Old_testing_grounds.ipynb

    {
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "from lib.graph_enumerator import *\n",
    "from lib.graph_local_classes import *\n",
    "from lib.subgraph_functions import *\n",
    "from lib.utils import *\n",
    "from lib.node_semantics import Node_Name_Rule, Edge_Semantics_Rule\n",
    "import sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "generator_dictionary ={ \"nodes\" : [\"A_int\",\"A_obs\",\"A_★\",\"B_obs\",\"B_★\",\"C_obs\",\"C_★\",\"D_obs\",\"D_★\"],\n",
    "#     \"query_edge_set\" : [\n",
    "#         (\"A_★\",'B_★'),\n",
    "#         (\"A_★\",'C_★'),\n",
    "#         (\"A_★\",'D_★'),\n",
    "#         (\"B_★\",'C_★'),\n",
    "#         (\"B_★\",'D_★'),\n",
    "#         (\"C_★\",'B_★'),\n",
    "#         (\"C_★\",'D_★'),\n",
    "#         (\"D_★\",'B_★'),\n",
    "#         (\"D_★\",'C_★')\n",
    "#     ],\n",
    "    \"filters\": {\n",
    "        \"explicit_child_parentage\"  : [[\n",
    "            (\"A_int\",[]),\n",
    "            (\"A_★\",[\"A_int\"]),\n",
    "            ('A_obs',['A_int','A_★']),\n",
    "            ('B_obs',['B_★']),\n",
    "            ('C_obs',[\"C_★\"]),\n",
    "            ('D_obs',[\"D_★\"])\n",
    "        ]],\n",
    "        \"explicit_parent_offspring\" : [[\n",
    "            ('A_int',['A_obs','A_★']),\n",
    "            (\"A_obs\",[]),\n",
    "            (\"B_obs\",[]),\n",
    "            (\"C_obs\",[]),\n",
    "            (\"D_obs\",[])\n",
    "        ]],\n",
    "        \"extract_remove_self_loops\": []\n",
    "    },\n",
    "    \"conditions\": {\n",
    "        \"create_path_complete_condition\" : [[(\"A_int\",\"B_★\"),(\"A_int\",\"C_★\"),(\"A_int\",\"D_★\"),(\"A_int\",\"A_obs\"),\n",
    "                                             (\"A_★\",\"A_obs\"),(\"B_★\",\"B_obs\"),(\"C_★\",\"C_obs\"),(\"D_★\",\"D_obs\")]],\n",
    "    }\n",
    "}\n",
    "\n",
    "\n",
    "\n",
    "node_semantics={\n",
    "        # \".*_int\" → intervener\n",
    "        \"intervener\": {\n",
    "            \"node_type\":\"intervener\",\n",
    "            \"where\":\"suffix\",\n",
    "            \"infix\":\"_\",\n",
    "            \"code\":\"int\"},\n",
    "        # \".*_obs\" → observed\n",
    "        \"observed\": {\n",
    "            \"node_type\":\"observed\",\n",
    "            \"where\":\"suffix\",\n",
    "            \"infix\":\"_\",\n",
    "            \"code\":\"obs\"},\n",
    "        # \".*_★\" → hidden\n",
    "        \"hidden\": {\n",
    "            \"node_type\":\"hidden\",\n",
    "            \"where\":\"suffix\",\n",
    "            \"infix\":\"_\",\n",
    "            \"code\":\"★\"}\n",
    "}\n",
    "\n",
    "edge_semantics={\n",
    "    \"hidden_sample\":{\n",
    "        \"source_types\":[\"hidden\"],\n",
    "        \"target_types\":[\"hidden\"],\n",
    "        \"edge_type\": \"hidden_sample\"\n",
    "    },\n",
    "    \"observed\":{\n",
    "        \"source_types\":[\"hidden\"],\n",
    "        \"target_types\":[\"observed\"],\n",
    "        \"edge_type\": \"observed\"\n",
    "    },\n",
    "    \"intervention\":{\n",
    "        \"source_types\":[\"intervener\"],\n",
    "        \"target_types\":None,\n",
    "        \"edge_type\": \"intervention\"\n",
    "    }\n",
    "}\n",
    "\n",
    "# todo(maybe): rework filters and conditions to take node types and edge types as arguments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# working_graph_iter = generate_graphs(**generator_dictionary)\n",
    "# working_graphs = list(working_graph_iter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "graphs = list(generate_graphs(**generator_dictionary))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "608"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(graphs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('B_★', 'C_★'),\n",
       " ('B_★', 'D_★'),\n",
       " ('B_★', 'B_obs'),\n",
       " ('A_int', 'A_★'),\n",
       " ('C_★', 'C_obs'),\n",
       " ('C_★', 'B_★'),\n",
       " ('A_★', 'D_★'),\n",
       " ('A_★', 'A_obs'),\n",
       " ('D_★', 'B_★'),\n",
       " ('D_★', 'D_obs')]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graphs[500].edges()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('B_★', 'C_★'),\n",
       " ('B_★', 'D_★'),\n",
       " ('B_★', 'B_obs'),\n",
       " ('A_int', 'A_★'),\n",
       " ('A_int', 'A_obs'),\n",
       " ('C_★', 'D_★'),\n",
       " ('C_★', 'C_obs'),\n",
       " ('C_★', 'B_★'),\n",
       " ('A_★', 'C_★'),\n",
       " ('A_★', 'D_★'),\n",
       " ('A_★', 'B_★'),\n",
       " ('A_★', 'A_obs'),\n",
       " ('D_★', 'C_★'),\n",
       " ('D_★', 'B_★'),\n",
       " ('D_★', 'D_obs')]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graphs[0].edges()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# working_graph_index = 0\n",
    "# test_me=working_graphs[working_graph_index].copy()\n",
    "\n",
    "# Node_Name_Rule.graph_semantics_apply(test_me,node_semantics)\n",
    "# Edge_Semantics_Rule.graph_semantics_apply(test_me,edge_semantics)\n",
    "\n",
    "# gs_in, gp_in = sub_graph_sample(test_me,edge_types=[\"hidden_sample\"], param_init=sf_big)\n",
    "# gs_out, gp_out = sub_graph_sample(test_me,edge_types=['observed'], param_init=sf_big)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def cond_to_data(cond):\n",
    "    a,b,c,d = cond\n",
    "    data_sequences = [\n",
    "        [a,b,c,d], \n",
    "        [a,b,c,-np.inf], \n",
    "        [a,b,-np.inf,d],\n",
    "        [a,b,-np.inf,-np.inf],\n",
    "        [a,-np.inf,-np.inf,-np.inf]\n",
    "    ]\n",
    "    return data_sequences\n",
    "    \n",
    "def p_graph_given_d(graphs,options):\n",
    "    # sets a catch for all numerical warningss to be treated as errors\n",
    "    np.seterr(all='raise')\n",
    "    \"\"\"\n",
    "    options includes \n",
    "    sparsity: the sparsity argument for the prior \n",
    "    param_sample_size: the number of parameters to be sampled\n",
    "    stigma_sample_size: the number of internal states to be sampled\n",
    "    data_sets: the different data_sets to be evaluated as likelihoods\n",
    "    data_p: the probability of each data_set in data_sets\n",
    "    num_data_samps: number of samples of observed data to be considered in the liklihood\n",
    "    \"\"\"\n",
    "    loglikelihood = np.empty(len(graphs))\n",
    "    param_sample_size= options[\"param_sample_size\"]\n",
    "    \n",
    "    for i,graph in enumerate(graphs):\n",
    "        loglikelihood[i] = parameters_monte_carlo_loglik(graph,param_sample_size,options=options)\n",
    "        # prints progres at roughly every 10% of progress\n",
    "        if i in [int(np.floor(j*len(graphs))) for j in np.arange(0,1,.1)]:\n",
    "            sys.stdout.write(\"{:.2%} \".format(i/len(graphs)))\n",
    "            sys.stdout.flush()\n",
    "    \n",
    "    sparsity = options[\"sparsity\"]\n",
    "    logposterior = logposterior_from_loglik_logsparseprior(graphs,loglikelihood,sparsity)\n",
    "#     import ipdb; ipdb.set_trace()\n",
    "    return graphs,np.exp(logposterior),logposterior,loglikelihood,options\n",
    "\n",
    "def logposterior_from_loglik_logsparseprior(graphs,loglik,sparsity=.5):\n",
    "    logp = log_sparse_graphset_prior(graphs,sparsity=sparsity)\n",
    "    unnormed_logposterior = loglik+logp\n",
    "    return unnormed_logposterior - mdp_logsumexp(unnormed_logposterior)\n",
    "\n",
    "def sparse_1graph_prior_unnormed(graph,max_edges,sparsity=.5):\n",
    "    return ((1-sparsity)**(max_edges-len(graph.edges())))*(sparsity)**(len(graph.edges()))\n",
    "\n",
    "def log_sparse_1graph_prior_unnormed(graph,max_edges,sparsity=.5):\n",
    "    return ((max_edges-len(graph.edges()))*np.log(1-sparsity))+len(graph.edges())*np.log(sparsity)\n",
    "\n",
    "def sparse_graphset_prior(graphs,sparsity=.5):\n",
    "    max_edges = np.max([len(x.edges()) for x in graphs])\n",
    "    unnormed_p = [sparse_1graph_prior_unnormed(graph,max_edges,sparsity=sparsity) for graph in graphs]\n",
    "    return unnormed_p/sum(unnormed_p)\n",
    "\n",
    "def log_sparse_graphset_prior(graphs,sparsity=.5):\n",
    "    max_edges = np.max([len(x.edges()) for x in graphs])\n",
    "    unnormed_logp = [log_sparse_1graph_prior_unnormed(graph,max_edges,sparsity=sparsity) for graph in graphs]\n",
    "    return unnormed_logp - mdp_logsumexp(unnormed_logp)\n",
    "                                                                   \n",
    "                                                                   \n",
    "def parameters_monte_carlo_loglik(graph, param_sample_size, options = None):\n",
    "    #\n",
    "    # initialize the dictionary with the scale_free_bounds specified in the options\n",
    "    init_dict = {\"scale_free_bounds\":options[\"scale_free_bounds\"]}\n",
    "    gs_in, gp_in = sub_graph_sample(graph,edge_types=[\"hidden_sample\"], param_init=init_dict)\n",
    "    init_dict[\"lambda0\"]=gp_in.to_dict()[\"lambda0\"]\n",
    "    gs_out, gp_out = sub_graph_sample(graph,edge_types=['observed'], param_init=init_dict)\n",
    "    \n",
    "    param_samples = _helper_iter_param_sampler(gs_in,gp_in,gs_out,gp_out,param_sample_size,options)\n",
    "    \n",
    "    return logmeanexp(np.fromiter(param_samples,dtype=np.float,count=param_sample_size))\n",
    "\n",
    "def _helper_iter_param_sampler(gs_in,gp_in,gs_out,gp_out,param_sample_size,options):\n",
    "    # a helper function for sampling parameters in inner graph \n",
    "    stigma_sample_size=options[\"stigma_sample_size\"]\n",
    "    for i in range(param_sample_size):\n",
    "        # reset the base_rate to None so it is resampled\n",
    "        update_dict = {\"lambda0\":None}\n",
    "        gp_in.update(d=update_dict)\n",
    "        # sample parameters for inner graph\n",
    "        gp_in.sample()\n",
    "        \n",
    "        # extract base_rate used for inner graph samples to be used for outer graph\n",
    "        update_dict[\"lambda0\"]=gp_in.to_dict()[\"lambda0\"]\n",
    "        gp_out.update(d=update_dict)\n",
    "        # sample parameters for outer graph\n",
    "        gp_out.sample()\n",
    "        \n",
    "        yield aux_data_monte_carlo_loglik(gs_in,gp_in,gs_out,gp_out,stigma_sample_size,options=options)\n",
    "\n",
    "def gen_simulations(gs_in,gp_in,M):\n",
    "    # builds simulation object and samples it returning an M lengthed list\n",
    "    inner_simul = InnerGraphSimulation(gs_in,gp_in)\n",
    "    return inner_simul.sample(M)\n",
    "\n",
    "def gen_iter_simulations(gs_in,gp_in,M):\n",
    "    # builds a simulation object and then samples returning an M lengthed generator\n",
    "    inner_simul = InnerGraphSimulation(gs_in,gp_in)\n",
    "    return inner_simul.sample_iter(M)\n",
    "\n",
    "def aux_data_monte_carlo_loglik(gs_in, gp_in, gs_out, gp_out, stigma_sample_size, options=None):\n",
    "    stigma_sample_size = options[\"stigma_sample_size\"]\n",
    "#     inner_samp = gen_simulations(gs_in, gp_in, stigma_sample_size)\n",
    "    inner_samp = gen_iter_simulations(gs_in, gp_in, stigma_sample_size)\n",
    "    \n",
    "    # get arguments to the loglikelihood \n",
    "    # data_sets are kinds of data\n",
    "    data_sets = options[\"data_sets\"]\n",
