{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC3 v3.5\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import pymc3 as pm\n",
    "from pymc3 import Model, Normal, Slice\n",
    "from pymc3 import sample\n",
    "from pymc3 import traceplot\n",
    "from pymc3.distributions import Interpolated\n",
    "from theano import as_op\n",
    "import theano.tensor as tt\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import theano\n",
    "\n",
    "plt.style.use('seaborn-darkgrid')\n",
    "print('Running on PyMC3 v{}'.format(pm.__version__))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize random number generator\n",
    "np.random.seed(123)\n",
    "\n",
    "# True parameter values\n",
    "alpha_true = 5\n",
    "beta0_true = 7\n",
    "beta1_true = 13\n",
    "beta2_true = 10\n",
    "# Size of dataset\n",
    "size = 100\n",
    "\n",
    "# Predictor variable\n",
    "X1 = np.random.randn(size)\n",
    "X2 = np.random.randn(size) * 0.2\n",
    "X3 = np.random.randn(size) * 0.3\n",
    "\n",
    "# Simulate outcome variable\n",
    "Y = alpha_true + beta0_true * X1 + beta1_true * X2 + beta2_true * X3 + np.random.randn(size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_all = np.array([X1, X2, X3])\n",
    "x = theano.shared(x_all)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta2, beta1, beta0, alpha]\n",
      "Sampling 4 chains: 100%|██████████| 6000/6000 [00:02<00:00, 2931.73draws/s]\n"
     ]
    }
   ],
   "source": [
    "basic_model = Model()\n",
    "\n",
    "with basic_model:\n",
    "\n",
    "    # Priors for unknown model parameters\n",
    "    alpha = Normal('alpha', mu=0, sd=1)\n",
    "    beta0 = Normal('beta0', mu=12, sd=1)\n",
    "    beta1 = Normal('beta1', mu=18, sd=1)\n",
    "    beta2 = Normal('beta2', mu=15, sd=1)\n",
    "\n",
    "    # Expected value of outcome\n",
    "    mu = alpha + beta0 * x_all[0] + beta1 * x_all[1] + beta2*x_all[2]\n",
    "\n",
    "    # Likelihood (sampling distribution) of observations\n",
    "    Y_obs = Normal('Y_obs', mu=mu, sd=1, observed=Y)\n",
    "\n",
    "    # draw 1000 posterior samples\n",
    "    trace = sample(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pm.traceplot(trace);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def from_posterior(param, samples):\n",
    "    smin, smax = np.min(samples), np.max(samples)\n",
    "    width = smax - smin\n",
    "    x = np.linspace(smin, smax, 100)\n",
    "    y = stats.gaussian_kde(samples)(x)\n",
    "\n",
    "    # what was never sampled should have a small probability but not 0,\n",
    "    # so we'll extend the domain and use linear approximation of density on it\n",
    "    x = np.concatenate([[x[0] - 3 * width], x, [x[-1] + 3 * width]])\n",
    "    y = np.concatenate([[0], y, [0]])\n",
    "    \n",
    "    return Interpolated(param, x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "traces = [trace]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta2, beta1, beta0, alpha]\n",
      "Sampling 4 chains: 100%|██████████| 6000/6000 [00:03<00:00, 1623.02draws/s]\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta2, beta1, beta0, alpha]\n",
      "Sampling 4 chains: 100%|██████████| 6000/6000 [00:03<00:00, 1531.26draws/s]\n",
      "The number of effective samples is smaller than 25% for some parameters.\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta2, beta1, beta0, alpha]\n",
      "Sampling 4 chains: 100%|██████████| 6000/6000 [00:03<00:00, 1617.53draws/s]\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta2, beta1, beta0, alpha]\n",
      "Sampling 4 chains: 100%|██████████| 6000/6000 [00:03<00:00, 1581.78draws/s]\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta2, beta1, beta0, alpha]\n",
      "Sampling 4 chains: 100%|██████████| 6000/6000 [00:03<00:00, 1562.58draws/s]\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [beta2, beta1, beta0, alpha]\n",
      "Sampling 4 chains: 100%|██████████| 6000/6000 [00:04<00:00, 1225.35draws/s]\n",
      "The gelman-rubin statistic is larger than 1.05 for some parameters. This indicates slight problems during sampling.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-27-760206cdef8e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     24\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     25\u001b[0m         \u001b[0;31m# draw 10000 posterior samples\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 26\u001b[0;31m         \u001b[0mtrace\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     27\u001b[0m         \u001b[0mtraces\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrace\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.5/site-packages/pymc3/sampling.py\u001b[0m in \u001b[0;36msample\u001b[0;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[1;32m    403\u001b[0m                 start_, step = init_nuts(init=init, chains=chains, n_init=n_init,\n\u001b[1;32m    404\u001b[0m                                          \u001b[0mmodel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrandom_seed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrandom_seed\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 405\u001b[0;31m                                          progressbar=progressbar, **args)\n\u001b[0m\u001b[1;32m    406\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mstart\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    407\u001b[0m                     \u001b[0mstart\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstart_\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.5/site-packages/pymc3/sampling.py\u001b[0m in \u001b[0;36minit_nuts\u001b[0;34m(init, chains, n_init, model, random_seed, progressbar, **kwargs)\u001b[0m\n\u001b[1;32m   1504\u001b[0m             'Unknown initializer: {}.'.format(init))\n\u001b[1;32m   1505\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1506\u001b[0;31m     \u001b[0mstep\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNUTS\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpotential\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mpotential\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1507\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1508\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mstart\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.5/site-packages/pymc3/step_methods/hmc/nuts.