{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Thorough Introduction to Boltzmann Machines\n",
    "\n",
    "The principal task of machine learning is to fit a model to some data. Thinking on the level of APIs, a model is an object with two methods:\n",
    "\n",
    "```python\n",
    "class Model:\n",
    "    \n",
    "    def likelihood(self, x):\n",
    "        pass\n",
    "        \n",
    "    def sample(self, n_samples):\n",
    "        pass\n",
    "```\n",
    "\n",
    "## Likelihood\n",
    "\n",
    "How likely is the query point(s) $x$ under our model? In other words, how likely was it that our model produced $x$? \n",
    "\n",
    "The likelihood gives a value proportional to a valid probability, but is not necessarily a valid probability itself.\n",
    "\n",
    "(Finally, the likelihood is often used as an umbrella term for, or interchangeably with, the probability density. The mainstream machine learning community would do well to agree to the use of one of these terms, and to sunset the other; while their definitions may differ slightly, the confusion brought about by their shared used sharply outweighs the pedagogical purity maintained by keeping them distinct.\n",
    "\n",
    "## Sample\n",
    "\n",
    "Draw samples from the model.\n",
    "\n",
    "## Denotation\n",
    "\n",
    "Canonically, we denote an instance of our `Model` in mathematical syntax as follows:\n",
    "\n",
    "$$\n",
    "x \\sim p(x)\n",
    "$$\n",
    "\n",
    "Again, this simple denotation implies two methods: that we can evaluate the likelihood of having observed $x$ under our model $p$, and that we can sample a new value $x$ from our model $p$. \n",
    "\n",
    "Often, we work with *conditional* models, such as $y \\sim p(y\\vert x)$, in classification and regression tasks. The same two implicit methods apply.\n",
    "\n",
    "## Boltzmann machines\n",
    "\n",
    "A Boltzmann machine is one of the simplest mechanisms for modeling $p(x)$. It is an undirected graphical model where every dimension $x_i$ of a given observation $x$ influences every other dimension. **As such, we might use it to model data which we believe to exhibit this property, e.g. an image.** For $x \\in R^3$, our model would look as follows:\n",
    "\n",
    "![](figures/boltzmann-machine.svg)\n",
    "\n",
    "For $x \\in R^n$, a given node $x_i$ would have $n - 1$ outgoing connections in total—one to each of the other nodes $x_j$ for $j \\neq i$.\n",
    "\n",
    "Finally, a Boltzmann machine strictly operates on *binary* data. This keeps things simple.\n",
    "\n",
    "## Computing the likelihood\n",
    "\n",
    "A Boltzmann machines admits the following formula for computing the likelihood of data points $x^{(1)}, ..., x^{(n)}$:\n",
    "\n",
    "$$\n",
    "H(x) = \\sum\\limits_{i \\neq j} w_{i, j} x_i x_j + \\sum\\limits_i b_i x_i\n",
    "$$\n",
    "\n",
    "$$\n",
    "p(x) = \\frac{\\exp{(H(x))}}{Z}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\mathcal{L}(x^{(1)}, ..., x^{(n)}) = \\prod\\limits_{i=1}^n p(x^{(i)})\n",
    "$$\n",
    "\n",
    "Note:\n",
    "\n",
    "- Since our weights can be negative, $H(x)$ can be negative. As a likelihood gives an optionally-normalized probability, it must be non-negative.\n",
    "- To enforce this constraint, we exponentiate $H(x)$ in the second equation.\n",
    "- To normalize, we divide by the normalization constant $Z$, i.e. the sum of the likelihoods of all possible values of $x^{(1)}, ..., x^{(n)}$.\n",
    "\n",
    "## Computing the partition function, with examples\n",
    "\n",
    "In the case of 2-dimensional binary $x$, the only possible \"configurations\" of $x$ are: $[0, 0], [0, 1], [1, 0], [1, 1]$, i.e. 4 distinct values. This means that in evaluating the likelihood of one datum $x$, the normalization constant $Z$ would be a sum of 4 terms.\n",
    "\n",
    "Now, with two data points $x^{(1)}$ and $x^{(2)}$, there are 16 possible \"configurations\":\n",
    "\n",
    "1. $x^{(1)} = [0, 0]$, $x^{(2)} = [0, 0]$\n",
    "2. $x^{(1)} = [0, 0]$, $x^{(2)} = [0, 1]$\n",
    "3. $x^{(1)} = [0, 0]$, $x^{(2)} = [1, 0]$\n",
    "4. $x^{(1)} = [0, 0]$, $x^{(2)} = [1, 1]$\n",
    "5. $x^{(1)} = [0, 1]$, $x^{(2)} = [0, 0]$\n",
    "6. $x^{(1)} = [0, 1]$, $x^{(2)} = [0, 1]$\n",
    "7. Etc.\n",
    "\n",
    "This means that in evaluating the likelihood of $\\mathcal{L}(x^{(1)}, x^{(2)})$, the normalization constant $Z$ would be a sum of 16 terms.\n",
    "\n",
    "More generally, given $d$-dimensional $x$, where each $x_i$ can assume one of $v$ distinct values, and $n$ data points $x^{(1)}, ..., x^{(n)}$—in evaluating the likelihood of $\\mathcal{L}(x^{(1)}, ..., x^{(n)})$ the normalization constant $Z$ would be a sum of $(v^d)^n$ terms. **With a non-trivially large $v$ or $d$ (in the discrete case), or a non-trivially large $k$ in the continuous case, this becomes intractable to compute.**\n",
    "\n",
    "In the case of a Boltzmann machine, $v = 2$, which is not large. Below, we will vary $d$ and examine its impact on the tractability (in terms of, \"can we actually compute $Z$ before the end of the universe?\") of inference.\n",
    "\n",
    "## The likelihood function in code\n",
    "\n",
    "In code, the likelihood function looks as follows:\n",
    "\n",
    "```python\n",
    "def _unnormalized_likelihood(self, x):\n",
    "    return np.exp(self._H(x))\n",
    "        \n",
    "def _H(self, x):\n",
    "    h = 0\n",
    "    for i, j in self.var_combinations:\n",
    "        h += self.weights[i, j] * x[i] * x[j]\n",
    "    h += self.biases @ x\n",
    "    return h\n",
    "\n",
    "def likelihood(self, x, log=False):\n",
    "    \"\"\"\n",
    "    :param x: a vector of shape (n_units,) or (n, n_units),\n",
    "        where the latter is a matrix of multiple data points\n",
    "        for which to compute the joint likelihood.\n",
    "    \"\"\"\n",
    "    x = np.array(x)\n",
    "    if not self.n_units in x.shape and len(x.shape) in (1, 2):\n",
    "        raise('Please pass 1 or more points of `n_units` dimensions')\n",
    "\n",
    "    # compute unnormalized likelihoods\n",
    "    multiple_samples = len(x.shape) == 2\n",
    "    if multiple_samples:\n",
    "        likelihood = [self._unnormalized_likelihood(point) for point in x]\n",
    "    else:\n",
    "        likelihood = [self._unnormalized_likelihood(x)]\n",
    "\n",
    "    # compute partition function\n",
    "    Z = sum([self._unnormalized_likelihood(config) for config in self.all_configs])\n",
    "\n",
    "    if log:\n",
    "        return sum([np.log(lik) - np.log(Z) for lik in likelihood])\n",
    "    else:\n",
    "        return reduce(np.multiply, [lik / Z for lik in likelihood])\n",
    "```\n",
    "\n",
    "This code block is longer than you might expect because it includes a few supplementary behaviors, namely:\n",
    "\n",
    "- Computing the likelihood of one or more points\n",
    "- Avoiding redundant computation of `Z`\n",
    "- Optionally computing the log-likelihood\n",
    "\n",
    "Above all, note that: the likelihood is a function of the model's parameters, i.e. `self.weights` and `self.biases`, which we can vary, and the data `x`, which we can't.\n",
    "\n",
    "## Training the model\n",
    "\n",
    "At the outset, the parameters `self.weights` and `self.biases` of our model are initialized at random. Trivially, such that the values returned by `likelihood` and `sample` are useful, we must first update these parameters by fitting this model to observed data.\n",
    "\n",
    "To do so, we will employ the principal of maximum likelihood: compute the parameters that make the observed data maximally likely under the model, via gradient ascent.\n",
    "\n",
    "## Gradients\n",
    "\n",
    "Since our model is simple, we can derive exact gradients by hand. We will work with the log-likelihood instead of the true likelihood to avoid issues of computational underflow. Below, we simplify this expression, then compute its various gradients.\n",
    "\n",
    "### $\\log{\\mathcal{L}}$\n",
    "\n",
    "$$\n",
    "\\mathcal{L}(x^{(1)}, ..., x^{(n)}) = \\prod\\limits_{k=1}^n \\frac{\\exp{(H(x^{(k)})}}{Z}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\log{\\mathcal{L}(x^{(1)}, ..., x^{(n)})} \n",
    "&= \\sum\\limits_{k=1}^n \\log{\\frac{\\exp{(H(x^{(k)})}}{Z}}\\\\\n",
    "&= \\sum\\limits_{k=1}^n \\log{\\big(\\exp{(H(x^{(k)})}\\big)} - \\log{Z}\\\\\n",
    "&= \\sum\\limits_{k=1}^n H(x^{(k)}) - \\log{Z}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "This gives the total likelihood. Our aim is to maximize the expected likelihood with respect to the data generating distribution.\n",
    "\n",
    "### Expected likelihood\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\mathop{\\mathbb{E}}_{x \\sim p_{\\text{data}}}\\big[ \\mathcal{L}(x) \\big]\n",
    "&= \\sum\\limits_{k=1}^N p_{\\text{data}}(x = x^{(k)}) \\mathcal{L(x^{(k)})}\\\\\n",
    "&= \\sum\\limits_{k=1}^N \\frac{1}{N} \\mathcal{L(x^{(k)})}\\\\\n",
    "&= \\frac{1}{N} \\sum\\limits_{k=1}^N  \\mathcal{L(x^{(k)})}\\\\\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "In other words, the average. We will continue to denote this as $\\mathcal{L}$, i.e. $\\mathcal{L} = \\frac{1}{N} \\sum\\limits_{k=1}^n H(x^{(k)}) - \\log{Z}$.\n",
    "\n",
    "Now, deriving the gradient with respect to our weights:\n",
    "\n",
    "### $\\nabla_{w_{i, j}}\\log{\\mathcal{L}}$\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\nabla_{w_{i, j}} \\frac{1}{N} \\sum\\limits_{k=1}^n H(x^{(k)}) - \\log{Z}\n",
    "&= \\frac{1}{N} \\sum\\limits_{k=1}^n \\nabla_{w_{i, j}}  H(x^{(k)}) - \\frac{1}{N} \\sum\\limits_{k=1}^n \\nabla_{w_{i, j}} \\log{Z}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "### First term\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\frac{1}{N} \\sum\\limits_{k=1}^n \\nabla_{w_{i, j}}  H(x^{(k)})\n",
    "&= \\frac{1}{N} \\sum\\limits_{k=1}^n \\nabla_{w_{i, j}} \\sum\\limits_{i \\neq j} w_{i, j} x_i^{(k)} x_j^{(k)} + \\sum\\limits_i b_i x_i^{(k)}\\\\\n",
    "&= \\frac{1}{N} \\sum\\limits_{k=1}^n x_i^{(k)} x_j^{(k)}\\\\\n",
    "&= \\mathop{\\mathbb{E}}_{x \\sim p_{\\text{data}}} [x_i  x_j]\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "### Second term\n",
    "\n",
    "NB: $\\sum\\limits_{\\mathcal{x}}$ implies a summation over all $(v^d)^n$ possible configurations of values that $x^{(1)}, ..., x^{(n)}$ can assume.\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\nabla_{w_{i, j}} \\log{Z}\n",
    "&= \\nabla_{w_{i, j}} \\log{\\sum\\limits_{\\mathcal{x}}} \\exp{(H(x))}\\\\\n",
    "&= \\frac{1}{\\sum\\limits_{\\mathcal{x}} \\exp{(H(x))}} \\nabla_{w_{i, j}} \\sum\\limits_{\\mathcal{x}} \\exp{(H(x))}\\\\\n",
    "&= \\frac{1}{Z} \\nabla_{w_{i, j}} \\sum\\limits_{\\mathcal{x}} \\exp{(H(x))}\\\\\n",
    "&= \\frac{1}{Z} \\sum\\limits_{\\mathcal{x}} \\exp{(H(x))} \\nabla_{w_{i, j}} H(x)\\\\\n",
    "&= \\sum\\limits_{\\mathcal{x}} \\frac{\\exp{(H(x))}}{Z} \\nabla_{w_{i, j}} H(x)\\\\\n",
    "&= \\sum\\limits_{\\mathcal{x}} P(x) \\nabla_{w_{i, j}} H(x)\\\\\n",
    "&= \\sum\\limits_{\\mathcal{x}} P(x) [x_i  x_j]\\\\\n",
    "&= \\mathop{\\mathbb{E}}_{x \\sim p_{\\text{model}}} [x_i  x_j]\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "### Putting it back together\n",
    "\n",
    "Combining these constituent parts, we arrive at the following formula:\n",
    "\n",
    "$$\n",
    "\\nabla_{w_{i, j}}\\log{\\mathcal{L}} = \\mathop{\\mathbb{E}}_{x \\sim p_{\\text{data}}} [x_i  x_j] - \\mathop{\\mathbb{E}}_{x \\sim p_{\\text{model}}} [x_i  x_j]\n",
    "$$\n",
    "\n",
    "Finally, following the same logic, we derive the exact gradient with respect to our biases:\n",
    "\n",
    "$$\n",
    "\\nabla_{b_i}\\log{\\mathcal{L}} = \\mathop{\\mathbb{E}}_{x \\sim p_{\\text{data}}} [x_i] - \\mathop{\\mathbb{E}}_{x \\sim p_{\\text{model}}} [x_i]\n",
    "$$\n",
    "\n",
    "The first and second terms of each gradient are called, respectively, **the positive and negative phases.**\n",
    "\n",
    "## Computing the positive phase\n",
    "\n",
    "In the following toy example, our data are small: we can compute the positive phase using all of the training data, i.e. $\\frac{1}{N} \\sum\\limits_{k=1}^n x_i^{(k)} x_j^{(k)}$. Were our data bigger, we could approximate this expectation with a mini-batch of training data and we do in SGD.\n",
    "\n",
    "## Computing the negative phase\n",
    "\n",
    "Again, this term asks us to compute then sum the log-likelihood over every possible data configuration in the support of our model, which is $O(nv^d)$. **With non-trivially large $v$ or $d$, this becomes intractable to compute.**\n",
    "\n",
