parameter_estimation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "18309201-ca89-4c2a-a656-e2f19f88391c",
   "metadata": {},
   "source": [
    "# Parameter estimation tutorial\n",
    "\n",
    "In this tutorial, we will put a couple of things together from previous ones (namely those involving PDE and optimization) and illustrate an example of an \"inverse problem\", more specifically a simple parameter estimation *given* a mathematical model. We will be using the following Julia packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "63e563f0-2442-4685-8c65-406e7702e3d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Random, LinearAlgebra, ApproxFun, Plots, LaTeXStrings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d372b9f0-4613-4331-a026-08a7fe157541",
   "metadata": {},
   "source": [
    "along with the matrix exponential (propagation) operation we saw [here](https://github.com/mjyshin/math-tutorials/blob/main/operator_exponential.ipynb)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3028a059-a686-46a4-b8e4-3507f9fa1bbe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "exp (generic function with 35 methods)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import Base: exp\n",
    "\n",
    "function exp(L::Operator,B::Operator,t::Real,u0::Fun,n::Integer)\n",
    "    C = Conversion(domainspace(L),rangespace(L))\n",
    "    \n",
    "    perm = [3;2;1;4:n]\n",
    "    P = I(n)[:,perm]    # permutation matrix\n",
    "    \n",
    "    B = B[1:2,1:n]*P    # permuted BCs\n",
    "    B = B[1:2,1:2]\\B    # Gaussian eliminated BCs\n",
    "    M = C[1:n-2,1:n]*P    # permuted masses\n",
    "    M = M - M[:,1:2]*B    # remove d.o.f.\n",
    "    L = L[1:n-2,1:n]*P    # permuted generator\n",
    "    L = L - L[:,1:2]*B    # remove d.o.f.\n",
    "    A = M[:,3:n]\\L[1:n-2,3:n]    # BC-merged generator\n",
    "    \n",
    "    c = P'*u0.coefficients[1:n]    # permuted coeffs\n",
    "    c0 = exp(A*t)*c[3:n]    # interior coeffs, Eq. (3)\n",
    "    ∂c = B*c - B[:,3:n]*c0    # BC coeffs\n",
    "    \n",
    "    c = P*[∂c;c0]    # de-permuted coeffs\n",
    "    u = chop(Fun(domain(u0),c))\n",
    "    \n",
    "    return u\n",
    "end\n",
    "\n",
    "exp(L::Operator,B::Operator,t::Real,u0::Fun) = exp(L,B,t,u0,ncoefficients(u0))\n",
    "exp(L::Operator,B::Operator,t::Real,u0::Fun,tol::Real) = exp(L,B,t,u0,ncoefficients(chop(u0,tol)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8f54b03-f388-43c2-9e37-92ca61b05b70",
   "metadata": {},
   "source": [
    "## Mathematical model\n",
    "\n",
    "Just for fun, we will motivate our problem with a biophysical experiment: the scratch assay. In this experiment, we grow a culture of cells on a Petri dish, scratch out a line in the middle, and watch the cells migrate to fill the gap. The usual starting point of a mathematical model for this process is the [**Fisher-Kolmogorov(-Petrovsky-Piskunov) equation**](https://en.wikipedia.org/wiki/Fisher%27s_equation), but as the crowded growth term $ru(1-u)$ makes the equation nonlinear in $u$, we will (unrealistically) neglect the effects of cell growth and competition, and just assume that the dynamics are dominated by motility. Here's a small pictorial of the experiment:\n",
    "\n",
    "```\n",
    "  ── sum over ─►\n",
    "  ╔════════════╗\n",
    "  ║ ooo o  ooo ║\n",
    "  ║o oo ooo oo ║\n",
    "x ║            ║ ◄─ scratched here\n",
    "  ║o  ooooo o o║\n",
    "  ║oo ooo  ooo ║\n",
    "  ╚════════════╝\n",
    "```\n",
    "\n",
    "The model then turns into a simple heat/diffusion equation with zero Neumann BCs since no cell enters or leaves the dish.\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\frac{\\partial u}{\\partial t}(x,t) &= Lu(x,t) := D\\Delta u(x,t),\\quad x\\in X\\setminus\\partial X:=(0,1)\\\\\n",
    "u(x,0) &=: u_0(x) = \\frac{1}{2}\\left\\{ \\tanh\\left(\\frac{x-0.7}{\\varepsilon}\\right)-\\tanh\\left(\\frac{x-0.3}{\\varepsilon}\\right) \\right\\}+1\\\\\n",
    "\\frac{\\partial u}{\\partial x}(x,t) &= \\frac{\\text{d}u_0}{\\text{d}x}(x)\\approx 0,\\quad x\\in\\partial X:=\\{0,1\\}.\n",
    "\\end{align*}\\label{eq:heat}\\tag{1}\n",
    "$$\n",
    "\n",
    "Here, $u(x,t)$ represents the cell density summed/averaged over the direction orthogonal to the $x$-axis at time $t$. We'll set $D=0.05$, and keep that in mind as we traverse through the tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fc787d1c-d322-4095-b1cb-19466f562195",
   "metadata": {},
   "outputs": [
    {
     "data": {
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = Chebyshev(0..1)\n",
    "D = 0.05\n",
    "Δ = Derivative(X)^2\n",
    "B = [lneumann(X);rneumann(X)]\n",
    "ϵ = 10^-1.5\n",
    "u0 = Fun(x->(tanh((x-0.7)/ϵ)-tanh((x-0.3)/ϵ))/2+1,X)\n",
    "\n",
    "fig1 = plot(u0,xlabel=L\"x\",ylabel=L\"u_0(x)\",title=L\"\\textrm{Figure\\ 1}\",legend=false,fmt=:png)\n",
    "display(fig1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49a3334b-1a2e-487c-ade4-db2c2c00c579",
   "metadata": {},
   "source": [
    "## Data generation\n",
    "\n",
    "Next, we will simulate some data by integrating the IC forward to $n$ time points $(t_j)_{j=1}^n\\in[0,2]^n$. At each time point $t_j$, we sample $m$ spatial points $(x_i)_{i=1}^m\\in[0,1]^m$. For both time and space, we will randomly sample the points. At each $t_j$, we have a data vector $\\vec u_j := (u_{1j},\\dots,u_{mj})$, where $u_{ij}:=u(x_i,t_j) + \\sigma\\,\\eta(x_i,t_j)$ with Gaussian noise $\\eta\\sim\\mathcal{N}(0,1)$ scaled by $\\sigma$. Therefore, we can encode the entire data as a temporal sequence of spatially sampled vectors $(\\vec u_j)_{j=1}^n$. (We could also just as easily have thought of the data as, e.g., an $m\\times n$ matrix $U = (u_{ij})$... But we won't do that here as we also have a vector of `Fun`s that correspond nicely to each $\\vec u_j$.)\n",
    "\n",
    "To make things more concrete, we'll take $n=5$ time samples, $m=20$ space samples, and add $\\sigma=0.02$ noise. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "15e13284-0936-48a6-88a7-d64f25eee218",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t = [0.4371733096376613, 0.6519534577271897, 0.7062232887984241, 1.0981022726311338, 1.7884908564019766]\n",