    "    \n",
    "    # data_probs are the probabilities of those data points\n",
    "    data_probs = options[\"data_probs\"]\n",
    "    \n",
    "    # num_data_samps is the number of \"sampled\" data that we're evaluating it for\n",
    "    num_data_samps = options[\"num_data_samps\"]\n",
    "\n",
    "    # get parameters for the relevant nodes to calculate the likelihood \n",
    "    obs_dict = gp_out.to_dict()\n",
    "    \n",
    "    # build generator for the simulated log_likelihood for a given parameter set\n",
    "    sim_loglike = (cross_entropy_loglik(data_sets, data_probs, num_data_samps, stigma, obs_dict) for stigma in inner_samp)\n",
    "\n",
    "    return logmeanexp(np.fromiter(sim_loglike,dtype=np.float,count=stigma_sample_size))\n",
    "\n",
    "def cross_entropy_loglik(data_sets,data_probs, k , aux_data, obs_dict):\n",
    "    # for a finite set of known kinds of data with known probs\n",
    "    # we can compute the expected cross-entropy for those kinds of data\n",
    "    return np.sum([data_probs[i]*k*multi_edge_loglik(obs_data, aux_data, obs_dict) for i,obs_data in enumerate(data_sets)])\n",
    "\n",
    "def multi_edge_loglik(obs_data,aux_data,parameters):\n",
    "    # special casing for my problem, this needs to be made more general\n",
    "    # extract non-intervention nodes as we know when the intervention node occurred\n",
    "    non_int_node_idx = slice(1,4)\n",
    "    obs_data = obs_data[non_int_node_idx]\n",
    "    aux_data = aux_data[non_int_node_idx]\n",
    "    grab = ['psi','r']\n",
    "    local_dict = {i:parameters[i][non_int_node_idx] for i in parameters if i in grab}\n",
    "    # end special casing\n",
    "\n",
    "    # loglik of data set is the sum of the loglikelihoods of the individual data points (they're independent)\n",
    "    return np.sum([one_edge_loglik(aux_data[i],obs_data[i],local_dict['psi'][i],local_dict['r'][i]) for i in range(len(aux_data))]) \n",
    "\n",
    "def one_edge_loglik(cause_time, effect_time, psi, r, T=4.0):\n",
    "    # if the cause never occurs it occurs at infinity\n",
    "    if np.isinf(cause_time):\n",
    "        # it is certain that the effect will not occur if the cause does not occur\n",
    "        if np.isinf(effect_time):\n",
    "            return 0\n",
    "        # it is impossible for the effect to occur if the cause does not occur\n",
    "        # previous check was elif not np.isinf(effect_time) but that must be true given top if statement\n",
    "        else:\n",
    "            return -np.inf\n",
    "\n",
    "    # if the cause does occur it happens at some time other than infinity\n",
    "    if not np.isinf(cause_time):\n",
    "        \n",
    "        # if the effect doesn't occur, loglik of no events between cause_time and max_time(T)\n",
    "        if np.isinf(effect_time):\n",
    "            try:\n",
    "                # test to make sure that you won't hit underflow\n",
    "                exp_val = np.exp(-r*(T-cause_time))\n",
    "            except FloatingPointError:\n",
    "                # it was a really small number, set it to 0\n",
    "                exp_val = 0         \n",
    "            return -(psi/r)*(1-exp_val)\n",
    "        \n",
    "        # if the effect occurred but before the cause_time, that's impossible\n",
    "        elif effect_time < cause_time: \n",
    "            return -np.inf\n",
    "        # if the effect occurred, after the cause_time, \n",
    "        # then loglik of no events from cause_time to effect_time + log of rate function\n",
    "        else:\n",
    "            try:\n",
    "                # test to make sure that you won't hit underflow\n",
    "                exp_val = np.exp(-r*(effect_time-cause_time))\n",
    "            except FloatingPointError:\n",
    "                # it was a really small number, set it to 0\n",
    "                exp_val = 0         \n",
    "\n",
    "            return np.log(psi) - (r*(effect_time-cause_time)) - (psi/r)*(1-exp_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "# def parameters_monte_carlo_lik(graph,param_sample_size,stigma_sample_size,\n",
    "#                                data_sets,data_p,num_data_samps,scale_free_bounds,options=None):\n",
    "#     init_dict = {\"scale_free_bounds\":options[\"scale_free_bounds\"]}\n",
    "#     gs_in, gp_in = sub_graph_sample(graph,edge_types=[\"hidden_sample\"], param_init=init_dict)\n",
    "#     init_dict[\"lambda0\"]=gp_in.to_dict()[\"lambda0\"]\n",
    "#     gs_out, gp_out = sub_graph_sample(graph,edge_types=['observed'], param_init=init_dict)\n",
    "# #     return np.mean([aux_data_monte_carlo_lik(gs_in,gp_in.sample(),gs_out,gp_out.sample(),\n",
    "# #                                          stigma_sample_size,data_sets,data_p,num_data_samps) \n",
    "# #                     for i in range(param_sample_size)])\n",
    "#     temp_arr = np.empty(options[\"param_sample_size\"])\n",
    "#     for i in range(options[\"param_sample_size\"]):\n",
    "#         update_dict = {\"lambda0\":None}\n",
    "#         gp_in.update(d=update_dict)\n",
    "#         gp_in.sample()\n",
    "#         update_dict[\"lambda0\"]=gp_in.to_dict()[\"lambda0\"]\n",
    "#         gp_out.update(d=update_dict)\n",
    "#         gp_out.sample()\n",
    "#         temp_arr[i] = aux_data_monte_carlo_loglik(gs_in,gp_in,gs_out,gp_out,\n",
    "#                                                   stigma_sample_size,data_sets,\n",
    "#                                                   data_p, num_data_samps)\n",
    "# #         import ipdb; ipdb.set_trace()\n",
    "#     return np.mean(np.exp(temp_list))\n",
    "\n",
    "\n",
    "# def aux_data_monte_carlo_lik(gs_in,gp_in,gs_out,gp_out,stigma_sample_size,data_sets,data_p,num_data_samps):\n",
    "#     obs_dict = gp_out.to_dict()\n",
    "#     inner_samp = gen_simulations(gs_in,gp_in,stigma_sample_size)\n",
    "#     return np.mean([np.exp(cross_entropy_loglik(data_sets,data_p,num_data_samps,stigma,obs_dict)) for stigma in inner_samp])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "param_sample_size = 100\n",
    "stigma_sample_size = 10000\n",
    "scale_free_bounds = (10**-1,10**1)\n",
    "# scale_free_bounds = (10**-3,10**3)\n",
    "cond1 = [0,0,0,0]\n",
    "cond2 = [0,1,3,2]\n",
    "cond3 = [0,3,2,1]\n",
    "cond4 = [0,1,2,2]\n",
    "data_sets = cond_to_data(cond2)\n",
    "sparsity = .1\n",
    "graph_subset = slice(0,7)\n",
    "\n",
    "options = {\n",
    "    'param_sample_size': param_sample_size,\n",
    "    'stigma_sample_size': stigma_sample_size,\n",
    "    'scale_free_bounds': scale_free_bounds,\n",
    "    'sparsity': sparsity,\n",
    "    'data_sets': data_sets,\n",
    "    'num_data_samps': 100,\n",
    "    'max_obs_time': 4,\n",
    "    'data_probs':[0.512,0.128,0.128,0.032,.2]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "graph_iter = generate_graphs(**generator_dictionary)\n",
    "graphs = list(graph_iter)\n",
    "for graph in graphs:    \n",
    "    Node_Name_Rule.graph_semantics_apply(graph,node_semantics)\n",
    "    Edge_Semantics_Rule.graph_semantics_apply(graph,edge_semantics)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00% 9.87% 19.74% 29.93% 39.80% 50.00% 59.87% 69.74% 79.93% 89.80% "
     ]
    }
   ],
   "source": [
    "# blah = p_graph_given_d(graphs[graph_subset],options)\n",
    "blah2 = p_graph_given_d(graphs,options)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pickle\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "output = open('data.pkl', 'wb')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pickle.dump(blah2,output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "output.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.99999996169 [('A_★', 'B_★'), ('A_★', 'A_obs'), ('A_int', 'A_★'), ('A_int', 'A_obs'), ('C_★', 'C_obs'), ('C_★', 'B_★'), ('C_★', 'D_★'), ('D_★', 'B_★'), ('D_★', 'D_obs'), ('B_★', 'C_★'), ('B_★', 'D_★'), ('B_★', 'B_obs')] \n",
      " [  1.65527938e-152   2.86803053e-180   1.79175801e-165   1.25769048e-115\n",
      "   6.14310205e-104   2.14438829e-131   5.88264913e-171   4.10128374e-061\n",
      "   4.71054598e-110   1.39934943e-118   1.38472974e-159   1.78028183e-163\n",
      "   2.65271370e-113   3.57187388e-203   1.71293804e-177   6.24974662e-177\n",
      "   1.27740528e-193   7.99141725e-164   4.01743671e-048   8.64749904e-159\n",
      "   2.98525456e-107   3.07176300e-089   7.82008652e-076   2.91914527e-153\n",
      "   5.49177848e-104   5.65395416e-097   3.66739966e-181   6.09374480e-085\n",
      "   3.48622291e-116   1.26127898e-151   1.87618367e-085   2.28505217e-155\n",
      "   3.16256690e-160   5.67527932e-127   1.85386073e-085   8.12142729e-128\n",
      "   5.72013956e-009   1.50583792e-124   1.08081814e-110   4.14368401e-152\n",
      "   6.13789015e-066   2.84427348e-079   9.34236077e-103   2.63349110e-133\n",
      "   1.00897414e-167   3.13782109e-078   1.68641590e-169   3.36595894e-191\n",
      "   1.18745150e-153   1.84089658e-109   4.73219515e-144   4.55264949e-211\n",
      "   1.46511693e-152   2.48247255e-206   4.37242930e-209   1.97607062e-109\n",
      "   6.74491050e-105   1.18674035e-140   1.93446934e-140   7.40030167e-174\n",
      "   6.01161833e-163   2.35471580e-202   4.59300193e-121   1.76529573e-147\n",
      "   1.23416581e-103   1.37289082e-166   9.05279639e-208   3.34495396e-166\n",
      "   3.14039444e-240   1.42696536e-166   8.82924992e-149   8.83592176e-251\n",
      "   2.48559326e-107   2.86539102e-173   1.50251279e-096   1.14682713e-141\n",
      "   1.40845160e-169   9.99999962e-001   2.60898419e-134   1.07447476e-068\n",
      "   5.63983303e-063   2.23271342e-158   7.70184795e-160   1.05287590e-107\n",
      "   6.37258391e-111   1.80390999e-150   8.11061358e-142   2.39238228e-163\n",
      "   1.73166651e-078   1.15439520e-136   8.95598174e-090   1.83094012e-153\n",
      "   2.81234543e-130   1.75599211e-093   8.77380132e-151   2.86745085e-059\n",
      "   1.12798300e-119   1.60756928e-157   9.17442928e-170   2.92134758e-142\n",
      "   4.75590322e-148   2.13829525e-133   7.79417259e-115   4.24059173e-146\n",
      "   2.21582847e-137   5.14662306e-113   7.44107091e-127   2.29045022e-123\n",
      "   1.18339615e-107   8.33181775e-112   6.30381742e-142   1.90945117e-154\n",
      "   1.11285394e-093   2.67005858e-122   1.09613873e-015   7.37864271e-131\n",
      "   4.14331636e-046   9.62647720e-163   5.98670139e-081   1.44896922e-158\n",
      "   1.12530681e-188   2.48830738e-109   2.39837278e-167   2.11241339e-131\n",
      "   4.72679519e-125   2.11663646e-038   1.63276153e-169   1.64762271e-207\n",
      "   3.93502109e-115   6.62220239e-182   7.21411084e-066   5.37293487e-144\n",
      "   4.16248018e-225   2.63122456e-192   1.67207691e-165   2.78266814e-224\n",
      "   7.93700556e-229   1.17382552e-129   1.36409147e-190   3.01685102e-234\n",
      "   1.21290295e-162   2.12198709e-234   8.12818146e-168   3.59967266e-196\n",
      "   3.33249729e-185   4.83424844e-147   1.73613215e-175   4.81595239e-158\n",
      "   1.21414785e-168   1.29432541e-171   2.67965486e-101   4.32092658e-181\n",
      "   5.69098904e-187   3.09360887e-188   6.25722390e-139   9.08563309e-101\n",
