{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning An Egocentric SBM Kernel for the UK\n",
    "\n",
    "The aim of this notebook is to provide an end-to-end pipeline that learns an `EgocentricSBM` for the UK using egocentric surveys from Understanding Society, and the UK Census data.\n",
    "\n",
    "## UK Census Microdata\n",
    "\n",
    "In this section we look at the [microdata](https://census.ukdataservice.ac.uk/use-data/guides/microdata.aspx) available for UK Census 2011. In particular, the England-Wales dataset which has 2.8 million samples. We wish to look at key Blau dimensions of interest, so that we can align our own survey's design along with the census. Also, using microdata gives us the full testing distribution of the population, instead of one that is factorized over the Blau dimenions.\n",
    "\n",
    "Different kinds of microdata have been made available (w/o a special license) corresponding to different geographical granularity. We consider the dataset at the local authority level (also referred to as boroughs in London, and council areas in Scotland). The dataset is available at a *grouped* LA level, wherein a few LAs can be grouped such that each grouped-LA contains roughly 120,000 people.\n",
    "\n",
    "First, we write a function to import any census microdata file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def import_data(name=('2011', 'ew'), memory_map=True, datapath='./census/'):\n",
    "    import pandas as pd\n",
    "    datadict = {(2001, 'isar'):'UKDA-7205-tab/tab/01uklicind-20061002.tab',\n",
    "                (2001, 'sam'):'UKDA-7207-tab/tab/01uklicsam-20070301.tab',\n",
    "                (2011, 'ew'):'UKDA-7682-tab/tab/recodev12.tab',\n",
    "                (2011, 'n'):'UKDA-7770-tab/tab/ni_safeguarded_la.tab',\n",
    "                (2011, 's'):'UKDA-7835-tab/tab/safeguarded_grouped_la.tab'\n",
    "               }\n",
    "    geogdict = {(2001, 'isar'):'region',\n",
    "                (2001, 'sam'):'lacode',\n",
    "                (2011, 'ew'):'la_group',\n",
    "                (2011, 'n'):'LA_CODE_14',\n",
    "                (2011, 's'):'COUNCIL_AREA_GROUP'\n",
    "               }\n",
    "    datapath += datadict[name]\n",
    "    df = pd.read_csv(datapath, memory_map=memory_map, sep='\\t')\n",
    "    df.rename(columns={geogdict[name]:'geocode'}, inplace=True)\n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2848149, 121)\n"
     ]
    }
   ],
   "source": [
    "data_2011_ew = import_data((2011, 'ew'))\n",
    "print(data_2011_ew.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Understanding Society Data\n",
    "\n",
    "We previously took a look at the Understanding Society data, and many of its variables of interest. In this notebook, we try to align USoc with the Census data, so that we can estimate the social access statistic for LAs. First, we import USoc data for wave 3, which has information on people's local social networks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [],
   "source": [
    "def import_usoc_data(category='ukhls', wave=3, survey='indresp', datapath='./usoc/'):\n",
    "    datadict = {'ukhls':'UKDA-6614-tab/tab/ukhls_w', \n",
    "                'bhps':'UKDA-6614-tab/tab/bhps_w', \n",
    "                'nurse':'UKDA-7251-tab/tab/', \n",
    "                'ip':'UKDA-6849-tab/tab/'}\n",
    "    from string import ascii_lowercase\n",
    "    prefix = {'bhps':str(wave)+'/', 'ukhls':str(wave)+'/', 'nurse':'', 'ip':''}\n",
    "    suffix = {'bhps':'', 'ukhls':'', 'nurse':'_ns', 'ip':'_ip'}\n",
    "    wave_num2sym = {'bhps': dict(zip(range(1,19), ['b'+s+'_' for s in ascii_lowercase[0:18]])), \n",
    "                 'ukhls': dict(zip(range(1,8), [s+'_' for s in ascii_lowercase[0:7]])), \n",
    "                 'ip': dict(zip(range(1,11), [s+'_' for s in ascii_lowercase[0:10]])),\n",
    "                 'nurse': {2:'b',3:'c'}}\n",
    "    if isinstance(wave, int): wave_sym = wave_num2sym[category][wave]\n",
    "    else: wave_sym = wave\n",
    "    datapath = datapath + datadict[category] + prefix[category] + wave_sym + survey + suffix[category] + '.tab'\n",
    "    from pandas import read_csv\n",
    "    return {'cat':category, 'wav':wave, 'sym':wave_sym, 'svy':survey, 'tab':read_csv(datapath, sep='\\t')}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_wave3 = import_usoc_data(wave=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we right functions that will extract and align the USoc and Census datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [],
   "source": [
    "def extract_usoc(data):\n",
    "    import numpy as np\n",
    "    from pandas import concat\n",
    "    \n",
    "    if data['cat']!='ukhls': \n",
    "        print('please use a ukhls dataset')\n",
    "        return\n",
    "             \n",
    "    var = {'sex_dv':'sex',\n",
    "           'netsx':'sex_nom',\n",
    "           'age_dv':'age',\n",
    "           'simage':'age_prop',\n",
    "           'netag':'age_nom',\n",
    "           'racel_dv':'ethnicity',\n",
    "           'simrace':'ethnicity_prop',\n",
    "           'netet':'ethnicity_nom',\n",
    "           'qfhigh_dv':'education',\n",
    "           'simeduc':'education_prop',\n",
    "           'jbstat':'employment',\n",
    "           'simjob':'employment_prop',\n",
    "           'netjb':'employment_nom',\n",
    "           'fimngrs_dv':'income',\n",
    "           'siminc':'income_prop',\n",
    "           'simarea':'distance_prop',\n",
    "           'netlv':'distance_nom',\n",
    "           'simfam':'family_prop',\n",
    "           'closenum':'num_friends'\n",
    "          }\n",
    "    \n",
    "    var_encoding = {'sex':{1:'male',\n",
    "                           2:'female', \n",
    "                           (-10, -9, -8, -7, -2, -1, 0):np.nan},\n",
    "                    'ethnicity':{1:'british-white', \n",
    "                                 (2, 3, 4):'other-white',\n",
    "                                 (5, 6, 14, 15, 16):'black',\n",
    "                                 (7, 8, 12, 13):'other-asian',\n",
    "                                 (9, 10, 11):'south-asian',\n",
    "                                 #11:'bangladeshi',\n",
    "                                 #13:'other-asian',\n",
    "                                 (17, 97):'other-ethnicity',\n",
    "                                 (-10, -9, -8, -7, -2, -1):np.nan\n",
    "                                },\n",
    "                    'education':{(1, 2, 3, 4, 5, 6):'level-4',\n",
    "                                 (7, 8, 9):'level-3',\n",
    "                                 (10, 11, 12, 13):'level-2',\n",
    "                                 (14, 15, 16):'level-1',\n",
    "                                 96:'level-0',\n",
    "                                 (-10, -9, -8, -7, -2, -1):np.nan\n",
    "                                },\n",
    "                    'employment':{(1, 2, 5, 10, 11, 97):'employed',\n",
    "                                  3:'unemployed',\n",
    "                                  4:'retired', \n",
    "                                  6:'housework', \n",
    "                                  (7, 9):'student',\n",
    "                                  (8, -10, -9, -8, -7, -2, -1):np.nan\n",