      "x = [0.07271614209221577, 0.07399570839268677, 0.09521752297832098, 0.1039294604697858, 0.1108168569969088, 0.20516767351768161, 0.42977508345153304, 0.5271837562207654, 0.6395615996802734, 0.7011158355140754, 0.7902073277833203, 0.8003933116303876, 0.806704115694322, 0.8396219340580711, 0.8455146021206799, 0.8520189384186997, 0.8705393388965176, 0.898931120705672, 0.9511618942933061, 0.967142768915383]\n"
     ]
    }
   ],
   "source": [
    "Random.seed!(1234)\n",
    "n = 5\n",
    "t = sort(2*rand(n))\n",
    "println(\"t = $t\")\n",
    "U = exp.(Ref(D*Δ),Ref(B),t,u0)    # sample in time\n",
    "\n",
    "m = 20\n",
    "x = sort(rand(m))\n",
    "println(\"x = $x\")\n",
    "σ = 0.02\n",
    "U⃗ = [max.(u.(x)+σ*randn(m),0) for u ∈ U]    # sample in space + add noise\n",
    "\n",
    "fig2 = plot(xlabel=L\"x\",ylabel=L\"u(x,t)\",title=L\"\\textrm{Figure\\ 2}\")\n",
    "fig2 = plot!(U,line_z=t',style=:dot,width=1.5,color=:roma,legend=false)\n",
    "fig2 = plot!(x,U⃗,line_z=t',color=:roma,cbar=true,cbartitle=L\"t\",fmt=:png)\n",
    "display(fig2)\n",
    "\n",
    "fig3 = heatmap(x,t,vcat(U⃗...)',xlabel=L\"x\",ylabel=L\"t\\to\",cbartitle=L\"u(x,t)\",title=L\"\\textrm{Figure\\ 3}\",fmt=:png)\n",
    "display(fig3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22173408-140f-4225-9baf-71fd40dc82b0",
   "metadata": {},
   "source": [
    "## System identification\n",
    "\n",
    "Imagine that an experimentalist gathered the data $(\\vec u_j)$ (visualized in Figs. 2 and 3) and handed it over to us. How should we go about \"discovering\" the equation of motion of the assay of cells, including the correct parameter(s)&mdash;in this case their motility $D$? This inverse problem is an example of **system identification**, meaning that we want to learn the structure of the PDE with the solution $\\hat u$. Sometimes, we have a good idea of the mathematical model that leads to the data $(\\vec u_{ij})$, which is called a white/grey box model. In other, more likely cases, we have very little knowledge of system, and we must use statistical methods to learn its properties.\n",
    "\n",
    "No matter which case we have, we need to compare the solution from our predicted model, denoted $\\hat u$, to the data $(\\vec u_j)$. We can do this with **loss functional** $\\mathcal{J}[\\hat u;(\\vec u_j)]$ that takes in the spatio-temporal solution from a candidate model and computes a scalar value of how *poorly* it fits the data. Ideally, once we have this, we just choose the candidate model whose functional value is lowest.\n",
    "\n",
    "This is much easier said than done since there is an infinite number of models that we could consider. So let's restrict our analysis to the whitest box model, where we are absolutely confident that the cell distribution in the assay observes Eq. ([1](#mjx-eqn-eq:heat)). (See [Lagergren et al., 2020](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008462) for an example of a sophisticated grey box approach using neural networks.) Then, we can define the loss functional as the squared difference summed over all time samples:\n",
    "\n",
    "$$\n",
    "\\mathcal{J}\\left[\\hat u_{\\hat D};(\\vec u_j)\\right] := \\sum_{j=1}^{n}\\left\\Vert \\left(\\hat u_{\\hat D}(x_i,t_j)\\right)_{i=1}^m-\\vec u_j \\right\\Vert_2^2,\n",
    "$$\n",
    "\n",
    "where $\\hat u_{\\hat D}$ is the solution that solves Eq. ([1](#mjx-eqn-eq:heat)) with $D=\\hat D$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ce92c21b-801e-4ac6-b621-5d5d1596efa1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "𝒥 (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function 𝒥(D̂::Real,Δ::Operator,B::Operator,u0::Fun,U⃗::Vector,x::Vector,t::Vector)\n",
    "    Û = exp.(Ref(D̂*Δ),Ref(B),t,u0)\n",
    "    return sum([norm(û.(x)-u⃗)^2 for (û,u⃗) ∈ zip(Û,U⃗)])\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "174ecc04-5a37-4114-b8d6-0ca78b24b884",
   "metadata": {},
   "source": [
    "### Parameter estimation\n",
    "\n",
    "Since the PDE ([1](#mjx-eqn-eq:heat)) is a 1-parameter system, we can think of the loss functional rather as a loss *function* $J(\\hat D)$, and the system identification problem becomes a simple **parameter estimation** problem. To minimize $J(\\hat D)$, we will evalute it at $p=50$ $\\hat D$ values in the search space from 0.001 to 1, interpolate it as a `Fun`, then minimize the interpolation. The argument of the minimum is the optimal parameter estimate ${\\hat D}^\\ast$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6f8da3d9-6a9d-4c5f-863a-7522946db853",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eIpudrYMhCLWOoZCMcKYjnAWEkMxKdjSb7Upjb11o8LWkoS7caBf6ggUaiaA0urq64lr+aa/WS/gmudUqQqFQIpG88cYbJ0+e1NHRuX///rhx49asWePj8+SVoNqlvr5+1apVAQEBiYmJoaGh3t7ejV9dv369g4NDWVmZSCQKDQ2VTkxJSVm5cuXmzZsJIZcuXTp9+rS3t/fdu3eXLl1KKb1582ZGRoaOjk5SUtK8efN++umnX3/9VdZFvGbNmuzs7P3797/zzjuDBg0ihEyYMKG8vNzQ0NDHx2f16tWEkP3792dkZNjZ2ZWUlMydO/fixYvXrl07e/bsvn37CCEJCQlRUVFdu3a9d+/ewoULhUJhfHx8Wlqarq5uYmLiW2+9tWnTpnXr1pmYmMjWWFBQYGFhkZ+f7+rqGhISQgi5ePHinTt3bG1t8/Pz33zzzZdeekksFktjz8bGJjIyMjU1tbS09OrVq+vWrZPeYqimpiYsLOyvv/6S7/9/ayEItZqLMZ3tTWd7kzqJ4Gw+i8rkQ6N5ASVjXWmYKxckQscpdLRu3XvERqU0+1JhVV32w0ftObdKV1e3oKBg6NChXl5ehBB3d3cTE5P58+fL/Yv4jz/+8PLyGjly5NChQ8PCwo4cOSJ76c6dO/fu3Zs/fz4hZPz48QMHDjQ1NeV5fuvWrTU1NYSQurq6qVOnJiYm6ujoLF++fM+ePRMmTDh06NDy5csJIS4uLnv37jU0NPzf//5nYmLC8/y2bdsGDBggFotPnTrF83//hnjxxRc9PDzc3Nykfb85OTn//e9/Y2NjCSGTJ08ODAz08/OzsbE5dOiQdP4lS5bs2rXLwMDgwIEDP/3007x58w4cOCBdo5eX1/bt2wUCwY4dO0xNTRljW7duLSgo6NOnj4eHByHkgw8+CAkJycrK+u6777Zv356WlhYdHS2RSMLCwsLDw/X09FJSUurr6zdu3PjTTz/p6emtWLHi448/Xrt2LSHkyJEjDx48kO9/fhvgdkFACCF6AjLMka4LFKRPEu4ZIjDVpW9fljhsa3jzguREDhM/9Qc6gJy99tprMZlFZx4UP/nSFzGpbq4uQUFB7Vn+mTNngoODZU89PDxiYmLas8BmHTlyxNXVlRCio6OTlpZWWloqe+nYsWPSlwgh5ubm586dk84/bNgw6cSUlBSxWCwdxePq6nr69GlCyKlTp/78809CSEJCQteuXcPCwrp37+7u7n79+vU5c+bo6Og0uSyllZVVaGioNO8JIdevX5fd5FW6TBMTE1kXZWVl5d27d6VLcHR0lMb2hQsXfvvtN0JIfHy8j4/P6NGje/To4e7uHhcXN3v2bD09vQULFhQVFVVUVEjf+NVXXw0bNiwnJ8fBweGHH34Qi8WzZ8/u2rWrs7NzRkZGaGhoaWlpWVkZIcTOzu7+/fuEkFu3br3wwguqcCNJtAihKen5+5H+XFoF25vBIm9IUh+xcDduojsXbI8T9kGx+vbtO2/unLd++eWj/h4TujoKOUoIKa6uXxNzf++9vOPRJ9p5Oe+zZ89+9NFHsqcPHjyQdfe1RElJSVxc3JPTfXx8Gp9ukZOTIzvuZWhomJubK8uhnJwcaUOKEGJsbJyTk5OZmWllZSU7qdrOzq6+vl76uKamJisrixDyzTffhIWF/fjjj0uWLJFdgTItLY3neWtr6yfrSU1NjY6Orq2tjY+Pj4yMdHZ2ljY3Gy9TJj8/X1//77vEmZiY5OTkEEK+/vrrsLCwX375ZeHChS+++KKs+KqqKjs7u7Fjxx4/ftzHx2fChAnr168nhMTHx5ubm5eUlGzbts3b23v06NF6enqEkJ9//vnll1+mlO7fv1+6kOjo6IiIiPr6+oyMDBU5ZQ5BCE/lbkLf9aXv+nIPKtnudPbBNUlWJZvUmXvFnWt86XAA+fpm7bc2NrYfrV793wv3u9iYVTeIkwvLnJ0cjx2PbtyYa4PMzEzGmKxBRgg5efKkrCnWElZWVi252zDP841vRCUWi5t9iTEmFouvXLkSERFx69Yt6URra+vZs2cfPXo0KCgoNTVV2mC6f//+jz/+eOzYsZkzZx49elR61ZFVq1Z99dVXzRbw4YcfSg+mfvPNN8OGDevXr1/37t1v3bplY2OTn59vb2/fpFpZnypjTHoLhJSUlLVr1545c2bu3LkuLi4BAQGEkNWrV0dGRhJCioqKvL29N27cuGjRonfffXft2rWVlZWurq5+fn5eXl5ubm45OTkcx1VWVl67dq3xqZ+HDh1yc3ObOnXq7t27VSQFCbpGoSVcjekiX+5qmPBcqNBSj047J/HaJV4Zx2dU4GaKIH8CgWB5ZGRmdvYPP/8yesacqQveP3rsWEpqmnRERnucPXu2cZTW1dVt2bLlAwVcrcbW1raiokL6+NGjRzY2NrKXbGxsZC9VVFSkp6enp6dv3Lhxz549aWlp27dvJ4RERkY6OTnFxcW5ubl5e3vn5ubevXt35MiR69at27Rp05dffkkIqa2tPXfunJmZ2RMrJ5mZmb/++qv0sZOTkzRif/jhh9ra2pycHJFI1GTwTuNqKyoqbG1tS0pKbty4ERoa+uWXX+7cuXPNmjWEELFYfOTIEVtbW0LI559//tZbb4WHh8fHx8fFxWVmZjo7O0vvka6np1dRUVFQUEAI2b9/f+PQvXPnTmZm5tdff52YmHjhwoXff/9948aN5eXlGzdulDVYlQItQmgFTzMa6U8j/bmrRWzrfT7ggMTHgk7vwk3oxBliVwK5srKymjJlinyXeebMGemgSkKIRCJ57733li9f3qqTJUpLS2/cuPHk9CZdoyEhIUVFRYQQnuctLCwcHBwSExM7depkYGAwePDgnTt3SmcrLi7+9NNPpW88ffp0UlLSK6+8QghZuXLl22+/7evru2HDhpUrV1ZWVso6TocPH37mzBlCyK1bt6R9j0968OBBXV2d9HF+fn737t15nl+6dOmqVas4jlu6dOl///vfxvObm5u7ubmJxWKhUFhQUDBw4MDq6mrZwgcNGnTs2DFCSFJSkuywYk1NjbTFaWxsHBYWZmBgEBAQIO1xLSsrMzQ0FIlEhJDLly/L2t85OTn37t2bO3euWCy+fv26dLBMTU3NypUrZ82a1fJNoAj49oK2CLChATaCL/sKojL53+7xC2IkEZ24Wd5cL2t0mYIqqqys3Lt374ULF7y9vXft2lVSUlJYWDhjxozu3bu3ajkWFhYt6RqdOXPm8uXLe/fuHRUVtWLFCkLIkiVLPvjgg8DAwH79+u3Zs+fmzZslJSVBQUHSFExJSdm5c+f9+/f3798/duzYnJyc1NTU2NjY0NBQ6aXGeZ4/cOCAh4fH+fPn33rrLULIo0ePZM3BqqqqnTt33r59e9u2bWKxeMiQISkpKTdv3rxx40ZwcHC/fv0YY5mZmUlJSUePHl2yZImpqenly5f37t2blZX1888/jx07dvny5T/++GNYWFh0dPRHH31kZWVlbGy8b98+Ly+vixcvvvHGG03W+Oabb65evXrs2LGZmZlOTk42NjZz5sxZtmxZXFxcVFTUL7/8Iu3RraiokL6F5/lXXnklISFBuihpK7y0tHTjxo3SAaXTp08XCpWWR5QxNe7devnll8PDw1t4h/qKiopWHRWHlsutZpuS2a/3eHM9Msubm9yZU/r1vrG5lWvixIkRERERERHKLkSZkpOTbW1tzc3Nn3wpNzeX53knJ6dm38jzfGJiooODg6WlpWxiUVFRcXGxp6enNDDEYnFxcbGdnV2zS2CMpaammpuby4bS1NXVJScnd+rU6Wlnr9fW1qampnp5eckCqaSkpKCgoEuXLtIpPM8XFBTIujobGhqSk5Pt7e1lRfI8f//+fQcHB9kqiouLjY2NZSNx2qlv377r168PCAiQ+6cbLUKQAwdDurQHXdKdO5nLNt7ll11reNWDe6sr19UcDUTQXl26dHnaS8++ojfHcd26dWsy0cbGpvGxRqFQ+LQUJIRQSmVjU6X09PR8fX2fsVJ9ff0m52haWVlJD/vJqmp8wE9HR6fJ/BzHNfmTmx3RqoIwWAbkhqNkmCPd/ZLg1jihuS556Yh42FHx4SzGq3GnAwBoPgQhyJ+jEf1vL0HGyzpTPbkVNyRdd4t/SOSrxc9/IwBAx0PXKCiKLkcme3CTPbiLBeybBP7juIY3vbm5PgJbg+e/FzTAyZMnG19RBaCdCgsLFbRkBCEoXJCIBokE9x9xX9/mu+5ueLkz954v52aCw4ea7LPPPvv888+bPdNAERoaGprcWRA0z+jRo5sc+JQXBCF0EA9T+kOQYEVPwdoESe/94lEu3AfdOW+MptFQ7u7uGzZs6LDVYZAwtAeOEUKHsjUgq/oIUifpeJnRQYfFk09LksowlgYAlAlBCEpgpkuW9uBSJ+r4WtLgw+LJpyUp5YhDAFAOBCEojbEOWdKdS52o082S9o8SzzwvyapCHAJAR0MQgpIZ65APunP3InREBsR/r3jRFcnDOmXXBADaBEEIKsFcl3zSW5A4QadWQrrubvginq+VPP9dAADthyAEFWJrQL5/UXA+VBhTyLx3if+XiovSAIDCIQhB5XQxo3uGCLYEC768zQ84JL5ejDQEAAVCEIKKGmBHr4YJp3txYdGSGeckRbXKLggANBSCEFQXR8n0LtzdCKG5Hum2p+HHJB5dpQAgdwhCUHUmOuSrvoK/Rgr/l8oHHBDHoqcUAOQKQQjqoZsFPRMqfKcbN+q4eNEVSRXuZQEAcoIgBLVBCXnNg7s9XqeklnTbIz6ahaYhAMgBghDUjLU+2TRI8MsAwbxLkmlnJWX1yi4IANQcghDU0ksONGG80M6QvLBbvC+DV3Y5AKDGEISgrgyE5LM+gm0hgveu8tPPSSoalF0QAKgnBCGot0H29PY4oYkO8dsrPpuHo4YA0GoIQlB7BkLybaBgfaDg1dOSD65JGtBRCgCtgSAEDRHqQm+OE94pJQOixOkVaBoCQEshCEFz2OiTA8ME07twgQfFuzIFyi4HANSDUNkFAMgTJWSWN9fHhk48ya6USr4NFOgjEAHgmdAiBA3kb0XPD6t/1ED6H0I3KQA8B4IQNJORkG0PEczy5voeEO/FiYYA8HToGgVNNsub87Okk05J4h+yj3oKqLLrAQAVhBYhaLh+tvTGWOG5PDb6uLgc12MDgCcgCEHzWeuT6BHCbpY04ID4bhkOGQLAPyAIQSsIOfJZH8EiXy7ksPgMLkADAI0gCEGLzPLmdg8Rvnpa/FMShs8AwN8QhKBdgkT0fKhwbQL/zmUJj5YhACAIQQt1NqUXxwjjStgrpyV1EmVXAwDKhiAEbWSlR06MEBJCRhzDUFIAbYcgBC2lJyD/GyzoZU37HxJnV6GTFEB7IQhBe1FCvugrmOzBDYySJJcjCwG0FIIQtN2S7txyfy7ksCT+IbIQQBshCAHIv7twPwZxw4+KLxciCwG0DoIQgBBCxrhyvw0UjokWn8xBFgJoFwQhwN9GONNdLwknnxFHIwsBtAmCEOCxYHu6b4hw8mlxVCayEEBbIAgB/uFFET0wVPjvc8hCAG2BIARoClkIoFUQhADNeFFE9w8VzjgvPotbVQBoOgQhQPOCRHTvEOHLp8TXipCFAJoMQQjwVEEi+kewMDRaHFeCLATQWAhCgGcZ5kh/DBKMOo5b2wNoLKGyCwBQdePcuNI6Muq45OIYoZ2BsqsBAHlDixDg+WZ4cTO8uGFHxWW4ZxOAxkEQArTI0h5ciD0dd0KMe/kCaBgEIUBLfdNPYKlPp52T8DhcCKBBEIQALcVRsmWQILuKLbuOViGA5kAQArSCgZDsHyrck8F+vssruxYAkA8EIUDrWOmRg0MFH96QnMZFZwA0AoIQoNW8zenOwcJXT4lTypGFAGoPQQjQFoPs6Uc9BWNOSHBCBYC6QxACtNGbXblhjnTKaTEGkQKoNQQhQNt91VdQJSYrYjGIFECNIQgB2k7Ikd1DhFvvs93pGFiaYbUAACAASURBVEQKoK4QhADtYqVH9gwRzL0kuVOKHlIAtYQgBGgvfyv6WR/BhL8kFQ3KLgUAWg9BCCAH/+7CDbSjb17AwUIA9YMgBJCPbwMFSWW44gyA+kEQAsiHvoDsfEnw4Q0JbmcPoF4QhABy42FK1wcKJp2SPMLBQgD1gSAEkKeJ7lywPX0LBwsB1AeCEEDOvu0nuPWQbbmPg4UA6gFBCCBnBkLyv8GC965IMipwsBBADSAIAeSvmwVd5CuYckYiQRQCqDwEIYBCLPLl9ARkTTw6SAFUHYIQQCE4SjYPEnybILlahFYhgEpDEAIoiqMR/TZQMO2spBZjSAFUGIIQQIEmuXMvWFDcpwlAlSEIARTrxyDB5hT+GjpIAVQVghBAsaz1yVd9BVPRQQqgqhCEAAr3Smeuqzn99CaSEEAVIQgBOsL3QYKNd/kbxeggBVA5CEKAjmBnQNYECGZfwCn2ACoHQQjQQaZ6cua65IdEnGIPoFoQhAAd58cgwco4SU4VWoUAKgRBCNBxPM3om125hVfQKARQIQhCgA61rIfgVgmLykSjEEBVIAgBOpSegKx/UTDvkqRKrOxSAIAQgiAE6HhDHWmgiH5+C6cVAqgEBCGAEnwZwP2YxOPOvQCqAEEIoASORvTtFwTvX8WoGQDlQxACKMd7ftz1YnYmD41CACVDEAIoh76AfB7AzbskEaNZCKBUj4NwxYoVum1iZGSkxD8AQH1FdOJs9MmvyUhCAGUSyh7p6+tv27atDYs4cuSI/OoB0C5rAwX/Oiqe5M6Z6yq7FABt9TgIDQ0NJ0yY0IZF5OXlya8eAO3S3ZKOduVW35R8HiBQdi2gZup5UtVAHjWwOgmpaPj7qZiRigZGCHlUT6RXeK9sIA3/3+lQJWb1/+yAqGog9a3vkmCElNW1t/42m+nODTWR5wIfB+Hbb7/dtkXMnz9fTsUAaKMVPTm/PeL5L3BORlTZtYBKqGwgWVWsoIbkVbOiWlJYw0rqSEkteVjHyupJWT0pq2OVYsIzYqxDTHSonoCY6hAdjhjrECElJjqUEGKiQ4QcIYQY6xCd/z8IZiikRsJ/rMvJiOi2fqwIJcRcr71/Zps5Gcp5iJnwaS8wxvLz8/Pz8/Py8kxMTEQikYuLi76+vnxXDwAOhnSWN7cilv9lABqF2qWeJ2mPWHI5S3lE0itYRgXLqCSZlYxnxNmY2hkQe0Nqo09s9KmvBbHSJ1Z6nLkeMdcl5rrUWIfoa+v+UiHvE3CbCcKkpKR169YdO3bM0tLS2trazMysrq7u4cOHeXl5Pj4+ERERr7zyilD41ASVl507d8bFxQ0fPjw4OFjR6wJQrve7C7x2NSSWcT7maBRqsrxqElvCYovZ7YfsTilLr2RORtTTlHQxo15mdLgTdTOmribUVEfZhWqZf+RZXV3d6tWrc3NzX3/99bVr1+rpNW36ZmRkHDp0aMKECUuWLOnXr5/iyvrhhx/Onj07b968JUuWrFq1atCgQYpbF4DSmeuS9/0ES6/x+4dq6498DSXmSWwJu1TALhSwmEJWK2Y9rWkvazrOjX7oz3mb0zZ0S4LcUcb+bmNWVlZGRkbOmTPHw8Pj2e+RSCRff/21p6fn2LFjFVSWr69vVFSUq6vroUOHduzYsXXr1mZne/nll8PDwydNmtSSZVZUVJiYyPUAK6gwtdvctRLivUu8LUTwogiNwlZTtc19r5wdy2J/5bJz+byrMe1vR1+0pS+KaCcTbFw5kPvmftwizMnJ+fTTTw0MDJ77HoFA8N577924cUOOdTSRnZ3t6upKCOnSpUtqaqriVgSgIvQFZEVPbvE1yflQhR93AEXgGblYwA4+4A9ksjoJGe5Ep3jQ3wbqWGNkhcp7/JHz8vJq1Tt79eol72Iek7VTOY6TSHCRftAKr3lyX93mj2axEc5oN6iT68Vseyq/I43Z6JNwN27HYM7fCltQnbSof5ox9tZbbxFC6urqDh48mJiY2J5VZmVl3bhxo7KysvHEioqKffv27du3TzpdJBJJT09MT0+XNg0BNJ6Aksie3IpY/PJTD6V1ZN0d3neP+NXTEmMhOTFCEBcujPRHCqqfFnXCUEoXLlxICDly5Ehubu7+/fuTkpJcXFyCg4NDQ0OdnZ1buDKe5+3t7WtraysrK8+dOxcUFCSdXlBQ0K9fv27duhFCFi1aFBMT89prr3366afvvvvu119/PXfu3Db9aQDqZ7wb999YNApV3a2H7Jvb/IEH/CgX7rsXBQPtKbaWWmvpiCVPT09CiJeXV2Bg4G+//Xb58uU1a9YYGhq+//77u3fvbuFCKKXnzp0rLS01NzdvPH3dunW9e/c+dOjQoUOHevXqtX79+qVLl3bu3DkyMnLatGmjR49u1Z8EoL44SiJ7ch/HoVGooo5ls6FHxaHHJV3Naeokna3BgkFIQfX3eNRoCyUkJFhYWDg6OkqfisXiHTt2TJ48uVULsbKyOnjwoKxF6Ofnt3z58oiICELIzp07P/3001u3brVkOSNGjDh27Jjs6Zw5cz777LOnzVxZWWlsbNyqOkF9qe/m5hl58bjeyu7iofaIw5bqgM19Ml/w6W1BHU/f9haPd5bo4LQH5WnV5jY0NBQInnNWUqvHp0k7MGVOnz4dFRXV2iBsIjs7W5asTk5Oubm5LXyjmZnZ//73vxaePkEIUakB1qBo6ru5P+rFr0ngxnXB8NFWUNzmPpfPPrgmKa8nH/XkxrtxHMX10ZVPvpu7vb9qhg4dun379nYuRCwWyxJbIBA0NDS0c4EAam1CJ66ygRzLxj17lSy9gkX8JZl6VjLXh4sfJ4zoxHHoBtVEKtG8d3BwKCwslD4uLCy0t7dXbj0AysVREumP4aPKVCMmy65LAg6Ie1jRxPHCVzsjAjVZ0yDcsWNHVVXVk/Ndvnz5jz/+KCoqUkQRAwcOPHHihPTxiRMncEE1gAmduIp6cioXjUIlOJPH/PaK0yrIrXHCZT04A3RRa7p/bOGsrKwrV66YmJiMHDkyNTV1/Pjxffv2DQ4ODgkJCQwM7N279/r16xcsWMBxbW9HrlixIi8vr6qqas2aNXZ2dp988omNjc2CBQsCAwMtLCwIIZs3b46JiWnvnwWg5jhK3vXj1sRLBjvga7jjlNeT965KjmWxH4IEoS5oA2qLf0Sas7NzQEDAyJEjCSHu7u5ff/21jY3N999/7+rq6uPjM3369FOnTrVzfT4+Pr169Vq3bt2oUaN69eolva63j49PTEwMz/M8z8fExHh7e7dzLQAaYLIHd6eU3CxBo7CDXCpg/vvEAkoSJgiRglrlqT82KaWDBw8ePHgwIaS6uvry5cs7duyIiIhoT3OQEDJx4sRmp3ft2nXlypXtWTKAhtHlyDvduC/i+T9DcEsKxeIZWX+H/zxesqG/YLSLSoycgI7UdJPT5s4NNTQ0fOmllzZu3JiVldUhVQEAIYTM8uaic/gMed+GFBorqCGDj4gPZvLXxwqRgtqp6VYPDw+XPnj48GF4ePgrr7yybdu2iooK6URDQ8O6uroOLRBAi5nqkDe8uK8TeGUXorGuF7OAA+JBdvTECKGDIbpDtVTTINTV/ftc0ejo6AULFgQEBHz//fcikSgoKGjixIkHDhx48m69AKA4C7oJtt3ni2uVXYcm2p7Kjzou/rov93EvAc6O0GZPPUY4aNCggwcPzp8//z//+U9mZubVq1fr6+vHjBnTkcUBgMiAjOvE/ZDER/qj105uGCHLrkl2prO/Rgq7WSADtd1Tg9De3j48PPy7776bOHGii4uLi4tLR5YFADKLfLlBUeL3/Th9DJqRBzFPZl2QJJWxK2FCK/RwwbOvLGNra7tgwQIHB4cOqwYAnuRlRntZ0/+l4kihHNRJyKRTkqwqFj0CKQh/Q2cLgBqY/4JgfSKCsL3K68ngI2ITHXJkuNBER9nVgMp4HIQPHz5s1TtLSkrkXQwANG+4E61sIBcLcB5F2z1qIP86Ju5tTX8fJMBNlKCxx7tDWVnZhx9+WFNT05K3nTlzZvPmzQqrCgD+gRIy14f7Do3CtqoSk9HHxb6WdG2gAGNjoInHQeju7j5z5sw333xzw4YNz4jDhISEOXPm3L59+z//+U+HVAgAhBDy7y7ciWw+uwqNwlarEpNRx8VdzOiG/khBaMY/Ro26urpu2rTpjz/+GDVqlEQi6dmzp5WVlaWlZU1NTWlpaUZGxo0bNwICAj766CN3d3dlVQygnUx0yMuduZ/v8h/3wuDRVqiTkNHHxV5m9CekIDxF09MnKKXTpk2bNm1adnb2pUuX8vLysrOzDQwMOnfuHBISsnHjRkNDQ6UUCgDvvMANiBJ/0EOA8yhaiBEy87zERJf+EIQUhKd66nmETk5OT7tANgAohacZ9bOku9P5KR4Y7NEi716RZFSy6BFCxCA8Az5OAOpk/gvc9xgy0zLfJvDHstiBoUI0oOHZEIQA6mSkM5dTRRJKMWTmOQ4+4L+8zR/9l8ACZ83D8yAIAdSJgJJpXeiv99AofJbkcjbrgmTPEIGLMbpE4flaEYRisfjmzZtJSUmM4dcogNJM78Jtvc/XSpRdh6qqbCDjTko+6S0IsEEKQos8NQgLCgrs7Oz27NkjmxIaGvrGG29UVVVt3LjxxIkTHVIeADTlZkL9rej+DDQKm8EI+fc5yUA7+oYXurugpZ46atTc3DwsLMzLy0s2JTQ0lFLau3fv3r17JyQkMMaavZ09ACjaG17cxrv8y53xXd/U6pt8bjX7M+Sp32wAT3rq7qKnp7dhw4bGU+bNmyd73K1bNwUWBQDPFObKzb8sSatg7ib4MfrYhXz2XaLk+lihLn4hQGtgfwFQP3oCMrkz93syekcfK68nr5+VbOgvcDDEjwNoHQQhgFqa5c39nswkGLj2/+ZclIxypqNd8J0Grda6nvSKioojR45UVFT4+voGBATgGCGAsnibUxcjcjSLhbrgY0h2PBDcLGHXx+LQILRFK349ZWZmDh48+MiRI6dPn54yZUpAQMCdO3cUVxkAPNsb3txv6B0lJL2CLb0p3D5YYIAchDZp0Y5TUVFhaGj4xx9/HDlyxMbGRjrx8uXLixYtWrt2rbe3tyIrBIDmTejELYxpeFgnsNTii6cwQqafk/zHW+JnqavsWkBdtahFuHfvXoFA4ODgIEtBQkhgYOD+/ft/++03hdUGAM9iqkOGOXK707W6UfjrPb5KTN7qIlZ2IaDGnh+EEomkqqqKEKKn1/Rnp76+fu/evQsLCxVSGgA8z2QP+ud97Q3C/Bqy9JpkQ38Bbi4B7fH8IBQIBEOHDpVIJFevXt20aVNGRkbjV729vfPy8hRVHQA80whnLrGMZVRo6eDR+Zcks7w5fyvEILRLi7pGPT09BQKBsbFxbGzsmDFjOnXqNG3atE2bNqWnpwsEAlx6FEBZdDky3o3bkaaNn8HDWSz+IfvQH/dYgvZqxSirKVOm+Pj4EEJKSkrOnTt35syZtWvX5uTk4LqjAEo02YObc1GyuLt2nT/3qIG8dUGyJViAew1C+7UiCKUpSAixsrIKDw8PDw8nhJw6dUohdQFAy/S3oxUNJP4h87PUoh7CT+MkQxzpIHst+pNBcdp73k3v3r0lEtwPBkBpKCGvdKZ/3uf9ArSlcZRWwX5L5uPH6Si7ENAQ7e1OMTU1tbCwkEspANA2r3lyf6YyXmsOFC6K4Rf5CuwNlV0HaIpnBWF9fb3s8eXLl3/99de4uDjFlwQAreNjTq31yPl8rUjC03ns1kO2oJt2HRMFhWpmZ9q3bx8hJDU11dTUtF+/fkuWLDl+/Lifn9+MGTNiYmLEYpy4CqByJntw21I1/4RCCSP/uSxZE8BhjAzIUdMg3Lp1q4ODAyGkc+fOmZmZixYtqqysXLRokYWFhZ+f3+7du4VCXM4PQOVEdKL7Mnixpkfhr/d4Yx0yvhOagyBPTVPt4sWLo0ePlj62tbWNiIiIiIgghBQVFe3atcvNza2D6wOAlnAzoc7G9GIB0+CBlFVisiJWcni4UGP/QlCSpj+sVq9eLe0abcLGxmbOnDnZ2dkdUhUAtNo4N25PhiY3Cb+7ww+yx3VkQP6aBqG5ufnIkSMJIWlpaZ06dfLx8Vm8ePG1a9ekl4+pq6urq6tTQpkA8DwRnejeDI29zlNlA1mbIIn0R6coyF8ze5WtrS0hJDY29tq1a999911lZeWoUaNMTU29vLxiY2OfvPQ2AKiCLmbUTIdcLdTMKFybwA915LqaozkI8vfUn1fDhw/ftGmTh4fH999/n5eXFxcXt2/fvt9//70jiwOAVhnfiWpk72h5PVl3R7IMzUFQjKfuWCYmJgsWLIiJicnLyxMIBB4eHrJLrAGAahrfidudroEtwq9uS8a4cl5maA6CQjzrXAihUDhx4sQOKwUA2qm7JeUouVnCemjQiJKSOvJDIn91LE7cAkVBVwOARhnnpmm9o1/FSyLcOXcTzYl2UDUIQgCNMt6N26tBvaMVDWTjXf49P3xTgQI93r0ePHjQtkW0+Y0AIHcBtrRSTJLKNCQLN97lhzqhOQiK9TgId+/e3bZF7NmzR07FAEB7UULCXOn+B5oQhGKerLvDL/JFcxAU6/Hx5+rq6tdee60Ni0hOTl64cKH8SgKAdgl14f4bK/lA/e9ZvyON72xCelujOQiK9TgIPT094+Pj27AId3d3+dUDAO01yI4mlLKSOmKl5le/+Oo2/0lv3GYCFO5xEL788sshISEikUiJ1QBA++kJSLA9dzybf7WzGjcKT+awGgn5lxOag6Bw//icbNiwobS0VFmlAIC8jHSmR7LU+zDhl7cl7/txHHIQFO8fQSgUCu3t7QcMGLB8+fK//vqrurpaWWUBQHuMdKbHs3mJ2kZhQimLf8jUukULauQfF2vw8vLavn27vr7+2bNnP/zww/j4+J49e4aEhAwZMiQoKEggQGc9gHpwMqJORjSmkAWJ1LJJ9UMi/1ZXgR6+cqBD/OMH1+DBg+/cuTNixIjPPvvs8uXLBQUFDg4OxcXF77zzjrOz8yeffFJTU6OsQgGgVUY606NZanmJmcoGsiONn95FLSMc1NE/gtDCwqK+vj4lJUX61NjYOCIiYt68eXFxcTExMZTS0NDQzMxMZdQJAK0z0pk7rJ6HCbel8oPsOUcjBCF0kKZd8O+///706dMXLVqUnJxMCAkPD9+2bRtjzMXFZdmyZfv27fv222/FYrEySgWAVuhnS7OrWHaV+mXhxrv8bG8cHYSO03RvMzY23rt3b1ZW1qJFiwghAoFg0qRJ69evl75qamr67rvvbty4saPLBIBWElAyzJE7qm6NwmtF7GEdGeqI5iB0nGZ+dtnY2OzcufPQoUPSp76+vs7Ozp9++qlEIiGE2NvbX7p0qUNrBIA2UceTKDbc5Wd546wJ6FAtusVXeHi4QCAYOHDgpEmT7O3tT58+reiyAKD9Rjhzcy811EnUZvhlRQPZm8HfGa+j7EJAu7S0I37MmDHbt2+/ffv24sWLX3/9dYXWBAByYalHulnQc/lq0yjcksIPceDsDZVdB2iZVtz02cXF5eeff1ZcKQAgd0MduZM5/FBH9WgS/nKP/7KvepQKmgRDswA02RBH+leuerQIrxezRw0kxAGHB6GjIQgBNFlfG3r/ESuuVXYdLbD1Pj/FgyIGoeMhCAE0mZAjQSJ6Ll/VLzEjYWRHKv8KLi4KyoDdDkDDveTAqX7v6Mkc5mJMvczQIAQlQBACaLiXHOlfOaoehH/e5yd74OsIlAN7HoCG87OkD+tYlgpfa61aTA5l8pPc8XUEyoE9D0DDUUJCHLhTKtw7uv8BHyiiIgNl1wHaCkEIoPleclDp3tE/7/OTMUwGlAc7H4Dme8lBdc8mLKollwpYmCu+i0BpsPMBaL7OplRXQO6WqWIW7kjjR7lwxri8KCgPghBAK7zkQE+qZKNwG/pFQdmw/wFohcEOVAXHy+RWs+RyhrsPgnIhCAG0wksO3Jk8XqJiUbg/g41y4YT4HgKlwg4IoBVEBsTRkMaVqFYS7n/Aj3VFcxCUDEEIoC0G2NHzqnRvwrJ6crWIDXPCtxAoGXZBAG3R345eLFChIIzK5EPsOaNW3BQVQCEQhADaYqAdvaBKt6HYl8HC3dAvCsqHIATQFk5GVE9AU8pVolFYIyZ/5fIjnfEVBMqHvRBAi/QX0Quq0Tt6IofvZU2t9ZVdBwCCEECrBInoBdUYL7PvAQt3w/cPqATsiABapL+dSrQIJYwczuTDcOIEqAYEIYAW6WZBi2tZfo2Syzifz1yNqbMRghBUAoIQQItwlATa0ksFSh47euABPxb9oqAysC8CaJcXRZzSzyY8ksVCXdAcBFWBIATQLgPslDxeJqOCPapnfpYIQlAVCEIA7RJgQxPLWGWD0go4nsOGOXGIQVAdCEIA7aInIN0t6dUipTUKj2ez4U7IQVAhCEIAraPEkyjEPDmTxw9xwDcPqBDsjgBaJ0iktIuOxhQydxNqa6CUlQM0D0EIoHX6i7iYQiZWRhQez+HRLwqqBkEIoHUs9IizEU0oVULvaHQ2G44bEIKKwR4JoI362iphvExJHUkuZ4G2aBGCakEQAmijPjb0WocH4YlsfpA9p4NvHVAx2CUBtFGAjRJahMdzcOIEqCIEIYA28rOkaRUdelo9IyQ6mw1zRBCCykEQAmgjHY74WtDYko5rFCY8ZIZC0tkUQQgqB0EIoKUCbDv0MOGJHDYM/aKgkhCEAFqqj3WHHiY8k8dC7BGEoIoQhABaqiPHy/CMXCrgB9jhCwdUEfZLAC3lYUYr6llBh9yt/nYpszWgIlxZDVQSghBAS1FCenfU2YRn89hAO/SLgopCEAJorwAbeq2oIy45ejaPDcIBQlBVCEIA7dWnQw4TMkIuFPD90SIEVYUgBNBefW24q0VM0UmYVMZMdaizEYIQVBSCEEB72RoQEx2a+kixUYgDhKDiEIQAWq0DTqI4l48DhKDSVDcIHz16FBcXV15eruxCADRZB9yG4hxahKDaVDQIo6KiBg0aNGbMmEuXLim7FgBNpugWYUo5E1DiZoIgBNWlokEYGhoaFxc3YMAAZRcCoOF6WdNbJUyssHMozuWzYPSLgmpT0SAEgI5hrEOcjWlimaIahTiDEFSfULmrj46O3rFjR+MpL7300quvvqqsegC0UE8rGlfC/CwVElfn8tlyf/zgBpWmhCAUi8W5ubl2dna6urr+/v4ikajxq9bW1h1fEoA287emscVsqqf8l5xRwep55mmGFiGoNEUF4YkTJz755JO4uDgvL69r167Jpl+4cGHSpElGRkYPHz7cuHHjuHHjbGxsFFQDALRETyt68IFCDhJeLGD9RWgOgqpT1D5qaWm5cOHCyMjIxhMZYzNmzFi5cmVycvKuXbtmzJhRVVXV7NsTExN79+6dnJy8fPnyiIgIBRUJAIQQfyt6s4TxCjhKeLmQBYrQHARVR5kir6+0ZcuWdevWyVqEV69eHT58eGFhoY6ODiHE19d3+fLlEydObPPyQ0ND79y5Y25uLn0aERExf/78p81cWVlpbGzc5nWBesHmbhXfKL19g+o9TOT8bTAgWvfrXuI+Vgq/rjc2t1Zp1eY2NDQUCATPnqdDjxGmp6d36tRJmoKEEE9Pz/T09PYs0MDAYNasWcOGDZM+tbW1NTExecb8z34VNAw2d8v1spHcqzH0d5BnF1G1mNyvaAhyNtJ7zreQfGBzaxX5bu4ODcJHjx4ZGDy+NaeRkdGjR4/as0CBQODu7t6rV692lwag1fytaFwJe7mzPJd5rYj5WtKOSUGA9ujQ49gikaisrEz2tLS01NbWtiMLAIBm9bSmcSVy7heNKWSBtjhACGqgQ4PQ19f3/v37paWlhBCe569fv969e/eOLAAAmtXLmsYWyz8I+yEIQR0oKggLCgp27dp19erV0tLSXbt2XbhwgRDSqVOnoUOHzp8///bt24sXL7axsRk0aJCCCgCAlhMZEF0ByayUZxbGFPIYMgpqQbFBWFBQ0LNnT1kQEkI2b95sYmIyffr0vLy8w4cPU4rPCYBK6GlFY+XXO5pewTiKm/GCelDUYBk/P7+dO3c+Od3S0vLHH39U0EoBoM38rWlcMRvrKp+l4QxCUCO46AMAEEKIv1xbhDhACGoEQQgAhPx96W25LQ1DRkGNIAgBgBBC3ExojZjl18hhUTVikljKelohCEE9IAgB4G/Si462fzk3itkLFtRAyTd5A2gpBCEA/M3fSj5nE17GAUJQKwhCAPibv5yuL4ORMqBeEIQA8Dfprerbv5wrRQhCUCcIQgD4WxczWljDyuvbtZCsKibmWScTBCGoDQQhAPyNo8TXsr3jZa4Usr62+GIBdYL9FQAea/9p9deKWIANmoOgThCEAPCYvxWNa9/A0SsIQlA3CEIAeKydNybkGYkrZr2tEYSgThCEAPDYCxY0rYJVi9v49julzN6QWujJtSYABUMQAsBjuhzxMqMJpW1sFF4tYn1x4gSoGwQhAPyDfzvOJrxaxPrgACGoGwQhAPyD9MaEbXvvVYyUATWEIASAf2hzi7BaTFLKWXdLBCGoGQQhAPxDd0uaUMoa+Fa/MbaYdbOkegIF1ASgSAhCAPgHYx3ibETvlbe6UYh+UVBTCEIAaKptt6HASBlQUwhCAGiqbdeXuVrE+iIIQQ0hCAGgqTZccbSolpTWMU8zBCGoHwQhADTV05reLGGtSkLpAULEIKgjBCEANGWlR0x1aHpFK6LwaiEfgGvKgHpCEAJAM/ytaWxrDhNiyCioLwQhADSjZ2tOq+eZNAjxfQJqCTsuADTD34q0vEWYUMps9KnIQKEVASgKghAAmvGiiLtcyCQti8Jz+WyQPfpFQV0hCAGgGdb6xN6Q3n7YoiQ8l8cG2CEIQV0hCAGgeQPs6Pn8FgXhhQJ+S3J2GQAAC8hJREFUIIIQ1BaCEACa18IgvFfO9ATUxRhBCOoKQQgAzRsgoufzn38TinN5bBCag6DOEIQA0Dw3E6rD0ZTn3YbiXD4OEIJ6QxACwFP1t6PnC54fhDhACGoNQQgAT/Xcw4QZFayBx7W2Qb0hCAHgqQY+LwjP5bNB9vgaAfWGPRgAnsrHgpbVsdzqp2bhuXw2QITmIKg3BCEAPBUlJMiOu/D0RuG5fDYQ15QBNYcgBIBnecZhwvwa8rCW+ZgjCEG9IQgB4FkGiJ4ahGfz+IH2HIccBDWHIASAZ+lpTdMqWGldMy/hDELQDAhCAHgWHY4E2NBLhU0bheX1ZFcaP8YFQQhqD0EIAM8x0J6Lzm56rbVvEiQjnbnOpghCUHsIQgB4jje86I40/lajWzKV1JHvE/nInvgCAU2A/RgAnsPBkK4JEEw9I6n//2bhF/GSCZ04dxM0B0ETCJVdAACogdc9ue3Xs4ZOWMFnxNo4OJ7uuTh+8UBlFwUgH2gRAsDz5ebmZn04aAZL+O1F27kWj9z/nHrzr4PKLgpAPhCEAPB8X6/+dFE3q8GuVgZCgZeV8eZhnT9ZukTZRQHIB4IQAJ4v4Vacv8hM9tRMT0dcV8Pzz79tL4DqQxACwPN1cu+cUV4teyrmGRHocBy+QEATYD8GgOebvWDRZ3H5eZW1hJA6Cb/8csZrM2YquygA+cCoUQB4vh49eny24fd3319UUZbBCXWmzZ4z950Fyi4KQD4QhADQIsEhIWevxSq7CgD506Ku0aFDhyYlJSm7Cuggvr6+ZWVlyq4COkJNTY2Xl5eyq4AOkpaWNnCgnM9h1aIgrKiokEgkyq4COkh5eTljT72dLGgSxhh+9GgPiURSUVEh32VqURACAAA8CUEIAABajap199HcuXNjYmIsLS1bMnN8fLynp6eBgYGiqwJVcOPGje7duwuFGA6m+Xiev3HjRp8+fZRdCHSE2trau3fv9ujRo4Xz//TTT507d372POodhFVVVZcvX1Z2FQAAoKL69u1rYmLy7HnUOwgBAADaCccIAQBAqyEIAQBAqyEIAQBAqyEIAQBAqwlWrFih7BraJTExMSoq6tGjR25ubs3O8PDhw/379ycnJ7u6uurq6sqmX7ly5cSJE4wxe3t72cSamprY2Njc3FxHR0dFVw7twfP8yZMnz58/b2Ji8rTzZxISEg4fPlxZWenq6iqb2NDQcOvWrZSUlMYTQY2UlpYeOHDg7t27Li4ujT/RMhKJJDExMT4+3tXVFTeKUnepqamxsbHW1tZ6enrNzvDgwYMDBw7k5+d36tSp7ZubqbPNmzfb2NjMnj3b29t75syZT86QmpoqEokmTZo0YsQILy+v0tJS6fTIyEhXV9fZs2c7OTl98cUX0om//PKLrq6ulZVVQEBAx/0N0CZjx47t0aPHzJkzraysoqKinpzhl19+sbW1nT17dpcuXebNmyedePz4cT09PWtra1tb246tF+TjwYMH9vb2ERERoaGhHh4excXFTWZISEgwMjKytrYmhFRVVSmlSJCL+vp6CwsLCwsLgUBw5cqVZuc5efKkpaXljBkz+vTp869//Yvn+batS42DUCwWOzs7Hz58mDFWVFRkbGyclJTUZJ4333xz9uzZ0sfDhw9fs2aNdGYDA4Pk5GTG2M2bN01MTB49esQYKygoKC8v37RpE4JQxZ0/f97Ozq6iooIxtnnz5u7duzeZob6+3s7O7uTJk4yx/Px8Q0PD1NRUxtjDhw+Li4vPnDmDIFRTb7/99r///W/p49GjR3/yySdNZqiqqsrNzc3IyEAQqjuJRCL92Jqamj4tCAMDA3/44QfGWHV1tZubW3R0dNvWpcb9Brdu3SorKxs+fDghxNraetCgQYcPH24yT1RU1Pjx46WPx48fHxUVRQg5ceKEl5eXp6cnIaR79+4ikejMmTOEEFtbW1NT0478E6BtoqKihg8fbmxsTAgZN27c7du3MzMzG89w/fr1+vr6kJAQQohIJAoKCpLuGxYWFlZWVkqpGeSi2U90Y4aGho0PdoD64jjO3d39GTMUFxdfvnx5woQJhBADA4ORI0c+uT+0dF1te5sqyMnJsbe3FwgE0qeOjo45OTmNZ+B5Pj8/38nJqckMOTk5sonNvhFUXOMtaGRkZGZm1mQL5uTkODg4yA4YODo65ubmdnSVIG+Msdzc3Cc/0aCdcnNzdXV1bWxspE/bsz+ocRBKJBJKqeypQCAQi8WNZ+B5nud52TyyGZq8USgUNnkjqLjnbsHn7hugphpvWWxWLSeRSBqPjmnP/qDGQWhvb19UVMT+/xJxBQUFTbpEhEKhjY1NUVGRbAYHBwfpGwsLC2WzyaaDumi8Bevr6x8+fNhkCz65idFdpgEopXZ2dk9+okE72dnZ1dbWPnr0SPq0PR9zNQ5CPz8/Qsj169cJIbW1tefOnZMeE6qvr5fdpTM4OPj48ePSx9HR0cHBwYSQgQMH3rx5s7i4mBCSnZ2dkpISFBSkjL8A2ig4OPivv/6S3mb5r7/+cnZ27tSpEyGksrKyurqaENKzZ8+amppbt24RQqqrq8+fPy/dN0DdNfuJJoSUlJSgdaglampqpDfmtbOz8/b2jo6OJv9/PlXbP+ZtHNCjGj755BNPT89vvvlm2LBhQ4YMkU7ctWuXo6Oj9PH169dNTU1XrFixcOFCa2vrzMxM6fTXX3+9b9++a9eu9ff3nzt3rnTinTt3Zs2aFRwcbGtrO2vWrO+++67j/yJoCbFY3LNnz7Fjx3711VdOTk4bNmyQTo+IiPjPf/4jfbx8+XJvb+9vvvlm8ODBo0aNkk7Mz8+fNWvW6NGjDQwMZs2a9fHHHyvnD4C2unnzpqmpaWRk5HvvvWdpaZmeni6dTgi5dOkSY6yhoWHWrFmvvvoqIWT69Olvv/22MsuF9vnwww9nzZqlq6s7duzYWbNmSc+WWbZsmewTvWXLFjs7uy+//HLixIkvvPBCXV1d21ak9nefOHjw4OXLl93c3KZOnaqvr08ISU9Pj4mJeeWVV6Qz3LlzZ9euXbq6ulOmTHFxcZFOlEgkf/75Z2JiYo8ePSZOnCjtaM7Ozj5y5Ihsya6urtIhqaCC/q+9+3dJLYzjOC7+iPIEwoFKcNGEhoZA0BAcLBAabbEhifAvkObGoP6IECIo0CEVF0GCI/0YxKYIwUGO6NBSmbpECHcQDhfpLrfLfXo879cgnC+in+l80Oec5wwGg7Ozs+fn583NzVgsNh5eX18rihIOh8eH+Xy+VqstLy/v7++P77zu9Xq5XM74EFVVx5ecQSKNRiOXy9nt9mQyaWyjcXp6Go/HFxcXR6NRJpMx3uxwOFKplJig+LZsNvv+/m4c7u7uzs/P1+v1l5cX4+SsaVqlUllYWEilUi6X6+++SPoiBADgOyReIwQA4PsoQgCAqVGEAABTowgBAKZGEQIATI0iBACYGkUIADA1ihAAYGoUITBV+v1+p9MRnQKQiV10AAD/zN3dXT6fn5mZCQQCiURCdBxADmyxBkyPZrO5srJisVi63a6qqk6nU3QiQAIUIQDA1PhrFJCepmmFQuH8/HxtbW388I3xSuHOzs7e3p7odMBPxy9CYBq0Wi2/3397e2s8Zfr19XVra2t7e/vw8FBsNuCH46pRYBpUq1VFUdbX142JqqonJydHR0dvb28CgwE/H0UITANN0yKRiMPh+H24urr68fFxf38vKhUgBYoQmAbVajUajU4Mh8Oh8QrgTyhCQHq6rrfb7Y2NjYn54+OjxWLxer3/PxIgEYoQkJ6maYqihEKhiXm5XF5aWgoGg0JSAbKgCAHpfblAOBwOr66uDg4ObDabqGCAFChCQHpfLhAeHx/7fL50Oi0kEiARbqgH5Kbruq7rEwuEl5eX5XK5VCrNzs4KygVIgyIEZPX5+fn09HRxcWG1Wq1W68PDw2g0arfbxWLR4/Hc3NwoiiI6IyABdpYBZNXr9SqVysTQ7XYHg8G5uTkhkQAZUYQAAFPjYhkAgKlRhAAAU/sFSYrpHNm6LKEAAAAASUVORK5CYII="
