bayesian-inference.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "_cell_guid": "b1076dfc-b9ad-4769-8c92-a6c4dae69d19",
    "_uuid": "8f2839f25d086af736a60e9eeb907d3b93b6e0e5"
   },
   "outputs": [],
   "source": [
    "import numpy as np # linear algebra\n",
    "import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)\n",
    "import matplotlib.pyplot as plt\n",
    "from time import time\n",
    "plt.rcParams['figure.figsize'] = (8.0, 8.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "_cell_guid": "79c7e3d0-c299-4dcb-8224-4455121ee9b0",
    "_uuid": "d629ff2d2480ee46fbb7e2d37f6b5fab8052498a"
   },
   "outputs": [],
   "source": [
    "def generate_samples(m, b, size=20):\n",
    "    \n",
    "    x = np.random.random(size) * 75 + 2\n",
    "    \n",
    "    y = m * x + b\n",
    "    \n",
    "    y_range = (y.max() - y.min())\n",
    "    \n",
    "    sigma = np.random.randn(size) * 0.1 * y_range\n",
    "    sigma = sigma + 2 * (sigma/abs(sigma))\n",
    "    y = y + sigma\n",
    "    \n",
    "    return x, y, sigma\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y, y_err  = generate_samples(0.736, 30)\n",
    "def plot_data(x, y, y_err):\n",
    "    plt.figure()\n",
    "    plt.errorbar(x, y, yerr=y_err, color='black', linestyle='', marker='^', capsize=4)\n",
    "    plt.xlim([x.min() - 30, x.max() + 30])\n",
    "    plt.ylim([y.min() - 50, y.max() + 50])\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"y\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plot_data(x, y, y_err)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Want to find $Pr(m,\\, b\\, |\\, Assumptions)$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### posterior distribution (parameter(s) | data) = sampling distribution (data | parameter(s)) * prior distribution ( parameters) / evidence (data)\n",
    "Note : sampling distribution with known data = likelihood\n",
    "### Therefore: ln(posterior distribution) = ln(sampling distribution) + ln(prior distribution) - log(evidence)\n",
    "\n",
    "sampling distribution = gaussian deviation from a straight line equation \n",
    "\n",
    "prior distribution = uniform distribution\n",
    "\n",
    "evidence = will not be considered as it acts as a normalisation factor only."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def natural_log_likelihood(parameters, x, y, error):\n",
    "    \"\"\"\n",
    "    Computes the gaussian of the deviation from the analytic straight line y = mx + b\n",
    "    \n",
    "    gauss = 1/(sqrt(2 * pi) * error) * exp(- 0.5 * ((y - m * x - b) ** 2 ) / error)\n",
    "    ln(gauss) = ln(1/(sqrt(2 * pi) * error)) + (- 0.5 * ((y - m * x - b) ** 2 ) / error)\n",
    "    \n",
    "    ln(gauss) needs to then be reduced to a signle probablility via summation\n",
    "    \"\"\"\n",
    "    m, b = parameters\n",
    "\n",
    "    return (np.sum(np.log(1./(np.sqrt(2.*np.pi) * error))) +\n",
    "            np.sum(-0.5 * (y - (m*x + b))**2 / error**2))\n",
    "\n",
    "\n",
    "def log_uniform_prior_dist(parameters, limits):\n",
    "    \"\"\"\n",
    "    returns log of uniform distribution if within limits, -infinity otherwise\n",
    "    \"\"\"\n",
    "    m, b = parameters\n",
    "    \n",
    "    mlimits, blimits = limits\n",
    "    \n",
    "    if (m >= mlimits[0]) and (m <= mlimits[1]):\n",
    "        log_uniform_prior_m = np.log(1.0/(mlimits[1] - mlimits[0]))\n",
    "    else:\n",
    "        log_uniform_prior_m = -np.inf\n",
    "    if (b >= blimits[0]) and (b <= blimits[1]):\n",
    "        log_uniform_prior_b = np.log(1.0/(blimits[1] - blimits[0]))\n",
    "    else:\n",
    "        log_uniform_prior_b = -np.inf\n",
    "        \n",
    "    return log_uniform_prior_m + log_uniform_prior_b\n",
    "\n",
    "\n",