    "                                 },\n",
    "                    'employment_nom':{(1, 2):'employed', \n",
    "                                      3:'unemployed', \n",
    "                                      4:'student',\n",
    "                                      5:'housework', \n",
    "                                      6:'retired',\n",
    "                                      (-10, -9, -8, -7, -2, -1):np.nan\n",
    "                                     },\n",
    "                    'distance_nom':{(1, 2):'similar', \n",
    "                                    (3, 4, 5):'dissimilar', \n",
    "                                    (-10, -9, -8, -7, -2, -1):np.nan\n",
    "                                   }\n",
    "                    }\n",
    "    \n",
    "    def expand_var(var_dict, prefix='', num_nom=3):\n",
    "        new_dict = dict()\n",
    "        for key, value in var_dict.items():\n",
    "            if key[:3]=='net':\n",
    "                for i in range(1, num_nom+1): new_dict[prefix+key+'_'+str(i)] = value+'_'+str(i)\n",
    "            else: new_dict[prefix+key] = value\n",
    "        return new_dict\n",
    "    \n",
    "    def expand_encoding(encoding_dict, atts=[], num_nom=3):\n",
    "        new_dict = dict()\n",
    "        for key, value in encoding_dict.items():\n",
    "            new_d = dict()\n",
    "            for k, v in value.items():\n",
    "                if not hasattr(k, '__iter__'): k = (k,)              \n",
    "                for i in k: new_d[i] = v\n",
    "            if key[-4:]=='_nom':\n",
    "                for i in range(1, num_nom+1):\n",
    "                    new_dict[key+'_'+str(i)] = new_d\n",
    "            else:\n",
    "                new_dict[key] = new_d\n",
    "                if key in atts and key+'_nom' not in encoding_dict:\n",
    "                    for i in range(1, num_nom+1):\n",
    "                        new_dict[key+'_nom_'+str(i)] = new_d\n",
    "        return new_dict\n",
    "    \n",
    "    def define_prop(x):\n",
    "        if x==1: return 1\n",
    "        elif x==2: return 3/4\n",
    "        elif x==3: return 1/2\n",
    "        elif x==4: return 1/4\n",
    "        else: return np.nan\n",
    "        \n",
    "    def derive_prop(df, atts=[], num_nom=3):\n",
    "        if not hasattr(atts, '__iter__'): atts = [atts]\n",
    "        dfs = list()\n",
    "        col = list()\n",
    "        self_atts = set(df)\n",
    "        for att in set(atts):\n",
    "            if att in self_atts:\n",
    "                idx = df[att].notnull()\n",
    "                friends = df[['_'.join([att, 'nom', str(i)]) for i in range(1, num_nom+1)]][idx]\n",
    "                dfs.append((friends.eq(df[att][idx], axis=0) & friends.notna()).sum(axis=1)/(friends.notna().sum(axis=1)))\n",
    "            else:\n",
    "                friends = df[['_'.join([att, 'nom', str(i)]) for i in range(1, num_nom+1)]]\n",
    "                dfs.append(friends.eq('similar').sum(axis=1)/(friends.notna().sum(axis=1)))\n",
    "            col.append(att+'_prop_dv')\n",
    "        dfs = concat(dfs, axis=1)\n",
    "        dfs.columns = col\n",
    "        return dfs\n",
    "    \n",
    "    def classify_age(x, granularity=20):\n",
    "        if np.isnan(x) or x < 16: return np.nan\n",
    "        else: return min(x, 99)//granularity*granularity\n",
    "        \n",
    "    def classify_age_static(x): #http://www.pgagroup.com/standardized-survey-classifications.html\n",
    "        if np.isnan(x) or x < 16: return np.nan\n",
    "        elif 16 <= x < 25: return 20.0\n",
    "        elif 25 <= x < 35: return 30.0\n",
    "        elif 35 <= x < 45: return 40.0\n",
    "        elif 45 <= x < 55: return 50.0\n",
    "        elif 55 <= x < 65: return 60.0\n",
    "        else: return 70.0\n",
    "        \n",
    "    def classify_income(x):\n",
    "        if np.isnan(x): return np.nan\n",
    "        elif x <= 584: return 'DE'\n",
    "        elif x <= 1342: return 'C2'\n",
    "        elif x <= 2115: return 'C1'\n",
    "        else: return 'AB'\n",
    "    \n",
    "    if data['sym']=='x': prefix = ''\n",
    "    else: prefix = data['sym']\n",
    "    var = expand_var(var, prefix)\n",
    "    out = data['tab'].loc[:,var.keys()]\n",
    "    out.index = data['tab']['pidp']\n",
    "    out.rename(columns=var, inplace=True)\n",
    "    var_encoding = expand_encoding(var_encoding, atts=['sex', 'ethnicity'])\n",
    "    out.replace(to_replace=var_encoding, inplace=True)\n",
    "    out.loc[out['employment']=='unemployed','employment_prop'] = 1-out.loc[out['employment']=='unemployed','employment_prop'] \n",
    "    out['age_raw'] = out['age']\n",
    "    #out['age'] = out['age'].apply(classify_age)\n",
    "    out['age'] = out['age'].apply(classify_age_static)\n",
    "    out['income_raw'] = out['income']\n",
    "    out['income'] = out['income'].apply(classify_income)\n",
    "    for i in range(1, 4):\n",
    "        out['age_raw_nom_'+str(i)] = out['age_nom_'+str(i)]\n",
    "        #out['age_nom_'+str(i)] = out['age_nom_'+str(i)].apply(classify_age)\n",
    "        out['age_nom_'+str(i)] = out['age_nom_'+str(i)].apply(classify_age_static)\n",
    "    for var_name in list(out):\n",
    "        if var_name[-5:]=='_prop': out[var_name] = out[var_name].apply(define_prop)\n",
    "    out[out._get_numeric_data()<0] = np.nan\n",
    "    out = concat([out, derive_prop(out, atts=['sex', 'age', 'ethnicity', 'employment', 'distance'])], axis=1)\n",
    "    out.dropna(axis=1, how='all', inplace=True)\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_wave3_atts = extract_usoc(data_wave3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def extract_census(data):\n",
    "    import numpy as np\n",
    "    \n",
    "    var = {'sex':'sex',\n",
    "           'ageh':'age',\n",
    "           'ethnicityew':'ethnicity',\n",
    "           'hlqupuk11':'education',\n",
    "           'ecopuk11':'employment',\n",
    "           'scgpuk11c':'income',\n",
    "           'religionew':'religion',\n",
    "           'mainglangg':'language',\n",
    "           'geocode':'geocode'\n",
    "          }\n",
    "    \n",
    "    var_encoding = {'sex':{1:'male',\n",
    "                           2:'female', \n",
    "                           -9:np.nan\n",
    "                          },\n",
    "                    'ethnicity':{1:'british-white', \n",
    "                                 (2, 3):'other-white',\n",
    "                                 (4, 11, 12):'black',\n",
    "                                 (5, 9, 10):'other-asian',\n",
    "                                 (6, 7, 8):'south-asian',\n",
    "                                 #8:'bangladeshi',\n",
    "                                 #10:'other-asian',\n",
    "                                 13:'other-ethnicity',\n",
    "                                 -9:np.nan\n",
    "                                },\n",
    "                    'education':{10:'level-0',\n",
    "                                 11:'level-1',\n",
    "                                 (12, 13, 16):'level-2',\n",
    "                                 14:'level-3',\n",
    "                                 15:'level-4',\n",
    "                                 -9:np.nan\n",
