{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3471b94b",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 2023-10-25 Multigrid"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4159be0e",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": ""
    }
   },
   "source": [
    "## Last time\n",
    "\n",
    "* Preconditioning building blocks\n",
    "* Domain decomposition\n",
    "* PETSc discussion\n",
    "\n",
    "## Today\n",
    "* Software licensing\n",
    "* Projects\n",
    "* Multigrid\n",
    "  * Spectral perspective\n",
    "  * Factorization perspective\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e82d841d",
   "metadata": {
    "hideOutput": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "advdiff_matrix (generic function with 1 method)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "default(linewidth=3)\n",
    "using LinearAlgebra\n",
    "using SparseArrays\n",
    "\n",
    "function my_spy(A)\n",
    "    cmax = norm(vec(A), Inf)\n",
    "    s = max(1, ceil(120 / size(A, 1)))\n",
    "    spy(A, marker=(:square, s), c=:diverging_rainbow_bgymr_45_85_c67_n256, clims=(-cmax, cmax))\n",
    "end\n",
    "\n",
    "function advdiff_matrix(n; kappa=1, wind=[0, 0])\n",
    "    h = 2 / (n + 1)\n",
    "    rows = Vector{Int64}()\n",
    "    cols = Vector{Int64}()\n",
    "    vals = Vector{Float64}()\n",
    "    idx((i, j),) = (i-1)*n + j\n",
    "    in_domain((i, j),) = 1 <= i <= n && 1 <= j <= n\n",
    "    stencil_advect = [-wind[1], -wind[2], 0, wind[1], wind[2]] / h\n",
    "    stencil_diffuse = [-1, -1, 4, -1, -1] * kappa / h^2\n",
    "    stencil = stencil_advect + stencil_diffuse\n",
    "    for i in 1:n\n",
    "        for j in 1:n\n",
    "            neighbors = [(i-1, j), (i, j-1), (i, j), (i+1, j), (i, j+1)]\n",
    "            mask = in_domain.(neighbors)\n",
    "            append!(rows, idx.(repeat([(i,j)], 5))[mask])\n",
    "            append!(cols, idx.(neighbors)[mask])\n",
    "            append!(vals, stencil[mask])\n",
    "        end\n",
    "    end\n",
    "    sparse(rows, cols, vals)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29e05a3f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Licensing and Copyright"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87446123",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "* In the US, all creative works are subject to copyright. This includes code.\n",
    "* At CU, you own copyright for anything you create in coursework or on your own time.\n",
    "* CU asserts copyright on work you while employed (e.g., as a GRA)\n",
    "  * My group has an exemption letter that applies in some cases.\n",
    "* **No permissions** are granted by default, even if you post your code publicly on GitHub."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffb979d9",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": ""
    }
   },
   "source": [
    "<blockquote class=\"twitter-tweet\"><p lang=\"en\" dir=\"ltr\"><a href=\"https://twitter.com/github?ref_src=twsrc%5Etfw\">@github</a> copilot, with &quot;public code&quot; blocked, emits large chunks of my copyrighted code, with no attribution, no LGPL license. For example, the simple prompt &quot;sparse matrix transpose, cs_&quot; produces my cs_transpose in CSparse. My code on left, github on right. Not OK. <a href=\"https://t.co/sqpOThi8nf\">pic.twitter.com/sqpOThi8nf</a></p>&mdash; Tim Davis (@DocSparse) <a href=\"https://twitter.com/DocSparse/status/1581461734665367554?ref_src=twsrc%5Etfw\">October 16, 2022</a></blockquote> <script async src=\"https://platform.twitter.com/widgets.js\" charset=\"utf-8\"></script> "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05dcb88e",
   "metadata": {},
   "source": [
    "Almost all licenses require these conditions (from BSD-2-Clause)\n",
    "1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.\n",
    "2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66ef5772",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# License compatibility"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdecb8ef",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "<img src=\"https://dwheeler.com/essays/floss-license-slide-image.png\" width=\"100%\" />\n",
    "\n",
    "[CC BY-SA-3.0](https://creativecommons.org/licenses/by-sa/3.0/) [David A. Wheeler](https://dwheeler.com/essays/floss-license-slide.html)\n",
    "\n",
    "## Recommendation\n",
    "\n",
    "Use the most standard license that meets your needs.\n",
    "\n",
    "License proliferation saps time and discourages users. See [OSI recommendations](https://opensource.org/licenses/category) and [Todd Gamblin's recommendations for LLNL](https://www.osti.gov/servlets/purl/1782513/)\n",
    "\n",
    "* [SPDX License names](https://spdx.org/licenses/)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e28d6e47",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "* Permissive (MIT, BSD, Apache-2.0)\n",
    "  * Can put into proprietary software, as a library or with customization.\n",
    "  * Can't plagiarize (attribution required)\n",
    "* Weak Copyleft (LGPL, MPL)\n",
    "  * Can use as a *dynamically linked* library in proprietary products\n",
    "    * Must be able to link modifications of library.\n",
    "  * Modifications are subject to LGPL (anyone who has the product can have the code, modify, redistribute)\n",
    "* Strong Copyleft (GPL, AGPL)\n",
    "  * \"viral\" -- anyone who has/uses the software product can access the source code, modify, and redistribute."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4206c8c2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Software patents and inbound=outbound"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f11a8e5",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "* Patent litigation is hugely destructive for open source communities.\n",
    "* There is no legal consensus about whether making a contribution implies a grant to any patents that may be infringed by that contribution.\n",
    "* Apache-2.0 $\\approx$ MIT/BSD plus patent grant and indemnification\n",
    "\n",
    "## Problem\n",
    "GPL/LGPL forbid adding new restrictions. The Free Software Foundation believes the Apache-2.0 indemnification clause violates GPL/LGPL.\n",
    "## Solutions\n",
    "* `(Apache-2.0 OR MIT)` (Rust Language)\n",
    "* `Apache-2.0 WITH LLVM-exception`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0f3b8eb",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "# Contributor License Agreements\n",
    "\n",
    "* [Apache-2.0 CLA](https://www.apache.org/licenses/contributor-agreements.html): paper signed documents granting terms of Apache-2.0 license.\n",
    "  * One per person or organization (signed by employer/counsel)\n",
    "  * Creates friction to contribute, bookkeeping for maintainers, coarse granularity.\n",
    "* [Developers Certificate of Origin](https://developercertificate.org/)\n",
    "  * Developed for the Linux Kernel in wake of SCO lawsuits.\n",
    "  * Low-friction for contributors, fine granularity with low bookkeeping.\\\n",
    "  * Confirms authority to contribute and **inbound=outbound**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68d90842",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Searching for projects"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10c2afc1",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": ""
    }
   },
   "source": [
    "## [GitHub codesearch](https://github.com/search)\n",
    "\n",
    "* Check Insights -> Contributors\n",
    "  * Sustained versus short-term activity\n",