      "   2.43388638e-202   4.57603647e-161   2.17231972e-161   1.38334366e-164\n",
      "   5.29229530e-120   1.53105080e-183   2.00754930e-148   9.58346514e-140\n",
      "   1.79678937e-131   2.02446762e-202   1.59092945e-163   4.32136271e-082\n",
      "   9.72688650e-102   2.25729734e-210   6.94025170e-157   1.63502260e-129\n",
      "   5.67198802e-034   7.71834600e-161   1.89823446e-084   4.28905745e-113\n",
      "   6.71212824e-131   2.20652219e-104   8.39849280e-079   1.39683173e-101\n",
      "   3.77863253e-126   2.36421197e-105   7.36285120e-071   4.04022665e-120\n",
      "   1.32021189e-103   1.19892928e-125   5.71245177e-085   4.32305242e-089\n",
      "   1.26724981e-161   4.66966258e-096   6.73361965e-111   1.07732246e-059\n",
      "   1.66232321e-142   7.09639521e-041   3.32058439e-186   1.40899015e-166\n",
      "   1.35991158e-098   6.62606782e-124   1.82667897e-158   3.12885262e-117\n",
      "   2.82899200e-082   4.57767617e-111   7.36812674e-148   5.83443920e-145\n",
      "   1.10683037e-130   4.15590834e-138   7.63605144e-107   1.37631908e-129\n",
      "   3.87913705e-154   1.52089063e-161   5.62380191e-069   1.26562046e-077\n",
      "   2.99085582e-166   1.37962077e-050   3.70852818e-131   8.92583098e-177\n",
      "   5.25212086e-115   3.50025653e-162   1.19208626e-164   7.02559269e-068\n",
      "   5.65673157e-142   1.94972985e-121   2.30666301e-106   8.27114823e-184\n",
      "   1.32249031e-073   7.64930381e-081   3.59896444e-172   9.81681068e-260\n",
      "   2.88352682e-078   1.14423583e-206   6.21831157e-191   1.91470841e-122\n",
      "   1.84103823e-166   1.16331873e-185   3.51558346e-153   1.07968028e-181\n",
      "   3.95931235e-126   5.10413241e-231   1.01500978e-301   1.27721924e-260\n",
      "   4.53479068e-155   1.14264679e-221   5.67867109e-179   2.45470691e-188\n",
      "   6.78970783e-206   8.04444349e-134   1.68540695e-119   3.02278817e-180\n",
      "   1.88337874e-186   2.44734267e-220   1.44776794e-199   4.19991404e-199\n",
      "   1.22040438e-103   4.50053827e-214   3.39345820e-115   2.34786001e-091\n",
      "   2.20864770e-040   6.69537416e-165   7.35982541e-135   2.30278385e-169\n",
      "   7.63498106e-038   4.15697606e-141   1.41415931e-114   6.07769314e-138\n",
      "   3.35873330e-101   9.64035756e-132   1.55768832e-077   2.43120627e-195\n",
      "   2.14677337e-174   5.44825074e-095   5.86510229e-079   2.05854049e-175\n",
      "   3.80535295e-019   5.33138580e-131   4.03874686e-134   1.90372471e-166\n",
      "   1.35762088e-162   3.25898575e-008   1.82393571e-126   1.14336570e-144\n",
      "   8.78205389e-149   3.30425874e-184   1.01628632e-182   3.27064944e-171\n",
      "   2.50497623e-167   1.17448914e-175   5.74336604e-129   2.32660332e-229\n",
      "   5.03778878e-113   6.31924648e-179   9.21930017e-162   3.02326353e-217\n",
      "   6.08168860e-139   8.86066548e-186   1.60048436e-186   7.14459072e-240\n",
      "   6.61375916e-126   8.66127605e-138   9.33664709e-154   9.57608384e-165\n",
      "   1.29921475e-040   6.18770585e-083   1.94886701e-147   6.22238004e-205]\n"
     ]
    }
   ],
   "source": [
    "print(np.amax(blah2[1]),blah2[0][np.argmax(blah2[1])].edges(),\"\\n\",blah2[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "file_pkl = open(\"data_2015_49_4_1132.pkl\",\"rb\")\n",
    "data1=pickle.load(file_pkl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<networkx.classes.digraph.DiGraph at 0x110b21c18>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21f28>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21470>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21cf8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21e48>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21550>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b213c8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21cc0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec6a0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec748>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec080>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec588>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec470>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec6d8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec7f0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec710>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec780>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec4a8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec2b0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec898>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec358>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec198>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec4e0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec5f8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec048>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec160>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec5c0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec908>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec550>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec128>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec3c8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec860>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec828>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec208>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec668>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec518>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec438>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec2e8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec400>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec320>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec978>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec630>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec390>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec1d0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec0f0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec240>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec0b8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2c50>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2cf8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2d30>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2da0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2d68>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2dd8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2e10>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2e48>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2e80>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2eb8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2ef0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2f28>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2f60>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2f98>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110cb2fd0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33518>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33b00>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33f28>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33cf8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33828>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b339e8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33240>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33208>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b337b8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33e10>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33ef0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33c50>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33550>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33748>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33a58>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b330f0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33668>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33a20>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33470>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33940>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33dd8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b336d8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33b38>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33c18>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b337f0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33048>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b330b8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b339b0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b336a0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33588>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b335c0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33080>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33ac8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33a90>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b332b0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33358>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33278>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4ae80>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a6d8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4ad30>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4acc0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4ae10>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a860>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a470>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a9e8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a240>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4ac50>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a128>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a438>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a320>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a940>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4add8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4ada0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a9b0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a908>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4acf8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a518>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a2b0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a198>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a4a8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a978>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a550>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a390>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a748>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4aa58>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a1d0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4ab70>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a278>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a208>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a358>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4aa90>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a3c8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a080>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a668>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