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, vars, max_treedepth, early_max_treedepth, **kwargs)\u001b[0m\n\u001b[1;32m    150\u001b[0m         \u001b[0;31m`\u001b[0m\u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msample\u001b[0m\u001b[0;31m`\u001b[0m \u001b[0mto\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mdesired\u001b[0m \u001b[0mnumber\u001b[0m \u001b[0mof\u001b[0m \u001b[0mtuning\u001b[0m \u001b[0msteps\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    151\u001b[0m         \"\"\"\n\u001b[0;32m--> 152\u001b[0;31m         \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mNUTS\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvars\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    153\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    154\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax_treedepth\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmax_treedepth\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.5/site-packages/pymc3/step_methods/hmc/base_hmc.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, vars, scaling, step_scale, is_cov, model, blocked, potential, integrator, dtype, Emax, target_accept, gamma, k, t0, adapt_step_size, step_rand, **theano_kwargs)\u001b[0m\n\u001b[1;32m     61\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     62\u001b[0m         super(BaseHMC, self).__init__(vars, blocked=blocked, model=model,\n\u001b[0;32m---> 63\u001b[0;31m                                       dtype=dtype, **theano_kwargs)\n\u001b[0m\u001b[1;32m     64\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     65\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madapt_step_size\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0madapt_step_size\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.5/site-packages/pymc3/step_methods/arraystep.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, vars, model, blocked, dtype, **theano_kwargs)\u001b[0m\n\u001b[1;32m    226\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    227\u001b[0m         func = model.logp_dlogp_function(\n\u001b[0;32m--> 228\u001b[0;31m             vars, dtype=dtype, **theano_kwargs)\n\u001b[0m\u001b[1;32m    229\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    230\u001b[0m         \u001b[0;31m# handle edge case discovered in #2948\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.5/site-packages/pymc3/model.py\u001b[0m in \u001b[0;36mlogp_dlogp_function\u001b[0;34m(self, grad_vars, **kwargs)\u001b[0m\n\u001b[1;32m    707\u001b[0m         \u001b[0mvarnames\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvar\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mgrad_vars\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    708\u001b[0m         \u001b[0mextra_vars\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mvar\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvar\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfree_RVs\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mvar\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mvarnames\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 709\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mValueGradFunction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlogpt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_vars\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextra_vars\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    710\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    711\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0mproperty\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.5/site-packages/pymc3/model.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, cost, grad_vars, extra_vars, dtype, casting, **kwargs)\u001b[0m\n\u001b[1;32m    446\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    447\u001b[0m         self._theano_function = theano.function(\n\u001b[0;32m--> 448\u001b[0;31m             inputs, [self._cost_joined, grad], givens=givens, **kwargs)\n\u001b[0m\u001b[1;32m    449\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    450\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mset_extra_values\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextra_vars\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/compile/function.py\u001b[0m in \u001b[0;36mfunction\u001b[0;34m(inputs, outputs, mode, updates, givens, no_default_updates, accept_inplace, name, rebuild_strict, allow_input_downcast, profile, on_unused_input)\u001b[0m\n\u001b[1;32m    315\u001b[0m                    \u001b[0mon_unused_input\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mon_unused_input\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    316\u001b[0m                    \u001b[0mprofile\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mprofile\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 317\u001b[0;31m                    output_keys=output_keys)\n\u001b[0m\u001b[1;32m    318\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/compile/pfunc.py\u001b[0m in \u001b[0;36mpfunc\u001b[0;34m(params, outputs, mode, updates, givens, no_default_updates, accept_inplace, name, rebuild_strict, allow_input_downcast, profile, on_unused_input, output_keys)\u001b[0m\n\u001b[1;32m    484\u001b[0m                          \u001b[0maccept_inplace\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0maccept_inplace\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    485\u001b[0m                          \u001b[0mprofile\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mprofile\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mon_unused_input\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mon_unused_input\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 486\u001b[0;31m                          