    "  * Number of stakeholders\n",
    "  * `git shortlog -se --since=2016 | sort -n`\n",
    "* Community signals\n",
    "  * Code of Conduct\n",
    "  * Contributing guidelines, pull request templates\n",
    "  * Active review and mentoring in pull requests\n",
    "* Continuous integration\n",
    "  * Actions tab, also report in pull requests\n",
    "  * Pipelines for repositories on GitLab"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d92ab6ea",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "## Journals\n",
    "\n",
    "### [Journal of Open Source Software](https://joss.theoj.org/papers)\n",
    "\n",
    "* Papers on mature software with many users\n",
    "* Immature research software with a few users, but best practices and intent to grow\n",
    "\n",
    "### [Geoscientific Model Development](https://geoscientific-model-development.net/)\n",
    "\n",
    "* Blends software and methods work"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb8e7b6b",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# PETSc experiments"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d8b65e2",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": ""
    }
   },
   "source": [
    "* Compare domain decomposition and multigrid preconditioning\n",
    " * `-pc_type asm` (Additive Schwarz)\n",
    "  * `-pc_asm_type basic` (symmetric, versus `restrict`)\n",
    "  * `-pc_asm_overlap 2` (increase overlap)\n",
    "  * Effect of direct subdomain solver: `-sub_pc_type lu`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba46a7e2",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "* Symmetric example: `src/snes/examples/tutorials/ex5.c`\n",
    "* Nonsymmetric example: `src/snes/examples/tutorials/ex19.c`\n",
    "* Compare preconditioned versus unpreconditioned norms.\n",
    "* Compare BiCG versus GMRES\n",
    " * `-pc_type mg` (Geometric Multigrid)\n",
    "* Use monitors:\n",
    " * `-ksp_monitor_true_residual`\n",
    " * `-ksp_monitor_singular_value`\n",
    " * `-ksp_converged_reason`\n",
    "* Explain methods: `-snes_view`\n",
    "* Performance info: `-log_view`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1d6705f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Geometric multigrid and the spectrum\n",
    "\n",
    "Multigrid uses a hierarchy of scales to produce an operation \"$M^{-1}$\" that can be applied in $O(n)$ (\"linear\") time and such that $\\lVert I - M^{-1} A \\rVert \\le \\rho < 1$ independent of the problem size.\n",
    "We'll consider the one dimensional Laplacian using the stencil\n",
    "$$ \\Big(\\frac{h^2}{2}\\Big) \\frac{1}{h^2} \\begin{bmatrix} -1 & 2 & -1 \\end{bmatrix} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f65e07be",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "laplace1d (generic function with 1 method)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function laplace1d(n)\n",
    "    \"1D Laplacion with Dirichlet boundary conditions eliminated\"\n",
    "    h = 2 / (n + 1)\n",
    "    x = LinRange(-1, 1, n+2)[2:end-1]\n",
    "    A = diagm(0 => ones(n),\n",
    "        -1 => -.5*ones(n-1),\n",
    "        +1 => -.5*ones(n-1))\n",
    "    x, A # Hermitian(A)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "592a5d02",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L[1:2] = [0.00048371770801235576, 0.0019344028664056293]\n",
      "L[end - 1:end] = [1.9980655971335943, 1.999516282291988]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, A = laplace1d(100)\n",
    "#@show A[1:4,1:4]\n",
    "L, X = eigen(A)\n",
    "@show L[1:2]\n",
    "@show L[end-1:end]\n",
    "scatter(L, title=\"cond = $(L[end]/L[1])\", legend=:none)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44c367f9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# What do the eigenvectors look like?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "609fd56e",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, A = laplace1d(100)\n",
    "L, X = eigen(A)\n",
    "plot(x, X[:,1:3], label=L[1:3]', legend=:bottomleft)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5f6ec119",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(x, X[:, end-2:end], label=L[end-2:end]', legend=:bottomleft)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28ca432c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Condition number grows with grid refinement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2fb37509",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ns = 2 .^ (2:8)\n",
    "eigs = vcat([eigvals(laplace1d(n)[2])[[1, end]] for n in ns]'...)\n",
    "\n",
    "scatter(ns, eigs, label=[\"min eig(A)\" \"max eig(A)\"])\n",
    "plot!(n -> 1/n^2, label=\"\\$1/n^2\\$\", xscale=:log10, yscale=:log10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0471c50",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Fourier analysis perspective\n",
    "\n",
    "Consider the basis $\\phi(x, \\theta) = e^{i \\theta x}$.  If we choose the grid $x \\in h \\mathbb Z$ with grid size $h$ then we can resolve frequencies $\\lvert \\theta \\rvert \\le \\pi/h$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "50fe3cd4",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "plot_symbol (generic function with 2 methods)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function symbol(S, theta)\n",
    "    if length(S) % 2 != 1\n",
    "        error(\"Length of stencil must be odd\")\n",
    "    end\n",
    "    w = length(S) ÷ 2\n",
    "    phi = exp.(1im * (-w:w) * theta')\n",
    "    vec(S * phi) # not! (S * phi)'\n",
    "end\n",
    "\n",
    "function plot_symbol(S, deriv=2; plot_ref=true, n_theta=30)\n",
    "    theta = LinRange(-pi, pi, n_theta)\n",
    "    sym = symbol(S, theta)\n",
    "    rsym = real.((-1im)^deriv * sym)\n",
    "    fig = plot(theta, rsym, marker=:circle, label=\"stencil\")\n",
    "    if plot_ref\n",
    "        plot!(fig, th -> th^deriv, label=\"exact\")\n",
    "    end\n",
    "    fig\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "765ddfb1",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_symbol([1 -2 1])\n",
    "#plot!(xlims=(-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58271476",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Analytically computing smallest eigenvalue\n",
    "\n",
    "The longest wavelength for a domain size of 2 with Dirichlet boundary conditions is 4. The frequency is $\\theta = 2\\pi/\\lambda = \\pi/2$. The `symbol` function works on an integer grid. We can transform via $\\theta \\mapsto \\theta h$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9bc3f0fe",
   "metadata": {
    "cell_style": "center"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatter(ns, eigs, label=[\"min eig(A)\" \"max eig(A)\"])\n",
    "plot!(n -> 1/n^2, label=\"\\$1/n^2\\$\", xscale=:log10, yscale=:log10)\n",
    "theta_min = pi ./ (ns .+ 1)\n",
    "symbol_min = -real(symbol([1 -2 1], theta_min))\n",
    "scatter!(ns, symbol_min / 2, shape=:utriangle)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9939381d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Damping properties of Richardson/Jacobi relaxation\n",
    "\n",