a400>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a588>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a7f0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a630>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a8d0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a5f8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4af28>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a160>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a828>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a710>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4af60>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4aef0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a4e0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4aa20>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a898>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a780>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a7b8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a5c0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4aeb8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4af98>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4afd0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14048>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14080>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b140b8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b140f0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b141d0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14198>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14278>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b143c8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14518>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14550>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14710>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14780>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14828>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b148d0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14940>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14358>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14438>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14160>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14978>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b149b0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14a90>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14b00>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14ba8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14c50>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14cc0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14d68>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14dd8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14e80>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14f28>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14f60>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14390>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14c88>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14b38>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14860>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14be0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14e10>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14eb8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14668>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14e48>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14470>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14da0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14d30>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14ac8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14b70>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b149e8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14cf8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14588>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b142e8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14128>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14c18>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14ef0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14a58>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14a20>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14240>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b145f8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b142b0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14400>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14908>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b144a8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14320>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14208>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b147b8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b145c0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14748>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14630>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14898>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b146d8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b147f0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b146a0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14f98>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b14fd0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc048>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc080>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc0b8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc0f0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc128>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc160>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc198>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc1d0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc208>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc240>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc278>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc2b0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc2e8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc320>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc358>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110bec278>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110af5f28>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110af5cc0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x10ef5f860>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x10ee92240>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x10ee92470>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33e48>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33c88>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33160>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b33710>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110adda90>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a2e8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a0f0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4ac88>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4aba8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4aac8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4ae48>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4a048>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b4ad68>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x10ef59630>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x10ef1ab38>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x10ef1ac18>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x10ef1a7f0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x10ef79518>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21b00>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21860>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b210b8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b216d8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b217b8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21748>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21390>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21358>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b210f0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b214e0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21630>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b211d0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b219e8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21a58>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21e10>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21ba8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21518>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21d30>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21208>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b219b0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21a90>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b218d0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21b38>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21ef0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21f60>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b21780>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b212e8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x110b215c0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc390>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc3c8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc400>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc438>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc470>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc4a8>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc4e0>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc518>,\n",
       "  <networkx.classes.digraph.DiGraph at 0x1111cc550>],\n",
       " array([  4.82173234e-126,   1.07092026e-161,   1.77225866e-103,\n",
       "          7.42567267e-140,   3.45012854e-127,   1.21913336e-139,\n",
       "          4.68517351e-080,   1.95365856e-143,   2.03325692e-133,\n",
       "          2.50710663e-079,   6.58149037e-109,   4.48976571e-206,\n",
       "          4.82690575e-173,   7.69390137e-189,   6.74707420e-198,\n",
       "          2.47349458e-136,   6.85375191e-217,   2.22673304e-193,\n",
       "          6.24051727e-092,   4.06880713e-057,   3.64015821e-135,\n",
       "          2.51249532e-114,   3.29880618e-136,   6.37878503e-055,\n",
       "          1.97652505e-085,   7.76310758e-022,   9.64075904e-166,\n",
       "          9.71675042e-134,   2.03119852e-150,   1.93224387e-145,\n",
       "          2.47935732e-107,   3.69827653e-143,   1.10884738e-142,\n",
       "          1.64074863e-129,   2.10251389e-122,   6.09264948e-084,\n",
       "          2.40175770e-084,   2.23504618e-167,   1.24105457e-098,\n",
       "          3.44503514e-117,   3.03527009e-154,   4.37806593e-088,\n",
       "          4.38671997e-099,   2.46187917e-166,   2.61063476e-159,\n",
       "          1.00000000e+000,   2.18591544e-159,   1.04914053e-180,\n",
       "          1.13134901e-167,   8.68151223e-209,   2.57217203e-240,\n",
       "          3.65962818e-171,   1.33488385e-218,   2.87891314e-215,\n",
       "          5.16826403e-251,   1.08509419e-097,   3.79313583e-155,\n",
       "          4.96503952e-132,   6.26567667e-150,   1.24161284e-177,\n",
