuueeekVZvyIn1osY+enp6WLFiBa+88gp2uz3S6gwJ77//PhkZ\nGRQXF8fkBHKhUIhDhw6xfv165s6dyxNPPMGLL77I888/P/AGI5Oh+nosXbpUfPLJJ/2f8/LyRHt7\newQ1GjqOHj0qMjIyRG5ursjNzRWKoogJEyaIlpaWSKs2pGzatEksWLBAeL3eSKsyJAymGPJKJxAI\niFtuuUW8/PLLkVZlSHn66adFTk6OyM3NFZmZmSIuLk7ce++9kVZryGhqahK5ubn9n3fv3i1uv/32\nC8pfEU5gw4YN4tlnnxVCCFFeXi7GjRsXYY2Gj1gcGP7www9FUVGRaGtri7QqQ0YwGBSTJk0S1dXV\nwu/3x9zAsKZp4t577xVPPPFEpFUZVj755BNxxx13RFqNIWfhwoWivLxcCCHEj370I/HUU09dUDZq\n0kEXY9WqVaxatYrp06djMpl46623Iq3SsBGLaYbHHnuMQCDA4sWLAbj22mt57bXLn/AqGrhQMWSs\n8Nlnn/H2228zY8YMiouLAXjhhRdYunRphDUbemKxz7366qt861vfIhAIkJeXd9FCXL1YTEdHR2cU\nE3tD4zo6Ojo6g0Z3Ajo6OjqjGN0J6Ojo6IxidCego6OjM4rRnYCOjo7OKEZ3Ajo6OjqjGN0J6Ojo\n6IxidCego6OjM4r5/79nN4/yLM/aAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x10d8a8290>"
]
}
],
"prompt_number": 157
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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