{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probabilistic Programming 3: variational Bayes\n",
    "\n",
    "#### Goal \n",
    "  - Know what is required to set up a variational Bayesian inference procedure.\n",
    "  - Learn how to infer the parameters of a Gaussian mixture model using a variational inference procedure.\n",
    "\n",
    "#### Materials        \n",
    "  - Mandatory\n",
    "    - This notebook\n",
    "    - Lecture notes on latent variable models\n",
    "  - Optional\n",
    "    - [Review of latent variable models](https://doi.org/10.1146/annurev-statistics-022513-115657)\n",
    "    - [Differences between Julia and Matlab / Python](https://docs.julialang.org/en/v1/manual/noteworthy-differences/index.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that none of the material below is new. The point of the Probabilistic Programming sessions is to solve practical problems so that the concepts from Bert's lectures become less abstract."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m  Activating\u001b[22m\u001b[39m project at `~/syndr/Wouter/Onderwijs/Vakken/tueindhoven/5SSD0 - Bayesian Machine Learning & Information Processing/2024-2025 Q2/BMLIP/lessons`\n"
     ]
    }
   ],
   "source": [
    "using Pkg; Pkg.activate(\"../../.\"); Pkg.instantiate();\n",
    "using IJulia; try IJulia.clear_output(); catch _ end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Random\n",
    "using JLD\n",
    "using Statistics\n",
    "using LinearAlgebra\n",
    "using Distributions\n",
    "using RxInfer\n",
    "using Optimisers\n",
    "using ColorSchemes\n",
    "using LaTeXStrings\n",
    "using Plots\n",
    "default(label=\"\", linewidth=3, margin=10Plots.pt)\n",
    "include(\"../scripts/clusters.jl\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Stone Tools\n",
    "\n",
    "Archeologists have asked for your help in analyzing data on tools made of stone. It is believed that primitive humans created tools by striking stones with others. During this process, the stone loses flakes, which have been preserved. The archeologists have recovered these flakes from various locations and time periods and want to know whether this stone tool shaping process has improved over the centuries."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data\n",
    "\n",
    "The data is available from the [UCI Machine Learning Repository](https://archive.ics.uci.edu/ml/datasets/StoneFlakes). Each instance represents summary information of the stone flakes for a particular site. We will be using the attributes _flaking angle_ (FLA) and the _proportion of the dorsal surface worked_ (PROZD) for now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = load(\"../datasets/stone_flakes.jld\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I've done some pre-processing on the data set, namely [z-scoring](https://nl.wikipedia.org/wiki/Z-score) and removing two outliers. This reduces the scale of the attributes which helps numerical stability during optimization. Now let's visualize the data with a scatterplot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter(data[\"observations\"][:,1], \n",
    "        data[\"observations\"][:,2], \n",
    "        color=\"black\",\n",
    "        xlabel=\"Proportion of worked dorsal surface (PROZD)\",\n",
    "        ylabel=\"Flaking angle (FLA)\",\n",
    "        size=(800,300))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model specification\n",
    "\n",
    "We will be clustering this data with a Gaussian mixture model, to see if we can identify clear types of stone tools. The generative model for a Gaussian mixture consists of:\n",
    "\n",
    "$$ p(X, z, \\pi, \\mu, \\Lambda) =\\ \\underbrace{p(X \\mid z, \\mu, \\Lambda)}_{\\text{likelihood}}\\ \\times \\ \\underbrace{p(z \\mid \\pi)}_{\\text{prior latent variables}} \\ \\times \\ \\underbrace{p(\\mu \\mid \\Lambda)\\  p(\\Lambda)\\ p(\\pi)}_{\\text{prior parameters}}$$\n",
    "\n",
    "with the likelihood of observation $X_i$ being a Gaussian raised to the power of the latent assignment variables $z$\n",
    "\n",
    "$$ p(X_i \\mid z, \\mu, \\Lambda) = \\prod_{k=1}^{K} \\mathcal{N}(X_i \\mid \\mu_k, \\Lambda_k^{-1})^{z_i = k}$$\n",
    "\n",
    "the prior for each latent variable $z_i$ being a Categorical distribution\n",
    "\n",
    "$$ p(z_i \\mid \\pi) = \\text{Categorical}(z_i \\mid \\pi) $$\n",
    "\n",
    "and priors for the parameters being\n",
    "\n",
    "$$ \\begin{aligned} p(\\Lambda_k) =&\\ \\text{Wishart}(\\Lambda_k \\mid V_0, n_0) \\qquad &\\text{for all}\\ k , \\\\ p(\\mu_k \\mid \\Lambda_k) =&\\ \\mathcal{N}(\\mu_k \\mid m_0, \\Lambda_k^{-1}) \\qquad &\\text{for all}\\ k , \\\\ p(\\pi) =&\\ \\text{Dirichlet}(\\pi \\mid a_0) \\quad . \\end{aligned}$$\n",
    "\n",
    "We can implement these equations nearly directly in ReactiveMP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data dimensionality\n",
    "num_features = size(data[\"observations\"],2)\n",
    "\n",
    "# Sample size\n",
    "num_samples = size(data[\"observations\"],1)\n",
    "\n",
    "# Number of mixture components\n",
    "num_components = 3;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mixture models can be sensitive to initialization, so we are going to specify the prior parameters explicitly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Prior scale matrices\n",
    "V0 = repeat(diageye(num_features), 1,1,3)\n",