    "def natural_log_post_disribution(parameters, x, y, error, param_limits):\n",
    "    \"\"\"\n",
    "    multiplication becomes addition as the log of the probability is taken\n",
    "    \"\"\"\n",
    "    return natural_log_likelihood(parameters, x, y, error) + log_uniform_prior_dist(parameters, param_limits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sample values for m and b using the Markov Chain Monte Carlo Methods : The Metropolis Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Metropolis Algorithm procedure:\n",
    "1. Sample a point from the posterior distribution\n",
    "2. Symmetrically sample a second point around the last point\n",
    "3. IF posterior(x$_{i+1}$) > posterior(x$_{i}$) accept the new point\n",
    "   ELSE generate a uniform random number (n$_r$) in \\[0, 1\\] and accept if $\\frac{p(x_{i+1})}{p(x_i)} > n_r$\n",
    "4. Repeat 2 and 3 for N times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Metropolis(posterior_function, data, parameters, param_limits, stepsizes, nsteps=10000):\n",
    "    \n",
    "    x, y, error = data\n",
    "    \n",
    "    # Generating an initial position probability\n",
    "    log_post = posterior_function(parameters, x, y, error, param_limits)\n",
    "    # print(log_post)\n",
    "\n",
    "    markov_chain = np.empty((nsteps, len(parameters)))\n",
    "    log_probabilities = np.empty(nsteps)\n",
    "    n_accepted = 0\n",
    "    \n",
    "    for i in range(nsteps):\n",
    "        new_params = parameters + stepsizes * np.random.randn(len(parameters))\n",
    "        new_log_post = posterior_function(new_params, x, y, error, param_limits)\n",
    "        # print(new_log_post)\n",
    "        if new_log_post > log_post:\n",
    "            parameters = new_params\n",
    "            log_post = new_log_post\n",
    "            n_accepted += 1\n",
    "        else:\n",
    "            n_rand = np.log(np.random.random())\n",
    "            if n_rand < (new_log_post - log_post):\n",
    "                parameters = new_params\n",
    "                log_post = new_log_post\n",
    "                n_accepted += 1\n",
    "            else:\n",
    "                pass\n",
    "        markov_chain[i] = parameters\n",
    "        log_probabilities[i] = log_post\n",
    "        \n",
    "    acceptance = n_accepted / nsteps\n",
    "    return markov_chain, log_probabilities, acceptance\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sampling using Metropolis Algorithm\n",
      "Ran with acceptance rate of 0.3306 in 0.6845327711105347 seconds average\n"
     ]
    }
   ],
   "source": [
    "start_parameters = np.array([0.5, 10])\n",
    "mlimits, blimits = ((0.01, 2), (0.1, 50))\n",
    "\n",
    "stepsize_m = 0.02 * (mlimits[1] - mlimits[0])\n",
    "stepsize_b = 0.05 * (blimits[1] - blimits[0])\n",
    "\n",
    "stepsize = np.array([stepsize_m, stepsize_b])\n",
    "\n",
    "data = (x, y, abs(y_err))\n",
    "\n",
    "print(\"Sampling using Metropolis Algorithm\")\n",
    "\n",
    "t = time()\n",
    "for i in range(50):\n",
    "    chain, log_probs, acceptance = Metropolis(natural_log_post_disribution, data, start_parameters, (mlimits, blimits), stepsize, nsteps=10000)\n",
    "t = (time() - t) / 50\n",
    "print(f\"Ran with acceptance rate of {acceptance} in {t} seconds average\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_chain(chain, mlimits, blimits):\n",
    "    fig, ax = plt.subplots(2, 1)\n",
    "    ax[0].plot(chain[:, 0], 'k-')\n",
    "    ax[0].set_ylabel(\"Gradient of data (m)\")\n",
    "    ax[0].set_ylim(*mlimits)\n",
    "    ax[0].set_xticks([])\n",
    "    ax[1].set_ylabel(\"Intercept of data (b)\")\n",
    "    ax[1].set_ylim(*blimits)\n",
    "    ax[1].set_xlabel(\"Sample Number\")\n",