    "Recall that we would like for $I - w A$ to have a small norm, such that powers (repeat iterations) will cause the error to decay rapidly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "10a1eedc",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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       "<path clip-path=\"url(#clip420)\" d=\"M516.986 164.636 Q515.18 169.266 513.467 170.678 Q511.754 172.09 508.884 172.09 L505.481 172.09 L505.481 168.525 L507.981 168.525 Q509.741 168.525 510.713 167.692 Q511.685 166.858 512.866 163.756 L513.629 161.812 L503.143 136.303 L507.657 136.303 L515.759 156.581 L523.861 136.303 L528.375 136.303 L516.986 164.636 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip420)\" d=\"M535.666 158.293 L543.305 158.293 L543.305 131.928 L534.995 133.595 L534.995 129.335 L543.259 127.669 L547.935 127.669 L547.935 158.293 L555.574 158.293 L555.574 162.229 L535.666 162.229 L535.666 158.293 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /></svg>\n"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, A = laplace1d(80)\n",
    "ws = LinRange(.3, 1.001, 50)\n",
    "radius = [opnorm(I - w*A) for w in ws]\n",
    "plot(ws, radius, xlabel=\"w\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "087ee3fa",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "* The spectrum of $A$ runs from $\\theta_{\\min}^2$ up to 2.  If $w > 1$, then $\\lVert I - w A \\rVert > 1$ because the operation amplifies the high frequencies (associated with the eigenvalue of 2).\n",
    "* The value of $w$ that minimizes the norm is slightly less than 1, but the convergence rate is very slow (only barely less than 1)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24691cd5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Symbol of damping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "6cd7ddf5",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = .7\n",
    "plot_symbol([0 1 0] - w * [-.5 1 -.5], 0; plot_ref=false)"
   ]
  },
  {
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   "id": "8b747093",
   "metadata": {
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    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Evidently it is very difficult to damp low frequencies.\n",
    "* This makes sense because $A$ and $I - wA$ move information only one grid point per iteration.\n",
    "* It also makes sense because the polynomial needs to be 1 at the origin, and the low frequencies have eigenvalues very close to zero."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3655413",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Coarse grids: Make low frequencies high (again)\n",
    "\n",
    "As in domain decomposition, we will express our \"coarse\" subspace, consisting of a grid $x \\in 2h\\mathbb Z$, in terms of its interpolation to the fine space.  Here, we'll use linear interpolation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "3de3af3e",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function interpolate(m, stride=2)\n",
    "    s1 = (stride - 1) / stride\n",
    "    s2 = (stride - 2) / stride\n",
    "    P = diagm(0 => ones(m),\n",
    "        -1 => s1*ones(m-1), +1 => s1*ones(m-1),\n",
    "        -2 => s2*ones(m-2), +2 => s2*ones(m-2))\n",
    "    P[:, 1:stride:end]\n",
    "end\n",
    "n = 100; x, A = laplace1d(n)\n",
    "P = interpolate(n, 2)\n",
    "plot(x, P[:, 4:6], marker=:auto, xlims=(-1, 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "af3a414c",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L, X = eigen(A)\n",
    "u_h = X[:, 40]\n",
    "u_2h = .5 * P' * u_h\n",
    "plot(x, [u_h, P * u_2h])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6606c70",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Galerkin approximation of $A$ in coarse space\n",
    "\n",
    "$$ A_{2h} u_{2h} = P^T A_h P u_{2h} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "789af8ff",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "size(A) = (100, 100)\n",
      "size(A_2h) = (50, 50)\n"
     ]
    },
    {
     "data": {
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      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, A = laplace1d(n)\n",
    "P = interpolate(n)\n",
    "@show size(A)\n",
    "A_2h = P' * A * P\n",
    "@show size(A_2h)\n",
    "L_2h = eigvals(A_2h)\n",
    "plot(L_2h, title=\"cond $(L_2h[end]/L_2h[1])\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "42bf3cf5",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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       "</svg>\n"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_spy(A_2h)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2a9adf1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Coarse grid correction\n",
    "\n",
    "Consider the $A$-orthogonal projection onto the range of $P$,\n",
    "$$ S_c = P A_{2h}^{-1} P^T A $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "629d978d",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sc = P * (A_2h \\ P' * A)\n",
    "Ls, Xs = eigen(I - Sc)\n",
    "scatter(real.(Ls))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc3f5c9f",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "* This spectrum is typical for a projector. If $u$ is in the range of $P$, then $S_c u = u$. Why?\n",
    "* For all vectors $v$ that are $A$-orthogonal to the range of $P$, we know that $S_c v = 0$. Why?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38497d54",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# A two-grid method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "e4533ed8",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = 2/3\n",
    "T = (I - w*A) * (I - Sc) * (I - w*A)\n",
    "Lt = eigvals(T)\n",
    "scatter(Lt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "089b2095",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "* Can analyze these methods in terms of frequency.\n",
    "* [LFAToolkit](https://jeremylt.github.io/LFAToolkit.jl/stable/examples/diffusion/#Diffusion-operator)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83dfac85",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Multigrid as factorization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8de0f9b4",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "We can interpret factorization as a particular multigrid or domain decomposition method.\n",
    "\n",
    "We can partition an SPD matrix as\n",
    "$$A = \\begin{bmatrix} F & B^T \\\\ B & D \\end{bmatrix}$$\n",
    "and define the preconditioner by the factorization\n",
    "$$      M = \\begin{bmatrix} I & \\\\ B F^{-1} & I \\end{bmatrix}\n",
    "      \\begin{bmatrix} F &  \\\\ & S \\end{bmatrix}\n",
    "      \\begin{bmatrix} I & F^{-1}B^T \\\\  & I \\end{bmatrix}\n",
    "$$\n",
    "where $S = D - B F^{-1} B^T$.  $M$ has an inverse\n",
    "$$\n",
    "      \\begin{bmatrix} I & -F^{-1}B^T \\\\  & I \\end{bmatrix}\n",
    "      \\begin{bmatrix} F^{-1} &  \\\\ & S^{-1} \\end{bmatrix}\n",
    "      \\begin{bmatrix} I & \\\\ -B F^{-1} & I \\end{bmatrix} .\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4296193",
   "metadata": {
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   "source": [
    "Define the interpolation\n",
    "$$ P_f = \\begin{bmatrix} I \\\\ 0 \\end{bmatrix}, \\quad P_c = \\begin{bmatrix} -F^{-1} B^T \\\\ I \\end{bmatrix} $$ and rewrite as\n",
    "$$ M^{-1} = [P_f\\  P_c] \\begin{bmatrix} F^{-1} P_f^T \\\\ S^{-1} P_c^T \\end{bmatrix} = P_f F^{-1} P_f^T + P_c S^{-1} P_c^T.$$\n",
    "The iteration matrix is thus\n",
    "$$ I - M^{-1} A = I - P_f F^{-1} P_f^T J - P_c S^{-1} P_c^T A .$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ba6e1af",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Permute into C-F split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "75b460cf",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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       "</svg>\n"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 100\n",