    "\n",
    "# Prior degrees of freedom \n",
    "n0 = num_features\n",
    "\n",
    "# Prior means\n",
    "m0 = [ 1.0 0.0 -1.0;\n",
    "      -1.0 0.0  1.0];\n",
    "\n",
    "# Prior concentration parameters\n",
    "a0 = ones(num_components);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to specify the full model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "@model function GMM(X, n0, V0, m0, a0, K, N)\n",
    "    \"Bayesian Gaussian mixture model\"\n",
    "\n",
    "    local μ\n",
    "    local Λ\n",
    "    \n",
    "    # Component parameters\n",
    "    for k in 1:K\n",
    "        Λ[k] ~ Wishart(n0, V0[:,:,k])\n",
    "        μ[k] ~ MvNormalMeanPrecision(m0[:,k], Λ[k])\n",
    "    end\n",
    "    \n",
    "    # Mixture weights\n",
    "    π ~ Dirichlet(a0)\n",
    "    \n",
    "    for i in 1:N\n",
    "        \n",
    "        # Latent assignment variable\n",
    "        z[i] ~ Categorical(π)\n",
    "        \n",
    "        # Mixture distribution\n",
    "        X[i] ~ NormalMixture(switch = z[i], m = μ, p = Λ)\n",
    "        \n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up the inference procedure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:06\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Inference results:\n",
       "  Posteriors       | available for (π, μ, Λ, z)\n",
       "  Free Energy:     | Real[198.944, 197.247, 196.218, 195.341, 194.82, 194.541, 194.341, 194.178, 194.041, 193.924  …  193.448, 193.448, 193.448, 193.448, 193.448, 193.448, 193.448, 193.448, 193.448, 193.448]\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Map data to list of vectors\n",
    "observations = [data[\"observations\"][i,:] for i in 1:num_samples]\n",
    "\n",
    "# Initialize variational distributions\n",
    "init = @initialization begin\n",
    "    q(π) = Dirichlet(a0)\n",
    "    q(μ) = [MvNormalMeanCovariance(m0[:,k], diageye(num_features)) for k in 1:num_components]\n",
    "    q(Λ) = [Wishart(n0, V0[:,:,k]) for k in 1:num_components]\n",
    "end\n",
    "\n",
    "# Iterations of variational inference\n",
    "num_iters = 100\n",
    "\n",
    "# Variational inference\n",
    "results = infer(\n",
    "    model          = GMM(n0=n0, V0=V0, m0=m0, a0=a0, K=num_components, N=num_samples),\n",
    "    data           = (X = observations,),\n",
    "    constraints    = MeanField(),\n",
    "    initialization = init,\n",
    "    iterations     = num_iters,\n",
    "    free_energy    = true,\n",
    "    showprogress   = true,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alright, we're done. Let's track the evolution of free energy over iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: both ExponentialFamily and ReactiveMP export \"MvNormalMeanScalePrecision\"; uses of it in module RxInfer must be qualified\n"
     ]
    },
    {
     "data": {
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       "</svg>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(1:num_iters, \n",
    "     results.free_energy, \n",
    "     color=\"black\", \n",
    "     xscale=:log10,\n",
    "     xlabel=\"Number of iterations\", \n",
    "     ylabel=\"Free Energy\", \n",
    "     size=(800,300))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That looks like it is nicely decreasing. Let's now visualize the cluster on top of the observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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       "</svg>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Extract mixture weights\n",
    "π_hat = mean(results.posteriors[:π][num_iters])\n",
    "\n",
    "# Extract component means\n",
    "μ_hat = mean.(results.posteriors[:μ][num_iters])\n",
    "\n",
    "# Extract covariance matrices\n",
    "Σ_hat = inv.(mean.(results.posteriors[:Λ][num_iters]))\n",
    "\n",
    "# Select dimensions to plot\n",
    "xlims = [minimum(data[\"observations\"][:,1])-1, maximum(data[\"observations\"][:,1])+1]\n",
    "ylims = [minimum(data[\"observations\"][:,2])-1, maximum(data[\"observations\"][:,2])+1]\n",
    "\n",
    "# Plot data and overlay estimated posterior probabilities\n",
    "plot_clusters(data[\"observations\"][:, 1:2], \n",
    "              μ=μ_hat, \n",
    "              Σ=Σ_hat, \n",
    "              xlims=xlims, \n",
    "              ylims=ylims,\n",
    "              xlabel=\"Proportion of worked dorsal surface (PROZD)\",\n",
    "              ylabel=\"Flaking angle (FLA)\",\n",
    "              colors=[:reds, :blues, :greens],\n",
    "              figsize=(800,500))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That doesn't look bad. The three Gaussians nicely cover all samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "Play around with the number of components. Can you get an equally good coverage with just 2 components? What if you had 4?