{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Basics\n",
    "\n",
    "*You are seeing the\n",
    "notebook output generated by\n",
    "[Literate.jl](https://github.com/fredrikekre/Literate.jl) from the\n",
    "[Julia source file](https://github.com/JuliaOptimalTransport/OptimalTransport.jl/blob/master/examples/basic/script.jl).\n",
    "The rendered HTML can be viewed [in the docs](https://juliaoptimaltransport.github.io/OptimalTransport.jl/dev/examples/basic/).*"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Packages\n",
    "\n",
    "We load the following packages into our environment:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "PythonOT"
     },
     "metadata": {},
     "execution_count": 1
    }
   ],
   "cell_type": "code",
   "source": [
    "using OptimalTransport\n",
    "using Distances\n",
    "using Plots\n",
    "using PythonOT: PythonOT\n",
    "using Tulip\n",
    "\n",
    "using LinearAlgebra\n",
    "using Random\n",
    "\n",
    "Random.seed!(1234)\n",
    "\n",
    "const POT = PythonOT"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Problem setup\n",
    "\n",
    "First, let us initialise two random probability measures $\\mu$ (source measure)\n",
    "and $\\nu$ (target measure) in 1D:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "M = 200\n",
    "μ = fill(1 / M, M)\n",
    "μsupport = rand(M)\n",
    "\n",
    "N = 250\n",
    "ν = fill(1 / N, N)\n",
    "νsupport = rand(N);"
   ],
   "metadata": {},
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we compute the quadratic cost matrix $C_{ij} = \\| x_i - x_j \\|_2^2$:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "C = pairwise(SqEuclidean(), μsupport', νsupport'; dims=2);"
   ],
   "metadata": {},
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Exact optimal transport\n",
    "\n",
    "The **earth mover's distance** is defined as the optimal value of the\n",
    "Monge-Kantorovich problem\n",
    "$$\n",
    "\\inf_{\\gamma \\in \\Pi(\\mu, \\nu)} \\langle \\gamma, C \\rangle =\n",
    "\\inf_{\\gamma \\in \\Pi(\\mu, \\nu)} \\sum_{i, j} \\gamma_{ij} C_{ij},\n",
    "$$\n",
    "where $\\Pi(\\mu, \\nu)$ denotes the set of couplings of $\\mu$ and $\\nu$, i.e., the set of joint\n",
    "distributions whose marginals are $\\mu$ and $\\nu$.\n",
    "If $C$ is the quadratic cost matrix, the earth mover's distance is known as the square of\n",
    "the **2-Wasserstein distance**.\n",
    "\n",
    "The function `emd` returns the optimal transport *plan* $\\gamma$"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "γ = emd(μ, ν, C, Tulip.Optimizer());"
   ],
   "metadata": {},
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "source": [
    "whilst using `emd2` returns the optimal transport *cost*:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.0014877814134910635"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "cell_type": "code",
   "source": [
    "emd2(μ, ν, C, Tulip.Optimizer())"
   ],
   "metadata": {},
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Entropically regularised optimal transport\n",
    "\n",
    "We may add an entropy term to the Monge-Kantorovich problem to obtain the\n",
    "**entropically regularised** optimal transport problem\n",
    "$$\n",
    "\\inf_{\\gamma \\in \\Pi(\\mu, \\nu)} \\langle \\gamma, C \\rangle + \\varepsilon \\Omega(\\gamma),\n",
    "$$\n",
    "where $\\Omega(\\gamma) = \\sum_{i, j} \\gamma_{ij} \\log(\\gamma_{ij})$ is the negative\n",
    "entropy of the coupling $\\gamma$ and $\\varepsilon$ controls the strength of the regularisation.\n",
    "\n",
    "This problem is *strictly convex* and admits a very efficient iterative scaling scheme for\n",
    "its solution known as the [Sinkhorn algorithm](https://doi.org/10.1214/aoms/1177703591).\n",