       "          5.18627457e-153,   1.72653428e-195,   4.43381821e-172,\n",
       "          6.88163135e-191,   2.16791098e-151,   9.69309800e-145,\n",
       "          1.74406839e-160,   6.57389801e-141,   6.53489030e-171,\n",
       "          6.53052441e-159,   5.09633816e-141,   2.61636697e-177,\n",
       "          1.56638425e-107,   1.11779463e-142,   7.00710461e-131,\n",
       "          1.30333541e-122,   3.29096830e-107,   2.50900646e-136,\n",
       "          4.05500983e-038,   2.16356839e-115,   1.44925956e-115,\n",
       "          1.64066160e-126,   9.18486571e-104,   2.33743378e-093,\n",
       "          2.26921752e-096,   4.25529624e-121,   1.59138608e-040,\n",
       "          8.50088365e-125,   2.18733144e-086,   1.35159413e-102,\n",
       "          1.55656364e-163,   2.27263441e-095,   2.24921656e-124,\n",
       "          6.43060058e-112,   2.11194755e-118,   2.05812450e-030,\n",
       "          6.91295799e-130,   1.23194051e-124,   2.33904694e-186,\n",
       "          2.93255915e-154,   3.28695555e-131,   3.27416418e-156,\n",
       "          5.83638092e-122,   3.43571793e-081,   2.61185409e-109,\n",
       "          5.93627807e-114,   4.67175376e-144,   1.10260546e-098,\n",
       "          3.23129313e-126,   1.46802392e-186,   3.16189990e-089,\n",
       "          5.25714978e-085,   6.62981847e-120,   2.39960440e-103,\n",
       "          9.02169823e-141,   3.66533875e-133,   7.72322937e-135,\n",
       "          2.26723799e-084,   1.42309573e-125,   2.36667743e-091,\n",
       "          1.24785234e-137,   3.88962982e-154,   1.34632560e-169,\n",
       "          2.94491215e-118,   3.84270189e-109,   2.16767130e-107,\n",
       "          3.38575068e-165,   2.17800488e-183,   2.94432568e-183,\n",
       "          6.03399832e-234,   3.67302241e-174,   1.93026867e-157,\n",
       "          2.39982718e-211,   3.56929708e-137,   1.40463875e-137,\n",
       "          1.65603109e-194,   3.87017533e-245,   6.75635807e-198,\n",
       "          3.42574608e-186,   1.44519466e-204,   7.46559750e-179,\n",
       "          2.74370783e-236,   1.90171514e-149,   4.09852188e-233,\n",
       "          3.03124028e-145,   7.87302488e-184,   9.11472587e-231,\n",
       "          2.00832914e-233,   6.90456077e-162,   8.06595455e-199,\n",
       "          2.22675636e-148,   1.22444195e-170,   1.86723926e-147,\n",
       "          3.19169615e-192,   5.50927472e-172,   9.85771115e-199,\n",
       "          6.20873506e-133,   8.20249706e-159,   5.35094600e-172,\n",
       "          2.39666018e-155,   4.03917036e-175,   3.47944822e-215,\n",
       "          4.74067085e-156,   3.78658731e-195,   1.08066328e-184,\n",
       "          3.96283088e-170,   8.92232480e-129,   5.43074575e-086,\n",
       "          3.03649995e-071,   4.24930739e-173,   2.07921931e-160,\n",
       "          3.33544949e-173,   4.82795081e-098,   2.38831381e-121,\n",
       "          1.35761465e-157,   1.35180974e-031,   4.62479909e-153,\n",
       "          1.39165354e-090,   5.76304861e-084,   5.58162361e-124,\n",
       "          1.96759027e-134,   4.20227530e-123,   8.48257843e-080,\n",
       "          7.69984068e-137,   3.30109151e-114,   4.98927237e-125,\n",
       "          1.78357629e-091,   3.02614720e-137,   5.21552603e-155,\n",
       "          1.11979844e-104,   2.36440784e-144,   3.25466825e-109,\n",
       "          2.41761532e-124,   8.81962570e-164,   1.26774519e-152,\n",
       "          8.62121253e-208,   1.29011398e-134,   1.34994500e-102,\n",
       "          4.33232953e-057,   1.41149731e-123,   1.27318142e-118,\n",
       "          3.25433837e-161,   7.49955765e-128,   7.58499503e-153,\n",
       "          3.20738589e-150,   1.82077530e-122,   9.73908524e-128,\n",
       "          7.43018271e-121,   1.82941845e-134,   8.29930095e-154,\n",
       "          3.42328435e-121,   9.73613540e-089,   1.24297767e-103,\n",
       "          2.25460630e-117,   1.36721389e-158,   4.78452865e-139,\n",
       "          1.84856785e-085,   1.26325712e-155,   4.54008595e-098,\n",
       "          2.39205206e-188,   9.84386548e-155,   6.19556313e-113,\n",
       "          3.89439715e-161,   2.56898195e-150,   1.30389530e-159,\n",
       "          4.13418353e-163,   4.00804850e-203,   1.17469872e-252,\n",
       "          1.29608962e-117,   2.89755109e-227,   2.77405701e-202,\n",
       "          3.73392060e-201,   6.32848005e-221,   9.16689986e-166,\n",
       "          2.08093617e-153,   2.97859332e-254,   4.04011042e-185,\n",
       "          4.36252209e-168,   3.44208883e-233,   4.39415614e-139,\n",
       "          8.99724255e-194,   2.97329604e-218,   2.54727696e-175,\n",
       "          4.49351062e-222,   1.13714686e-205,   1.10233534e-184,\n",
       "          4.84607879e-138,   4.35748500e-159,   1.06812398e-165,\n",
       "          9.94545346e-229,   1.21510957e-189,   8.97413503e-199,\n",
       "          5.87040448e-178,   1.25121183e-225,   1.13005384e-051,\n",
       "          7.56395563e-109,   2.05282355e-149,   1.01450114e-165,\n",
       "          4.28017281e-133,   3.71059712e-176,   1.45172794e-147,\n",
       "          1.38170990e-092,   8.66742370e-135,   6.92280894e-153,\n",
       "          2.28925131e-059,   1.87475051e-098,   1.28613636e-084,\n",
       "          8.34091578e-121,   1.05906221e-158,   7.61554471e-116,\n",
       "          6.94275152e-102,   1.53979968e-102,   1.57105985e-083,\n",
       "          5.52524242e-142,   2.66033498e-190,   3.21792094e-178,\n",
       "          2.44558056e-112,   1.48488024e-165,   1.39582326e-128,\n",
       "          1.15631850e-127,   5.61050174e-158,   2.50978542e-094,\n",
       "          1.84223413e-187,   3.79665332e-174,   8.44758411e-174,\n",
       "          3.43489912e-094,   3.36608734e-153,   4.57492397e-103,\n",
       "          9.96406361e-167,   1.00624597e-229,   1.63025101e-177,\n",
       "          5.26522219e-236,   5.61698025e-228,   7.45570960e-206,\n",
       "          4.82439321e-182,   4.23809215e-143,   4.84846726e-144,\n",
       "          4.59101067e-171,   7.05173868e-092,   3.69281063e-094,\n",
       "          6.97767138e-117,   1.24190827e-152,   5.71974900e-135,\n",
       "          1.34207916e-137]),\n",
       " array([-288.55258845, -370.64768164, -236.59400976, -320.35696974,\n",
       "        -291.18989532, -319.86118768, -182.66240449, -328.5999645 ,\n",
       "        -305.53417847, -180.98509299, -249.09751392, -472.83072864,\n",
       "        -396.77301546, -433.14815459, -454.00273945, -312.24594069,\n",
       "        -497.73616895, -443.59838744, -210.00676548, -129.84400043,\n",
       "        -309.55696041, -261.57342419, -311.95801201, -124.78920247,\n",
       "        -195.03839263,  -48.60748933, -379.96312559, -306.27255122,\n",
       "        -344.67913792, -333.21615653, -245.46860557, -327.96180139,\n",
       "        -326.86376212, -296.53832438, -280.17224763, -191.61006477,\n",
       "        -192.54094697, -383.72744864, -225.43737764, -268.16552178,\n",
       "        -353.48780391, -201.15088112, -226.47734242, -381.32820049,\n",
       "        -365.15143639,    0.        , -365.32899508, -414.41734545,\n",
       "        -384.40829979, -479.0790887 , -551.67567163, -392.44468935,\n",
       "        -501.67470599, -493.99838215, -576.30632149, -223.26908723,\n",
       "        -355.56749634, -302.33881102, -343.55267736, -407.34115024,\n",
       "        -350.6495036 , -448.45797704, -394.55537488, -437.86489702,\n",
       "        -346.91658502, -331.6034244 , -367.85739434, -322.78139115,\n",
       "        -391.86489534, -364.23454254, -323.03597584, -406.59577476,\n",
       "        -245.92783501, -326.85572554, -299.6917226 , -280.65045466,\n",
       "        -245.18542311, -312.2316858 ,  -86.09828042, -264.0255268 ,\n",
       "        -264.42623292, -289.63062214, -237.25129257, -213.29136   ,\n",
       "        -220.22873386, -277.16463187,  -91.63879833, -285.68296651,\n",
       "        -197.23963572, -234.56239475, -374.87888956, -217.92464414,\n",
       "        -284.70996957, -256.02846248, -270.95743044,  -68.35575766,\n",
       "        -297.40266447, -285.31196096, -427.43108374, -353.52222885,\n",
       "        -300.44868541, -358.01721188, -279.15127045, -185.27516663,\n",
       "        -250.02171479, -260.71361825, -330.03071885, -225.55566313,\n",
       "        -288.95283931, -427.89691007, -203.7789002 , -194.06014389,\n",
       "        -274.41863374, -236.29096069, -322.46486552, -304.94489661,\n",
       "        -308.80475497, -192.59858547, -287.47030204, -208.67375642,\n",
       "        -315.23273379, -353.23979033, -388.83950161, -270.62496199,\n",
       "        -249.6355994 , -245.60295149, -378.7069647 , -420.59466275,\n",
       "        -420.2931922 , -537.0075019 , -399.34879131, -360.8482004 ,\n",
       "        -484.9700579 , -314.18178906, -315.11437759, -446.19708421,\n",
       "        -562.78004797, -454.00136441, -427.04950802, -469.35911494,\n",
       "        -410.15242618, -542.40077172, -342.44242267, -535.09170028,\n",
       "        -332.76586662, -421.61221477, -529.68726515, -535.80502357,\n",
       "        -371.08660289, -456.12678144, -339.98204778, -391.23698062,\n",
       "        -337.85554766, -440.93578537, -394.33820301, -455.9261795 ,\n",
       "        -304.41786019, -364.00659116, -394.36736263, -356.02661324,\n",
       "        -401.55635196, -493.80892127, -357.64709585, -447.67262797,\n",
       "        -423.59808211, -390.06250717, -294.84492046, -196.33024153,\n",
       "        -162.37283608, -396.90046508, -367.68162239, -397.14261364,\n",
       "        -224.078917  , -277.74220865, -361.20013037,  -71.07869364,\n",
       "        -350.7640863 , -206.90216573, -191.6656812 , -283.80107183,\n",
       "        -307.86959288, -281.78234032, -182.06879298, -313.4129581 ,\n",
       "        -261.30044743, -286.21584654, -208.95662296, -314.34686748,\n",
       "        -355.24904946, -239.35570096, -330.71172578, -249.80168479,\n",
       "        -284.63776988, -375.44697582, -349.75569426, -476.7834736 ,\n",
       "        -308.29167189, -234.56361563, -129.78124491, -282.87331538,\n",
       "        -271.46352215, -369.53621098, -292.71604786, -350.26934727,\n",
       "        -344.22230771, -280.31611895, -292.45474471, -276.6072458 ,\n",
       "        -307.94240433, -352.48193303, -277.38219583, -202.65422901,\n",
       "        -236.94875473, -268.58948051, -363.49566968, -318.49394041,\n",
       "        -195.1053217 , -356.66699601, -224.14039317, -432.01384588,\n",
       "        -354.61384095, -258.3682821 , -369.35666108, -344.44425426,\n",
       "        -365.84567362, -373.9020803 , -466.03646941, -580.09043173,\n",
       "        -269.14310414, -521.62295018, -464.10187791, -461.50214491,\n",
       "        -507.02624546, -380.01352628, -351.56270135, -583.76516247,\n",
       "        -424.58197018, -385.36124527, -535.26624816, -318.57905242,\n",
       "        -444.50458989, -500.87387916, -402.01736634, -509.67125637,\n",
       "        -471.9014217 , -423.57822615, -316.17857295, -364.63913473,\n",
       "        -379.86063653, -524.99487079, -434.99374832, -456.02008695,\n",
       "        -408.09022302, -517.85753338, -117.30957447, -248.95838085,\n",