\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also plot the evolution of the parameters over iterations of the variational inference procedure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GHfz+979/7ty57u0FCxb89re//eY3v5nP56+77rqBK6sYY2woAnbl6Y8HaW+ZiLC7SE8epH3ty6cSXvHOuDpjhmlKxL1YnRSrk9LPW1owxsaaOJaWdd93332PPPLIUa/BqlarvAaLsenI7Wi14aDO1NHU2Jqmjb0oNNt+uc0L4j0zxElRYTebizq8PBvI2LHNXeR+LK/BYoyx8VNs0lM9tCWNuqJ8kzansSVN9YELrSSWR8VZM0WnD6bEKR1iRcBZmPJP3pAZY8cFDliMsWkpU6ene2lLmhyNrio29dD2POmBC60snNohzkghbImgiXcm5RmdImyhvVEMY4yNCw5YjLFpZm+Znuym3UVoopfztKGH9rcvtOr0Ye0McUpMGBIJH05PidVJYUmeDWSMTRwOWIyx6cFdw/5EN71ZIVtjW4Y29iLXaFtodWIEZ3bKhWEIYH5InDVDLI7yvoGMsUnAAYsxNtX1rWGnTJ0qNp5O0zO9VGtfaLUqLtZ2ipQPphTL4zhrhuzkdVaMscnDAYsxNnVVHDzTS0/16JqDXIOe6sWzGbIHbH3hlTg1Ic7qRNjTttCKMcYmFwcsxthU1FujjT30fBaOJncN+wu5tqYyMY9Ym8JpSWFJzPBjbadc2QGTF1oxxqYGDliMsanljTJtOEi7CtCahm0WOtOPtZ1iZVxIgRMj4t0zxMIwL7RijE0tHLAYY1OCu4b9yYO0r0xKY3uenjyIdL1tDfvCMM5IicVRYQixNIZ3zxBzgpyrGGNTEQcsxtgkczS9mMMT3TpdR8XGM2l6Jk1V59AB7hr2MzuR9AmvIU5N4N0zRNTD0YoxNnVxwGKMTZqqg2fT+qkelGzKNempntHWsIcsrEnJM1LwmxytGGNTHQcsxtgkyDVoUw9tzaCp6M0KNvTQjkLbzqgxjzizE+9MCEtiZkCc2SlWdMDghVaMsWmCA9ZxjYjgNAGAQI4NAKTdG6Q1tAMASpFSAKAVaQWAHAekRnrNqUsawjCF5YGQwjSFaUEawrBgmkIawuQr+ydIV5U29dALWVIau4q0oYf2ltsOmB3AuzvFsrjgZqGMsemLA9YkI+VAu/FFuzlmwD19gUYpDIo4Iz3riJ7iNNF22TsDpCE9XkgJaUjLC2nAMKTlgTQGPiQMU0gDlkcYhpAGTI8wTGEYsDxCGpP9HqYud4ubXQVShO05+uNB9I64hh0rOgQ3C2WMTV8csA6hWkU5dQAgTcpBW0xxSGsAUE5fFccGAQNiCvWXguzmwBeB1qTsvhvtWWfiqdYbIccGNADYtvs+YNto1bTcG7p1A333aO3+aZBWkzb+t0MabqVKGAakAdMSxqEKFkwThimkofvemh791UYgpAGjrzzm1smEFJZH+gIyEBb+oBEISX8Ix1MOU+T2Ydc9NTQ0tqXpj70oNQ9FK0NgeUy8Z6ZI+eAzsCYlzuiU3CyUMTatccA6pLl9g6qVxu/1SakBpam+2Tc3tzl2X0qzD8W1gbkNINt2/9uay2vLbW6SG1C1UhoAtD0gFx5dYDguSUMYhjC9kFIYBkyPkBKmKQxLSAOm5UYx0ZfJhOWBlG6u6gtYJoQc5QzC8spASAZC0h/uvyH8ATHqs6adhqKtGdp4EIUm5Ru0OYPNaWoMCOfuGvZ3z0DEEjGvWJPEmpT0HUfhkzF2zOKA1aLyadX9OtUqwIAyVX+pxnFocNxpusWd/sKVu5iJQLAdAEQKbhmsP/ew6UIr0qpViTxqQh5KYKYHXr8MhAx/UPhDMhCSvqCyG6qQaX+GFL6A9Ielzy+8gQHBKzjtViAVm/RUL7b0Ul1Rdw0bD9L2POkB84EhE6tTYm1K+AzMCuDdM+TyuOA27IyxYwYHLABQhczBr15FjdpkD2T8mVbrq9q0BCQAWKaAAADLA0BAwLIACCFgegAIARgeAEIKGCbcWbDpOMOlHNKaHNud8CW70Sr+OTZpBUeRakK31viPAdJkN2EfmglTwMCXFh6v9IekPyQCIekLikBI+kNCObpaHvxS0pA+/8BalwyEZDAyNRfmd1fxTK9+LkuOxt4y/tijdxXaDpjhx5l9fdh5DTtj7Fg1fMDK5/NvvvnmihUrJng0k0XleicgXQkpBwQUEwAMQ0gJAIYJKQH0Ty25a3daNyAACMv9NpXCNN2Xa32/SiEM98aA1zckAEiztebaNI+xuafxpRxSilQTSpNWsJtuGZJUk5SCcuA4pBX133CaUApakW27lcvDqX5Rs6Gag4tYAIQvKANB4Q9JX1AGwtIfkoGQdoNX+7HS6xf+oOEu7QrFZDhmhGKYpKRCRHvK2HSQdhfhaNqeow091NP+qVoYxlkz5MIweA07Y+yYN3zA6u7uXrly5erVq6+66qq/+qu/CgaDEzysCeY5YWnkg5+sbP0/4U4ISlMYBgAYfbnEMFuzF6bVX+8Rrdzjab2KWwESAqYJQAgJw8KAXDUJpCHcyGUYrQBnWH03BiQ5KVoPif53NDDSib73KPoiXV/Im1bIcaAVObZ7kQHZNrQi5ZBjQytyHCibtHbT0tufIiTS6H9Nu0H1qq5WqFbWtbKulalWHmlVHNUrql4BegbeKaQU/lCr4uUPuQmM/CHRqKl8+tBx0jDCMSMcl5EOIxI3wvEJqHK5fdif7Na9dTQUtmVoQw+K9qHpQCFwUgTvmynnBMB92Bljx4nhvyYXLlz4/e9//3vf+95nP/vZG2644fLLL7/qqquWLVs2wYObSOF1f+lYPmPMF7kPijj9P/bPshmGG+YO3TMkFR3ds4TlHeP3clxqzSEqt17VJK1a15Zqpe0GtILWuuneUNpuDnqIlCK7AYQRHfS6RM26rpZ1rayrJV2vULWsa2WqV4cfhtZUKepKcdD9wvQIf1AGgjIQkeG4jMShnIFVMekLyEiHGU3ISIcRislAaAz/cCoOnumlp3t01UGmQZt68Fy2rQ+7R+K0hFjbiahHhC2xOiXWdgpew84YOx4IGrUT0o4dO37wgx/cfffdmUzGLWh9/OMfDwQCEza+I3Lfffc98sgj995771E8l4gKO7b63FqOabZqOaan78aAebr+hwAI0XcDrVJB/8wdYwDcUpZt63pF1yqtRFUrU62sq+XW5Z/tB1Otomtlqpb7U5eulanZONzzGYYRistI3AjHZThuhGMDC6jC4zMicSOSMCJxIxIXgfDRzR0frOHpHv18FramPSVs6tW7i21d1cIecUYSq5PCZ0y5PuylUikcDk/2KBhj40trXa/XJzGxvEXActVqtQceeODf/u3fNm/e3NHR8alPfWr9+vXz5s2bgPEdkbcZsKrV6jE/GcqmFLIbulrW1bKulXS1rBs1atR0uTBM8NKaGhWqVnS1pGsVXStRtayrpcNZki+9fhnpMKIJIxIXoaj0D8gWUspA2K1vmdGEDHe85eSv2yzUXWi1s0Abemh/pe2AmX6sSYpVCWFO1TXsHLAYOx5MesA6rJU0r7zyyubNm1955RXTNE899dS77777O9/5zne+852rrrpqvMfH2DFMWF4j6jWiiYF3Emmq19wql6oe+jcZBvnDRmJm28HNunaLYeWCKuVUKTd0klE3arp3v9O73/1RevwyEpPhDhmOGeEOKNUsF7D/NQBCSBkMG5EOGY4b0YQRTfSXYx2N57O08eBoC60WhFp92E0pVsRx5gw5g9ewM8aOV6MFrGq1+sADD3zve9/buHHj7Nmz169ff+WVV86ZM6dUKl1//fXr16+fytOFjE1TQkjhD0p/EJjRNtmsta5XW7WuapkaVV2v6VpJev0UTfYfRU5Tlwq6mFHFrC4XdDk/aDW9btZ0uoZ0V//pZDAsIx1GpENGEobTVOUCsMd9VPoCTiS5G8lnGx09VkfGNp7qxbOZtoVWpsCymHjvTCR9wmeIVQmcNUNGPGCMsePZ8AGrWCzeeOONP/7xjwuFwjnnnPOzn/3sz//8z82+uYNwOHzTTTd997vfPXDgwKJFiyZwtIwdx6R0+2ChreAFcmxdK+tKURWyupRTpZwwPUY85YYzUkpX8rqU04WcKudUMYf2+UcircoFVS7YB/YAgBAyGDbCcRnucELJbjO+//WKojcCTRhVkbWjYSuxxJM4aHRkrFjAFKtT4oyU8Bvo8OJdnWJ1UlrcD4QxxkYKWAcOHPiP//iPT33qU1dfffXixYuHHhCPx7/61a8mEomhDzHGJpIwLSMcN8Jxa+Y73HvIbuhywSlkdDGrygVlWUYkgTnuY6RrZV3K6WJOlXKqmB3cAY5Il4u6XETXGwCSQMAb2W8kCrLDYyZmmnbKya2svRKyMCsoo/5w3ZkRV6kVcxKLZkVbTd0YY4yNFLBOOOGE/fv3+/0jLqAIBALXX3/9uI2KMXb0hOU14p1GvNP9kbTWlaIuZp1CRpcLqpiVgTBmzG89OmBKUZULupzHgClFAQQbxcUoLsYeABqyaIWq/g5lJWq6IwQ1V5aC+VeQR+kly+2/5S6Zl6HolFrYzhhjE2z4gOXz+SZ4HIyxcSKkNMIxIxyz5iwEACJVLeliTpWyqpjTpZwwPdVQqitGB2vQSolqThVyvkp2hpNJOEWJQ3lLQsfsYswuovg6AOwxRCTeiCZkJGFEEuTYyPW47VmFx2fGkkY0IaMJI5qUHu7Kxhg7vgwfsF5//fWLLrpo6P1SytmzZy9evPiTn/zksd13lLFjlhBGMGIEI9asdzQUtudoS1ejmMt5rWzeyaRLBZRNQyYQBgBJOkWlk0XvfJUO1bLeeqGtKqWVyqcPtZI3TCMcN6Kt9fLUqNk9b7qP9Pc7NeIpI5YSk7W3AWOMTZThf81ZljV37tzf/va30Wh05cqVoVBo9+7dO3fuPO2004rF4l133fWtb33rV7/61XnnnTfBw2WMjYkDFdqSphey1NTINcwthdS2bLJiAwGYAZWw8zOdzFKRe5cvu1CahFjec1IkKCKWo4q51iWKxayqtHcXVY7K96p8r/uTMD0yFDXinWY8qaMJWa86bt4SwnDbQMSSRqTDCMcna/9ExhgbP8MHrNmzZzcajU984hPf+ta3+ntv/uY3v/n0pz/94x//uLOz88Mf/vC1117LAYux6cXR2FmgLb30Wok0YVeBNqfptXJbTNLC6EglT02lTgihKgVF9ZnBQqzW467igmkdukTRbqhCRhWyqpChYka3r5cnp+nmraZ7eaI/aEQTRiRhRJOwm6qYxb7dAISUMhw3YilevMUYO5YMH7Cefvrpxx9/vFAoeDyHutlccMEFF1544e23337nnXfeeuutZ599djqdTiaTw74CY2xKSddpWwbPpqnqUMmm57N4Jo1Cs20jh7AlTunA6UlEPSJo4p1JeUanCFsSSKCvOQTZTVXMqkJGFdKqkBWW10zObj1Ur6piRhWyuphRhcyg3bKpVnFqFad7L+A2g4gY0aSMdhjRhHQcVcj0Ld7ymtGkEUvKSIcRS0oPrwdljE1LwwesPXv2BAKBgenKFY/Hn3/+eQAnnXQSgEqlwgGLsanM0fRyHpt76Y0yEWFPGVvStKNAekCycpuwr06KpVEhBeYGxZqUWBGHKYepJAnLYyZmmn0N5clu6nLebQnh5HqEL2B2tjbRonpVl7JOLq1yPaqUhVKHXoVIlwu6XMD+V+EWsQJhGekwYikj3knNht3fd37AZtVmPMVbmDPGposR2zRks9n/+q//+uhHP9p/Zzab/dnPfnbuuecC6O7uFkJwHyzGpqxsg55NY2taVxxUHGzL0OY08u0lq5CJVQmxJoGYV3gNsSKONSkxK3AEM3TC8gxsCaHrVVXIqEJGFzNOPiN8ASM1FwBI63JB5dOqmFGFjC4XQYcuTiTd1uxUmB4Z7XAnE41oh+5bvCWElKGoEXPvTxrhGC/eYoxNWcMHrDPOOOO888679NJLL7744rVr14bD4V27dv3whz8sl8t/+7d/C+CXv/zlsmXLQqHQxI6WMfYWCNhToi299HIemmhvGU/1Di5ZAVgYPlSymh0Uq98mVkoAACAASURBVJNiZYfwvO1GodIXkL6ANaNVxNLVkpNPt8KW6ZHhuIWTAEA5qphTxYwupFUho6vltrfgNFWmW2W63R+FL2BEOmQ0YUQThl1XpRz2vQJAGGb//WYsKQO8fzNjbAoRRDTsA9Vq9Stf+co999yTyWQAeDyes88++xvf+MYpp5wCoFwuA5hqAeu+++575JFH7r333qN4LhFVq9X+Ff2MTTslm55zy1QNqiu8mKOneqm33naMz8DyuDgjhZRPmBJLomJ1SiwMT0QdiEjrcl+/02JWFTKkW5OG1Gy0KluFjC5kdbM24qsIIf0hI5aQkaQRTchwXBhG6xG3o32804inzFhSjLx4q1QqhcOcxhg7xmmt6/X6JO6YPHwFK5/Pv/rqqzfffPPXvva1TCZTrVZnz55t9P0iw9SLVowdt5qKXini+SztKkATdVWxJUPPZ9v2YwYwK4DVCbGqQ5gSM/xYk5KndAivMcKLjgMh2vqduv3lVb5X5XqcQkZ4fQMWy1f6F9GrQqZt80QiXS3pagkHXgcgpBShmOEWt6IJsptOrsc9sLV4K54y450y0sGdtxhjE2z4XzoPP/zwJz/5SbdMlUgkeK0VY1NNzaHXSthVoJdz1NRoaGzP0jNpOthe/fFKrOgQpyfFDD9MKZZEMWElq9H195fHvJPQujgxo/IZVcyofFr4gmbfZj66VtK5XlXMqkJWl7I0YLE8aU3FrC5m7X27AcC0jFCsv9Npf+etVieIaNKMJYxoEjT5b58xdswbPmDNmTPHcZxms2lZ1gQPiDE2iopNrxTxYo5eLUIROYTXini5QC/mBpes5gSxJiGWx4UlkfDhnQlxWlIGpmodR1geMzHLTMxyf6RGzcmn++pYXukPm7P76l6lrMpndDGjihldKbW18HLsgZ1OpdffWrkVTcpmXRUyzb0A0FRads4xYkkjlhx9MpExxo7a8L9uzzrrrFNOOeX222+/6aabJnhAjLGhcg3aWaCXcthXARE1FHYX6eU8XilRU7Ud6ZFYGRdrUmKmH4bA0phYnRILQphe3TuF12/NmNe/WJ4atVYniGyPsjxGtNUdhpymLmT7S19Urw58Ed2o6Z43+9vHy2BYRpJGLKH9UVvAyXS5hw2cTDSiCcgJnDdljB27RlyDdc455/zTP/3Tww8/fOaZZw5sdjVv3rzLLrtsoobH2HGtp0Yv5bGrQAcqBKDqYHeRXsrTqyUoPfjgpE+c2oHVCeEz0eHFaUnxzoQIWtMpV41EeP1W51x0zvUOXSzv8Rv9TbnqVV3KqmJOFTIq39vW6ZRIl4u6XHQOvAbAkVKGYkY81ZpMrFUG5LCIGe90V25xW3nG2FEb/irCHTt2nHzyycM+4eyzz3788cfHd1BHi68iZMcAAvaVaVcBL+cpUycAuQbtKODlPL1ZxdDPa8IrlsawLCZmByCFWBTB2hnTr2R11Eg5uph18m7nrbSulvof0uWCKqR1IesU0lTOkx6SSftIj1/G+iYTowlhtpZGCI/PiCXNeMqIdRpRXinP2HQyRa8iXLp06UjtG47Ogw8++Nxzz5100kkf+9jHpBzcbGf79u1PPPFEb2/vzJkzL7rooo6ODgCNRuPBBx/sP2bZsmXLly8fwyExNqU4mvZWsDNPL+VQsglAbx27CrSzQPsqwxyf8ollcSyJiFkBAIh4xCkd4vQUop7jIlf1E4Y5sNNpq7N8rsfJ9WqvX4aimHOiF4BWqpjVhYwqZJx8mmptnbd0c8BkIiBDUSOaNGJJI5qkRq2/zakIhs1owoh3GrEUF7cYY6ObiL+Q3XjjjT//+c8/8YlP3HbbbY888sj3v//9QQfccccdUsoZM2Y88sgjX/7ylzdv3jxv3rxCoXDJJZdcccUV7jE+n48DFjv2NBS9UsTLedpdoIYCEbpr2Fmk7VlkGoP/kiOAuUEsiYqTY+jwCgBxr1gaw9KomB/mb3tgQGd5d0sdXS2rQtrJp3UxKzxeiqUsoNlsWlLoQkble1Uho/JpshsDX8Tdxsfe/yoAGKYRjhvRDiPWaXR06nIB+18DIL1+d5k8F7cYY8MasdEogL179/785z/fuXPnySeffM011yilfv7zn69du3bevHmHf4J8Pj9nzpwtW7YsXbo0k8nMmzdv+/btCxcuHOn4s84669JLL/385z/f09MzZ84c27YP/1w8Rcimi5qDXQXaVaDdRTQVacKbFbyUpxfzVB7yv7wpMD+ExRGxvEOETABI+bAkJhdHMS94vEwFjgEiVc6rQqZ8YK+nWdXlArnb9RDpSsntKe8U0rqUH7iNzyAyEDZiSRlNmfGkDEUhJNyWE+5GirGkEe+UvkmbkmCM9ZuiU4QAHnzwwUsvvZSIAoGAu/+gYRjf+c53Nm7c+K//+q+Hf4INGzbMnDlz6dKlABKJxOmnn/6///u/IwWsfD5/4MCBRYsWuT8S0Y9+9CMp5VlnnbVgwYIjeFuMTUmFJl4p0s58q8mCrbGnRC/msLNIDTX4YEtiQRjLYuLkmPBICGBWUCyOihVxJH0cqo6cEEY4boTjVnRGKBwmx9GlbP821ToUMecs9AJQShWzqpBW+bQqpAdfmdhqc7qnAcC03FxlxhK6XnPyafeYth6n0YTgyxIZOy4NH7AKhcLll1/+F3/xF3feeedtt922a9cu9/6PfOQj99xzzxGdoKura8aMGf0/zpw588CBA0MPu/POO++4447XXnvti1/84nnnnQdACHH66ac//fTTBw8evPrqq++8886Pf/zjo5+rp6fn2Wef/cIXvtB/z2c+85nDTGZE1Gg0TJPr/GyMaUJvHbuL2FkUXVUAqCnsLuLlAl4ri6EXAwZMnBjCshgtDMMQMIReEMKSKBZHqP+SwEZj8LPY4Ws0Gh6PBwACUQSictZCD6DrVV1I62JWF9IwDCPSYcxbDIAaNV3K6mJO5Xt1Pg09IAg7tsoeVNmD7sWKwuuXsaQRTclYUlZKja43AEAaRjQhY0kjmpTRpPB4J/79MnZ80lo3Go2Bm9AcEcuyhi4ZPyLD54knn3yyVqt973vfCwQCAycgFi5c+Oabbx7RCaSUA2chlVLDvtu//Mu//NM//dOtW7euX7/+3e9+97p161Kp1MaNG91H77///quvvvqyyy4b/d1aluX1euPxeP89gUDgMP+AiEhK+Tb/NBkDoIgydXTXxIEqdddEV5UcEgAKTewsYFcJb5Shh8zMxzxYHMGyKOYGIQRMgQVhsSyGJdEJ3dDmeDDsJ10GQgiEMOsEACBSpZx220Dke7UvgNRcAESaCjlVTOt8RuV7qdFW3KJGTR3cpw7uAyBMS0aTMpowYknYDZ3vdbf7kcGIjCaNWFJGk0YoCp7eZWw8vZ2v9be/+mL4gFUqlSKRyNCZy2q1qke+1HlYs2fP7urq6v+xq6vrgx/84NDD4vF4PB5fsmTJs88++6Mf/WjdunUDH123bl0+nz948OCsWbNGOVc8Hl++fPmNN954RCN0EZFlWdy5nh2FhsLBGh2oUm8NvXUcqMLpC1A1ha4q9lZoZ566h9vCeFYAS6NiaUx0+gAgYOKkqFgWEydGYEr+9h0Xh/NJtxIzkGiV3smxdSnXujLRH9Qdqdb99WprJjGf1sXMwDYQ5Ngq06UyXe6COhmKGfGkGUshlkKtrLtfx6DdqeMpYXFxi7GxpLVWSk3i1/rwAWvRokXpdPrFF19cvnz5wBD361//+kgv5TvrrLNyudzWrVvf+c53HjhwYOvWre9///sBpNPpdDrtrs1yHKd/bu7ll192W3ANrHU9+uijsVhs4FQjY5Oo5lBvHQeq1FXFgQql6+gvSJVs6qqit46eGrpq6K0PcxGJEJgbwJKoODmKDl/rYsDFUSyJiRNCgmPVVCNMa/CVibkep5BR+V7hb+2ZSFrrYkbl0+5Mom60pWldzuty3t73CgDh8cpoyowljXiKGnV3d+r+HhAy0mHGO41IBxe3GJvuhg9Yq1evfte73nXRRRfdeeedjuMA6Orquv3223/yk58c6TV6oVDopptu+vCHP3zxxRc/9NBDV1111dy5cwH87Gc/++53v/vcc88R0QknnPBnf/Zn8Xj8qaeeymQyd911F4Bvf/vbv/rVr0455ZTu7u6HH37YbeXwtt8vY0ejZONAhbpqOFCh3jrl+pZAEZCpU3cNXTV0V6mritqQter9TIGFESyNiiVREei7GHB5h1wcwewgf5tOGzIQkoGQNWch3EpVvtctYjlenxFLASej1R6iV+czTr5HlwoDL0ukZkP1vql63cbx0gjHjXhSRpNmLNXfA0KYVqsRVyxpxlK8coux6WjENg179+694IILXnjhBQCmaTqOI4S49tprv/71rx/FaTZs2LBt27bFixf3z/29+eab+/btO/PMMwHs2rXr6aefLpVKCxYsOOecc9yCXrFYfOKJJ9544414PH7WWWfNnz//Lc/CbRrYmNBEhaboqbUS1f4qKnbrY6LILU1Rdw3dVequwR51ztyUmOHHLL9YEMaisPAYkELMDWJxFCfHRIIvBpwMpVIpHA6P/esS6UrRyfW6G07rSrH129WxVTHr5Hu1e1lic8QrFKTXJ/sanBrRBPp6a8lA2GjtWp0wIh39jeYZY6OY9DYNo/XBchznoYce2rRpUy6Xmzt37oUXXrhy5cqJHNyR4oDFjo67LL2r2pr1666hqVqfi6ZGdxW99UNzgs6oexx4JTr9mB0QswLo9IlOPwwBAKbEwrBYEhNLoggdE/sDTl/jFbDakWOrQlrlep1CRuV6W71MiXSlpAq9KpdWhV5dLoz4fCFkMNrqZRpNylC0/5G2NhDhDsHXPjM2nEkPWKN9Mk3TvPDCCy+88MIJGw1jE6Oh0F2jrip1V9FVpd76ocv66go9NXRV6UAVXTWkG2+xa1TIQqcPKZ+YFcDsgEj60J+eoh7MCoiZATHLj4URYfEU9/FEmJaZmGUmZrU2qC7l3RVaTq5XhiLWnBMBkNNU+bRb2VL5DDmDdqfO63LefvMVADAtIxyX0YQR6TAiHf27U7uLt4xw3IjEZThuhOPc5pSxKeIt/upj23Z3d/fAduo+n2/27NnjPCrGxpIiKtvoraG7hq4qdVUp1zxUu3WXpR+ooatKvTWRa77FLpwhC7MDmBUQs/2YHWy1VgcghUj4MNPvhirM8gs/VxYYAEAI6QYjzF8MgJp