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lucianopaz/Windows broken pipe.ipynb

Created November 27, 2018 16:41
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Notebook that gets a BrokenPipeError raised on windows. Sometimes, this is caused because the multiprocessing backend in windows creates an entirely new process instead of forking it, so it needs an if __name__ == "__main__" statement that encloses the process pool
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Windows broken pipe.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING (theano.configdefaults): g++ not available, if using conda: `conda install m2w64-toolchain`\n",
"C:\\Users\\chulo\\Anaconda3\\lib\\site-packages\\theano\\configdefaults.py:560: UserWarning: DeprecationWarning: there is no c++ compiler.This is deprecated and with Theano 0.11 a c++ compiler will be mandatory\n",
" warnings.warn(\"DeprecationWarning: there is no c++ compiler.\"\n",
"WARNING (theano.configdefaults): g++ not detected ! Theano will be unable to execute optimized C-implementations (for both CPU and GPU) and will default to Python implementations. Performance will be severely degraded. To remove this warning, set Theano flags cxx to an empty string.\n",
"WARNING (theano.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n",
"C:\\Users\\chulo\\Anaconda3\\lib\\site-packages\\h5py\\__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
" from ._conv import register_converters as _register_converters\n"
]
}
],
"source": [
"import pymc3 as pm\n",
"from theano.compile.ops import as_op\n",
"import theano.tensor as tt\n",
"from numpy import arange, array, empty\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Time series of recorded coal mining disasters in the UK from 1851 to 1962\n",
"disasters_data = array([4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n",
" 3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n",
" 2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3, 0, 0,\n",
" 1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n",
" 0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n",
" 3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n",
" 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])\n",
"years = len(disasters_data)\n",
"\n",
"\n",
"@as_op(itypes=[tt.lscalar, tt.dscalar, tt.dscalar], otypes=[tt.dvector])\n",
"def rate_(switchpoint, early_mean, late_mean):\n",
" out = empty(years)\n",
" out[:switchpoint] = early_mean\n",
" out[switchpoint:] = late_mean\n",
" return out"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Multiprocess sampling (2 chains in 2 jobs)\n",
"CompoundStep\n",
">CompoundStep\n",
">>Slice: [late_mean]\n",
">>Slice: [early_mean]\n",
">Metropolis: [switchpoint]\n"
]
},
{
"ename": "BrokenPipeError",
"evalue": "[Errno 32] Broken pipe",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mBrokenPipeError\u001b[0m Traceback (most recent call last)",
"\u001b[1;32m<ipython-input-3-12cdcddba70f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 23\u001b[0m \u001b[0mstart\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m{\u001b[0m\u001b[1;34m'early_mean'\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;36m2.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'late_mean'\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;36m3.\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 24\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 25\u001b[1;33m \u001b[0mtr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msample\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1000\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtune\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m500\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstart\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mstart\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstep\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mstep1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstep2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcores\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 26\u001b[0m \u001b[0mpm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtraceplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtr\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pymc3\\sampling.py\u001b[0m in \u001b[0;36msample\u001b[1;34m(draws, step, init, n_init, start, trace, chain_idx, chains, cores, tune, nuts_kwargs, step_kwargs, progressbar, model, random_seed, live_plot, discard_tuned_samples, live_plot_kwargs, compute_convergence_checks, use_mmap, **kwargs)\u001b[0m\n\u001b[0;32m 447\u001b[0m \u001b[0m_print_step_hierarchy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstep\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 448\u001b[0m \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 449\u001b[1;33m \u001b[0mtrace\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_mp_sample\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0msample_args\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 450\u001b[0m \u001b[1;32mexcept\u001b[0m \u001b[0mpickle\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mPickleError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 451\u001b[0m \u001b[0m_log\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mwarning\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Could not pickle model, sampling singlethreaded.\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pymc3\\sampling.py\u001b[0m in \u001b[0;36m_mp_sample\u001b[1;34m(draws, tune, step, chains, cores, chain, random_seed, start, progressbar, trace, model, use_mmap, **kwargs)\u001b[0m\n\u001b[0;32m 994\u001b[0m sampler = ps.ParallelSampler(\n\u001b[0;32m 995\u001b[0m \u001b[0mdraws\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtune\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mchains\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcores\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrandom_seed\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstart\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstep\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 996\u001b[1;33m chain, progressbar)\n\u001b[0m\u001b[0;32m 997\u001b[0m \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 998\u001b[0m \u001b[1;32mwith\u001b[0m \u001b[0msampler\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pymc3\\parallel_sampling.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, draws, tune, chains, cores, seeds, start_points, step_method, start_chain_num, progressbar)\u001b[0m\n\u001b[0;32m 273\u001b[0m ProcessAdapter(draws, tune, step_method,\n\u001b[0;32m 274\u001b[0m chain + start_chain_num, seed, start)\n\u001b[1;32m--> 275\u001b[1;33m \u001b[1;32mfor\u001b[0m \u001b[0mchain\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mseed\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstart\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mchains\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mseeds\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstart_points\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 276\u001b[0m ]\n\u001b[0;32m 277\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pymc3\\parallel_sampling.