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "J(D̂::Real) = 𝒥(D̂,Δ,B,u0,U⃗,x,t)\n",
    "log10D̂min,log10D̂max = -3,0\n",
    "S = Chebyshev(log10D̂min..log10D̂max)\n",
    "p = 50\n",
    "D̂ = 10 .^points(S,p)\n",
    "JD̂ = J.(D̂)\n",
    "j = Fun(S,ApproxFun.transform(S,JD̂))\n",
    "D̂opt = 10 .^argmin(j)\n",
    "\n",
    "fig4 = plot(j,xticks=(log10D̂min:log10D̂max,10.0.^(log10D̂min:log10D̂max)),ylabel=L\"\\mathcal{J}\\left[\\hat u_{\\hat D}\\,;(\\vec u_j)\\right]\",label=false)\n",
    "fig4 = scatter!([log10(D̂opt)],[minimum(j)],yscale=:log10,xlabel=L\"\\hat D\",label=L\"{\\hat D}^\\ast=%$D̂opt\",title=L\"\\textrm{Figure\\ 4}\",fmt=:png)\n",
    "display(fig4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99f7261b-579f-499c-a9cf-2d94212366c1",
   "metadata": {},
   "source": [
    "That's pretty close (to the $D=0.05$ that was used to simulate the data)!\n",
    "\n",
    "---\n",
    "\n",
    "## Interfacing with nonlinear optimization and automatic differentiation\n",
    "\n",
    "In the last section, our method to estimate ${\\hat D}^\\ast$ was very crude indeed. What if there were many more parameters in the model? What if function evaluations of $J$ were much more expensive? It would be nice to minimize the loss functional defined above, that includes ApproxFun types, with Julia-optimized nonlinear optimization packages like Optim."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b833da81-2b5f-42e1-ab5e-d1370ef086c8",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching optimize(::typeof(J), ::Int64, ::NelderMead{Optim.AffineSimplexer, Optim.AdaptiveParameters})\n\u001b[0mClosest candidates are:\n\u001b[0m  optimize(::Any, ::Any, ::Any, \u001b[91m::AbstractArray\u001b[39m; inplace, autodiff, kwargs...) at C:\\Users\\matth\\.julia\\packages\\Optim\\DmCp2\\src\\multivariate\\optimize\\interface.jl:102\n\u001b[0m  optimize(::Any, ::Any, ::Any, \u001b[91m::AbstractArray{T}\u001b[39m, \u001b[91m::Optim.AbstractOptimizer\u001b[39m) where T at C:\\Users\\matth\\.julia\\packages\\Optim\\DmCp2\\src\\multivariate\\optimize\\interface.jl:157\n\u001b[0m  optimize(::Any, ::Any, ::Any, \u001b[91m::AbstractArray{T}\u001b[39m, \u001b[91m::Optim.Options\u001b[39m; inplace, autodiff) where T at C:\\Users\\matth\\.julia\\packages\\Optim\\DmCp2\\src\\multivariate\\optimize\\interface.jl:129\n\u001b[0m  ...",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching optimize(::typeof(J), ::Int64, ::NelderMead{Optim.AffineSimplexer, Optim.AdaptiveParameters})\n\u001b[0mClosest candidates are:\n\u001b[0m  optimize(::Any, ::Any, ::Any, \u001b[91m::AbstractArray\u001b[39m; inplace, autodiff, kwargs...) at C:\\Users\\matth\\.julia\\packages\\Optim\\DmCp2\\src\\multivariate\\optimize\\interface.jl:102\n\u001b[0m  optimize(::Any, ::Any, ::Any, \u001b[91m::AbstractArray{T}\u001b[39m, \u001b[91m::Optim.AbstractOptimizer\u001b[39m) where T at C:\\Users\\matth\\.julia\\packages\\Optim\\DmCp2\\src\\multivariate\\optimize\\interface.jl:157\n\u001b[0m  optimize(::Any, ::Any, ::Any, \u001b[91m::AbstractArray{T}\u001b[39m, \u001b[91m::Optim.Options\u001b[39m; inplace, autodiff) where T at C:\\Users\\matth\\.julia\\packages\\Optim\\DmCp2\\src\\multivariate\\optimize\\interface.jl:129\n\u001b[0m  ...",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[7]:3",
      " [2] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [3] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "using Optim\n",
    "\n",
    "Optim.minimizer(optimize(J,1,NelderMead()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "679bd9f7-7c13-4711-9f2c-093129883d3e",
   "metadata": {},
   "source": [
    "Similarly, being able to use automatic differentiation packages like Zygote would allow gradient-required optimization algorithms like (L-)BFGS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "025c54bd-ed9f-4331-a67f-247685ff073b",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching AbstractFloat(::Infinities.InfiniteCardinal{0})\n\u001b[0mClosest candidates are:\n\u001b[0m  (::Type{T})(::Real, \u001b[91m::RoundingMode\u001b[39m) where T<:AbstractFloat at C:\\Users\\matth\\AppData\\Local\\Programs\\Julia-1.7.1\\share\\julia\\base\\rounding.jl:200\n\u001b[0m  (::Type{T})(::T) where T<:Number at C:\\Users\\matth\\AppData\\Local\\Programs\\Julia-1.7.1\\share\\julia\\base\\boot.jl:770\n\u001b[0m  (::Type{T})(\u001b[91m::AbstractChar\u001b[39m) where T<:Union{AbstractChar, Number} at C:\\Users\\matth\\AppData\\Local\\Programs\\Julia-1.7.1\\share\\julia\\base\\char.jl:50\n\u001b[0m  ...",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching AbstractFloat(::Infinities.InfiniteCardinal{0})\n\u001b[0mClosest candidates are:\n\u001b[0m  (::Type{T})(::Real, \u001b[91m::RoundingMode\u001b[39m) where T<:AbstractFloat at C:\\Users\\matth\\AppData\\Local\\Programs\\Julia-1.7.1\\share\\julia\\base\\rounding.jl:200\n\u001b[0m  (::Type{T})(::T) where T<:Number at C:\\Users\\matth\\AppData\\Local\\Programs\\Julia-1.7.1\\share\\julia\\base\\boot.jl:770\n\u001b[0m  (::Type{T})(\u001b[91m::AbstractChar\u001b[39m) where T<:Union{AbstractChar, Number} at C:\\Users\\matth\\AppData\\Local\\Programs\\Julia-1.7.1\\share\\julia\\base\\char.jl:50\n\u001b[0m  ...",
      "",
      "Stacktrace:",
      "  [1] float(x::Infinities.InfiniteCardinal{0})",
      "    @ Base .\\float.jl:269",
      "  [2] ChainRulesCore.ProjectTo(x::Infinities.InfiniteCardinal{0})",
      "    @ ChainRulesCore C:\\Users\\matth\\.julia\\packages\\ChainRulesCore\\oBjCg\\src\\projection.jl:161",
      "  [3] rrule(#unused#::typeof(-), x::Infinities.InfiniteCardinal{0}, y::Int64)",
      "    @ ChainRules C:\\Users\\matth\\.julia\\packages\\ChainRules\\AL6Lg\\src\\rulesets\\Base\\fastmath_able.jl:163",
      "  [4] rrule(::Zygote.ZygoteRuleConfig{Zygote.Context}, ::Function, ::Infinities.InfiniteCardinal{0}, ::Int64)",
      "    @ ChainRulesCore C:\\Users\\matth\\.julia\\packages\\ChainRulesCore\\oBjCg\\src\\rules.jl:134",
      "  [5] chain_rrule",
      "    @ C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\chainrules.jl:216 [inlined]",
      "  [6] macro expansion",
      "    @ C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0 [inlined]",