    "Below, we'll begin our toy example computing the true negative-phase, $\\mathop{\\mathbb{E}}_{x \\sim p_{\\text{model}}} [x_i  x_j]$, with varying data-dimensionalities $d$. Then, once this computation becomes slow, we'll look to approximate this expectation later on.\n",
    "\n",
    "## Parameter updates in code\n",
    "\n",
    "```python\n",
    "def update_parameters_with_true_negative_phase(weights, biases, var_combinations, all_configs, data, alpha=alpha):\n",
    "    model = Model(weights, biases, var_combinations, all_configs)\n",
    "    model_distribution = [(np.array(config), model.likelihood(config)) for config in all_configs]\n",
    "\n",
    "    for i, j in var_combinations:\n",
    "        # positive phase\n",
    "        positive_phase = (data[:, i] * data[:, j]).mean()\n",
    "\n",
    "        # negative phase\n",
    "        negative_phase = sum([config[i] * config[j] * likelihood for config, likelihood in model_distribution])\n",
    "\n",
    "        # update weights\n",
    "        weights[i, j] += alpha * (positive_phase - negative_phase)\n",
    "        \n",
    "    for i, _ in enumerate(biases):\n",
    "        # positive phase\n",
    "        positive_phase = data[:, i].mean()\n",
    "        \n",
    "        # negative phase\n",
    "        negative_phase = sum([config[i] * likelihood for config, likelihood in model_distribution])\n",
    "        \n",
    "        # update biases\n",
    "        biases[i] += alpha * (positive_phase - negative_phase)\n",
    "        \n",
    "    return np.array(weights), np.array(biases)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train model, visualize model distribution\n",
    "\n",
    "Finally, we're ready to train. Using the true negative phase, let's train our model for 100 epochs with $d=3$ then visualize results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "from functools import reduce\n",
    "from itertools import product, combinations\n",
    "from time import time\n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "seed = 42\n",
    "alpha = .01\n",
    "\n",
    "\n",
    "def reset_data_and_parameters(n_units=3, n_obs=100, p=[.8, .1, .5]):\n",
    "    \"\"\"\n",
    "    Generate training data, weights, biases, and a list of all data configurations\n",
    "    in our model's support.\n",
    "    \n",
    "    In addition, generate a list of tuples of the indices of adjacent nodes, which\n",
    "    we'll use to update parameters without duplication. \n",
    "    \n",
    "    For example, with `n_units=3`, we generate a matrix of weights with shape (3, 3); \n",
    "    however, there are only 3 distinct weights in this matrix that we'll actually \n",
    "    want to update: those connecting Node 0 --> Node 1, Node 1 --> Node 2, and \n",
    "    Node 0 --> Node 2. This function returns a list containing these tuples \n",
    "    named `var_combinations.\n",
    "    \n",
    "    :param n_units: the dimensionality of our data `d`\n",
    "    :param n_obs: the number of observations in our training set\n",
    "    :param p: a vector of the probabilities of observing a 1 in each index\n",
    "        of the training data. The length of this vector must equal `n_units`\n",
    "        \n",
    "    :return: weights, biases, var_combinations, all_configs, data\n",
    "    \"\"\"\n",
    "    np.random.seed(seed)\n",
    "    \n",
    "    # initialize data\n",
    "    data = np.random.binomial(n=1, p=p, size=(100, n_units))\n",
    "    \n",
    "    # initialize parameters\n",
    "    biases = np.random.randn(n_units)\n",
    "    weights = np.random.randn(n_units, n_units)\n",
    "    \n",
    "    # a few other pieces we'll need\n",
    "    var_combinations = list(combinations(range(n_units), 2))\n",
    "    all_configs = list(product([0, 1], repeat=n_units))\n",
    "    \n",
    "    return weights, biases, var_combinations, all_configs, data\n",
    "\n",
    "\n",
    "class Model:\n",
    "    \n",
    "    def __init__(self, weights, biases, var_combinations, all_configs):\n",
    "        self.weights = weights\n",
    "        self.biases = biases\n",
    "        self.var_combinations = var_combinations\n",
    "        self.all_configs = all_configs\n",
    "        self.n_units = len(self.biases)\n",
    "        \n",
    "    @staticmethod\n",
    "    def _inv_logit(z):\n",
    "        return 1 / (1 + np.exp(-z))\n",
    "        \n",
    "    def _unnormalized_likelihood(self, x):\n",
    "        return np.exp(self._H(x))\n",
    "        \n",
    "    def _H(self, x):\n",
    "        h = 0\n",
    "        for i, j in self.var_combinations:\n",
    "            h += self.weights[i, j] * x[i] * x[j]\n",
    "        h += self.biases @ x\n",
    "        return h\n",
    "    \n",
    "    def likelihood(self, x, log=False):\n",
    "        \"\"\"\n",
    "        :param x: a vector of shape (n_units,) or (n, n_units),\n",
    "            where the latter is a matrix of multiple data points\n",
    "            for which to compute the joint likelihood.\n",
    "        \"\"\"\n",
    "        x = np.array(x)\n",
    "        if not self.n_units in x.shape and len(x.shape) in (1, 2):\n",
    "            raise('Please pass 1 or more points of `n_units` dimensions')\n",
    "           \n",
    "        # compute unnormalized likelihoods\n",
    "        multiple_samples = len(x.shape) == 2\n",
    "        if multiple_samples:\n",
    "            likelihood = [self._unnormalized_likelihood(point) for point in x]\n",
    "        else:\n",
    "            likelihood = [self._unnormalized_likelihood(x)]\n",
    "        \n",
    "        # compute partition function\n",
    "        Z = sum([self._unnormalized_likelihood(config) for config in self.all_configs])\n",
    "        \n",
    "        if log:\n",
    "            return sum([np.log(lik) - np.log(Z) for lik in likelihood])\n",
    "        else:\n",
    "            return reduce(np.multiply, [lik / Z for lik in likelihood])\n",
    "        \n",
    "    def sample(self, n_samples=100, init_sample=None, burn_in=25, every_n=10, seed=seed) -> np.array:\n",
    "\n",
    "        np.random.seed(seed)\n",
    "\n",
    "        if burn_in > n_samples:\n",
    "            raise(\"Can't burn in for more samples than there are in the chain\")\n",
    "\n",
    "        init_sample = init_sample or [0 for _ in self.biases]\n",
    "        samples = [init_sample]\n",
    "\n",
    "        def _gibbs_step(sample, i):\n",
    "            z = sum([self.weights[i, j] * sample[j] for j in range(len(sample)) if j != i]) + self.biases[i]\n",
    "            p = self._inv_logit(z)\n",
    "            return np.random.binomial(n=1, p=p)\n",
    "\n",
    "        for _ in range(n_samples):\n",
    "            sample = list(samples[-1])  # make copy\n",
    "            for i, _ in enumerate(sample):\n",
    "                sample[i] = _gibbs_step(sample=sample, i=i)\n",
    "            samples.append( sample )\n",
    "\n",
    "        return np.array([sample for i, sample in enumerate(samples[burn_in:]) if i % every_n == 0])\n",
    "    \n",
    "    def conditional_likelihood(x, cond: dict):\n",
    "        joint = np.array(x)\n",
    "        for index, val in cond.items():\n",
    "            if isinstance(joint[index], int):\n",
    "                raise\n",
    "            joint[index] = val\n",
    "\n",
    "        evidence = [cond.get(i, ...) for i in range(len(x))]\n",
    "\n",
    "        return self._unnormalized_likelihood(joint) / self.marginal_likelihood(evidence)\n",
    "    \n",
    "    def marginal_likelihood(self, x):\n",
    "        \"\"\"\n",
    "        To marginalize, put ellipses (...) in the elements over \n",
    "        which you wish to marginalize.\n",
    "        \"\"\"\n",
    "        unnormalized_lik = 0\n",
    "        for config in product(*[[0, 1] if el == ... else [el] for el in x]):\n",
    "            config = np.array(config)\n",
    "            unnormalized_lik += np.exp(self._H(config))\n",
    "        return unnormalized_lik\n",
    "\n",
    "\n",
    "def update_parameters_with_true_negative_phase(weights, biases, var_combinations, all_configs, data, alpha=alpha, **kwargs):\n",
    "    model = Model(weights, biases, var_combinations, all_configs)\n",
    "    model_distribution = [(np.array(config), model.likelihood(config)) for config in all_configs]\n",
    "\n",
    "    for i, j in var_combinations:\n",
    "        # positive phase\n",
    "        positive_phase = (data[:, i] * data[:, j]).mean()\n",
    "\n",
    "        # negative phase\n",
    "        negative_phase = sum([config[i] * config[j] * likelihood for config, likelihood in model_distribution])\n",
    "\n",
    "        # update weights\n",
    "        weights[i, j] += alpha * (positive_phase - negative_phase)\n",
    "        \n",
    "    for i, _ in enumerate(biases):\n",
    "        # positive phase\n",
    "        positive_phase = data[:, i].mean()\n",
    "        \n",
    "        # negative phase\n",
    "        negative_phase = sum([config[i] * likelihood for config, likelihood in model_distribution])\n",
    "        \n",
    "        # update biases\n",
    "        biases[i] += alpha * (positive_phase - negative_phase)\n",
    "        \n",
    "    return np.array(weights), np.array(biases)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:  0 | Likelihood: -209.63758306786653\n",
      "Epoch: 10 | Likelihood: -162.04280784271083\n",
      "Epoch: 20 | Likelihood: -160.49961381649555\n",
      "Epoch: 30 | Likelihood: -159.79539070373576\n",
      "Epoch: 40 | Likelihood: -159.2853717231018\n",
      "Epoch: 50 | Likelihood: -158.90186293631422\n",
      "Epoch: 60 | Likelihood: -158.6084020645482\n",
      "Epoch: 70 | Likelihood: -158.38094343579155\n",
      "Epoch: 80 | Likelihood: -158.20287017780586\n",
      "Epoch: 90 | Likelihood: -158.06232196551673\n"
     ]
    }
   ],
   "source": [
    "weights, biases, var_combinations, all_configs, data = reset_data_and_parameters(n_units=3, p=[.8, .1, .5])\n",
    "\n",
    "\n",
    "for i in range(100):\n",
    "    weights, biases = update_parameters_with_true_negative_phase(weights, biases, var_combinations, all_configs, data, alpha=1)\n",
    "    \n",
    "    lik = Model(weights, biases, var_combinations, all_configs).likelihood(data, log=True)\n",
    "    if i % 10 == 0:\n",
    "        print(f'Epoch: {i:2} | Likelihood: {lik}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualize samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_n_samples(n_samples, weights, biases):\n",
    "    \"\"\"\n",
    "    NB: We add some jitter to the points so as to better visualize density in a given corner of the model.\n",
    "    \"\"\"\n",
    "    fig = plt.figure(figsize=(12, 9))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    \n",
    "    samples = Model(weights, biases, var_combinations, all_configs).sample(n_samples)\n",
    "    x, y, z = zip(*np.array(samples))\n",
    "    \n",
    "    x += np.random.randn(len(x)) * .05\n",
    "    y += np.random.randn(len(y)) * .05\n",
    "    z += np.random.randn(len(z)) * .05\n",
    "    \n",
    "    ax.scatter(x, y, z)\n",
    "    ax.set_xlabel('Node 0')\n",
    "    ax.set_ylabel('Node 1')\n",
    "    ax.set_zlabel('Node 2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAD4kAAAH3CAYAAAAcg4gKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_samples = 1000\n",
    "\n",
    "plot_n_samples(n_samples, weights, biases)\n",
    "_ = plt.title(f'{n_samples} Samples from Model')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot roughly matches the data-generating distribution: most points assume values of either $[1, 0, 1]$, or $[1, 0, 0]$ (given $p=[.8, .1, .5]$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sampling, via Gibbs\n",
    "\n",
    "The second, final method we need to implement is `sample`. In a Boltzmann machine, we typically do this via [Gibbs sampling](http://www.mit.edu/~ilkery/papers/GibbsSampling.pdf).\n",
    "\n",
    "To effectuate this sampling scheme, we'll need a model of each data dimension conditional on the other data dimensions. For example, for $d=3$, we'll need to define:\n",
    "\n",
    "- $p(x_0\\vert x_1, x_2)$\n",
    "- $p(x_1\\vert x_0, x_2)$\n",
    "- $p(x_2\\vert x_0, x_1)$\n",
    "\n",
    "Given that each dimension must assume a 0 or a 1, the above 3 models must necessarily return the probability of observing a 1 (where 1 minus this value gives the probability of observing a 0).\n",
    "\n",
    "Let's derive these models using the workhorse axiom of conditional probability, starting with the first:\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "p(x_0 = 1\\vert x_1, x_2)\n",
    "&= \\frac{p(x_0 = 1, x_1, x_2)}{p(x_1, x_2)}\\\\\n",