       "        -342.36596267, -379.91214334, -304.78982398, -403.94378356,\n",
       "        -338.10725414, -211.51450677, -308.68941596, -350.36069763,\n",
       "        -135.02429566, -225.02486353, -193.16550516, -276.49162324,\n",
       "        -363.75106088, -265.06967927, -232.92598132, -234.43202715,\n",
       "        -190.66281226, -325.25775608, -436.51271562, -408.69141107,\n",
       "        -256.99524787, -379.53120622, -294.39740751, -292.28306556,\n",
       "        -362.08380454, -215.52280148, -429.97243336, -399.31568621,\n",
       "        -398.51592568, -215.20901118, -351.08176819, -235.6456745 ,\n",
       "        -382.23272555, -527.28575975, -407.06882746, -541.7489586 ,\n",
       "        -523.26360701, -472.32354903, -417.49680196, -327.8255551 ,\n",
       "        -329.99359076, -392.21795071, -209.88455435, -215.13661089,\n",
       "        -267.45974063, -349.77628501, -309.10506263, -315.15993772]),\n",
       " array([-102.08740148, -186.37971925,  -52.32604737, -136.08900735,\n",
       "        -106.92193293, -135.59322528,    1.6055579 , -144.3320021 ,\n",
       "        -121.26621607,    3.2828694 ,  -67.0267761 , -290.75999082,\n",
       "        -214.70227764, -251.07741677, -271.93200164, -130.17520287,\n",
       "        -315.66543114, -261.52764962,  -27.93602766,   52.22673738,\n",
       "        -127.48622259,  -79.50268637, -129.88727419,   57.28153535,\n",
       "         -12.96765481,  133.46324849, -197.89238778, -124.2018134 ,\n",
       "        -162.60840011, -151.14541871,  -63.39786775, -145.89106357,\n",
       "        -144.79302431, -114.46758656,  -98.10150981,   -9.53932695,\n",
       "         -10.47020915, -201.65671082,  -43.36663982,  -86.09478396,\n",
       "        -171.41706609,  -19.08014331,  -44.4066046 , -199.25746267,\n",
       "        -183.08069858,  182.07073782, -185.45548184, -234.54383222,\n",
       "        -204.53478655, -299.20557546, -371.80215839, -212.57117611,\n",
       "        -321.80119275, -314.12486891, -396.43280825,  -43.39557399,\n",
       "        -175.6939831 , -122.46529778, -163.67916412, -227.467637  ,\n",
       "        -170.77599036, -268.5844638 , -214.68186164, -257.99138378,\n",
       "        -167.04307178, -151.72991116, -187.9838811 , -142.90787791,\n",
       "        -211.9913821 , -184.3610293 , -143.1624626 , -226.72226152,\n",
       "         -66.05432177, -146.9822123 , -119.81820936, -100.77694142,\n",
       "         -65.31190987, -132.35817256,   93.77523282,  -84.15201356,\n",
       "         -84.55271968, -109.7571089 ,  -57.37777933,  -33.41784676,\n",
       "         -40.35522062,  -97.29111863,   88.23471491, -105.80945327,\n",
       "         -17.36612248,  -54.68888151, -195.00537632,  -38.0511309 ,\n",
       "        -104.83645633,  -76.15494924,  -91.0839172 ,  111.51775558,\n",
       "        -117.52915123, -105.43844772, -247.5575705 , -173.64871561,\n",
       "        -120.57517217, -178.14369864,  -99.27775721,   -5.40165339,\n",
       "         -70.14820155,  -80.84010501, -150.15720561,  -45.68214989,\n",
       "        -109.07932607, -248.02339683,  -23.90538696,  -14.18663065,\n",
       "         -94.5451205 ,  -56.41744745, -142.59135228, -125.07138337,\n",
       "        -128.93124173,  -12.72507223, -107.5967888 ,  -28.80024318,\n",
       "        -135.35922055, -173.36627709, -208.96598837,  -90.75144875,\n",
       "         -69.76208616,  -65.72943825, -201.03067603, -242.91837409,\n",
       "        -242.61690354, -359.33121324, -221.67250265, -183.17191174,\n",
       "        -307.29376923, -136.5055004 , -137.43808893, -268.52079555,\n",
       "        -385.10375931, -276.32507575, -249.37321935, -291.68282628,\n",
       "        -232.47613752, -364.72448306, -164.76613401, -357.41541161,\n",
       "        -155.08957795, -243.9359261 , -352.01097649, -358.1287349 ,\n",
       "        -193.41031423, -278.45049278, -162.30575912, -213.56069195,\n",
       "        -160.179259  , -263.25949671, -216.66191435, -278.24989084,\n",
       "        -126.74157152, -186.3303025 , -216.69107396, -178.35032458,\n",
       "        -223.8800633 , -316.13263261, -179.97080719, -269.9963393 ,\n",
       "        -245.92179345, -212.38621851, -117.16863179,  -18.65395287,\n",
       "          15.30345258, -219.22417642, -190.00533373, -219.46632498,\n",
       "         -46.40262834, -100.06591999, -183.52384171,  106.59759503,\n",
       "        -173.08779764,  -29.22587707,  -13.98939254, -106.12478317,\n",
       "        -130.19330422, -104.10605166,   -4.39250431, -135.73666944,\n",
       "         -83.62415877, -108.53955788,  -31.2803343 , -136.67057882,\n",
       "        -177.5727608 ,  -61.6794123 , -153.03543712,  -72.12539612,\n",
       "        -106.96148122, -197.77068716, -172.07940559, -299.10718494,\n",
       "        -130.61538323,  -56.88732697,   47.89504376, -105.19702671,\n",
       "         -93.78723349, -191.85992232, -115.0397592 , -172.59305861,\n",
       "        -166.54601905, -102.63983028, -114.77845605,  -98.93095714,\n",
       "        -130.26611567, -174.80564437,  -99.70590716,  -24.97794035,\n",
       "         -59.27246606,  -90.91319185, -185.81938102, -140.81765175,\n",
       "         -17.42903304, -178.99070735,  -46.46410451, -254.33755722,\n",
       "        -176.93755228,  -80.69199343, -191.68037242, -166.76796559,\n",
       "        -188.16938496, -198.42301622, -290.55740533, -404.61136764,\n",
       "         -93.66404005, -346.1438861 , -288.62281383, -286.02308083,\n",
       "        -331.54718138, -204.5344622 , -176.08363727, -408.28609839,\n",
       "        -249.1029061 , -209.88218119, -359.78718408, -143.09998833,\n",
       "        -269.02552581, -325.39481507, -226.53830226, -334.19219229,\n",
       "        -296.42235761, -248.09916206, -140.69950887, -189.16007065,\n",
       "        -204.38157244, -349.5158067 , -259.51468423, -280.54102287,\n",
       "        -232.61115893, -342.3784693 ,   58.16948962,  -73.47931677,\n",
       "        -166.88689858, -204.43307925, -129.3107599 , -228.46471947,\n",
       "        -162.62819005,  -36.03544268, -133.21035187, -174.88163354,\n",
       "          40.45476842,  -49.54579944,  -17.68644107, -101.01255915,\n",
       "        -188.2719968 ,  -89.59061519,  -57.44691723,  -58.95296307,\n",
       "         -15.18374818, -149.778692  , -261.03365153, -233.21234699,\n",
       "         -81.51618379, -204.05214213, -118.91834343, -116.80400147,\n",
       "        -186.60474046,  -40.0437374 , -254.49336927, -223.83662212,\n",
       "        -223.0368616 ,  -39.7299471 , -175.6027041 ,  -60.16661041,\n",
       "        -208.95088604, -354.00392024, -233.78698795, -368.46711909,\n",
       "        -349.9817675 , -299.04170952, -244.21496245, -154.54371559,\n",
       "        -156.71175126, -218.9361112 ,  -36.60271484,  -41.85477138,\n",
       "         -94.17790112, -176.4944455 , -135.82322312, -141.87809821]),\n",
       " {'data_probs': [0.512, 0.128, 0.128, 0.032, 0.2],\n",
       "  'data_sets': [[0, 1, 3, 2],\n",
       "   [0, 1, 3, -inf],\n",
       "   [0, 1, -inf, 2],\n",
       "   [0, 1, -inf, -inf],\n",
       "   [0, -inf, -inf, -inf]],\n",
       "  'max_obs_time': 4,\n",
       "  'num_data_samps': 100,\n",
       "  'param_sample_size': 100,\n",
       "  'scale_free_bounds': (0.1, 10),\n",
       "  'sparsity': 0.1,\n",
       "  'stigma_sample_size': 10000})"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.99999996169 [('A_★', 'B_★'), ('A_★', 'A_obs'), ('A_int', 'A_★'), ('A_int', 'A_obs'), ('C_★', 'C_obs'), ('C_★', 'B_★'), ('C_★', 'D_★'), ('D_★', 'B_★'), ('D_★', 'D_obs'), ('B_★', 'C_★'), ('B_★', 'D_★'), ('B_★', 'B_obs')] \n",
      " [  1.65527938e-152   2.86803053e-180   1.79175801e-165   1.25769048e-115\n",
      "   6.14310205e-104   2.14438829e-131   5.88264913e-171   4.10128374e-061\n",
      "   4.71054598e-110   1.39934943e-118   1.38472974e-159   1.78028183e-163\n",
      "   2.65271370e-113   3.57187388e-203   1.71293804e-177   6.24974662e-177\n",
      "   1.27740528e-193   7.99141725e-164   4.01743671e-048   8.64749904e-159\n",
      "   2.98525456e-107   3.07176300e-089   7.82008652e-076   2.91914527e-153\n",
      "   5.49177848e-104   5.65395416e-097   3.66739966e-181   6.09374480e-085\n",
      "   3.48622291e-116   1.26127898e-151   1.87618367e-085   2.28505217e-155\n",
      "   3.16256690e-160   5.67527932e-127   1.85386073e-085   8.12142729e-128\n",
      "   5.72013956e-009   1.50583792e-124   1.08081814e-110   4.14368401e-152\n",
      "   6.13789015e-066   2.84427348e-079   9.34236077e-103   2.63349110e-133\n",
      "   1.00897414e-167   3.13782109e-078   1.68641590e-169   3.36595894e-191\n",
      "   1.18745150e-153   1.84089658e-109   4.73219515e-144   4.55264949e-211\n",
      "   1.46511693e-152   2.48247255e-206   4.37242930e-209   1.97607062e-109\n",
      "   6.74491050e-105   1.18674035e-140   1.93446934e-140   7.40030167e-174\n",
      "   6.01161833e-163   2.35471580e-202   4.59300193e-121   1.76529573e-147\n",
      "   1.23416581e-103   1.37289082e-166   9.05279639e-208   3.34495396e-166\n",
      "   3.14039444e-240   1.42696536e-166   8.82924992e-149   8.83592176e-251\n",
      "   2.48559326e-107   2.86539102e-173   1.50251279e-096   1.14682713e-141\n",
      "   1.40845160e-169   9.99999962e-001   2.60898419e-134   1.07447476e-068\n",
      "   5.63983303e-063   2.23271342e-158   7.70184795e-160   1.05287590e-107\n",
      "   6.37258391e-111   1.80390999e-150   8.11061358e-142   2.39238228e-163\n",
      "   1.73166651e-078   1.15439520e-136   8.95598174e-090   1.83094012e-153\n",
      "   2.81234543e-130   1.75599211e-093   8.77380132e-151   2.86745085e-059\n",
      "   1.12798300e-119   1.60756928e-157   9.17442928e-170   2.92134758e-142\n",
      "   4.75590322e-148   2.13829525e-133   7.79417259e-115   4.24059173e-146\n",
      "   2.21582847e-137   5.14662306e-113   7.44107091e-127   2.29045022e-123\n",
      "   1.18339615e-107   8.33181775e-112   6.30381742e-142   1.90945117e-154\n",
      "   1.11285394e-093   2.67005858e-122   1.09613873e-015   7.37864271e-131\n",
      "   4.14331636e-046   9.62647720e-163   5.98670139e-081   1.44896922e-158\n",
      "   1.12530681e-188   2.48830738e-109   2.39837278e-167   2.11241339e-131\n",
      "   4.72679519e-125   2.11663646e-038   1.63276153e-169   1.64762271e-207\n",
      "   3.93502109e-115   6.62220239e-182   7.21411084e-066   5.37293487e-144\n",
      "   4.16248018e-225   2.63122456e-192   1.67207691e-165   2.78266814e-224\n",
      "   7.93700556e-229   1.17382552e-129   1.36409147e-190   3.01685102e-234\n",
      "   1.21290295e-162   2.12198709e-234   8.12818146e-168   3.59967266e-196\n",
      "   3.33249729e-185   4.83424844e-147   1.73613215e-175   4.81595239e-158\n",
      "   1.21414785e-168   1.29432541e-171   2.67965486e-101   4.32092658e-181\n",
      "   5.69098904e-187   3.09360887e-188   6.25722390e-139   9.08563309e-101\n",
      "   2.43388638e-202   4.57603647e-161   2.17231972e-161   1.38334366e-164\n",
      "   5.29229530e-120   1.53105080e-183   2.00754930e-148   9.58346514e-140\n",
      "   1.79678937e-131   2.02446762e-202   1.59092945e-163   4.32136271e-082\n",