output_keys=output_keys)\n\u001b[0m\u001b[1;32m    487\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    488\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/compile/function_module.py\u001b[0m in \u001b[0;36morig_function\u001b[0;34m(inputs, outputs, mode, accept_inplace, name, profile, on_unused_input, output_keys)\u001b[0m\n\u001b[1;32m   1839\u001b[0m                   name=name)\n\u001b[1;32m   1840\u001b[0m         \u001b[0;32mwith\u001b[0m \u001b[0mtheano\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mchange_flags\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcompute_test_value\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"off\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1841\u001b[0;31m             \u001b[0mfn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcreate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdefaults\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1842\u001b[0m     \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1843\u001b[0m         \u001b[0mt2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/compile/function_module.py\u001b[0m in \u001b[0;36mcreate\u001b[0;34m(self, input_storage, trustme, storage_map)\u001b[0m\n\u001b[1;32m   1713\u001b[0m             \u001b[0mtheano\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtraceback\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlimit\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtheano\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtraceback\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile_limit\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1714\u001b[0m             _fn, _i, _o = self.linker.make_thunk(\n\u001b[0;32m-> 1715\u001b[0;31m                 input_storage=input_storage_lists, storage_map=storage_map)\n\u001b[0m\u001b[1;32m   1716\u001b[0m         \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1717\u001b[0m             \u001b[0mtheano\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtraceback\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlimit\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlimit_orig\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/link.py\u001b[0m in \u001b[0;36mmake_thunk\u001b[0;34m(self, input_storage, output_storage, storage_map)\u001b[0m\n\u001b[1;32m    697\u001b[0m         return self.make_all(input_storage=input_storage,\n\u001b[1;32m    698\u001b[0m                              \u001b[0moutput_storage\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0moutput_storage\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 699\u001b[0;31m                              storage_map=storage_map)[:3]\n\u001b[0m\u001b[1;32m    700\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    701\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mmake_all\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minput_storage\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moutput_storage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/vm.py\u001b[0m in \u001b[0;36mmake_all\u001b[0;34m(self, profiler, input_storage, output_storage, storage_map)\u001b[0m\n\u001b[1;32m   1089\u001b[0m                                                  \u001b[0mcompute_map\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1090\u001b[0m                                                  \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1091\u001b[0;31m                                                  impl=impl))\n\u001b[0m\u001b[1;32m   1092\u001b[0m                 \u001b[0mlinker_make_thunk_time\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mthunk_start\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1093\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthunks\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'lazy'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/op.py\u001b[0m in \u001b[0;36mmake_thunk\u001b[0;34m(self, node, storage_map, compute_map, no_recycling, impl)\u001b[0m\n\u001b[1;32m    953\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    954\u001b[0m                 return self.make_c_thunk(node, storage_map, compute_map,\n\u001b[0;32m--> 955\u001b[0;31m                                          no_recycling)\n\u001b[0m\u001b[1;32m    956\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mNotImplementedError\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mutils\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMethodNotDefined\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    957\u001b[0m                 \u001b[0;31m# We requested the c code, so don't catch the error.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/op.py\u001b[0m in \u001b[0;36mmake_c_thunk\u001b[0;34m(self, node, storage_map, compute_map, no_recycling)\u001b[0m\n\u001b[1;32m    856\u001b[0m         \u001b[0m_logger\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdebug\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Trying CLinker.make_thunk'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    857\u001b[0m         outputs = cl.make_thunk(input_storage=node_input_storage,\n\u001b[0;32m--> 858\u001b[0;31m                                 output_storage=node_output_storage)\n\u001b[0m\u001b[1;32m    859\u001b[0m         \u001b[0mthunk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode_input_filters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode_output_filters\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moutputs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    860\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/cc.py\u001b[0m in \u001b[0;36mmake_thunk\u001b[0;34m(self, input_storage, output_storage, storage_map, keep_lock)\u001b[0m\n\u001b[1;32m   1215\u001b[0m         cthunk, module, in_storage, out_storage, error_storage = self.