    "&= \\frac{p(x_0 = 1, x_1, x_2)}{\\sum\\limits_{x_0 \\in [0, 1]} p(x_0, x_1, x_2)}\\\\\n",
    "&= \\frac{p(x_0 = 1, x_1, x_2)}{p(x_0 = 0, x_1, x_2) + p(x_0 = 1, x_1, x_2)}\\\\\n",
    "&= \\frac{1}{1 + \\frac{p(x_0 = 0, x_1, x_2)}{p(x_0 = 1, x_1, x_2)}}\\\\\n",
    "&= \\frac{1}{1 + \\frac{\\exp{(H(x_0 = 0, x_1, x_2)))}}{\\exp{(H(x_0 = 1, x_1, x_2)))}}}\\\\\n",
    "&= \\frac{1}{1 + \\exp{(H(x_0 = 0, x_1, x_2) - H(x_0 = 1, x_1, x_2))}}\\\\\n",
    "&= \\frac{1}{1 + \\exp{(\\sum\\limits_{i \\neq j} w_{i, j} x_i x_j + \\sum\\limits_i b_i x_i - (\\sum\\limits_{i \\neq j} w_{i, j} x_i x_j + \\sum\\limits_i b_i x_i))}}\\\\\n",
    "&= \\frac{1}{1 + \\exp{(-\\sum\\limits_{j \\neq i = 0} w_{i, j} x_j - b_i)}}\\\\\n",
    "&= \\sigma\\bigg(\\sum\\limits_{j \\neq i = 0} w_{i, j} x_j + b_i\\bigg)\\\\\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Pleasantly enough, this model resolves to a simple Binomial GLM, i.e. logistic regression, involving only its neighboring units and the weights that connect them.\n",
    "\n",
    "With the requisite conditionals in hand, let's run this chain and compare it with our (trained) model's true probability distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## True probability distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 0, 0]: 0.07327\n",
      "[0, 0, 1]: 0.09227\n",
      "[0, 1, 0]: 0.01366\n",
      "[0, 1, 1]: 0.01938\n",
      "[1, 0, 0]: 0.3351\n",
      "[1, 0, 1]: 0.3622\n",
      "[1, 1, 0]: 0.04693\n",
      "[1, 1, 1]: 0.05715\n"
     ]
    }
   ],
   "source": [
    "model = Model(weights, biases, var_combinations, all_configs)\n",
    "\n",
    "distribution = [(np.array(config), model.likelihood(config)) for config in all_configs]\n",
    "assert sum([likelihood for config, likelihood in distribution]) == 1\n",
    "\n",
    "for config, likelihood in distribution:\n",
    "    print(f'{list(config)}: {likelihood:.4}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Empirical probability distribution, via Gibbs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 0, 0]: 0.07327 (true), 0.05102 (empirical)\n",
      "[0, 0, 1]: 0.09227 (true), 0.09184 (empirical)\n",
      "[0, 1, 0]: 0.01366 (true), 0.0102 (empirical)\n",
      "[0, 1, 1]: 0.01938 (true), 0.02041 (empirical)\n",
      "[1, 0, 0]: 0.3351 (true), 0.3673 (empirical)\n",
      "[1, 0, 1]: 0.3622 (true), 0.398 (empirical)\n",
      "[1, 1, 0]: 0.04693 (true), 0.03061 (empirical)\n",
      "[1, 1, 1]: 0.05715 (true), 0.03061 (empirical)\n"
     ]
    }
   ],
   "source": [
    "empirical_dist = defaultdict(int)\n",
    "samples = model.sample(n_samples=1000)\n",
    "n_samples = len(samples)\n",
    "\n",
    "for sample in samples:\n",
    "    empirical_dist[tuple(sample)] += 1 / n_samples\n",
    "assert np.round(sum(empirical_dist.values()), 8) == 1\n",
    "    \n",
    "for config, likelihood in distribution:\n",
    "    empirical_probability = empirical_dist[tuple(config)]\n",
    "    print(f'{list(config)}: {likelihood:.4} (true), {empirical_probability:.4} (empirical)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Close, ish enough."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scaling up, and hitting the bottleneck\n",
    "\n",
    "With data of vary dimensionality `n_units`, the following plot gives the time in seconds that it takes to train this model for 10 epochs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x114f80400>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAAGQCAYAAABh1COdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAAIABJREFUeJzt3Xu8VXWd//HXB1BJRTREU1DBNPNO\nRoxlZo3VOHlvtChLaiw1rWlscnLEqWnG0i7jZOlcnMy8azDeulrRaI32UzERBSzFSAEvhKLgLZHP\n74+1jmyOZ59zOJvD/sJ5PR+P82Dvtdfls9fe7Pde37X29xuZiSRJKtOgdhcgSZKaM6glSSqYQS1J\nUsEMakmSCmZQS5JUMINakqSCGdRqu4g4PSK+3e461raImBQRP253HY0i4v8i4iO9mG9IRGREjGny\n+Db1upZGxFfWcJnrnIg4MyK+2+46tG4yqNXvImJZw9+KiHiu4f4xmfnlzPzYWqhjTB0uQ/qw7DEN\nNT9XP4+Xn1df6snMizPzL/uybP3BnxFxcqfpf1dPP6Mv612DTgQWAptl5udaXVlEjIqI70fEI/Xz\nG93p8aER8d2IeLqe59PdrOtjEfFSp/flsojYqtU6pf5gUKvfZeamHX/AQ8ChDdMub3d9vZGZlzc8\nh78EFnZ6Xqvoy5eBPvgdcGynacfW09ttB2B29qFHpSb7bgXwI+CoJov9CzAG2B54F3B6RLyzm838\nqvH1q/8eX91apbXBoFbbRcQ/RcRl9e2Oo96PRsTDEfFkRJwYEW+KiJkRsSQizuu0/F9HxJx63hsj\nYocmm/pl/e+S+gjqzRExKCLOiIg/RMTjEXFJRAzv4/OYHxGnRsQ9wDP1tDMi4sG6CXhWRBzWMP/H\nIuKm+nZHU/IJEfFA/Vy+2cMmfw28OiJ2qdcxjur/9F2d6jqxXufiiLguIrZpeOygiPhtRDwVEecC\n0WnZj0XEfXU9P46I7XqxHy4FjqEKy2UR8fb6iPeb9dHugog4JyI2rOd/Z0TMi+oUyKPAf3deZ2Y+\nkpn/AdzZZLPHAv+cmUsy817gO8BHeqq1Sf3zI+JzDe+pCyNio4bHu9ufe0bEzyPiiYh4NCL+vmHV\nG0XEZfV74d6I2KdhudMjYmHdInBfRLy9L7Vr/WRQq1R/BuwMvB/4BjAZeCewO/C+iDgAICIOB04H\n3guMBH4FXNlknW+r/928PoL6NdWH+UeAdwA7ApsC53W5dO9MpDri3ry+/ztgP2A48CXgiojYupvl\n3wO8EXgD8KEejgoBLmXlUfWxwCWND0bEu4F/pjoSHUXVHH15/dhWwFTgNGBLYD7Vfu9Y9q+AU4HD\nqfbtbcAVPdRDZn4YuBr4cr2fbwI+D4wH9qqf237APzQsNppq328PnNTTNjo9x5HAVsDdDZPvpnqv\n9NUxVEfmO9fr+Yd6W93tz+HAz4HvA9sArwNualjnEVSv1+bAj4Fv1svtDpwA7JOZm1G9fx5qoXat\nZwxqlepfMvP5zPwp1dHplZn5eGYuoArjN9TznQiclZlzMnM58GVgXDdH1Z0dA5yTmQ9m5jKqD+SJ\nLTRdn5uZ8zPzOYDM/F59NLgiM68A5lEFVjNnZeZTmTmP6kN+XA/buxQ4JiI2oPpS0/lUwjHAtzNz\nRmY+TxXKB9TneA8BZmTmtZn5IvCvwKKGZU+kCtvf1vv2TGBCRIzqaSd04RjgnzJzUd3E/M/Ahxse\nX14//qeOfbcaOk49PNUw7SlgWDfLvLVunen4+22nx79Zv45/pHpPfaDheTTbn4cBD2XmuZn5QmY+\nnZm3N6zz5sy8MTNfonrdOl7b5cBQYPeIGJKZv8/MB1dzH2g9ZlCrVI813H6ui/sdH847AOd2fOAC\nT1A13/Y2TLYF/tBw/w/AEKC7o97uPNx4JyI+EhF3N9T3eqqj12Yebbj9LCufZ5cy8/dUR19fBu7N\nzIWdZlnl+WXm08CTVPtn28Z6M3MF1VF1hx2A8xtq/yPVueJVLuTqpa72c+Nr9Fhm/qkP6wXouJhv\ns4ZpmwFLu1nm/zJz84a/XTo93vg6/oGqfuh+f24HzO1mm51f203qdfwW+DuqLy+PR8SVEfGabtaj\nAcag1rruYeCETh+6r8rMW7uYt6sLmxZSBVKH7amOcB7rYt7eeHkbEbEj8B/AJ4ARmbk5cB+dzgOv\nAZdQfdBf0sVjqzy/iBgGbAEsAB6hCpeOxwaxagg/DBzXxb69rQ81drWfFzTc7/Mwfpm5iKolYO+G\nyXsDs/q6Thr2C1WtHV+AutufDwOv7cvGMvOyzNwPGAsMBs7qy3q0fjKota77T+Af6vN8RMTwiDi6\nybyLqI4Id2yYdiVwSkSMjYhNqY5Mr66belu1KVUALapKi49THVGvaVcA7wb+p4vHrgSOi4i96gui\nzqK64nk+8AOq0wSH103np1Cdi+7wn8DkiNiV6glsHhHNrrruyZXA5yNiy/qc8j8Cl63OCiJiKNBx\nUddGjRd4UX1J+ce6xt2Avwa+28daAT4Z1U/CRlCdDrm64Xk02583ANtHxCcjYqOI2CwiJvTiee0a\nEe+o1/dc/beihdq1njGotU7LzGuBrwBXRcTTwL1UF+N0Ne+zVBd03VI35+5LdXXwpVRXhP8eeB74\n1BqqbSbwLeB2qqPXXaguyFqjMvPZzPx5fc6082M/oWpSvbauYXuq86xk5mNU57W/RtWsvX1jfZk5\nBTgHmFLv25nAX/SxzC9SXeB1b72e21iNo8b6moHngCX1pAeor6yv/SPVEe3DwC+ozvX/vJtV7h+v\n/B31Gxoev5LqwrC5wG+pvsD1tD+foroA7a+oWmR+BxzQi6e3EfBVqtfgUaoj9Mm9WE4DRPThZ46S\ntN6KiPnAh+qr1aW284hakqSCGdSSJBXMpm9JkgrmEbUkSQUzqCUNCBGxcURMjoiN211LKyLi/RHx\n5nbXobXHoNZaUf/8ZcduHp/Xi36t1ykRsX8XXVO2VVQDa0xaC9vJiNipvv2fEfGP/b3NelufiIjH\n6vfbiMbH6p/nDaL+qVU7tfjemAlcWHe2ogHAoNZaUQ/O8CBAVOMGn9nXddXdcjaOJ/z7iLgoIl63\nGutotYZ/iogX65GQlkbE7yLivGgYSSkzf9VF15RtlZl/mZkXr+VtnpiZ/wIQ1Uha83tapi/qTlvO\nAd5dv98WdzHbl4CdI+It/VFDb3V+b6zOF9XMnEPV7/pX+6s+lcWg1rrq1/U40MOpRtV6DrgzIvZY\nizVcnZnDgFcDRwKvqWvYpvvF1E+2phrcomnXofXgKAc36WJ2nZGZV2TmJ9pdh9YOg1p9FtWY0d9v\nuH9/RExpuP9wVGMkv9wUGhHHU/Xk9Pf10fD3G1Y5Lqoxp5+KiKvrLiO7lZkvZebczDwJuBn4p4bt\nT4lqTOCnIuKXDd2MdllDRJwWEXPrI+TZEXFkb/ZDZr6YmbOoevlaRNXv9iuOHuujplPr5/hMVOMc\nb103Ry+NahzjLRrm3zcibq17Ubs7GsYojoibIuJfIuKWetmfRsSW9WNDoxr3eHG97B1RD61ZL/ex\n+nbTsbhj5bjgkyLioYj4Y0RMbtj+hIj4db3+R+rWhA272j8drRcRsQnV8I7bNrSGbBsRzzY2U0fE\nPhGxqD5C7ryujSLiG1GN3bywvr1R3ZrS0ZS8JCJ+0ZvXrjfPtZvlVmmVafJ6f7ar93TjvFGN3709\n8P16n/x9d6+hBh6DWq24maorxkERsS2wIfBmeHlAik2pzqe9LDMvoBqK8at18+ShDQ+/DziIamCC\nvajGiV4d1wD7N9z/MdV4wlsBv6m3210Nc+vlh1N1eXlZrMbRcT184fWdaujsr6i6mXwdcGhd4+lU\nfWwPAv4GIKqhJH9I1cT5auCzwP9E1U92hw8CH62f34b1PACT6uewHTCCarjKroaO/Ag9j8X9Vqqu\nTw+k6qt713r6S1R9g29J9ZofSA/jSGfmM1Tduy6s9/um9WhfN1G99h0+DFxVD73Z2WRgX6ohIvcG\nJgBnZObvWDn+9OaZ+efd1dJEs+faih7f0/X43Q8Bh9b75Kv0/jXUAGBQq8/qc85LqT403wbcCCyM\niNdT9XH8q3roxN76ZmYuzMwngO/T81jMnS2kCrWO+r6TmUsz8wWqI+29O44YmzyfKfX2V2Tm1cD9\nVEHQ5xq68K3MfCxXjqt9W2beVffTfS0rx9n+EPCjzPxRXc/PgOnAexrWdVFm/q4ev/l7rNxfL1J9\nuO9UtzjcWQ/H2FlvxuL+YmY+l5l3U/XVvTdAvc7/l5nLsxo7+7/oXb/WXbm4fr5ExGCqsZ8vbTLv\nMcA/ZzU2+SKqL1QfbjLv6uryubaor+/p3r6GGgAMarXqZuDtVEF9M9XR0QH1382rua7VGou5C6Oo\nxqMmIgZHxNl1U/bTwLx6nqZjQUfEsRExI1aOv7xHd/P3VEMTqzPO9tEdtdT1vBVoPMJvtr8upfrS\ndFXdPPzVrpqR6d1Y3F1uIyJeFxE/iOrUwtNUV1Kv7r7qcD2wW0SMpWpteCozb28yb1c1b9tk3tXV\n6vtvTa6zt6+hBgCDWq3qCOr969s303NQ91d3eEdSHaVC1Sx8ONWFZsOBMfX0jrGgV6khInYA/hv4\nJCvHjr63Yf4eRTWe86ENNbTiYeDSTmNBb5KZZ/e0YH3O/IuZuRvwFuAQ4NguZm1lLO7/oBpbe+fM\n3Iyq+b43++oVr33dmvA9qqPqD9P8aLpZzQubzNvfngEaf5P9mhbWtcp+WY3XUAOAQa1W3Ux1jvNV\n9Zi8v6I6JzcCuKvJMo+x6pjQfVYfOY+NiG9RfWH4Yv3QMOAFYDHVh2nn3852rmETVo4dTUR8lOqI\nujc1DKnPZ15J9WF9Tp+ezKouAw6NiL+on+PQ+gKk0b2o5x0RsWfdjPw0VTNqV6cgWhmLe1i97mX1\nqY7eXoH8GDCii1MQl1Cdvz2M7oP6SuCMiBgZ1cVzn2c1x7Veg2YA74mIV0fEa4C/bWFdq7wfV+M1\n1ABgUKsl9UU8y6iPIuvzaA8Ct9QXV3XlQqqmziURcV0fN/3miFhG9SF2E7AZ8KbMvKd+/BKqZtEF\nwGzg/3VXQ2bOBv4V+DXVh+aewC091PD+uoangBuovhS8sb5AqiWZ+TBVi8DpVF8eHgZOpXf/Z18D\nTKXaN3Oovkx1FX6tjMX9WapWi6VULRFX92ahzLyPKmwfrPf9tvX0W6iC6DeZ+YduVnEm1bn6mcA9\nVBcJ9vn38C26lOpc9jzgp/RyHzRxFtUXkCUR8Vl6/xpqAHBQDklFqH9SdUVmfrvdtUglMagltV1E\nvAn4GbBdZi5tdz1SSWz6ltRWEXEx8HPgb0sL6ag6o1nWxd/p7a5NA0ePR9QR8R2qKw4fz8w96mmv\npjofM4bq/Mz7MvPJiAjgXKrfej4LfCQzf9Nv1UuStJ7rzRH1d6mu4m10GjAtM3cGptX3oep1aOf6\n73iqn3BIkqQ+6tU56ogYA/yg4Yj6t8DbM/ORuovFmzJzl4j4r/r2lZ3n6279W265ZY4ZM6alJyJJ\n0rrizjvv/GNmjux5zqoXor7YuiF8H2VlT0ajqH5G0mF+Pa3boB4zZgzTp0/vYymSJK1bIqK7nyGu\nouWLybI6JF/tS8cj4viImB4R0xctWtRqGZIkrZf6GtSPdYwqVP/7eD19AdVoLx1G19NeITMvyMzx\nmTl+5MheHf1LkjTg9DWob6Aaho363+sbph8blX2pOtfvttlbkiQ11+M56oi4kqoP5S3rgc6/AJwN\nfC8ijqPqprFjLNkfUf006wGqn2d9tK+Fvfjii8yfP5/nn3++r6vQemLo0KGMHj2aDTZw8CBJA0+P\nQZ2ZH2jy0IFdzJvAya0WBTB//nyGDRvGmDFjqH6erYEoM1m8eDHz589n7Nix7S5Hkta6Ynsme/75\n5xkxYoQhPcBFBCNGjLBlRdKAVWxQA4a0AN8Hkga2ooNakqSBrq8dnqx1Y0774Rpd37yzD16j65Mk\nqT94RN3EkiVL+Pd//3cAFi5cyFFHHdVv27ruuuuYPXt2n5adMmUKu+++O4MGDXpF725nnXUWO+20\nE7vssgs33njjmii1T2666SYOOeSQtm1fktZlBnUTjUG97bbbMnXq1H7bVitBvccee3DNNdfwtre9\nbZXps2fP5qqrrmLWrFn85Cc/4aSTTuKll15aE+VKktYig7qJ0047jblz5zJu3DiOPvpo9thjDwC+\n+93vcsQRR/Cud72LMWPGcN5553HOOefwhje8gX333ZcnnngCgLlz53LQQQfxxje+kf3335/77ruv\ny+3ceuut3HDDDZx66qmMGzeOuXPnMmPGDPbdd1/22msvjjzySJ588smmde66667ssssur5h+/fXX\nM3HiRDbaaCPGjh3LTjvtxO233950PZdddhkTJkxg3LhxnHDCCS+H+qabbsopp5zC7rvvzoEHHkhH\nd6/NanzggQd45zvfyd57780+++zD3LlzAVi2bBlHHXUUr3/96znmmGPoGAzmtNNOY7fddmOvvfbi\ns5/9bLeviSQNRAZ1E2effTavfe1rmTFjBl/72tdWeezee+/lmmuu4Y477mDy5MlsvPHG3HXXXbz5\nzW/mkksuAeD444/nW9/6FnfeeSdf//rXOemkk7rczlve8hYOO+wwvva1rzFjxgxe+9rXcuyxx/KV\nr3yFmTNnsueee/LFL35xtetfsGAB2223sjfX0aNHs2BBl725MmfOHK6++mpuueUWZsyYweDBg7n8\n8ssBeOaZZxg/fjyzZs3igAMOeLmWZjUec8wxnHzyydx9993ceuutbLPNNgDcddddfOMb32D27Nk8\n+OCD3HLLLSxevJhrr72WWbNmMXPmTM4444zVfp6StL5bZy4mK8k73vEOhg0bxrBhwxg+fDiHHnoo\nAHvuuSczZ85k2bJl3HrrrRx99NEvL/PCCy/0at1PPfUUS5Ys4YADDgBg0qRJq6ynP0ybNo0777yT\nN73pTQA899xzbLXVVgAMGjSI97///QB86EMf4r3vfW/TGpcuXcqCBQs48sgjgapHsQ4TJkxg9OjR\nAIwbN4558+ax7777MnToUI477jgOOeQQz2NLUhcM6j7YaKONXr49aNCgl+8PGjSI5cuXs2LFCjbf\nfHNmzJjRrhIZNWoUDz+8csTR+fPnM2rUqC7nzUwmTZrEWWed1eN6+/qb5sZ9NnjwYJYvX86QIUO4\n/fbbmTZtGlOnTuW8887jF7/4RZ/WL0m9taZ/RdShv35NtM4E9dr+OdWwYcNYunRpn5bdbLPNGDt2\nLFOmTOHoo48mM5k5cyZ77713j9saPnw4W2yxBb/61a/Yf//9ufTSS18+cl0dhx12GB/84Af5zGc+\nw8KFC7n//vuZMGFCl/MeeOCBHH744ZxyyilstdVWPPHEEyxdupQddtiBFStWMHXqVCZOnMgVV1zB\nW9/61qY1Dhs2jNGjR3PddddxxBFH8MILL3R7AduyZct49tlnec973sN+++3HjjvuuNrPU5LWd+tM\nUK9tI0aMYL/99mOPPfZg1113Xe3lL7/8cj7xiU9w5pln8uKLLzJx4sSmQT1x4kQ+/vGP881vfpOp\nU6dy8cUXc+KJJ/Lss8+y4447ctFFFzXdzrXXXsunPvUpFi1axMEHH8y4ceO48cYb2X333Xnf+97H\nbrvtxpAhQzj//PMZPHhwl+vYbbfdOPPMM3n3u9/NihUr2GCDDTj//PPZYYcd2GSTTbj99ts588wz\n2Wqrrbj66qsBmtZ46aWXcsIJJ/D5z3+eDTbYgClTpjStfenSpRx++OE8//zzZCbnnHNOb3evJA0Y\n0XH1bTuNHz8+O/8GeM6cOX0KSK1Zm266KcuWLWt3Gb4fJK0xJTR9R8SdmTm+N/N61bckSQWz6Xst\n+tKXvvSKpuCjjz6ayZMn97jsySefzC233LLKtE9/+tN89KO9H/J78eLFHHjgK0YnZdq0aYwYMaLL\nZUo4mpakgazooM7M9WrkpMmTJ/cqlLty/vnnt7z9ESNGtPVK9L4q4fSMJLVLsU3fQ4cOZfHixX5I\nD3CZyeLFi1f5TbYkDSTFHlGPHj2a+fPnv9xlpQauoUOHvtxZiiQNNMUG9QYbbMDYsWPbXYYkSW1V\nbNO3JEkyqCVJKppBLUlSwQxqSZIKZlBLklQwg1qSpIIZ1JIkFcygliSpYAa1JEkFM6glSSqYQS1J\nUsEMakmSCmZQS5JUMINakqSCGdSSJBXMoJYkqWAGtSRJBTOoJUkqmEEtSVLBDGpJkgpmUEuSVDCD\nWpKkghnUkiQVzKCWJKlgBrUkSQUzqCVJKphBLUlSwQxqSZIKZlBLklQwg1qSpIIZ1JIkFcygliSp\nYAa1JEkFM6glSSqYQS1JUsEMakmSCmZQS5JUsJaCOiJOiYhZEXFvRFwZEUMjYmxE3BYRD0TE1RGx\n4ZoqVpKkgabPQR0Ro4C/AcZn5h7AYGAi8BXg3zJzJ+BJ4Lg1UagkSQNRq03fQ4BXRcQQYGPgEeDP\ngan14xcDR7S4DUmSBqw+B3VmLgC+DjxEFdBPAXcCSzJzeT3bfGBUq0VKkjRQtdL0vQVwODAW2BbY\nBDhoNZY/PiKmR8T0RYsW9bUMSZLWa600fb8T+H1mLsrMF4FrgP2AzeumcIDRwIKuFs7MCzJzfGaO\nHzlyZAtlSJK0/molqB8C9o2IjSMigAOB2cD/AkfV80wCrm+tREmSBq5WzlHfRnXR2G+Ae+p1XQB8\nDvhMRDwAjAAuXAN1SpI0IA3peZbmMvMLwBc6TX4QmNDKeiVJUsWeySRJKphBLUlSwQxqSZIKZlBL\nklQwg1qSpIIZ1JIkFcygliSpYAa1JEkFM6glSSqYQS1JUsEMakmSCmZQS5JUMINakqSCGdSSJBXM\noJYkqWAGtSRJBTOoJUkqmEEtSVLBDGpJkgpmUEuSVDCDWpKkghnUkiQVzKCWJKlgBrUkSQUzqCVJ\nKphBLUlSwQxqSZIKZlBLklQwg1qSpIIZ1JIkFcygliSpYAa1JEkFM6glSSqYQS1JUsEMakmSCmZQ\nS5JUMINakqSCGdSSJBXMoJYkqWAGtSRJBTOoJUkqmEEtSVLBDGpJkgpmUEuSVDCDWpKkghnUkiQV\nzKCWJKlgBrUkSQUzqCVJKphBLUlSwQxqSZIKZlBLklQwg1qSpIIZ1JIkFcygliSpYAa1JEkFaymo\nI2LziJgaEfdFxJyIeHNEvDoifhYR99f