    "    ax[1].plot(chain[:, 1], 'k-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_chain(chain, mlimits, blimits)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_PDF_walk(chain, start_parameters, mlimits, blimits, title=\"MCMC: Posterior PDF for parameters m and b\"):\n",
    "    plt.figure()\n",
    "    plt.plot(chain[:, 1], chain[:, 0], linestyle=\"\", marker='H', alpha=0.01, color=\"blue\")\n",
    "    plt.plot(start_parameters[1], start_parameters[0], linestyle=\"\", marker='H', alpha=1, color=\"red\", label=\"RW Starting Position\")\n",
    "    plt.ylim(*mlimits)\n",
    "    plt.xlim(*blimits)\n",
    "    plt.title(title)\n",
    "    plt.legend()\n",
    "    plt.ylabel(\"Gradient of data (m)\")\n",
    "    plt.xlabel(\"Intercept of data (b)\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_PDF_walk(chain, start_parameters, mlimits, blimits, title=\"MCMC: Posterior PDF for parameters m and b\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x396 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import corner\n",
    "corner.corner(chain[500:], labels=['m','b'], range=[mlimits,blimits],quantiles=[0.16,0.5,0.84],\n",
    "                show_titles=True, title_args={\"fontsize\": 12},\n",
    "                plot_datapoints=True, fill_contours=True, levels=[0.68, 0.95], \n",
    "                color='b', bins=80, smooth=1.0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Performed estimates using corner and extracted the median values of the simulated parameter distributions.\n",
    "\n",
    "The estimates are incredibly accurate as $m_{estimated} = 0.72 \\pm 0.05$, compared to a true value of $m = 0.736$;  and $b_{estimated} = 31.50 (+1.98, -2.43)$, compared to a true value of $b=30$. Both are with estimated error range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oRkbUChgaKicaXcRzz2mju1dfVWHQOQlXAjnEYkHg1w/OCVcle0HwAejiYs1OqqoKWldceqkKhJ/d7C2E2WhZkUmYOBiGkZH4gTYnT2oKanv7/0Jv7zK++lUtXOvtDaqSIQYMU1CwaFQXVH91n58fWAl+Kpofn3nFFZppVF2tQuFbbHtBmK+YOBiGMausX7+eRx55ZJxnc3jggQbuv/+vaWvTtNNdu9RKOHTofwcW0NurG79vTSEC0agD8kdVLPssI+8uKisLYgjeQqitDQTBWwjpbFmRSYgvLMlm1q5d67Zt25buZRiGMUVuueUWGhsb2bGjidLSGjo6tB7BC8Kbb2qdQjQKQ0M9gKOgoAyA4eEunBtIvJML3YaAKIsXl3LFFcvPuowuvVRvdXXBPIS5lmE0VURku3Nubarn5umfxDCMdBOLwaFDx+jp6eELX2jgjjs2sGOHZhs1N2vNgh96o+6hKJB71lUUiSwmJ2fxWZeRH6tZXh4ElS+5RAPL9fUaVC4tndsZRtOJiYNhZAgTu1vg4YcfZv369bO3oBkgPFHtzTfbOH78GADPPLOJrVsforu7hmhU3UZKNxANxRaiDA4eA0aAGEVFpVRVVVFRoXUHvlL50kvVfVRWpvEFHz+Y6xlG00la3Uoi8pfAx1Fb8E10LGgt8CRQAWwHPuSci477JphbyZh7TOfwmkwgGtXgcmenVi7v2gUbNtxPc/O3gGGgAN0KtB2G71kUzjTyx/x8hKqqoP316tVBLcJYQZhPGUZTJSPdSiKyFPgssMY5NyAiPwY+gM6Q/rpz7kkR+SbwMeDxdK3TMGaSc1kL69evz1prwReqnTyp2UVNTbB1K2zbBvv3t9HdvQkVBlCX0SZycx8iN7fmbG2Cr2guKNANf8kSvdXVqcvoyivVWli8OBCEbG5ZkUmkzXJIiMMrwLXAaeBnwD8C3wdqnHMxEbkFWO+c+6OJ3sssB2MuELYWstlyGBpSt1FHh9YjvP46vPSS1iScOqUpqnA/8AQqCp4C4N8DX0XdRlGgl5qaBdxwwypWrdLhOFdfrfGE8vIghmAZRudHRloOzrmjIvL3wGFgAPg31I3U7ZxL1DLSCixN9XoRuQ+4D2D58uUzv2DDMM6S2uIpBpYAy3j3u79ARcUfs2OHWg39/eGahD7gfzJaGEg83gr0cOONl1NdrRXKK1fCVVepy6iiIqhDsIDyzJJOt9Ji4G5gJRp1+hfgzsm+3jm3EdgIajnMxBoNw0iNd3cNDsJFF62io+Mg7373R7jiig1s2aKuozNngpYVYfLySojH3zzbKjs/P2h9vW/fbygt3cmf/dnlXH11MBOhpCRzh+JkI/F40IxwPNL5p343cNA51+mcGwZ+AvwBUCYiXrTqgaPpWqBhZAvr169HRMa9TWfcIhbTOEJjI/zoR210dLQC8Otfb+Lxx9vZvl3nKISFISdHb35AzoIFmm66ahW87W3w3vfCn/0ZLF/+P6iv/wUf/SjcfjtcfrkGnouLTRgulOFhFewTJ7QxYVfXxOenM5X1MPB2ESlG3UrvArYBvwXej2Ys3Qs8nbYVGkaWEA5cz0S8ws9K6OzUuQi7d8MLL8AvftEA+HSgEWKxBjTj6AwabBYgTjweAwaIxweIxXqoqirmrruu5uKLYc0anZxWXQ0//el2mpreYHi4naKi858Rbeh3NjSkMZ6hoSA92IvzuVqDpDPmsFVEngJeQxuj7EDdRL8AnhSRv00ceyJdazSM+U40qkHko0d1TsLWrfDb32oVc29vG7CJIHYQTTx+iJycGvLzNXOot/cQkUg/t922hksuUSG44gpNPV2yJOiKCnD48H56enrOa0a0odaaF4NoNGgl4tN6fevyyZDWIjjn3MPAw2MONwM3pWE5hmGgG0pPj7oeDh3SiuXf/EaH55w8GbTAhgYgPubVI+TlNVBRsYHycm1s98YbOygpOcLnPreGyy9XC6G4OLllRVtbG8ePHweY9Izo+Y5zKgKDg3rz1kFeXhCnyc8/v1oPq5A2jAxkaGiIxsZG2tvbp7xBnu9rBwY0/bSlRVNQn38eXn5ZrYagYtnTD7xIqoyjWOyXVFX9nj//85tYswYaGn5IJHKa97znsxNetTY0NOBT6881I3o+MzISWAdDQ4F1EIkEqb3TkclljfcMI0PwTeiampq44YYbaGtr4/7775/yBllXVzfp146MaICytVVdRVu2wHPPaRXzwECqV/SjsQQHDKJpqd1AB9DK7bcv4wtfuJOrrw5cRu985zpg4hhIW1sbq1atYlCLIAAoKiqiubl53lsP3jrw8QMf6M/LC+ZS+BkWUyUj6xwMwxhNS0sLPT09PPDAA+ftXpmsa8a7jQ4eVLfRL36hHVBPnx7/vTXbqJjiYi1AO3r0ZYqLu/jLv3wP116rtQi1tbpZTXWjamhoIB4f7aKaz9bDyMjoYHK4DXlJiYrCTHeSNXEwjAwgvKl/73vfO2/3ykSumaEhaGuDI0c02+jZZ+GVV9RyiI8NHYTwIzTLy9UaWLFCG9v94Aff5fjxf+FDH3qTiy6quaAeRi+//DLR6GgXVTQaZcuWLef/pllG2DoYTnQV8aNO09EnysTBMDKAsZu6JxqNsmnTJoqKiviHf/iHcV//8MMP84lPfIJNmzadfR//2k996iGi0RqammDzZo0lHDkSbECpyM0NJqYtXRo0t7vhBrjxRj32rW/9jDNnTvC1r1341f2OHTuAuddwcCJ8IZq3DrxAFxTovAlfIJguTBwMI820tbWN2tTHMjIywsDAwNnnw7GJsMvo/vvvT3LNDA+PcO+9DcTjG9izZ2wcYQDtYZRL0MtoCOhiZKSd6uoK3ve+a1m7Fm66SRvc+c3KMovOj+Hh0ammoO66cKppphT7mTgYRppJ5W8PM9a94mMTY91NL72U7JqJxaK89tp4rpkiQNNK+/u3IvIp7rjjWdasWcP116/httvUYkjl27bMosnhrQNvIfivOVyIlqldZDNEowxj/pLK3w5QUlKCcw7n3Fm3y9gr9mPH2uno0F5Gn/nMDv74jx1wCM0g8mMzdyS9d2GhtqW45hr4wz+EwsKv4NxOKioa+C//BT70IW14l0oYxlo63n3V3t4+LX+PbCcW0zYVJ08GbSoGB1UIysq09qOqSsUhU4UBTBwMY1LMZO+iHTt24Jzj9ttv5/bbbz97f+3a5AzD8BV7LKYuowcfhD/5E/jkJ+FnPwPtjJq86+TnaxO7K66Adev0NZ/9LHz5y21Eo78FHD/96SZOnJh4k58os+h8CP9tX3jhBV544YUZ6ws1Ezinm39Pj8677ujQrK94PGgoWFOjMyeyqUeU1TkYxhSZqaDpueY5HDzYxhVXrGJoaDD0qiK0qUDY3z9w9rm8PL1CrarSLKOlS7XR3a23auppbq7GKr75zW/inKOgoICPf/zjE7qIrr/+enbu3Jl0/Lrrrjtr4YQZL0aSzfhCtMHB0W0qfN3BVNpUpJOJ6hyyRMMMY34Si6lr4oUX4P3vbyAaTW5XoW0sBhK33sTPDuBVYrGf09W1keXLn6GhATZuhE99Cq69VjevqbqI1q9fn1IYAHbu3JnyKj8cI8lWfBM7P8To+HG1FEZG1BqoqFDroLxcH2eDMJwLC0gbRoahFbEl9PdX8+ijmnr6+uvQ1fUyqQfkbAGKKClRF8by5bB0aTnXXHMR73gHXH+9blipmGrx2VTHlmZzVlMmFKKlkzn80Qwju4jFIgwMVPHYY/D665+jv381u3aF5yJ4l03gNopEtDCtvl5dRldeCbfdpqmnCxee+3fOdPFZtmU1+SZ2Q0OjC9GKi4NU09ksREsnFnMwjCkynT70oSGdj/C738EXv/g/6Om5lEjkMoaG+tFZCEWJM70gDKP9jU6hrqMjwB7uuedS/vEfP0xV1eQ3r9SjPgMefvjhCwoGZ0O/pHh8dBO7cCFaYaHe5rJ1MFHMwcTBMKbIVBrbpSIW00Z3r7yiLSx859OBgTNoQVoRYesA9Oq1rEytg+XLdULaDTfAzTdrLUI6K2nH4/777+eJJ54YZZlMJuA902RTIdpMc0GN90TkL4DvOefOMVTOMOY+5+tDd04FYft2bXK3dau2xh7d6M5HMQfQ+VdDQDvQwcjIES6+uJJPfWodN96oA3PGiyNkCpnSL2m8QrSCAs3k8jMPjNFMxmCqBl4VkdeAbwP/6qbJ3BCRMuBbwFVotc5HgT3Aj4AVaDXPPSZMRqYwFR96PK6N7nbtgl/+El58UbugdnWN1+guDgyzYEEZ1dWwbNkCLr+8kquvXsmNN97MxRdrNky2+LzT2S9peDgQg7B1EE41nS/WwfkyKbeSiAhwB/AfgLXAj4EnnHMHLuiXi3wH+J/OuW+JSAFQDPw1cMo596iIPAAsds791UTvY24lYzaYjA/dz0d46y2di/DSS7Bvn47aTG50N4AKQgyduXwKOAo0AbuBJj7/+ffxta99Kav93rMhDhPNS/ZikMnVyOniguc5OOeciLSjNm4MWAw8JSLPOee+fJ6LWgS8A/hI4ndEgaiI3A2sS5z2HWAzMKE4GMZsMF7a5yOPNPDIIxtobNR6hBdfhKYm6OzUzWo0A6iR7APL3eh/q33A63zwgzfz0EOfZ9kyra41xicWG20dhAvRfN+iuVBvkC4mE3P4HPBh4ATqAvo/nXPDIpKD/os+L3EAVgKdwCYRuRbYDnwOqHbOtSXOaUfdWqnWdR9wH8Dy5cvPcwmGMXnG86E//fQWWlt1RkJb23gT1JT8/KKz/XVaWn7BwMB/5BvfeJFvfON7RCIn+O53N9iGNg7heclDQ6Mnovm6g/OdiGYkMxnLoRz4P5xzLeGDzrm4iLz3An/3DcBfOOe2ishjwANjfocTkZR+L+fcRmAjqFvpAtZhGJNi69YddHfDHXfcR1fX5dx00xd46y04dkyDzON5aEU002jJEm1md801Wpj26U9/leHhA7z6agMLF6qH1oRhNBPNSy4pmb55yUYy5xQH59zDEzzXeAG/uxVodc5tTTx+ChWH4yJS65xrE5FaNJnbMNLC4CB0d2tm0e9/r2mnu3Z9hliskqNHA992KhYu1ADyypU6Oe2WWzQNtaoKcnPb6O7W/z7f/e4mrrvuOgrMKY5zQappeF6yL0S7kHnJxtRIW5jLOdcuIkdE5DLn3B7gXWgUbjdwL/Bo4ufT6VqjMf9wTt1CPT2aeuoFobFRi9W6uyEWuxjISSkMpaVqJSxfDpdcAmvXak3C4sU6X7myUq96779/dNZTc3Mzg4ODtLe3Z0yB2GwRLkQbHAwssEgkEIRsDshnK+n+k/8F8P1EplIzmg2VA/xYRD4GtAD3pHF9xjwgHldB6OpSF9Fbb8GWLfrz8GHNNBoaCr9idA5kYaFu/kuW6CjN667TxnaVlXrzvft96mSqZne+diLT20tMF5k2L9lIJq3i4JzbiabGjuVds70WY34xMgL9/WoJtLVpMHnrVnjzTTh0SAe1jM40CkeZh4FB1DN6isHBI6xYUcZnP/tu6urUlVRVpRZEJJL8uyea/JZtzekmi3PCwEDmzks2kkm35WAYs0YspoLQ1aVtl5uatGL5jTeguVlTT/v7w6/waaeCtsYeRFtidwHHuPHGBXzyk7dz8cU3n40vVFZqoHSiAqvxJr9BdjSnmyy+EG14eBHxeB5dXVaIlk2YOBhzmmg0sBA6OmDvXtixQ1tgHzqkffnPnBnv1UWIqEvo9On9FBWd5E//9Gauvnoll19+A5WV6k4qLw+ufs/FRPMQdL3RrLUexitEcw5yc/uprLRCtGzCxMGYU/hceC8InZ1aobx7t85ZPnxYBaG7e/zUU9DA8qJFUF2tE9S2bn2eoqIjfPzjN58Vg7KyqQ92GTsPIVVzumyyHmKx0U3sfKqptww0u6gHMGHINkwcjKzHz/Dt79cso85O7WG0a5daCQcP6jS13t7xWljE0DYWg0AP0MmZM8c4c2YP1157BZ/4xJ9w8ODvycvrY82aIL9+OsiU5nSTJVyINjgYWAe+EM03sXvkkeR24BKKMF9oO3Bj5rGW3UZW4tMfw4Jw6JC6jV57TWMIbW0qCKMzjUaTnx/MWG5t/R2Fhcd54FhzCcgAAB2sSURBVIE/ZfVqTT0tK1Mr4p577iI3d4gXXvjNjHyedDSnmywTFaJ568AK0bKTC+6tZBiZgN+k+vq01XVnpxan7dmjWUbNzToX4fTpVD2NAvLzg7m/dXU6D+GSS+AHP3ie4uKT3HXXn1JaqqIR5NlP0BNjjuGtAx8/CLepsEK0+YOJg5HR+GrZ/n7d9E+cCAShqUkthfZ2jSEMDIwfR8jJ0Rz6xYtVEOrqtHJ5xQoVhqVL4Ve/2kNu7hDLl8+dIfGTZb7PSzaSsa/byDi8T7uvTzOJOjrgyBE4cEDjCPv2abFaT89ov3cqSkrUAqiuVgGor9fq5dWr1WKoqFDR0CviU4hEWbBg9j5rOrFCNGMiTByMtBNOgezvV0Ho7FRB2L9fLYQDB9Rl1N09ejNLRWGhCkJlpQrAkiUqCqtW6a22NrgaLi7W+7m5kJOTuvZgpkg1w3kmg7Z+IpoVohmTwcTBSAvhjaqvT0Who0MFwAvC/v0aVO7uDlIlUxUWe/eH72tUX68B5upqdR2tWqXuo4ULg6Hx3neezivjsWmtM4HNSzbOFxMHY9bwPYwGB/VnX59aCIcPazB5zx5NOz16VLOM+vo0GOoDomFE9CrXxxFqavRWWamWwaWXqjAsWaLn+GBqcfHc9p3bvGRjupjD/02MTMAXSXlB8BZCa6taBgcOqDD4GIIXhJGRZCtBRDf2SEQthMpKzvYyqqzUwLIPMpeU6CboA6rpthJmknAhmk/btTYVxoVi4mBMO96VMTCgm5W3EHxQubk5qEPwgjA8rIIwNrick6PxAO82Ki9Xt1FZmbqOli1Tt9HKlZxtz+CDqiUlU7MShoaGaGxszPi22T5G462D8Lzk0tIg1dQwLgQTB2Na8BuVn+fb26udTQ8f1uyiQ4c0BfX4cW1819cXxBDCVoK/us/N1Ste7zaqrtbMovLyoDX2qlWagVRcrCJyoVZCS0sLPT09Gdm6wuYlG7ONiYMxLqmyacJ85SsNfOlLf3M2e6i3V2cfeMvg4EG1Fnzrir6+4Eo3bCWIBBZCXp5u7mVlKgZLlgT3vYWwcqUey8sL6hemaiWMpa2t7exMhUxofDdRIZrNSzZmAxMHY1zC2TTr1q3DOeFXv/rtWXdRLKaxgpMnA3fR4cMaT2hvV5dRf3/QodPHEnJyfKfO4FZYqI3uFi1S91B5uVoMS5eOTkH1nU8LCtRiKCqang2yoWH0ZLZ0WA9WiGZkEmn/pyYiucA24Khz7r0ishJ4EqgAtgMfcs7NbgK6cZagZUUBe/a8xq5d7ZSU1HDiRBBQPnxYRaKjQwXBZyT5OIJzQeVyXl5gKUQiml5aWhoIwqJFmnV00UVqISxfriIB+jqfcTSdGTepJrPNlvXgC/507oEe8/OSfaqpWQdGOki7OACfAxqBhYnHfwd83Tn3pIh8E/gY8Hi6Fjcf8dkvAwO6YcVicOjQIXp7T/LlLzdw660bzs5COHFC21r09QXnOzdaFLzLyAeWfdVyWZne/EyE+vqgLmHJEj3XORWCkpLpsxLGkmoy21jrYbqC1eF5yeFCNC+UNi/ZyBTS+s9QROqBfwf8X8AXRMtD3wn8+8Qp3wHWY+Iw4/gr2IaGr/H3f/91IBfIB04AtwEHAdi8+Qk6Oh5icLDmbAGbr0XwgpCTE1gHeXm6uRcWqoVQUqJWgheF2lq1DlatUnFYsCBwp/hYwkzn5U+mbfaFBKt99la4stsXovnMIks1NTKNtLbsFpGngP8MLAC+BHwEeMU5d0ni+WXAL51zV6V47X3AfQDLly+/saWlZbaWPSdI1ZffP25rU3fR5z//Tvr6NlNSsoa+vr3o7OQCIpGPU1S0gVgsqLqNxwMLwYuC71lUWqpXxT6eUFGhKagXXaS3mhoVA28l+FjCbG+Y47XNbmtro76+nng8TlFREc3NzRNaDxMVovnaAytEMzKBjGzZLSLvBTqcc9tFZN1UX++c2whsBJ3nMM3Lm5P4/HgfUI7H9Uq2v18DyPv2aRzh6FE4erSNvr4tgKOvb1foXaIMDW0iHn+InJwacnICSyEsCP6qv6xMXUbl5UHju5UrgxTUeDywEoqLMzM/fzLBaj8v2aeaghWiGdlNOt1KfwC8T0TeAxSiMYfHgDIRyXPOxYB64Gga15j1eB93OAPGC0JrqwpCc7OmnPb0aObRwAAcPtyATkdLxQjxeAOFhRvIywsyh3zPotJStQ4qK7VQra5OXUfLlmm9QjgWsWBBeqyEyTJesPpv/uYhFi+uSZqX7IcH+VRTw8hW0iYOzrkHgQcBEpbDl5xzfy4i/wK8H81Yuhd4Ol1rzFZ8htHAQHAVG4tpfODwYbUO9u/XDKPu7iCgHBSwtdHbuwl1I6UiisgWqqpG9y1avFhFoaJCLYSlS1UU6ur0PB+TKCxUqyIbNs/xgtUPPtjAV7+6wQrRjDlLJuZF/BXwpIj8LbADeCLN68kKUgU9R0Z00z9wQAvS9u0LKpRPn1bxGBjQ83w9gloVqayGAuAeVq787lmfuc+wqagIuqDW1ARWQnm5vtK7jhYuDKqZswHn4KWXUgerX3ttCxUVVohmzF0yQhycc5uBzYn7zcBN6VxPtuADyH6Dh0AQvLvowAEVhO5unZPgBcH7yP0tFgtqEZx7GRhbWhIFtnLw4EtAL3CKa69dwdveditLlwaiUFenwhG2EnzOfjbgXA59fcHf5Ze/3IEIvP/9/xs5OcNs3vwrsw6MeUFGiIMxOcJDcXwWjIhuxKdPqxB4UfAFaT7d1FsF4dfHYkFvI38FHI2eIB5/EugD+gEH5KDicJIrr8znjjvupK4uGKazdKlaCfF49lkJ4TYV0WgZzuXS0xMUovlU0/z8XsDcRsb8wcQhwwkPxRkcDGoA4nHd/H2G0f79Gkzu6Ulugjc8PNpiCNcj+NRRX41bUlJJXl4l8XjQ5bOyUovSamr0Z1WVWgm1tXqOr3PwGUeZbiX4NhX+7+T/piJxcnOHWLLECtEMw/4LZCA+w8gHlP3mNTKim39jo1oJhw4FFco+5tDfr+eFBcFn04yMBFXKvmGdH5Xpq5F9iwrfCdVnG5WVBVbCwoWBleBcdlgJ481LfuyxR/m7v1sPDJ09Nz9/5kZ1Gka2YOKQIYSH4vj4Z26ubsAnTsDevUHrax9Q9m2cvcsoFlNx8KLgq5bz8iAaPcXwcDe6CQ4AZxI/84FCamqqufrqi6mqUgvBt8iurtbMI3817a0En3GUqVbCZOclP/roAzz66APpXaxhZCAmDmkkPBQn3JIZNIi8Z4+6i1patBX22ECyFwQ/cnNsr38/RrOoCAoLyykqKqewEN5441WgjDVr3kFpaZBpVFsbFKzV1+vjRYuC2IRzmrJZXJyZvvfx5iVbIZphTB0Th1kmHA8IF06Btq1oalILwbfCDscNvHtoeDgYqOOnqPkr4/z8IM3UVyn71FPvptJYw0muv16thKoqvZqurVW3UWWlbv6+PYbPOCosTM/fbDzCAXorRDOM6cXEYYYZL8PIp3u2tqqFsHevtrA4eVI3e3/zaab+fl+fuo7GiktRkW6E3t1TUqIbvL+ajsU0uFxXB+3tu8nPP8XNN/8hZWUqCHV1+ryPTWSqlRCel+ytJG8deAvBrAPDuHBMHGYA7+/2weBwZtDgoMYNmpqCGoRTpwJfvr9a937yaFTrE3yNgnfv5OUFV8beQvA9jbzbaWREj190UVCxvGgRbNvWQiTSxa23alxBYxJ6i0T0nEyxEiaalxy2iqwQzTCmFxOHacK3rPBXtRDMQR4cVMtgzx4VhM5OFQRfY+Bf63370agGnHt7gw1xrCD46mSfaSSiAtLVpRtmZaW6jOrrNZ5QUqKbvgrEm+TlDVFZGUxo8+20M8FKCP8tx85LLi3Vz5cJ6zSMuYyJwwUwdigOBDOQz5xRQWhs1NYVHR264fumc+HAMgQWQk9PEGOIxQKXkY8j+DRTf7U8OKivycnRjbOmRgWgtlbdQgsXBjUKlZV63shIH01Nv+fkyXZWrqyhsDC9V94TzUsOF6KZdWAYs4eJwxQJz0Dwm5gvJPM1CE1NKggnTujVvxeEeDwICnurobd3dFsLX4vgG9p5QfBWQn6+xh1On9Zzi4rUOvC3sjI9r6IiEIWSksBllZMDx469RW/vSTZsmP05yR6bl2wYmY399zsHqYbiQODe6e6Gt95Sl9GhQxpQ7u0d/fpw7MH3Pgp3Qh0eDiwO/76+9bXPuhkcVBEZHFSB8IHk5ctVBPz53p1UUaEi46/IvRuqq6uNjg7tgj5bc5I9Ni/ZMLIHE4cUpBqK433ehYUqADt2qJXQ2hrUIARtGILX+wByX5+Khk8/DVcrL1gQuI/KyoIsoaEhPb+jQ6/4i4vh4ovVQli2LIgTlJVxtnituDiII8TjQaDaX4V/8YvnHlwzXZyrEM3mJRtG5mL/NROkGorj5/yKaBD51VfVZdTWpgLR38/ZSWjhOEI4sNzdPboewWctLVoUCIKPDZSU6OtOn9b39/2K6us11dQHl72glJfrYx9L8FZCQYHGJcbGEsYbXDOd1sN4hWjeKrJCNMPIDua1OKQaiuP9/aB1B42NsHu3Xr2fOjV6QLxPAfVZNTk5Khg+0+jMmUAoCgr0Ct/HJ0pKAlHIydE1HD+ur8/PD4rSfApqcXEQe/AVzT6W4EXHv+94V+PjDa65EOthonnJCxZk97zk9evX88gjj4w6JmJ9l4z5gfiryGxm7dq1btu2bZM6N9VQHO/vd07HZTY2agzBz0EYHg4K13wdgg9IOxe0xe7p0Z/exeSFwG+QCxaoK6i8XH/nwICmnp45o+cXFQXpp3V1el5hob5m0aIgluCtBOeC+ERR0bn99ddffz07d+5MOn7dddexY8eOSf+9U/WBsjYVhpF9iMh259zaVM+lzXIQkWXAPwPV6NCAjc65x0SkHPgRsAI4BNzjnOu6kN+VKsPIX9nGYioIb72lfYw6OnTDHhkJXEC+lURYKHw8oKcnaHbnm9z5K2Ztga2b++LFuokPD6vLyDfOKyjQgHJdnRarLVkSVDkXF+tjbyX4qmnfOdVnL00WLwDr1q0DYPPmzZN63USFaL7uwNpUGMbcIp1upRjwRefcayKyANguIs8BHwGed849KiIPAA+go0Mnjc8wGhgY3bLCX2VHo1qM5ttWnDoVpIb6VtZeSHp6AgsjFlNB6O4O2lj4wHJhod60yZ1e6ZeWqispN1cF4dAhfU1urm72tbXB9DQfoC0s1NcsWRLEEnxw22cpTcZKuFB8x9dUhWg2L9kw5j5pEwfnXBvQlrjfKyKNwFLgbmBd4rTvoONDzykO3r0zdiiOv6odHNSGdo2NOinNC4JzwebuW0h0dQVB6XhcN3R/vhcE70YJup7qBu/dRgUFKiStrcHvKSpS66C2VrONqqqC10YiKgi1tXrMu69EgvYYM+m7D6fs+qA6qCXk6w6sEM0w5g8ZEZAWkRXA9cBWoDohHADtqNsp1WvuA+4DqK9fQXt7kGHkm9D19sKuXZph1Nysm35fn77eB569q6a7OxAVUBHo7tbX9PcHm6XvPeRFwaedVlbqc8PDGsju7tbNNj9fn/OCUFMTBKbz8lRIlizRWziF1mc0FRfP3IbsA/LeZWSFaIZheNL+X19ESoH/DnzeOXc6nA3inHMikjJi7pzbCGwEuPbatc5fWXd3w+uva4ZRS4s+7u/X1/jAs68W9m6nkZGgFUVXl97CXVQjkcCd42sLiorUUli8WDfVjg4VoLDbaMUKzTSqr9dAckFB0BfJVy/7OMTAQGAl+H5J00mQeaPDfSBCXl5d4tkR/uqvPs/69Q9aIZphGECas5VEJB/4OfCvzrn/mji2B1jnnGsTkVpgs3Pusone55pr1rqvf30bTU1w+HDg/gkHlH2vonCmUW6ubsrd3Rpb8BXIEFgW4bRTnxVUVaVC09Ojcxd6e/X9wq4hX5PgC9xE1ILw85ghsFS866aoaPqzfHz9hrcOfKppuMW1WQeGMT/J1GwlAZ4AGr0wJHgGuBd4NPHz6XO9V0cHPPWUuox8P6JwP6FwczwRPdbVpXGEcKZRbq5aBj4TqLRUbz6jqLRUf8eRI4F1kZ+v1kNdXdDwrqIiEITCQhWTcCxhpq2EVPOSfSGaj2+YdWAYxkSk85rxD4APAW+KiE++/2tUFH4sIh8DWoB7zvVG3i20aNHojqb+allEz+nqUivh9OnkJnc+dbS4OKheLivTjX54WC2EpiYVh5wcPX/58sBKqKrSY759RkWFWgnV1UEsob9fxcvHLKbLSpioTUW2F6IZhpEe0pmt9CIw3vXru6b6ft5vH26DPTKiQuAFoa9vdEqmdxP5LCM/DnPJEt1YT5yAN99U91G4lUVNjVoK1dVBgzsIrISlS/X+8LAKgrcgSkqmz0rwrTqsEM0wjJlgTnib43G1CiBocnfyZFCx7Iu2fBaOb0PhA8z5+bqpl5Zq3MEP5PF9ihYuDGIIfsZyUVFQP+HbY1dV6e/xFdN5eUGr7QvdqG1esmEYs8mcEAffFtsLgp+x7NMyfRxhwQK9+f5D5eW60Q8NaT3Cm28Gqa7FxYHbqKZGN/+KiqDLakGBikVt7WgrAYJYQiRyYZ8r1bxkK0QzDGM2mBPiMDCgqau+CZ2PF/jWFf7m5w5XVenm3tEB27cHDfV8b6OlS4Oso8rKYPOPx4Nso8pK/d3eSsjNvXArwQrRDMPIFOaEOPispIICtQb8vGQ/gD4S0c28pETdRvv2qTD4moSyMo0h+NqD6mrNQBoeDvol1dUFVkIsFlgJPpZwvlbCeIVoPuPK5iUbhpEO5oQ45OerC8jPRPDZOeXlehsagqNH4bXX9CrfD8FZtUo3fG8l+EI1v1n7bKPKytHdV3Nzg7qHqW7c481L9hPRbF6yYRiZwJwQh0hEN3ofX6is1M22o0MH9Jw6pZtxYeFod5F3Hy1YELTRyMkJKpsLCvSYj0P4bKbCwqmtb6J5yf79rBDNMIxMYk5sSfn5sHKlbvJdXdpt9dgxjUXk5OjxlSsD15GPGYQzgLyVUFGhG/fAgLqgztdKSFWI5msqrBDNMIxMZ86IQ0cHbNsWzEkoLtYOqNXVequpCeIO/gq+pEQFo64uaJrnrQTfYG+yVsK55iVHIlaIZhhG9jAnxOH0adi5Uzdyn01UXR24kMrKdLMeGNBbRUUwVQ30WG9vYGVM1kqwecmGYcxV5oQ45OTA5ZcHLiN/i0SCoTzhALSf3XDmjL7eWwnncvVYIZphGPOFOSEOpaVwyy1qDSxcGFzRx2JqSXiXknMqFKdPq6D44riJgsHhQjTflsO3qfCtKsw6MAxjrjEnxKGkRC2H3l7d+EtLAyvBxxJOn9ZzI5FgJGcqK8HmJRuGYcwRcYjHVRiqqkbXJQwMTM5K8IVoqeYle0GwQjTDMOYTc0IcIhG49dagLqG3N+h/tHhxspUwXiFaXp4VohmGYcAcEgcfG8jJCaa3ha2EiQrRbF6yYRjGaObEdjgyoqLg5zz7K/5wE7twIZrvmGqFaIZhGKnJWHEQkTuBx4Bc4FvOuUfHOzcvT+MMfl7yeIVo1qbCMAxjcmTkVikiucAG4H8FWoFXReQZ59zuVOc7p1PbrBDNMAxjeshIcQBuAvY755oBRORJ4G4gpTj4dFObl2wYhjE9ZKo4LAWOhB63AjePd3J+fjB8xzAMw7hwstbhIiL3icg2EdnW2dmZ7uUYhmHMKTJVHI4Cy0KP6xPHzuKc2+icW+ucW1tVVTWrizMMw5jrZKo4vAqsFpGVIlIAfAB4Js1rMgzDmDdkZMzBORcTkc8A/4qmsn7bObcrzcsyDMOYN2SkOAA4554Fnk33OgzDMOYjmepWMgzDMNKIiYNhGIaRhImDYRiGkYSJg2EYhpGEiYNhGIaRhImDYRiGkYSJg2EYhpGEiYNhGIaRhImDYRiGkYSJg2EYhpGEiYNhGIaRhImDYRiGkYSJg2EYhpGEiYNhGIaRhImDYRiGkYSJg2EYhpGEiYNhGIaRRFrEQUS+JiJNIvKGiPxURMpCzz0oIvtFZI+I/FE61mcYhjHfSZfl8BxwlXPuGmAv8CCAiKwBPgBcCdwJfENEctO0RsMwjHlLWsTBOfdvzrlY4uErQH3i/t3Ak865IefcQWA/cFM61mgYhjGfyYSYw0eBXybuLwWOhJ5rTRxLQkTuE5FtIrKts7NzhpdoGIYxv8ibqTcWkV8DNSme+opz7unEOV8BYsD3p/r+zrmNwEaAtWvXugtYqmEYhjGGGRMH59y7J3peRD4CvBd4l3POb+5HgWWh0+oTxwzDMIxZJF3ZSncCXwbe55zrDz31DPABEYmIyEpgNfD7dKzRMAxjPjNjlsM5+H+ACPCciAC84pz7pHNul4j8GNiNups+7ZwbSdMaDcMw5i0SeHSyFxHpBFou8G0qgRPTsJxMwD5LZjKXPgvMrc8zXz/LRc65qlRPzAlxmA5EZJtzbm261zEd2GfJTObSZ4G59XnssySTCamshmEYRoZh4mAYhmEkYeIQsDHdC5hG7LNkJnPps8Dc+jz2WcZgMQfDMAwjCbMcDMMwjCRMHAzDMIwk5rU4zMW5EiJyZ2LN+0XkgXSvZyqIyDIR+a2I7BaRXSLyucTxchF5TkT2JX4uTvdaJ4uI5IrIDhH5eeLxShHZmvh+fiQiBele42QQkTIReSrx/6VRRG7J1u9FRP4y8e/rLRH5oYgUZtP3IiLfFpEOEXkrdCzldyHKf0t8rjdE5IbJ/p55LQ7MsbkSiTVuAO4C1gAfTHyWbCEGfNE5twZ4O/DpxPofAJ53zq0Gnk88zhY+BzSGHv8d8HXn3CVAF/CxtKxq6jwG/Mo5dzlwLfqZsu57EZGlwGeBtc65q4Bc9P96Nn0v/4TuS2HG+y7uQtsQrQbuAx6f7C+Z1+IwB+dK3ATsd841O+eiwJPoZ8kKnHNtzrnXEvd70Q1oKfoZvpM47TvAH6dnhVNDROqBfwd8K/FYgHcCTyVOyYrPIiKLgHcATwA456LOuW6y9HtB2wYViUgeUAy0kUXfi3Pud8CpMYfH+y7uBv7ZKa8AZSJSO5nfM6/FYQznNVciw8jWdSchIiuA64GtQLVzri3xVDtQnaZlTZX/G20wGU88rgC6Qxck2fL9rAQ6gU0JF9m3RKSELPxenHNHgb8HDqOi0ANsJzu/lzDjfRfnvSfMeXEQkV8nfItjb3eHzjnvuRLG9CMipcB/Bz7vnDsdfi7R3j3j869F5L1Ah3Nue7rXMg3kATcAjzvnrgf6GONCyqLvZTF6Nb0SqANKSHbRZDXT9V2kqyvrrDHP5kpk67rPIiL5qDB83zn3k8Th4yJS65xrS5jEHelb4aT5A+B9IvIeoBBYiPrty0QkL3GVmi3fTyvQ6pzbmnj8FCoO2fi9vBs46JzrBBCRn6DfVTZ+L2HG+y7Oe0+Y85bDRMzBuRKvAqsTmRcFaKDtmTSvadIkfPJPAI3Ouf8aeuoZ4N7E/XuBp2d7bVPFOfegc67eObcC/R5+45z7c+C3wPsTp2XLZ2kHjojIZYlD70Lb6mfd94K6k94uIsWJf2/+s2Td9zKG8b6LZ4APJ7KW3g70hNxPE+Ocm7c3NNB8BNiZuH0z9NxXgAPAHuCudK91Cp/pPWjm1QF0JGva1zSFtd+GmsNvhL6T96C++ueBfcCvgfJ0r3WKn2sd8PPE/VXohcZ+4F+ASLrXN8nPcB2wLfHd/AxYnK3fC/AI0AS8BXwXnS2TNd8L8EM0XjKMWnUfG++7AATNYDwAvIlmaU3q91j7DMMwDCOJee1WMgzDMFJj4mAYhmEkYeJgGIZhJGHiYBiGYSRh4mAYhmEkYeJgGIZhJGHiYBiGYSRh4mAYM4CIvC3RP79QREoS8wOuSve6DGOyWBGcYcwQIvK3aF+lIrQ30X9O85IMY9KYOBjGDJHob/UqMAjc6pwbSfOSDGPSmFvJMGaOCqAUWIBaEIaRNZjlYBgzhIg8g07jWwnUOuc+k+YlGcakmfPzHAwjHYjIh4Fh59wPErO9t4jIO51zv0n32gxjMpjlYBiGYSRhMQfDMAwjCRMHwzAMIwkTB8MwDCMJEwfDMAwjCRMHwzAMIwkTB8MwDCMJEwfDMAwjif8fKSNOsq5NGx8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_axis = np.linspace(x.min() - 30, x.max() + 30, 50)\n",
    "\n",
    "plot_data(x, y, y_err)\n",
    "\n",
    "for i in np.random.randint(len(chain), size=100):\n",
    "    m, b = chain[i]\n",
    "    plt.plot(x_axis, m* x_axis + b, color='blue', alpha=0.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performing the same procedure using a Fortran engine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "!rm FortranEngine.cpython-36m-x86_64-linux-gnu.so \n",
    "!f2py3 engine.f90 -m FortranEngine -c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['_FortranEngine_error', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__spec__', '__version__', 'data_generator', 'mcmc', 'probability']\n"
     ]
    }
   ],
   "source": [
    "import FortranEngine\n",
    "print(dir(FortranEngine))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m, b = (0.736, 30)\n",
    "x, y, y_err = FortranEngine.data_generator.generate_data(m, b, 20)\n",
    "\n",