1lU87uV6V75HeACVnAwCRqhZ1PuNemajLbSu34Ngq16NyPe7vYmFaMtJhRBMy0mFE4rpcsLtedw+UHq+MdBjhmBGOi2DUCEV5SpGxSTHiN8CGDRuuu+66p59+Wqm2Vbtnn332448/Pu7jYuwI2ZrKtijZVLKRa1DJRtlGyUbJpkJT6L44RUC+Sb01chPVmxVUnYEvMzhdSYGEV8zyo9OPlA/zQsLf15XKEKLDS7ODrdrVTD88Bs/9sbcmPD6zc67ZORcAiPpWaGWcfK8ORt3l81COKmRVIa0KvSqfofbLEqmvx2nrZ8M0QjEZictwzAjFZLXkpA81x5H+oAxGjWBEhiLSjVxe/0S9V8aOX8MHrEwmc+6553Z2dt5yyy3z589vdT0GAKRSqYkaG2NtFKHqoNSkko2yg5KNUpNyDZRsKtoYutUMESoOijZKti42cbCG7hodrMMZdVm6JTHTD3deb6b/0CIqAF4DM/xiVgCdfpHyYXYAJl/Zyt4mIdzV63gHAJDdVMWMu3JL+INGR6d7lG7UdDGri1lVyOhiRjfqbS+iHFVIq0K6/w4ZCMlQTIZirVAVyDsD61jSkD6/9IfdKyJbN0JR3rKasTE0/Mfp6aefrlQqjz322OFcu8fYGHILUbkmlZpwy1H9hah8Y0h9CXA0Sg6VmqLsUKmJkgM3cpVtUbBpaMP0obwGOn2tZemDFlGFLZHyIdW3aD3l595EbHwJyzNg5RbpSlHl026oUv4Qpea4h1G9qopZXcioYlaXsoPzFqCrZV0to+fQxhvCFzRCERmMyGBUBsPaH5a+0sBuW0JI4fVJf0j4AsLrl/6g9AWkLyh8AeHxCf67BGNHaPiA1Wg0QqEQpys2HhxNNSVKTco1W0moZLfiVKGJ5pDykiKUbSr2HVZ0ULZRbFLJFkWb+rokDE1SI2arqEfM9GOWHzMDmOlH1HPoOyZsiVkBzA6KWX7MCYoQr11hk0cIYYSiRiiKuSfC7WVazqtCxv1HBkLkTjIC1KzrUl6VcqqU16UclQtEgz9IVK849QoGTB0KIYU/JANB6Q8Lt47lDwqfX3h8wwzG4xUen/T4hC8gPT7h8QrL2/Zvy8MFMMYGGv7zcPbZZwshnnnmmdNPP32CB8SODTWnbyKviZLtTuS1fiw7aP/tTwAqNsqt6bz+FEXFJko2Ks6hw9q9dXkqaCFkImIhbImEFzMDYlYA/YuopEDCC3cRVadf8LJ0NpUJ2bdSft5JAKC1KuVUIaOKWVXKaX/ISMx0jyStqVpUpTyVC6pSpEpBV0rDRC7SVC3qahHoajuRYQhvQPj8rfKV1y+9AeHxCa9Pev0YJUVJQ5iWtDwwLWF6hGnBtKRpwrCEaUEawjSFaUFIYVkQUhgmDFNIQxgGpISQvB6fHUuG/6iEQqF/+Zd/ueSSS77yla+sWbPG6z3UR5ivImQuR7dm7tx/9xeick0qNoUa0tvAIdScAdN/rbBFJVsUbGqO3AB9dKaAz0TYQtwjwhbCFkIWwpYIW4ha8LRvk+w1xAw/+mf9ZgeEyfMebJqSsrV4y0Wka2VVyrVKWcWcEY4fajFCWtcqulzQlYKuFHWlRLXS0InF1rFKUbWEamn4D6U0hNcnPX5heYTHIywv3PKV5RWWV5gWLEu66epoC1rC8gACgOjbRU6Ynv7ZTGF5+v9uJQwDRtuHXJgWMNxMvmEK+Ra7prdy3jgQhjVOr8xGobWmWCcwxfpgvfrqq5/73OcAXH755YMe4qsIp7WGIk2oK6GImgoOwSE0FJRGQ0MRmopsLRShrqCJGgoOwVZoamig5pAm0dSwNQ1ZKk4A6g5KjluyopLjLp9yExjK9qHDhj5xdD4TYVOELYp7RchC2ETYQtgSIYtC1jDrovwmwhYilghZiHpEyELEg5RPxD309jdIZ2wqEkIGwjIQxozW0g5ybFUuUKWoKgVdKapSgULRgTtSQyldK+lqmaolXavoWknXKlSvtbXjGkorqlVUrXI4QxKmBcMShiEME6YlDAOGKQwPpBCmB26EcktZ/bnKMFpJyDQhJAAhzdaVJiSEdeiKq4G3GRuKiMw175/EAQwfsObMmfPAAw8M+xBfRTjxbE11JZy+WOOmIluh7qaf1p2tA+oKjoat4R5Zc8ghOFq4QUqP3jSzpe0YTXCjmE3UVEIT1RQ0oeJQ0UbJRrHZWiNVtg/r1YflM9xIhJAloh6ETEQ8biFqYIQ6lI1MKfwGwh4RcstXXoQtEfYgZCLqEd4R/6bK6YodL4RpmbEkYsn+WTfSmmolVSroaknXyrpa1tUS1SttqQuAY6tGlepVqtd0vUKNGjXq1KxTs6YbdShnyKlGQER2E/ZbdZYbK+5U4yCGKcSohSsph3nWERECPLM5NRGM7r3+j37uUKF3Yg0fsMLh8MUXXzzBQzmW9IeemnPEkcgh2Irqyo1Eh3UdHIBBqcjRcDRsaqWrvphFDvWdSKPWd6M1Nk2tYbiBTMMmqjuDdoYZZTRvMVBDtApLfcUnhE3EvcLNVcNGIr/p5icR9iBsibgXbpwKe0TI5FoUY0dGSCmCURmMtt1LpGuVVuSqVahR1fWqrFWpXqFhs5RSulmlRoPsBuwG2U2yG+TeaDbJscmxyWmScuDYwzx9/GhFesis5oTFOzYlqWx3MRyNX/z/TcrZj2yOPJPJ2LY9c+bMcRrN5Co7otlAzSENNDVshb6qD+qKFMHWoqmob/oMjb4ptqaCIqoroTQNvQhuZIc++G6VyM1DTeXO0JEmNDW5eaih3WFAadiEpobSaChShIaG0rC1aBIpQn2YX4lH8RvmKH8pBd25Obf4ZCLiQcgSEQthC4Hh/l/zm6IvciHSKlyJsIWIRwRNkqNFKE5XjI0FIdxuWEMfIbuhW0WsQxUsatSpWaNmQzfreKuaNdlNcmxSDrSC3YR2SGl3W0ZymkQExyHSblWstV2jcloVNcd2X5+U07eVlaYBoY36DmBsFNaMSeuH0Pal98YbbyxatOiJJ55Yu3YtgOeee+7aa6994IEHOjo63ANuvPHGHTt2/N///d8kjHT8/fR1kXZGX2s9ZpHI0XBGjERH9ytjvH7RCAGvAQPwSGEZZAj4DEiBoCnCJsKeVkUqYlHIEkM7mffN5R0qPrkzeu4koG+01uccoRibTMLyGpbXCMdGOoAcm+wGNRtkN3WzDqdJjk22TY4Nt47lpivHJuWQUuQ0xzESqeEqWFqRHm1Ok5TG0GcdEaKJrtWxw0MgY+V7QqvePVkDaAtYROQ4ju6bj89ms48++mij0ZiMgU20p3vp0W5ZUlRXUARbtyKRG5uOjUjklcIUsAx4JKSA34AU8EhYBkwBjxT9R3oMsqQwAa85KOYMH3pGm8uzOCgxdmwSpiVMC/5hql8jIa2gHFIKWrt5ixwbIHIcaE2koBRa1SkNuLFJu888VL4iIjUg0xCRPTjikBq5vkX0Fgv5h9Ka1NvLYVOBVsNP+x6jiMictWASB8BtfwBgd4He8xvlaPlWoWd8I5EJWBMViYYyJSwpPBJSkN+UEvBI986+s5tCCvJIWFKYEkETob5l6ZIzFGPsMAhpQBqCF4Wz8ae1rteH70UyMThgAUBNvcX+dEO9zUhkCFj9kchA+1qjI0grbioyBXwGLEOYAqaAKeE3WzfcMGQKMiX8hnu7NZi+I4UpyGMMM7s37Ps+sj8mxhhj7LjEAQsATukQ9/+ZvPtlp6qNQZHIK4Uc60jkN4QpyRTi7UQir3FEdaPRD+XYxBhjjI2lYQJWoVBIp9MAisUigGw2a/W1053catu4uniB7CnptDP4D6S/RDQwEvkMWBJu9OmPRD43fgkMjEQ+41Bg8hoY9bK4QTgSMcYYY9PVMAHr/PPPH/jjihUrBv74vve9b3xHNHkunEeWT/oMYQiyJA571qwfRyLGGGOMAYMCVjQavf7660d/wsKFC8dzPJMp4aVgwI1BHIYYY4wxdvTaAlY8Hv/qV786WUNhjDHGGDs28P7ejDHGGGNjjAMWY4wxxtgY44DFGGOMMTbGOGAxxhhjjI0xDliMMcYYY2OMAxZjjDHG2BgbLWA99thjV1xxxdlnn/2lL30JgNb6tttue+GFFyZqbIwxxhhj09KIAeub3/zmOeecs2HDht7e3j179gCQUv7hD3/41re+NYHDY4wxxhibfoYPWN3d3TfccMM//MM/vPjii5dcckn//eedd96TTz45UWNjjDHGGJuWhg9YGzZsME3zy1/+smjfnHj+/PkHDhyYkIExxhhjjE1Xwwcsx3E8Ho9hGIPuT6fTHo9n/EfFGGOMMTaNDR+wVq1alc/nH3vsMQADi1j33nvv6aefPkFDY4wxxhibnoYPWEuWLPnwhz988cUX33HHHV1dXeVy+fe///2HPvShxx577LrrrpvgITLGGGOMTS/mSA/88Ic/vOKKKz7/+c8TEYAHH3wwEoncfffd55xzzgQOjzHGGGNs+hkxYEUikQceeOCVV17ZuHFjpVKZOXPmn/zJn8RisYkcHGOMMcbYdDRiwHItWrRo0aJFEzMUxhhjjLFjw2id3Dds2PDXf/3X73//+/s7uX/jG9/Yvn37RI2NMcYYY2xaGjFg/fu///t73vOe3/3ud3v37u3v5P74449/+9vfnsDhMcYYY4xNP8MHrIMHD1577bU33HDDzp07L7vssv77zz///CeeeGKixsYYY4wxNi2N2MldSnnzzTdLKQf2wXrHO96xf//+iRobY4wxxti0NHzAajabXq/XNAcvgc9kMpZljf+oGGOMMcamseED1sqVK/P5vDsbOLCC9eMf/3j16tUTNDTGGGOMselp+IC1bNmyCy644KKLLrr77rt7enpqtdof/vCHj370o//zP/9zFJ3cn3nmmXPPPXf58uXXXHNNpVIZesDnPve5M888c/ny5RdddNHWrVv77//Nb37z3ve+d9WqVbfccovW+kjPyxhjjDE2KUbsg3Xvvfd+8pOfvPLKK90ff/GLXwSDwTvuuOMDH/jAEZ2gVCqdd955t95667p166655povfOELd9xxx6BjVqxY8ZnPfCYUCt1///3r1q3bs2dPJBLZsWPHZZdddu+99y5atOjSSy+NRCLr168/0rfHGGOMMTbxhLsTzkheeumlTZs25XK5uXPnrlu3LpFIHOkJ7rrrrnvuuWfjxo0AXnzxxTPOOKO7uzsUCg17MBH5fL6nnnrq1FNPve6669Lp9A9+8AMAv/jFL9xLGkc/13333ffII4/ce++9RzpI99TVajUYDB7Fcxlj00ipVAqHw5M9CsbY+NJa1+v1QCAwWQMYvoJ1//33X3bZZdlsdtmyZcuWLXs7J9i+ffuaNWvc28uXL9dav/baa6eccsqgww4cOJBOp3/605+uWLFi+fLl7hMvuOAC99E1a9bs3r270Wh4vd63MxjGGGOMsQkwfMCKRCKmaY5J7uvp6Rm42U48Hu/p6Rl62D/+4z9u3Lhx//79d9xxh3uhYk9PT//Wh/F4nIh6enrmzZs3yrl27979y1/+csGCBf333HXXXWvXrj2ccRJRrVYbvZ7HGDsGVCqVgdfuMMaOSW4F66gXcPv9fsMw3s4Ahg9Y73vf+2Kx2K9//euPfOQjb+fVAUSj0YEL20ulUjweH3rYXXfdBeDll19eu3btSSedtGbNmmg0Wi6X+58FYNgnDrRo0aJ169bddttt7o+mac6dO1fK0bYD6kdEUkqeImTs64bOUgAAIABJREFUmEdEI61SYIwdM7TWY1UqOjojLnJfv379pz/96U2bNp155pkD1yvE4/Ej6tSwYMGC/ubvXV1d1Wp1/vz5Ix188sknL1++fNu2bWvWrFmwYMHu3bvd+3ft2pVKpd7yd6IQIhQKLVy48PCHxxhjjDE25oYPWPv27bvpppsAfP3rXx/00Nlnn/34448f/gkuvfTSW2655YUXXli5cuXtt99+7rnnplIpAP/5n/8ZDAY/9KEPdXV1/f/t3XmUFtWdN/Bb+/Lse9Ms0iKbvFFBg86oEAFhZIljFBgnCgTFECVMZoxKNG7jkRMcMzrOGEckigueSZAZZFTEcDADnqBRQCCyit3S9PLsW+3r+0c1xWPT3ULT3Q/Qv8/h9Km6td16zNP9zb23bpVKpZEjRyKEtmzZsnv37vHjxyOEbrvttttuu+2+++6Lx+P/9m//dtttt3XrBgEAAAAA+lrHAWvo0KGfffZZh5tO9+mbIUOGPPPMMxMnTmRZNh6P//d//7dTvnnz5lgsNmvWrEwmM2vWrEKhgOO4z+d74YUXnCHwkyZNWrBgwahRoyiKuuyyyx5++OHTui4AAAAAQLV8Y5qGfD7/q1/96u67777gggsQQrZt67pO0/SZX0bTNFEUuxhEJQiCbdsnpzdFUVRVDQQCp3IVmKYBAPCtYJoGAPqDs2uahmKx+NRTT914441OwNq8efPUqVNTqZTTqXcmaJruOqh1Nr6KZVmWZc/w6qdoV2ovojCaoCicogmaISiaoGmCpnGKIigapxmyB7ImAAAAAM57nQ5y729KanlvZp+CNJqgaJwi8Y4/GQIjGJJ2whZN0CROEBhBEzRD0BRBMwRNExRDMM5PhqAJ/Iwe8gQAAADAuQgCFkII5eT8/HeWlLSyW4JjGIXTNEkxOE0RFEPQFE7RBEUTNEVQDE7RBEMRJI3TNEnROE0TVIdndgIZgRFtyawthHUcyJx9+uqmAQAAANBbIGAhhFCzkKxMVwghy7ZVU1VNtdzZMSehCcrNWxRB0gRDH89kTrcj0xbOaJqkKJzGO5nqsF0j2cmBjMRJAiOcTMZRLIZgykQAAADg7NJBwNq2bZsz2fru3bsRQhs3bvT7/e7WaDR6zTXX9Fn9+saY2Mjb/t/szV9tlS1FM1Td0g3LPN2TaKaumTrST3V/EiedBEY57Vh42wLt/sSdnyRNMhROkZ30NnYRyI73YJ5oJGNJtrNgBwAAAICe0kHAWrZsWeXq/PnzK1cnTJjwf//3f71bqT6HIezOS24Lk4GSKbiFhm1qpqaamm5qqqlphqaaulNi2qZpmZqpOauqqSmGZqPTm4/fsAzDMiRDPvVDCJygcYo5nqJo4kSiInGCwHCaPNHWxZEMhjqYxf7kQEZgBIETHfZasiSDY6c0FT4AAAAAXN8IWIlE4p133un6gEgk0pv1qabxNeMQhemWrpm6Zmq6pauGppmaVlGimbphGR0efnIgM23LsNoKteP/1OOrpn3aL0gyLVO2TNlQTnH/kwMZgRMERhxv5aIqAxlDMERHWYoiqIq+Ttp9ypIjWZ7ieIr3kBxHcZDDAAAAANc3AhbHcTNmzKhWVaouzIZOcR4swzI0U1dNteJnW64yLdO0TSdCqYamWZpiKFZH75BuO4ml6YauWZpu6pqla6Z2/Gy6ZuqapbVlO1M37NPutTzdQEbiJE1QDE5TbSPJqLZuSqJtAFnbOLPjYasykDEkzREcT7X9Y0mOJzkf7eUpDgaKAQAA6G9gkHt3kDhJ4iRPcae4f7tAZlqWE8L0461ZlYFMNTSzkyzVRa+lVtFxebzXUrVRB8Gu63oaliEhGamntD9D0BzJchTHkxxPcRzJ8RTnpT08xXEE5471cvof23YgOS/tdUIYR7Je2kt1MiMGAAAAcO6Cv219oRuB7HgI66CRTKtsKmtrJFOtkzocbWRX9myqRtuC01qmmrpuapql66aumm3tZKcbyJwkV1BLJ2/CMYInWQ/FcRTPU6yH8nAk46E8HMXyFE9iJwbsExjBU21tXW7Tl7PspT3Q9AUAAOBcBAHrbETiJIkjhFC3G8mcQGZapuX2V36j17KDQIYQ0k1DtzTN1FVL14+nLs0yNFN1npE8Htc0zTIUXekikFm2KeiioIsdbqUJykPyHMUdz17s8ezFceSJ/kQcw1mScZu+eIrjKM5HezmS9dIeCu947jEAAACg6iBgnSe612tp2uY3k1kHvZambZq2KRuKfdJIMtXUJENWdKWsCZIuS4Ys67JsKKIudd1BqZm6ZhbzarHDrW7Po4/2Hs9VLNfWC3kifjlNX84/H+2tbPryUDwMugcAAFBFELD6KSeQnfr+lm1VPlCpmbqbpWRDlnRZ0iXV1Nz9TctULU3SZUETJV1u28eQZV0WdKmzJzEdbs9jC0q22+Q8F+mheC/tcSIXT7I8xbMU66M87h3hGM5RnIfkeIp3HnXkKc5Pe/2MnyFgrnwAAAC9DgIWOCU4hrMky6KuXrxtWqZqapIuS4YkG4rgNGvpsqTLoi7p1ok5WN2mL0mXJENxEpisy5KhCJrYRdOX+1xkRs6dvLXDQfc8xXLkieFcDEn7aK+P9gaZQIAJ+GhvgPXDQHsAAAA9C/6ugB5D4ASPczzFIRQ+eathGbKhOHmrrAmycbxZS5dFXXRnsjBtS24LXicavZx2MlGXup5hv4tB9wSGeyiPn/EFGL+f8fppn5/xeSje2cqQdJAJBJmA18lerD/A+KGTEQAAQLdBwAJ9hMRJp+mow62qoTntXk7kEjRBOp7AKod/aZYu6bKsy5IuibosmydayGRd7WIyfdO2Slq5pJWPlZsrq+QkLT/jCzA+Z9npQ8Qx3EPxPtobZANBNuDUvLPKAwAAAO1AwAJnBYakGZIOdbSp2z2PZU3oetC9YRk5JZ9T8t+oCUH7aK+X9gSZQJANeGlPkPE7o7togvYzbUkrwASCTAC6FwEAAHQI/jaAs12P9DwalllSyyWt7PwsquWSVlIN7eQTqqamyrmMnEOo0SnBMMSTngDr89MnGroqB3VB9yIAAIB2IGCBc1sXPY+WbSmG6rRmiZoo6GJJLRfVUlkTnGnAVFMra4KgiWVNKCjFoloqqKWTn3C0bSTqoqiLzajVLcQxzEN5nIauEBtwGr2c1IVjuJ/2BVi/89yin/EFGT9LdvV8AAAAgPMMBCxw3sIx3JkWq125ZduiLpY1oawJgibklWJBKYq65KauolosKCVnh4JSLKrCyaO7LNt2dmgRTswlQeCEj/K4Y7aCrD/IBmmcQscbuiJcOMKFI1wIWrkAAOD8BgEL9Ds4hp3c6GXZlqhLZU3IK8WiUmyLX7po27ZpW4ImltRyUSuV1FJJFYpqqcNXaJuWWVBL7R5j5Eg2wPhDXCDEBMNcKMQECJxwWrmifDjMhaNcOMKFTmtaMgAAAGc5+J0OAEII4RjupK5ab41bqJlaSRXctq6CWszJBWdYvW4aRa1U0oSyWiqq5aJWLinlyhH3LtlQZENpFVPOKobwAOsLs6EwF4ywoTAXZAjGeWgxyAaiXDjMhWJ8lIMuRQAAOJdBwAKgUzRBR/lwlP/G4HrV0MqaUFCLRbV4vBuxbeSWO6iroBQLalHQxIJabDd3l42sglIsKMWvCm0lDEEHGX+YC0e5UJgPB+kAhrXvUgyyAXjvNQAAnEMgYAFwehiSZsj2qUvS5YJaPHlQl41sp3sxp+SzciGv5Etaud1LHVVTS0qZpJRxVkmcDHPBEBOMcKEwFwyyQRIjKIIKML4gE4AuRQAAOCfA72gAesDJo+lNyyxpQkktFdVySS3l1UJeLpq26Ux5mpNyGTmfk3NZpdDuuUXDMlJiJiW25S0MYc5cXBEuHOFDUS7CkSyOYQHGH2ZDYS4U5kJhNsSSTN/dLQAAgG8DAQuAXkHgRIgNhNiAW+I8vZhXCjk5n5FzWTkn6TJCSDLkrJzLSvmsnCuopbImVJ7HRm2PKzYen4O+fZci48cQxlNchAvH+VjCE4vyYQIj+vJmAQAAtAMBC4A+4j69OMQ/yClRDa2gFjNyLifnMlKupJUt21IMJacUcnIhq+Tzcr6oltvNQX9yl2KIDYTZUIyPxviwn/ERGB7mQnE+5ozfCrHBvr5VAADo9yBgAVA1DEknyFjCE3NWLdsqqqWsnM/KuYJSzCl5xVAN2ywoxZyczymFnJLPyR10KaalbFrKHsx9iRBiCDrKR2JcJMZHonyEIWincSvKheOeWJyPwuAtAADoA/CrFoCzBY7hITYYYoMXheqcEkmXM3I2J+cLajEvF4taybZtt0uxoBYLSrFdE5dqak3llqZyi7PKkWzCE4vzsSgfirJhkqCc+becsBVkAhgGDycCAEDPg4AFwNmLp7gh1CC3S1EztbxSzMi5olIsqMWsnDcsQzXVnFxIS5m0lMvIGdlQK88gG0pDsbGh2IgQInEiwoVjXCTmica4CE9xFE7F+EjCEwtzoYQnzhB0FW4SAADORxCwADhn0ASd8HyjS7GgFJ2uw4yUy8k53TKc9q2UmEmJ6YySNytm4TIsMymmk2IaZRBCiCPZKBeOcOGEJxbjoxROBtlAjI/E+GiMj0DjFgAAnAkIWACcq3AMd6ZpQKgOfXMIV0pKZ6W8hcyCWk6LmaSYzsq5dp2JsqE0lpudhxMxhAcYb1vY8kSDjJ8m6BgXGeCtSXhiUS5M4PBYIgAAnAYIWACcJ9oN4dJNPacUMnIuLaVbhJRiKLIup+VcRsqkpGxGzlUOlreR5bxF8UihASHEkHSciyU80YQnFuEiNEFFuFDCExvgrYFh8gAAcCrgFyUA5yeKoI73J45Ex8fLp6VMUkxnpJxhG3mlmJGyaSmTlrJFrVQ5v7xqaI3lpsZyE0KIxIkoF0l44jWeWIyP0ATlzAER52O1vhoYtgUAAB2CgAVAv1A5Xt6y7aJaTEmZlJjOSLmiVtIMPa/mM1I+JaWTYqpypLxhma1iqlVM7UYIQ1iA8cU9sVpvTY03xhFcgPEnPLG4JzbAG/dQnurdHwAAnF0gYAHQ7+AY5nQmjgxfhBDSTC0j51JiOiPn0lJGMdSiWnaSVlLMVM4sbyPb6Uk8lDvihK2EJx73RBN83EvzPtrrhK04H4XZTQEA/RwELAD6O5qga701td4ahJCN7KJaSkvZViGVltJFtSzrckbJpcRMi5DMKjm3J9ENW84Ep+6EW3FPNMKGvTRf440n+PgAb8LP+Kp4dwAAUBUQsAAAJ2AICzKBIBMYHroQISTrcvr4yK20lJUNJSVlkmIqJWWyUs60LffAygm3GIJJeKIJTzzhiUW4EE/xNZ5YjI8l+FiEC8HsDwCA/gACFgCgU1zFyC3dMnJyPimmW4TWlJRRTDUjZZNiOimlU2Km8plE1VSPlpqOlpoQQhRO1XhiCW+8xhOPcEGe8kDYAgD0BxCwAACnhMJJ57HES+IXW7adk/NJKZ2W0i1CUjaUglpKi5lmobVVSCum4h6lW7o72xaJkzE+kuBjCU8swUc9jBfCFgDgfAUBCwBw2nAMi/LhKB925oAoa0JSTKfEdLPQWtLKJaWUlDKtYrpVTEq67B5lWEaLkGwRkgghEifbkpY37ry3J8ZH4nys1lsDYQsAcB6AgAUAOFM+2uujvc4Ep4ImJqV0UkglpXRBKUqGnBIzzUJrs9AqaKJ7iGEZTUJLk9CCkojEiQgbcmZ/iPNRL+Ot8cQSfLzGmwgyfghbAIBzEQQsAEBP8tIeL+0ZFhyKEFIMJSVl0lKmWWjNSvmyJrSKqVYx2SqkBb0ybJlJKZOUMnvT+0mMiPKRGm+8xhOP8hGOYGN8ZIC3ptZbE+FDGIKwBQA4N/RRwJIkqb6+fsiQIT5fxw9s5/P51tbWgQMH+v1+p8S27UKh4O7AsizHcX1RVwBAD2FJdoh/0BD/oMsR0k09LWdbhFbngcSyVm4VUq1iqlVMV061Zdht85oihHCMiHLhGm+8xhOL81GO4tzXI8b4CI7h1bszAAD4Fn0RsN5///3bb7/9ggsuqK+vf+655374wx+22+Haa6/du3fv4MGDjx49umTJkieffBIhlE6nE4lEKBRy9rn//vuXLVvWB7UFAPQGiqDc2bZ0y0hLGTdsiZqYbJsJIpOV8+4bqS3bTEnplJTegxCGsAgXivHRhCc2wBv3Uh5nOe6J1XjiELYAAGebXg9YpmkuXrz4+eefnzNnzp/+9Kcbbrjhxhtv9Hq9lfssXbr0pptuIkny8OHDY8eOnT59+tVXX40QIkkyl8v1dg0BAH2MwskTYcvUk2K6VUwlxVRGzgm62Cqmk0IqKaaKatkNWzayM3IuI+f2Zw9hCAtzwYQnVuNJJPiYl+bjnlicj9V441EuDO+iBgCcDXr9N9H27dtFUbzlllsQQn/91399wQUXvPfee3PmzKncZ/bs2c7C8OHDhwwZcuzYMXdTuVwmCILn+d6uJwCgKiiCGuSvHeSvRcdbtpJiqkVIZaSsaIhJId0qppNSKq8UKieRz8r5rJzflzmEISzI+mu88Rgfq+FjXtoT4cIJTyzBx+KeKEuy1bw3AEA/1usBq6Ghoa6uDsfbGvAvvPDChoaGznb+05/+1NzcPHHiRGfVNM1Ro0bl8/mxY8e+/PLLI0eO7PpahmHkcrkdO3a4JWPGjGFZ+A0LwLnBbdkam0DOVFvNQmtKSifFdFkTUmKmVUy1SqmclK9s2corxbxS3I8OI4S8lCfhicU90QQfCzABP3Pi9YhBJgAPJAIA+kyvByxRFBmGcVd5nhcEocM9jx49euutt/77v/97TU0NQigYDDY2Ng4cOFBV1aVLl86dO/fzzz/v+lqNjY0ff/zxnXfe6aySJPn000+PGzfuVOpp27Ysy5ZlffuuAIA+wSCqjhtcxw22wnZOyaXkTFrOpqSMbMgZJZ+WMmk5k5KzVsUbewRdFArikUIDQojCyQgbinHRGB+NcWEv5YlxkRgX5S12oD0Qh7AFwHnNsixVVU3T7N7hPM8TBHEmFej1gJVIJPL5vLuay+Wc/NROU1PT5MmT/+mf/un22293SmiaHjhwIEKIYZjHH398wIABmUwmGo12ca26urrp06e//vrr3ainbdsEQXg8nm4cCwDobQG/vw4NRc5LppViSsqkxHSLkGx7NbWYTknptJStfGOPbhmtUrpVSqMsIjA8wofjfCzBx4KUP1D2h7lgnI9FuHCEC4XYYNVuDADQOyzLoiiqikOMej1gXXbZZYcPH87lcuFw2DCMTz/99LHHHmu3TyqVmjp16sKFC//hH/6hw5Mkk0lIPwAAhBCGsBAbDLHBkeGLbNsuaqWkkGoV00kxLejlrFxIiZmklE5JGbliEnnTtlJiJiVm/oL2YwjzM94oH41x4RgXCXEhH+2J8pEYH4nz0TAXpmCYPADgjPX675GhQ4dOnz590aJF99577+rVq4cPH37VVVchhN588801a9a8++67hmFcd911DMNEIpGVK1cihK666qpLLrnk7bffbmxsHDNmTCqV+ud//ud58+bBPFgAgEoYhgWZQJAJjIwMRwiJupQS00kxnZIyeaVQVEpJKZOS0kkpU1JKlcO2imq5qJaP5OsRQiRGhPlQjItE+Eicj/hpb5ANxvhonI9EuYif8cEcEACAbuiL/6P26quvPvHEE4888siIESM2bNjgFA4aNMhJWpZlXXPNNQghd3B6XV2ds8OGDRvWr18fDAbvueeeRYsW9UFVAQDnLg/F1wUvqAtegBDSLSMn55Ni2hkjL+hiVsolxXRSSqfEjGmfGJZh2KbTuOWsUjgV5cMJPhbhQ3EuxlGsn/ZF+XCYC0e5cJQPE9gZDcsAAPQTmO0++nzue+ONNzZt2tTtMViSJEEvJADnH8u2imrJGbbVKqayQk6ylbSYSYrprJyrnG3rZBzJRrlwhAtH+FCUDXto3k/73bwV5kLQnwjA2cmyLEVRzucxWAAAUF04hrvDthBCrbmkjCspKZORsjmlIOhCRsqlpWxGyqXljGbqlcfKhtJYbm4sNzurPMVH2FCYC4XZYJQ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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "# Extract mean and standard deviation from \n",
    "mean_π_iters = cat(mean.(results.posteriors[:π])..., dims=2)\n",
    "vars_π_iters = cat(var.( results.posteriors[:π])..., dims=2)\n",
    "\n",
    "plot(1:num_iters, \n",
    "     mean_π_iters', \n",
    "     ribbon=vars_π_iters', \n",
    "     xscale=:log10,\n",
    "     xlabel=\"Number of iterations\", \n",
    "     ylabel=\"Free Energy\", \n",
    "     size=(800,300))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "Plot the evolution of one of the component means over iterations of variational inference, including its variance.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: robot arm localization\n",
    "\n",
    "A manufacturing company has a robot arm with servo motors that rotate the joints. The engineers at the company want a probabilistic description of the location of the arm in the world frame (i.e., Cartesian coordinates). They want to be able to do this from the measured angle at the joint. This is an example of a Cartesian to polar coordinate transformation, described by the following function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f(x) = [atan(x[2],x[1]);\n",
    "        sqrt(x[1]^2 + x[2]^2)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nonlinear transformations of random variables are challenging, because they can drastically change the shape of a probability distribution. For example, suppose we have a random variable $x$ that is Gaussian distributed: $x \\sim \\mathcal{N}(x | \\mu, \\Sigma)$. The new random variable $y = f(x)$ will not be Gaussian distributed. We can visualize this by sampling from $x$ and applying the transformation to each sample. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D = 2\n",
    "μ = ones(D)\n",
    "Σ = 1/2 *diageye(D)\n",
    "\n",
    "N = 10_000 \n",
    "x_samples = rand(MvNormal(μ,Σ),N)\n",
    "y_samples = hcat([f(x_samples[:,i]) for i in 1:N]...)\n",
    "\n",
    "p1 = scatter(x_samples[1,:], \n",
    "             x_samples[2,:], \n",
    "             color=\"black\", \n",
    "             alpha=0.5,\n",
    "             xlabel=\"x-coordinate\", \n",
    "             ylabel=\"y-coordinate\", \n",
    "             xlims=(-2.,4.), \n",
    "             ylims=(-2.,4.))\n",
    "\n",
    "p2 = scatter(y_samples[1,:], \n",
    "             y_samples[2,:], \n",
    "             color=\"black\", \n",
    "             alpha=0.5,\n",