    "\n",
    "We compute the optimal entropically regularised transport plan:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "ε = 0.01\n",
    "γ = sinkhorn(μ, ν, C, ε);"
   ],
   "metadata": {},
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can check that one obtains the same result with the Python Optimal Transport (POT) package:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "5.79577190277028e-12"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "cell_type": "code",
   "source": [
    "γpot = POT.sinkhorn(μ, ν, C, ε)\n",
    "norm(γ - γpot, Inf)"
   ],
   "metadata": {},
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can compute the optimal cost (a scalar) of the entropically regularized optimal\n",
    "transport problem with `sinkhorn2`:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.00599172263125863"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "cell_type": "code",
   "source": [
    "sinkhorn2(μ, ν, C, ε)"
   ],
   "metadata": {},
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Quadratically regularised optimal transport\n",
    "\n",
    "Instead of the common entropically regularised optimal transport problem, we can solve the\n",
    "[quadratically regularised optimal transport problem](https://doi.org/10.1007/s00245-019-09614-w)\n",
    "$$\n",
    "\\inf_{\\gamma \\in \\Pi(\\mu, \\nu)} \\langle \\gamma, C \\rangle + \\varepsilon \\frac{\\| \\gamma \\|_F^2}{2}.\n",
    "$$\n",
    "One property of the quadratically regularised optimal transport problem is that the\n",
    "resulting transport plan $\\gamma$ is *sparse*. We take advantage of this and represent it as\n",
    "a sparse matrix."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "quadreg(μ, ν, C, ε; maxiter=100);"
   ],
   "metadata": {},
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Stabilized Sinkhorn algorithm\n",
    "\n",
    "When $\\varepsilon$ is very small, we can use a\n",
    "[log-stabilised version of the Sinkhorn algorithm](https://doi.org/10.1137/16M1106018)."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "ε = 0.005\n",
    "γ = sinkhorn_stabilized(μ, ν, C, ε; maxiter=5_000);"
   ],
   "metadata": {},
   "execution_count": 10
  },
  {
   "cell_type": "markdown",
   "source": [
    "Again we can check that the same result is obtained with the POT package:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "8.684136200941273e-12"
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "cell_type": "code",
   "source": [
    "γ_pot = POT.sinkhorn(μ, ν, C, ε; method=\"sinkhorn_stabilized\", numItermax=5_000)\n",
    "norm(γ - γ_pot, Inf)"
   ],
   "metadata": {},
   "execution_count": 11
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Stabilized Sinkhorn algorithm with $\\varepsilon$-scaling\n",
    "\n",
    "In addition to log-stabilisation, we can use [$\\varepsilon$-scaling](https://doi.org/10.1137/16M1106018):"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "γ = sinkhorn_stabilized_epsscaling(μ, ν, C, ε; maxiter=5_000);"
   ],
   "metadata": {},
   "execution_count": 12
  },
  {
   "cell_type": "markdown",
   "source": [
    "The POT package yields the same result:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.665707076935717e-11"
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "cell_type": "code",
   "source": [
    "γpot = POT.sinkhorn(μ, ν, C, ε; method=\"sinkhorn_epsilon_scaling\", numItermax=5000)\n",
    "norm(γ - γpot, Inf)"
   ],
   "metadata": {},
   "execution_count": 13
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Unbalanced optimal transport\n",
    "\n",
    "[Unbalanced optimal transport](https://doi.org/10.1090/mcom/3303) deals with general\n",
    "positive measures which do not necessarily have the same total mass. For unbalanced\n",