__compile__(\n\u001b[1;32m   1216\u001b[0m             \u001b[0minput_storage\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moutput_storage\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstorage_map\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1217\u001b[0;31m             keep_lock=keep_lock)\n\u001b[0m\u001b[1;32m   1218\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1219\u001b[0m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_CThunk\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcthunk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minit_tasks\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtasks\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0merror_storage\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodule\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/cc.py\u001b[0m in \u001b[0;36m__compile__\u001b[0;34m(self, input_storage, output_storage, storage_map, keep_lock)\u001b[0m\n\u001b[1;32m   1155\u001b[0m                                             \u001b[0moutput_storage\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1156\u001b[0m                                             \u001b[0mstorage_map\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1157\u001b[0;31m                                             keep_lock=keep_lock)\n\u001b[0m\u001b[1;32m   1158\u001b[0m         return (thunk,\n\u001b[1;32m   1159\u001b[0m                 \u001b[0mmodule\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/cc.py\u001b[0m in \u001b[0;36mcthunk_factory\u001b[0;34m(self, error_storage, in_storage, out_storage, storage_map, keep_lock)\u001b[0m\n\u001b[1;32m   1618\u001b[0m                 \u001b[0mnode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprepare_node\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstorage_map\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'c'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1619\u001b[0m             module = get_module_cache().module_from_key(\n\u001b[0;32m-> 1620\u001b[0;31m                 key=key, lnk=self, keep_lock=keep_lock)\n\u001b[0m\u001b[1;32m   1621\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1622\u001b[0m         \u001b[0mvars\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minputs\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutputs\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0morphans\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/cmodule.py\u001b[0m in \u001b[0;36mmodule_from_key\u001b[0;34m(self, key, lnk, keep_lock)\u001b[0m\n\u001b[1;32m   1145\u001b[0m         \u001b[0;31m# Is the source code already in the cache?\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1146\u001b[0m         \u001b[0mmodule_hash\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_module_hash\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msrc_code\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1147\u001b[0;31m         \u001b[0mmodule\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_from_hash\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodule_hash\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeep_lock\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mkeep_lock\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1148\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mmodule\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1149\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mmodule\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/cmodule.py\u001b[0m in \u001b[0;36m_get_from_hash\u001b[0;34m(self, module_hash, key, keep_lock)\u001b[0m\n\u001b[1;32m   1055\u001b[0m                 if (key[0] and not key_broken and\n\u001b[1;32m   1056\u001b[0m                         self.check_for_broken_eq):\n\u001b[0;32m-> 1057\u001b[0;31m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcheck_key\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey_data\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkey_pkl\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1058\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_update_mappings\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey_data\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodule\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__file__\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcheck_in_keys\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mnot\u001b[0m \u001b[0mkey_broken\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1059\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mmodule\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/cmodule.py\u001b[0m in \u001b[0;36mcheck_key\u001b[0;34m(self, key, key_pkl)\u001b[0m\n\u001b[1;32m   1226\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1227\u001b[0m                 \u001b[0;32mwith\u001b[0m \u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey_pkl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'rb'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1228\u001b[0;31m                     \u001b[0mkey_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpickle\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1229\u001b[0m                 \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1230\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mEOFError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/scalar/basic.py\u001b[0m in \u001b[0;36m__setstate__\u001b[0;34m(self, d)\u001b[0m\n\u001b[1;32m   4125\u001b[0m         \u001b[0;31m# self.perform will not work.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4126\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprepare_node_called\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 4127\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minit_fgraph\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   4128\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minit_py_impls\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4129\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/scalar/basic.py\u001b[0m in \u001b[0;36minit_fgraph\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m   3918\u001b[0m         \u001b[0;31m# the fgraph to be set to the variable as we need to pickle\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3919\u001b[0m         \u001b[0;31m# them for the cache of c module to work.