    "x, A = laplace1d(m)\n",
    "my_spy(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6b1f5489",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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       "</svg>\n"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx = vcat(1:2:m, 2:2:m)\n",
    "J = A[idx, idx]\n",
    "my_spy(J)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dae6c74e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Coarse basis functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b2ce33c0",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": ""
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F = J[1:end÷2, 1:end÷2]\n",
    "B = J[end÷2+1:end,1:end÷2]\n",
    "P = [-F\\B'; I]\n",
    "my_spy(P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ebc6104f",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VJ28b5QB0jslLAwYGZKlJCUIFIdAk7QkpFzh8Bs5FnJwgBOAUHLWu6qHYSFJKBaPBBk+9cQsgTKZq5eddBx8lJ2YfAX+k9NNXn33yS0un+Kg7FOsYiR5/3e2NTY1TfDweW6BpQl8Iu91+4YUX3nPPPW63+wtf+EJVVXo3ZsuWLZ/5zGduv/32U089NatvRj9ICInKZXKljMKCTERodOGoZgBTs/a8LdCU3PMRADHYiwUG2q161Ihw3F+0Zm/TUGwEQHeol4SwzLA3Lcjmsq9eduVB6+97dffgUfPGjW6SgRtf+eiU1Se1Lv9E3mtYu3bt8uXLBUF45plnlDPbt29ftWrVzTfffNZZZ+X92LyhrVGicumYZCJUaDXLSjhtRFjH0oTGeuo1EeG4BVCakFi4cOH/++nPvvz05vvf2RnJ7JFuHwyve+bf74xJP7/r7kIe3traeuSRR7a1tS1btkw5c8stt3R3d3/jG98IBAKBQGDp0qlCUcOgiJCoXJjOtU4QQq8ECDA1IhynQzZ/Y+YCY3WoO6NzzRMjQjaVkISwcvnaxRfPmz//qm9dduM//m+OvzqWTA2GI2efedYbP/tZY+Psm6IzMzIy8rWvfY19+bOf/eymm25iX/K8qUEaCSFRuTCda59ma7TTYAcFc9Pbxm+NmhYRMoNEy/iIkKUMqblMhXPyySeffPLJ27dv37Fjh9vtXrZsWeFzdDdu3PiHP/xh165d55xzDjvp8Xg8Hj06meYFCSFRuUw2ESq0qs1ljK8aBTBpa9ScvtuiLA5EgkibCMclAjVd1igiJLDffvvtt99+ej0tGAw2NDT8/e9/dzqzmHBvCiSEROWiHcmrPV/vlKvsGEtiNImhOPzG/LbKyYQ4NgQAvCDU1mk/Yn1HRSOthH3hAVEWAdR5Ag5hnF+ymfpuExpu3njH273vArhqxX8e0vSxAp+2evXq1atX67Eu3aBiGaJCUUQOgNuGJvfET1t9hveXYSZCm7+B9d1Q4Jxu3lMFrVgagLov6p2Y72n2NmSshGmxJCqZwdjQ3lDP3lBPLDW77yI/Pvzww3Xr1h133HErV6684YYbwuGwQS+aEhJCokJRw0HfFAFXW6bRjHGe+tQ03gmFcUGhMfRMmjvBcAiOgLsWmu1TgjCUSCRy2GGH/eAHP7jqqqueffZZ7fB6EyAhJCqUTnVfdIpP2zIRoXHjeadLECoIxqcJWSFMs3eKBagdRylNSOhHMplUumwrX7Ie3AcffPBFF1109NFHr1y58uqrr/7HP/5h5qooR0hUKJqRvFNk4EyYQTG53bYWtfV20KjC0e6p2sowWnxN7w28D6A71Lus8SCD1kCYzPvB7b9461fZ7HD2hPviqYRynJTSB9e99GOeS4dP9R6/1+6d9Tn7+tsvP/xiO5/WGrvd/te//rWhoeHCCy8E8Nhjjz3++ONK021ZloeHh/fu3XvvvfeefvrpuX9z+UNCSFQoXdOUjKZPGl84mm1EOGRUQNYzjYkwfdJHUwnLkF+/+/t3+t7L+/ZERhEB7B7rzuaWbYMffnL+kUfOXc7OXHzxxT/5yU8UIdQ23R4eHl6+fPng4ODcuXNvv/32vBeZB7Q1SlQoqolwqq1R1mvGuK1RdSRv3Yw5QgMjwqlNhOmTXrISliGHNB1s8hurnVX7+tu0Z0477bRdu3b961//+uijj9555x3WU83v93/00UfBYPCcc85ZtWqVmUPqKSIkKpROTbHM5E9NmEo4XX81BaNzhEpDbQA8x7NJhFpYjpAiwnLi7APWfHL+irHE7OOTesJ9cTG9g/qHrY9/ONgB4KwD1uwXaFdO1rvqvI5ZLPB23t7sbfTYx5Vl22y2r371q/fee6/b7T7vvPMm+Oh5nv/yl7987bXXDg0NBQIBmAIJIVGhTOemVwg4UePASCI9qqnepfPb5WRCGbHECTahpm7yBePG8xpgJWQjlho8dbbx5g0FmlNfrszxTbEDMZlFgX3Z8fOd//gQHQAObTpYu8mZN2vXrl26dCnP888//7xyZtu2bW1tbU6nU5KkBx54oLW11TQVBG2NEpWJMnQXgNeGhmlEzlArYSrYk55E6G+cUuQ4h4v31UAZ3js6qPsCZk4QAmjyNvIcB83wXoLQi7lz5x5zzDH777//QQel67Aef/zxxsbGAw44oLm5+be//e0jjzxi5npICIlKZLq5E1rajSwcFTNNRG1TJQjTH2X8hSkD0oTdofQzp0wQArDztjp3HQBJlvoi/bovgKhwenp6tE23v/Od7/T29j711FNbtmx59913Dz/8cDMXQ1ujRCWi2Red9hrVU29AvczM3on0R3VN2LkNyu7owgP1XUBPOK1tU5oIMx819kcGAPSE+rLcTyPKkq8uPe/MxacB2NffXvjTNm7c+MADDwwMDGhn0wNwuVz77rvvdHcZCgkhUYl0zmginPCRMRHhTJUyEz4yol6GlYxOaSJUaPE1vdu/BZQmrHj29S/U8WmRSGTx4sXXXHON3W7X8bGFQEJIVCIzV8pkPspcbEiOMIuIUK2X0X9rdLrZ9FpaMhrZS81lCP04/vjjjz/+eKtXMQ7KERKViCYinPaadtVBof8CLI8Ip5tNr0XtskYzKIiyhoSQqERyLZbRPSRkE3endNMrsGIZMaizDiXExGBsCIDACQ2eKcwbCjSnnqgQSAiJSmTm/moK1fb0JMJoCn1RPd8ux6NSeBQAZ3cIVf7pLhMCTYqzQhzuhyTpuICejImw0VsvcFOYCBXISkhUCCSERMUxEMNYEgCq7AjMOHS3zRgroVoyOo2JUIGzO4SqWihWwpEBHRegmTsxbYIQQJO3QZHJwehgUkzquACCKCqoWIaoOLLZF2UXvB2UAXSOySsadevtwnyBMyQIFYRAkzg6BCAV7BX8M4lWTmhKRmdagMAJ9Z663nCfJMu9kf55VXP0WgBhGna7/YwzznA6Z/wXXykQCoVOPvlkgx5OQkhUHKxkdFYh1Izn1XMBrFJmhgShgi3QnOh8H+nC0Y/ptYDejIlwhpJRdoFSMtoT6iMhLEWeeOKJoaEhq1ehD42Nuv1bcAIkhETFoZaMTu+mT1+gjuc1ZGvUNluQZ1DrbTUinE0Im32N6AMoTViy+P1+v3/aPDShQDlCouJQTYTTu+nTF6gRoZ5CKGZRMqowrvW2fqgmwhm3RqGdQUFWQqJ8ISEkKg51ANNsEaFBVsKZBzBpMSwinN1EqMCUkqyERBlDQkhUHJqRvLMXyygHXSFZ0i8mZL7AGTpuT7ggpV9zmbiYGI6NALDxQr17lkk3NKeeqARICInKQtaaCGfbGvXa0pMI4yJ6ovoooRQLS9EQAM7u4L01M1+ssRIOyGJKlwV0h3plyEgPWprlLwDNqScqARJCorLoiyKSAgC/EzWO2a/X1MvoswAxqBnANNu4XU6wCdUBAJAkcVgfK2GWJkKFBk+9MrZ3MDocS8V1WQBBFBskhERloSYIZwsHFTRpQn0iwmwGMGkRWKM1ndKEbJNz1koZADzHN3oaAMiQaSohUa6QEBKVRfZuegXdrYRqRBjIasKfrY7Vy+iTJpx1Nv0EKE1IlD0khERlwfRs1pLR9GV6WwlTQ2k5yTIi1Dgo9NGhbCYRalFbb1OakChTSAiJyiLXrdG2Kp3H82pyhLltjeoVEXarkwizCklVKyFFhESZQkJIVBaakbxZXc8u08tKmGuOUI0IdRrGpJlEmFVE2EIzKIhyh4SQqCw61JG82RXL+NKVnTtDsqhHTMh2OLPMEWo89TpEhNFUbCQ+CsDO2wOurDpvsZoaigiJcoWEkKggZGBnFpMItbhtaHQDQFLC3kihSiiFR6VYGADndPPe6mxuEfwN4HkA4khQThU6C0mbIORnM2+kryQrIVHukBASFUR3RI6JAFDvQpU927vUNGHBu6PZN1djcIJNqKkHAFkWhws1MKhdRr3ZLqDOXWfn7QCGYiPRVKzABRBEEUJCSFQQnTnui064uHAroTqAKbt9UQUdW29355ggBMBzXKO3Xjmm1ttEWUJCSFQQHWO57YsqtOtnJUzlWDKqoKYJg4WmCXM1ESpQmpAob0gIiQqCKVl7diWjCpqt0YIjwhxNhAqs9XbhVsKe7GbTT4DShER5Q0JIVBBMyVrz2hotXAjViDAXIRQy83sLLxxlxTKzzqbX0kJWQqKsISEkKghmIsyyv5qCjl3WRLVYJpccoTqMqdCAjG2NZtNolKF2WaMcIVGOkBASFYRaLJPL1mirj+M5ANgVllNSQQvItb/ahIsLLJYJJyNjiRAAp+Codc0yAUoLjeclyhsSQqJSkGTsCuezNeoS0OzmAKQk7A7nvzsqhUbkeBQA7/LyHl/2N9pq6znBBkAcHZSTibwXoDERNnHI4b8A67JGzWWIsoSEkKgU9kTkuAgATW54bbndq8vuKMvwCbMNpp8ILwi1GSvhUP6bk5oEYQ7xKICAu9YpOACMxsciyWjeCyCI4oSEkKgUNPuiOQRD6Vv0qJdhzUJzqpRR0DRayz8mU70TWZsIFThwTd6GCQ8hiLKBhJCoFNR227nsiyporIT5C2Gu7ba16OKpz2k2/QSaKU1IlC8khESlwNpt52QiVGhVm8vkvwAx9/5qDH0iwlxm009AdVBQmpAoO3JIlWzatOk3v/kNz/Nf+tKXDj744Amfvvzyy6+88or2zOWXX+5wOJ588smtW7cqZ1wu1ze/+c0CV0wQ+dGVl4lQoV0PT71OEWH+VsL82sqkb6E59UT5km1E+Pbbb3/qU5+aN29eY2PjJz/5yS1btky4IBqNDmV49tln169fb7fbAfz+979//vnnlfPDw8M6L58gsob1V8vJRKigb7GMLddiGU19TaqAqYRqsUzuEaFmTj0JIVFuZBsR/vSnP7344ouvvPJKAHv37r399tvvuusu7QUrV65cuXKlcnzCCSd8+ctf5jJDXk477bSvf/3r+q2ZIPKBaVhOJkKFVh8ncBBl7AnLCQmOPFIKmoJPIZBzQFZ4jnA0MRZORgC4bK4aZ1YToLSQlZAoY7L9hX755ZePP/545fjTn/70yy+/PN2VnZ2dL7744vnnn8/O/N///d9//dd/PfTQQ/F4vJC1EkTeiHLaAsjltTVq5zHHwynP2ZVXvYw4Niwn4gB4TxXv8uZ6u1CTsRKODcmJfGYhFZIghNZKGNJhPjBBFBXZRoTd3d319elRLA0NDd3d3dNdef/9969cuXL+/PnKl4sXL45EIna7/Y477rjlllv++c9/ejyeKW+MRqMXXHCBw+FQvjziiCMuvfTSbL8PAgAQjUbtdrvNlqNLrgLoCiEp2QE0uWUpHolMf6Usy5FIhOcn/htxgde2K8wB2BaMt9hybjCT2tupHHC1DZGZ3j8tfG29GOwBENq7U2icl+vtncGdykGjqy6PBThhd9lcsVQsnIz0jwx47VP/FjOi0aggCLm+hdASiUREUaT/jIUgSZIoirNelu1fTIfDkUqllONEIuFyuaZ76wMPPHDrrbeyM9dff71y8N3vfnfp0qUPPfTQunXrprzXbrevWbPG50t33GhtbXU6nVkuj1CQJImEcEq6hwBIANqruJl/rmRZTqVSk69pr5Jf6ZMB7InZnM6cY0opNKQc2Otb8vvBFgLNihAKoSHn/H1yvT2YSC9gTnWeC2j2NnSO7AIwlBoO+PwzX5xIJOj3t0BEUXQ6nSSEhSBJUjY7kdn+xZw3b96uXbuOOOIIALt27ZozZ86Ulz333HOhUOjkk0+e/JHdbl+2bFlXV9e0S7HZTj/99EAgkOWSiMkIGaxeSNGxM5yO4dqr+Jn/+8iyPOV/w4XVIiAD2Bnh8vgvLGeGy9vrmvP7H2Sva05sBwBpuD+PJ/RF0wto8TXlt4AWX5MihL2R/v3r9p35Yvo5LBz6dS4cjuNYtcoMZJsjXLNmzcMPPwxAluU//OEPa9asUc5v2LBhcHCQXfarX/3q/PPPZ/8SlGU5FEqXKAwMDLz44v4mTaAAACAASURBVItLly7N/nsgCL1Q3fS5V8ootKoOinxuL8Q7kb6xriAHRYE5QozrOEqFo0RZkW1E+M1vfvPoo48+4YQTRFHs7+9/8MEHlfNr1qx57rnnjj32WADBYPCJJ554/fXX2V3JZHLOnDkrVqxwu90vv/zySSeddMYZZ+j+PRDErKj91XKvlFFgpouOvKyEhbjpJ9yYn6e+uwATYfpGshISZUq2QtjY2Lh58+aXXnqJ5/lPfvKTLOb717/+1dbWphzb7faNGzdqvfYOh+ODDz7YvHlzPB6/9dZb9913lu0UgjCIQkyECm2ZcRH5WQnZSN6cO25nYCMMxbyshL15TSLUQnPqiXIlh6oKl8t14oknTji5ZMkSdlxdXb1s2bIJFzQ3Nzc35/mbTxB6UYiJUGG+l7PxSEnYG5ZjIlw5JW5kWczkCG3+PAMyTZe1nLdGh+MjytQIr91T5chhApSWFi9ZCYnyhHqNEuVPUsKesAyA5zDfm2dEaOMx18MBkIGdOVoJ2RxB3lfDOd35LUCoDnB2BwApPKrMNcyewhOE2ntpAAVRZpAQEuXPrrAsygAwx8M5CyjBa8+30Rorb8k7QQgAHCfUpmch5ZomLKTLKKPaWeWxuwFEktHReAHdxwmiyCAhJMqfQuZOaGnLt/U2axCad4JQgTUpzbVwtJAuo1o0HUdpd5QoH0gIifKH6VbeJaMTbs9ZCAsuGVVQ04Q51suwiLCpgIgQ4xqtkRAS5QMJIVH+FG4