    "                                },\n",
    "                    'employment':{(1, 2, 3, 4, 7):'employed',\n",
    "                                  (5, 6):'unemployed',\n",
    "                                  (8, 9, 11):'student',\n",
    "                                  10:'retired',\n",
    "                                  12:'housework',\n",
    "                                  (13, 14, -9):np.nan\n",
    "                                 },\n",
    "                    'income':{1:'AB',\n",
    "                              2:'C1',\n",
    "                              3:'C2',\n",
    "                              4:'DE',\n",
    "                              -9:np.nan\n",
    "                             },\n",
    "                    'religion':{1:'atheist',\n",
    "                                2:'christian',\n",
    "                                3:'buddhist',\n",
    "                                4:'hindu',\n",
    "                                5:'jewish',\n",
    "                                6:'muslim',\n",
    "                                7:'sikh',\n",
    "                                8:'other-religion',\n",
    "                                (9, -9):np.nan\n",
    "                               },\n",
    "                    'language':{1:'english/welsh',\n",
    "                                2:'polish',\n",
    "                                3:'punjabi',\n",
    "                                4:'urdu',\n",
    "                                5:'bengali',\n",
    "                                6:'gujarati',\n",
    "                                7:'arabic',\n",
    "                                8:'french',\n",
    "                                9:'other-language',\n",
    "                                -9:np.nan\n",
    "                               }\n",
    "                   }\n",
    "    \n",
    "    def expand_encoding(encoding_dict):\n",
    "        new_dict = dict()\n",
    "        for key, value in encoding_dict.items():\n",
    "            new_d = dict()\n",
    "            for k, v in value.items():\n",
    "                if not hasattr(k, '__iter__'): k = (k,)              \n",
    "                for i in k: new_d[i] = v\n",
    "            new_dict[key] = new_d\n",
    "        return new_dict\n",
    "    \n",
    "    def decode_age(x):\n",
    "        return (x-0.5)*5\n",
    "        \n",
    "    def classify_age(x, granularity=20):\n",
    "        if np.isnan(x) or x < 4: return np.nan\n",
    "        else: return ((x-0.5)*5)//granularity*granularity\n",
    "        \n",
    "    def classify_age_static(x): #http://www.pgagroup.com/standardized-survey-classifications.html\n",
    "        if np.isnan(x) or x < 16: return np.nan\n",
    "        elif 16 <= x < 25: return 20.0\n",
    "        elif 25 <= x < 35: return 30.0\n",
    "        elif 35 <= x < 45: return 40.0\n",
    "        elif 45 <= x < 55: return 50.0\n",
    "        elif 55 <= x < 65: return 60.0\n",
    "        else: return 70.0\n",
    "    \n",
    "    out = data.loc[:,var.keys()]\n",
    "    out.rename(columns=var, inplace=True)\n",
    "    var_encoding = expand_encoding(var_encoding)\n",
    "    out.replace(to_replace=var_encoding, inplace=True)\n",
    "    out['age_raw'] = out['age'].apply(decode_age)\n",
    "    #out['age'] = out['age'].apply(classify_age)\n",
    "    out['age'] = out['age_raw'].apply(classify_age_static)\n",
    "    out[out._get_numeric_data()<0] = np.nan\n",
    "    out.dropna(axis=1, how='all', inplace=True)\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_c2011_atts = extract_census(data_2011_ew)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating SBM from USoc\n",
    "\n",
    "Now that we have parsed and aligned USoc-Census data, we are ready to learn the SBM. $\\rho$s are derived from prop-type questions for `education` and `income`, and from nominee-type questions using `nom2prop()` for `sex`, `age`, `ethnicity` and `employment`. The $\\omega$s are derived from the response of the question \"how many close friends do you have?\" (discounting for family). And $\\pi$s are derived from simple counts, **not from USoc but the census**, since the latter is more representative.\n",
    "\n",
    "Given that the expected number of friends in an SBM follows Poisson distribution, and the number of friends within the same community follow a Binomial distribution, we can place appropriate conjugate prior distributions on $\\omega$, $\\rho$ and $\\pi$ for every community. Namely, if there are $k$ communities, then $\\forall i \\in \\{1,2,\\dots k\\}$:\n",
    "\n",
    "$$\\omega_i\\sim\\mathrm{Gamma}(\\alpha_\\omega,\\beta_\\omega)$$\n",
    "$$\\rho_i\\sim\\mathrm{Beta}(\\alpha_\\rho,\\beta_\\rho)$$\n",
    "$$\\boldsymbol\\pi\\sim\\mathrm{Dirichlet}(\\alpha_\\pi, k)$$\n",
    "\n",
    "Upon observing appropriate data for these parameters, we can update the priors appropriately. Let us observe dataset $\\mathcal{D}$: $n_i$ people in community $i$, with number of friends $f_{i1},f_{i2},\\dots,f_{in_i}$ within $i$ and $g_{i1},g_{i2},\\dots,g_{in_i}$ outside of $i$. Then posterior distributions are given by:\n",
    "\n",
    "$$\\omega_i|\\mathcal{D} \\sim\\mathrm{Gamma}\\left(\\alpha_\\omega + \\sum_{j=1}^{n_i}{(f_{ij}+g_{ij})},\\beta_\\omega + n_i\\right)$$\n",
    "$$\\rho|\\mathcal{D} \\sim\\mathrm{Beta}\\left(\\alpha_\\rho + \\sum_{j=1}^{n_i}{f_{ij}},\\beta_\\rho + \\sum_{j=1}^{n_i}{g_{ij}}\\right)$$\n",
    "$$\\boldsymbol\\pi|\\mathcal{D} \\sim\\mathrm{Dirichlet}\\left(\\{\\alpha_\\pi+n_1, \\alpha_\\pi+n_2, \\dots \\alpha_\\pi+n_k\\}, k \\right)$$\n",
    "\n",
    "We can use the mean/mode of the posteriors as the parameter to feed into the SBM, while the variance of the posteriors can inform us about the errors of the model. We demonstrate with a simple example below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def posterior(priors={'pi':0.1, 'rho':(1.0, 1.0), 'omega':(3.0, 1.0)}, data={}, d=2, tol=1e-2, plot=False):\n",
    "    from scipy.stats import beta, dirichlet, gamma\n",
    "    import numpy as np\n",
    "    rv, x = dict(), dict()\n",
    "    data = data.copy()\n",
    "    posteriors = dict()\n",
    "    if data:\n",
    "        if 'pi' in data:\n",
    "            d = len(data['pi'])\n",
    "            posteriors['pi'] = dirichlet(priors['pi'] + data['pi'])\n",
    "        if 'rho' in data:\n",
    "            a = data['rho'][0]\n",
    "            b = data['rho'][1] - data['rho'][0]\n",
    "            posteriors['rho'] = beta(priors['rho'][0] + a, priors['rho'][1] + b)\n",
    "        if 'omega' in data:\n",
    "            posteriors['omega'] = gamma(priors['omega'][0] + data['omega'].sum(), scale=1/(priors['omega'][1] + len(data['omega'])))\n",
    "    #plot\n",
    "    if plot:\n",
    "        import matplotlib.pyplot as plt\n",
    "        rv['pi'] = dirichlet(priors['pi']*np.ones(d))\n",
    "        rv['rho'] = beta(priors['rho'][0], priors['rho'][1])\n",
    "        rv['omega'] = gamma(priors['omega'][0], scale=1/priors['omega'][1])\n",
    "        x['rho'] = np.linspace(tol, 1-tol, 100)\n",
    "        max_omega = 3*priors['omega'][0]/priors['omega'][1]\n",
    "        if 'omega' in posteriors: max_omega = max(max_omega, 3*posteriors['omega'].mean())\n",