      "   9.72688650e-102   2.25729734e-210   6.94025170e-157   1.63502260e-129\n",
      "   5.67198802e-034   7.71834600e-161   1.89823446e-084   4.28905745e-113\n",
      "   6.71212824e-131   2.20652219e-104   8.39849280e-079   1.39683173e-101\n",
      "   3.77863253e-126   2.36421197e-105   7.36285120e-071   4.04022665e-120\n",
      "   1.32021189e-103   1.19892928e-125   5.71245177e-085   4.32305242e-089\n",
      "   1.26724981e-161   4.66966258e-096   6.73361965e-111   1.07732246e-059\n",
      "   1.66232321e-142   7.09639521e-041   3.32058439e-186   1.40899015e-166\n",
      "   1.35991158e-098   6.62606782e-124   1.82667897e-158   3.12885262e-117\n",
      "   2.82899200e-082   4.57767617e-111   7.36812674e-148   5.83443920e-145\n",
      "   1.10683037e-130   4.15590834e-138   7.63605144e-107   1.37631908e-129\n",
      "   3.87913705e-154   1.52089063e-161   5.62380191e-069   1.26562046e-077\n",
      "   2.99085582e-166   1.37962077e-050   3.70852818e-131   8.92583098e-177\n",
      "   5.25212086e-115   3.50025653e-162   1.19208626e-164   7.02559269e-068\n",
      "   5.65673157e-142   1.94972985e-121   2.30666301e-106   8.27114823e-184\n",
      "   1.32249031e-073   7.64930381e-081   3.59896444e-172   9.81681068e-260\n",
      "   2.88352682e-078   1.14423583e-206   6.21831157e-191   1.91470841e-122\n",
      "   1.84103823e-166   1.16331873e-185   3.51558346e-153   1.07968028e-181\n",
      "   3.95931235e-126   5.10413241e-231   1.01500978e-301   1.27721924e-260\n",
      "   4.53479068e-155   1.14264679e-221   5.67867109e-179   2.45470691e-188\n",
      "   6.78970783e-206   8.04444349e-134   1.68540695e-119   3.02278817e-180\n",
      "   1.88337874e-186   2.44734267e-220   1.44776794e-199   4.19991404e-199\n",
      "   1.22040438e-103   4.50053827e-214   3.39345820e-115   2.34786001e-091\n",
      "   2.20864770e-040   6.69537416e-165   7.35982541e-135   2.30278385e-169\n",
      "   7.63498106e-038   4.15697606e-141   1.41415931e-114   6.07769314e-138\n",
      "   3.35873330e-101   9.64035756e-132   1.55768832e-077   2.43120627e-195\n",
      "   2.14677337e-174   5.44825074e-095   5.86510229e-079   2.05854049e-175\n",
      "   3.80535295e-019   5.33138580e-131   4.03874686e-134   1.90372471e-166\n",
      "   1.35762088e-162   3.25898575e-008   1.82393571e-126   1.14336570e-144\n",
      "   8.78205389e-149   3.30425874e-184   1.01628632e-182   3.27064944e-171\n",
      "   2.50497623e-167   1.17448914e-175   5.74336604e-129   2.32660332e-229\n",
      "   5.03778878e-113   6.31924648e-179   9.21930017e-162   3.02326353e-217\n",
      "   6.08168860e-139   8.86066548e-186   1.60048436e-186   7.14459072e-240\n",
      "   6.61375916e-126   8.66127605e-138   9.33664709e-154   9.57608384e-165\n",
      "   1.29921475e-040   6.18770585e-083   1.94886701e-147   6.22238004e-205]\n"
     ]
    }
   ],
   "source": [
    "print(np.amax(blah[1]),blah[0][np.argmax(blah[1])].edges(),\"\\n\",blah[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lag_slo_results = {(\"A_★\",\"B_★\"):[1.00, .96, .58,.92], (\"A_★\",\"C_★\"):[.38, .17, .88, .29], (\"A_★\",\"D_★\"):[.33, .13, .54, .33],\n",
    "           (\"B_★\",\"C_★\"):[.75, .79, .21, .79], (\"B_★\",\"D_★\"):[.75, .96, .38, .88],\n",
    "           (\"C_★\",\"B_★\"):[.63, .38, .79, .50], (\"C_★\",\"D_★\"):[.29, .21, .33, .29],\n",
    "           (\"D_★\",\"B_★\"):[.50, .46, .50, .46], (\"D_★\",\"C_★\"):[.25, .83 ,.71 ,.21]}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "graph_test = blah[0]\n",
    "posterior = blah[1]\n",
    "edges_of_interest = {edge:0 for edge in lag_slo_results}\n",
    "for idx,g in enumerate(graph_test):\n",
    "    for edge in edges_of_interest:\n",
    "        if edge in g.edges():\n",
    "            edges_of_interest[edge]+=posterior[idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{('A_★', 'B_★'): 1.0,\n",
       " ('A_★', 'C_★'): 1.0,\n",
       " ('A_★', 'D_★'): 1.0,\n",
       " ('B_★', 'C_★'): 1.1982043390600511e-54,\n",
       " ('B_★', 'D_★'): 8.6266451758226808e-20,\n",
       " ('C_★', 'B_★'): 8.6266451758226808e-20,\n",
       " ('C_★', 'D_★'): 1.0,\n",
       " ('D_★', 'B_★'): 1.0,\n",
       " ('D_★', 'C_★'): 1.0}"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "edges_of_interest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "run_2015_49_1_1102 = {('A_★', 'B_★'): 1.0,\n",
    " ('A_★', 'C_★'): 1.0,\n",
    " ('A_★', 'D_★'): 1.0,\n",
    " ('B_★', 'C_★'): 1.1982043390600511e-54,\n",
    " ('B_★', 'D_★'): 8.6266451758226808e-20,\n",
    " ('C_★', 'B_★'): 8.6266451758226808e-20,\n",
    " ('C_★', 'D_★'): 1.0,\n",
    " ('D_★', 'B_★'): 1.0,\n",
    " ('D_★', 'C_★'): 1.0}\n",
    "\n",
    "run_2015_49_1_1059={('A_★', 'B_★'): 1.0,\n",
    " ('A_★', 'C_★'): 1.0,\n",
    " ('A_★', 'D_★'): 1.0,\n",
    " ('B_★', 'C_★'): 8.8901140884189542e-28,\n",
    " ('B_★', 'D_★'): 1.0,\n",
    " ('C_★', 'B_★'): 4.4582821340587969e-34,\n",
    " ('C_★', 'D_★'): 8.1965813529476814e-38,\n",
    " ('D_★', 'B_★'): 8.8901140875992973e-28,\n",
    " ('D_★', 'C_★'): 1.0}\n",
    "\n",
    "run_2015_48_7_1426 = {('A_★', 'B_★'): 1.0,\n",
    " ('A_★', 'C_★'): 2.0708959078396752e-86,\n",
    " ('A_★', 'D_★'): 1.0,\n",
    " ('B_★', 'C_★'): 1.0,\n",
    " ('B_★', 'D_★'): 1.0,\n",
    " ('C_★', 'B_★'): 1.0,\n",
    " ('C_★', 'D_★'): 1.0215809716219825e-83,\n",
    " ('D_★', 'B_★'): 1.0215809716219807e-83,\n",
    " ('D_★', 'C_★'): 1.0}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('B★', 'D★') ('C_★', 'B_★') False\n",
      "('B★', 'D★') ('C_★', 'D_★') False\n",
      "('B★', 'D★') ('C_★', 'C_obs') False\n",
      "('B★', 'D★') ('D_★', 'C_★') False\n",
      "('B★', 'D★') ('D_★', 'D_obs') False\n",
      "('B★', 'D★') ('D_★', 'B_★') False\n",
      "('B★', 'D★') ('A_★', 'C_★') False\n",
      "('B★', 'D★') ('A_★', 'D_★') False\n",
      "('B★', 'D★') ('A_★', 'B_★') False\n",
      "('B★', 'D★') ('A_★', 'A_obs') False\n",
      "('B★', 'D★') ('A_int', 'A_★') False\n",
      "('B★', 'D★') ('A_int', 'A_obs') False\n",
      "('B★', 'D★') ('B_★', 'B_obs') False\n",
      "('B★', 'D★') ('B_★', 'C_★') False\n",
      "('B★', 'D★') ('B_★', 'D_★') False\n",
      "('B★', 'D★') [('C_★', 'B_★'), ('C_★', 'D_★'), ('C_★', 'C_obs'), ('D_★', 'C_★'), ('D_★', 'D_obs'), ('D_★', 'B_★'), ('A_★', 'C_★'), ('A_★', 'D_★'), ('A_★', 'B_★'), ('A_★', 'A_obs'), ('A_int', 'A_★'), ('A_int', 'A_obs'), ('B_★', 'B_obs'), ('B_★', 'C_★'), ('B_★', 'D_★')]\n"
     ]
    }
   ],
   "source": [
    "[print(test_edge,edge,test_edge==edge) for edge in graph_local_test.edges()]\n",
    "print(test_edge,graph_local_test.edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "FloatingPointError",
     "evalue": "underflow encountered in exp",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mFloatingPointError\u001b[0m                        Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-24-7d074ae8a050>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1472.12616223\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m451.77893777\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mFloatingPointError\u001b[0m: underflow encountered in exp"
     ]
    }
   ],
   "source": [
    "np.exp(-1472.12616223+451.77893777)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{('A★', 'B★'): 0,\n",
       " ('A★', 'C★'): 0,\n",
       " ('A★', 'D★'): 0,\n",
       " ('B★', 'C★'): 0,\n",
       " ('B★', 'D★'): 0,\n",
       " ('C★', 'B★'): 0,\n",
       " ('C★', 'D★'): 0,\n",
       " ('D★', 'B★'): 0,\n",
       " ('D★', 'C★'): 0}"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "edges_of_interest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-27-76986cc32345>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmulti_edge_loglik\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcond\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvals\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtest_obs_dict\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-8-6a1fd1bdbee4>\u001b[0m in \u001b[0;36mmulti_edge_loglik\u001b[0;34m(obs_data, aux_data, parameters)\u001b[0m\n\u001b[1;32m     84\u001b[0m     \u001b[0mlocal_dict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mparameters\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnon_int_node_idx\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mparameters\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mgrab\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     85\u001b[0m     \u001b[0;31m# end special casing\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 86\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mone_edge_loglik\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maux_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mobs_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlocal_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'psi'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlocal_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'r'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maux_data\u001b[0m\u001b[0;34m)\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[0m\u001b[1;32m     87\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     88\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mone_edge_loglik\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcause_time\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0meffect_time\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpsi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m4.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-8-6a1fd1bdbee4>\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m     84\u001b[0m     \u001b[0mlocal_dict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mparameters\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnon_int_node_idx\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mparameters\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mgrab\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     85\u001b[0m     \u001b[0;31m# end special casing\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 86\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mone_edge_loglik\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maux_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mobs_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlocal_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'psi'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlocal_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'r'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maux_data\u001b[0m\u001b[0;34m)\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[0m\u001b[1;32m     87\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     88\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mone_edge_loglik\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcause_time\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0meffect_time\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpsi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m4.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-8-6a1fd1bdbee4>\u001b[0m in \u001b[0;36mone_edge_loglik\u001b[0;34m(cause_time, effect_time, psi, r, T)\u001b[0m\n\u001b[1;32m     88\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mone_edge_loglik\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcause_time\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0meffect_time\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpsi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m4.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misinf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcause_time\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 90\u001b[0;31m         \u001b[0;32mif\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misinf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0meffect_time\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     91\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     92\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misinf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0meffect_time\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()"