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3920\u001b[0;31m         \u001b[0mfgraph\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFunctionGraph\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minputs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutputs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3921\u001b[0m         \u001b[0mgof\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMergeOptimizer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moptimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfgraph\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3922\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mnode\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mfgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mapply_nodes\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/fg.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, inputs, outputs, features, clone, update_mapping)\u001b[0m\n\u001b[1;32m    173\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    174\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0moutput\u001b[0m \u001b[0;32min\u001b[0m \u001b[0moutputs\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 175\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__import_r__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moutput\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreason\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"init\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    176\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moutput\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moutputs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    177\u001b[0m             \u001b[0moutput\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclients\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'output'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/fg.py\u001b[0m in \u001b[0;36m__import_r__\u001b[0;34m(self, variable, reason)\u001b[0m\n\u001b[1;32m    344\u001b[0m         \u001b[0;31m# Imports the owners of the variables\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    345\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mvariable\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mowner\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mvariable\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mowner\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mapply_nodes\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 346\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__import__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvariable\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mowner\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreason\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mreason\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    347\u001b[0m         elif (variable.owner is None and\n\u001b[1;32m    348\u001b[0m                 \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvariable\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mConstant\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/theano/gof/fg.py\u001b[0m in \u001b[0;36m__import__\u001b[0;34m(self, apply_node, check, reason)\u001b[0m\n\u001b[1;32m    401\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__setup_r__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moutput\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    402\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvariables\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moutput\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 403\u001b[0;31m             \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minput\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minputs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    404\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0minput\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvariables\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    405\u001b[0m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__setup_r__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "for _ in range(10):\n",
    "\n",
    "    # generate more data\n",
    "    X1 = np.random.randn(size)\n",
    "    X2 = np.random.randn(size) * 0.2\n",
    "    X3 = np.random.randn(size) * 0.3\n",
    "    Y = alpha_true + beta0_true * X1 + beta1_true * X2 + beta2_true * X3 + np.random.randn(size)\n",
    "    \n",
    "    x_temp = np.array([X1,X2,X3])\n",
    "    x.set_value(x_temp)\n",
    "    \n",
    "    model = Model()\n",
    "    with model:\n",
    "        # Priors are posteriors from previous iteration\n",
    "        alpha = from_posterior('alpha', trace['alpha'])\n",
    "        beta0 = from_posterior('beta0', trace['beta0'])\n",
    "        beta1 = from_posterior('beta1', trace['beta1'])\n",
    "        beta2 = from_posterior('beta2', trace['beta2'])\n",
    "        # Expected value of outcome\n",
    "        mu = alpha + beta0 * x[0] + beta1 * x[1] + beta2 * x[2]\n",
    "\n",
    "        # Likelihood (sampling distribution) of observations\n",
    "        Y_obs = Normal('Y_obs', mu=mu, sd=1, observed=Y)\n",
    "\n",
    "        # draw 10000 posterior samples\n",
    "        trace = sample(1000)\n",
    "        traces.append(trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "X1 = np.random.randn(size)\n",
    "X2 = np.random.randn(size) * 0.2\n",
    "x_temp = np.array([X1,X2])\n",
    "x.set_value(x_temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/50 [00:00<?, ?it/s]INFO (theano.gof.compilelock): Refreshing lock /home/pdguest/.theano/compiledir_Linux-4.13--generic-x86_64-with-Ubuntu-16.04-xenial-x86_64-3.5.2-64/lock_dir/lock\n",
      "100%|██████████| 50/50 [00:00<00:00, 93.06it/s]\n"
     ]
    }
   ],
   "source": [
    "ppc = pm.sample_ppc(trace, samples=50, model=basic_model)\n",
    "y_obs = np.array(ppc['Y_obs'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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