    "source and target marginals $\\mu$ and $\\nu$ and a cost matrix $C$, entropically\n",
    "regularised unbalanced optimal transport solves\n",
    "$$\n",
    "\\inf_{\\gamma \\geq 0} \\langle \\gamma, C \\rangle + \\varepsilon \\Omega(\\gamma) + \\lambda_1 \\mathrm{KL}(\\gamma 1 | \\mu) + \\lambda_2 \\mathrm{KL}(\\gamma^{\\mathsf{T}} 1 | \\nu),\n",
    "$$\n",
    "where $\\varepsilon$ controls the strength of the entropic regularisation, and $\\lambda_1$ and\n",
    "$\\lambda_2$ control how strongly we enforce the marginal constraints.\n",
    "\n",
    "We construct two random measures, now with different total masses:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "M = 100\n",
    "μ = fill(1 / M, M)\n",
    "μsupport = rand(M)\n",
    "\n",
    "N = 200\n",
    "ν = fill(1 / M, N)\n",
    "νsupport = rand(N);"
   ],
   "metadata": {},
   "execution_count": 14
  },
  {
   "cell_type": "markdown",
   "source": [
    "We compute the quadratic cost matrix:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "C = pairwise(SqEuclidean(), μsupport', νsupport'; dims=2);"
   ],
   "metadata": {},
   "execution_count": 15
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we solve the corresponding unbalanced, entropy-regularised transport problem with\n",
    "$\\varepsilon = 0.01$ and $\\lambda_1 = \\lambda_2 = 1$:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "ε = 0.01\n",
    "λ = 1\n",
    "γ = sinkhorn_unbalanced(μ, ν, C, λ, λ, ε);"
   ],
   "metadata": {},
   "execution_count": 16
  },
  {
   "cell_type": "markdown",
   "source": [
    "We check that the result agrees with POT:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.2458106547243164e-9"
     },
     "metadata": {},
     "execution_count": 17
    }
   ],
   "cell_type": "code",
   "source": [
    "γpot = POT.sinkhorn_unbalanced(μ, ν, C, ε, λ)\n",
    "norm(γ - γpot, Inf)"
   ],
   "metadata": {},
   "execution_count": 17
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Plots\n",
    "\n",
    "### Entropically regularised transport\n",
    "\n",
    "Let us construct source and target measures again:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=2}",
      "image/png": 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       "<path clip-path=\"url(#clip710)\" d=\"M2226.51 196.393 Q2226.51 196.603 2226.33 197.33 Q2226.16 198.032 2225.62 199.414 Q2225.11 200.773 2224.31 202.295 Q2223.54 203.794 2222.11 205.691 Q2220.68 207.589 2218.9 209.252 Q2215.55 212.39 2211.97 214.077 Q2208.41 215.763 2205.36 216.302 L2204.68 216.302 Q2203.94 216.302 2203.94 215.716 L2204.45 213.561 L2207.38 201.827 Q2208.29 198.243 2208.29 197.939 Q2208.29 197.657 2208.17 197.517 Q2208.08 197.353 2207.52 197.236 Q2206.98 197.119 2205.9 197.119 Q2205.46 197.119 2205.25 197.095 Q2205.06 197.072 2204.9 196.955 Q2204.73 196.814 2204.73 196.533 Q2204.73 196.135 2204.9 195.924 Q2205.08 195.69 2205.22 195.643 Q2205.36 195.596 2205.65 195.573 Q2206.04 195.549 2207.38 195.432 Q2208.71 195.292 2209.86 195.198 Q2211.01 195.104 2211.5 195.104 Q2211.78 195.104 2211.95 195.245 Q2212.11 195.362 2212.11 195.503 L2212.13 195.62 L2207.43 214.709 Q2209.16 214.147 2210.87 213.21 Q2212.6 212.273 2214.48 210.727 Q2216.35 209.158 2217.94 207.214 Q2219.53 205.27 2220.94 202.553 Q2222.37 199.812 2223.26 196.674 Q2223.42 196.041 2223.82 195.667 Q2224.24 195.292 2224.55 195.198 Q2224.85 195.104 2225.13 195.104 Q2225.77 195.104 2226.14 195.456 Q2226.51 195.784 2226.51 196.393 Z\" fill=\"#000000\" fill-rule=\"evenodd\" fill-opacity=\"1\" /></svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "cell_type": "code",
   "source": [
    "μsupport = νsupport = range(-2, 2; length=100)\n",
    "C = pairwise(SqEuclidean(), μsupport', νsupport'; dims=2)\n",
    "μ = normalize!(exp.(-μsupport .^ 2 ./ 0.5^2), 1)\n",