    "        x['omega'] = np.linspace(0, max_omega, 100)\n",
    "        for i in x:\n",
    "            plt.plot(x[i], rv[i].pdf(x[i]), label='prior of $\\%s$'%i)\n",
    "            if i in posteriors: plt.plot(x[i], posteriors[i].pdf(x[i]), label='posterior of $\\%s$'%i)\n",
    "            plt.legend()\n",
    "            plt.show()\n",
    "    if posteriors: return posteriors\n",
    "    else: return rv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_data(params={'pi':[0.5, 0.5], 'rho':0.5, 'omega':5}, n=100):\n",
    "    from scipy.stats import multinomial, poisson, binom\n",
    "    return {'pi': multinomial.rvs(n=n, p=params['pi']),\n",
    "            'rho': (binom.rvs(n=n, p=params['rho']), n),\n",
    "            'omega': poisson.rvs(params['omega'], size=n)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = generate_data({'pi':[0.2, 0.3, 0.5], 'rho':0.8, 'omega':5})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pi mean [0.2003988  0.33000997 0.46959123] var [0.00158183 0.00218266 0.00245879]\n",
      "rho mean 0.8333333333333334 var 0.001348435814455232\n",
      "omega mean 4.891089108910891 var 0.04842662484070189\n"
     ]
    }
   ],
   "source": [
    "param_posteriors = posterior(data=data, plot=True)\n",
    "for k in param_posteriors: print(k, 'mean', param_posteriors[k].mean(), 'var', param_posteriors[k].var())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We thus recover the original parameters. We now do the same with actual data from USoc, learning parameters for every Blau dimensions separately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nom2prop(df, atts=['sex', 'age', 'ethnicity', 'employment', 'distance'], group=True, num_nom=3):\n",
    "    if not hasattr(atts, '__iter__') or isinstance(atts, str): atts = [atts]\n",
    "    dvs = dict()\n",
    "    self_atts = set(df)\n",
    "    for att in set(atts):\n",
    "        if att in self_atts:\n",
    "            if group:\n",
    "                dvs[att] = dict()\n",
    "                for name, data in df.groupby(att):\n",
    "                    idx = data[att].notnull()\n",
    "                    friends = data[['_'.join([att, 'nom', str(i)]) for i in range(1, num_nom+1)]][idx]\n",
    "                    #dvs[att][name] = (friends.eq(data[att][idx], axis=0) & friends.notna()).sum(axis=1).sum()/friends.notna().sum(axis=1).sum()\n",
    "                    rho_post = posterior(data={'rho':((friends.eq(data[att][idx], axis=0) & friends.notna()).sum(axis=1).sum(), friends.notna().sum(axis=1).sum())})\n",
    "                    dvs[att][name] = (rho_post['rho'].mean(), rho_post['rho'].var())\n",
    "            else:\n",
    "                idx = df[att].notnull()\n",
    "                friends = df[['_'.join([att, 'nom', str(i)]) for i in range(1, num_nom+1)]][idx]\n",
    "                #dvs[att] = (friends.eq(df[att][idx], axis=0) & friends.notna()).sum(axis=1).sum()/friends.notna().sum(axis=1).sum()\n",
    "                dvs[att] = (friends.eq(df[att][idx], axis=0) & friends.notna()).sum(axis=1).sum()/friends.notna().sum(axis=1).sum()\n",
    "        else:\n",
    "            friends = df[['_'.join([att, 'nom', str(i)]) for i in range(1, num_nom+1)]]\n",
    "            dvs[att] = friends.eq('similar').sum(axis=1).sum()/friends.notna().sum(axis=1).sum()\n",
    "    return dvs    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 508,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_sbm_params(df, df_pi=None, prop=['education', 'income'], prop_dv=[], prop_dv_global=['sex', 'age', 'ethnicity', 'employment'], ignore_family=True, plot=False, save='', fmt='.pdf', fontsize=6):\n",
    "    if df_pi is None: df_pi = df\n",
    "    all_atts = list(df)\n",
    "    prop = dict([(i, i+'_prop') for i in prop if i in all_atts and i+'_prop' in all_atts])\n",
    "    prop_dv = dict([(i, i+'_prop_dv') for i in prop_dv if i not in prop and i in all_atts and i+'_prop_dv' in all_atts])\n",
    "    print('using prop for dims:', set(prop.keys()))\n",
    "    print('using prop-dv for dims:', set(prop_dv.keys()))\n",
    "    prop.update(prop_dv)\n",
    "    prop_dv_global = set([i for i in prop_dv_global if i not in prop and i in all_atts and i+'_nom_1' in all_atts])\n",
    "    print('using prop-dv-global for dims:', prop_dv_global)\n",
    "    prop_dv_global = nom2prop(df, prop_dv_global)\n",
    "    dimnames = []\n",
    "    pis = []\n",
    "    rhos = []\n",
    "    omegas = []\n",
    "    #meanomegas = []\n",
    "    for dim in list(prop.keys())+list(prop_dv_global.keys()):\n",
    "        df_given_dim = df.groupby(dim)\n",
    "        names = []\n",
    "        pi = []\n",
    "        rho = []\n",
    "        omega = []\n",
    "        #tot = 0\n",
    "        for name, data in df_given_dim:\n",
    "            names.append(name)\n",
    "            pi.append(df_pi[df_pi[dim]==name].size)\n",
    "            if dim in prop:\n",
    "                rho_data = data[prop[dim]].values\n",
    "                rho_data = rho_data[~np.isnan(rho_data)]\n",
    "                rho_post = posterior(data={'rho':(rho_data.sum(), len(rho_data))})\n",
    "                rho.append((rho_post['rho'].mean(), rho_post['rho'].var()))\n",
    "            else: rho.append(prop_dv_global[dim][name])\n",
    "            if ignore_family: om_data = data['num_friends']*(1-data['family_prop']).values\n",
    "            else: om_data = data['num_friends'].values\n",
    "            om_data = om_data[~np.isnan(om_data)]\n",
    "            om_post = posterior(data={'omega':om_data})\n",
    "            omega.append((om_post['omega'].mean(), om_post['omega'].var()))\n",
    "            #tot += pi[-1]\n",
    "        #pi = [p/tot for p in pi]\n",
    "        pi_post = posterior(data={'pi':np.array(pi)})\n",
    "        dimnames.append((dim, names))\n",
    "        pis.append((pi_post['pi'].mean(), pi_post['pi'].var()))\n",
    "        rhos.append(rho)\n",
    "        omegas.append(omega)            \n",
    "        #meanomegas.append(sum([(o*p) for o,p in zip(omega, pi)]))\n",
    "    if plot:\n",
    "        import matplotlib.pyplot as plt\n",
    "        plt.figure(dpi=120)\n",
    "        for i in range(len(dimnames)):\n",
    "            for j in range(len(dimnames[i][1])): plt.errorbar(i, pis[i][0][j], yerr=pis[i][1][j], fmt='o', label=dimnames[i][1][j])\n",
    "        plt.title('pi')\n",
    "        plt.xticks(np.arange(len(dimnames)), [d[0] for d in dimnames])\n",
    "        plt.legend(bbox_to_anchor=(1.02,1.0), loc='upper left', prop={'size':fontsize})\n",
    "        if save: plt.savefig(save+'/param_pi'+fmt, bbox_inches='tight')\n",
    "        plt.show()\n",
    "        plt.figure(dpi=120)\n",
    "        for i in range(len(dimnames)):\n",
    "            for j in range(len(dimnames[i][1])): plt.errorbar(i, rhos[i][j][0], yerr=rhos[i][j][1], fmt='o', label=dimnames[i][1][j])\n",
    "        plt.title('rho')\n",
    "        plt.xticks(np.arange(len(dimnames)), [d[0] for d in dimnames])\n",
    "        plt.legend(bbox_to_anchor=(1.02,1.0), loc='upper left', prop={'size':fontsize})\n",
    "        if save: plt.savefig(save+'/param_rho'+fmt, bbox_inches='tight')\n",
    "        plt.show()\n",
    "        plt.figure(dpi=120)\n",
    "        for i in range(len(dimnames)):\n",