    "plot_data(x, y, y_err)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Comparing the between the Python functions and the Fortran engine, gives us an indication of the uncertainty that arises from the choice of technology"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-56.51816177368164\n"
     ]
    }
   ],
   "source": [
    "out= FortranEngine.probability.log_likelihood(np.array([m, b]), x, y, y_err, 20)\n",
    "print(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-56.518166\n"
     ]
    }
   ],
   "source": [
    "out2 = natural_log_likelihood(np.array([m, b]), x, y, abs(y_err))\n",
    "print(out2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.749506965389945e-06\n"
     ]
    }
   ],
   "source": [
    "print(abs(out - out2) / abs(out) * 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.3862943649291992\n"
     ]
    }
   ],
   "source": [
    "parameters = np.array([2, 0.5])\n",
    "limits = np.array([[0, 4],\n",
    "                  [0, 1]])\n",
    "out = FortranEngine.probability.ln_uniform_prior_dist(parameters, limits)\n",
    "print(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.3862943611198906\n"
     ]
    }
   ],
   "source": [
    "out2 = log_uniform_prior_dist(parameters, limits)\n",
    "print(out2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.747835339063086e-07\n"
     ]
    }
   ],
   "source": [
    "print(abs(out - out2) / abs(out) * 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-692.7340698242188\n"
     ]
    }
   ],
   "source": [
    "parameters = np.array([2, 0.5])\n",
    "limits = np.array([[0, 4],\n",
    "                  [0, 1]])\n",
    "out = FortranEngine.probability.ln_posterior_dist(parameters, x, y, y_err, limits, 20)\n",
    "print(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-692.7340726814324\n"
     ]
    }
   ],
   "source": [
    "out2 = natural_log_post_disribution(parameters, x, y, abs(y_err), limits)\n",
    "print(out2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.124546155312138e-07\n"
     ]
    }
   ],
   "source": [
    "print(abs(out - out2) / abs(out) * 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The uncertainty is negligible in all cases. We can now run our simulation using the Fortran Engine!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The MCMC simulation ran with an acceptance rate of 0.2596000134944916 in 0.2828431272506714 seconds average\n"
     ]
    }
   ],
   "source": [
    "start_parameters = np.array([0.5, 10])\n",
    "# mlimits, blimits = ((0.01, 2), (0.1, 50))\n",
    "limits = np.array([[0.01, 2.0],\n",
    "                  [0.1, 50.0]])\n",
    "stepsize_m = 0.02 * (limits[0, 1] - limits[0, 0])\n",
    "stepsize_b = 0.05 * (limits[1, 1] - limits[1, 0])\n",
    "\n",
    "stepsize = np.array([stepsize_m, stepsize_b])\n",
    "data = (x, y, abs(y_err))\n",
    "\n",
    "\n",
    "t = time()\n",
    "for i in range(50):\n",
    "    chain, probs, acceptance = FortranEngine.mcmc.metropolis(data, start_parameters, limits, stepsize, 10000, 20)\n",
    "t = (time() - t) / 50\n",
    "\n",
    "print(f\"The MCMC simulation ran with an acceptance rate of {acceptance} in {t} seconds average\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_chain(chain, *limits)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_PDF_walk(chain, start_parameters, limits[0], limits[1], title=\"Fortran MCMC: Estimating m and b\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x396 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "corner.corner(chain[500:], labels=['m','b'], range=[mlimits,blimits],quantiles=[0.16,0.5,0.84],\n",
    "                show_titles=True, title_args={\"fontsize\": 12},\n",
    "                plot_datapoints=True, fill_contours=True, levels=[0.68, 0.95], \n",
    "                color='b', bins=80, smooth=1.0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}