     ]
    }
   ],
   "source": [
    "gp_in_fail_vals = {'names': [('A_★', 'B_★'), ('A_★', 'C_★'), ('A_★', 'D_★'), ('B_★', 'C_★'), ('B_★', 'D_★'), ('C_★', 'B_★'), ('C_★', 'D_★'), ('D_★', 'B_★'), ('D_★', 'C_★')], \n",
    "                   'psi_shape': 1.0, 'scale_free_bounds': (0.01, 100), 'r_shape': 1.0, 'lambda0': [0.037349167467439832], \n",
    "                   'psi': array([ 0.01195408,  0.02494409,  0.00407828,  0.07041525,  0.01168542,\n",
    "                                  0.01013971,  0.0046222 ,  0.01029149,  0.0621953 ]), \n",
    "                   'p': 0.8, \n",
    "                   'r': array([ 0.0239634 ,  0.02811854,  0.0336865 ,  0.02064403,  0.00664095,\n",
    "                                0.06360037,  0.02304081,  0.15325807,  0.03603926]), \n",
    "                   'mu': array([ 0.49884723,  0.88710491,  0.12106568,  3.41092559,  1.75960088,\n",
    "                                0.15942848,  0.20060942,  0.06715135,  1.72576522]), \n",
    "                   'n': 9}\n",
    "\n",
    "gp_out_fail_vals = {'names': [('A_★', 'A_obs'), ('B_★', 'B_obs'), ('C_★', 'C_obs'), ('D_★', 'D_obs')], \n",
    "                    'psi_shape': 1.0, 'scale_free_bounds': (0.01, 100), 'r_shape': 1.0, 'lambda0': [19.686293142206129], \n",
    "                    'psi': array([  1.38592213,   3.41047513,  13.52959655,   5.91527893]), \n",
    "                    'p': 0.8, \n",
    "                    'r': array([ 27.80976062,   9.96873594,   4.88959094,  19.21709961]), \n",
    "                    'mu': array([ 0.04983582,  0.34211711,  2.76702013,  0.3078133 ]), \n",
    "                    'n': 4}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  0.00000000e+00   4.39708118e-03   3.56390243e-05   2.34457398e-03]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   2.92711169e-04   1.32436979e-05   4.04063932e-04]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   1.40804714e-03   2.58542260e-05   1.44274609e-03]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   5.30002450e-03   1.09208375e-05   5.16324886e-03]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   2.87249148e-02   8.66971173e-07   1.20610594e-02]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   1.45246954e-02   1.51809662e-05              inf]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   1.33380125e-03   1.17790467e-05   2.29996792e-04]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   4.19636151e-06   2.23568314e-06   7.59963574e-05]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   7.44406249e-04   3.12735120e-06   4.57198663e-05]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   3.73669284e-03   2.43061334e-05   2.52999236e-03]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   1.32428528e-02   8.17643301e-06   1.32553038e-02]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   4.41817953e-03   6.84906671e-06   4.42565859e-03]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[ 0.          0.00057774  0.00372301  0.00060458]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00              inf   4.03313810e-06              inf]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   1.88856371e-03   6.69340322e-05   3.43900141e-04]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   2.07326341e-04   1.69890712e-05   1.30922649e-04]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   1.94485148e-03   4.54318430e-06   7.90476270e-04]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[ 0.          0.00093952  0.00154976  0.00103241]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   1.36765247e-02   1.27494886e-05   1.17631982e-02]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n",
      "[  0.00000000e+00   8.44875006e-04   1.80939965e-05   8.56664031e-04]+these are the hidden states\n",
      "[-358.83800760864631, -238.01125912136806, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, -238.01125912136806, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, -1561.2847809127313] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[-358.83800760864631, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "[0.0, 2.7541403718603701e-141, 0.0] one edge loglik for BCD with psi [ 331.06420177  303.6097455   331.98830824] and r [ 364.74708547   81.24269274  783.70327345]\n",
      "\n",
      "-143861.987171\n"
     ]
    }
   ],
   "source": [
    "cond = cond_to_data(cond2)\n",
    "local_stigma_sample_size = 20\n",
    "local_graph = graphs[0]\n",
    "local_gs_in, local_gp_in = sub_graph_sample(local_graph,edge_types=[\"hidden_sample\"], param_init=sf_big)\n",
    "local_gs_out, local_gp_out = sub_graph_sample(local_graph,edge_types=['observed'], param_init=sf_big)\n",
    "vals = gen_simulations(local_gs_in,local_gp_in,local_stigma_sample_size)\n",
    "test_obs_dict = local_gp_out.to_dict()\n",
    "local_probs=[0.512,0.128,0.128,0.032,.2]\n",
    "for val in vals:\n",
    "    print(\"{}+these are the hidden states\".format(val))\n",
    "    print(cross_entropy_loglik(data_sets= cond,probability=local_probs,k = 100,aux_data= vals[1],obs_dict=test_obs_dict))\n",
    "# for i,cond_i in enumerate(cond):\n",
    "#     print(\"\\n\\n\"+str(i+1)+\"th\"+\"condition\")\n",
    "#     print(cond_i)\n",
    "#     for samp in vals:\n",
    "#         local_vals =[]\n",
    "#         for i in range(1,4):\n",
    "#             here = one_edge_loglik(samp[i],cond_i[i],test_obs_dict['psi'][i],test_obs_dict['r'][i])\n",
    "#             print(here)\n",
    "#             local_vals.append(here)\n",
    "#         print(\"{} is sum of lls\".format(sum(local_vals)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('B_★', 'D_★'),\n",
       " ('B_★', 'C_★'),\n",
       " ('B_★', 'B_obs'),\n",
       " ('A_★', 'D_★'),\n",
       " ('A_★', 'C_★'),\n",
       " ('A_★', 'A_obs'),\n",
       " ('A_★', 'B_★'),\n",
       " ('D_★', 'D_obs'),\n",
       " ('D_★', 'B_★'),\n",
       " ('D_★', 'C_★'),\n",
       " ('C_★', 'B_★'),\n",
       " ('C_★', 'C_obs'),\n",
       " ('C_★', 'D_★'),\n",
       " ('A_int', 'A_★'),\n",
       " ('A_int', 'A_obs')]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graphs[0].edges()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 2]"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cond[0][slice(1,4)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data from lagnado & Sloman\n",
    "\n",
    "value_sequences = ['ABCD', 'ABC', 'ABD', 'AB','A']\n",
    "data_vals = np.random.choice(value_sequences, size = 100, \n",
    "cond1timings= {\"A\":0,\"B\":0,\"C\":0,\"D\":0}\n",
    "cond2timings= {\"A\":0,\"B\":1,\"C\":3,\"D\":2}\n",
    "cond3timings= {\"A\":0,\"B\":3,\"C\":2,\"D\":1}\n",
    "cond4timings= {\"A\":0,\"B\":1,\"C\":2,\"D\":2}\n",
    "\n",
    "\n",
    "results = {(\"a\",\"b\"):[1.00, .96, .58,.92], ('a','c'):[.38, .17, .88, .29], ('a','d'):[.33, .13, .54, .33],\n",
    "           (\"b\",\"c\"):[.75, .79, .21, .79], ('b','d'):[.75, .96, .38, .88],\n",
    "           (\"c\",\"b\"):[.63, .38, .79, .50], ('c','d'):[.29, .21, .33, .29],\n",
    "           (\"d\",\"b\"):[.50, .46, .50, .46], (\"d\",\"c\"):[.25, .83 ,.71 ,.21]}\n",
    "\n",
    "\n",
    "pdf of k arrivals in interval (0,T) is $\\frac{(Λ_{0,T})^k \\exp(Λ_{0,T})}{k!}$\n",
    "\n",
    "so pdf of 0 arrivals between 0 and T is $\\exp(-Λ_{0,T})$, pdf of the first arrival occuring at $\\tau$ is the product of the itstantaneous rate at $\\tau$ and the probability that no event occurred before $\\tau$ (from 0 to $\\tau$) is $λ(T)\\exp(-Λ_{0,T})$\n",
    "\n",
    "lets say a cause at $t_0$ initiates our rate function so that it's 0 before $t_0$ and $λ(t;t_0)$\n",
    "\n",
    "if our $λ(t; t_0) = 𝜓\\exp(-r(t-t_0))$ then $Λ_{0,T} = \\frac{𝜓}{r}(1 - \\exp(-r(T-t_0)))$\n",
    "\n",
    "so the log likelihoods of the pdf for no events by T is $\\frac{𝜓}{r}(1 - \\exp(-r(T-t_0)))$ and for 1 event exactly at $\\tau$ is $$\\log(λ(\\tau;t_0))+ \\log(\\exp(-Λ_{0,T})) = \\log(𝜓) - (r(\\tau-t_0)) + \\frac{𝜓}{r}(1 - \\exp(-r(T-t_0)))$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "def p_graph_given_d(graphs,options):\n",
    "    \"\"\"\n",
    "    options includes sparsity,param_sample_size,stigma_sample_size,data_sets,data_p,num_data_samps\n",
    "    this creates p a 5 dimensional array which it passes the first value of to p_d_given_graph\n",
    "    \"\"\"\n",
    "    \n",
    "#     graphs = list(generate_graphs(**generator_dictionary))\n",
    "    max_edges = max([len(x.edges()) for x in graphs])\n",
    "#     maxd = max([len(d[i]) for i in range(len(d))])\n",
    "#     shape = (len(graphs), options['num_parameter_samples'], len(d), options['num_state_samples'], maxd)\n",
    "#     p = np.empty(shape)\n",
    "#     p.fill(np.nan)\n",
    "    param_sample_size= options[\"param_sample_size\"]\n",
    "    stigma_sample_size = options[\"stigma_sample_size\"]\n",
    "    data_sets = options[\"data_sets\"]\n",
    "    data_p = options[\"data_p\"]\n",
    "    num_data_samps = options[\"num_data_samps\"]\n",
    "    scale_free_bounds = options[\"scale_free_bounds\"]\n",
    "    \n",
    "    q = np.empty(len(graphs))\n",
    "    unnormed_posterior =  np.empty(len(graphs))\n",
    "    posterior = np.empty(len(graphs))\n",
    "    likelihood = np.empty(len(graphs))\n",
    "    loglikelihood = np.empty(len(graphs))\n",
    "    q.fill(np.nan)\n",
    "    for i,graph in enumerate(graphs):\n",
    "#         p_d_given_graph(p[i,:,:,:,:], d, graphs[i], options)\n",
    "#         likelihood[i] = parameters_monte_carlo_lik(graph,param_sample_size,stigma_sample_size,\n",
    "#                                                    data_sets,data_p,num_data_samps,scale_free_bounds)\n",
    "        loglikelihood[i] = parameters_monte_carlo_loglik(graph,param_sample_size,stigma_sample_size,\n",
    "                                                   data_sets,data_p,num_data_samps,scale_free_bounds)\n",
    "        q[i] = graphs_prior(graphs[i],max_edges,sparsity=options[\"sparsity\"])\n",
    "    q = q/sum(q)\n",
    "    for i,graph in enumerate(graphs):\n",
    "#         unnormed_posterior[i] = np.log(q[i]*likelihood[i])\n",
    "        unnormed_posterior[i] = np.log(q[i]) + loglikelihood[i]\n",
    "    posterior = np.exp(unnormed_posterior)/sum(np.exp(unnormed_posterior))\n",
    "    return graphs,np.log(posterior),(unnormed_posterior),(loglikelihood),np.log(q)"
   ]
  }
 ],
 "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": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}