    "            for j in range(len(dimnames[i][1])): plt.errorbar(i, omegas[i][j][0], yerr=omegas[i][j][1], fmt='o', label=dimnames[i][1][j])\n",
    "        plt.title('omega')\n",
    "        plt.xticks(np.arange(len(dimnames)), [d[0] for d in dimnames])\n",
    "        plt.legend(bbox_to_anchor=(1.02,1.0), loc='upper left', prop={'size':fontsize})\n",
    "        if save: plt.savefig(save+'/param_omega'+fmt, bbox_inches='tight')\n",
    "        plt.show()\n",
    "    #mo = sum(meanomegas)/len(meanomegas)\n",
    "    #print('mean omega', mo)\n",
    "    #for i in range(len(omegas)):\n",
    "    #    for j in range(len(omegas[i])):\n",
    "    #        omegas[i][j] *= mo/meanomegas[i] #a *small* correction to ensure mean omega is same across all dimensions\n",
    "    return {'shape':[len(i) for i in pis], 'name':dimnames, 'pi':pis, 'rho':rhos, 'omega':omegas}    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 509,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "using prop for dims: {'education', 'income'}\n",
      "using prop-dv for dims: set()\n",
      "using prop-dv-global for dims: {'age', 'ethnicity', 'sex', 'employment'}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sbm_params = generate_sbm_params(data_wave3_atts, data_c2011_atts, plot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We note the following:\n",
    "\n",
    "1. We note a monotonicity in $\\rho$ for the education and age dimensions. Indeed, $\\rho$ is higher for lesser educated and younger people. This seems to align well with Smith 2014's observation trends of homophily in the US.\n",
    "2. We note interesting trends in $\\omega$ across all Blau dimensions: people who are better educated, richer, younger and from a majority ethnicity have more number of friends on average. For employment too, we note students have the highest $\\omega$, followed by employed, retired, unemployed, and houseworkers.\n",
    "3. The posterior variances are negligible (the error bars are practically invisible in the above plots), which is assuring. However, we did use weak priors.\n",
    "\n",
    "So we can now simply import the `EgocentricSBM` class and explore the learnt SBM. (See the egosbm notebook for more details on this class.)\n",
    "\n",
    "## Continuous Dimensions\n",
    "We also note that at least 3 of these dimensions are ordinal: age, education, and income. For these dimensions, the EDA assumption (the community discriminate against all other communities equally) may not hold, but an ordinal smooth kernel which favours people \"closer\" on the dimension may enjoy a higher propensity than those further away. We can infer the said exponential kernel even from proportion-type data: \"what proportion of your friends are within a window $w$ of you along dimension X?\" (See the cont2cat notebook for more details.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func_theta(theta, window=0, rho=0):\n",
    "    import numpy as np\n",
    "    def f(x, y=0): return (x**(2-2*y)*(2*x**y-1)**2 + x**(2*y)*(2*x**(1-y)-1)**2 + 2*x*(1-2*x))/(1-x)**2\n",
    "    def g(x, y=0): return (1-x)**0.5/(1+(x**(1-y)-x**y)/(2*(x**(y-1)-1)))\n",
    "    a = np.exp(-theta)\n",
    "    b = np.exp(theta)\n",
    "    logterm = f(a, window)\n",
    "    arctanh = g(b, window)\n",
    "    return window + (1/(2*theta))*np.log(logterm) + ((b**window-1)/(2*theta*(1-b)**0.5))*np.log((1+arctanh)/(1-arctanh)) - rho"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_contour(func, domain=((0,1),(0,1)), args=False, n=1000, aspect='auto', xlabel='', ylabel='', zlabel='', colorbar=True, refresh=False, levels=None, save='', fmt='.pdf'):\n",
    "    import numpy as np\n",
    "    import matplotlib.pyplot as plt\n",
    "    if isinstance(domain, dict):\n",
    "        x = np.linspace(domain['x'][0], domain['x'][1], n)\n",
    "        y = np.linspace(domain['y'][0], domain['y'][1], n)\n",
    "    else:\n",
    "        x = np.linspace(domain[0][0], domain[0][1], n)\n",
    "        y = np.linspace(domain[1][0], domain[1][1], n)\n",
    "    xx, yy = np.meshgrid(x, y, sparse=True)\n",
    "    if args: z = func(xx, yy, args)\n",
    "    else: z = func(xx, yy)\n",
    "    h = plt.axes(aspect=aspect)\n",
    "    if levels is None: plt.contourf(x, y, z)\n",
    "    else: plt.contourf(x, y, z, levels=levels)\n",
    "    if xlabel: plt.xlabel(xlabel)\n",
    "    if ylabel: plt.ylabel(ylabel)\n",
    "    if colorbar:\n",
    "        if zlabel: plt.colorbar(label=zlabel)\n",
    "        else: plt.colorbar()\n",
    "    if save: plt.savefig(save+xlabel+'_vs_'+ylabel+'_vs_'+zlabel+fmt, bbox_inches = 'tight')\n",
    "    elif refresh: plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we plot how $\\rho$ (proportion of friends within $w$) varies as the homophily is made stronger (more negative $\\theta$) or as the window of query $w$ increases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in true_divide\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:4: RuntimeWarning: invalid value encountered in true_divide\n",
      "  after removing the cwd from sys.path.\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:9: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  if __name__ == '__main__':\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:9: RuntimeWarning: invalid value encountered in true_divide\n",
      "  if __name__ == '__main__':\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_contour(func_theta, ((-10,0),(0,0.5)), xlabel='theta', ylabel='window', zlabel='rho', levels=np.linspace(0, 1, 11))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The contour plot makes it clear that $\\rho$ monotonically increases with the window $w$ (for a given $\\theta$) and with homophily $-\\theta$ (for a given $w$). Now if we know $w$ and $\\rho$, we can solve for $\\theta$. However, USoc survey does not ask questions at a quantitative window $w$, instead going for \"what proportion of your friends have a similar X as you?\"\n",
    "\n",
    "However, because we are using nominee type questions converted to prop-type questions for age, and because we know the distribution of people along income and education, we can assume people too treat others as being \"similar\" based on these categories. Under this assumption, we can use the exponential kernel characterization to infer a $\\theta$ that satisfies that $\\rho$ for the category-windows we have determined to be appropriate.\n",
    "\n",
    "For a quick analysis, we will assume equiproportioned population across our dimensions of interest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 663,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_theta_window(rho, window, init=-1):\n",
    "    from scipy.optimize import fsolve as solve\n",
    "    if hasattr(rho, '__iter__'): return [solve_theta(r, window, init) for r in rho]\n",
    "    assert(window<=0.5)\n",
    "    assert(init<0)\n",
    "    assert(0<rho<1)\n",
    "    return solve(func_theta, init, (window, rho))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 686,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_theta_self(rho, boundaries=None, init=-1):\n",
    "    from scipy.optimize import fsolve as solve\n",
    "    from numpy import exp, log\n",
    "    def f_rho_self(c, a, b, val=0.):\n",
    "        try:\n",