    "             xlabel=\"angle\", \n",
    "             ylabel=\"distance\", \n",
    "             xlims=(-4., 4.), \n",
    "             ylims=(-1,5.))\n",
    "\n",
    "plot(p1,p2, layout=(1,2), size=(800,400))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution of the transformed samples looks like a triangle, which is different than the elliptic shape of a Gaussian distribution. \n",
    "\n",
    "When models have nonlinear operations, we are often faced with a computation-vs-accuracy trade-off. We can spend a lot of time and effort to obtain an accurate description of the transformed random variable or we try to obtain a fast, cheap approximation. For example, we could approximate the transformed variable $y$ with a Gaussian distribution. This is not exactly the same as variational Bayesian inference, because it does not necessarily employ a prior distribution and a likelihood function. But it is similar in nature in that we want to optimize an approximation with a pre-specified alternative distribution.\n",
    "\n",
    "Suppose the manufacturing company provides you with an angle measurement of $0.5 \\pi\\, (\\pm 1.0)$ and a distance measurement of $0.5\\, (\\pm 1e-3)$. We can infer a Gaussian distribution over the 2-dimensional coordinates. In this case, we also know the inverse function, so we can test against that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "@model function demo_nonlinear(z, μx,Σx,Σz)\n",
    "\n",
    "    x ~ MvNormalMeanCovariance(μx,Σx)\n",
    "    y := f(x)\n",
    "    z ~ MvNormalMeanCovariance(y,Σz)\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To incorporate the known nonlinear function as a factor node in the model, we must add a \"meta\" specification that selects the type of approximation. There are a few options for nonlinear functions:\n",
    "- `Linearization`: the toolbox will automatically perform a first-order [Taylor series](https://en.wikipedia.org/wiki/Taylor_series) approximation. This is a general technique, but suffers from a lack of accuracy. \n",
    "- `Unscented`: this refers to the [unscented transform](https://en.wikipedia.org/wiki/Unscented_transform), a popular technique that approximates the result of the transformation with a Gaussian distribution. \n",
    "- `CVI` (Conjugate-computational Variational Inference): this is an advanced technique that uses both variational inference and importance sampling to approximate the transformed variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:03\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Inference results:\n",
       "  Posteriors       | available for (x)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "demo_meta = @meta begin\n",
    "    # f() -> Linearization()\n",
    "    # f() -> Unscented()\n",
    "    f() -> CVI(MersenneTwister(256), 1000, 10, Optimisers.Adam())\n",
    "end\n",
    "\n",
    "μx = zeros(D)\n",
    "Σx = diageye(D)\n",
    "Σz = [1.0  0.0;\n",
    "      0.0  1e-3]\n",
    "\n",
    "inits = @initialization begin\n",
    "    q(x) = MvNormalMeanCovariance(μx,Σx)\n",
    "    μ(x) = MvNormalMeanCovariance(μx,Σx)\n",
    "end      \n",
    "\n",
    "z_i = [0.5π, 0.5]\n",
    "\n",
    "results = infer(\n",
    "    model          = demo_nonlinear(μx=μx, Σx=Σx, Σz=Σz),\n",
    "    data           = (z = z_i,),\n",
    "    meta           = demo_meta,\n",
    "    initialization = inits,\n",
    "    iterations     = 10,\n",
    "    returnvars     = (x = KeepLast(),),\n",
    "    showprogress   = true,\n",
    ")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 3.061616997868383e-17\n",
       " 0.5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polar to Cartesian transformation\n",
    "f_inv(y) = [y[2]*cos(y[1]),\n",
    "            y[2]*sin(y[1])]\n",
    "\n",
    "# Cartesian coordinate of point\n",
    "x_i = f_inv(z_i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px = convert(MvNormalMeanCovariance, results.posteriors[:x])\n",
    "p1 = contour(range(-2,5, length=201),\n",
    "             range(-3,4, length=201),\n",
    "             (x,y) -> pdf(px, [x,y]),\n",
    "             color=:blues,\n",
    "             levels = 3,\n",
    "             xlabel=\"x-coordinate\",\n",
    "             ylabel=\"y-coordinate\",\n",
    "             xlims=(-2.,5.),\n",
    "             ylims=(-3.,4.),\n",
    "        )\n",
    "scatter!([x_i[1]], [x_i[2]], label=\"inverse measurement\")\n",
    "\n",
    "pz_i = MvNormalMeanCovariance(z_i, Σz)\n",
    "p2 = contour(range(-π, π, length=201),\n",
    "             range( 0,2, length=201), \n",
    "             (x,y) -> pdf(pz_i, [x,y]),\n",
    "             color=:reds,\n",
    "             levels = 1,\n",
    "             xlabel=\"x-coordinate\",\n",
    "             ylabel=\"y-coordinate\",\n",
    "             xlims=(-π,π),\n",
    "             ylims=( 0.,2.)\n",
    "        )\n",
    "scatter!([z_i[1]], [z_i[2]], label=\"measurement\")\n",
    "\n",
    "plot(p1,p2, layout=(1,2), size=(800,400))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have produced a Gaussian approximation of the inverse of the nonlinear function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "Try out some of the other approximations for various angle and distance measurements. What works and what doesn't?\n",
    "\n",
    "---"
   ]
  }
 ],
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