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[1;34m(.0)\u001b[0m\n\u001b[0;32m 273\u001b[0m ProcessAdapter(draws, tune, step_method,\n\u001b[0;32m 274\u001b[0m chain + start_chain_num, seed, start)\n\u001b[1;32m--> 275\u001b[1;33m \u001b[1;32mfor\u001b[0m \u001b[0mchain\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mseed\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstart\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mchains\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mseeds\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstart_points\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 276\u001b[0m ]\n\u001b[0;32m 277\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pymc3\\parallel_sampling.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, draws, tune, step_method, chain, seed, start)\u001b[0m\n\u001b[0;32m 180\u001b[0m draws, tune, seed)\n\u001b[0;32m 181\u001b[0m \u001b[1;31m# We fork right away, so that the main process can start tqdm threads\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 182\u001b[1;33m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_process\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstart\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 183\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 184\u001b[0m \u001b[1;33m@\u001b[0m\u001b[0mproperty\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m~\\Anaconda3\\lib\\multiprocessing\\process.py\u001b[0m in \u001b[0;36mstart\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 103\u001b[0m \u001b[1;34m'daemonic processes are not allowed to have children'\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 104\u001b[0m \u001b[0m_cleanup\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 105\u001b[1;33m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_popen\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_Popen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 106\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_sentinel\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_popen\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msentinel\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 107\u001b[0m \u001b[1;31m# Avoid a refcycle if the target function holds an indirect\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m~\\Anaconda3\\lib\\multiprocessing\\context.py\u001b[0m in \u001b[0;36m_Popen\u001b[1;34m(process_obj)\u001b[0m\n\u001b[0;32m 221\u001b[0m \u001b[1;33m@\u001b[0m\u001b[0mstaticmethod\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 222\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m_Popen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprocess_obj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 223\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0m_default_context\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_context\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mProcess\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_Popen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprocess_obj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 224\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 225\u001b[0m \u001b[1;32mclass\u001b[0m \u001b[0mDefaultContext\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mBaseContext\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m~\\Anaconda3\\lib\\multiprocessing\\context.py\u001b[0m in \u001b[0;36m_Popen\u001b[1;34m(process_obj)\u001b[0m\n\u001b[0;32m 320\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m_Popen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprocess_obj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 321\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[1;33m.\u001b[0m\u001b[0mpopen_spawn_win32\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mPopen\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 322\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mPopen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprocess_obj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 323\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 324\u001b[0m \u001b[1;32mclass\u001b[0m \u001b[0mSpawnContext\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mBaseContext\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m~\\Anaconda3\\lib\\multiprocessing\\popen_spawn_win32.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, process_obj)\u001b[0m\n\u001b[0;32m 63\u001b[0m \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 64\u001b[0m \u001b[0mreduction\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdump\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprep_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mto_child\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 65\u001b[1;33m \u001b[0mreduction\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdump\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprocess_obj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mto_child\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 66\u001b[0m \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 67\u001b[0m \u001b[0mset_spawning_popen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m~\\Anaconda3\\lib\\multiprocessing\\reduction.py\u001b[0m in \u001b[0;36mdump\u001b[1;34m(obj, file, protocol)\u001b[0m\n\u001b[0;32m 58\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mdump\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfile\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mprotocol\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 59\u001b[0m \u001b[1;34m'''Replacement for pickle.dump() using ForkingPickler.'''\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 60\u001b[1;33m \u001b[0mForkingPickler\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfile\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mprotocol\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdump\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 61\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 62\u001b[0m \u001b[1;31m#\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;31mBrokenPipeError\u001b[0m: [Errno 32] Broken pipe"
]
}
],
"source": [
"with pm.Model() as model:\n",
"\n",
" # Prior for distribution of switchpoint location\n",
" switchpoint = pm.DiscreteUniform('switchpoint', lower=0, upper=years)\n",
" # Priors for pre- and post-switch mean number of disasters\n",
" early_mean = pm.Exponential('early_mean', lam=1.)\n",
" late_mean = pm.Exponential('late_mean', lam=1.)\n",
"\n",
" # Allocate appropriate Poisson rates to years before and after current\n",
" # switchpoint location\n",
" idx = arange(years)\n",
" rate = rate_(switchpoint, early_mean, late_mean)\n",
"\n",
" # Data likelihood\n",
" disasters = pm.Poisson('disasters', rate, observed=disasters_data)\n",
"\n",
" # Use slice sampler for means\n",
" step1 = pm.Slice([early_mean, late_mean])\n",
" # Use Metropolis for switchpoint, since it accomodates discrete variables\n",
" step2 = pm.Metropolis([switchpoint])\n",
"\n",
" # Initial values for stochastic nodes\n",
" start = {'early_mean': 2., 'late_mean': 3.}\n",
"\n",
" tr = pm.sample(1000, tune=500, start=start, step=[step1, step2], cores=2)\n",
" pm.traceplot(tr)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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