      "  [7] _pullback(::Zygote.Context, ::typeof(-), ::Infinities.InfiniteCardinal{0}, ::Int64)",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:9",
      "  [8] _pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\ApproxFunBase\\vVgJc\\src\\Operators\\Operator.jl:173 [inlined]",
      "  [9] _pullback(ctx::Zygote.Context, f::typeof(bandwidths), args::ApproxFunBase.ConcreteEvaluation{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, typeof(leftendpoint), Int64, Float64})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [10] _pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\ApproxFunBase\\vVgJc\\src\\Operators\\Operator.jl:171 [inlined]",
      " [11] _pullback(::Zygote.Context, ::typeof(BandedMatrices.bandwidth), ::ApproxFunBase.ConcreteEvaluation{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, typeof(leftendpoint), Int64, Float64}, ::Int64)",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [12] _pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\ApproxFunBase\\vVgJc\\src\\Operators\\Operator.jl:119 [inlined]",
      " [13] _pullback(ctx::Zygote.Context, f::typeof(ApproxFunBase.isbandedbelow), args::ApproxFunBase.ConcreteEvaluation{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, typeof(leftendpoint), Int64, Float64})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [14] _pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\ApproxFunBase\\vVgJc\\src\\Operators\\Operator.jl:121 [inlined]",
      " [15] _pullback(ctx::Zygote.Context, f::typeof(ApproxFunBase.isbanded), args::ApproxFunBase.ConcreteEvaluation{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, typeof(leftendpoint), Int64, Float64})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [16] _pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\ApproxFunBase\\vVgJc\\src\\Operators\\SubOperator.jl:102 [inlined]",
      " [17] _pullback(::Zygote.Context, ::typeof(view), ::ApproxFunBase.ConcreteEvaluation{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, typeof(leftendpoint), Int64, Float64}, ::UnitRange{Int64}, ::UnitRange{Int64})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [18] _pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\ApproxFunBase\\vVgJc\\src\\Operators\\general\\InterlaceOperator.jl:348 [inlined]",
      " [19] _pullback(ctx::Zygote.Context, f::Type{Matrix}, args::ApproxFunBase.SubOperator{Float64, ApproxFunBase.InterlaceOperator{Float64, 1, Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, ApproxFunBase.ArraySpace{ConstantSpace{DomainSets.Point{Int64}, Float64}, 1, DomainSets.Point{Int64}, Float64}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SVector{1, Int64}, StaticArrays.SVector{1, Int64}}}}, Tuple{Int64, Infinities.InfiniteCardinal{0}}}, Tuple{UnitRange{Int64}, UnitRange{Int64}}, Tuple{Int64, Int64}, Tuple{Int64, Int64}})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [20] _pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\ApproxFunBase\\vVgJc\\src\\Operators\\Operator.jl:781 [inlined]",
      " [21] _pullback(ctx::Zygote.Context, f::Type{AbstractMatrix}, args::ApproxFunBase.SubOperator{Float64, ApproxFunBase.InterlaceOperator{Float64, 1, Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, ApproxFunBase.ArraySpace{ConstantSpace{DomainSets.Point{Int64}, Float64}, 1, DomainSets.Point{Int64}, Float64}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SVector{1, Int64}, StaticArrays.SVector{1, Int64}}}}, Tuple{Int64, Infinities.InfiniteCardinal{0}}}, Tuple{UnitRange{Int64}, UnitRange{Int64}}, Tuple{Int64, Int64}, Tuple{Int64, Int64}})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [22] _pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\ApproxFunBase\\vVgJc\\src\\Operators\\Operator.jl:228 [inlined]",
      " [23] _pullback(::Zygote.Context, ::typeof(ApproxFunBase.defaultgetindex), ::ApproxFunBase.InterlaceOperator{Float64, 1, Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, ApproxFunBase.ArraySpace{ConstantSpace{DomainSets.Point{Int64}, Float64}, 1, DomainSets.Point{Int64}, Float64}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SVector{1, Int64}, StaticArrays.SVector{1, Int64}}}}, Tuple{Int64, Infinities.InfiniteCardinal{0}}}, ::UnitRange{Int64}, ::UnitRange{Int64})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [24] _pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\ApproxFunBase\\vVgJc\\src\\Operators\\Operator.jl:208 [inlined]",
      " [25] _pullback(::Zygote.Context, ::typeof(getindex), ::ApproxFunBase.InterlaceOperator{Float64, 1, Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, ApproxFunBase.ArraySpace{ConstantSpace{DomainSets.Point{Int64}, Float64}, 1, DomainSets.Point{Int64}, Float64}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SVector{1, Int64}, StaticArrays.SVector{1, Int64}}}}, Tuple{Int64, Infinities.InfiniteCardinal{0}}}, ::UnitRange{Int64}, ::UnitRange{Int64})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [26] _pullback",
      "    @ .\\In[2]:9 [inlined]",
      " [27] _pullback(::Zygote.Context, ::typeof(exp), ::ApproxFunBase.ConstantTimesOperator{ApproxFunBase.ConcreteDerivative{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Int64, Float64}, Float64}, ::ApproxFunBase.InterlaceOperator{Float64, 1, Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, ApproxFunBase.ArraySpace{ConstantSpace{DomainSets.Point{Int64}, Float64}, 1, DomainSets.Point{Int64}, Float64}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SVector{1, Int64}, StaticArrays.SVector{1, Int64}}}}, Tuple{Int64, Infinities.InfiniteCardinal{0}}}, ::Float64, ::Fun{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Float64, Vector{Float64}}, ::Int64)",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [28] _pullback",
      "    @ .\\In[2]:27 [inlined]",
      " [29] _pullback(::Zygote.Context, ::typeof(exp), ::ApproxFunBase.ConstantTimesOperator{ApproxFunBase.ConcreteDerivative{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Int64, Float64}, Float64}, ::ApproxFunBase.InterlaceOperator{Float64, 1, Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, ApproxFunBase.ArraySpace{ConstantSpace{DomainSets.Point{Int64}, Float64}, 1, DomainSets.Point{Int64}, Float64}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SVector{1, Int64}, StaticArrays.SVector{1, Int64}}}}, Tuple{Int64, Infinities.InfiniteCardinal{0}}}, ::Float64, ::Fun{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Float64, Vector{Float64}})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [30] (::Zygote.var\"#1098#1102\"{Zygote.Context, typeof(exp)})(::ApproxFunBase.ConstantTimesOperator{ApproxFunBase.ConcreteDerivative{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Int64, Float64}, Float64}, ::Vararg{Any})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\lib\\broadcast.jl:186",