    "ν = normalize!(νsupport .^ 2 .* exp.(-νsupport .^ 2 ./ 0.5^2), 1)\n",
    "\n",
    "plot(μsupport, μ; label=raw\"$\\mu$\", size=(600, 400))\n",
    "plot!(νsupport, ν; label=raw\"$\\nu$\")"
   ],
   "metadata": {},
   "execution_count": 18
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we compute the entropically regularised transport plan:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=1}",
      "image/png": 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       "  \"/>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 19
    }
   ],
   "cell_type": "code",
   "source": [
    "γ = sinkhorn(μ, ν, C, 0.01)\n",
    "heatmap(\n",
    "    μsupport,\n",
    "    νsupport,\n",
    "    γ;\n",
    "    title=\"Entropically regularised optimal transport\",\n",
    "    size=(600, 600),\n",
    ")"
   ],
   "metadata": {},
   "execution_count": 19
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Quadratically regularised transport\n",
    "\n",
    "Notice how the \"edges\" of the transport plan are sharper if we use quadratic regularisation\n",
    "instead of entropic regularisation:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌ Warning: Semi-smooth Newton algorithm (100/100): not converged\n",
      "└ @ OptimalTransport ~/work/OptimalTransport.jl/OptimalTransport.jl/src/quadratic_newton.jl:216\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=1}",
      "image/png": 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icnJyunfvTo9PGRoafvjhh4SQvXv3svtyHPfxxx8/8UnB4zSxwTL0dLkgCOXl5UqjRURlZWWEEDs7O3UPXlxcvGzZskOHDmVmZubk5Ijb2Wny8fHxHMcpjVlo1qyZm5vbnTt3lA7o5uamdH6fOnTo0Pr16xMSEjIzM9kJEnl5eerWmX6p0V66Wvz111/r1q2r5yM6OzuPHDly796958+fp83S1q1bS0tLZ82aZWxs/MTd6VlQUWFhYXJysqmp6c8//6xUkn6npKSkPPfcc7dv31bdlxCi7mCf2h0+fHjdunW3bt3KysqiX0OU6uvzxMf19PTs16/f+fPn3dzchg0bNmDAgCFDhtDzmRRt4AsLCz/99FOlfU1NTVNSUujt+Ph4Qgj9+c/y9fUV88LHofsqjarQ09Pz9fVNSkq6efMmPTNJqT5E165dt2/fTg+iAaXeKdooenp6Kv2AaN68eVZWVmFhIW05CCEJCQmLFy++evVqRkYG+0NWg/+LWrRq1arG2Ud1/wwoPUHaLSJ+YwQEBHh4eBw4cMDd3X348OH9+/cfPHhwjV9HSq+8ubm5l5dXdHT0nTt3OnXqVOObSAjp3r07IeTmzZtKddDgGw9ETawhbN68ubGxcUVFRVJS0uMmMCUnJxNCWrZsqdaRZTJZnz59YmNjvb29x48fb29vT5O87777rrq6mpYRBKGkpMTKykr1e9/BwUG1IaxxFOXSpUs//PBDa2vrYcOGubu70//JkydPnjx5UnyguqPfF6rDVlnLly+fO3eu0iOeOnUqLCxM3UecNWvW3r17f/nlF9oQ/vrrrxzHzZw5sy77Kr0aBQUFhJDKysoNGzaoFra1tZXL5YQQ+pWkOna3xtG8mlmxYsX7779vZWU1bNgwDw+P2l8f1UGzSjiOO3z48DfffLN9+/atW7du3bqV47gBAwasWbOGdr/l5+cTQuLi4pKSkpT2NTAwMDAwkMvl+vr6NKFUfTjVYTiqSkpKOI5TLUm/souLi2t/RnRHpWJ1p/QLlWalbF7LbhczwsjIyP79+1dUVAQEBLz00ku2trYcx6Wnp69Zs4Z+EqRS43/lzz///N577yl9Bk6fPn3ixAnVz4DSc1F6ImZmZhcvXlywYMG+ffs2bNiwYcMGfX39sWPH/vzzz+z/qZ6enmrTRd8L+srTD4Dqm1jju/O4AdtQR02sITQ2Nu7Ro8fFixfDwsIe1xCGhYURQmiPF/n3Y6r6v6R05mrLli2xsbGTJ0+m31x0Y3V19YIFC8TxivSUbFFRUXl5OTv+jRCSm5urWhPVc2ilpaULFy5s1qxZdHQ0O50jJSXl5MmTtT3zx6C/psWuU1VlZWULFiywtbWNjo6mA3CotLQ0+kKp5YUXXvD29t6zZ8/y5cuTk5OvX78+cOBAtc7Kiuh3ja2t7YMHD2opRhs81SeYmZmptIW+2jzPsxurqqpqP0Mlk8kWLFhgY2MTHR0tDgclhKSnp2vw+lAWFhaLFy/+4Ycf4uPjT506tXXr1tOnTw8ZMuTmzZsWFhb0ib/xxhu0J+9xaLH79+8rba/xk6a6r0wmu3//PnvOk/ybtShNL3ncQzTwog1ffPFFaWnpjh072DOohw4dWrNmjbQPpPpfKZPJ5s+fr/oZyMjIOHHihAYP4ejouGHDhnXr1kVHR586dWrz5s27d+9OT0+nI8sonufz8vKUfoXQ94K+QbV/AJTexNpP18MTNbE+QkLItGnTCCGrV6+mp0CVnD59OjIy0szMjA4qIYTQDmfVrw862UhEzzFOnDiR/UjduHGjqqqKLdaxY0dBEOjZLVFeXl4dF/+8c+dOWVmZv7+/0qRG1b4o2vo+MWOj57hqnHFBJSUllZaW+vn5sa1gjY9YRzNnzqyoqPj9999pJhcSEqLZcej55Ly8PHry83F8fX05jrt06ZLSIjtnz55VKlnjG52YmFj7a5icnFxSUtKrVy/2G5DU4/URcRzn4+Pz7rvvXrlypU+fPmlpadeuXSP/vmXsd2KN6DlYpU8aqfW9VtqXDrcRiV2eSr8gVR+CFhNn0dXxo1hPf//9t6GhofhvS9XlyapSt8JP6TOgr6/fs2fPTz/99Pr1625ubpcvXxbH0FFKrzydkGpsbEyH5NDXX+lNJITQT1FdFvSh57SkzaefVU2vIXzttdc6dep07969119/XamVSk5Ops3kp59+Kv7UcnV1NTAwiIiIKCwsFEv+9ddfsbGx7L703ALbngn/DmtkjR07lhBCx3eJVq5c+cSOcYrWio60ZiujOhyA/pZX+s9RNWHCBCMjo99+++1xPTr0EdPT09lHPHLkyOXLl+tSYVVTp041MzNbu3btrl27HBwcRo8erdlxCCF0xOm8efOU0jjC5OstWrQIDAzMzs6mgyqpzMzMVatWKe1CB5ceO3aM3UhH+dZCfH3YOhw9evSJDdXj0EGe7BaO4+g5MdqW+/v7t2vX7urVq3RqphLxidNP2rp168Rl0Akh4eHhdVlvmjYnS5YsYZ/UH3/8cffu3Xbt2il9h+7cuZP9mN29e3ffvn1mZmbiFEbawZmenv7Ex60Pe3v7qqoqNvXPy8tTfZfrQt0K1/gZOHbs2BP7YmukOkjKxMSEnthQ+jH3008/sR8V+l6/9NJLtOfFz8/PxcUlJiaGjl2nKisrf/rpJ0LIuHHjnlgT+h3ytN+4Z4R2BqvWT0JCAu0C9PHxWbly5enTp//666+PP/6YnkyYMGFCdXU1W55+L/Tu3fvQoUOnT5/+4osvzMzM6OxdcfoEHQRva2u7cePGW7dunT9//uWXX27evLmlpaWZmZl4qJKSEvqFO2PGjGvXrsXGxi5YsMDY2Jh+5lQn1KtWnv7ce/31169evRoXF7d06VJLS0t6TDpPmaJTMnr06LF48eLQ0NBt27axz4WdR0j/Mezs7JYtWxYVFRUZGbljx44RI0aI8w1o3/60adPoI9LZ9/QR2RnWdV90+/XXX6cfnk8++aQu7xedPrF+/Xql7aWlpeIsiG3btkVFRUVERGzbtm3KlCnshIf4+Hhra2uO415++eXly5d/8sknDg4OdCgdO30iLy/PysqK47i5c+eeO3du//79o0ePdnNzMzIyqn36BJ1yN3Xq1KtXr968eZN9ff73v/+Jxegbp7oMutIBd+/e7eHh8e233x49evTWrVuRkZELFizQ09NzdnYWJ8NcuHDB2NjYwMBgzpw5hw8fjo2NPXHixOrVq/39/d9++23xyHSZQD8/v7CwsNu3b2/evFlcv6b26RPl5eV0PNfIkSPPnDlz48aNn376yczMjPZfisXo9AlXV9d27dr9+eefiYmJ+/btoyN72Wk/BQUFZmZmxsbG77///urVq0NDQxMTE4XHT59Qml2ekJBACBkyZIhSJWlm/OjRIxq+99579AN/7Nix27dv7969u3379vRdmDRpkrhXXaZPCP++WdOnT1+5cqW4Yrg4oV61vNJnYPny5VZWVvTR2adDDyvO4aPobyZxxuH333/ftWvXFStWnDx58vbt2xcvXqRnTbp16ybuQucRtmjRYvLkyZcvX46Li/vuu+8MDQ1NTEzi4+PFYnQmho2NzZo1a+Li4sLCwujSB35+fuLnUJxQr/qkbt26xXGcra3tvHnz1q1bFxoamp2dXfvrprOaZEMoCEJmZubkyZOVFoKxsrJatWqV0jQvQRCys7PZAVomJia//PKL6jzChQsXssPNW7VqdeXKFWdnZ7YhFAQhMTGRHcRoYmKyZcuWx60so1rzqKgotudGT09vwYIFNPVkG8Li4uKJEyeKo3JqX1lm3bp1SoNHbGxsxDLR0dHsqEU9Pb3PP/+cfmdp1hDS/JXjODpP+Yke1xAKglBQUDB16lSl99HExERpqtb169d79+5Nz1pbWlrOnTuXnrYaNmwYW+zAgQNsz5aXl9fNmzefOI8wJiaGHVpFXx+6dLsGDeGZM2dU1yjx9vaOiYlh97p06ZLqcE1nZ2f2a7esrEzpVGFISAjNcZ+4skxOTk5gYCC7b/PmzXfu3MmWoQ3hli1b2OVj9PT0PvjgA6V/or1797Kn1mtfWUazhrCoqIjOYRcNHjyYJkMaNISXL19mh3YrrSyjWl71MzBv3jw6A1LdhvC3335THSvep0+f1NRUcRe6ssyVK1fYrwJ7e/vjx48rVWzjxo3iqFpq5MiR4osm1NoQCoKwevVqdsFCrCzzOJzQlK9Q//Dhw4sXL2ZlZZWWls6fP7+6uvrPP/8cPny4asnq6uqzZ88mJydbWVkFBgY2b978wYMHxcXFzs7O7CC3lJSUa9euFRQUtGnTpl+/fkZGRqmpqTzPK3UeiEezsbEJDAy0s7PLzs6WyWT0NCwtkJaWZmJiojRagZLJZBcvXrx3756lpWW/fv1atGiRn5+fn5/v4OCgND9SEITc3NyysjIDAwOaCuTk5BQXF7u6uiqNXC0tLaXHNDU1dXV19fPzYws87hFpykvLpKenl5eXe3h4iKPgkpKSjI2NVddRjIiI6N27d2BgYB2HkxQUFDx69Mje3l6ph1+Um5sbERGRm5trYWHRsmXL7t271zhSo6CgoKSkxNHR0dDQ8MCBA6NHj541a5bS9fAePnwYFhZWWFjYpk2bAQMGGBoa3rt3T09PT+yUlclkGRkZ1tbW7Hg88fWxsLAICAh43OtTVVXVpk0bpYEJqgfkef7GjRtJSUl5eXm2traenp60p1Pp6QiCcOPGjevXr5eVlTk6OrZu3bpLly5K65ESQq5fvx4VFWVoaPj888+3a9fuiS8mKy4uLioqSiaTtWnTpm/fvkrDHT/44INly5bt3bt37NixkZGRsbGx+vr6ffr0UZruyT7TnJwcQRDoB7WysjI1NdXCwkIcDKn6ohFCqqqq0tPTTU1NlcY205k8rVu3Fp+yIAhRUVFxcXEcx3Xp0qVr164VFRWZmZkWFhbia/vo0aOHDx86OTnVZSxPRUVFbm5udXW1jY1Ns2bN5HJ5amqqsbEx+7uQfXbiZ6Bfv34uLi70pX7iZ0C1klVVVdHR0SkpKQUFBQ4ODu3bt2cXGiWE0A+YTCYrLy8/depURkaGg4NDYGBgjU+qpKTk3Llz6enpZmZm9DPA3svzPF0DoZZx8sXFxXRIWosWLZRG+cE/tNkKS+rgwYMGBgampqbi0mLwlNClv1TXRWxI9OfO7t27tViHpo5mhHv37tV2RXQOzQi1XQv4T9MbLPM4I0aM2Lhxo7e399dffy3tDFyg8vLy7t69GxoaumfPHh8fnxEjRjTM48rl8oEDB27duvXGjRv37t07fvz4mDFjDh8+3KlTJ7ryCABAfTSxeYS1mzJlypQpU7Rdi2fWl19+SSd1mZub/+9//2vIqUuXL19WuvRd3759t23bxl6SAgBAM89UQwhP1ahRo1q1auXo6DhkyJDa17KRlr6+/qNHjy5fvpyampqfn29tbd29e3e1rswHNRo+fLiDg4PqVffgafv888/ZVdxA65r2YBkAAIB6enb6CAEAADSAhhAAAHQaGkIAANBpaAgBAECnoSEEAACdhoYQAAB0GhpCAADQaWgIAQBAp6EhBAAAnYaGEAAAdBoaQgAA0GloCAEAQKdJc/UJeqFtU1PT/v3729vbS3JMAACABiBBRvj555+PHj36+PHjv//+u5eXV0RERP2PCQAA0DAkuAxTampqq1at9PT0CCEff/xxXFzckSNHaiy5Zs2ac+fCnZyc5HK5vr5+PR8X6oLneY7jGvIiuroMH+wGIwgCz/N4tRuG+MFeuXLFEwsLJF4QytQ6/vXriVcuF86aNUvD+tWbBKdG3dzcxNsODg5VVVWPK3nmzNm9e/+s/yMCAEDDq1NDKKQIJF+tw6akRJ04cU+LDaGUg2UePXq0atWqmTNnPq5AZWWlhA8HAAAN6Vm9kLs0g2UIIWVlZWPHjh06dOj48eOlOiYAADQegiA8sZ+FF+QCqVbvsERej0pJQJqMsLy8fMyYMa6urqJTPMwAACAASURBVGvXrq2lmJGRkSQPBwAADY+OBXn2SJARVlZWjh8/3srKatOmTc/qywQAAHUhELkgqJfhCQL/lCpTRxI0hPPnzz9+/Pirr746e/ZsQoi9vf13331X/8MCAAA0AAkawuHDh3t6eoqhpaVl/Y8JAABNES/IBUHNPkI1M0jJSdAQBgQEBAQE1P84AAAADU+yUaMAAABEg4zw2Rg1CgAA0EQhIwQAAMkIfLXaGSGv5VGjyAgBAECnISMEAADJCOgjBAAAaFqQEQIAgGQEonZGSLQ9jxAZIQAA6DRkhAAAIBmBrxZ4dUeNIiMEAADQHmSEAAAgHUFO1O0jJJhHCAAAoD3ICAEAQDpN8OoTyAgBAECnISMEAADpCHKi5qhRzCMEAADQJmSEAAAgHb6a8FVq7oKMEAAAQHuQEQIAgHSEavXnEcoJ0X8qlakbZIQAAKDTkBECAIB0NBg1yiMjBAAA0B5khAAAIB0e8wgBAAAkdfny5XHjxg0ZMmTt2rWCIKgWePDgwezZswMDA+fMmZOfny9uP3To0IgRI4YPH7537162/MGDB8eOHTto0KA5c+bI5XI0hAAAIB169Qn1/mq7+kRmZuaQIUMGDhz4ySefrFixIjQ0VLVMUFBQaWnpN998c//+/VdeeYVuvHTp0muvvTZ16tSQkJCQkJDTp0/T7Rs2bJg9e/bo0aPnzZvXqlUrnudxahQAABqvX3/9ddCgQbNmzSKEfP/99wsWLHjzzTfZAjExMdHR0cePHzcxMenUqVPz5s1v377drl27VatWvfXWW0FBQYSQuXPnrly5cuDAgaWlpR999NGRI0d69+5NCBkwYADBqVEAAJCSUM3xav7V2kcYExPj5+dHb/v5+d26dausrEypgK+vr4mJCSHEwsKiU6dOMTExdLu/v7+4Y3R0NCHkxo0bxsbGlZWVM2fOfP/99xMTEwkaQgAAaMxycnJsbW3p7WbNmhFCcnNz2QK5ubliAVomJydHaXuzZs3oXmlpaTKZ7Ntvvx09enSzZs169uyZnp6OU6MAAKBlYWFhHh4e7JbJkyd/8803hBBLS0uZTEY30lzQ0tKSLWlhYVFeXi6GpaWltICFhQW7I91obm5eUlLyyy+/uLu7Dx8+/MKFC9u2bUNDCAAA0uF5tRfR5nl/f//169ez2xwcHOgNV1fXu3fv0tt37961sLCws7NjS7IFBEG4d++em5sbIcTNzY3d0dXVlW4khDg5OdHtTk5O+fn5ODUKAABaZm5u7q7IwsKC3jVx4sTdu3c/evSIELJhw4YJEyZwHEcI+eOPP2hf4ODBg/Pz80+dOkUIOXz4MM/zAQEBhJAJEyZs2rSpqqpKLpdv3Lhx4sSJhJCOHTt27dqVzqYoKCg4ffq0n58fMkIAAJAMx8s5NSfU1z5YJjAwcNiwYR06dHBwcBAE4fjx43T78uXLJ02a5Ovra2pqun79+gkTJrRu3To1NXXTpk2GhoaEkBkzZhw5csTLy0tfX79169azZ8+mO65fvz4oKGj16tUpKSkTJ04cPXo0V+PkxKckKGjc3r1/NtjDAQCAhAThyRcaLMv5jK9KVeuwfx3P2HnYbv/+/bWUycnJKSgoaNu2rZ7ePycyq6qq9PT09PX/WaS0pKQkNTW1TZs2ZmZm7I6pqak8z7dp04bdWFVVlZSU1KJFC2tra4Il1gAAQEqCXO0+wlon1FNOTk5ixx5F0z6RhYWFj4+P6o60U1CJoaFhhw4dxBB9hAAAoNOQEQIAgHQ0WHRb3QxSasgIAQBApyEjBAAAyXC8nHsKfYRPFTJCAADQacgIAQBAQnIi4MK8AAAATQcyQgAAkAzH8+r2EXLoIwQAANAiZIQAACAd/qmsLPNUISMEAACdhowQAAAkwwnq9xHyyAgBAAC0BxkhAABIB32EAAAATQsyQgAAkI4G8wjRRwgAAKBFyAgBAEA6Ak/UzfAE4elUpa6QEQIAgE5DRggAAJLheB6jRgEAAJoSZIQAACAdQf15hBg1CgAAoEXICAEAQDroIwQAAGhakBECAIBkOF7teYS4Qj0AAIA2ISMEAADpCOr3EWLUKAAAgBahIQQAAJ2GU6MAACAd9QfLYNFtAAAAbUJGCAAAkuF4Qe3pExgsAwAAoEXICAEAQDoaLLqNCfUAAABahIwQAACko34fodZHjaIhBABojDjCsaFAtNxaPMPQEAIAgHQE9ecR8phHCAAAoD3ICAEAQDIcj1GjAAAATQoyQgCARoFTzEwEouU8SUOajBpFRggAAKA9yAgBAEA6GDUKAADQtCAjBAAA6TTBPkI0hAAA2sFxiqNjtN0e6Cw0hAAAIB0NrlCPPkIAAAAtQkYIAAAS4tXv80NGCAAAoD3ICAEAGo7CAJlncnSMBqNG1S0vNWSEAACg05ARAgCAdDQYNartK9QjIwQAAJ2GjBAAAKSjwVqjyAgBAAC0CBkhAMBTxHGKX7PCf1dv13Ie9JTw6q8Ug5VlAAAAtAgZIQAASAejRgEAAJoWZIQAACAdQVC7z0/bGSEaQgAAKXGcoeIGhfOEwjM6RKZJw6lRAADQacgIAQBAOlh0GwAAoGlBRggAANLRZLDM06lJnaEhBACoFz3OWHGDwvc6zywlA40TGkIAAJAOrzROtm67aBX6CAEAoLF79OhRenp6LQUqKiru3r1bWVmptD03NzcnJ6f2g6MhBAAA6QiC2n9P6iR8//33PT09AwICevToUWOrdvDgwZYtW7700kutWrU6ceIE3VhZWfnyyy936dKlW7duL730kkwmo9vt7e25f02YMIGgIQQAgMbszJkzO3fuvH379t27d318fL788kulAhUVFTNmzPjtt9/i4+PXrVsXHBxcXV1NCNm0aVNqampKSkpqamphYeG6devEXRITEwVBEARh586dBA0hAIC69PTM2D+OM2T/eKGS/dN2ZRscr9Hf423fvn3ChAnNmzcnhMyePXv79u2C4pJsJ06csLCwGDZsGCFkzJgxcrn8/PnzdMfg4GATExNDQ8M33nhj+/bt4i5VVVUVFRViiIYQAAAar5SUFE9PT3rb09OzuLj40aNHSgW8vLzobY7jPD09U1JSlLaLGyk/Pz8bG5vu3btfuXKFYNQoAABISVB/FKhA7t+/f/LkSXabu7u7u7s7IaS4uNjU1JRuNDc3J4QUFhba2dmJJdkChBAzM7OioiJCSElJCbsj3UgIOXfunI+PT3V19aJFi0aNGpWUlISGEAAAtOzOnTuLFy9mt4wYMeLdd98lhDg6OhYUFNCNNBd0dHRkSzo6Oubn54thfn4+LeDg4MDuKO7l4+NDCDEwMFiwYMHy5cuvX7+OhhAAACQj8ERQPyPs3bv3/v37a7yzS5cu9AQmIeTKlSteXl40L2QLXL9+vbKy0sjIqKys7MaNG126dBF3HD58ON2xa9euSkcuKysrLy+3sLBAQwgAAI1XcHBw586df/vtt/bt23/++edvv/023T5p0qRhw4a99tprPXr08Pb2fvfdd998882VK1f6+/t7e3sTQmbPnj1mzBg/Pz9DQ8Nly5Zt2bKFEBIdHR0eHt6jR4/y8vIff/yxc+fOHTt2REMIAPAE+noWCqG+GRtWVt1v2Oo0bhr0EdZa3s3N7dChQz/++GNBQcHrr7/+zjvv0O3t2rVzcHCgt/fv3z9//vxZs2Z16dLljz/+oBv79eu3fv36pUuX8jy/fPnyIUOGEEKsra1jYmJ2795tYmLy/PPPf/DBBwYGBpzQgJcGDgoat3fvnw32cAAAkkBDSAlC1RPLVO/qKeTFqnXYg3/zW++/9LhTow0AGSEAAEhHg7VGtX31CcwjBAAAnYaMEAAApMNzhOfU20VQs7zU0BACACgzMLBlQ2N9GzYsrbjXsNWBpwsNIQAASEYQOEHNDK8Bh2zWTII+wnv37r355ps9evTo2LFj/Y8GAADQkCRoCGUyWZs2baZOnXrvHk4XAADoNkHiq080AAlOjXp7e3t7e0dFRdX/UAAAAA2sQfsIG3LyPgBA3ZkYtVAIDRRGxxTKEhq2Ok0ZT5rcqNEGnUdYVlbWkA8HAAASksvl2q7CU9GgGaHSkuEAANCE6OvrP7GMIOgJvHopltZPFmJlGQAA0GkSZIRVVVWxsbG3bt3ieT4qKsrY2BjzKAAAdJQGK8s8A6NG8/PzQ0JCCCE+Pj4hISEtWrQ4ePBg/Q8LAADQACRoCB0cHCIjI+t/HACABmNp4sWGpoqLqOXJbrKhoPY113WYwKk/ClSXRo0CAAA0NlhrFAAAJCPwRFC7jxAZIQAAgPagIQQAAJ2GU6MAoBPszX3Z0JxrxoY5FXFsyPNYBktTgh5Rc0K9bi2xBgAA0NggIwQAAOnwnLqDZdS9kK/kkBECAIBOQ0YIAADS0WBCvbYv0IeGEACeTS4WfdmwmeDEhhl8PBtWVOU2RJ2gUUJDCAAAkhEETu3LMKk7ylRq6CMEAACdhowQAACko8FlmLTdR4iMEAAAdBoyQgB4RrQ3H82GdnKFKytl6WexYX6pwoWWQCqCgHmEAAAATQoyQgAAkIwg6AkC1hoFAABoOpARAgCAdHj1L7SLjBAAAECLkBECQFOip2cq3u5lPJ69y5YzYcMsrogNU0pOPNWKASVocPUJdTNIqSEjBAAAnYaMEAAAJKRH1B01SpARAgAAaA8yQgAAkI5mfYRaTcrQEAJAo2ZkYM+G/YzGiLedTAzZu7LLK9nwZmUYG2p7YWdovNAQAgCAZARe/VGgmEcIAACgRcgIAQBAQpzaGZ62T1sjIwQAAJ2GjBAAGhdLEy82DDQKZMMWpv9lG48UBseQWC6GDSur86SvHDyJwOsJvHopltpXq5AaMkIAANBpyAgBAEAygsCpe8V5AX2EAAAAWoSMEAAAJKPB1Se0Po8QDSEAaJmLRV82HGLSiQ1bmCmcOCtkBsjcqnjI3vWgLEr6yoEOQEMIAADSETii5qhRta9oLzX0EQIAgE5DQwgAADoNp0YBAEA6GkyfwIV5AQAAtAgZIQA0tE7m49hwuI3CFQddzCrYsLBS4Wvqeglzu2yn9JWD+tFg+oTa0y2khowQAAB0GjJCAACQjEDU7iPUOmSEAACg05ARAgCAZASeU/syTOpOwJcaGkIAeOoGms1gw6FOCl98bhaFbFhcacSGsaXGbHiiYo/UtQNdh4YQAAAko8llmDCPEAAAQIuQEQIAgGQ0uQwT/3SqUmfICAEAQKchIwQA6U2weYsNh7qUsKGbVQEbyqoM2TC+wIoNj8pusmFl1X1pqghPC/oIAQAAmhRkhAAAIB2eU/tCu1hrFAAAQIuQEQIAgGQEgRMENVeW0fbapGgIAUATepzCgi9vOwaz4dBWuWzYyu4BG5Yrrh1zt6AlG568r3AZpgzZufrUE54BeXl5v//+e2Fh4YgRI7p3765aQC6X79q1Ky4urkuXLuPGjeO4f1rWlJSUHTt28Dw/YcIET09PdpeCgoJdu3b5+fl16tQJp0YBAEAydGUZ9f5qHTVaXFz83HPPRUdHGxoaDho06MSJE6plQkJCli1bZmtru2jRojlz5tCNd+/e7datW15eXnFxcY8ePRISEthdPvzww7lz5546dYogIwQAgMZs69atLi4uv//+OyGENnWDBw9mC6SlpW3dujU1NdXR0XHChAlt27adP3++g4PDqlWrxowZs3TpUkKITCZbvnx5aGgo3eX06dNZWVm9e/emITJCAACQjCBwdHGZuv/VvrLM6dOnX3zxRXr7xRdfDA8Pr6qqYgucO3euS5cujo6OhJBWrVp5eXlduHCB7jh06FBxR5r8EUJKS0vnzJmzevVq8QwqGkIAAGi8srOzHRwc6G0nJyee53NyctgCOTk5YgFCiKOjY1ZWluqO2dnZ9PbHH38cHBzs7u4u7oJTowAAIBnNrj5x7dq18ePHsxuHDBkSHBxMCNHX1+f5f3JGuVxOCDEwUGi59PT0xAK0DC3Abhc3njt3LioqauXKlewR0BACQJ1YmLiz4adOg9hwqHsiGzq3yGbDygqFIabp99qw4ZlcMza8IFtbn3pCU9SiRYtx48axWzp06CDeJSZzWVlZBgYGbP5HC9AUUCzTokULQoiLiwu7o7OzMyFk8+bNRUVF9FxrTEzMvXv3ioqK0BACAIBkBIHw6maEAufi4qLUEIqGDx++dOnSBQsW6Ovr79u3b8iQIfr6+oSQmzdv2tnZOTk5BQYGBgcHJycne3h4xMfHZ2RkBAQEEEKGDRu2b9++SZMmEUL2798/fPhwQsgXX3zx8OFDeuR33nnH39//1VdfRUMIAACN17hx41auXDlo0CAPD499+/YdPXqUbn/99dcnTZr03nvvNW/e/IMPPhg0aNDw4cMPHjz4+eefW1tbE0Jmz579/PPPBwUFGRoanj9//vLly4SQ1q1bt27dmh7BysqqZcuW7u7uaAgBAEAygqAn8FKuLGNsbBweHn7kyJHCwsIvv/zSxcWFbl+7di0dKUoI+eabb4YNGxYXFzdlypSePXvSjU5OTrGxsUeOHOF5fu3atba2tkpH/v777+3s7Aj6CAEAoJEzNjYeM2aM0kalJWb8/Pz8/PyUylhbW9NTozXy9fWlN9AQAkDNXC0GsuGClm5sOKjTNTa0c89gQ3m5wiJq9+O92PB8jsJgh235ofWpJzQqmowa1fZao5hHCAAAOg0ZIQAASEaDjJAIT6cqdYaMEAAAdBoyQgAAkIzAE0HNK85rvY8QDSEA/KOH2Sts+LmXnA379TrLhpYd0thQqFD4MnkQ05YNL6YqrEqz9qHCoQRB4YEAGhhOjQIAgE5DRggAANLB9AkAAICmBRkhAABIRiDqT5/QNmSEAACg05ARAui04RYh4u1PumSyd/UIvMCGRp0Vx3ZWK1xisOyaFRtGJXiz4drMAjYslN3SpK7QFAiCniCou+i2llMyZIQAAKDTkBECAIBkeJ7j1Z1Qr2Z5ySEjBAAAnYaMEAAApCOoPS9Q22tuoyEE0DGzHN9iw7e73RBvtx15kb2L79peIeR5hQNdS2KjhMjObBiaaMOGN0txxUFovNAQAgCAZDSYR6j1eYfoIwQAAJ2GjBAAACSjwYV5kRECAABoEzJCgGcNxyn8wP3a7Q02nNn/NBvaj84Rb5d3GaFwIF5hKRmTSIUdU891Y8MNNz3Z8EjJ2rpXGJ4lvMDxTW3UKDJCAADQacgIAQBAMugjBAAAaGKQEQIAgHTUX1mGaDsjREMI0OS5WPRlwx9at2bDkYMPsqHJBDs2LPV67b9AXsXeZRZ1gA1zD7mz4bqrPdjw1wcYHQNNFRpCAACQjCbXIyToIwQAANAeZIQAACAZXsD1CAEAAJoUZIQAACAZTeYRPqWq1BkaQoCmZ6h5CBt+3jWdDXuO/YMN5UP7sCHvMZYNufIs8bbp3wo7PtplxYbrzimMTf0pE8NE4RmBhhAAAKSDlWUAAACaFmSEAAAgGV4gal99AhkhAACAFiEjBGgCPmk5iw3f8r/Mhi6T7rJhaT+FCxCa2viyYVVVvsK9kTvE2w+3mLB3rTw1gA0Xpa9To8agqwTS9EaNIiMEAACdhowQAAAkIxBO/bVD0UcIAACgPWgIAQBAp+HUKECj4GkxnA2/aWPDhsNeULqmoMK95V3nsaG5iSMblj68qnBvxE42TP3ff1cZ/PFiT/au9fexdgyoTRA4dadPqFtecsgIAQBApyEjBAAAyWiw6DZBRggAAKBFyAgBAEAyGiyxxmt7Rj0aQoAGYqCvMMIlxH4yGwZ3vM2GncbuYMOqF/qzodKllAw4hX/k8rt72ND0r2NsGLX/BTZceM1NvH28FKNjQBehIQQAAMlodGFe9BECAABoDzJCAACQjAbzCHEZJgAAAG1CRggAAJLR5DJMz8ao0fDw8D179piZmc2YMcPDw0OSYwLUh5VpWzbsSvqwYUsThQvvVSkO335QVcmGGXrZbHiv7DwbyvkS8baenhl713PGQWw43sWYDfu5JrKhV89YNuQcFQ5lmJmkcG/Sl2xYHVvGhndO92LDX28oXJ5wTS6GhgIokODUaFhY2MiRI728vAghvXr1ys7OfuIuAADwTKKjRtX60/plmCTICJcsWfLFF1+8/fbbhJA7d+788ssvCxcurP9hAQAAGoAEGeGFCxdeeOGfKboDBw4MDw+v/zEBAKApEgjHq/+n3TrXtyEsKCgoLy+3t7enoYODQy2nRisqKur5cAAAoC08z2u7Ck9FfU+NGhkZEUKqq6tpWFlZaWxs/LjC+vr69Xw40GWzHd9iwxmdEtiww8DLbGjQ+REbCqYn2ZDLV7hXFmnKhrevdmHD82lt2HBXpsLyZlcr/lvPjOcVBq1cq9jHhnk5/djwYJYbGzaP8mJDQz2F38gZ5eVseJ1cYMMiWR5RcLrWEEBDHPfk1E0Q1J8XqO1Ro/XNCM3MzGxsbDIyMmiYkZHh4uLyuMIGBpitAQDQVNWlIWyKJOgjHDVq1I4dOwgh1dXVe/bsGTVqVP2PCQAATREvcBr8abfOEqRon3/+eUBAQGpqam5urqGh4eTJk5+8DwAAQOMgQUPo5eWVkJBw/vx5c3Pzvn374vwnAIDOEgTtrxSjLmkaLSsrq5deekmSQ4GOG2L+3zIoX/dMZe/yHbOBDStfelFhT7dlbFQlVLOhkKwwbsUw4Swb3rn2PBv+76bCqjShedvZsFpeUGPNVbGLzhBCkkqOKIR1PAoAPGXI3gAAQDICUbvPT+t9hLj6BAAA6DRkhAAAIBmBcFq/4ry6kBECAIBOQ0YIAACS0WBeoNb7CNEQgpa96aCwcNpHva+Jt92m32XvKvVXuK6eud1zbFhensuGhte3KNy7U2Go54FTk9hwwT2Fe5NKcMU+AB2ChhAAACSjwVqjWu9TRB8hAAA0an/88UenTp1atmz5zjvvVFZWqhZISEh44YUXnJ2dhwwZkpycLG7/6aefPD093d3dFy1aRLdUVVWNHTv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       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 20
    }
   ],
   "cell_type": "code",
   "source": [
    "γquad = quadreg(μ, ν, C, 5; maxiter=100);\n",
    "heatmap(\n",
    "    μsupport,\n",
    "    νsupport,\n",
    "    γquad;\n",
    "    title=\"Quadratically regularised optimal transport\",\n",
    "    size=(600, 600),\n",
    ")"
   ],
   "metadata": {},
   "execution_count": 20
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Sinkhorn barycenters\n",
    "\n",
    "For a collection of discrete probability measures $\\{\\mu_i\\}_{i=1}^N \\subset \\mathcal{P}$,\n",
    "cost matrices $\\{C_i\\}_{i=1}^N$, and positive weights $\\{\\lambda_i\\}_{i=1}^N$ summing to $1$,\n",
    "the entropically regularised **barycenter** in $\\mathcal{P}$ is the discrete probability\n",
    "measure $\\mu$ that solves\n",
    "$$\n",
    "\\inf_{\\mu \\in \\mathcal{P}} \\sum_{i = 1}^N \\lambda_i \\operatorname{OT}_{\\varepsilon}(\\mu, \\mu_i)\n",
    "$$\n",
    "where $\\operatorname{OT}_\\varepsilon(\\mu, \\mu_i)$ denotes the entropically regularised\n",
    "optimal transport cost with marginals $\\mu$ and $\\mu_i$, cost matrix $C$, and entropic\n",
    "regularisation parameter $\\varepsilon$.\n",
    "\n",
    "We set up two measures and compute the weighted barycenters. We choose weights\n",
    "$\\lambda_1 \\in \\{0.25, 0.5, 0.75\\}$."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=5}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 21
    }
   ],
   "cell_type": "code",
   "source": [
    "support = range(-1, 1; length=250)\n",
    "mu1 = normalize!(exp.(-(support .+ 0.5) .^ 2 ./ 0.1^2), 1)\n",
    "mu2 = normalize!(exp.(-(support .- 0.5) .^ 2 ./ 0.1^2), 1)\n",
    "\n",
    "plt = plot(; size=(800, 400), legend=:outertopright)\n",
    "plot!(plt, support, mu1; label=raw\"$\\mu_1$\")\n",
    "plot!(plt, support, mu2; label=raw\"$\\mu_2$\")\n",
    "\n",
    "mu = hcat(mu1, mu2)\n",
    "C = pairwise(SqEuclidean(), support'; dims=2)\n",
    "for λ1 in (0.25, 0.5, 0.75)\n",
    "    λ2 = 1 - λ1\n",
    "    a = sinkhorn_barycenter(mu, C, 0.01, [λ1, λ2], SinkhornGibbs())\n",
    "    plot!(plt, support, a; label=\"\\$\\\\mu \\\\quad (\\\\lambda_1 = $λ1)\\$\")\n",
    "end\n",
    "plt"
   ],
   "metadata": {},
   "execution_count": 21
  },
  {
   "cell_type": "markdown",
   "source": [
    "---\n",
    "\n",
    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
   ],
   "metadata": {}
  }
 ],
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