    "            if all(a==b): return a-a\n",
    "        except: pass\n",
    "        logterm = (exp(2*c*(1-b))-2*exp(c*(1-b))+exp(c))/(exp(2*c*(1-a))-2*exp(c*(1-a))+exp(c))\n",
    "        arctanh = ((exp(c*a)-exp(c*b))*(1-exp(c))**0.5)/(exp(c)+exp(c*(a+b))-exp(c*a)-exp(c*b))\n",
    "        return exp(-c*a) + (exp(-c*a)-exp(-c*(1-b)))/(2*c*(b-a))*log(logterm) - (exp(-c*a)+exp(-c*(1-b))-2)/(2*c*(1-exp(c))**0.5*(b-a))*log((1+arctanh)/(1-arctanh)) - val\n",
    "    \n",
    "    if boundaries is None: boundaries = np.linspace(0, 1, len(rho)+1)\n",
    "    assert(boundaries[0]==0)\n",
    "    assert(boundaries[-1]==1)\n",
    "    assert(len(rho)==len(boundaries)-1)\n",
    "    solutions = []\n",
    "    for i in range(len(rho)): solutions.append(solve(f_rho_self, init, (boundaries[i], boundaries[i+1], rho[i]))[0])\n",
    "    return solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 709,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func_rho(theta, k=4, boundaries=None):\n",
    "    from numpy import exp, log\n",
    "    \n",
    "    def f_rho_self(c, a, b):\n",
    "        try:\n",
    "            if all(a==b): return a-a\n",
    "        except: pass\n",
    "        logterm = (exp(2*c*(1-b))-2*exp(c*(1-b))+exp(c))/(exp(2*c*(1-a))-2*exp(c*(1-a))+exp(c))\n",
    "        arctanh = ((exp(c*a)-exp(c*b))*(1-exp(c))**0.5)/(exp(c)+exp(c*(a+b))-exp(c*a)-exp(c*b))\n",
    "        return exp(-c*a) + (exp(-c*a)-exp(-c*(1-b)))/(2*c*(b-a))*log(logterm) - (exp(-c*a)+exp(-c*(1-b))-2)/(2*c*(1-exp(c))**0.5*(b-a))*log((1+arctanh)/(1-arctanh))\n",
    "    \n",
    "    def f_rho_low(c, a, b, p, q):\n",
    "        try:\n",
    "            if all(a==b): return a/a\n",
    "            elif all(p==q): return p-p\n",
    "        except: pass\n",
    "        logterm = (exp(2*c*(1-b))-2*exp(c*(1-b))+exp(c))/(exp(2*c*(1-a))-2*exp(c*(1-a))+exp(c))\n",
    "        arctanh = ((exp(c*a)-exp(c*b))*(1-exp(c))**0.5)/(exp(c)+exp(c*(a+b))-exp(c*a)-exp(c*b))\n",
    "        return (exp(-c*q)-exp(-c*p))/(2*c*(b-a))*(-2*c*(b-a) - log(logterm) + 1/(1-exp(c))**0.5*log((1+arctanh)/(1-arctanh)))\n",
    "    \n",
    "    def f_rho_high(c, a, b, p, q):\n",
    "        try:\n",
    "            if all(a==b): return a/a\n",
    "            elif all(p==q): return p-p\n",
    "        except: pass\n",
    "        logterm = (exp(2*c*(1-b))-2*exp(c*(1-b))+exp(c))/(exp(2*c*(1-a))-2*exp(c*(1-a))+exp(c))\n",
    "        arctanh = ((exp(c*a)-exp(c*b))*(1-exp(c))**0.5)/(exp(c)+exp(c*(a+b))-exp(c*a)-exp(c*b))\n",
    "        return (exp(-c*(1-p))-exp(-c*(1-q)))/(2*c*(b-a))*(log(logterm)+1/(1-exp(c))**0.5*log((1+arctanh)/(1-arctanh)))\n",
    "    \n",
    "    if isinstance(theta, int) or isinstance(theta, float):\n",
    "        if boundaries is None: theta = theta*np.ones(k)\n",
    "        else: theta = theta*np.ones(len(boundaries)-1)\n",
    "    if boundaries is None: boundaries = np.linspace(0, 1, len(theta)+1)\n",
    "    assert(boundaries[0]==0)\n",
    "    assert(boundaries[-1]==1)\n",
    "    assert(len(theta)==len(boundaries)-1)\n",
    "    rho_mat = []\n",
    "    for i in range(len(boundaries)-1):\n",
    "        rhos = []\n",
    "        a, b = boundaries[i], boundaries[i+1]\n",
    "        for j in range(i):\n",
    "            p, q = boundaries[j], boundaries[j+1]\n",
    "            rhos.append(f_rho_low(theta[i], a, b, p, q))\n",
    "        rhos.append(f_rho_self(theta[i], a, b))\n",
    "        for j in range(i+1, len(boundaries)-1):\n",
    "            p, q = boundaries[j], boundaries[j+1]\n",
    "            rhos.append(f_rho_high(theta[i], a, b, p, q))\n",
    "        rho_mat.append(rhos)\n",
    "    return np.array(rho_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 694,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_matrix(matrix, labels=False, title='', save='', fmt='.pdf'):\n",
    "    import seaborn as sns\n",
    "    import matplotlib.pyplot as plt\n",
    "    plt.figure(dpi=120)\n",
    "    ax = sns.heatmap(matrix, square=True, cmap='Spectral', xticklabels=labels, yticklabels=labels)\n",
    "    if title: plt.title(title)\n",
    "    if save: plt.savefig(save+title+fmt, bbox_inches='tight')\n",
    "    else: plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we use the $\\rho$s inferred above from USoc, and apply the exponential kernel setup to infer $\\theta$s for every block of the Blau dimension, and correspondingly the proportion of friends a community will have across the entire Blau dimension. Let's do this for age first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 703,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rho age: [0.8795737122557726, 0.7168223720843903, 0.6294147582697202, 0.5571218949795619, 0.4888313982836951, 0.6322679175302717]\n",
      "theta age (inferred): [-25.43643367737479, -20.217316373274414, -14.774885140955782, -11.462509542541532, -8.173592046656891, -8.036897889800269]\n",
      "rho age (inferred): [0.8795737  0.71682237 0.62941476 0.55712189 0.4888314  0.63226792]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rho_age = [i[0] for i in sbm_params['rho'][2]]\n",
    "theta_age = solve_theta_self(rho_age)\n",
    "rho_all_age = func_rho(theta_age)\n",
    "print('rho age:', rho_age)\n",
    "print('theta age (inferred):', theta_age)\n",
    "print('rho age (inferred):', np.diag(rho_all_age))\n",
    "plot_matrix(rho_all_age, sbm_params['name'][2][1], title='$\\\\rho$ for age')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Things to note:\n",
    "1. Clearly, $\\theta$ increases perfectly monotonically with age, strengthening the idea that homophily is stronger in younger people.\n",
    "2. Although $\\rho$ for age group 70 itself is quite high (compared to say 50 or 60 year olds, which broke the monotonicity), its $\\theta$ is the smallest. This observation neatly captures the edge effect which was previously missing from our analysis, that is, people at the edges of the Blau dimension will have a higher $\\rho$ than those in the bulk, even for the same $\\theta$, by the virtue of being positioned at the edge. This becomes more obvious when we look at the matrix of $\\rho$s for all pairs of ages.\n",
    "\n",
    "We repeat this analysis for income groups (or employment-type groups)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 702,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rho inc: [0.5988417554491252, 0.6181683899556869, 0.6073896518960007, 0.5743704401035538]\n",
      "theta inc (inferred): [-4.659429871873838, -9.060005101766219, -8.680419488906448, -4.243070605874064]\n",
      "rho inc (inferred): [0.59884176 0.61816839 0.60738965 0.57437044]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rho_inc = [i[0] for i in sbm_params['rho'][1]]\n",
    "theta_inc = solve_theta_self(rho_inc)\n",
    "rho_all_inc = func_rho(theta_inc)\n",
    "print('rho inc:', rho_inc)\n",
    "print('theta inc (inferred):', theta_inc)\n",
    "print('rho inc (inferred):', np.diag(rho_all_inc))\n",
    "plot_matrix(rho_all_inc, sbm_params['name'][1][1], title='$\\\\rho$ for income')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, although the $\\rho$s are all quite comparable, the bulk is much more homophilous than the edges. This adds more credulity to the exponential kernel assumption, over the EDA one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 701,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rho edu: [0.7873970345963757, 0.7829450309428467, 0.7601093801789858, 0.7342526109660574, 0.7125576986482031]\n",