      " [31] _broadcast_getindex_evalf(::Zygote.var\"#1098#1102\"{Zygote.Context, typeof(exp)}, ::ApproxFunBase.ConstantTimesOperator{ApproxFunBase.ConcreteDerivative{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Int64, Float64}, Float64}, ::ApproxFunBase.InterlaceOperator{Float64, 1, Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, ApproxFunBase.ArraySpace{ConstantSpace{DomainSets.Point{Int64}, Float64}, 1, DomainSets.Point{Int64}, Float64}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SVector{1, Int64}, StaticArrays.SVector{1, Int64}}}}, Tuple{Int64, Infinities.InfiniteCardinal{0}}}, ::Float64, ::Function)",
      "    @ Base.Broadcast .\\broadcast.jl:670",
      " [32] _broadcast_getindex",
      "    @ .\\broadcast.jl:643 [inlined]",
      " [33] getindex",
      "    @ .\\broadcast.jl:597 [inlined]",
      " [34] copy(bc::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, Zygote.var\"#1098#1102\"{Zygote.Context, typeof(exp)}, Tuple{Base.RefValue{ApproxFunBase.ConstantTimesOperator{ApproxFunBase.ConcreteDerivative{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Int64, Float64}, Float64}}, Base.RefValue{ApproxFunBase.InterlaceOperator{Float64, 1, Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, ApproxFunBase.ArraySpace{ConstantSpace{DomainSets.Point{Int64}, Float64}, 1, DomainSets.Point{Int64}, Float64}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SVector{1, Int64}, StaticArrays.SVector{1, Int64}}}}, Tuple{Int64, Infinities.InfiniteCardinal{0}}}}, Vector{Float64}, Fun{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Float64, Vector{Float64}}}})",
      "    @ Base.Broadcast .\\broadcast.jl:899",
      " [35] materialize(bc::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, Zygote.var\"#1098#1102\"{Zygote.Context, typeof(exp)}, Tuple{Base.RefValue{ApproxFunBase.ConstantTimesOperator{ApproxFunBase.ConcreteDerivative{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Int64, Float64}, Float64}}, Base.RefValue{ApproxFunBase.InterlaceOperator{Float64, 1, Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, ApproxFunBase.ArraySpace{ConstantSpace{DomainSets.Point{Int64}, Float64}, 1, DomainSets.Point{Int64}, Float64}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SVector{1, Int64}, StaticArrays.SVector{1, Int64}}}}, Tuple{Int64, Infinities.InfiniteCardinal{0}}}}, Vector{Float64}, Fun{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Float64, Vector{Float64}}}})",
      "    @ Base.Broadcast .\\broadcast.jl:860",
      " [36] _broadcast(::Zygote.var\"#1098#1102\"{Zygote.Context, typeof(exp)}, ::Base.RefValue{ApproxFunBase.ConstantTimesOperator{ApproxFunBase.ConcreteDerivative{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Int64, Float64}, Float64}}, ::Vararg{Any})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\lib\\broadcast.jl:163",
      " [37] adjoint",
      "    @ C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\lib\\broadcast.jl:186 [inlined]",
      " [38] _pullback(::Zygote.Context, ::typeof(Base.Broadcast.broadcasted), ::Base.Broadcast.DefaultArrayStyle{1}, ::typeof(exp), ::Base.RefValue{ApproxFunBase.ConstantTimesOperator{ApproxFunBase.ConcreteDerivative{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Int64, Float64}, Float64}}, ::Base.RefValue{ApproxFunBase.InterlaceOperator{Float64, 1, Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, ApproxFunBase.ArraySpace{ConstantSpace{DomainSets.Point{Int64}, Float64}, 1, DomainSets.Point{Int64}, Float64}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SVector{1, Int64}, StaticArrays.SVector{1, Int64}}}}, Tuple{Int64, Infinities.InfiniteCardinal{0}}}}, ::Vector{Float64}, ::Function)",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\ZygoteRules\\AIbCs\\src\\adjoint.jl:65",
      " [39] _apply(::Function, ::Vararg{Any})",
      "    @ Core .\\boot.jl:814",
      " [40] adjoint",
      "    @ C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\lib\\lib.jl:200 [inlined]",
      " [41] _pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\ZygoteRules\\AIbCs\\src\\adjoint.jl:65 [inlined]",
      " [42] _pullback",
      "    @ .\\broadcast.jl:1303 [inlined]",
      " [43] _pullback",
      "    @ .\\In[5]:2 [inlined]",
      " [44] _pullback(::Zygote.Context, ::typeof(𝒥), ::Float64, ::ApproxFunBase.ConcreteDerivative{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Int64, Float64}, ::ApproxFunBase.InterlaceOperator{Float64, 1, Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, ApproxFunBase.ArraySpace{ConstantSpace{DomainSets.Point{Int64}, Float64}, 1, DomainSets.Point{Int64}, Float64}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{FillArrays.Ones{Int64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}, ApproxFunBase.CachedIterator{Tuple{Int64, Int64}, ApproxFunBase.BlockInterlacer{Tuple{StaticArrays.SVector{1, Int64}, StaticArrays.SVector{1, Int64}}}}, Tuple{Int64, Infinities.InfiniteCardinal{0}}}, ::Fun{Chebyshev{IntervalSets.ClosedInterval{Int64}, Float64}, Float64, Vector{Float64}}, ::Vector{Vector{Float64}}, ::Vector{Float64}, ::Vector{Float64})",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [45] _pullback",
      "    @ .\\In[6]:1 [inlined]",
      " [46] _pullback(ctx::Zygote.Context, f::typeof(J), args::Float64)",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface2.jl:0",
      " [47] _pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface.jl:34 [inlined]",
      " [48] pullback",
      "    @ C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface.jl:40 [inlined]",
      " [49] (::Zygote.var\"#59#60\"{typeof(J)})(x::Float64)",
      "    @ Zygote C:\\Users\\matth\\.julia\\packages\\Zygote\\FPUm3\\src\\compiler\\interface.jl:82",
      " [50] top-level scope",
      "    @ In[8]:3",
      " [51] eval",
      "    @ .\\boot.jl:373 [inlined]"
     ]
    }
   ],
   "source": [
    "using Zygote\n",
    "\n",
    "J'(D̂opt)"
   ]
  }
 ],
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