/brGmipUkaaBp9Yj6XOAnmfl6YG9gDnAaMC0zdwam1fcl\nSVIf9DmoI2I48DbgQoDM/FNmLgEOBy6uZ7sYOKLVIiVJGqhaOaIeCywCLoqIuyLi2xGxCbB1Zj5S\nz/MosHWrRUqSNFC1EtRDgH2A/8jMNwDP0KmZOzMTyK4WjojjI2J6RExftGhRC2VIkrT+aiWo5wPz\nM/O2+v5UquB+LCK2Aaj/fbyrhTPzgswcn5njR44c2UIZkiStv/oc1Jn5KPBwROxSTzoQmA3cAEyq\np00Crm+pQkmSBrAhLS7/KeDyiNgQeBD4KFX4fy8ijgP+ALyvxW1IkjRgtRTUmTkDGN/FQwe2sl5J\nklSxZzJJkgpmUEuSVDCDWpKkghnUkiQVzKCWJKlgBrUkSQUzqCVJKphBLUlSwQxqSZIKZlBLklQw\ng1qSpIIZ1JIkFcygliSpYAa1JEkFM6glSSqYQS1JUsEMakmSCmZQS5JUMINakqSCGdSSJBXMoJYk\nqWAGtSRJBTOoJUkqmEEtSVLBDGpJkgpmUEuSVDCDWpKkghnUkiQVzKCWJKlgBrUkSQUzqCVJKphB\nLUlSwQxqSZIKZlBLklQwg1qSpIIZ1JIkFcygliSpYAa1JEkFM6glSSqYQS1JUsEMakmSCmZQS5JU\nMINakqSCGdSSJBXMoJYkqWAGtSRJBTOoJUkqmEEtSVLBDGpJkgpmUEuSVDCDWpKkghnUkiQVzKCW\nJKlgBrUkSQUzqCVJKphBLUlSwVoO6ogYHBF3RcQP6vtjI+K2iHggIq6OiA1bL1OSpIFpTRxRfxqY\n03D/K8C/ZeZOwJPAcWtgG5IkDUgtBXVEjAYOBr5d3w/gz4Gp9SwXA0e0sg1JkgayVo+ovwH8PbCi\nvj8CWJKZy+v784FRLW5DkqQBq89BHRGHAI9n5p19XP74iJgeEdMXLVrU1zIkSVqvtXJEvR9wWETM\nA66iavI+F9g8IobU84wGFnS1cGZekJnjM3P8yJEjWyhDkqT1V5+DOjP/ITNHZ+YYYCLwi8w8Bvhf\n4Kh6tknA9S1XKUnSANUfv6P+HPCZiHiA6pz1hf2wDUmSBoQhPc/Ss8y8Cbipvv0gMGFNrFeSpIHO\nnskkSSqYQS1JUsEMakmSCmZQS5JUMINakqSCGdSSJBXMoJYkqWAGtSRJBTOoJUkqmEEtSVLBDGpJ\nkgpmUEuSVDCDWpKkghnUkiQVzKCWJKlgBrUkSQUzqCVJKphBLUlSwQxqSZIKZlBLklQwg1qSpIIZ\n1JIkFcygliSpYAa1JEkFM6glSSqYQS1JUsEMakmSCmZQS5JUMINakqSCGdSSJBXMoJYkqWAGtSRJ\nBTOoJUkqmEEtSVLBDGpJkgpmUEuSVDCDWpKkghnUkiQVzKCWJKlgBrUkSQUzqCVJKphBLUlSwQxq\nSZIKZlBLklQwg1qSpIIZ1JIkFcygliSpYAa1JEkFM6glSSqYQS1JUsEMakmSCmZQS5JUMINakqSC\nGdSSJBXMoJYkqWAGtSRJBetzUEfEdhHxvxExOyJmRcSn6+mvjoifRcT99b9brLlyJUkaWFo5ol4O\n/F1m7gbsC5wcEbsBpwHTMnNnYFp9X5Ik9UGfgzozH8nM39S3lwJzgFHA4cDF9WwXA0e0WqQkSQPV\nGjlHHRFjgDcAtwFbZ+Yj9UOPAluviW1IkjQQtRzUEbEp8D/A32bm042PZWYC2WS54yNiekRMX7Ro\nUatlSJK0XmopqCNiA6qQvjwzr6knPxYR29SPbwM83tWymXlBZo7PzPEjR45spQxJktZbQ/q6YEQE\ncCEwJzPPaXjoBmAScHb97/UtVShJKtaY037Yb+ued/bB/bbudUmfgxrYD/gwcE9EzKinnU4V0N+L\niOOAPwDva61ESZIGrj4HdWYVBGJXAAAIUUlEQVT+HxBNHj6wr+uVJEkr2TOZJEkFM6glSSqYQS1J\nUsEMakmSCmZQS5JUMINakqSCGdSSJBXMoJYkqWAGtSRJBTOoJUkqmEEtSVLBDGpJkgpmUEuSVDCD\nWpKkghnUkiQVzKCWJKlgBrUkSQUzqCVJKphBLUlSwQxqSZIKZlBLklQwg1qSpIIZ1JIkFcygliSp\nYAa1JEkFM6glSSqYQS1JUsEMakmSCmZQS5JUMINakqSCGdSSJBXMoJYkqWAGtSRJBTOoJUkqmEEt\nSVLBDGpJkgpmUEuSVDCDWpKkghnUkiQVzKCWJKlgBrUkSQUzqCVJKtiQdhcgSVppzGk/7Jf1zjv7\n4H5Zr/qfR9SSJBXMoJYkqWAGtSRJBTOoJUkqmEEtSVLBDGpJkgpmUEuSVDCDWpKkghnUkiQVzKCW\nJKlgBrUkSQUzqCVJKphBLUlSwfpl9KyIOAg4FxgMfDszz+6P7UhSdxyJSuuDNX5EHRGDgfOBvwR2\nAz4QEbut6e1IkjQQ9EfT9wTggcx8MDP/BFwFHN4P25Ekab3XH03fo4CHG+7PB/6sH7YjvWxdbOJc\n12rur3rBpmSpO5GZa3aFEUcBB2Xmx+r7Hwb+LDM/2Wm+44Hj67u7AL9do4VUtgT+2A/r7U/W3P/W\ntXrBmteGda1esOa1ob/q3SEzR/Zmxv44ol4AbNdwf3Q9bRWZeQFwQT9s/2URMT0zx/fnNtY0a+5/\n61q9YM1rw7pWL1jz2lBCvf1xjvoOYOeIGBsRGwITgRv6YTuSJK331vgRdWYuj4hPAjdS/TzrO5k5\na01vR5KkgaBffkedmT8CftQf615N/dq03k+suf+ta/WCNa8N61q9YM1rQ9vrXeMXk0mSpDXHLkQl\nSSqYQS1JUsH65Rx1u0TE66l6QRtVT1oA3JCZc9pX1fql3sejgNsyc1nD9IMy8yftq6y5iJgAZGbe\nUXdnexBwX30tRfEi4pLMPLbddfRWRLyVqofCezPzp+2upysR8WfAnMx8OiJeBZwG7APMBr6cmU+1\ntcAuRMTfANdm5sM9zlyAhl/9LMzMn0fEB4G3AHOACzLzxbYW2ERE7Ai8l+pnxi8BvwOuyMyn21bT\n+nKOOiI+B3yAqsvS+fXk0VRvlKvWtYFBIuKjmXlRu+toVH9QnEz1H20c8OnMvL5+7DeZuU876+tK\nRHyBqt/5IcDPqHrJ+1/gXcCNmfmlNpb3ChHR+aeMAbwD+AVAZh621ovqQUTcnpkT6tsfp3qPXAu8\nG/h+if/3ImIWsHf9K5ULgGeBqcCB9fT3trXALkTEU8AzwFzgSmBKZi5qb1XNRcTlVP/vNgaWAJsC\n11Dt48jMSW0sr0v1Z9whwC+B9wB3UdV+JHBSZt7UlsIyc734o/rWs0EX0zcE7m93fX14Pg+1u4Yu\naroH2LS+PQaYThXWAHe1u75uah5M9WHxNLBZPf1VwMx219dFvb8BLgPeDhxQ//tIffuAdtfXpOa7\nGm7fAYysb28C3NPu+prUPKdxn3d6bEa762u2n6lOV74buBBYBPwEmAQMa3d9XdQ7s/53CPAYMLi+\nHyX+36tru6ehzo2Bm+rb27fzM259avpeAWwL/KHT9G3qx4oTETObPQRsvTZr6aVBWTd3Z+a8iHg7\nMDUidqCquUTLM/Ml4NmImJt181VmPhcRJb4vxgOfBiYDp2bmjIh4LjNvbnNd3RkUEVtQhUhkfZSX\nmc9ExPL2ltbUvQ2tVndHxPjMnB4RrwOKbJKlOn2zAvgp8NOI2ICqtegDwNeBXnVHuRYNqpu/N6EK\nveHAE8BGwAbtLKwHQ6iavDeiagUgMx+q93fbClpf/C0wLSLuZ+WgINsDOwGfbLpUe20N/AXwZKfp\nAdy69svp0WMRMS4zZwBk5rKIOAT4DrBne0tr6k8RsXFmPgu8sWNiRAynwC9w9Qfxv0XElPrfxyj/\n/+lw4E6q921GxDaZ+UhEbEq5X+A+BpwbEWdQ9eP864h4mOqz42Ntray5VfZlVud4bwBuiIiN21NS\nty4E7qNq0ZoMTImIB4F9qU5RlujbwB0RcRuwP/AVgIgYSfUloy3Wm3PUABExiOoilsaLye6oj6iK\nExEXAhdl5v918dgVmfnBNpTVVESMpjpCfbSLx/bLzFvaUFa3ImKjzHyhi+lbAttk5j1tKKvXIuJg\nYL/MPL3dtayuOjy2zszft7uWZiJiM2As1Zeh+Zn5WJtLaioiXpeZv2t3HasjIrYFyMyFEbE58E6q\n03q3t7ey5iJid2BXqosh72t3PbCeBbUkSesbf0ctSVLBDGpJkgpmUEuSVDCDWlKXIuJHEbF5/XdS\nu+uRBiovJpPUrYgYA/wgM/docynSgOQRtbSOiogxETEnIv47ImZFxE/rfqu7mvemiBhf394yIubV\ntz8SEddExE8i4v6I+GrDMvPqn7GdDbw2ImZExNciYpuI+GV9/96I2H8tPF1pwDKopXXbzsD5mbk7\nVZ/Ef9WHdYwD3k/Vac37I2K7To+fBszNzHGZeSrwQap+0scBewMz+ly9pB6V3uORpO79vqOnOKre\nwcb0YR3Tsh4tKiJmAzuwsne/rtwBfKfuUvG6hu1L6gceUUvrtsZe116i+Zfv5az8/z60j+sAIDN/\nCbyNque/70bEOjMEp7QuMqilgWEeK/s6P2o1l10KDOu4Uw/C8lhm/jdV38jFDW8qrU9s+pYGhq8D\n34uI44Efrs6Cmbk4Im6JiHuBHwP3AqdGxIvAMsAjaqkf+fMsSZIKZtO3JEkFs+lbWo9ExPnAfp0m\nn5uZF7WjHkmts+lbkqSC2fQtSVLBDGpJkgpmUEuSVDCDWpKkghnUkiQV7P8DglmEaOikpyIAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results = []\n",
    "\n",
    "for n_units in range(10):\n",
    "    p = np.random.uniform(size=n_units)\n",
    "    weights, biases, var_combinations, all_configs, data = reset_data_and_parameters(n_units=n_units, p=p)\n",
    "    start = time()\n",
    "    for i in range(10):\n",
    "        weights, biases = update_parameters_with_true_negative_phase(weights, biases, var_combinations, all_configs, data, alpha=1)\n",
    "    elapsed = time() - start\n",
    "    \n",
    "    results.append( {'n_units': n_units, 'time_to_10_epochs': elapsed})\n",
    "    \n",
    "    \n",
    "results_df = pd.DataFrame(results)\n",
    "title='Time to Train Model for 10 Epochs\\nwith Data Dimensionality of `n_units`'\n",
    "results_df.plot(x='n_units', kind='bar', figsize=(8, 6), title=title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To reduce computational burden, and/or to fit a Boltzmann machine to data of non-trivial dimensionality (e.g. a 28x28 grey-scale image, which implies a random variable with 28x28=784 dimensions), we need to compute the positive and/or negative phase of our gradient faster than we currently are.\n",
    "\n",
    "To compute the former more quickly, we could employ mini-batches as in canonical stochastic gradient descent.\n",
    "\n",
    "In this post, we'll instead focus on ways to speed up the latter. Revisiting its expression, $\\mathop{\\mathbb{E}}_{x \\sim p_{\\text{model}}} [x_i  x_j]$, we readily see that we can create an unbiased estimator for this value by drawing Monte Carlo samples from our model, i.e.\n",
    "\n",
    "$$\n",
    "\\mathop{\\mathbb{E}}_{x \\sim p_{\\text{model}}} [x_i  x_j] \\approx \\frac{1}{N}\\sum\\limits_{k=1}^N x^{(k)}_i  x^{(k)}_j\\quad\\text{where}\\quad x^{(k)} \\sim p_{\\text{model}}\n",
    "$$\n",
    "\n",
    "So, now we just need a way to draw these samples. Luckily, we have a Gibbs sampler to tap! \n",
    "\n",
    "**Instead of computing the true negative phase, i.e. summing $x_i  x_j$ over all permissible configurations $X$ under our model, we can approximate it by evaluating this expression for a few model samples, then taking the mean.**\n",
    "\n",
    "We define this update mechanism here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def update_parameters_with_gibbs_sampling(weights, biases, var_combinations, all_configs, data,\n",
    "                                          seed=42, n_samples=1000, alpha=alpha, **kwargs):\n",
    "    model_samples = Model(weights, biases, var_combinations, all_configs).sample(n_samples=n_samples, seed=seed)\n",
    "\n",
    "    for i, j in var_combinations:\n",
    "        # positive phase\n",
    "        positive_phase = (data[:, i] * data[:, j]).mean()\n",
    "\n",
    "        # negative phase\n",
    "        negative_phase = (model_samples[:, i] * model_samples[:, j]).mean()\n",
    "\n",
    "        # update weights\n",
    "        weights[i, j] += alpha * (positive_phase - negative_phase)\n",
    "        \n",
    "    for i, _ in enumerate(biases):\n",
    "        # positive phase\n",
    "        positive_phase = data[:, i].mean()\n",
    "        \n",
    "        # negative phase\n",
    "        negative_phase = model_samples[:, i].mean()\n",
    "        \n",
    "        # update biases\n",
    "        biases[i] += alpha * (positive_phase - negative_phase)\n",
    "        \n",
    "    return np.array(weights), np.array(biases)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we'll define a function that we can parameterize by an optimization algorithm (computing the true negative phase, or approximating it via Gibbs sampling, in the above case) which will train a model for $n$ epochs and return data requisite for plotting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def train_model_for_n_epochs(optim_algo, n_units, p, run_num, epochs=100, alpha=alpha, verbose=True, n_samples=1000):\n",
    "    weights, biases, var_combinations, all_configs, data = reset_data_and_parameters(n_units=n_units, p=p)\n",
    "\n",
    "    timestamps, updates = [], []\n",
    "    for i in range(epochs):\n",
    "        timestamps.append(time())\n",
    "        \n",
    "        weights, biases = optim_algo(\n",
    "            weights=weights, \n",
    "            biases=biases, \n",
    "            var_combinations=var_combinations, \n",
    "            all_configs=all_configs, \n",
    "            data=data, \n",
    "            alpha=alpha,\n",
    "            seed=run_num,\n",
    "            n_samples=n_samples\n",
    "        )\n",
    "        \n",
    "        elapsed = timestamps[-1] - timestamps[0]\n",
    "\n",
    "        lik = Model(weights, biases, var_combinations, all_configs).likelihood(data, log=True)\n",
    "        algo_name = optim_algo.__name__.split('update_parameters_with_')[-1]\n",
    "        if i % 10 == 0 and verbose:\n",
    "            print(f'Epoch: {i} | Likelihood: {lik}')\n",
    "\n",
    "        updates.append( {'likelihood': lik, 'algo': algo_name, 'step': i, 'time': elapsed, 'run_num': run_num})\n",
    "        \n",
    "    return pd.DataFrame(updates)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How does training progress for varying data dimensionalities?\n",
    "\n",
    "Finally, for data of `n_units` 3, 4, 5, etc., let’s train models for 100 epochs and plot likelihood curves.\n",
    "\n",
    "When training with the approximate negative phase, we’ll:\n",
    "\n",
    "- Derive model samples from a **1000-sample Gibbs chain. Of course, this is a parameter we can tune, which will affect both model accuracy and training runtime. However, we don’t explore that in this post;** instead, we just pick something reasonable and hold this value constant throughout our experiments.\n",
    "- Train several models for a given `n_units`; Seaborn will average results for us then plot a single line (I think)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "all_updates = []\n",
    "alpha = .1\n",
    "min_units, max_units = 3, 7\n",
    "\n",
    "for n_units in range(min_units, max_units):\n",
    "    \n",
    "    np.random.seed(n_units)\n",
    "    p = np.random.uniform(size=n_units)\n",
    "    n_epochs = 100\n",
    "    \n",
    "    if n_units % 5 == 0:\n",
    "        alpha /= 10\n",
    "\n",
    "    for run in range(5):\n",
    "        updates = train_model_for_n_epochs(\n",
    "            update_parameters_with_gibbs_sampling, \n",
    "            n_units=n_units, \n",
    "            epochs=100,\n",
    "            verbose=False, \n",
    "            alpha=alpha,\n",
    "            run_num=run+1,\n",
    "            p=p\n",
    "        )\n",
    "        all_updates.append(updates.assign(n_units=n_units))\n",
    "\n",
    "\n",
    "    for run in range(1):\n",
    "        updates = train_model_for_n_epochs(\n",
    "            update_parameters_with_true_negative_phase, \n",
    "            n_units=n_units, \n",
    "            epochs=100,\n",
    "            verbose=False, \n",
    "            alpha=alpha,\n",
    "            run_num=run+1,\n",
    "            p=p\n",
    "        )\n",
    "        all_updates.append(updates.assign(n_units=n_units))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10221e978>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA08AAAHwCAYAAAB+PVSTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.concat(all_updates)\n",
    "\n",
    "plt.figure(figsize=(14, 8))\n",
    "plt.title('True vs. approximate negative phase, 100 epochs')\n",
    "sns.lineplot(x=\"step\", y=\"likelihood\", hue=\"n_units\", style=\"algo\", \n",
    "                legend=\"full\", data=df, ci=None, alpha=.8, palette=sns.color_palette(\"colorblind\", max_units - min_units))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**When we let each algorithm run for 100 epochs, the true negative phase gives a model which assigns higher likelihood to the observed data in all of the above training runs.**\n",