      "theta edu (inferred): [-12.31575224190963, -22.701746543767943, -20.49290465808315, -18.145701618263384, -8.983709612312476]\n",
      "rho edu (inferred): [0.78739703 0.78294503 0.76010938 0.73425261 0.7125577 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rho_edu = [i[0] for i in sbm_params['rho'][0]]\n",
    "theta_edu = solve_theta_self(rho_edu)\n",
    "rho_all_edu = func_rho(theta_edu)\n",
    "print('rho edu:', rho_edu)\n",
    "print('theta edu (inferred):', theta_edu)\n",
    "print('rho edu (inferred):', np.diag(rho_all_edu))\n",
    "plot_matrix(rho_all_edu, sbm_params['name'][0][1], title='$\\\\rho$ for education')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additionally, once we have inferred $\\theta$, it leaves us free to change the number of blocks in our analysis, allowing us to move from discrete to near-continuous settings, as evidenced by the plots below. We assume the same $\\theta$ for all blocks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 711,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Es9L6UYDM/AFNSB8WEXN7jt0L+A2az0FPmS1rSdJWIzNXRMRK4MyImA/cCywE9gMOG/8MckScTRPSu2XmA+22S4BbgVtowndnYAlNIB/dt3J7KbASuDAizqBZkX0qTXV8TsnYDWRJUlUd+Lang4BTgJNp5nTvAhZm5gU9x8xtX721+PXAIcAHgfk0VfE3gXf0rbImM69uH0JyMnAp8DPgMuCjmflkyaANZElSVaP+tqfMXE/zKMtjN3PMEprqt3fbZ4DPTOE+K2mq5CqcQ5YkqQOskCVJVfn1i2UMZElSVaNuWW+pDGRJUlXhbGgR/9UkSeoAK2RJUlXNszQ0VQayJKkqW9Zl/FeTJKkDrJAlSVXZsi5jIEuSqrJlXcZAliRVFVghl/DXGEmSOsAKWZJUVYS1XgkDWZJUlS3rMv4aI0lSB1ghS5KqsmVdxkCWJFVly7qMv8ZIktQBVsiSpKp8MEgZA1mSVJWPzixjIEuSqrJCLuO/miRJHWCFLEmqylXWZQxkSVJVfg65jP9qkiR1gBWyJKkqW9ZlDGRJUlW2rMsYyJKkqvzYUxn/1SRJ6gArZElSVc4hlzGQJUlVOYdcxn81SZI6wApZklSVLesyBrIkqSpb1mX8V5MkqQOskCVJVdmyLmMgS5Kq8sEgZQxkSVJVEVbIJSIzp3WB7x34juldQJPyii8dMeohzApL73hy1EOYNT796m1HPYTZ44V/+Bwn5KpKufCWWZXsVsiSpLpqlWmzKo4NZElSbTlW5zqzLJCdeZckqQOskCVJddWqkGcZA1mSVJeBXMRAliTVZSAXcQ5ZkqQOsEKWJNU1ZoVcwkCWJNVly7qILWtJkjrAClmSVJcVchEDWZJUl4FcxJa1JEkdYIUsSarLVdZFDGRJUl22rIsYyJKkugzkIs4hS5LUAVbIkqS6rJCLGMiSpKoyN1a5TlS5ypbDlrUkSR1gIEuS6hobq/MqFBHzIuL0iFgTERsi4paIOHQS5x0UEcsi4t6IeCIi7o+IL0fEr09w3gsj4u6IyIj4SOm4bVlLkuoa/RzyRcDrgI8BdwOLgGURMSczz9/MeUuBh4FTgPuAlwN/AXwrIvbKzDuGnPdXwLbTHbSBLEmqa4SBHBEHAPsCizJzWbt5VUTsApwWEctz+CT3OzPzkb7rXQXcD3wYOHLA/V4PHAO8B7hwOmO3ZS1J2pocCKxn03A8B9gZ2HPYif1h3G5bA3yfplp+loh4HvBPwOeAb5YPuWGFLEmqq1KFHBE7ATsO2LV2UHi29gDuzMyn+7av7tl/wxTG8EpgF+CrA3Z/iqZV/ckh45wSK2RJUl05VucFRwG3D3gdtZm77wCsG7B9Xc/+SYmIbYCzaSruv+/b99vA8cCfZebjk73m5lghS5K66gwGz8uuneC8LNz3CxERNGH8RuDgzHywZ982NK3q5Zn59clcbzIMZElSXZW+7altSw9rTQ/zKIOr4O3b90HV87O0YfwF4DBgcWZe0nfIccArgT+JiO3abfPb9xe02366mcVjA9myliTVVa9lXeI2YPe2iu21oH2/fXMn94TxEcCRmXnegMP2AF4M3AP8v/Z1a7vvr9q/Lxhw3mYZyJKkrcnFwDzg4L7ti4E1wE3DTmzD+CyaMP5AZp4z5NBTgbf0vRa2+z7f/v3eqQ7clrUkqa4Rfg45M1dExErgzIiYTxOMC4H9gMPG28gRcTZNSO+WmQ+0p/8j8D6a+eHbImKvnks/mZnfbu9xF3BX730jYtf2j/83M68uGbuBLEmqa/RP6jqI5mlbJ9PMHd8FLMzMC3qOmdu+er/D4p3t+3vbV68HgF1nYrDjDGRJUl2VFnWVysz1wLHta9gxS4Alfdt2ncY972eaX1DlHLIkSR1ghSxJqmv0LestkoEsSarLQC5iy1qSpA6wQpYk1TXiRV1bKgNZklTX2KQeF60+BrIkqS4r5CLOIUuS1AFWyJKkuqyQixjIkqS6nEMuYstakqQOsEKWJNVly7qIgSxJqstALmLLWpKkDrBCliTV5aKuIgayJKkuW9ZFDGRJUl1WyEWcQ5YkqQOskCVJddmyLmIgS5LqMpCL2LKWJKkDrJAlSVVl1lnUFVWusuUwkCVJddmyLmIgS5LqMpCLOIcsSVIHWCFLkurywSBFDGRJUl22rIvYspYkqQOskCVJdVkhFzGQJUl1OYdcxJa1JEkdYIUsSarLlnURA1mSVJeBXMRAliTV5RxyEeeQJUnqACtkSVJdtqyLGMiSpLoM5CK2rCVJ6gArZElSXS7qKmIgS5LqsmVdxECWJFWVG62QSziHLElSB1ghS5Lqcg65iIEsSarLlnURW9aSJHWAFbIkqaq0ZV3EQJYk1WXLuoiBLEmqa6OfQy7hHLIkSR1ghSxJqso55DIGsiSpLueQi9iyliSpA6yQJUl12bIuYiBLkqryyyXK2LKWJKkDrJAlSXX5fchFph3IV17yRI1xaAILP3vuqIcwK3zguHeNegizxuKFG0c9hFnji199jm9oy7qIFbIkqSo/h1zGOWRJ0lYlIuZFxOkRsSYiNkTELRFx6CTOe1l73jUR8eOIyIhYMuTY50fERyPi9oh4PCJ+GBErIuL3SsdtIEuS6tqYdV7lLgIWAycB+wPfAJZFxKIJzvs14D3Az4ErJjj2LOBU4KvAO4GjgR2BayLi9SWDtmUtSaprhHPIEXEAsC+wKDOXtZtXRcQuwGkRsTwzhy1guDYzd2yv81pg4ZB7PB9YBJyfmZ/o2X49sIYm1G+e6titkCVJW5MDgfXAhX3bzwF2BvYcdmJmTnZ5+Fj7eqxv+0/a7RsmeZ1nsUKWJFVVa1FXROxE0wbutzYzHxly2h7AnZn5dN/21T37b5jOuDLzqYg4A3hfRPwbcBWwPfA3NCF9Vsl1DWRJUl31vg/5KOCEAdtPAk4ccs4OwH0Dtq/r2V/Dh2nC9195ptv8PWDvzLy35IIGsiSpqoofezqDTVvPAGsnGkLhvqn4S+AjNL8Y/DswH/ggsDIi3paZ357qBQ1kSVIntW3pYa3pYR5lcBW8ffu+bsC+KYmI3YGTgeMz87/1bF8BfAf4LPCWqV7XRV2SpLpG+7Gn24DdI6K/4FzQvt9e/HM94z8DQfNxql/IzKeAW2nmqafMQJYk1TWWdV5lLgbmAQf3bV9M85Gkm6bxk41b077v1bux/TjU7wLfL7moLWtJ0lYjM1dExErgzIiYD9xL83ni/YDDxj+DHBFn04T0bpn5wPj5EXFI+8dXtu+vjYj17bW/0m67jqY6PjEiXgRcC7wYOAb4VeDwkrEbyJKkqjrwfcgHAafQzPNuD9wFLMzMC3qOmdu+ou/c/kVkR7cvxo/NzLGI2Bf4KPDHNIu71tPMHx+QmStKBm0gS5LqGvGXS2TmeuDY9jXsmCXAkgHb+wN62PmPAZ9oX1U4hyxJUgdYIUuS6qr3YJBZxUCWJFXl9yGXMZAlSXWNflHXFsk5ZEmSOsAKWZJU1aS/xFDPYiBLkqrKsUl9ckh9bFlLktQBVsiSpKrGbFkXMZAlSVVN8mFX6mMgS5KqclFXGeeQJUnqACtkSVJVrrIuYyBLkqpyUVcZW9aSJHWAFbIkqSpb1mUMZElSVa6yLmPLWpKkDrBCliRV5YNByhjIkqSqbFmXMZAlSVWNuairiHPIkiR1gBWyJKkqW9ZlDGRJUlV+DrmMLWtJkjrAClmSVJUt6zIGsiSpKj+HXMZAliRV5bc9lXEOWZKkDrBCliRV5RxyGQNZklSVH3sqY8takqQOsEKWJFVly7qMgSxJqsovlyhjy1qSpA6wQpYkVWXLuoyBLEmqyid1lTGQJUlVWSGXcQ5ZkqQOsEKWJFXlg0HKGMiSpKr8cokytqwlSeoAK2RJUlVjG3PUQ9giGciSpKpsWZcxkCVJVW0cs0Iu4RyyJEkdYIUsSapqbOOoR7BlMpAlSVWN2bIuYstakqQOsEKWJFVly7qMgSxJqsqWdRlb1pIkdYAVsiSpKh8MUsZAliRV5aMzyxjIkqSqNlohF3EOWZKkDrBCliRVZcu6jIEsSarKRV1lbFlLktQBBrIkqaqxsazyKhUR8yLi9IhYExEbIuKWiDh0Eue9rD3vmoj4cURkRCwZcNz8iPjLiLg6Ih6OiPURcVtELI2IF5SO20CWJFU1trHOaxouAhYDJwH7A98AlkXEognO+zXgPcDPgSs2c9wrgOOAbwHvB94FfAU4EbgsIqJk0M4hS5KqGuWjMyPiAGBfYFFmLms3r4qIXYDTImJ5Zg6L+2szc8f2Oq8FFg457rvArpn5eM+2qyLiceA04A3AdVMduxWyJGlrciCwHriwb/s5wM7AnsNOzMxJLUfLzMf7wnjcze37yydznX5WyJKkqmo9GCQidgJ2HLBrbWY+MuS0PYA7M/Ppvu2re/bfUGeEm9i7fb+j5GQDWZJUVcXPIR8FnDBg+0k087WD7ADcN2D7up791UXEq4HjgYszc/VExw9iIEuSuuoMNm09A6yd4LzN/UZQfYI7InYFLgMeBI4svY6BLEmqqtaDQdq29LDW9DCPMrgK3r59XzdgX7F2sdgq4GngrZlZfH0DWZJU1YgfnXkbsDAitumbR17Qvt9e60ZtGF8NBPDmzPz+dK7nKmtJ0tbkYmAecHDf9sXAGuCmGjeJiFfQhPFcYO/MfGC617RCliRVNcpnWWfmiohYCZwZEfOBe2k+T7wfcNj4Z5Aj4myakN6tN0wj4pD2j69s318bEevba3+lPWYnmjb1S4D3ATu128Z9v6RaNpAlSVWN8sEgrYOAU4CTaeaO7wIWZuYFPcfMbV/9T9XqX0R2dPui59jf4pnAPm/A/Te3CnwoA1mSVNXG6T32ctoycz1wbPsadswSYMmA7RM+9jIzr2bTIJ8255AlSeoAK2RJUlUdaFlvkQxkSVJV0/ymplnLlrUkSR1ghSxJqmrx0/9WfcHTbBCZ9volSRo1W9aSJHWAgSxJUgcYyJIkdYCBLElSBxjIkiR1gIEsSVIHGMiSJHWAgSxJUgcYyJIkdYCBLElSBxjIkiR1gIEsSVIHGMiSJHWAgSxJUgf8f06AS5U5qhFMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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K3PyXu1uJC7B48z+3Fnuvw1/XStxvb7qvlbgAzzv0kNZi77T5wlbi5qp7W4kL7f2d3mqtG5/rEczYpo3tVX5j86jP24FFXZ8BXgy8B/gOsBxYERFjmfnJSa47EbgDeD9wC/DzwB8D34yIfTPzWyOu+3Ngu9kO2pa1JKmquWxZR8TBwIHA8sxc0exeFRG7AadGxHmZuXnE5a/LzLsG4l0K3Ar8PvC2Ifd7CfAO4DeB82czdlvWkqT5ZCmwli2T41nArsA+oy4cTMbNvtXA7fSq5ceIiCcBHwP+Fvj38iH3WCFLkqqq1X2PiCXALkMOrRmWPBt7ADdm5qaB/df1Hb9iBmN4NrAb8Nkhh/+MXqv6T0eMc0ZMyJKkqhbUa1kfB7xvyP6TgZNGXLMzvfnfQff2HZ+WiNgGOJNexf2/B469EHg3vTb3wxFhQpYkdUvF9WmnM3xeds0U1032E8G0flqIiKCXjF8JHJ6ZP+w7tg29VvV5mfnl6cSbDhOyJKmTmrb0qNb0KPcwvApe3GynfJSiScb/CBwNHJOZnxs45feAZwNHRsSOzb4dmu2iZt9DkyweG8pFXZKkqsYiq3wKXQ+8oKli++3ZbG+Y7OK+ZPxm4G2Zec6Q0/YAngp8F7iv+VzbHPvz5t/3HHLdpKyQJUlVzfFzyBcAbwcOB87r238MsBq4atSFTTL+B3rJ+Lcz86wRp34QOHtg388CK4C/a+5780wHbkKWJM0bmbkyIi4GzoiIHeglxmXAa4GjJ9rIEXEmvST9nMy8rbn8o8Bb6c0PXx8R+/aF3pCZ/6+5x03ATf33jYjdm3/8XmZeVjJ2E7IkqaoOvHTsMHpv2zqF3tzxTcCyzDy375wFzad/tBOvRHxL8+l3G7B7G4OdYEKWJFU1118ukZlrgROaz6hzjgWOHdi3+yzueSuPTe4zZkKWJFXVgXdZb5VcZS1JUgdYIUuSqprrlvXWyoQsSaqqA4u6tkq2rCVJ6gArZElSVRW/XOIJxYQsSarKlnUZW9aSJHWAFbIkqSpXWZcxIUuSqrL1WsaELEmqykVdZWadkB96cEbfv9wBi9oLvWrK770uttP451uJ+9wjDmklLsAtsba12M867OBW4u40flErcQHysvtbiw0LW4y9lVk3PtcjKLJpo0nsic4KWZJUlausy5iQJUlVuairjHPvkiR1gBWyJKkqv36xjAlZklSVLesyJmRJUlUu6irjHLIkSR1ghSxJqsoXg5QxIUuSqrJlXcaWtSRJHWCFLEmqKqz1ipiQJUlVRdizLuGPMZIkdYAVsiSpKlvWZUzIkqSqbFmXMSFLkqqyQi7j75okSR1ghSxJqiqwZV3ChCxJqirC5msJf9ckSeoAK2RJUlW2rMvMOiGvXzdeYxzzxKLWIudl97cSdzEXtRIX4FmHHdRa7Nu2XddK3N1aHPNiVrYWm5b+fsDCluJupfz/3bTYsi5jhSxJqsoKuYw/xkiS1AFWyJKkqnwxSBkTsiSpKl+dWcYfYyRJ6gArZElSVbasy5iQJUlVucq6jAlZklSVzyGX8XdNkqQOsEKWJFVly7qMCVmSVJUt6zL+rkmS1AFWyJKkqnzsqYwJWZJUlXPIZfwxRpI0r0TE9hFxWkSsjoj1EXFNRBw1jet+rrnu8oi4PyIyIo4dce7CiHhXRNwQEQ9HxJ0RsTIiXlY6bhOyJKmqiLEqn1n4DHAMcDJwEPBvwIqIWD7Fdb8A/CbwCPDFKc79B+CDwGeB1wHHA7sAl0fES0oGbctaklTVXLasI+Jg4EBgeWauaHaviojdgFMj4rzM3Dzi8q9m5i5NnL2BZSPusRBYDnwyM9/bt/8bwGp6Sf3qmY7dClmSVNUcV8hLgbXA+QP7zwJ2BfYZdWFmjk/zHuPN54GB/Q82+9dPM85jmJAlSfPJHsCNmblpYP91fcdnJTM3AqcDx0TEoRGxQ0TsTq+N/UCznTFb1pKkqmq1rCNiCb152UFrMvOuEZftDNwyZP+9fcdr+H16yfef+Wlx+wPg1Zl5c0lAK2RJUlXBWJUPcBxww5DPcVMMIQuPzcSfAO8ETgJeBbwB+DZwcUT8SklAK2RJUledzpZzwQBrJrnmHoZXwYub7b1Djs1IRLwAOAV4d2b+r779K4H/BP6KXpKekVkn5I0ba/2wMWDddOfWnygWthP2svvbiQssZmVrsXc77KBW4t62bdFajGlpa8zQ4u91i38/Wvs7vbWaR//Pi6jTsm7a0qNa06NcDyyLiG0G5pH3bLY3VBjaLwNB73GqR2Xmxoi4FtivJKgta0lSXVnpU+YCYHvg8IH9x9B7JOmq4sg/tbrZ7tu/s3kc6leB20uC2rKWJNU17aeHplBQaGfmyoi4GDgjInYAbqb3PPFrgaMnnkGOiDPpJennZOZtj94y4ojmH5/dbPeOiLVN7E83+75Orzo+KSKeAnwVeCrwDuBZwJtmPnITsiRp/jkMeD+9ed7FwE3Assw8t++cBc1nMO0Pzlkf33yYODczxyPiQOBdwBvpLe5aS2/++ODMLJpDMiFLkuqqVSGX3j5zLXBC8xl1zrHAsUP2T6suz8wHgPc2nypMyJKkuuY4IW+tXNQlSVIHWCFLkuqyQi5iQpYk1TVuQi5hy1qSpA6wQpYk1WXLuogJWZJUlwm5iAlZklSXCbmIc8iSJHWAFbIkqS5XWRcxIUuS6rJlXcSWtSRJHWCFLEmqywq5iAlZklSXCbmICVmSVFXm5ipxpvU9iPOIc8iSJHWAFbIkqS4feypiQpYk1eUccpFZJ+RNG7PGOB4/6/yL8lgL2wt92f2thV7Mylbi7nbEIa3EBfj+Nj9pLfazWhr3Yi5qJS5AXH5fS5EXtRRXapcVsiSpLivkIiZkSVJdJuQirrKWJKkDrJAlSXVZIRcxIUuS6vKxpyImZElSXVbIRZxDliSpA6yQJUl1WSEXMSFLkuoyIRexZS1JUgdYIUuS6nKVdRETsiSpLlvWRUzIkqS6TMhFnEOWJKkDrJAlSXU5h1zEhCxJqms853oEWyVb1pIkdYAVsiSpLlvWRUzIkqS6TMhFbFlLktQBVsiSpLpc1FWkswl508at8A90nW2ax1rYWuS4/L5W4i4e+2IrcQGeffjrWov9bR5uJe7z3vj6VuICLB67sJ3Aq+5tJy4Ai1qMPY/Ysi7S2YQsSdpKmZCLOIcsSVIHWCFLkupyDrmICVmSVJct6yK2rCVJ6gArZElSXbasi5iQJUl12bIuYkKWJNVlQi7iHLIkaV6JiO0j4rSIWB0R6yPimog4ahrX/Vxz3eURcX9EZEQcO+S8HSLiTyLisoi4IyLWRsT1EXFiRBS/PcaELEmqKjOrfGbhM8AxwMnAQcC/ASsiYvkU1/0C8JvAI8Bkr+17JvB7wDeB3wJeD3waOAn4QkREyaBtWUuS6prDlnVEHAwcCCzPzBXN7lURsRtwakScl5mbR1z+1czcpYmzN7BsxHnfB3bPzP531l4aEQ8DpwIvB74+07FbIUuS5pOlwFrg/IH9ZwG7AvuMujAzp/WTRGY+PJCMJ1zdbH9+OnEGWSFLkuqqVCFHxBJglyGH1mTmXSMu2wO4MTM3Dey/ru/4FVUGuKVXN9tvlVxshSxJqms863zgOOCGIZ/jJrn7zsCwr/y6t+94dRGxF/Bu4ILMvG6q84exQpYkddXpbNl6BlgzxXWTrQir/taSiNgd+ALwQ+BtpXFMyJKkuiq1rJu29KjW9Cj3MLwKXtxsq35hdrNYbBWwCXhNZhbHNyFLkuqa2xeDXA8si4htBuaR92y2N9S6UZOMLwMC2D8zb59NPOeQJUl11ZtDLnEBsD1w+MD+Y4DVwFWz+JU9KiKeSS8ZLwBenZm3zTamFbIkad7IzJURcTFwRkTsANxM73ni1wJHTzyDHBFn0kvSz+lPphFxRPOPz262e0fE2ib2p5tzltBrUz8deCuwpNk34faSatmELEmqa+7fZX0Y8H7gFHpzxzcByzLz3L5zFjSfwbdqDS4iO7750Hfuf+WnCfucIfc/md5bu2bEhCxJqmuOE3JmrgVOaD6jzjkWOHbI/ilfe5mZl7FlIp8155AlSeqAWVfI4y19EfXYWPUfPgDYtHEr/eLsdXPeAuqUsbHiL1SZVFxe9YmIx9hpwUWtxX7e4UtbiXvdI/e3EhdgryMH19zUsXjBBa3EBYhL724tdlt/p+dES3lhvrNlLUmqa+7nkLdKJmRJUl0m5CLOIUuS1AFWyJKkupxDLmJCliTVZcu6iC1rSZI6wApZklRVbrZlXcKELEmqyznkIrasJUnqACtkSVJdtqyLmJAlSVWlLesiJmRJUl1WyEWcQ5YkqQOskCVJdW32xSAlTMiSpKqcQy5jy1qSpA6wQpYk1eWiriImZElSXbasi5iQJUlV+S7rMs4hS5LUAVbIkqS6/D7kIiZkSVJdtqyLdDYhj7e0KGBsLFqJC+2NGWDjxpYCr9s6f5Jd0NJkS4wtbCcwEJetaS32Tos+30rcvQ49spW4AF+/r53fj1cctayVuACLF32qtdgLvnJHa7G1dehsQpYkbZ18MUgZE7IkqS5b1kVMyJKkukzIRXzsSZKkDrBCliRV5RxyGROyJKkuv36xiC1rSZI6wApZklSVLesyJmRJUl2usi5iy1qSpA6wQpYk1WXLuogJWZJUld+HXMaELEmqywq5iHPIkiR1gBWyJKkuXwxSxIQsSarK55DL2LKWJKkDrJAlSXW5yrqICVmSVFU6hVzEhCxJqirHY66HsFVyDlmSpA54wlXI462u/mvzp8J2xr1xYythARhb317f6qEH24k7tqC9P8MYW9Ra7G0u/XErcXfY7nOtxAV42SFHthL33O/d2UpcgDceeXRrsXfc7vzWYj/exm1ZF3nCJWRJUrsybVmXsGUtSZpXImL7iDgtIlZHxPqIuCYijprmtUsi4uyIuDsi1kXElRHxmhHnbhcRp0TEdyJiQ0TcExGrIuIXS8ZthSxJqqoDq6w/A7wYeA/wHWA5sCIixjLzk6MuioiFwCXAjsAJwF3A8cCXIuKAzLy879ztgVXArsAHgeuApwIvA55SMmgTsiSpqrlcZR0RBwMHAsszc0Wze1VE7AacGhHnZebmEZe/FdgDeFlmXtnEWwVcC3wY2Kfv3L8AXgDslZm39O3/fOnYbVlLkuaTpcBaYHCV3Fn0qtl9trjisdd+eyIZA2TmJuAc4CUR8QyAiHgK8Dbg/IFkPCsmZElSVePjdT6F9gBubBJpv+v6jk927XVD9k/s+6Vm+yJgO+C7EXFGRNwXEY9ExL9HxCGlA7dlLUmqqlbLOiKWALsMObQmM+8acdnOwLCq9d6+46Ps3HfeZNc+o9meCFwP/A9gHPhD4MKIOCgzvzzJfYYyIUuSqqq4qOs44H1D9p8MnDTZEAqPTffaie7yI8BBmfkQPDrf/F3gTwETsiRp3jidLeeCAdZMcs09DK+CFzfbYRXwTK+9p9leMZGMATJzXURcDhw6yT1GMiFLkqqq9WKQpi09qjU9yvXAsojYZmAeec9me8MU1+45ZP/gtcPmmScEvfb1jLmoS5JUVY7X+RS6ANgeOHxg/zHAauCqKa59fkQ8uhI7IrYBjgauyszVAJn5Y+BK4OURsUPfuU8B9gP+tWTgJmRJ0ryRmSuBi4EzIuLtEfGqiPh74LXAuyeeQY6IMyNiU/N88oSPAd8Czo+I5RFxAPAp4Hn0FnD1eyfwM8CXI+LQiHgD8CXgafTmkGfMlrUkqarxuf/6xcOA9wOn0Jv/vQlYlpnn9p2zoPk8OtjM3NC8JvPDwN/Qe+PWNfQWbl3edy2ZeUVz7l8An2h2/yuwf/9zzDNhQpYkVTXXr87MzLX0Xn15wiTnHAscO2T/nfTa29O5z9eB/UvGOIwJWZJU1Vy+OnNr5hyyJEkdYIUsSapqrlvWWysTsiSpqlrPIT/R2LKWJKkDrJAlSVXN4puantBMyJKkqpxDLmPLWpKkDrBCrmh8fKpv9ZqNthZJtDfmTYNfD17Rhg3tjPuhBza3Ehdgm23aW+iy7cKFrcR90qpbW4kLsGjxjL+dblr++4t+uZW4ACdcMdmXDM3OSQe8vLXYT2st8nA+h1zGhCxJqspAHuo4AAAEdElEQVSWdRkTsiSpqg68y3qr5ByyJEkdYIUsSarKlnUZE7IkqSrf1FXGlrUkSR1ghSxJqsqWdRkTsiSpKp9DLmNCliRV5busyziHLElSB1ghS5KqGt/c5muE5y8TsiSpKlvWZWxZS5LUAVbIkqSqNrf6zXfzlwlZklTVeHvfYjqv2bKWJKkDrJAlSVWN27IuYkKWJFVly7qMCVmSVJUVchnnkCVJ6gArZElSVb4YpIwJWZJUla/OLGNCfoJrc/HF5hYnRDZtbOc/+A1j7f1o//Da9n6zH75/21biPvjjBa3EBdj22h+0Enen576glbgAez9tYWux//Co9v6D+afPthZaFZmQJUlVbbZlXcSELEmqypZ1GROyJKkqF3WV8bEnSZI6wApZklSVLwYpY0KWJFXlqzPL2LKWJKkDrJAlSVXZsi5jQpYkVeVzyGVsWUuS1AFWyJKkqnwxSBkTsiSpKl8MUsaELEmqygq5jHPIkiR1gBWyJKkqW9ZlTMiSpKp8DrmMLWtJkjrAhCxJqmrz5jqfUhGxfUScFhGrI2J9RFwTEUdN89olEXF2RNwdEesi4sqIeM2Icw9ojq9rzj87IpaUjtuWtSSpqg60rD8DvBh4D/AdYDmwIiLGMvOToy6KiIXAJcCOwAnAXcDxwJci4oDMvLzv3P2AlcBFwBuAJcCHgEsiYu/M3DDTQZuQJUlVzeW3PUXEwcCBwPLMXNHsXhURuwGnRsR5mTlqhG8F9gBelplXNvFWAdcCHwb26Tv3VHrJ/ojM3NSc+33gG8BbgDNmOnZb1pKk+WQpsBY4f2D/WcCuPDapDrv22xPJGKBJtucAL4mIZwA02xcDH59Ixs25V9BL0ktLBm6FLEmqqlbLupmP3WXIoTWZedeIy/YAbuxPlI3r+o5fMcm1Xxuyf+LaXwJ+1JzXv3/w3JePiD+pWSfkN49fErONIUlbg2Of1mLsz7YX+/FWKy+8JeIk4H1DDp0MnDTisp2BW4bsv7fv+Cg795032bU7D+wfPHeye4xkhSxJ6qrT2bL1DLBmiusmK9GnKt9ncu2oc4taBCZkSVInNW3pUa3pUe5heIW6uNkOq2pneu09zXbUuZPdYyQXdUmS5pPrgRdExGDBuWezvWGKa/ccsn/w2hsG9g+eO9k9RjIhS5LmkwuA7YHDB/YfA6wGrpri2udHxKMrsZvEfjRwVWauBsjMHwFXA0dHxIK+c/cFnkfvOegZi8w5f4BbkqRqIuIrwN7AicDNwDLg7cDRmfmJ5pwz6SXp52Tmbc2+hcB/ADvQe6nIXcBxwOuAwReD7A9cDFxIb657CfBB4AGg6MUgVsiSpPnmMODjwCnAl+g9e7xsIhk3FjSfR1eEN0n0NcAq4G/oJdunAwf1J+Pm3MuAg5vjFzbnrwJeU5KMwQpZkqROsEKWJKkDTMiSJHWACVmSpA4wIUuS1AEmZEmSOsCELElSB5iQJUnqABOyJEkdYEKWJKkDTMiSJHWACVmSpA4wIUuS1AEmZEmSOuD/A6kTRinvcDl4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for theta in [-0.5, -2, -8]:\n",
    "    for k in [4, 16, 64]:\n",
    "        plot_matrix(func_rho(theta, k), title='$\\\\theta$: '+str(theta)+', k: '+str(k))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, the edge effects are much more visible as we increase the number of blocks. Another place where this becomes apparent is in the asymmetry of the matrix--- proportion of friends in a certain block will not be identically reciprocated by another block, even if they have the same $\\theta$, owing to the edge effects in ordinal dimensions."
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}