    "\n",
    "Notwithstanding, the central point is that 100 epochs of the true negative phase takes a long time to run.\n",
    "\n",
    "As such, let’s run each for an equal amount of time, and plot results. Below, we define a function to train models for $n$ seconds (or 1 epoch—whichever comes first)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def train_model_for_n_seconds(optim_algo, n_units, p, run_num, n_seconds=10, alpha=alpha, verbose=True, n_samples=1000):\n",
    "    weights, biases, var_combinations, all_configs, data = reset_data_and_parameters(n_units=n_units, p=p)\n",
    "\n",
    "    elapsed = 0\n",
    "    step = 0\n",
    "    timestamps, updates = [], []\n",
    "    \n",
    "    while elapsed < n_seconds:\n",
    "        timestamps.append(time())\n",
    "        \n",
    "        weights, biases = optim_algo(\n",
    "            weights=weights, \n",
    "            biases=biases, \n",
    "            var_combinations=var_combinations, \n",
    "            all_configs=all_configs, \n",
    "            data=data, \n",
    "            alpha=alpha,\n",
    "            seed=run_num,\n",
    "            n_samples=n_samples\n",
    "        )\n",
    "        \n",
    "        elapsed = timestamps[-1] - timestamps[0]\n",
    "        \n",
    "        lik = Model(weights, biases, var_combinations, all_configs).likelihood(data, log=True)\n",
    "        algo_name = optim_algo.__name__.split('update_parameters_with_')[-1]\n",
    "        if len(timestamps) > 1 and int(timestamps[-1]) - int(timestamps[-2]) > 0 and verbose:\n",
    "            print(f'Elapsed: {elapsed:.2}s | Likelihood: {lik}')\n",
    "\n",
    "        updates.append( {'likelihood': lik, 'algo': algo_name, 'step': step, 'time': elapsed, 'run_num': run_num})\n",
    "        \n",
    "        step += 1\n",
    "        \n",
    "    return pd.DataFrame(updates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "all_updates = []\n",
    "n_seconds = 1\n",
    "alpha = .1\n",
    "min_units, max_units = 3, 10\n",
    "\n",
    "for n_units in range(min_units, max_units):\n",
    "    \n",
    "    np.random.seed(n_units)\n",
    "    p = np.random.uniform(size=n_units)\n",
    "    n_epochs = 100\n",
    "    \n",
    "    if n_units % 5 == 0:\n",
    "        alpha /= 10\n",
    "\n",
    "    for run in range(5):\n",
    "        updates = train_model_for_n_seconds(\n",
    "            update_parameters_with_gibbs_sampling, \n",
    "            n_units=n_units, \n",
    "            n_seconds=n_seconds,\n",
    "            verbose=False, \n",
    "            alpha=alpha,\n",
    "            run_num=run+1,\n",
    "            p=p\n",
    "        )\n",
    "        all_updates.append(updates.assign(n_units=n_units))\n",
    "\n",
    "\n",
    "    for run in range(1):\n",
    "        updates = train_model_for_n_seconds(\n",
    "            update_parameters_with_true_negative_phase, \n",
    "            n_units=n_units, \n",
    "            n_seconds=n_seconds,\n",
    "            verbose=False, \n",
    "            alpha=alpha,\n",
    "            run_num=run+1,\n",
    "            p=p\n",
    "        )\n",
    "        all_updates.append(updates.assign(n_units=n_units))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How many epochs do we actually get through?\n",
    "\n",
    "Before plotting results, let’s examine how many epochs each algorithm completes in its allotted time. In fact, for some values of `n_units`, we couldn’t even complete a single epoch (when computing the true negative phase) in $\\leq 1$ second."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Log # of epochs')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGTCAYAAAD6CBJZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.concat(all_updates)\n",
    "n_steps_df = df.groupby(['algo', 'n_units'])['step'].max().map(np.log).reset_index()\n",
    "\n",
    "plt.figure(figsize=(9, 6))\n",
    "plt.title('Log # of training epochs finished in 1 seconds\\nfor varying data dimensionality `n_units`')\n",
    "sns.lineplot(x='n_units', y='step', hue='algo', data=n_steps_df)\n",
    "plt.ylabel('Log # of epochs')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we look at performance. With `n_units <= 7`, we see that 1 second of training with the true negative phase yields a better model. Conversely, **using 7 or more units, the added performance given by using the true negative phase is overshadowed by the amount of time it takes the model to train.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1155ca8d0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA08AAAHwCAYAAAB+PVSTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAAIABJREFUeJzs3Xl8VNX9//HXJ8lkDwn7Ggy7rLKK\niiJuiBZF3HBfavFri1X7025a26pttbWtW23Vtkqtxb2tK+5ScUFFDLKJCLLJHsieSTIz5/fHvQkB\nkhAgM5Pg+/l4zIOZe86993OXGe4n59xzzTmHiIiIiIiINC4h3gGIiIiIiIi0BkqeREREREREmkDJ\nk4iIiIiISBMoeRIREREREWkCJU8iIiIiIiJNoORJRERERESkCZQ8iYi0EmZ2qZnNjnccLZ2ZLTez\nY2K8zl+Z2cxYrvObwsz6mtl+PVfFzNLN7CUzKzKzx5s7Nn8dE8xsSXPXFZGWScmTiOwTMyut84qY\nWUWdzxfGO76DmXPuH865U6KxbDN718wui8ayo8nMHjOzX9ad5pwb4JybG6eQWgwz+42ZLTazkJn9\nLN7xxMk0oB3Q3jl3/u6FzZH0OufmOOcGN3ddEWmZkuIdgIi0Ls65zJr3ZrYa+I5z7o2G6ptZknMu\nFIvYWjozSwBwzkXiHYt8I3wB3ABcHe9A4ugQYPn+/gbpOysiu1PLk4g0K/8vuU+a2eNmVgJctHvr\ngJmd6CdeNZ97mNl/zGyrmX1lZjMaWPY4M/u65oLGn3aOmS3w3x9hZgvMrNjMNpvZnU2M+Ugzm2dm\nhWa20czuNbOAX5ZkZs7Mvu/Hts3M7qiJwcy+Y2bvmNmf/a5By8zsuDrLftfMbjOzD4AyoKe/vS+a\n2XYzW2Fm3/brmpm9ama/rTP/M2b2UJ11zdktru+a2UozKzGzX5hZP39biv1jULMd7c3sZX8f7zCz\nF8ysu1/2W+BI4AG/BfFuf/ogM3vDj/NzMzurkX34rpndYmbv+7G8Ymbtdjt2Nfs438zG1ynr489f\nYmavmdlfaloDzCzB3web/HnnmNlAv+x7eC0LN/px/8efvt687lG55rWMZtdZ1xgz22JmSXX26ef+\nPpltZrkNbF9ff39PN7MN/usHu1VL8c/1EvNafEbWmf9nZrbKL1tiZqfXKevvn0NF/vk1q05Zk4/B\n7pxzM51zrwCle6trjXx39nLs2pvZTPO+NzvM7Nk6ZVeZ2ZdmVmBm/zWzrv70mnP3//zyHWZ2b535\nEs3sLn++VcCkvcQ+2Mz+58e3yMy+5U//NXAjcKF/fly623yTgR/VKf/En17fd/Y75n23S8z7vn2n\nznJ2/z1bb2b/z4+lyLzvYcq+1vXLf+qf+1/7554zs7zG9oeIRJlzTi+99NJrv17AauDE3ab9CqgC\nTsP7A00a8Bjwyzp1TgRW++8TgHy8i5xkoK+/3BPqWZ/5ZcfVmfYf4Ab//cfA+f77LGBsE7djDDAW\nrzW+N95f7K/2y5IAB7wBtMX7S/aXwGV++XeAEHANEAAuAHYAOX75u37MA/3yJOA94D4gFRgJbAOO\n9et3A7YC44FL/XVl1FnXnN3i+re/rcP8/f46kOfH+jlwoV+/IzDVPx5t/PmeqbMP3q3ZJv9zJvA1\ncIm/rlFAATCggX34LrAC6AekA3OBX/lluf68J/vHe5K/ze3rHLff+sd/PFACzKxzflzmb2Mq8Cdg\nfp317nJu+dPWAxP89+8Al9cpuwv4k//+LGA5MMDfxl8CcxvYvr7+/v6nv32H+dtUs55fARX+NiYC\ndwLv1pn/XKCrvz0X4CU0nf2yp4Ef+2WpwLj9OQaNnN9PAD/bS516vztNOHavArP88y0AjPenTwS2\nAMP9bfoz8NZu5+5zQDbe+bod/7cEr6VsCdADaO8fQ9dA3MnAV3hJUADvt6UU6FvnuMxsZLv3KKf+\n7+xpeL8NBhzvH+thu/+e1Tn/5gFd/Pi/wGuh39e6k4ENfhwZwOP+fstrzt9xvfTSa99eankSkWh4\n1zn3gnMu4pyr2EvdI4E2zrnfOOeqnHNfAn8Hztu9onPO4V0Ing9gZjl4F3VP+FWqgX5m1t45V+Kc\n+7ApwTrnPnbOfeicCznnVgEPAcfuVu0O59wO59wa4N6aGHwbgfucc9XOuVl4F3N170162Dm3zDlX\njXcxejjwE+dc0Dm3AHgEuNiPZQPexeNjwB+Bi51zZY2E/1t/Wz8DlgGvOOdWO+d24F3YjvCXu9U5\n9x/nXIVzrhj4TT3bWNcU4Avn3KP+fvkE+C9wdiPz/N05t8I5V46XEAz3p18CPO+ce9U/J14BFgKT\nzKw3XuL3S//4vwO8VLNAv/5MfxuDeAnOKDPLaCSOumax83xJwGupqmnZuQr4jXOuplvXr4DDzW+R\na8Atzrly59xC4B/seh78z9/GMF6SVbP9OOeecs5t9LdnFt7F+Wi/uBovgejqnxPv+dP35xjsr4a+\nO40du1zgBOC7/nej2j9+ABcCf3PO5fvH7SfAsWbWo846b3fOFTnnVgNz2Lm/zgXucs6td84VAHc0\nEvc4vATqTn/9bwCzqef3Yx/Vfmf9ff+Cc26V87wFvAk0NijJ3c65TX78L9bZtn2pey7ed2qZ/xtw\nywFuk4g0AyVPIhIN6/ah7iF43WIKa154f0Xu0kD9WcBZ5nVHOwv40Dm33i+7HBgELDezj8zs1KYE\nYGaHmjci1yYzKwZuBTo0sk1r8FqIaqz3E7uGyuvO2w3YtltCtAaoe8H+HJACLHbOfbCX8DfXeV9R\nz+dMADPLNLO/mdlafxvfYs9trOsQYNxux2UaXutJQzbVeV9es25/Wefvtqwj8PZFN6BgtyS7dn/5\nXbh+53d5K8ZriWMvsdf1NHCMmXUGjgOCzrn368R1f52YtgERvBaPhjR2Huy+/bUJnpldZmYL66zr\n0DrbcD1eC8d8v/tWTfey/TkG+6uh705jxy4X71wuqmd53fD2DwB+wr6DXc/zhs6Xbuy5nxvSDVhb\nz/evsQS4KXb5DTOzyWb2od99shCvZa2xc7ChbduXurvvh335XRWRKNGAESISDbsPK1yG19WpRt3E\naB2wwjk3sEkLdu4zM9uE1+J0ATtbEXDOLQfO81sYzgGeNbO2/l++G/MgXteZac65UjO7Aa/LTF25\neF28AHridaepsfvF9u7ldffHBqCDmWXUSaB64nXPqnE73l/3B5jZOc65p/cSf1P8EOgFHO6c22Rm\no/G6atUXI3jH5U3XPKP7rQMecc59d/cCM+sDtDez1DrHKReoeX8JcCpeV6k1eF2btuJ1n6ov7l04\n5wrM7C2882EEXtenunHd7Jx7ch+2JZedCdzux7lefuvaX/BaaT50zoXNbHHNNjjnNuJ1ycS8+4le\nN7N3aN5j0KiGvjs0fuxy8c7lNn5yVNcGvMSrpm4WXte+r9m7jXj7uUbPRupuAHLNzOokUD2Bz5qw\nHmj4/KmdbmZpwDN4rVkvOeeqzexFdp6D0bKRXX9b6r0fT0RiSy1PIhIL+cC3zKyteTeNX1On7AOg\nysyuN7NUv6VhqJmNamR5s4Af4HX5e6ZmopldbGYdnDcyVhHeBVBTRsnK8uuXmTcYwf/VU+dHZpZj\nZj39+OtecHc1s6vNuxH+PKAP8Ep9K3LOfQXMB35jZilmNhzvr/6P+dtwPF6Xp0vw7nn6s7/PDlQW\n3l+1d5hZe+Dnu5Vvxruno8bzwGAzu8DMAv7rcDMbsB/r/icw1cxO8o9vqpkdZ2bdnHMrgUXAL8ws\n2cyOBr61W9yVePfdpAO/3kvc9ZmFty/PpE6yDTwA3GQ7B6DIMbO9dYm72czSzGyov8ymJF6ZeOfi\nVm81Nh2v5Ql/vefW6SpY6NcNs5djYN4gBl/SAL9+Kt7/9Un+fq/3//1GvjuNHbt1ePcC3u/vu4Dt\nHEziceAKMxtm3gAIt+PdT7a+ntXv7ingOjPr7p+rP26k7vt49xxe76//eLxku6kJ8WYgz8waS4RS\n8LoGbgXC5g00cUITl38gnsLbhwPMLB24OQbrFJG9UPIkIrEwE+9+nDV4SUXNPUr495qcincf0Gq8\nrlMP4g1q0JBZeC0Rr/v39tQ4FVhm3ih/v8drSaryL/pKzezIBpZ3Pd6FcIm/7vouvF7ASwI/xRuk\nYmadsveBwXg3vf8SOGu3uHY3DW9ghU14yd+Nzrk55t3DNRP4nn8PxBzgUbx7wA7UH/Fuzi/w4939\nYbt3s7N71h/9rlgnAxfh/QV8E94FcAr7yL+nZSrexd9WYC3ePq/5P+h8vIEiCoBf4O3/Sr/sEbzW\nhQ14gwjUdLmr8TfgMPNGbHuG+v0Xr0vaWudc7QNK/Ra9PwJPm9cl8DN/mxvzLrAKeA3vnp239lIf\n/360+4CP8PblAKDu/XhjgY/NrAxvII8Zzrm1TTgGuXiDjzTkEbyum+fg7dcKvNba+tT73WnCsbvI\n//cLvETk+/42v4LX/fU/fuw98f4o0BR/wbunaBFe62hDxxXnXCXeYA5T8H477gUucM6taOK6nsRL\njLab2UcNrKMQ7481/8H7jp+Nd29SVDnnXsDbF+/gDcZSc6wrG5xJRKLOdu0mLCIidZk3pHU10Mu/\nkNy9/DvARc65CTEO7aBl3nDX+c652+IdSw0z64vXvTTaXbWazMzexBus4Yt4xyLR57d2LgBSnJ47\nJRI3ankSEZG48rui9TLvmU6n4t1v9t94x9XSOedOUOJ0cDOzqX531nZ4ow4+p8RJJL6UPImISLx1\nw+uaVIL3HKbpzrlF8Q1JpEWYgdcd8Uu8QVTqfYC4iMSOuu2JiIiIiIg0gVqeREREREREmkDJk4iI\niIiISBMc1A/J7dChg8vLy4t3GCIiIiIi0oJ98skn25xzHfdW76BOnvLy8pg/f368wxARERERkRbM\nzNY0pZ667YmIiIiIiDSBkicREREREZEmUPIkIiIiIiLSBAf1PU8iIiIicnCrrq5m/fr1BIPBeIci\nrUBqaio9evQgEAjs1/xKnkRERESk1Vq/fj1ZWVnk5eVhZvEOR1ow5xwFBQWsX7+eXr167dcy1G1P\nRERERFqtYDBI+/btlTjJXpkZ7du3P6BWSiVPIiIiItKqKXGSpjrQc0XJk4iIiIiISBMoeRIRERER\nacFOPfVUCgsLKSws5M9//nO8w/lGU/IkIiIiItKCvfzyy+Tk5Ch5agGUPImIiIiIHIDVq1czcOBA\npk+fzuDBg5k4cSIVFRX11p0wYQLz588HYNu2beTl5QEwc+ZMzjzzTCZNmkS/fv340Y9+VDtPXl4e\n27Zt4yc/+QkrV65k+PDh/PCHP2Tjxo2MHz+e4cOHM2TIEObOnRv1bf2mU/IkIiIiInKAVqxYwYwZ\nM1iyZAk5OTk8++yz+7yM/Px8nnzySRYtWsSTTz7JunXrdim/44476NOnD/n5+dx5553MmjWLk08+\nmfz8fBYuXMjw4cOba3OkAXrOk4iIiIjIAerVq1dt8jJq1ChWr169z8s44YQTyM7OBmDQoEGsWbOG\n3NzcBuuPGTOGb3/721RXV3PGGWcoeYoBtTyJiIiIiByglJSU2veJiYmEQqF66yUlJRGJRAD2eN5Q\nU5dRY/z48bzzzjt0796dyy67jEcffXR/w5cmUvIkIiIiIhIjeXl5fPLJJwA888wz+zRvVlYWJSUl\ntZ/XrFlD586dmT59Ot/5zndYsGBBs8Yqe1K3PRERERGRGLnhhhs499xzeeihh/jWt761T/O2b9+e\ncePGMWTIEE455RSGDBnCnXfeSSAQIDMzUy1PMWDOuXjHEDWjR492NaOZSMtQc77pSeAiIiLSHJYt\nW8bAgQPjHYa0IvWdM2b2iXNu9N7mVcvTN5RzDhcO4qrLcdVlRELluFAFlphCcvtBuEiY8lUv4MKV\nuHAVLlwJ4Sqci5A94moAivP/THXRqto6RKpxkWraHvkLAjl9KVkyk7LlT+Mi1TgXgkgIF6mmzWHf\nJWvQJXHeAyIiIiIi+0bJUyvnnCNSWUSkcjuRyiIC2X1ISGlDcONHVG54j0hloVdeVUSkuoyM/ueQ\n2f8cKjd+SMGc6/ZYXkqXMXQ4/j7AUfjRHbuUWUIAC6TXJk/h8s2Ey7dgiSlYYjKWlAYJATDvtEpq\ncwipPY6GhACWkOT/GyC5w9Co7xcRERGReJoxYwbvvffeLtOuvfZaLr/88jhFJM1ByVMr4EKVhErW\nECpZT2rucZgZhfP/QOXGDwiXb/FafXwdjr+PlC5jqN6+lLJVL5CYkk1CSlsSUnJIzOhGYloHAJKy\nD6HN8BkkBNKxJO+VEEgnIa29tyBLpMsZz2OJKVCTHNmu44u0PeqWRuNOyz2OtNzjmndniIiIiLQC\n999/f7xDkChQ8tQCOecIrn+Hqi2fULVtEdXbv8C5MABdznyZxNR2JCRnEWg7gNTu40lM70RiWgcS\nUnIItO0PQOagS8kafFmD60jK6ErWoIsbLDczEtM7Net2iYiIiIi0ZkqeWpBIVQkJyVmYGSWfPUCo\ndAPJ7QeROegiAm37k5TVk4Rk78FpbYZd2eiyNCCDiIiIiEjzUvLUQpStfIHiBXfTYeJfCWT3pt2x\nfyAxvZN3r5CIiIiIiMSdHpLbApQs/SeFH/6aQLtDSUjKACAps5sSJxEREZFWIBgMcvjhh3PYYYcx\nePBgfvGLX8Q7JIkSXZ3HWXDDPIrz7yftkBNpe+QvlTCJiIiItDIpKSm89dZbZGZmUl1dzdFHH80p\np5zCEUccEe/QpJmp5SmOXLiKwo9+QyC7Fzljf6bESURERKQVMjMyMzMBqK6uprq6WvefH6R0tR5H\n1YVf4kIVZB9xMwlJqfEOp1HOOaq3LSLQYQiRykKCX79HRp/TiFQWEdz0EWk9T8SFgxCuwpLSiVQV\n1Q6LXrV9OYHsXlhiMpFQBZHyrSS16blz2eEqLDE5XpsmIiIiB4nrnlvMwq+Lm3WZh3Vvw91Thuy1\nXjgcZtSoUXz55ZfMmDGDsWPHNmsc0jIoeYqj5PaD6DzlOe/hsi1IxZo3SO40gnDZBra+Np2sodOx\nxGSK8++n7VG3UrTgLiLBHaR0GkHhh7+mcsun7Hjv5tr5k9sPpKpgGZmHXkDW4EvZ+sqlpOVOoN0x\nd7Dt9Sup3rGC7hfMA7zEausrl9L+2N+T2v3oeG2yiIiIyAFJTEwkPz+fwsJCpk6dyuLFixkyZO9J\nl7QuSp7iJBzcjiUkk5CcGccYdmCWiCVnseXFc8noewYZ/c9h+3s/A6hN6koW/bV2nh3v/7z2fcHb\n3ydUunGP5VYVLAOg9PNZpOVOAKBi3RwAqnes2KVu+aoXvHm2LVHyJCIiIgekKS1E0ZaTk8Nxxx3H\nK6+8ouTpIKR7nuKkdOmjbH7uDFy4KmbrdOEqQmWbvPfOsXX2JWx6bgqhwi8Jlayj6NP72Pb2NTtn\niIRq36Z03dn03OH4P5Ez9sbaxCm5/WACbfvVu87yNa/tXFxV6c5YQpUUvPMjyr54BkDd9kRERKTV\n2rp1K4WFhQBUVFTw+uuvc+ihh8Y5KokGJU9xElz/DsmdRsQ0aSj9/Ak2P3cGRQvuZsPjRxKu2IoL\nVVC04O7aOlVb8gFI7jSc9sd50wM5felw3D21dVK6jCY97xQAkrJy6TDxb3Q65Z+0GT4DgHbj7yTz\n0PMAapMjgMIPf1X7vnLLAoLr36n9HKkqau7NFREREYmJjRs3ctxxxzFs2DDGjBnDSSedxOTJk+Md\nlkSBuu3FQbh8C6HSDWT0Pydq6wgVr2XLq5fRceLfCGT3JlSyjuKFfwa8JKpGSufRVG6eD0Cb4TOo\n2voZwa/nkpZ7HEnZvbw6XUYDkD3yWgLtvL+iWGKAzqf/m4RAZu1oMlmDLiZr0MUApPU4hqzBl3sJ\nWriSHR/cUtt1D6Bk0d92iTdSWRiFvSAiIiISfcOGDePTTz+NdxgSA0qe4qBy60IAkjse1uzLLl/9\nKqldj6Bi/f9w1eWULX+S1O7jKfjf9bV1Am37U73jCwDaHnEzm1+ahgsFSe89mbSeJ1BVsISkzB4k\npraj8+n/JjG9EwCZh56/y7qSMrs1GktCSjYJKdkAdPrWk4RL1gGwY95tVG1btLNechsilWp5EhER\nEZGWTclTHFRtyccC6QTaDmjW5YZK1rPj/V+Q2u0oghve96aVbaodlKFGRr+pFH70WwLtDiUxozNt\nDvsuZSueJSElG0ttS5epL9W2Ju0tQWoqM6sdnrzDSQ9RteVTIlXFVG3Np7roK7U8iYiIiEiLp+Qp\nDiwpjbTc47GExANelnMRSj77K0lZPWpbeWoSJ4DqHV/gqkpJSMn2WncsgbRDTqbwo9+S3MEbASZz\nwDQy+p9bmzBF+6FuZkZK55EApOVOoGTpP4kEt0d1nSIiIiIiB0rJUxxkj7i62ZZVuWk+JUseabA8\nEtwBQLujbqXg7WsJtDmEhEA6Xc96FQtk1NaL51Owa+6TEhERERFpyZQ8xZgLV+EiIRIC6Qe0nIp1\nb1NdsIzqolW109J6Hk/F2rdqP6f3mkT5V68QaHcoKV0OJ3vE90k75CSA2lYqERERERFpGg1VHmPB\nDe+z8enjawds2F/Fn95HydJHCX79bu20NsNnkNHvLMBLnLIGfxuAjD6nY2ZkDrywdvAHERERERHZ\nN0qeYixU9BUAiZk99nne6h1fULL0UaqLVhGu2LbHM6IsKZ3EjM4AJHcaSVKbnnQ69THS+55x4IGL\niIiISKPC4TAjRozQM54OYuq2F2PVRStJyuy6X932tsy+BIDifO95TdkjryU1dwKbn5sKQEJKDoG2\nA7DEZFK6jAG8B9zur6pQhGAoTCjiqA47qsIRqsMRumSlkJ6cxMbiIOsKKwhFHKGwozoSoTrs6N0+\nnf4dM9lSUskbK7Z65RFHddgr75KVwtmHNc8ofiIiIiItxT333MPAgQMpLi6OdygSJUqeYixUvIak\nNr32aZ5IdTmWsOehCgXaUWztqQ5HiDhYtLGE9hnD6HrWq+yoTOR/izZSXhWmvDpMsNr7t3NmCpcf\n3hPnHNOf/oyK6jAV1WHKq8IEQ2Gqw453ZowjMcG49rnFzF+35xDi9585lMN7tuXlZVt44IPVe5Rf\nPqYn/TtmsqE4yF3vrNqlLCnBGN49W8mTiIiIHFTWr1/PSy+9xE033cQf//jHeIcjUaLkKcbCpRub\n9HDc91dvZ/GmEjqteYBu22ezPnkYnSvK6ZyVQlogkYKyKq594WvWMI/bKWcDudz3VD4Xj+rBNcf0\nZuPWYm5/c0Xt8lKSEkgLJDK0axvAG10vIzmRNqlJpAUSSA8kkpqUSCDRcM4BxllDu3JMr3YEEhNI\nTkwgkGgkJRh92nuj9J1yaCdGdG9DwC8LJCSQlGDkpAUAGNIli7euOqp2vsQEi+uofiIiInJwK5hz\nPVVbFzbrMpM7Hkb7CX/Ya73rrruO3/3ud5SUlDTr+qVliUvyZGZ3AqcBVcBK4HLnXKFf9lPgCiAM\nXOOce9WfPgm4B0gE/uacuyMesR+ISCiIJWc26cGzzy3exJwvt3CHvUAwwegUzifBjODou0lbeD3p\nyYmcNXAIiZk9qEr4L91T0rgnJY3cnDQABnTKZPb0sbVJUULCnknLPWcMaTSGE/t3bLS8W3Yq3bJT\nGyxPSkwgK1G31YmIiMjB7cUXX6RTp06MGjWKOXPmxDsciaJ4tTy9DvzUORcys98CPwV+bGaDgPOA\nwUA34A0z6+/Pcz9wErAe+NjMnnfOLY1D7PstISmVLlP+W2+Zc47b3/qSMbk5nNi3HT8aUshNgyop\nmZe5S72ufYeyaXEKaVQy7YhhJCTVn7wEEhPokJHS7NsgIiIi0lI1pYUoGt577z2ef/55Xn75ZYLB\nIMXFxVx00UU89thjcYlHoicuyZNz7rU6H+cBZ/vvpwBPOOcqga/M7EvgcL/sS+fcKgAze8Kv26qS\np8bMXbWd/yzaSE5qgCNCrxDMv5/gbnWSOwwlIaUNnb41i8rNCxpMnEREREQkdm6//XZuv/12AObM\nmcPvf/97JU4HqZbQp+rbwGz/fXdgXZ2y9f60hqa3KmUr/s3mF84hUlW6y/RIxHHXOyvp1S6dK4/o\nSaRiW21ZWt5EkrJyAUjvcxoASZndyfDfi4iIiIhIbESt5cnM3gC61FN0k3PuOb/OTUAI+FczrvdK\n4EqAnj17Ntdim0WoZB3h8i1YIGOX6Us3l7C+KMhvjs0mvPUTqv1nQQGk9TyJhOQ2hErWkdbzxFiH\nLCIiIiL7YMKECUyYMCHeYUiURC15cs41eqVvZpcBk4ETnDe8G8DXQG6daj38aTQyfff1PgQ8BDB6\n9GhXX514CZdtJDGjyx4jzr2/ZgdD+JQBS2axbdmuZSmdR5Ha7UjaDJ2+X8+GEhERERGR5hGXbnv+\nyHk/Ak53zpXXKXoeOM/MUsysF9AP+Aj4GOhnZr3MLBlvUInnYx33gQqXbyYpo+se0zcVVzIx/RMS\n/RHxOp26syEuIZCOJSSRkJIdszhFRERERGRP8Rpt709ACvC63wozzzl3lXNuiZk9hTcQRAiY4ZwL\nA5jZ1cCreEOVP+ycWxKf0PdfuKKApOzee0z/+cT+bHopTLgIkjK7EcjpQ0bfM6jc/EkcohQRERER\nkfrEa7S9vo2U/Rr4dT3TXwZejmZc0eRchEhwO4mp7XeZtv3jP+BK1hAuWlk7DSDn8J/EJU4RERER\nEalfvFqevoGMLlNfAnbe0xQqXMlXC/5FaTiJQb0GUl24gkj51viFKCIiIiIiDWoJQ5V/I5gZCSnZ\nJKS0qZ1WuTWfsqowc7r/gY6nPApAWt7J8QpRREREREQaoZanGKna/jmlS/5Bm+HfIykrF+ccpavf\nYlskmx5d8zAzup7zFpaYEu9QRURERGQf5eXlkZWVRWJiIklJScyfPz/eIUkUKHmKkVDxGirWvU3m\noRey9f2fU1WwjGAoQpg08tp6Q5BrKHIRERGR1uvtt9+mQ4cO8Q5Dokjd9mIkEiwAoPSLJ6kqWEZi\nRheqQhHW0Ie8dkqaRERERERaOrU8xUi4YjsuXEn56tdoM/hSsg67ivzX/s7zxb25Jic13uGJiIiI\ntHo/+PA5Fm7/ulmXeVi77tzFyqIpAAAgAElEQVQ1dspe65kZEydOxMz4v//7P6688spmjUNaBiVP\nMRIu30y4YiupXY8ka8gVmCUw6eTpnHBihECiGgBFREREWrN3332X7t27s2XLFk466SQOPfRQxo8f\nH++wpJkpeYqR4NdzIRIiZ+yNWNLOQSGUOImIiIg0j6a0EEVL9+7dAejUqRNTp07lo48+UvJ0ENKV\neww4FyEpuzcZ/c8hpdOI2unfeWohj85fF8fIRERERORAlZWVUVJSUvv+tddeY8iQIXGOSqJBLU8x\nYJZAx4l/h0iodlo44li0sZjRPbLjGFn8fbR2B73apdMxU0O0i4iISOu0efNmpk6dCkAoFOKCCy5g\n0qRJcY5KokHJU4yYGSQGaj8XlFURcY5OWd/cpCESccz49yLy2qbz9KWj4x2OiIiIyH7p3bs3Cxcu\njHcYEgPqthcnW0orAeiUmRznSGLvv4s3Mubud9hQHARgs78vRERERERaMrU8xcmW0ioAOn2Duqt9\nuGYH2WlJPPjBGgCWbPb6BrdLDzQ2m4iIiIhIi6DkKU62lnmtLR0zvjktT1f/ZxEAOWlesrRscykA\n7dK/OftARERERFovdduLk8kDO/OvC0fWJhIHq3WFFYy5+x1WbiurnRaOOACWquVJRERERFoRJU9x\nkpGSRP+Omd5AEgeh8qoQpZUhXl2+BYBXl2+tLatJnj7f4rU8/W9lAW9/uS32QYqIiIiI7AN124uT\nv85bQ3ZqgHOHd4t3KFHxqzdWsK2siqFd2wCQFtiZpwdDEQAqqsO10wrKqmIboIiIiIjIPlLLU5y8\n8vkWPt1QFO8wmt1XBeWUV4XYUlrFwg3F7CivBiA9ObG2TsS5PeYLJOpUFBERkdarsLCQs88+m0MP\nPZSBAwfywQcfxDskiQK1PMWBc44tpZWM69Uu3qE0q+pwhEseX8BFo3pQGQoTcY5P1hcCkBZIbHTe\n7FSdiiIiItJ6XXvttUyaNIlnnnmGqqoqysvL4x2SRIGuWOOgtDJMMBQ5qIYp/2xDMUkJRjAUYWVB\nOcFqr2tezbOc9uZg2hciIiLyzVJUVMQ777zDzJkzAUhOTiY5WaMJH4yUPMVB7TDlB8kDcjcUBbni\nqXyOyvNa0tbuqNjlfiaAv3+4dpfPD51zGG1SkjjvsU8A6Jyl5ElEREQOzKZ/XUdwbX6zLjO153C6\nXHh3o3W++uorOnbsyOWXX87ChQsZNWoU99xzDxkZGc0ai8SfbjSJg5oH5B4Mz3hasqmED9ZsB2DF\nVm/0vHWFeyZPu7dADe6cRZ8OO39Q2h7kQ7aLiIjIwSsUCrFgwQK++93v8umnn5KRkcEdd9wR77Ak\nCtTyFAe926Vz80n96dO+df814vMtJVz2xKe1n7f6I+ZVhSNUhSO0Sw+w3R8wAmD6EYfw13lrAEhO\n2jVvT0g4OIdsFxERkdjZWwtRtPTo0YMePXowduxYAM4++2wlTwcptTzFQaesFE4f3IXsVtzasqWk\nko3FlXtMrztq3ri89ruUndSvY9TjEhEREYm1Ll26kJuby/LlywF48803GTRoUJyjkmhQy1McfLB6\nOxXVEY7v1yHeoeyX/K+LmP70Qo7t036PshHds/lo7Q4AeuSk8uqVR3DyQ/NqP+/uuvG99zoSn4iI\niEhLd99993HhhRdSVVVF7969eeSRR+IdkkSBkqc4ePqzjWwqDrba5OmLrWUAvL96xx5lw7pm1SZP\nEefITN55itX3LKcLR/aIUpQiIiIisTN8+HDmz58f7zAkytRtLw62llbSoRUOzb1mezlH3juXxZuK\nAe+5TruLODhveHcAEsxI2u1epu8f3YubTuwX/WBFRERERJqZkqc4KCirapUj7X22sZhQxDH78y27\nTB/WrU3t+3F57UipMxjE7gNBXDI6lzOGdI1uoCIiIiIiUaDkKQ6KgiGyU1tPj8mlm0r467w1tGkg\n5gtGdK99P6xbG9xu5Sf278jtpw6MYoQiIiIiItHXeq7gDxJVIW8Y76yU1rPrf/zSUjaVVPL/ju1T\nb/noHjm7fHbOS59q2pyUOImIiIjIwUAtTzEWdo5zDuvG4C5Z8Q5lrzYUBYlEHOn+aHgfryusLRuT\nuzNhSg3sehpNHtQZw2txEhERERE5WLSe5o+DRFogkR8d1zfeYezVlpJKpjzyEZeP6Um7jGRWbS9n\n7qoCAP5x3ggGdMrkiHvnApC82yh6vdtn8NF142Mes4iIiIhINKnlKcbKKkN8ua2MylA43qE0as2O\nCgBeXb6FoorqXcoyUxJJrDMQhJmRYLsODCEiIiLyTbF8+XKGDx9e+2rTpg133313vMOSKFDLU4zl\nbyjmuucW88i04Qzp2mbvM8TYWyu24XAUBUMAlFaGCIbC9GqXzlfby4H6n9f01lVH7jFQhIiIiMg3\nwYABA8jPzwcgHA7TvXt3pk6dGueoJBrU8hRjxUGvFaelDhjx45eW8pOXlrGu0Gt5Kq4Msb28muP7\n7nyg7+7d9AAyUpLIbKHbJCIiIhIrb775Jn369OGQQw6JdygSBbrajbGSSq+7XlYLH6p8+ZbSXT6f\nO7wbf/9oLQCBRK+L3j/OG8Hm0sqYxyYiIiJSn3UvfEH5xpJmXWZ61yxyT+vf5PpPPPEE559/frPG\nIC2HWp5irKTS6w7XklqeLvzXAm57/Ytdpn28rpDM5J0xtkvf+VDfmpanQV2yOK5Oi5SIiIjIN1lV\nVRXPP/8855xzTrxDkShpOVfw3xDFldWkJiXUe99QvHyxtZQvtpZy80n9aZceYHu517XwmN7tmP35\nltp61xzTi3vnflVvtz0RERGReNuXFqJomD17NiNHjqRz585xjUOiR8lTjGWnBhjYuWU+46kyFKZD\nRgrby6t57IKRdMlK2SV5unhULhePyo1jhCIiIiIt1+OPP64uewc5JU8x9u3De/Ltw3vGO4xaVaFI\n7fvb3/yScMQxoU8HBnTKJBLR+HkiIiIiTVFWVsbrr7/Ogw8+GO9QJIqUPH1DrS+sIOLcLvdevbRs\nM+mBRPLapQOQkGD89IR+DOnSMlvKRERERFqKjIwMCgoK4h2GRJluXomxy5/4lJ+/8nlc1h2JOEr9\nASsuffxTzvrHfDYWe6Pl/ei4vvRul055dZg6z7/lzKFd6d8xMx7hioiIiIi0KHFJnszsNjP7zMzy\nzew1M+vmTzczu9fMvvTLR9aZ51IzW+G/Lo1H3M2hZjCGeHj0k/Uc95f32VpaSXFNEvXEpwB0ykzm\nztMGkZGcqOc1iYiIiIjUI14tT3c654Y554YDLwI/96efAvTzX1cCfwEws3bAL4CxwOHAL8ysbcyj\nbgallaG4JSevLfcGf3jF//fE/h1ryzKSk+jZNp0nLx7N98f1ikt8IiIiIiItWVySJ+dccZ2PGUDN\nyARTgEedZx6QY2ZdgZOB151z251zO4DXgUkxDbqZVIQipAUSY7rO6nCESMSR4SdtLy7ZDMA1R/ei\njT+tJqbOWSkt/gG+IiIiIiLxELd7nszs12a2DriQnS1P3YF1daqt96c1NL1VCUcc1eEIqUmx3e1H\n3fcuVz7zGflfFwGwans5bdMCdMlK4foJfQDokpUS05hERERERFqbqF3Fm9kbZra4ntcUAOfcTc65\nXOBfwNXNuN4rzWy+mc3funVrcy22WQSrwwAxbXmqGW584YaiXaYf1i0bM+PUgZ358JpjaJ+RHLOY\nRERERERao6glT865E51zQ+p5Pbdb1X8BZ/nvvwbqPoW1hz+toen1rfch59xo59zojh071lclbtKT\nE/nf947inMO6xmydW8uq6p1+SNu02vcJdYfXExEREZF9dtdddzF48GCGDBnC+eefTzAYjHdIEgXx\nGm2vX52PU4CasbufBy7xR907Aihyzm0EXgUmmllbf6CIif60VsXMSE9OIiUp+i1Px/zpXW58eRmL\nNxXvMn1Ilyy6ZqUyZUiXqMcgIiIi8k3w9ddfc++99zJ//nwWL15MOBzmiSeeiHdYEgXxGhngDjMb\nAESANcBV/vSXgVOBL4Fy4HIA59x2M7sN+Nivd6tzbntsQz5w6wsruHPOSqaP7cmQrm2ith7nHMFQ\nhNe/2MrrX+zsujiiezZ/mjqU5BjfcyUiIiJysAuFQlRUVBAIBCgvL6dbt27xDkmiIC7Jk3PurAam\nO2BGA2UPAw9HM65o215ezfurtzNteHS/TFXhSL3T/9+xvZU4iYiIyEFr7TuzKN+6bu8V90F6x1x6\njr+g0Trdu3fnhhtuoGfPnqSlpTFx4kQmTpzYrHFIy6Ar6RgKhrwBI6I12t67XxXwu7e/pLwqvEfZ\nkXnt6N8hMyrrFREREfkm27FjB8899xxfffUVGzZsoKysjMceeyzeYUkU6IE+MRSs9lqEojXa3h/m\nrGR9UZCubXYOO942LcAfTx8c1W6CIiIiIi3B3lqIouWNN96gV69e1AxWduaZZ/L+++9z0UUXxSUe\niR61PMVQRSi6Q5V3y/ZG0Kt5CC5AVkqSEicRERGRKOrZsyfz5s2jvLwc5xxvvvkmAwcOjHdYEgVK\nnmKoojo63fY+21BMKBypXf6q7eWAN7Lez07q36zrEhEREZFdjR07lrPPPpuRI0cydOhQIpEIV155\nZbzDkihQt70YOvKQdvzhtMG0S2++B9Ku3VHOFU/l061NKiH/gbgAPXPSeHjacMz0DCcRERGRaLvl\nllu45ZZb4h2GRJmSpxjqnJVC56yUvVfcBzUJ04biXR/EdnjPtkqcRERERESakbrtxdD8dYXMWrC+\nWZdZt7UJ4NLRufTvmMklo3s063pERERERL7plDzF0DurCnjwgzUHvJzNJZX8v+eXUFRRzbayqtrp\nSQnGGUO68K8LR9K1TeoBr0dERERERHZSt70YCoYipAYOPF99adlm5q4q4PSHP6Juu9P/vjdOD8EV\nEREREYkSJU8xVFEdJjXpwIcpT/TvZSqv3vkw3AQzAom6x0lEREREJFqUPMVQsDpyQM94CoW9h+zW\n7aoHcOrAztxy8oADik1ERERERBqnPl4xVFEdJu0Auu2d8+h8pjzyMQXlO5OnTpkpXH9s7+YIT0RE\nRET20z333MOQIUMYPHgwd999d7zDkShRy1MMndCvA9Vht/eKDVhf5A1H/voXW2un/fSEvrRJDRxw\nbCIiIiKyfxYvXsxf//pXPvroI5KTk5k0aRKTJ0+mb9++8Q5NmplanmJo6tCunDu8237NG4nsmXS9\ndMVYju7V/kDDEhEREZEDsGzZMsaOHUt6ejpJSUkce+yx/Pvf/453WBIFanmKoWWbS8hODdAte9+G\nEd9aWrnH85wuHtWDTs38wF0RERGR1iz8WSGuqLpZl2nZARKH5TRaZ8iQIdx0000UFBSQlpbGyy+/\nzOjRo5s1DmkZlDzF0A0vLGVsz7b8fGL/Js8TjjhO/duHdKvz3KbOmSlcc4zucxIRERFpCQYOHMiP\nf/xjJk6cSEZGBsOHDycx8cBHWJaWR8lTDFVUh/f5OU81I+ttKPbud7p6XC8mHdqp2WMTERERae32\n1kIUTVdccQVXXHEFADfeeCM9evSIWywSPUqeYigY2vehymuSphpTh3bRABEiIiIiLcyWLVvo1KkT\na9eu5d///jfz5s2Ld0gSBUqeYiQccVSHI00eqnxzSSXt0gPMXVVQO+38Ed2VOImIiIi0QGeddRYF\nBQUEAgHuv/9+cnLi1wom0aPkKUYqqsMATWp5Kg5WM/nvH3JM7/Ys/LoIgGnDu/P/ju0T1RhFRERE\nZP/MnTs33iFIDCh5ipFwxDG0axu6NGGEvMWbSgBqW51uPXkApwzsHNX4RERERESkcUqeYiQ7LcDD\n04Y3qe6Ha3fs8vnYPnqWk4iIiIhIvCl5ihHnHGbWaJ2qUASAl5ZuqZ327KWjSU/WYRIRERERiTdd\nlcfIwg3FfPfZz7hv6lBG5+55A2FxsJoTHviAjOREyqrCfP/oXhzftwM9ctLiEK2IiIiIiOxOyVOM\nVFSHCUUcyYn1j7b338WbACir8gaWuGhkDxISGm+pEhERERGR2Nm3J7bKfquo9rrkNfSQ3Nmf7+yq\n9/2jeylxEhERERFpYZQ8xUgw1PBQ5WWVIVZuKwOgd7t0Lh6lJ1KLiIiItHZ5eXls27Yt3mFIM1K3\nvRjZ+ZynnflqdTjCD19cyqDOWTjgrimDOfKQdnsdWEJERERERGJPLU8xEvRH0ktL2tnytLE4yHtf\nbeev89YAMKxrGxLVXU9ERESk1TnjjDMYNWoUgwcP5qGHHtqj/LbbbmPAgAEcffTRnH/++fz+978H\nID8/nyOOOIJhw4YxdepUduzYsce80nIoeYqRC0Z0572rjyY92UueIhHHlU9/Vls+skc2bVID8Qov\nZpxzfLZ9Az9f8Ap/++LDeIcjIiIi0iwefvhhPvnkE+bPn8+9995LQUFBbdnHH3/Ms88+y8KFC5k9\nezbz58+vLbvkkkv47W9/y2effcbQoUO55ZZb4hG+NJG67cWImZGctLNV6YEP1lBQXgXAo+ePYGDn\nrHiFFhNV4RCvbfiCJ1Z9yhdFW8lISuaCPiPjHZaIiIhIs7j33nv5z3/+A8C6detYsWJFbdl7773H\nlClTSE1NJTU1ldNOOw2AoqIiCgsLOfbYYwG49NJLOeecc2IfvDSZkqcYeeLTr1nwdRG/mzyIV5dv\n4ZGP1zJlSBduOqHfQX2PU83DgdeVFXLrp6/RK6sdPxl2ApN6DCA9KTne4YmIiIgcsDlz5vDGG2/w\nwQcfkJ6ezoQJEwgGg/EOS6JA3fZi5MuCMhZvLAbgZ7M/p2dOGj8+ru9BmTg551hauInbF77Jd957\nCuccfdp0YOb483hiwsWcmTdUiZOIiIgcNIqKimjbti3p6el8/vnnzJs3b5fycePG8cILLxAMBikt\nLeXFF18EIDs7m7Zt2zJ37lwA/vnPf9a2QknLpJanGAlWR0gNJPKK/zynwopqAg08MLe1qgqHeHHd\nMp5ZvZAvi7eRkpjExO79qQyHSE0KMCinS7xDFBEREWl2kyZN4oEHHmDgwIEMGDCAI444YpfyMWPG\ncPrppzNs2DA6d+7M0KFDyc7OBuAf//gHV111FeXl5fTu3ZtHHnkkHpsgTaTkKUaCoTCJBne9sxKA\ne84YEueImt+MD/7Nwu0bGJDdiR8NO46Tuw8gK5Aa77BEREREoiolJYXZs2fvMX316tW172+44QZ+\n+ctfUl5ezvjx4xk1ahQAw4cP36OlSlouJU8xEqyOsGJbGalJifzrwpH075gZ75AOiHOOTwrW8+K6\npVzWdwx5We24rN8YUhKTGNW+x0HZHVFERERkf1155ZUsXbqUYDDIpZdeysiRGjirNVLyFCNrdpSz\nobiSW08e0KoTp5pR8/61cgEri7eRkZTM+M69yctqx7jOveIdnoiIiEiLNGvWrHiHIM1AyVMMRCKO\nylCEUT2yuWJsz3iHs9/mblrFbfmvU1hVQa+sdvxs+Emc3H0AKYk6jURERETk4Ker3hhISDAeOW84\nwepIqxskoqQ6yLqyQgbldKF/dkdGtO/OWXnDGNMhV13zREREROQbRclTjHTPTot3CPukOhLmqa8W\n8vAXH5IRSOa/J1xO57QsfjtmcrxDExERERGJCyVPsod5W9Zw56K3WVdWyBGdDuHqgUeTYK2rxUxE\nREREpLkpeZJd/HHxHJ5YlU+PjBzuHnsGR3XOi3dIIiIiIiItgpoThFUlBawp3Q7A0Z178/1Bx/DE\nhIuUOImIiIgcgJ///Oe88cYbAOTl5bFt27Y96lx22WU888wzsQ5tv02YMIH58+cDcOqpp1JYWBjn\niGIrrsmTmV1vZs7MOvifzczuNbMvzewzMxtZp+6lZrbCf10av6gPHsVVQW5f+CYXzHmMh5Z7D2c7\nvGNPLu47imSNoCciIiJyQG699VZOPPHEeIcRNS+//DI5OTnxDiOm4naFbGa5wERgbZ3JpwD9/NdY\n4C/AWDNrB/wCGA044BMze945tyO2UR8cIi7Cy+s/596lcymuCnJO3mFc0X9svMMSEREROSB/+MMf\nWL58ebMuc8CAAVx//fV7rXfbbbfx2GOP0bFjR3Jzcxk1ahSLFy9m8uTJnH322QD87ne/Y/bs2aSl\npTFr1iz69u0LwBtvvMEdd9xBcXExf/zjH5k8eTJLlizh8ssvp6qqikgkwrPPPku/fv32WG9ZWRnn\nnnsu69evJxwOc/PNNzNt2jRuvfVWXnjhBSoqKjjqqKN48MEHMTMmTJjAiBEjmDt3LmVlZTz66KPc\nfvvtLFq0iGnTpvGrX/2K1atXM2nSJEaNGsWCBQsYPHgwjz76KOnp6busOy8vj/nz51NaWsopp5zC\n0Ucfzfvvv0/37t157rnnSEtL4+OPP+aKK64gISGBk046idmzZ7N48eJmODLxEc+Wp7uAH+ElQzWm\nAI86zzwgx8y6AicDrzvntvsJ0+vApJhHfBBwznHdh89x66ev0T09m0fHX8D1QyeQk9K6RgMUERER\naSk+/vhjnn32WRYuXMjs2bNru7XtLjs7m0WLFnH11Vdz3XXX1U5fvXo1H330ES+99BJXXXUVwWCQ\nBx54gGuvvZb8/Hzmz59Pjx496l3mK6+8Qrdu3Vi4cCGLFy9m0iTvEvnqq6/m448/ZvHixVRUVPDi\niy/WzpOcnMz8+fO56qqrmDJlCvfffz+LFy9m5syZFBQUALB8+XK+973vsWzZMtq0acOf//znRvfB\nihUrmDFjBkuWLCEnJ4dnn30WgMsvv5wHH3yQ/Px8EhMTm75TW6i4tDyZ2RTga+fcwt2eFdQdWFfn\n83p/WkPT61v2lcCVAD17tt4H0ja3jeXFtE1OIzUpwLhOvTixW38m5w7UKHoiIiJy0GhKC1E0vPfe\ne0yZMoXU1FRSU1M57bTT6q13/vnn1/77gx/8oHb6ueeeS0JCAv369aN37958/vnnHHnkkfz6179m\n/fr1nHnmmfW2OgEMHTqU66+/nh//+MdMnjyZY445BoC3336b3/3ud5SXl7N9+3YGDx5cG9fpp59e\nO+/gwYPp2rUrAL1792bdunXk5OSQm5vLuHHjALjooou49957ueGGGxrcB7169WL48OEAjBo1itWr\nV1NYWEhJSQlHHnkkABdccMEuSVxrFLUrZzN7w8wW1/OaAtwI/Dwa63XOPeScG+2cG92xY8dorKJV\nCUXCzFzxMee+/SiPrvwEgGm9h3N6z8FKnERERERiqG6jQUPvaz5fcMEFPP/886SlpXHqqafy1ltv\n1bvM/v37s2DBAoYOHcrPfvYzbr31VoLBIN/73vd45plnWLRoEdOnTycYDNbOk5KSAkBCQkLt+5rP\noVCowZgaU3c5iYmJtcs52ETt6tk5d6JzbsjuL2AV0AtYaGargR7AAjPrAnwN5NZZTA9/WkPTpQER\nF+GNDV9w3pzH+POy9ziqUx5Teg6Od1giIiIiB51x48bxwgsvEAwGKS0tbbB15cknn6z9t6Y1BuDp\np58mEomwcuVKVq1axYABA1i1ahW9e/fmmmuuYcqUKXz22Wf1LnPDhg2kp6dz0UUX8cMf/pAFCxbU\nJkodOnSgtLR0v0bzW7t2LR988AEAs2bN4uijj97nZeTk5JCVlcWHH34IwBNPPLHPy2hpYt5tzzm3\nCOhU89lPoEY757aZ2fPA1Wb2BN6AEUXOuY1m9irwGzNr6882EfhpjENvNcpDVVw7778s3L6BXlnt\n+MPhp3NMl97xDktERETkoDRmzBhOP/10hg0bRufOnRk6dCjZ2dl71NuxYwfDhg0jJSWFxx9/vHZ6\nz549OfzwwykuLuaBBx4gNTWVp556in/+858EAgG6dOnCjTfeWO+6Fy1axA9/+EMSEhIIBAL85S9/\nIScnh+nTpzNkyBC6dOnCmDFj9nmbBgwYwP3338+3v/1tBg0axHe/+919XgbA3//+d6ZPn05CQgLH\nHntsvfulNTHn3N5rRTOAXZMnA/6ENxhEOXC5c26+X+/beN39AH7tnHtkb8sePXq0a+iGvYNRKBIm\nKSER5xy/Wvg6w9p247Seg9Q9T0RERA5ay5YtY+DAgfEOg9LSUjIzMykvL2f8+PE89NBDjBw5cu8z\ntkCrV69m8uTJzTIqXs1+AbjjjjvYuHEj99xzzwEv90DUd86Y2SfOudF7mzfuD/NxzuXVee+AGQ3U\nexh4OEZhtTpfFG3l5gWzuWbQMYzr3Iubh0+Md0giIiIi3xhXXnklS5cuJRgMcumll7baxKm5vfTS\nS9x+++2EQiEOOeQQZs6cGe+QDkjckyc5MBEX4V8rP+WBz98nK5BCckLrHwJSREREpLWZNWtWVJdf\nUFDACSecsMf0N998k/bt2zfruvLy8prtWUzTpk1j2rRpzbKslkDJUyu2eMdG7lw0h2WFm5nQtQ8/\nHXYCbVPS9z6jiIiIiLQq7du3Jz8/P95hfOMpeWqlwpEINy94hWA4xC0jT2ZS90P3OoSkiIiIiIjs\nPyVPrcx7m7+iX5sOdErL4g+Hn06XtCzSk5LjHdYBW1u6g23BMkZ2qP/p2SIiIiIi8aZh2FqJynCI\nOxe9zQ8+fI6ZKz4GoHdW+1aTODnnKKqqqP389FcLuW/pXCIuwvbKcs5+6x9c9f6+P4NARERERCRW\n1PLUCqwo2srNC15hVUkB5/cewYyB4+Id0l5FXITn1i5hfOfebKss46Hl85i7aRUzx59HdiCNOxe9\nDUD39Bz+t2ll7XyV4RApiTotRURERKTl0VVqC/fPLz/hgc/fJzOQwt1jz+Co/8/encfJVdV5H/+c\ne2vtvTvd6aydhGyQEAKkCVFkk1UNYBzEMDojsxBHcR2HGR0QdcTncUFHHZd5QBlQQWAU2RGMCgii\nkAQC2fels3SS3tfa7nn+uNXV1WsKku5Kwvf9ekFX3fV3qyt17/eeU6erp+a7pAzPehzs7qA6Woy1\nlu+vf54NLQf41JzzWDVay6oAACAASURBVNlQx3+ueZb/y+/6rPPN15/BAEXBEEEnwG1r/kDS8/jX\n0y7k6qnz83MgIiIiIm9Sc3Mz9957Lx/72MfyXcoReeihh5g1axZz5swB4JZbbuG8887j4osvHtH9\nXnfddSxevJirr756RPdztCg8HeO6UgnOrZ7Gv532zryPpLe3s4VfbH2FlPX40IwFfGftczyzbyuf\nmnse5aEoP9uyEoBbVv2G/V2tfdb9ztnv5VCsg1tf/S0AX13wbiojhXzkhf/lwvEz+Kspp4368YiI\niIgcqebmZn74wx8OCE/JZJJA4Pi51H7ooYdYvHhxJjz9x3/8R54rOjYdP7/RtwjPety3zR+G8q+n\nn8k/zlqIY0bvq2mNsU62tB5iTLiAhOfxxVd+w97OVq6qmcsf67ezr9MPRS8e3MmejhYAfrD+eaJu\nkHkV47lo/Ey+s/Y5ooEgD150HV9+5Wlea9rLqeXjKA6GWdu0n+JgmEsmzgLg7vOuZXrxGI0UKCIi\nIkfFsmXLBp1+++23A/Ctb32LjRs3Dpj/2c9+ltmzZ/Poo4/y6KOPDlhvKJ/73OfYunUrp59+OsFg\nkEgkQnl5ORs2bODpp59m8eLFmb+ZdNttt9He3s6XvvQltm7dyg033MDBgwcpKCjgjjvu4OSTTx50\nH9dddx0lJSWsWLGC/fv3841vfCPTUvPNb36TBx54gFgsxpIlS/jyl78MwFe+8hV+/vOfU1VVxeTJ\nk1mwYAH/8i//wh133MHtt99OPB5nxowZ/OxnP+PVV1/lkUce4dlnn+XWW2/lV7/6FV/5yldYvHgx\nRUVF/OQnP+F///d/AXjmmWe47bbbeOyxx3j66af54he/SCwWY/r06fzP//wPRUVFgx7D1KlTueaa\na3jyySeJRqPce++9zJgxA4DnnnuOb3/7232Orb29nauuuoqmpiYSiQS33norV111FR0dHVxzzTXU\n1dWRSqX4whe+wAc+8AFWrlzJP//zP9Pe3k5lZSV33XUX48ePH/Z392YoPB1D9na28OVXnuaVhj1c\nOH4G1550xogFJ896AKxrrue3ezYRclz2drXy2z2bACgOhikNRWmNdzGhoIQHtq8G4G9n1LLi0G7W\nNddz/rjp/Pv8i/jAMz+jIxHn5vkXUx0tZvneTVw9dT6TCsu4beEVrGuupyQUAeDz8/v+cbdTyqpH\n5PhERERERsPXvvY11qxZw6uvvsozzzzDe97zHtasWcO0adPYsWPHkOstW7aM//7v/2bmzJn85S9/\n4WMf+xi///3vh1x+3759PP/882zYsIErr7ySq6++mqeffprNmzfz0ksvYa3lyiuv5LnnniMajfKr\nX/2K1atXk0gkOPPMM1mwYAEA73vf+7j++usBuPnmm/nJT37CJz7xCa688spBu89dfPHFLFu2jI6O\nDgoLC7n//vtZunQphw4d4tZbb2X58uUUFhby9a9/nW9/+9vccsstQx5DaWkpr7/+Oj/96U/59Kc/\nzWOPPTbksUUiEX79619TUlLCoUOHWLRoEVdeeSW/+c1vmDBhAo8//jgALS0tJBIJPvGJT/Dwww9T\nVVXF/fffz0033cSdd96Z0+/wjVB4OgZ41uPBna/zX+uex8Fw8+mXcMXkOUelNSaWSrKrvYmD3R28\nbewUvrvuj/x+32b2d7ZxwfjpvHRwF53JRGb5kONy8cRZPLF7PV2pBD96+9Wsa67nP9c8y5Ip8/j4\nnHdw/7ZXORTr4PPz/T/K+/1F76M10c20Yv+vW9957tLM9kpDUd42duoRH4eIiIhILg7XUvTZz352\n2PlXXHEFV1xxxZve/8KFC5k2bdqwy7S3t/OnP/2J97///ZlpsVhs2HXe+9734jgOc+bMob6+HoCn\nn36ap59+mjPOOCOz3c2bN9PW1sZVV11FJBIhEon0OZ41a9Zw880309zcTHt7O5dddtmw+w0EAlx+\n+eU8+uijXH311Tz++ON84xvf4Nlnn2XdunWcc44/kFk8Hudtb3vbsNu69tprMz8/85nPDHts1lr+\n/d//neeeew7HcdizZw/19fXMmzePz372s/zbv/0bixcv5txzz2XNmjWsWbOGSy65BIBUKjUirU6g\n8HRM+K91z3PP1lWcVTWZL8y/hHEFJW96W8/u38pDO9cwu7SKSyfO5vrnH6At4f9jvHD8DJ7Zv4Wy\nkP/dqWf2bWVstIi7z7uW9//+pwD8/l0fZVdHM0/WrefGeRcyv2ICUwrL6UjG+dBJZwLwgZNO55pp\n8zPhblZp1ZEcvoiIiMgJo7CwMPM4EAjgeV7meXd3NwCe51FWVsarr76a83bD4XDmsbU28/Pzn/88\nH/nIR/os+53vfGfI7Vx33XU89NBDzJ8/n7vuuotnnnnmsPteunQp3//+96moqKC2tpbiYn+wsEsu\nuYRf/OIXOR9DdsNA9uPBju2ee+7h4MGDrFy5kmAwyNSpU+nu7mbWrFmsWrWKJ554gptvvpmLLrqI\nJUuWMHfuXF588cWca3mz9Hee8sQfqa4dgL+aehpfOuMyvr/ofTkFp/quNuq72kh5Hs/s28KiR7/L\nwke+w/9uX82NLz3KC/XbuXPTS/zts/fSlohRFSnilLJq/rBvC1OLKvj1RddxRc0cioNhvrdoCVOK\nKrhx3oV8rfY9hNwAM0oq+f3lH2XJlHkAlIWj/OOss4kEgpka9B0lERERESguLqatrW3QedXV1Rw4\ncICGhgZisVimm1pJSQnTpk3LfI/IWsvq1avf8L4vu+wy7rzzTtrb/WvKPXv2cODAAc455xweffRR\nuru7aW9vz+wXoK2tjfHjx5NIJLjnnntyOo7zzz+fVatWcccdd7B0qd/DaNGiRbzwwgts2bIFgI6O\nDjZt2jRsvffff3/m5+FaqVpaWhg7dizBYJA//OEP7Ny5E4C9e/dSUFDAhz70IW688UZWrVrF7Nmz\nOXjwYCY8JRIJ1q5dO+z23yy1POVBS7yLL73yNDvbm7j3/A8yqbCMSYVlQy6/4tBuVjXs4b01c9ne\n3sgn//xrrIVJhWWkrIeXTug9fzvpA9NOZ17FeL78ytPUVk7mh2//K/Z0tPBf6/7Ix045h4JAiH+e\nez4fPfkcKiP+3ZH3T+s7THhhMIyIiIiIDG/MmDGcc845nHrqqUSjUaqre7/PHQwGueWWW1i4cCET\nJ07sMyDEPffcw0c/+lFuvfVWEokES5cuZf78N/ZnWy699FLWr1+fCSJFRUX8/Oc/56yzzuLKK6/k\ntNNOo7q6mnnz5lFaWgr4A0mcffbZVFVVcfbZZ2cC09KlS7n++uv53ve+xy9/+cs++3Fdl8WLF3PX\nXXdx9913A1BVVcVdd93Ftddem+lyeOuttzJr1qwh621qauK0004jHA4ftsXqgx/8IFdccQXz5s2j\ntrY289q9/vrr3HjjjTiOQzAY5Ec/+hGhUIhf/vKXfPKTn6SlpYVkMsmnP/1p5s6d+4Zez1yYnqax\nE1Ftba1dsWJFvsvoY1PLQW58+VEOdXfwqbnn8v6p8/u04lhr+faaZ3m8bh3XzVzI7NIqPvHirwFw\njKEkGKE53sXc8nHs72qjobuDv5u1kH+cdTZ3bnqJ9c31fGvhlbiOw/a2BsaECzODNYiIiIicaNav\nX88pp5yS7zKOOe3t7RQVFdHZ2cl5553H7bffzplnnpm3eqZOncqKFSuorKzMWw09BnvPGGNWWmtr\nD7euWp5GibWWB3e+znfWPkdRIMSn5p7HBeNOAuBH61/gfza/zPSSSqYVVbB8r9/k+f11z2fW//ic\nd9AS7+KJug184fRLuKJmLvFUkufqt/H2sVMJOi4fOblv82fPAA4iIiIi8taybNky1q1bR3d3Nx/+\n8IfzGpxOJGp5GiV3b36ZL77yFIWBEAVuAJMegjwaCNKVHu1ubvk4NjTXc2blJL5z9ntp6O7gj/Xb\nmVBQwjnVw4/aIiIiIvJWdCK1PH31q1/NfA+qx/vf/35uuummPFX0xi1ZsoTt27f3mfb1r3/9sKP6\njaYjaXlSeBol1z33C1Y21HFW5WQWjJlEyA1QFAyzt6OFgkCQ62cvIuC4xFJJAsbBdTSWh4iIiMjh\nnEjhSUaHuu0dB7664N2MCRf0GbFuMGFXvxIRERGRN8Jaq5GAJSdH2nCk5o1RMrGw9LDBSURERETe\nmEgkQkNDwxFfFMuJz1pLQ0MDkcibH0xNzRwiIiIictyaNGkSdXV1HDx4MN+lyHEgEokwadKkN72+\nwpOIiIiIHLeCwSDTpmlgLRkd6rYnIiIiIiKSA4UnERERERGRHCg8iYiIiIiI5EDhSUREREREJAcK\nTyIiIiIiIjlQeBIREREREcmBwpOIiIiIiEgOFJ5ERERERERyoPAkIiIiIiKSA4UnERERERGRHCg8\niYiIiIiI5EDhSUREREREJAcKTyIiIiIiIjlQeBIREREREcmBwpOIiIiIiEgOFJ5ERERERERyoPAk\nIiIiIiKSA4UnERERERGRHASGm2mMOXO4+dbaVUe3HBERERERkWPTsOEJ+Fb6ZwSoBVYDBjgNWAG8\nbeRKExEREREROXYM223PWnuhtfZCYB9wprW21lq7ADgD2PNmd2qM+ZIxZo8x5tX0f+/Omvd5Y8wW\nY8xGY8xlWdMvT0/bYoz53Jvdt4iIiIiIyJtxuJanHrOtta/3PLHWrjHGnHKE+/5Pa+1t2ROMMXOA\npcBcYAKw3BgzKz37B8AlQB3wsjHmEWvtuiOsQUREREREJCe5hqfXjDE/Bn6efv5B4LURqOcq4D5r\nbQzYbozZAixMz9tird0GYIy5L72swpOIiIiIiIyKXEfb+ztgLfCp9H/r0tOOxMeNMa8ZY+40xpSn\np00EdmctU5eeNtR0ERERERGRUZFTy5O1ttsY8wNgOWCBjdbaxHDrGGOWA+MGmXUT8CPgK+ltfQV/\nYIq/fwN1D7ffZcAygJqamqOxSRERERERkdzCkzHmAuBuYAf+aHuTjTEfttY+N9Q61tqLc9z2HcBj\n6ad7gMlZsyfROzDFUNP77/d24HaA2tpam0sNIiIiIiIih5Nrt71vAZdaa8+31p4HXAb855vdqTFm\nfNbTJcCa9ONHgKXGmLAxZhowE3gJeBmYaYyZZowJ4Q8q8cib3b+IiIiIiMgbleuAEUFr7caeJ9ba\nTcaY4BHs9xvGmNPxu+3tAD6S3u5aY8wD+N+pSgI3WGtTAMaYjwNPAS5wp7V27RHsX0RERERE5A0x\n1h6+Z5sx5k7Ao+9oe6619qh8T2mk1NbW2hUrVuS7DBEREREROYYZY1Zaa2sPt1yuLU8fBW4APpl+\n/kfgh2+yNhERERERkeNOrqPtxYwx3wd+S46j7YmIiIiIiJxIRmy0PRERERERkRNJrt32ekbb2whg\njJkF/AJYMFKFiYiIiIiIHEtyHap8wGh7wJGMticiIiIiInJcybXlaYUx5sf0HW1Pw9jJUWFTSTAO\nxnGw1uJ1NOEWVeS7LBERERGRPjTanoyaZPN+4k11pFoPEqtbQ2zPGuIHt5Fqa8AJF1B11S10rFtO\norGOif90L04oku+SRUREREQych5tD/h2+j+RQVlr8TpbSDTsomvHCrq2vYzX0Uiqo4nw5NPo3PAM\niUM7wFq8RDfGcTGBMG5xJQAHH/4PTCBMxaWfwgTD+T0YEREREZF+ch1t7xzgS8CU7HWstSeNTFly\nLLOeR7K1ntjeDbS+9ABeVwuhqmnED+2ka8ufwDikOhqxiRgmEMIEQqQ6mwFwS8cRrJhE6aK/Jjr9\nbEJV0/ASMYwbpHPjs4QnnEJwTE2ej1BEREREZKBcu+39BPgMsBJIjVw5cqyw1mITMRKNuwFL9/YV\ndKz/A+2rn8AmuiEQAi+FF+vACUXxpi/CphJgXIzjEiyfRPFZV1O66FqMcQiUTwAgcXA7ofEnY5ze\nsUrcQAiAonmX5eNQRURERERykmt4arHWPjmilciosp4H1sMm41gvhRMpomPd72h44ja6d6zEpuL+\nIA6BMMHyCWAcAhU1BMon4ISL8Lrb8eKdVFz2Gaqu+Ly/zfRgD14yhk3ECFZMwrh932LhiXPycbgi\nIiIiIkds2PBkjDkz/fAPxphvAg8CsZ751tpVI1ibHAWJQ7twCstxo8V0162h/dXH6dz4HN27V2OT\ncUwgRKB4LMGx04jt3UCycbff1S5USKTmNGysExMME5l2FmOXfBkT6B2h3npenxYkYwxuUQVuPg5U\nRERERGSEHa7l6Vv9ntdmPbbAO49uOfJG+AM0NONES8FL0fz8XcT3byTZ3kh8zzrih3bgdbcRnfF2\niuZeRPMLPyPZsAvcAG5hOVgLToDguJkES6spOXspBTPPoeVPP6PsvH8gkB7IYSjZwUlERERE5ERn\nrLX5rmHE1NbW2hUrTpw/R9W55c90bXmR2J61pDqbSDbvx+tuY9yHf0Trn++lbdXDeF2t4AYxbpBA\n2XiCFZOIH9yBEy6gcM7FuCWVlJx+JaHq6XRtfYlUZzNF8y7N96GJiIiIiOSNMWaltbb2cMsdrtve\nh6y1PzfG/PNg8621Grr8KLLWkmzZT/fu1+na9LzfctTRSMW7/xXb1UL9ff9CorEO4wQyo9iZQJj9\nP70B4wYou2AZ0akL8Lpaic5YRKhqGtZaOtf/gdC42QQrJvbZX3T6wjwdqYiIiIjI8edw3fYK0z+L\nR7qQtxLreSQad9O17SUSB7cTrJyC9TwO/upmf4jvZBzAD0nBMPX3fMofwa5yKhWXfYaCGW8n2VqP\nTSUwxvEHdgiGKZh17oCudMYYCueod6WIiIiIyJEaNjxZa/9f+ueXR6ecE1fLi/fR9NyPSTbuJtl2\nyB/uG/xQVD0TYwwmFKVgwjuITFtA4ezzcEuqMY4L1gM3QGjsDH3PSEREREQkTw7Xbe97w8231n7y\n6JZz4mpf+xSxna/gFlcSmXIGoeoZRCbNIzJ1AeFxswBwCssxxuS5UhERERERGczhuu2tHJUq3gLG\n/80PMP9wp8KRiIiIiMhx6nDd9u7Ofm6MKbDWdo5sSScmJ1yQ7xJEREREROQI5PQFGmPM24wx64AN\n6efzjTE/HNHKREREREREjiG5jj7wHeAyoAHAWrsaOG+kihIRERERETnW5Dx0m7V2d79JqaNci4iI\niIiIyDHrcANG9NhtjHk7YI0xQeBTwPqRK0tEREREROTYkmvL0z8BNwATgT3A6ennIiIiIiIibwm5\ntjx51toPZk8wxkwj/R0oERERERGRE12uLU+PGmNKep4YY04BHh2ZkkRERERERI49uYan/4MfoIqM\nMQuAXwIfGrmyREREREREji05dduz1j6eHijiaaAYWGKt3TSilYmIiIiIiBxDhg1Pxpj/AmzWpFJg\nK/BxYwzW2k+OZHEiIiIiIiLHisO1PK3o93zlSBUiIiIiIiJyLBs2PFlr7x6tQkRERERERI5lh+u2\n94C19hpjzOv07b4HgLX2tBGrTERERERE5BhyuG57n0r/XDzShYiIiIiIiBzLDtdtb1/6587RKUdE\nREREROTYdLhue20M0l0PMIC11pYMMk9EREREROSEc7iWp+LRKkRERERERORY5uS7ABERERERkeOB\nwpOIiIiIiEgOFJ5ERERERERyoPAkIiIiIiKSA4UnERERERGRHOQtPBljPmGM2WCMWWuM+UbW9M8b\nY7YYYzYaYy7Lmn55etoWY8zn8lO1iIiIiIi8VQ07VPlIMcZcCFwFzLfWxowxY9PT5wBLgbnABGC5\nMWZWerUfAJcAdcDLxphHrLXrRr96ERERERF5K8pLeAI+CnzNWhsDsNYeSE+/CrgvPX27MWYLsDA9\nb4u1dhuAMea+9LIKTyIiIiIiMiry1W1vFnCuMeYvxphnjTFnpadPBHZnLVeXnjbUdBERERERkVEx\nYi1PxpjlwLhBZt2U3m8FsAg4C3jAGHPSUdrvMmAZQE1NzdHYpIiIiIiIyMiFJ2vtxUPNM8Z8FHjQ\nWmuBl4wxHlAJ7AEmZy06KT2NYab33+/twO0AtbW19k0fgIiIiIiISJZ8ddt7CLgQID0gRAg4BDwC\nLDXGhI0x04CZwEvAy8BMY8w0Y0wIf1CJR/JSuYiIiIiIvCXla8CIO4E7jTFrgDjw4XQr1FpjzAP4\nA0EkgRustSkAY8zHgacAF7jTWrs2P6WLiIiIiMhbkfEzy4mptrbWrlixIt9liIiIiIjIMcwYs9Ja\nW3u45fL2R3JFRERERESOJwpPIiIiIiIiOVB4EhERERERyYHCk4iIiIiISA4UnkRERERERHKg8CQi\nIiIiIpIDhScREREREZEcKDyJiIiIiIjkQOFJREREREQkBwpPIiIiIiIiOVB4EhERERERyYHCk4iI\niIiISA4UnkRERERERHKg8CQiIiIiIpIDhScREREREZEcKDyJiIiIiIjkQOFJREREREQkBwpPIiIi\nIiIiOVB4EhERERERyYHCk4iIiIiISA4UnkRERERERHKg8CQiIiIiIpIDhScREREREZEcKDyJiIiI\niIjkQOFJREREREQkBwpPIiIiIiIiOVB4EhERERERyYHCk4iIiIiISA4UnkRERERERHKg8CQiIiIi\nIpIDhScREREREZEcKDyJiIiIiIjkQOFJREREREQkBwpPIiIiIiIiOVB4EhERERERyYHCk4iIiIiI\nSA4C+S5ABKDxtXqwlvJ51RjH5LscEREREZEBFJ5kVMVbYwSLQn0CUuumBuqf2wlA+84WJl46HTei\nt6aIiIiIHFvUbU9GTcMr+9n609W0bWsCoGNPKzsfXM+ep7cSqSqk+rwpdNa1Uv/HnXmuVERERERk\nIN3el6Mu0R6n/vldVMwbS8HEErxEikMv76Vh1T4AUl0Jdj++mfbtTQQKglSfW0PZ3LE4AYfOulba\ntjcTb+kmVBrJ85GIiIiIiPRSeJI3zXqW2KFOwpUFGMeQaI/TWdeKTVnatjTStqWRkpkVdO1rJ9Ee\np3ByKR27W+g+1EX79ibKT6tm7Nsn4wR6G0DLTx1Lx+5WWjc3Ulk7IY9HJyIiIiLSl8KT5Mx6ts93\nlQ7+ZQ8NK/cSHVdE1dkT2f/sTuLN3RRNLQOg4oxxNL5aT7g8wpT3nUKksoCNd6yiee0BAMrnVvUJ\nTgCFNaWc9MF5+s6TiIiIiBxz8nKFaoy5H5idfloGNFtrT0/P+zzwD0AK+KS19qn09MuB7wIu8GNr\n7ddGvfC3qGRHnL2/3UbHnjYmL55F0ZRS2nc207ByL4WTSug+1Mmuhzdi0kGofWeL3x3vnBrGnDEe\nNxLIhK7pH5xH5942vKRHqCI66P6CRaFROzYRERERkVzlJTxZaz/Q89gY8y2gJf14DrAUmAtMAJYb\nY2alF/0BcAlQB7xsjHnEWrtuVAs/wSXa47RsPETZyVUECoMAxFu62fXwRpKdCbCWuic3M+nyGez9\n7TbClQVMWjwLm/RoeGU/RVNK6ahrpXntQaLjiwAIFAT77CNUFiFUpu8yiYiIiMjxJ699o4wxBrgG\neGd60lXAfdbaGLDdGLMFWJiet8Vauy293n3pZRWejpJEe5xdv95AvKWbzj1t1Fw5m1iD36JkU5Yp\n7z2ZeHM3e5dvY/djm3CCLpMun+F3uws4jH3bJAAKJhRTtXBino9GREREROToy/cXS84F6q21m9PP\nJwJ/zppfl54GsLvf9LNHvrwTU8fuVuqe3EzxtDLGX3QSqe4kux7eQLIzQXRcER27W9ly16sk2uME\nCoJMed/JhMcUEB1XRHRcEV317YRK1YIkIiIiIm8tIxaejDHLgXGDzLrJWvtw+vG1wC+O8n6XAcsA\nampqjuamjzvx1hjx5m5CJeE+QadtWyNePEXLxgYCRSHadzSTaItTc+VsAgVBDry4Gy+ewo0Gmfiu\nGYRKwpl11e1ORERERN6qRiw8WWsvHm6+MSYAvA9YkDV5DzA56/mk9DSGmd5/v7cDtwPU1tbaN1b1\niaOrvp3dj24i1Z0EoGbJySRa47SsP0jn3jaKppZhHEPDyn0Y12Hy4pkUTCgGYNK7Zuaz9JxZa/ES\nHqnuJF53klBZBCfk0rm3jc69baS6kxRPL6dgfHG+SxURERGRE0A+u+1dDGyw1tZlTXsEuNcY8238\nASNmAi8BBphpjJmGH5qWAn89yvUeszr3tbH/DztwowGM649417WvDTcazISnXb/eAECoNELVokmU\nnzrWDxp1rTiRANGxhXmr31qLTVmcgIO1ls7draS6k6RiSVLdKf9xPMn4d07DGMOep7bSUecvg+3N\nx1OWnEzBxBI66lo59NIenKBDuCKq8CQiIiIiR0U+w9NS+nXZs9auNcY8gD8QRBK4wVqbAjDGfBx4\nCn+o8juttWtHud68s9bSfaADjMFxDTgG4zq0bWki1thFdFwRXsIPSwUTSxh/4VTirTF2/mo9padU\nUnZKFdHxRfjjdPgKa0qPao1e0iPVlUiHnoQffLqTfoiZWEKsqYsDL+weEI6i1YVMvXoOALsf24T1\nekORE3Rxwy42ZTEBQ7gyihNycSMubjiAG/H/6xn6fMwZ4xhz5vgBf0NKRERERORIGGtP3J5ttbW1\ndsWKFfku46hpWLmPAy/uHnSeE3SZdf2Zff6I7ZGwnsWLpzLhJzK2EOMY2rY10VXfkQ4+vf9VnzOZ\nwsmlNLyynwMv7BqwvfLTqhl33hRiTV3seWorgUgAJxLIhJ9QaZiyOVUAdO1v98NROIAbcTOtaSIi\nIiIiI8EYs9JaW3u45fI92p4MIt7cTcMr+7BJD4zBS6SIN3UTa+yieHo5pbPGYK0fcGzSw3qWwkkl\ngwYn61ms53eJ85IeXfvb+wafriTG7R1qfMcv1xFv7iYVS/XpEjfjutMJFoVo3dJI6+ZG3LCbafEJ\nFoUyAadwcgnjLpyKGwkQiPS2CrkR/60WLo9y0tJThz3+6Liio/RKioiIiIgcPQpPeebFU9ienymP\nhpX7aF5/COMY24KW8QAAIABJREFUAtEAnmdxwy7GGCJVBZSdOhZSFq87SSqewoslKawpJVQWoWN3\nK4dW7CUVS/qtRrEkXixF6ewxTLhkOqmuBLse2tBn/8Z1CJdHIB2eotWFhCsLcMMBAtGs8BN2ARj/\nzmlMuPikIVu4IpUFRCoLRvQ1ExERERHJB4WnUWI9S6I1RrI7Sdf+djrrWunc10a8OUYg6v8aEm1x\nrOcRKo0QiAbxUhYvlmTKe08mXBFl/7M72P3wxgHbdsIBotVFmf0Ei0K4YRcn7IeeSJU/GESgIEjN\nkpNxQ353ODcSwAm6fbZVfe6UYY9D3yMSERERkbcqhadR0rzuALse3oQX7+0OZwIObiTA2LdPxgk6\nHFq5DzfoEigK4UZcnJAffpyQH3DK5o6laFq532UuHMAJu7ght0+XucLJJUPWYFyHwolDzxcRERER\nkaEpPI2S5g0NBItDFIwvpmBSsd/VrjTih6N060/5vOpht6HucCIiIiIi+aPwNEomv2cmbjhw1EbD\nExERERGR0aXwNEoC0WC+SxARERERkSOgb/+LiIiIiIjkQOFJREREREQkBwpPIiIiIiIiOVB4EhER\nERERyYHCk4iIiIiISA4UnkRERERERHKg8CQiIiIiIpIDhScREREREZEcKDyJiIiIiIjkQOFJRERE\nREQkBwpPIiIiIiIiOVB4EhERERERyYHCk4iIiIiISA4UnkRERERERHKg8CQiIiIiIpIDhScRERER\nEZEcKDyJiIiIiIjkQOFJREREREQkBwpPIiIiIiIiOVB4EhERERERyYHCk4iIiIiISA4UnkRERERE\nRHKg8CQiIiIiIpIDhScREREREZEcKDyJiIiIiIjkQOFJREREREQkBwpPIiIiIiIiOVB4EhERERER\nyYHCk4iIiIiISA4UnkRERERERHKg8CQiIiIiIpIDhScREREREZEcKDzJMctai7ezA9uVyncpIiIi\nIiIE8l2AvHXYjiS2I4kpDUJXyg9FPT8tmMIAFAWgJYFtjmNKg3h7unAsmKmF+S5fRERERN7iFJ7k\niNnWBLYtgakMQ8KDbs8PRN0pbMLDqY5g25N42zsGrmzARFwAvEOxvtttT2LGhDBTCkbjMERERERE\nhqXwJEOy3SnsgRimOAAFLsQ8bMyD7hTEPIi62P1d2Lakv8Lm9r4bcA3GQOqAH4pMVRhTEgTHYKIu\nRF2IOBhj/P2lLHQmsZ0pTHkQ25jAVIYy80VERERE8ikv4ckYczrw30AESAIfs9a+ZPyr5O8C7wY6\ngeustavS63wYuDm9iVuttXePfuXHLxtLYQ/FIelhykNQGPBDUE+3Oc/6waYogG2KY/d1Y5vih92u\nibo4M4swhQFsa9IPQxEXIi4EDaQs9mAMUxDwu+sNty3XQHEQU+wvZ8a5R+XYRURERESOhny1PH0D\n+LK19kljzLvTzy8A3gXMTP93NvAj4GxjTAXwRaAWsMBKY8wj1tqmfBR/rLBtCWxHClMWhJDjtwbF\nUuDhf3fIs9gDMezB7t7WIYDBus/1Y8IOzpRCTFUI25zwW4tCDoQdCLvQmgADVPS2DJmy0MANBQxm\nfPToHLCIyAnGWtvnuTHGn2b7L5ie72a11Nv+C5Fu8Tf+fM8OWB/XYFyD9SwkvYH7Mf5nvbXWP6dk\nr9uzSNS/sWW7U3330SPs+vuIe35X7v41hBx/H8l0T4b+m3ANpiDg19Bz7spexuDf7ANsewKSg9RQ\nFMAEHGxnsvc4srcTdTFR16+xLTFw/aCDKQn6NTT4NxKzX25j8Luqg3/DMfs4e5YpD2GCjn+u7hx4\nnKY44N947E4NvFlpwUQcTEUY61ns/u5BXwdngn9+9Q50Q9wbuI3qiP9aN8f964D+NZQF/ePsTGIP\nxgasT4GLMzbi17Crc/Aa0t9J9vZ0+dcg2esDZlIUE3axh2L+9US/BcyYMKY85H8vem8XAxQEcCZG\n/Rq2tA98vzjgzCz2a9jR4b+nevaQXtaZWoiJunj13diG7NfaX8AZG8FUhrFtCbye48xaxBQHcKYU\nYlMWb31rerWsQhyDO7fUr2FzW+9AV9mLzCzCFATw9nb5r7XN2gFgJkT917olgbctqydPz+tYGsSZ\nXuTXsLp58BrOKAcgtb4VOrKu+9KLOnNKMIUBvF2dve+prG2YyQU446PYpjjeprYBx2DKgjgnl/g1\nvNTIgF+GY3DPHuPX8FoztA/89+vML8UUBfG2d2DGRTKfJ8eTfIUnC5SkH5cCe9OPrwJ+av2zyZ+N\nMWXGmPH4weq31tpGAGPMb4HLgV+MatUjKHOi6k75wcc1kLCAhaDjfyh2e/7Jqjvlf8gciB12uwCm\nKIAzrdD/oA/6H6J0pSDinzyIuP64iy0JvNaEf1IqD/aGokL/bdLnpF4R8n96YLH+ycxJz0/1+8dk\n8ecH0ifk5CAXBuCHM/BPZoNdFAQdfx8Jb/CTZcD4J6qU7fsB3lODazAR16+hc+AHW89rBfgn3Ozj\n6HlYGPAvCnq6LvYXcfyTRMIb9IOLoIMpSl8U9JxEsj9AjfFbBgHbkvAvbvrXWRr0j7PD7+LYnyl0\n/QuPWMrfRr8aTNjBlIWw1g/XfV8DvwanOuI/OxTrvSjI/gCtDPsn5JYEtj3Zd338CxtTHMR2pbAN\nsYHHEHFxqtIXBXX9T5bpGib733Xz9nX1XhRk1zA+4r/WjfF+x5muoTzkH2dHEls/yIVHgeufJDyL\n3dbBgAWMwZle5Newq3Pwi4KaAkzExTsYg8Z+J2Sb7qo6JoxtT2SOs88FWFEAZ3IB1rN4G9oGrcE9\nxf+o9La1ZwZXyeacVOifkPd1YQ8NvPgx46P+a92a8C8s+u+iOIBzUvqE/HpL35kW/2Q4v8yvYWMr\ntmPge86ZXeyfkOs6e1/r7NdpUgHOuAi2OY63pX1gDaVBnFnFfg0rmwbW4Brc2goAUmtaek/I2TWc\nWoopCvgjdA5yAWZqCv0LsKZ41sVPlvIg7pxSv4YXD/WZZa0fWty3V/o1vNLkv+/7bcM9vQxTEsTb\n1o63O+sCrOcC7qQinJoCbEOM1OstA2usCOGeVgYepP54cMB8HEPgvCoAvFeb+t4U66nhzHIoCWJ3\ndPStoWcTJxVhagqgKX74Gv7cMHwNa1uGr2F35/A1NCf83+dQNaQsqVWD3CPNrmFDW7/PoOwaHOze\nbry6YWpozaGGQeb3qWFr+9A1BB1sfWzoGgoD0J7E29g2YL6pCOFWhMGzvRey/WroCU92V+fgNZT6\nN1ftofjQNZQEoTM16PeSTUUIxkb8GnYMcuPVNZnwZPd3+2G2zwYM7tgwhF3/M2hvl3/jNbuGiOuf\n92Kpvp8fPSpCMDHqf6xmB7ye7TjGv+WO/x3sAedeTO/5vDvl3/zttw1b5vkPU7bf+ukFQlmDU/cE\no+zjcHqf2KTte9Mgs5OeBbKuk4b6VkL2dGP859nTXNO7YPbr0DM1aLDh7AG1Td/thhz/6xj99m+C\n6XUCBooDfdcFv9dSz6SyYKa8jOwaSoP+zfb+xxVI76PnWvc4lK/w9GngKWPMbfiX7W9PT58I7M5a\nri49bajpAxhjlgHLAGpqao5u1UfApiypvzT4d+l67gimLHj+G8x2p6BjiLt4Udd/g8VSfqCy+K9a\n0PHv4JWH/G3EU70Xoj3/MIN+S1HPHZPU8+kTcvZuXEPg3CoYE4YdHXg7B37AZk6G2w5zQm7M4YT8\nwqEB8/uciF5vHv6EvOtwJ+Qcani5cfga1rcOX8OeruFraE0cvobVzcPXsKVt6BqCDnZ/9zA1pE/I\n61oHr6EsBJ5/nIPV0BOevJ0dg9dQFEifkGND11AchM5k78VyvxqoCoOl7x227BrS4cnu7Rq8hoqQ\nf0Juig9eg+uHRLpTfef33BQoD8F4/4Ts7RvkYtsxkA5PtjEOfS4K/BOWGR/xbz50JP3g0v88UBz0\nJyVsvzvL/U6Glt4T+qAnSPzg1JFkwEmw599y0g4e6Hs+CywDT+gGv6U6s5NBPn+yGeOfHPsfZ/bJ\nOzjIX8DoOQ7H+K3X2fuH3gsTAxQOchcy+4Rc6GKznme20bOPqJu5AdGnxEh6H0EHMyY8cP2e/Rr/\nbv2Aw8uuoTKc6V7c57VIH4cpDeIwcKAbUxLI1OhMKRz4OkZ7a3CmDTLCaHYNEwswPTcVsreTPk4z\nJoQT7ve7yGqxoTCQuVufvb4J9/4unNnFA2vIulJyphZiE3bI4zDVYZzirMsM4//P9LzWJQGc9N16\nM8jriGtw55UOX8Os4oE37MC/MATMxChuZb/3gzGZ14nSYOZufZ/jCJjeGhaU9zuGvgs7c0oGvSFI\nejAkU1OAO6HvewpjevdRHvLv1vd/HZ2sGt42pl8NfRd25pdlblT2kd6HOakQd2q/92TPRTnAmBBu\n+tzTdxl6azi/Kr3a4Be8fV6nQTgnFeGcVDTkfFMRxn3HIDX0zHcN7jmVw+7DPa1s+BqmFMKUoUfv\nNWUh3IVjhp7vGtyzKoav4ZSSYec7Ewtg4tADYZnSIO7pQ7+Wxu29oTXkPmYM8m83e/64CIyLDDnf\nFPs3k4ac75jDH+cwrzOAUxUedv6xzPTvMnDUNmzMcmDcILNuAi4CnrXW/soYcw2wzFp7sTHmMeBr\n1trn09v4HfBv+C1PEWvtrenpXwC6rLW3DVdDbW2tXbFixVE7piORfLUJ9ve7o2IMhAymym+2tO1J\nSHn+gAmu8dN5wvO7xhUHoTuJ7fb8k3/2TYfsJu993QM/PLPvsPe/c2T8OjLN7nu7Bjb9Q+9d/qa4\nf2cne31Mb9N/V2rg3W/o29LQc1e4352VTPeDg7F+F3npRXpaO1oT2Ow7Qz019HSBiKX6dQ1IL5bd\n4tJz9yrrJNSnG0ZzfPDWraxWn0zXgOyTaXZXkP53v9J3XDItT9mtJT2/0OzuKB3JwS8Kelq/Yin/\nd9Xn9236dokZ7GI6YPzfpbW9d9Cya4Debjmxfi0dPYv0tAImvXTg7/emy+4aNNgxOOn5fe7A9d1G\npntS/xsK2Rd66dZQDSoiIiIiR8IYs9JaW3vY5UYqPA27U2NagDJrrU0PEtFirS0xxvw/4Blr7S/S\ny23ED04XABdYaz+Snt5nuaEcS+HJ29XhXyRGXX9AhQI3HYJ00SciIiIikk+5hqdB+leMir3A+enH\n7wQ2px8/Avyt8S3CD1X7gKeAS40x5caYcuDS9LTjhlNTiDOtCGdcFFMWwoRcBScRERERkeNIvr7z\ndD3wXWNMAOgm/R0l4An8Ycq34A9V/ncA1tpGY8xXgJfTy/1Hz+ARIiIiIiIioyEv4Sn9naYFg0y3\nwA1DrHMncOcIlyYiIiIiIjKofHXbExEREREROa4oPImIiIiIiORA4UlERERERCQHCk8iIiIiIiI5\nUHgSERERERHJgcKTiIiIiIhIDhSeREREREREcqDwJCIiIiIikgOFJxERERERkRwoPImIiIiIiORA\n4UlERERERCQHCk8iIiIiIiI5UHgSERERERHJgcKTiIiIiIhIDhSeREREREREcqDwJCIiIiIikgOF\nJxERERERkRwoPImIiIiIiORA4UlERERERCQHCk8iIiIiIiI5UHgSERERERHJgcKTiIiIiIhIDhSe\nREREREREcqDwJCIiIiIikgOFJxERERERkRwoPImIiIiIiORA4UlERERERCQHCk8iIiIiIiI5UHiS\nY9q+lU9S96df5bsMEREREREC+S5ABCAV76Jl1zpad62lpGYuFTMWANDduBcTCOW5OhERERERhSfJ\nI2s9OvZvo3n7alrrNmC9JE4gRFfjXoonzCDe3kyis4XCcTPyXaqIiIiIiMKT5Efb3s3se/kxEl2t\nuKEo5dPPpGzqaTihCFuf+CHbnvoxyVg7AMHCkjxXKyIiIiKi8CQjyFpL6661HFr3POPOvIzC6mkA\ntO/fxu7nHyBcUsm4My+naMJMHLf3rVg+fQGNW17GGAdrPSKl1fk6BBERERGRDIUnGRGJzlb2rXiC\ntr0bMcZh74rHqZrzDuIdzTSs/xPh4jFMvfBvccPRAetWnXoezTteI1JWzaRzriYQKcrDEYiIiIiI\n9KXwJEeVtR5NW1/hwOrleKkk1fMvIVxSya4//oI9f3kYgFDxGKZc+KFBgxNAIFJEzbkfwAmECEaL\nR7N8EREREZEhKTzJEfGSCXb84acUVE6mZPIp7F/1FF2NeyismsL4hVcQLh4DQPGEWbTt3QTA1Av+\n5rCtST1d/EREREREjhUKT3JEYi0H6Gqoo6uhjoaNLxIIFzFx0RJKp8zDGJNZrvqMy2jbu4nSmlMJ\nFpbmsWIRERERkTdH4UlylkrEaNqyAuMGKJ0yj0C4gFhbAwDjF7ybVKyTilkLcUMDu+OFiyuY8a6P\nEVA3PBERERE5Tik8yZCstbTsWM3BtX+keNLJtGxfTTLWAUD9q8spmXQyXQ17MkONG8cddnvh0qrR\nKFtEREREZEQoPMmgUokY+1Y8TsvO1wFo2PAnCsdOpWb+tRg3QNPWVbTseB3jGKac/8HDBicRERER\nkeOdwpNgvRStu9YRLCyloKqGroY91L34IImOZsaeeiFl0+YT72imoKom8z2m8QveRfXpl2C9FG4w\nnOcjEBEREREZeQpPbzEdB3ay58UHCRWVEykfT7CojMbNLxNPf3epoHIynYfqCEaLmXLh31I4dgrA\noIM8OG4AXL2FREREROStwcnHTo0x840xLxpjXjfGPGqMKcma93ljzBZjzEZjzGVZ0y9PT9tijPlc\nPuo+3lkvxb4Vj2Oth+elaNyygv2rfoMxDpPfsZSqU88n1nKQiplnMf1dH80EJxERERERyV/L04+B\nf7HWPmuM+XvgRuALxpg5wFJgLjABWG6MmZVe5wfAJUAd8LIx5hFr7bo81H5cSXa303loD0Xjp9O4\n6S/EWg9Sc+5SiifOxnop4h0thArLMI5DyaTZVM09v88Q4yIiIiIi4stXeJoFPJd+/FvgKeALwFXA\nfdbaGLDdGLMFWJhebou1dhuAMea+9LIKT/gtSruevZdEZyvBonJCReW44Sgd9TvoPLgLsAQixSS7\n2yieMJOiCX4eNY5LuLiiz7YUnEREREREBpev8LQWP/w8BLwfmJyePhH4c9ZydelpALv7TT97hGs8\nbjRseJH2+m0UjZtBsrudroO7SCVjRMqqqTr1PLx4Nx0HdlI55x2Un3S6ApKIiIiIyJswYuHJGLMc\nGDfIrJuAvwe+Z4z5AvAIED+K+10GLAOoqak5Wps9psTbmwhEi3HcALG2Bg6seZaSSacw+R3XAP7f\nZ7KpBE4glOdKRUREREROHCMWnqy1Fx9mkUsB0t9pek962h56W6EAJqWnMcz0/vu9HbgdoLa21r6x\nqo9N3U37qX/td6RiXQQLS2ndvZ5AOEq4rJrOg7tx3CDjF7w7s7wxBqPgJCIiIiJyVOWl254xZqy1\n9oAxxgFuBv47PesR4F5jzLfxB4yYCbwEGGCmMWYafmhaCvz16Fc+ulLxLg6seZamzS/jhiKES6vp\nPLiLksmnYD2PREczFTNqKTvpdALRonyXKyIiIiJyQsvXd56uNcbckH78IPA/ANbatcaYB/AHgkgC\nN1hrUwDGmI/jDyzhAndaa9eOftkjz3opAFp2rqH+1eUkYx1UzFjA2HnvxA1H81ydjCRrPazn+X8/\nC0jGOrGpJNZLpeelwPMIFY/BCQSJtTWQ6GjGev562BTW84iUjyNcUkmsrZH2fVsga33reYRLKimd\nciqpRIwDq5en1+9dxnGDTFz0XgD2/OVh4m2NffZvvRSTz1tKuHgM9at/R/O2VdiUv75xApz8V/+a\nz5dRREREZMTkJTxZa78LfHeIeV8FvjrI9CeAJ0a4tFHnJeO07FpLy841GMeho34H1ksCEB0ziZrz\nryVaMSHPVR67rLX+Rb31wDg4bgAvmSAZ60iHgmTmgt8JRQgXj8F6Kdrrt/uhIis4GONQOuVUAJp3\nvEayq82fb3tDQ8XsRQSjxbTsXEP7/m2ZwNITTMqnn0HxxNl0HNjJgdd+l5nes4+i6mmMr30PqVgX\nmx/7L2zW+mBxQ1FOfp8fPnb8/m5iLQcGHPP0y/+JSFk1jZteonHzSwPmjzvzcj88Ndezf9WTA+aX\nTDrFP07Po3X3OjAuxnEwjosxTt+Qbi3GcXGcIMZx0su6OI7/0REpq6Zk8hxw0tP1R5NFRETkBKYr\nnTzpbtpP09aVNO94HS8ZI1xcCY5DMFpM4bhpFFRNoXTKqfg9G48uay2kQ4e1Hnhe5oI50dmCl0z0\nXvSng0O4rBo3GKa75YDfEtHTCpG++I+OmUikrJpYWwNtu9dn1s1u7SiffiZeMs6+FU/0aenoaW3p\nGfCi7sUHibUc7FOf9VLUXPBBIqVjqV+9nMZNL/XOTxt3xmWMmb2I9n1b2P3CAwOOu3jibGrOXYqX\njLPr2XsGzHcD4Ux4atjwIt3N+zPzjHHAOJROmUcwWkys9RAd+7diHBccB2P88OEl4unlDcYN4gTD\nmKxwEioe4893A5ROnecHFsfJLJM9yEfV3PPwErHMfNLbCBaUAlAxayGlNXPT++/dRyBSCEDRhJnM\nXnJjpjY//DiZ0RbdcJTZS24c9r3S0wI1lNIpp2ZeMxEREZETncLTKLFeipada+io307b3k3E2how\nxqGgcjITzlpMtHIyzdteIdHZivVSdDfX0924F+t5VJ5yDsHCUpp3vEbbnk2QFTqsTVE+fQGlNXPp\nOLCT/auezGoJ8ZcpGjeNiYuWkErE2PjgN0n3hMxwAmFOufpzAOz64/10N+0bUP9Jl15PtGICzVtf\noWHTnwfMr55/CZGyauKth6h/7XeZ6cYJYByH4gmzKJ9+JtZaOg7s7G3pSF/422A4s44bihIsKPGD\niXEyyzpuEICCysmZFpHs4FBQ6Y8pEqkYz4SFV2ZaUnr2E4gWZ4532sV/n5lHphY3U8PUi65L199T\nY98QO3beBYydd8GQv++CqhqmXvg3Q853AkHGL3jXkPMBPxgNI1w8BtJhbNB9uAG1BImIiIgcRbqy\nGgXWWvateJJ9Kx/3L/rdAG64EDcYJtHRTEGVP6R609aVdDXuzbRy9Fy4l510BsHCUpJdbcSa63sv\n9tPBAusPKui4AYKF5X26YBnHJVJWDfhBYMzJb+vT0mEcF5MOJeCHAi8eywoU/rKh/9/e/YfaXddx\nHH++du823Q+2TBG9E7dkTcfSVrdYChHZH/YDN6Ki6IeF9E9lK/rB8p/+CoQk6g8LhllCYtQyMpF+\nYEIQIk0t3JyhaepstpWoo4HL9u6P852c1u49X2T3fr/39Hz8c7/ne84Zr403O+d1v9/v57ticDPd\nV1+4hVXrLv7v9y9axKLFpwGw4pz1XPS+a5vik/+5p9TE4qW89srts/57jSoVK6c2sHJqw4zPL1m+\nmiWv2Tzj88NFayYTQ2VOkiRJAkjVWKzmfVLT09O1e/furmMAsP+en/Lvo0dYdf7rOP2MKTLRlJuJ\nSSaXLgMYXPR/ksIhSZIkae4kua+qpke9ziNP82Rqy7aRpSiLTv31TZIkSZJODb+tzxOPJkmSJEkL\nm+VJkiRJklqwPEmSJElSC5YnSZIkSWrB8iRJkiRJLVieJEmSJKkFy5MkSZIktWB5kiRJkqQWLE+S\nJEmS1ILlSZIkSZJasDxJkiRJUguWJ0mSJElqwfIkSZIkSS1YniRJkiSpBcuTJEmSJLVgeZIkSZKk\nFixPkiRJktSC5UmSJEmSWkhVdZ1hziQ5BDzRdY4hZwJ/7zqEes0Z0SjOiEZxRjQb50Oj/L/OyPlV\nddaoF411eeqbJLurarrrHOovZ0SjOCMaxRnRbJwPjeKMzM7T9iRJkiSpBcuTJEmSJLVgeZpfO7sO\noN5zRjSKM6JRnBHNxvnQKM7ILLzmSZIkSZJa8MiTJEmSJLVgeZoHSa5I8qckjybZ0XUe9UuS85Lc\nneShJHuTbO86k/opyUSSB5Lc0XUW9U+S1Ul2JXk4yb4kb+k6k/olyeebz5k9SW5NclrXmdStJDcl\nOZhkz9C+M5L8Oskjzc9XdZmxbyxPcyzJBHAD8E5gI/ChJBu7TaWeeQn4QlVtBLYAn3ZGNIPtwL6u\nQ6i3vgX8oqouBC7BWdGQJFPAZ4HpqtoETAAf7DaVeuD7wBUn7NsB3FVV64G7msdqWJ7m3puBR6vq\nsao6CvwQ2NpxJvVIVR2oqvub7cMMvvBMdZtKfZNkDfBu4Maus6h/kqwC3gp8F6CqjlbVc92mUg9N\nAqcnmQSWAX/tOI86VlW/BZ49YfdW4OZm+2Zg27yG6jnL09ybAp4aerwfvxhrBknWApuBe7tNoh76\nJvBl4FjXQdRL64BDwPeaUztvTLK861Dqj6p6GrgeeBI4ADxfVb/qNpV66uyqOtBsPwOc3WWYvrE8\nST2RZAXwE+BzVfVC13nUH0neAxysqvu6zqLemgTeAHynqjYD/8RTbTSkuW5lK4OifS6wPMlHuk2l\nvqvBstwuzT3E8jT3ngbOG3q8ptknvSzJYgbF6Zaquq3rPOqdy4Ark/yFwam/b0/yg24jqWf2A/ur\n6vhR610MypR03DuAx6vqUFX9C7gNuLTjTOqnvyU5B6D5ebDjPL1ieZp7vwfWJ1mXZAmDizNv7ziT\neiRJGFynsK+qvtF1HvVPVX2lqtZU1VoG/4f8pqr8jbFeVlXPAE8l2dDsuhx4qMNI6p8ngS1JljWf\nO5fjoiI6uduBq5rtq4CfdZildya7DjDuquqlJJ8BfslgZZubqmpvx7HUL5cBHwUeTPKHZt+1VXVn\nh5kkLTzXALc0v6h7DPhEx3nUI1V1b5JdwP0MVnl9ANjZbSp1LcmtwNuAM5PsB74KXAf8KMnVwBPA\nB7pL2D8ZnMooSZIkSZqNp+1JkiRJUguWJ0mSJElqwfIkSZIkSS1YniRJkiSpBcuTJEmSJLVgeZIk\nLXhJVif7T9ywAAABWUlEQVT5VLN9brMksyRJp5RLlUuSFrwka4E7qmpTx1EkSWPMm+RKksbBdcAF\nzY2mHwEuqqpNST4ObAOWA+uB64ElDG5M/SLwrqp6NskFwA3AWcAR4JNV9fD8/zUkSX3maXuSpHGw\nA/hzVb0e+NIJz20C3gu8CfgacKSqNgP3AB9rXrMTuKaq3gh8Efj2vKSWJC0oHnmSJI27u6vqMHA4\nyfPAz5v9DwIXJ1kBXAr8OMnx9yyd/5iSpL6zPEmSxt2LQ9vHhh4fY/A5uAh4rjlqJUnSjDxtT5I0\nDg4DK1/JG6vqBeDxJO8HyMAlpzKcJGk8WJ4kSQteVf0D+F2SPcDXX8Ef8WHg6iR/BPYCW09lPknS\neHCpckmSJElqwSNPkiRJktSC5UmSJEmSWrA8SZIkSVILlidJkiRJasHyJEmSJEktWJ4kSZIkqQXL\nkyRJkiS1YHmSJEmSpBb+A4mCfHjl+Wc6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14, 8))\n",
    "plt.title('True vs. approximate negative phase, 1 second of training')\n",
    "sns.lineplot(x=\"time\", y=\"likelihood\", hue=\"n_units\", style=\"algo\", \n",
    "             legend=\"full\", data=df, ci=None, alpha=.8, \n",
    "             palette=sns.color_palette(\"colorblind\", max_units - min_units))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, we re-stress that the exact ablation results are conditional (amongst other things) on **the number of Gibbs samples we chose to draw. Changing this will change the results, but not that about which we care the most: the overall trend.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary\n",
    "\n",
    "Throughout this post, we've given a thorough introduction to a Boltzmann machine: what it does, how it trains, and some of the computational burdens and considerations inherent.\n",
    "\n",
    "In the next post, we'll look at cheaper, more inventive algorithms for avoiding the computation of the negative phase, and describe how they're used in common machine learning models and training routines."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}