inHB73lujeZsIFfJuva1XREhpQqIsISEkyh/VRJivd0Ihbyuh/hGhFTlCkJWQKFNICInyR40IC90azTwwRyEUC24ro8CshDkJoQy5cBNh+nayEhLlCAkhUf7oVSwz18vZeQDojSKSyvo2SRKH+gGA42z+wiLCvLqsDcdGYqk4gCqHb9apETPTzLZGKSIkyggSQqLMSUjojsgABA7z8jURKggZG2JOVkJxZEAWUwCEqlrOUdBABsGXfoIUCUmxcJZ36ZUgBDDHlw5Ju8N9MvJpNUcQRQgJIVHmdI3JkgwA8zLxXCGwmLIjax9d4e22VThOyMSU2TdaK7zLKMNr9/gcXgCxVGw4Nlrg0wiiSCAhJMqcjoKbq2lRrYTZR4RBPdz0GWy5N1pjEWFzwREhNA4KShMSZQMJIVHmdBbcbltLHlZCTUSoQ9NdW13ODope/SJCAC1UOEqUHSSERJnDFKs1z17T48jDSlj4ACYtbGs0+8JRTY5QDyFUpxJSREiUCSSERJnDFEvfiDB7K6GeOcJxXday1SFmImQaVgisNw1FhETZQEJIlDl69VdTUPtuZy2EakRYWKNRhVw99TLk3nB6AlSB/dUUWOkpRYRE2UBCSJQ5mpG8OjxtjpdTJhH2xxBKZnGDJKaGB4BxsyMKQY0Ig1kVywSjQwkxAaDGWa3MjigQai5DlB8khEQ5ExPRGwUAO4+5hZkIFThgfiay7MqicDQ11A9JhGaaYIHw3mploqEUi0iR2T0cOpoI089Rq0bJSkiUCSSERDnTOSYrf6rnezlBBx0EgPZM0U02VkJR15JRhZxabzOTgy4lowA8dne1swpAQkwMRod1eSZBWAsJIVHOdOpqIsw8KgcroV7ttrXklCbUZTb9BFrISkiUFySERDnToauJUCGn8byaShnddIilCVNZpAn1mjuhhdKERJlBQkiUMyyN16pHyaiCOoMiCyuhvt6J9KP8aR0Sh2bXIU1bGd2EsIXG8xLlBQkhUc7oNXdCS24RodpfTb8cYS4RoVoso4eJUEG1EtJ4XqIsICEkyhl9TYQKOY3nNSIizL5YRpLl/sgAAA6cLiZCBbISEmUGCSFRzqgjefWLCJvc8NgAYDCOkcRMV8piShwNAsrUCB1MhApqscxsEeFANJiUUgBqXTUuW0EToLRQjpAoM0gIibIlnEJ/FAAcPOZ4dIsIOWBBdlZCcagfkgRAqKnnBJteC+A9VbzLC0BOxKTwTLOQenTtMspgc+p7w32STFZCouQhISTKFmYibK3ieN10ENDUy8y8O8rmyOvSXE0LG1U/c1BoRIIQgMvmqnXWAEhKqWA0qOOTCcISSAiJskU1Eeoxd0JLu1ovM9NlRiQIFbJME6reCf1MhAosTUj1MkQZQEJIlC0sXGvTz0SowMwYM3vq2RB5Hd30ClmmCXWcTT8BlibspjQhUfqQEBJlS5cBJaMKmhkUM11mRkQ4NGNEaICJMP1ALxNCKhwlSh4SQqJs6TCgv1rmgVlFhCmWIzQwIpxJh1Q3va45Qmi2Rntpa5QofUgIibKl04D+ahMeOFuxTCYi1LtYhtnzZ2g3KspifyQIgAPX7NXNvKFAc+qJcoKEkChbjHDTKzS44LMDwEgCQ/Gpr5FTSXF0EAB4wVZbr+8CBHVOfQ+mMTD0R4KiLAKoc/sdgg4ToLSQlZAoJ0gIifJkLIlgHABcApo9+j9/1noZcahPkShbbT14Qd+38y4P7/EBkJMJMTT1LCTjEoQAmr2NHDgAfZF+SZZ0fz5BmAkJIVGeaEtGdY4Hlcey1tvT7I6yek7d90XTjw2wUfVTb05qTIT6L8AhOPzuWgApKb0BSxClCwkhUZ5o9kUNeb4mTTj1BaIBkwi12NSphFM7KHrC/cqBEREhKE1IlBEkhER5ohnJa0RAiNaqWbqsGeedUJjVU9+t92z6CVCakCgbSAiJ8sS4ShmFdrXL2tQXiIZ5JxRmnVOvaTRqyAJa1GFMFBESpQ0JIVGedBpmIsw8dpZiGcMjwrpZIkIjZtNrYW3bKCIkSh0SQqI86TDMRKgw63hetb+awcUyU3ZZYzUsPMc1enQ2byhQcxmibCAhJMoTo7dG65yocQDAWBIDsYmfMlcDJ9iE6jojFsD0lfk0tDBXQ727zi7YjViAZjwvRYREaUNCSJQhIwkMJwDAbUOD26i3zGAlTGV87oK/Abwhv2Wcw8V7q6F17mtQm6sZkyAE0ORt5DkOQH9kICWJBr2FIEyAhJAoQ9R9UZ8hJkKFGXZHRYMThAqs0drkNKHRCUIAdt4WcAcASLLUHxkw6C0EYQIkhEQZokkQGviWtukLR1PqACZDEoQK6njeSVZCVsBiUMlo+uGUJiTKAhJCogwx2kQ44eGTrYTMO2FwRDitg0Izd8KoiBA0npcoF0gIiTKk07CRvFpYuDl5BgVTJmZyMIIZuqwxb5+hESGb7kRWQqKkISEkyhA1IjSmv1rm4SxHOPEjo/urTXj4FBGh8TlC0Jx6olwgISTKkA6TIsJMu9HQRPuC2nHb0Byh2mVtXI4wKSYHo4MAeI5vMMZEqNCsNpchISRKGBJCogwxbiSvlhoHah0AEE2hP6qelxMxKTwKgLPZheqAcQuw1TWD4wCIQ/2Q1FlIPeE+SZYBNHjqbXpPgNKiWgmpWIYoZUgIiXIjGMdYEgCq7KhzGvuuKUfVq+GgvxEG2jfA2R2CrxaALKbEUXUWEovPDE0QAmj0NPAcDyAYDSbFpKHvIgjjICEkyg1zKmUmvELrqVcThMY0V9MyZettVQiNTBACsPFCg6cOgCTLfWQlJEoWEkKi3DC6y6gWzXhe9aQmQWhsQAZt621Nx1FDZ9NPgNKERBlAQkiUG+aUjKZfMWVEOJSWBENLRhXU1tuaiFBTMmr4AjRpwqnnAxNE8UNCSJQbpm6Nqs1lpsoRmhARTjWet9vgSYRamr3UepsoeUgIiXJDM3fC8He1V01hJVTd9EZ6JxRmzhEaaiJMv4Lm1BOlDwkhUW6Y019twiu6NFZCczpuK0yOCONiYig6DE0li6HQnHqiDCAhJMoN1vnThGIZ5tCIieiJAIAUi0iRMSjehqpaoxfAHBqpoX5IIoDecJ8MGRpvg6GQlZAoA0gIibKiL4pQEtC43Y1mgpVQ1PaUMdJEqMDZHWnPviSmhgdgboIQGs/+YHQ4ISZMeCNB6A4JIVFWdJoYDipMKBxNmdJlVIswfnfUzAQhNF3cZMg94X4T3kgQukNCSJQVmkoZs4RwvJXQnHbbWia03u420USYfhGlCYkSh4SQKCvYjFxDR/JqmS4iNKFSRmHCnPoeE02ECpQmJEodEkKirGBbo62mRYSqg0KGZhCEiVuj6YBM8S9qcoRmR4S9tDVKlCYkhERZoZk7YdIbNeN5AW1EaHyjUQXW0TQdEYZYo1GKCAkiK0gIibLCTBOhQrsvXRu6MyRLsjos3vximdRgbywVG46PALDztoDbwAlQWihHSJQ6JIRE+SADO03fGnXb0OAGgISEvcExKRYGwDlcvK/GnAUI/kbwPABxZGDvWLdyssnbyBtv3lBopoiQKHFICInyoSeCSAoAAk7UmGIiVGAVqnv3mJ0gBMAJtoyVUNrT84Fy0rSSUQD17jo7bwcwFBuJpWKmvZcg9IKEkCgfzDcRTnjdYK/ZCUIFVjjaPdCpHJiWIATAc1yjt145JishUYqQEBLlg5lzJ7S0ZeplIv1mJwgVhMxUwu7RPcpBsyltZRiUJiRKGhJConxQTYTGz53QwrZGZdNNhAosIuyJpAMyo2fTT4AKR4mShoSQKB9Yu+1WsyPC9OscoxZFhBkrYW9iRDkwM0cIshISJQ4JIVE+dIxZlSNMH9SGM8UyFuUIe6WocmBmjhAUERIlDgkhUT6oJkJzt0ZbM1bChljazG7y1qjyuiiPEC8CcAgOv9vwCVBaNHPqSQiJ0oOEkCgTJNkCE6GCS0CzBwFx1CdFAXBON+8xq7ENAMDmbwAv9LvS33Wzt5GDqf8FaE49UdKQEBJlQndEjosA0OCCz27229t83LxEJkFo7r4oAPCCUFs34MgIobkJQgB1br9DcAAYiY9GklGT304QBUJCSJQJmrkTpgZD7KULEulgyAIhBGyB5j5n+hs3OUEIgAPX7G1Qjtn4C4IoFWxZXpdKpW699dbnn3++vr7+mmuuWbJkyYQL/va3v/3xj39kX954442NjY0AQqHQjTfe+NZbby1cuPD73/9+S0uLXksnCC1/3S0pB/PN3RdVaKtCV/97r+0ZmlvlWmRuglBB9je8nZQAAVZEhAAaPQ07R/cAeKP7rYW1reYvgCDyJtuI8Ac/+MEjjzxyzTXXHHjggZ/61KfGxsYmXLB58+Z33333sAxOp1M5v3bt2i1btlx//fWCIJx00kmyLOu5fILIcMeW9I9Wg8vsn7GdO3c+c+lxXY/+6Nkdfde9+P7nvn/bRx99ZOYCtmzZ8tn/d8+/G9M7wr+97Z6enh4zFwDA50xXKP1h6xMmv5ogCiSriDCZTP7iF7947LHHjj766GOOOWbDhg0PP/zw2rVrJ1y2aNGidevWac/s3bv3scce6+rqam5uPuqoo1paWl566aVjjz1Wt+UTRIZURv7meU2NCBOJxOdOWnXdgTWHrThIObO5d/TM1Z959V/vulwuExYwMjJyzqmr/+e4eTdnzpwojZ2x+jMvvfEWz5uX+6jPDLtISSnTXkoQupDV78muXbsGBgZWrFihfHnkkUdu2rRp8mWvv/76Oeecc+WVV27ZskU5s3nz5gULFjQ3NwPgef6II46Y8kaCyJundkrLH08tfzwVySjhvdvk5Y+n/vstyZwFfPtXzxzoEw5rUe0KBzdVr6hzXvoLkwKj6//0g/n/uegPR6gLePPwgOe8pruf+5U5C7jr7V+v+8u3Xtz5qvJlKBFa95dvXfbitW/1bDZnAQRRIFlFhL29vdXV1TZb+uK6urrt27dPuGbRokVr165taWl54403li9f/sILLxx++OG9vb1+v59dU1dXN8OOTTgcPu6449hbjjvuuBtuuCG376biiUajdrud/TesBPaMCJsGxn2/nWNy5xgOqEqEQvmEJrIsRyKR7K/f/t7m1X5hwsmP1zkefHdTKLQ6jwXkyq7gzrE5Dm2uYqeHg8e5bef2UCg07W36sXN497bBD9mXoiwpX/aPDoR8ZiygXIlEIslkUhAm/nQR2SNJUjb5uKz+Yvp8vmhULYmORCLV1dUTrlm9Ov07f/bZZ8disdtuu+23v/2tz+eLxWLaG6uqpvVXud3u2267jT25sbHR5zPXF136CIJQaULodEqAOPm83W73+fLZmZRlmeO47H/23P6GvvjE6LMvmnLVNZvzA+z2eIApHAvV1dXmLGC6nzeXy0W/woXA87zT6SQhLARJkrTiNR1ZbY3OmzcvlUrt3r1b+XLHjh0LFiyY4fqFCxcGg0EACxYs2LlzZyqVYje2tk5bTsbz/NKlS1m5zfz587NZG1HhnNrKv7nG9r8nqn8snjpReHON7bpDTEqPXXv+6ie7RpOiqoUpSX60c+y6L51mzgK+esSF/K8+/Oye9G+ZIOPazbHQ3R9ceOx55izga4d8af1//L/rj/42O/OzE374s2N/cGjzweYsgCAKJKs/Fn6/f9WqVXfffTeAPXv2bNiw4eyzzwbQ3d192223Kdds27ZNORgYGHjggQeOOuooAMuXL29oaHj44YcBbNq0aevWraeeeqoR3wZRsdQ5cVg957OrBTIfC3CH1XOmTWI6ZN95F1/x7XM3bHm+s3/nSPSFroEz/vLB+RdfeuRB+5izgOOWH/Ppoz/3+IeD6a8l+bt/fO/bF13b3mySh2GOr3lRYN+2GvUfx1UO77417VUOCgeJ0iDbfzX/5Cc/eeihhw455JBly5ZdcsklH/vYxwB0dHRcdtllygUXXXRRS0vL0qVL29vbDzzwwKuuugoAx3F33XXXFVdc8fGPf/zEE0+84447amtNbYFIVAhsJG+zBy7BbB/huq9f+ov/uvL1PUM/fuWDX/VXL/+fJ//zW1eYuYBr//vGFaedpBzbhxMP3nzj579gUjjIcNtc1U4l8SF3U6M1oqTINpm0ZMmS7du3b9u2rampqb4+PY36yCOPZCnAF154Yffu3UNDQ62trdoM4qc//enOzs6PPvpowYIFkzOLBKELnZlakQv345vcFiygzcNf/Yn9AVzXsi7cMLHdhBl4eQwDwEVDwtx2C9y6Lb6m41s/+fgHGwCuJ9yH2gPNXwNB5EcOVRU2m+3AA8f9cHMcx4zzAObNmzdv3rzJN7rd7oMOOijvJRLErLCI0OTZ9AwxM5J3t6MpGrJAh9ho+IaEnBq0ZgQEzaknSpQKKi8kypjOMYuFkGnPLkdTaGLbJTNgHT4b4hCD1ugQm0pIMyiI0oKEkCgH1I7bltRnyLI4lP7Tv9veGInIcRFOE4veR+NjyswHtwRfSk4Nmt1fTYE1+6bxvERpQdMniJInJWFPRAbAWdRxWxwdlJMJAMO26hDv1k5GNAcmPA1xAJBCI3LcgllIrNk3jeclSgsSQqLk2RWWUxIAzPFyLivMxyxBOORJh0Sd5jZUYcLTKDuUg9SQBZuTNc5qj90NIJKMjiWppwxRMpAQEiUPU502i3xrbCsynEmSsZylObAEYaMt3blJtKhepilTL9MXGbBkAQSRBySERMnTkVEdS0byQlMpI/lZRGiuEGaKU5rddeklBS1OE9J4XqKEICEkSh5Nyag1C2BVmo66tAx0mFs4ynKErG7TqoiQpQn7ohQREiUDCSFR8jA3fZsVlTLQRIQ1jc2ZJZm8NZpewJxA64QlmUxLZmu0N0IRIVEykBASJU/xuOkb51i0NRruVw7mNO43YUkm05wJSSlHSJQQJIREydOhRoRWvF6WxeG0Ds2d22TnAaAngohZc9qHYiOxVAyA1+6pacxEhBblCJvViLDfkgUQRB6QEBKlTULC3ogMQOAsMhGODMipJAChym9zuuZ5OQAyzLMSahKEzUKVn3M4AUiRMSkWNmcBWtTmMiSEROlAQkiUNjtDsiQDwFwv57Dix5ll44RAE4D2TMGOaVZCliBs8TWB4wR/OiYTBy3I0lU5fF67B0BcjA/HR8xfAEHkAQkhUdp0WrsvqikZtQWaoCnYMa1ehhkVlEIVZRmwsF6GOo4SpQYJIVHaFIGJMJ2NE+qaoSnYMa1eRjUR+hQhTFeuilZZCX3UcZQoMUgIidKmK2S1iTCzA2nzN2qX0WmWlZD1V2v2NgEQAumtUUu6rGHcMCaKCInSgISQKG06rDcRjosI2zPL6DBta3S8m97yiLCZZlAQpQYJIVHaFI+JMJ0jVItlzBBCGXJvxkSohGJCncU5QtZchiJColQgISRKG4uLZSRJHB4AwMo153g4ZRJhXxRh462Eg9HhuJgAUO2sUiY/sGIZ6yJCEkKixCAhJEqYmIieqAzAxkMx8JlMarhfFlMAhCo/Z3cA4DnMz6yky/igUPVOZDYkeV8t53QDkGJhKWrBLCRN1WivDFM77BBEfpAQEiVMV8ZEON/L2az4WWb7okqCUIFZCU1ovT253TYyZTvQWDvMxGv3VDuqAMTFxFB02PwFEESukBASJYzlJsLU+ARhejFV5lkJVe9EZkMSGWs/KE1IENlBQkiUMMVTKSNohdBET73qnfCpQqimCQctThN2kxASpQAJIVHCaCYRWjyAaXxEmD4wocsaC7mYaQFFEBGSp54oLUgIiRLG4rkTmspMmyZH2GailZApzbiIkDkorMgRAmhihaMkhEQpQEJIlDBsa9S6/mpTbI22m5UjlGS5L5we+zc+R5jx1Fu0NaoWjtLWKFEKkBASJYxma9SCt8tiShzJmAhrG9j5Zg9cAgAE4xhLGriAYDSYlJIA/K4at83Fzlvfd5ushERJQUJIlCrRFPqiAGDnMcdjxSTC4X5IEgChpo6z2dl5Dmg1pV5mygQhAN5brVgJ5XhUCo8at4Dp0A6gkGSyEhLFDgkhUap0hNJ/Yhf4OMGKnVHNAKbmCR+1qVZCA2VgygRhZkksKLRgd9RlcylWwqSUHIwOmr8AgsgJEkKiVGEmwnaL5k6oCcK6pgkfqWlCIwtHu0NsEuHEBbDiHdGi3dEmT3qvmBwURPFDQkiUKmqC0KK5E6wUReudUDDHStgzlYlQQXVQWFU4mhFCtkiCKFpICIlSxXI3/ZQlowrmWAk1s+knRYSqp97qiJAcFETRQ0JIlCrW91cLTuGmVzApIhw/m14Lc1BYVTja6K5XDtiUKIIoWkgIiVKF1aFYZSJkW6PCpGIZtqQdhgmhJEt9kX4AHLhGT8OET5mn3vouaxQREkUPCSFRqmi2Ri14uyymxNFBAOB5obZ+wqeNbnhtADCSwHDCkAX0RwZSkggg4K512ZwTPmXTMFLBHlhhYGARIQkhUfyQEBIlSTiFgRgAOAU0u60wEQ72KgIj1NZzgm3yBUZbCbunMREq8C4v7/YBkJMJKTxixAJmptHTwIED0Bfpl2TJ/AUQRPaQEBIlCdsXbfVxvBU7oynWZXTSvqiCpl7GECGcIUGoYG3rbafgqHXVAEhJ4gBZCYnihoSQKEk0CUJrFiBONXdCC0sTGjSed8qRvFo0rbct7jhKu6NEkUNCSJQkmpLRovNOKLCt0S5jIsLe8BQjebVoWm9b3XGUhJAobkgIiZLEchNhFhFh+sDwiHCqHCGKoPV2M82gIEoEEkKiJLHeRKhGhNPlCM0qlpktR2hVREhz6olSgYSQKEk6rJ5Nr/ZXm9RoVMHQ8byiLA5EggB4jmuaZCJMLyxgcY6QKTTlCIkih4SQKEmsHckrJxPi2DAATrAJNRNNhAr1LlTZAWAsiWBc5wX0hvtFWTERBuyCfcpr1L7bQ32WWAnZni3lCIkih4SQKD1GkxiKA4Dbhka3BQvQmAgbwE/7S2Tc7mjP9HMnGJzTzXurkZbtIX0XkA3N3kae4wD0R4KKbBNEcUJCSJQeHZq5E5ZsjKbU5mrT6hCM7DiqttueJkGoYG3rbbtgD7j8AERZ7I8EzV8AQWQJCSFRemgShNYsgFXKTJcgVFDH8+o9g0IdwDR9RIhxw5goTUgQ00JCSJQempG8FnsnBH9WEWGX3hFh92xtZRQsH8/b4k0vgNKERDFDQkiUHqqJ0Go3PVOaKdFYCXUXwllMhArWdlmDNiIkBwVRxJAQEqWHaiK0qr9acJa2MgpqsYz+W6PZRYRFYyUkTz1RzJAQEqVH55jlESEzEc4UERpULJOUUsGoYiLkJ08i1GJ5RMjajdLWKFHMkBASpYfFJsJETAqNQDERVgdmuNLvRK0DAMIp9Md0W0BfuF+SZQANnjobL8xwpS3QBI6Dxu9hMtR3mygJSAiJEmMwjpEEAHhtqHdZsIBx7bZns2+0VenfXybLBCEAzuHivTVQxgiPWGBgaPQ08BwPYCAaTEop8xdAENlAQkiUGJ1jVoaDyKLdthYjdkdV78SMCUIFa1tv23ih3h0AIMlyf2TA/AUQRDaQEBIlhmbuhDULYJ48YcYEoYJmPK9uC5h5Nv0EhDqr62Vod5QoekgIiRKjw3IT4VBah2z+2QMyQyLC7EyECrbMcAwaz0sQ00FCSJQYbM5tq1Ulo3lGhPpvjbZMM5JXixBIXyMOWeyg6A33W7IAgpgVEkKixOhQc4TWLCCnHGG7Wiyj2wLUYhnf7AvQRIQWz6mniJAoWkgIiRJDM5LX6ogwFyHsHNPHvpAQE4PRYQACJ9R76ma93npPvTqnnoSQKFJICIkSoytk5UheOR6VImMAOLtDqPLPen2VHQEnAMRE9EZ1WEBPuF+GDKDRWy9wM5kIFZjHQxzuhyTpsIIcaaaIkCh6SAiJUqI/hrEkAFRnBMZkxoWD2c2A0tdKyFq0NGeRIERasGuhWAmHLTAwMMEORocSYsL8BRDErJAQEqWE5SbCVC4JQoV2XcfzdodzSBAqCCxNaMXuqMAJDZ46ADJkqpchihMSQqKU6LR0XxSAmIkIWRHKrLT50ge6WAlV70R2ESHGpQmtmkrI0oTUepsoRkgIiVKiw+q5E6mMiZDZEmalTdeIUDObPvuI0OrW25QmJIobEkKilOiyehJhXhGhvkKYW44QRVE4yqyEFBESxQgJIVFKWG4iVDtu4UcWjwAAIABJREFU12WfI0wfdOixNZqTiVCBGf9TFm2NsubgFBESxQkJIVFKaEbylkDHbQW21K4xWSosJoyLieHYKAAbL9S5Z5oApcXavtvQthuliJAoSkgIiZJBtnprVIqFpWgImvFG2eC1ocEFAAkJ3ZGClLA71KuYCJu8jcp4o2zQWAkHZNGCWUg0p54ockgIiZKhL4pICgD8TtQ4LFiAOMAShNmaCBXUepnCdkfzSBBCO0BYkiyxEjZ46uy8DcBQdDiWipu/AIKYGRJComToKBoTYTbN1bS06+SpzyNBqGDLpAktcVDwHN/gqUfaSkhBIVF0kBASJQOrurSsy+igJiLMBdVKWFjrbWZIzykiRDE4KMhKSBQxJIREycD2Fa0yEYr5RoSarVGLIkLLHRSUJiSKGBJComSwPiLMTDKyZe2dUNDLStit5ghzW4C1XdagsRKSg4IoQkgIiZJB01/NmgWwBJuQtZteQTOet6AF5DSbXosaEVo0lZApN0WERBFCQkiUDKy/muXFMrnnCNM1pjtDsphvTBhJRkfiowAcgiPgmn0ClBZm/7fMU+8jTz1RvJAQEqWBDOzMRIStlpgIw6NyPAqAc7p5b3VO97ptaHIDQFLCnnCeSshiqWZvA5+LeQOAUNsAngcgjgTlVDK/BRQCazfKglqCKB5yEMJbbrll8eLFS5YsueOOOyZ/+sorr5x55pmLFi06+OCDr7322ng87Rb64Q9/uDLD6aefrs+qicqjOyLHRACod6HKbsEC1JLRutz2RRUKtxL25JsghGIlrKkHAFkWhy2YhVTnCTgEB4Dh+EgkqceEYoLQD1uW1z366KN33nnn008/nUqlVq9evc8++5x00knaC957771Vq1b9z//8z+jo6Je//OVkMnnTTTcB+Pe//71kyZJTTjkFgN1uxR8woixQ505Y1W47331RhbYqbmOfDKBjTD6mOZ9vgW0q5pogVLAFmsShPgCpYI+tfk4eTygEDlyjp3732F4AveG+9tpWkxdAEDOQrRDefffdl19++UEHHQTg0ksvvfvuuycI4bp169jxJZdccv/997MvFy1adMIJJ+ixWqJysX4kbzBP74RCe8FWwp58TYQKQl0zPnoX1jkoWnxNihB2kxASRUa2W6P//ve/Dz30UOX40EMP3bJlywwXv/LKKx/72MfYlz//+c9XrFhx3nnnvfvuu3kvlKhwisdEmF9E2FqwlVATEeazAOtbb1OakChWso0Ig8FgdXW6QKCmpqavb9of5UcfffQvf/nLO++8o3x59tlnX3TRRW63+8knn/zEJz7xzjvvtLe3T3nj2NjYwoULuUwVwH/8x3+sX78+2++DAABEo1G73W6zZfu/tYTYPmgDBAAt9kQoJBr3IlmWI5HI5POxvj3KQdJTGwrlnOhrtvGAHcBHw6lQKJ8k2d7RbuWglq/OYwEpb61yEO/bk8ftuRIOh7nxFT0BR7rSddfwbhMWUAZEIpFkMikIgtULKWEkSZLl2f/pme1fTL/fPzaW3tMZGxurq6ub8rJnnnnmkksu+ctf/tLS0qKcWbNmjXJwxBFHvPbaa3/84x+vuuqqKe/1+XybNm3y+9O/LW632+VyZbk8QkEQhHIVwj3xFCADWFTv8hmZJpRlmeM4n8834Xx4NN2u2je31T7p01k5oEEGUgB2RQWfz5nHwvqi6QUsbGj1uXJeQLxlQVreR4OTvzvdkWV5wlta/fOUg2BiyIQFlAE8zzudThLCQpAkKRqd/d+d2W6N7rPPPu+//75yvHXr1n322WfyNX//+98vuOCCxx9//LDDDpvyIbW1tTOsieO42tpafwZSQUKLxkRozQJSg+ldkPxyhK0+jucAYHdYTko53x5ORsYSIQBOwVHrynYClBZbpgmAGCQrIUGMI1shvOCCC37+85+PjY0NDw/ffffd559/vnL+sssu+/DDDwG8+OKLZ5555j333LN48eKhoaGRkREAoig+88wziURCluWnn356w4YNq1atMug7IcoYScauTGptgSUmwtCwnIgB4F1e3p1PNOMU0OLhAKQk7M7dStgdSqtXi6+JQz7/BYTaek6wARDHhuRkIo8nFAjlCImiJVsh/MpXvvLxj3983rx5ra2txx9//Be+8AXl/JNPPjkwMADgmWee8fv9l19++fLly5cvX674JWRZvvrqq30+n8/nu+yyy+6+++4VK1YY9J0QZcyeiJyQAKDJDa8V+76pTBQl5GUiVFBnUOSeIOtmzdVyNxGm4XmhNmMlHLJAivzuWpfNCWA0MRZOTpGFJQiryPaPis1mu+eee375y19yHKfds96xY4dy8KMf/ehHP/rR5Lv+9a9/ybKcSCScznzyIgQBjeWgzfLmajm229bSVsW90itDsYK05PaNqG1l8jIRKgiBJkXRU4O9tsZ5eT8nPzhwjZ6GnaO7AfSE+/apbTN5AQQxHbm1WLPZbHlkbjmOIxUkCsHykbyaAUz5R4Qsu5nHDIr8ZtNPgNKEBDEl1GuUKAFUE6FFxYZ5t9vWwlqk5rE1yvJquU4i1CIE0iKasmJrFJQmJIoVEkKiBFAnEVofEeavQyyc7cg9IlRH8uadIyymiJAFuARRDJAQEiVAEYzkLajjtkJbAV3W9MkR1hVNcxmaSkgUEySERAnQYW1/NU2ZZSFbowt8nMABwJ6IHM+lNw4rs3TZXDXO3CZAaVG7rFkUEdKceqI4ISEkih1mvOMsmkTIjHe8t5pzuvN+jp3HHA8HxRaZi5VQ3RctIEEIQKip52x2aGyRJkPFMkRxQkJIFDu7w3JKAoAWD+eyottUge22tWgKR3O4S62UKSBBCAAcJ9Q2KIesUY6Z1Dpr3DYXNI1yCKIYICEkih3L506obvoCvBMKbXnNoNAlQajAin2sGsZEaUKiCCEhJIqdDqsrZUQ93PQKmnqZnISQlYwWKoSaYUyUJiSINCSERLHTFWJuemsWkNLDO6GgiQhzuIttjeY3iVALKxy1cDyvctBDQkgUDSSERLHD5k5YUikDXXOEbXlZCdWRvDpGhEFrdKgp8y1009YoUTSQEBLFTqfV/dU0OcKCi2XyshKydFqBVaPQeuqtigi9LCIkISSKBRJCotixuFhGlsXhfuXQ5i80IJvn5Ww8AHRH5Fh2VsLh+Eg0FQPgtXuqHIW2mBOKJkdIzWWI4oGEkChqkhL2hGUAPIf5XitMhCNBOZUEwPtqCzERKth4zPNyAGRgZ3aFo7p0GWUI1QHO7gAghUfl+OyTu3VH02WNIkKiWCAhJIqanSFZlAFgrodzWmEi1KXdtha2O9qR3e6oXm76NBwnZOJaSxqtVTuqvHYPgEgyOhIfNX8BBDEZEkKiqLHcRCjq0WVUS65WQtVEWHCljIJNtRJatDtKMyiIIoOEkChqrG+3rZ93QkEVwuwKRzUlo/osQLC6cFS1ElKakCgOSAiJoqbTahOhjt4JBdVTn52VUMe2Mgo2q5vLUMdRotggISSKGmYzaLXKO2F1RKj71qimcNRiK2FvuN+SBRDEBEgIiaKmw2oToe4RIQtts/HUy5B79TMRKrBkp1UOCmYlpIiQKBJICImiRi2WKdRBlxeSlDYRaootC2Suh3PwANAXRSQ1y8VD0eFYKg5NsWXhWN53u4WshESRQUJIFC9xEd0RGYDApe13JiMOD8hiCoBQ5eccTl2eyXOY70tbCbtmKxzVPUEIQPDVKt+LFAlJUQtmIbX40iFpd6hXRg6t5gjCIEgIieKlKyRLMgDM83J2K35UdU8QKrRlbSXUscuoCscJfiuDQq/d43N4AcTFxHBsxPwFEMQESAiJ4oXti1o3dyJjItRVCNuzrpfp1jtBqMDmSVlVL6NJE5KVkLAeEkKieFFNhFZXygg6uekV2BiNWT31bFZRk44RYRE4KJrVRmuUJiSsh4SQKF6Kx01feLttLSzAnXUGhY5zJ7QIAVY4alVESON5iSKChJAoXqzvr5bZGtU3Isy+y5oqhOUWEZKVkCgiSAiJ4sVyE6HuHbcVsrQSypCZTui7Ncrm1LNRiyZDzWWIooKEkCheNFujVrxeEsXhIKCniVChxcO5BAAYiGEsOe1lwchgQkwAqHXWeOyFToDSwsbzWiWErG8q5QiJYoCEkChSoin0RgHAzmOuFSbC1FAfJBGAUFPH2ew6PpkDFmSynjNYCbsNMBEq8N5qZbaiHI9KkezGQemKOoAi3E9WQsJySAiJIqUrJCt/IOd7OcGKnVHdm6tpUVtvTy9DLFrS00SYwdo0ocfurnZWAUiIicHosPkLIAgtJIREkcLM5taZCA1x0yuwrOcMaUKdR/KOR7B6d5TShETxQEJIFCmsotJyE6FeI3m1sGEaM2yNskoZQyLCovHUU5qQsBwSQqJIKR4TIWtIpiPtWXRZMzgitNpBQXPqiaKBhJAoUqw3EWb2DFnwpCPZWAkNaTSawWb1VEKaU08UDySERJFSRBGhEcUys7UblWSpPzIAgAOnr4lQwXpPvbo1ShEhYTEkhESRonHTW/B2WUyJI0EA4HmhtkH35ze54bEBwGAcI4kpLhiIDialFIBaV43Lps8EKC1ULEMQDBJCohgJp9AfAwAHjxaPFZMIB3shywCEmnpOsOn+fG621tuGJggB8B4f7/ICkBMxKWTBLKQWXxMHDkBfuF+SyUpIWAkJIVGMsA3D1iqOt2JnVG2uZkCCUKFNbb09hQywuRP6dhnVIlhaOOoUHLWuagBJKRWMBs1fAEEwSAiJYoTVUlrTXE07gCmgv3dCgeU+pywcZSUkzcZEhNCmCa1utEa7o4S1kBASxQjbLSyzdtta2ma0EvYYaSJUsH4Yk4/qZYiigISQKEbUrVGLSkZFI0tGFdpmtBKq3gm9G40ybIH0ky23EtKcesJaSAiJYoSZCC3rr8ZMhIZtjbbP6KDQ5AiNUmLLI0Km8dRchrAWEkKiGFFNhJb3VzN+a3Ryu1FRFvsjQaRNhPqbNxQs99S3kJWQKA5ICIlixNqRvHIyIY4NAQAvCLV1Br2lwQWfHQBGkxiKj/uoPxIUZRFAndvvEBwGLUDI9FAVB3tghYGhmayERHFAQkgUHWNJDMYBwCWgSc95tNkijwwowmDzN4AXjHuRpnB0nA4ZbSJU4F0e3lOFtPBbMAup2duQsRIOKMJPEJZAQkgUHR2afVFLNkZN8E4oqFbC8YWjPWqXUQOFEFa33nYIjoC7FoAoiwMRshISlkFCSBQdmi6j1ixAHk5bF4xLECqwiHDCeF7jZtNPQJMmtNpKSGlCwjpICImiQzOS16JKmaH0H2XjvBMK082gYMUjxpkIFWxqmtBiKyGlCQkLISEkig5mMLfKRGhiRJg+mBAR9piSIwQg+NNCa72DgqyEhHWQEBJFhyYitGYBao7QsEajCu3TOCjMKZZBMUSEXrISEtZDQkgUHWyf0CoToaRGhEYXy0whhClJHIgOAuA5rsFTb+gC2N6vVcOY1KmEFBES1kFCSBQd1o7klZMJOTIKgBNsQo1RJkKFgBM1DgAIpzAQS5/si/RLsgSg3l1n5/WfAKVFjQiH+iyyErI59SSEhGWQEBLFxUgCwwkA8NrQYIWJMBVMu8sFfyOMt29Mnkqo6TJq7L4oAM7h4r3VAORUUhwdNPp1k2nyNvIcB6A/MpCSyEpIWAMJIVFc7LDeRJjpMlpn7L6owuQ0oWkJQgWbtr+M6dh5W527DoAkS32RfvMXQBAgISSKDctNhCnj505o0YznTR+Y5p1QEKzuOMq+TUoTElZBQkgUF+pIXqsqZTImQqO9Ewptk7ZGmR4YN5tei+qpD1plJWRpQiocJayBhJAoLrqsLhllemB6RJgRQuNn02thbeQs99T3Ur0MYREkhERxoUaEFm2NmjCASYum73b6jFosY3JEaFGXtSZ1PC9FhIQ1GFucTRC5wnYIreqvxvRAMLdYpjMky0BKTA7GhgAInGC0iVCBNQ2wzlPPuqxRREhYA0WERHFh7UheOR6VwqMAOLtDqPKb8MYaB/xOAIim0BdFT7hPkmUADZ46m5EToBi2QLPiEhGH+iFJJrxxApo59SSEhDWQEBJFRDCOsSQAVNlR57RgAWrJqCkmQgXNDApZLRk1JUEIRfJ9tQBkMSWOWjALqdHTwHM8gGA0mBST5i+AIEgIiSLC2sH00HQaMydBqKC1EppsIlRgu6OWNFqz8elNYEmWe8lKSFgBCSFRRFi7L4px7bbNSBAqaMbzqpWTzd4G0xZgs3Q8L7SttylNSFgBFcsQRURnKH1guZve5jejYlNBuzWaQCYiNHg2vRbmoLByGFMfQDMoCIsgISSKiCKICE0tGVXQRIQyx5mdI0QRRIQ0p56wFhJCoogonv5qZuYINREh3IKp/dUUrO+yRuN5CUuhHCFRRGhG8loUEWbaypjTcVuBhb+7QvGh6DDS9SPGToDSovbdtmgqIasMIk89YQkkhEQRYW1/NSkWlqIhAJzdwXtrTHtvlR31LmUFfTJkaBwF5sC8IqnhAVgxC4nm1BPWQkJIFAt9UYRTAFDjQK3DggWweIg30USooOyOuvhMu20TE4QAOJtdqA4AgCSmhgfMfLVCg6de6R4wGB2OiwnzF0BUOCSERLFQBM3V0uEIb2LJqIISAbu4tIvOzAShgmBpvQzP8YqVUIbcGyYrIWE2JIREsWC5m16NCGvN1qH2KgBwqiWjZi/AxhwUVqcJeyhNSJgOCSFRLHRaPXfCwoiwVdka5djcCVO3RlEUDgqaSkhYBgkhUSx0Wj2JUFSF0LyuLgrt47dGTc4RQttlzWorITkoCPPJTQiTyVla4kqSJIpTVJ3NeiNBFI+JkKs1WwgVT70qhKbnCC2PCFtoBgVhHdka6nt6es4999w333zT6XT+5Cc/ueCCCyZcIMvyFVdcce+99wI466yz7rrrLpvNBuC9994799xzOzo6/H7/fffdd8IJJ+j7DShc+Ydfvdb1EmT5kPmfuP3cdbne3rVn7/mP/kAMD9t9dY998Qa/P7f5O7Isr33g9m29mzjedvx+J35/zedzXcDLW9773rN3SLExT1XLny/8b6/Xm9Ptoiiec99N3cGtsNnPWnrGf554Uq4LeGTjK3e+8mspEQnULHz0q//lcORWtRmPx8+498ah0Q7e6fnG0ReecfhRuS7g9r8+vWvTY0tS8SHuwAXeq3K9PRQKffdP1/cO9Xiqqq867htL9jkg1yc8+Lff/e/oVsktfiyMb/nzCch++sZdoiQCuPzwrwlcbhOU2n1ck/APOzcCQIAQcAdyfXsoiSteEwH47Lj1iJznN3G1Dc/t6Hu3b5T7V99Bi9648MSP5/qEV//94Xfu/rMY3DNnyaEPXXlWrrfXO9Pf8vPbNy6Qnr/wmONzfcL9Lz1//xu/kxKxxtr9H1n7PeXvT/ZEo9HP3ff90dHdvNt3zXEXrTrk0FwX8OOn/7Rhy9OymGxrWPrgl6/gciw8HhkZ+ewD18VD/YK35penXrWkvT3XBVz5h/tf73pJlqWl84668wsX5Xr7ru7u8x65UQwP23yBP3/xxnz+DD5457aeN8ALx+934n+vOSfXBbz6/tar/3KbFBvzepsf+8oNefwZ/MKvbt4zsIWzO85Y+rlvrMzhz2C2EeEVV1zR1tY2NDT07LPPXnrppV1dXRMueOSRR5566qkdO3bs3bv37bffXr9+vXL+ggsu+PznPz8yMnLbbbd9/vOfj0aj2S8uG6LR6JrPrPz3C/fxcwf5eUPbNz64+tPHhcPh7J/wyO9/t+bTR6H+/7d3pnFNXF8fP9kIQSNbZBUEAUVkCQK1oogi4AYooFUr4kZdihaltdaFam21LXVt3fe6tyKiCCjgEhQVC4psoqwBwiKRBAgESDLzvBjNQxFlsP8Clvt9wedOcs7ML5d775m7zNwy2kAJaBSPdeTGxcaQdxeJRO6jPq7IiaQOEFMMhMlROwOm+3aqB7z/112r5vlRdMppxvVAz3HmWqc8eEDevaysbLSDXUPlDapxLdVAeOHAhpCli3EcJ3+GzRvW7QpbQtGrohnXyxtTRtp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      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idxinv = zeros(Int64, m)\n",
    "idxinv[idx] = 1:m\n",
    "Pp = P[idxinv, :]\n",
    "plot(x, Pp[:, 5:7], marker=:auto, xlims=(-1, -.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "348a2373",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# From factorization to algebraic multigrid"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80cece69",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "* Factorization as a multigrid (or domain decomposition) method incurs significant cost in multiple dimensions due to lack of sparsity.\n",
    "  * We can't choose enough coarse basis functions so that $F$ is diagonal, thereby making the minimal energy extension $-F^{-1} B^T$ sparse."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3d33e65",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "* Algebraic multigrid\n",
    "  * Use matrix structure to aggregate or define C-points\n",
    "  * Create an interpolation rule that balances sparsity with minimal energy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e693acf",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Aggregation\n",
    "\n",
    "Form aggregates from \"strongly connected\" dofs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "0886df9a",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "agg = 1 .+ (0:m-1) .÷ 3\n",
    "mc = maximum(agg)\n",
    "T = zeros(m, mc)\n",
    "for (i, j) in enumerate(agg)\n",
    "    T[i,j] = 1\n",
    "end\n",
    "plot(x, T[:, 3:5], marker=:auto, xlims=(-1, -.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d9099656",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sc = T * ((T' * A * T) \\ T') * A\n",
    "w = .67; k = 1\n",
    "E = (I - w*A)^k * (I - Sc) * (I - w*A)^k\n",
    "scatter(eigvals(E), ylims=(-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45942b28",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* simple and cheap method\n",
    "* stronger smoothing (bigger `k`) doesn't help much; need more accurate coarse grid"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78ac2292",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Smoothed aggregation\n",
    "\n",
    "$$ P = (I - w A) T $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2d4871a6",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
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6Z8dOeU4nAKfT+eyzzxYVFckpo08//fQTTzxx/fXXqx/U1NS0cuXKBF+RJpAQEsagKqWf5l7zJ46Ge9tYJAzAnlfMp0zOpeNsdnthudjdDMbEnlZn1QYjbJwDVbvtyR4hgBpX5Uttr4I6ji4tRp99KHD43USu7Dk6dOr6kmnv4jluZVZKR3PjZvv4nOuE2g6lrN2asvYDypmrr7765z//uSyE9913386dO9XXv/XWW/fff/+///3vRIzUCgqNEsag1AjWTdkgBLA6m0uzA0DnBBsM6GlXoqiaq02jIlD1mjFnWX0gHOga6wFg42yVOdP0gaN8mSWJsyLRji3pgm1CjMx070QonCYk5EfxKelCQbn6zMc+9rGWlpb333+/paVl165dl156qXLX/v37d+zY8bvf/W7NmjUJ2qkJ5BESxjB7aNTGYYOL23WUAdg3zD5SbLp8GaWnjKNk8gahjFBSDbwIszZaax5pkxgDUJZd6rA5pl6gFFQ0edokxiZl0xAWJfPM/5uy6SQWmnvs9Tbpp288/5fPTNdNoXc80DrqP/3mu/IL8udcx+4u4NOPaU4kCMKVV175q1/9KjU19ROf+ERmZqZ8vqGh4aMf/ehdd911/vnnJ/RitIOEkDCArpifl+NA+QxJoZtzo0K4d8iUQqgMpp9NCAEgZEqPUAl4ThsXBZDjzM5LdQ/6h2XfsSxr+igZYTkSbAT/+f/4+ob77n+ja/ik0mNGNzHg+683n7f9nPKtH1ywDVddddXWrVttNttzzz0nn2lsbDz77LNvu+22Sy65ZMHLLhgKjRIGoK4gnEni6sy8TciYqNROTEkZjZ/nOADhvnZ5N9FUNA4rKaPTZMrE7qLo6PKlqqrqJz/92Wf/tv+3+zp8sRhp4/DEzufe2zcm/eKX9y5m8fLy8m3btlVUVNTX18tnbr/99t7e3q9+9atut9vtdtfV6drYj4SQMIC9sVzQWXpqbzaxEIaH+qTABAA+I8eWNf2oUz4lze4uAMDCYjS/1EzM6RHimOgo5cssR7549dWP/fGJR7tDG+79x8mP7Nr6wBtnP/pm3nGnvP3unuLi4kUuPjo6+sUvflG5+bOf/ezo0aPNMV599dVFrj8vKDRKGMDU6UtT2eTmbBwiDAdHmC+MNDP9q4rdM1YQqhFKqsNDfQDE7maheEbHS38kJrWOtsvH1a6KmS6LDyYkj3C5cu6555577rmNjY0tLS2pqan19fWLn6P71ltv/eEPf+js7LzsssuUk2lpaWlpWnQyXRBm+nYhlg2JCGGaHbXZ3KERJveg+UBi00T1YdrpS1MRSqr8+18HEOpuSfvALBfqjdwvBkBB+opZpiypJvSacZuT0I3a2traWs1qSYeGhlasWPHSSy85nWbpWERCSOiNV0TrGAPg4LE2ZzZ5q8/lDo1E82VMJYShuBDOGFeEejChyfrLNHnm3iAEUJJZlC6kTYg+T2B02O9xpxo2JYcwltveuntP/wEA15/4lc0FGxe5GjXdJgjsHYr2013v4hyz/gMq45n2mWwwYby52qweYbzRWlcz9G0iPDvNnjb5YGpzNTUcuKqcCvmYtgmXM8MBT894X894nxxISAZNTU07d+487bTTzjzzzO9973sTExNJeqJpISEk9Gb2CkI1qkZrJlIRZcog53DaV8xWVGDLWSFXUEn+8YjnqE72JcCRWKizdlaPEECtO3rBEdomJJKJz+fbsmXLD37wg+uvv/75559XD6/XAQqNEnqjCGHdXEK4WdV6W2KYruuhAShz54XiSvBz/JQUSqqCR/YCCHU3pbrnrj7WB1WX0dk8QvUFzeQRElogiuJPf/rTa665Jj09HUAwGLzzzju/8pWvbNq0adOmTfI1gUDg2muv1dMqEkJCbxL3CPNTUZSGXh8mwmjyslXZplBCVU+ZmjkvdpRUy0IodrekbjwpuZYlxlHf4GjQCyDDkV6YMYc2U+LoEuPQUOM97/4mkQhn38RAMBySj0UpenDzq7fwXPTHX16aK12Yu5t8javyuuOvFvio1giC8MILL6xYseLKK68E8OSTTz711FNy023G2MjISE9Pz69//esLL7xw/i9u4ZAQEroSktAwwgBw040hnMrmXK7XF82XMY0QztFlVI0J82UaVe4ghzne0qrscjtvC0uR7rEefziQap8yMYuwFA8ceHTfwPsLfngopogAusZ6E3nI4eGmD63ctq0kPtT+6quv/vGPfywLobrp9sjIyNatW4eHh0tKSu66664FG7kAaI+Q0JUGDwtGAKAqi8uepsPlZEw4hmKeQhi9xjyj6pWeMnNuEAIQbEJZVikAiTElxYawLpsLNun8jFnOzJpja1UvuOCCzs7OvXv3Njc379u3T+mp5nK5mpubh4aGLrvssrPPPlvPIfXkERK6kkgFoRplNsVecySOMjEkDnQDAM8LU8YQTkUoWMkJDiaGIsMDkm+MT8tMuolz0TwS9QirExBCADWuqpaRdgBNnpYNK3SdCUBozqVrd3xo5YljobnHJ/VNDAQj0QjqHw4+1TTcCuCStTuU/Km8lNx0xxwl8AIvFKbnpwmp6pN2u/3zn//8r3/969TU1CuuuGJSHT3P85/97Gdvuukmj8fjdk/ftklzSAgJXVEKIeoTiIvCfI3WxJ4WSBEAQn4p50igHJi3CYUVoc4jAMTuFmetrh0Up0XlEc7t0QKodVW+0PoP0DbhUqE4ozCRy1a741vgL7f9qwmtAI4r2KQOci6Yq666qq6ujuf5l19+WT5z+PDhiooKp9MpSdKDDz5YXl6umwqCQqOEzuyZp0dYk81lCQDQ60OfP3l2JUqCPWXUKF25zbBNOCH6esf7AQi8vTw7oSHgqtbblDhKaENJSckpp5yyatWqDRuiM6ufeuqp/Pz8tWvXFhYWPvLII48//rie9pAQEvrBgP2KRzjdYPqpcMBGt4mcwoUIYXyb0HiPqsnTysAAVGSXKYl8s1PrjubUtIy0R9iMk1oJYl709fWpm25/85vf7O/vf+aZZxoaGg4cOHD88cfraQyFRgn9aBtjniAA5DpRmp5oCmh9Lvd6fzRx9KOlBieOhmLtthPJlJFxmClxNN5czZ2o/ZmOjPz0Ff0TA6FIqMPbXZmd0DQ7Yinx+borLl5zAebqyZcgb7311oMPPjg4OKieTQ8gJSWlpmbukqRkQB4hoR+KS3dc3jz0zESJo4yJvdGhDY6EhVAoqZIHE4p9HUwMzXl9UmmMT1+axzdabbz7tvFOLaE/Na6qLYV1WwrrZmnRnjg+n2/NmjUvv/yyIAiLX00TSAgJ/Zhvyuikiw0XwvBAFwv6Adiyc/mMnAQfxTlS7HnFACBFxL725JmXCE3xebyJCjmovwyhKaeffvq1115bWlpqtCFxSAgJ/dg7HD2oSyxlVGajixN4AGj0snExCWYljFILKJTOL4Cjypcx0qMKS5G20U4AHLh5xbiovwyxtCEhJPRjz2Csudp8QqNOG1ZncwAkhgMeI51CVXO1ebhTMM02YdtohyiJAIoyCtKFeQxBVUbVkxASSxISQkInhoLonGAAUu1YlTW/nBelmlCRUkOYV08ZNcr1xgqhImO1CWfKyBSkr8h0ZADwBscGfIPaW0YQhkJCSOiEssO30cXZ5/l/p8ypMHYwoap2Yp6h0ZhHGOpuMXAwobLDV50zv9w/DpzShqaJnEJiyUHlE4ROLCxTRsYM/WUio0ORMQ8APiXNnptQbw4FW5bbluWKeD0s6A8P9UZzZ3QnnjI6T48QwCpX1d7+AwAah1tOKtG1xotYDIIgXHTRRU5nAl2QzM34+Pi5556bpMVJCAmdWIwQKg854GFhCfN1KDUh7g4WR8sh5oVQUh3xvgNA7G42RAgZWPOCaidkVB4hJY5aiaefftrj8RhthTbk5ydroicJIaETixFCtxNlGVzHOPOHcXiUrXcZUFYf3yAsTbSnjBqhpDpw8B0AYldLat2HtLQsMfrGB+RWy1nOzBVpefN9uOJEkhBaC5fL5XK5jLbC7NAeIaEHwQgOjzIAPIeNC5Ixw6sJQwvNlIk+qrhy0jo6o+ztJdhrexIV2SsdNgeA3vH+RGYXEISFICEk9OCAh4kSANRmcRkL6iZRH+tEb5QQqmonFuIROmKlh0Yljqp6yixECG2crSJ7JeQQ60ibhoYRhOGQEBJ6sLAKQjVxj9CIxFEW9IcHewBwNru9YCHNNu0rSjhnKlRJNzqj6jK6wHaRSlm9PJqOIJYMJISEHihlD/PqKaOm3tBSQrEnWvZgLyzjBMdCluA4oagiupoR/WWUvb15NVdTo5rHRBUUxJKChJDQAyWeuXn+mTIyFZmcywkAQ0F0TeithaEuZYNwIXFRGVV/Gb2FxBsa6584CsBpc5RllSxskXjrbcqXIZYWJIRE0pGYegzhAoWQU3mTe4e0MSxx4huExQuMK8LQ/jJKMLMqp8LG2Ra2SLWrUh5M2D7aIUphzYwjCKMhISSSTpOXjYkAUJSGgtSFrxOPjuqeLyMutN22GqXuQv8JvUpztcXMk0sX0ooyCgCIUrh9tEMbywjCBJAQEklnMRWEahSPUO9Ga8r4JI4Tihe4wQZAKKoEbwMQPtrFQkGtrEsE1QbhogarrnJHtZwGExJLCRJCIunEhXChmTIySsapzvkyYn+nPFDX7srn0zIWvA4nOIT8EgCQJLFX1222BbfbnkS1q0I+aBqhbUJi6UBCSCSdvYveIJRZl8M5bQDQOsZGdZz0LmqRKRNbIVZN2KXfNqEYETu9XQB4jqvKqVjMUrWu6DtAFRTEUoKEkEg6WoVGBR7rcjgATN/o6IKnL01FWSHUo19osWWkPSxFAJRmFqfaUxazlCpxtIXByEkgBKEhJIREchnwo9cHABkCauY5hnAqhjRaC8WnLy3WI3SUGjChV5Ups1ghz0vLdaVkA5gQfb3j/Yu1jCDMAQkhkVyUDM86N8cvule2IUIoxrw3x4LabatRpFTsaYUkLXK1BNEqU0aGxlAQSw8SQiK57NEoLjppEd2EMOIZkCa8APi0DFvOikWuxqdn2XLyALBQUDzapYF9CbDIdtuTqKX+MsSSg4SQSC77NMqUURaRV3nfw0K6OFSqnjI1CxhDOBVB3/4yDKxlpF0+1sQjVBZppHwZYqlAQkgkF6XUQRMhzBJQlcUBCEk4OKKHU6hs5jkWnSkTXUffbcLusd4J0QcgN9XlTtVgLh11HCWWHiSERBKZCKPRywDYeWzQaJquzt23Re0yZaLrFCuN1vQQEqXyffGZMjJlWSUpdieAAd/gaNCryZoEYSwkhEQS2T/MJAYAa7K5lAV2uJyMzv1lFjmYfiqKoIa6mjRZcHaUyvdaLeKiAHiOr8opjy5O+TLEkoCEkEgiWlUQqtmsY76M5B8PewYAcHbBnl+qyZr23EI+JR2AND4aGU16+3Cl8l0rj1C9VCNFR4klAQkhkUSSIYT1ufHFk62EYnd0DKFQVMHZ7NosynGqMRRJF5JGT9Sj1SRTZtJSzeQREksCEkIiiSRDCEvTubwUABgJoW0suVKo6imjTVw0tlqsv0x3cqOjnsDokN8DIMWeUpJZrNWySgUFtd4mlgYkhESyiDC851nsYPpp0a2aUNVTRrO4InSsoFC5gxW8FrUfMlU5FTzHA2j3dgXCuo7RIIhkQEJIJIvDo8wXBoCyjKgPpxW6bRPGayc0ypSJrqYIYZJbbyvJLEqzbE1IsTtLM4sBSExqo8GEhPUhISSShbYVhGrio+qHtV34GFgkHO7rAACOsxdptsEGwF5ULu84hod6pYBPw5Un0RSvnajQdmVlnBNVExJLgHns/+/evft3v/sdz/Of+cxnNm3aNOne11577fXXX1efue666xwOx1/+8peDBw/KZ1JSUq699tpFWkxYhXhPGbfGK+sTGg33trFIGIA9r5hPSdNwZc5mtxeWyZk4Yk+rs2q9hourafRonzIaW7DypbZX1U9BENYlUY9wz549H/7wh7dHKO0AACAASURBVEtLS/Pz8z/0oQ81NDRMusDv93tiPP/88/fdd58gCAAeffTRl19+WT4/MjKisfmEiUlGpozMmhwuzQ4AHeNsMKDt2nFC2k1fmopqmzBZ0dFAONg11gOA5/iK7DJtF6+Jt94mj5CwPIl6hD/96U+vvvrqr3/96wB6enruuuuuX/7yl+oLzjzzzDPPPFM+PuOMMz772c9ysc35Cy644Etf+pJ2NhPWIHlCaOOwwcXtOsoA7B9mpxdrvL6Mksni0DRlNLZmlS/6LMkSwpaRNolJAMqzV8q9YDQkPqHX0yYxpmEmDkHoT6Ie4WuvvXb66afLxx/5yEdee+21ma5sa2v75z//+alPfUo5849//OO//uu/Hn744WCQEsyWC10T7GgAAHIcqMjU/lsy3mgtadFRDQfTT0WHxNHG+NAJLTc4ZVwp2XmpbgCBcKB7rEfz9QlCTxL1CHt7e/Py8uTjFStW9Pb2znTlb3/72zPPPHPlypXyzTVr1vh8PkEQ7r777ttvv/3NN99MS5t+u8Xv93/60592OBzyzRNOOOHLX/5yoq+DAAD4/X5BEOx2jUq/F8G/e3jABmCji/l92ueDrMuMrr+7X/RVRzRcmTHm8/l4jlNqJ8LuIp/WL4G5i8BxYEzsbZsY82pWra/i0NFG+aA8Y6Xm9gOozCof9A8DeK/vYK59cjtvv99vs2nUVW+54vP5IpEIvY2LQZKkSGTu74dEP34OhyMcDsvHoVAoJWX6dHhJkh588ME77rhDOfOd73xHPvjWt75VV1f38MMP79y5c9rHCoKwY8eOjIwM+WZ5ebnTqXE8Z8kjSZJJhPB9LwMYgOPy+GT8HbcWAJAA7B/hnU4tXy9jLBwO28Y9LOgDwGfkpK4o0nD9KE6n3V0QHupjYdHuHbQXlmv+DC2j0elLq/NqkvEnWJVX/Xb/HgCdE91T1w+FQvT5XSSRSMTpdJIQLgZJkhKJRCb6DVJaWtrZ2XnCCScA6OzsLC6evkvFiy++OD4+fu655069SxCE+vr69vb2GU2x2y+88EK3W+sUw+WELYbRhmD/SEQWwvpc3mbTvkqnPg88J0kMh70QYdOqozcAxpjNZpP62uSbjtLqJL2fQklVeKgPQKSnxal1Po7EpDZvtMJvVW5SXsIqdzS62zjSOnV9k/wfWhrzfJytC8dxXAIb2Il+Q+3YseOxxx4DwBj7wx/+sGPHDvn8s88+OzwcL+b6zW9+86lPfUr5JcgYGx8fl48HBwf/+c9/1tXVJf4aCOuSvEwZmXQ7arM4AGEp3r9GQ5LUXE1NUucxdXi75Z4v+Wl52c4szdfHMRN69RisSBDJI1GP8Nprrz355JPPOOOMSCRy9OjRhx56SD6/Y8eOF1988dRTTwUwNDT09NNP79q1S3mUKIrFxcUnnnhiamrqa6+9ds4551x00UWavwbCbHhFtHgZAAePdRqNIZxKfS53eJQB2DvEtuZp/CxJaq6mRiitiT2X9kKiVDVoXkGoUJJZlC6kTYg+T2B02O/RZOovQRhCokKYn5+/f//+V199lef5D33oQ4rPt3fv3oqKCvlYEIS33npLXWvvcDiOHDmyf//+YDB4xx131NTUaGo8YVKUuRDrXZwjac2L6nO5P7REn07zxcXYsMBk1E7EVo55hF3NYAyaViDEm6u5kyWEHLiqnPIDRw/KT3c8CSFhWeaRZZCSknLWWWdNOrlu3TrlOCsrq76+ftIFhYWFhYWFC7aPsCLJjotOWlxzIWS+MXlSIOdw2leUaLu4gs2Vz6dnSRNeyT8e8Ry1ufM1XLwx7hFqXzuhUOuukoXwiKfl+OLjkvdEBJFUqNcooT37dBHC42KL7xtmkqZSGO6JxUWLK8En8TOibBNqHh1tjrfbTpZHCKA6hwYTEksBEkJCe/boIoT5qShKA4BxEc1eLZVQ6ovmNicvU0ZGGWqhbX+ZQd+QJzAKIF1IK8zQ0tGcBLXeJpYGJISExogSGkYYAE7rMYRTSVJ/mUhv1L9J3gahTJISR4/Ee8pUcUjin6Aqu9zO2wB0jfX4w0nr+koQSYaEkNCYhhEWjABAZSaX7Ujuc9W749FRDZdVhDB5KaPR9ZPjEcZTRt1J3CAEINiEsqxSABJjzZ62pD4XQSQPEkJCY/TJlJn0FBp6hEwMRQZ7AYDnBU3HEE5FKFjJCQ4AYc+A5BvTatmmpE1fmoryFBQdJawLCSGhMYYIoYaJo2JvK6QIACG/lHMkuUkYbxMKKwCAMQ2jo43DSWy3PQnlKRpJCAnLQkJIaIxKCJP+XDVZXIYAAL0+9Pu1WTOpQyemokRftYqOToi+3vF+AAJvL9d6DOFUVB4hJY4SVoWEkNASptqu25x8j5DnsMmtsVMY7oltEBYnPa4I1TZhqEcbIWn2tDIwAOXZZQKf9Pbrte5oPk7LSHuEaTkGhCB0g4SQ0JL2MeYJAkCuE6Xpegxr3ax1dDTUHe0po0hUUlH1l2nSZMHG5PeUUZPpyMhPzwMQioQ6vN06PCNBaA4JIaElStLKZq2bf86EUqGxV5PEUcbE3mgRoSPJKaMyQnGV3FxN7OtgYmjxC8ZTRnOSvkEoo9TsK3uTBGEtSAgJLVHiovVJriBU0DZfJjzQxYJ+ALbsXD4jZ/ELzgnnTLXnFQOAFAn3dyx+wXjKaJJrJxSUbULqL0NYFBJCQkv2DEUPdEgZldno5gQeAI6MsnFxsauFkj99aSpKvsziG62FpUjbaCcADlx1TsUiV0uQGkocJSwOCSGhJXrWTsik2LA6mwMgMRxY9GBCpYbBocsGYfS5SpSy+sUKSdtoRygSAlCUUZDpyFisZYmhbEaSEBIWhYSQ0AxPEJ3jDCpx0gcNo6Oqebx6bBDGnismhF2L9QhVpfQ6xUUBFKSvkEXXGxwb8A3q9rwEoRUkhIRm7ImNIdzo5uw6/mcpQrhPAyFU5vHqNzsz3mitpwVsUS+hWceeMgocuOqY7lJ/GcKKkBASmqE4ZDpUEKrRqtFaxDscGfNATmDJ1W+Ipi3Lbct0AZACvvBQ32KWirfb1itTRmZVPHGU8mUI60FCSGiGIoTJHjoxCUUID3hYWFr4Okpk0lZYoe28+DlR9ZdZeDUhAzPEIwRAHiFhaUgICc1QKvl0y5SRyXViZToHwB/GkUUMJlQ2CG3FurpTUG8TLiJfpn/i6FhoHECWMzM/LU8byxKjJi6E5BES1oOEkNCG1/vZQQ/DsW3PdEOR3ocbWWBBfb78fv/br/9rT9/oeChsK6rQ0LZEEEqqJsTI3r7RXa+/5vP5FrBCWIo81/KyfJzUqfTTUpFd5rA5APSO97/Tu1fnZyeIRUJCSGjD1a9HwgwAStOjjbD1ZHOswfeP9kX6/fN2Ch+4/1cnblz7mz//7YmDPZf86e27/vS/bHFJK/Plnj8/d/ETux4/2P3gX1/YtnHtvb+4e74rTIgTv93/e/lYfyG087aijAIADOyOXb/Q+dkJYpEkvScvsUzwxYrZV+lYOKFQt4hg7J+f/NMTd976xEdrU+02AGGJff/Nl39y6y1fu+Fb2hk4G/fcdee+5/78l0tPtPMcgEA48o1f3ZWZnXP5FZ9c2ILVOtZOKJRllbSPdgIIRjRoFEcQesLp/Mt3Ftxud1NTk9vtNtoQC+P3+wVBsNv1+33z5gD7yhsRAPuHmSgBwIoUlGVw2/K5u0+y6WDAMx3Sf78rBSN4L1ZNv9HNOXicV8Z/57iEAh6nHX/cT+qy89PjowdDEenC/23c16TTdtfm1dWPn1kly7DMSEDc+Vb/G3vfS+ThjzY8+Y/21yIsouzPVWSXOW2Oy9Z97MPlJyfF4mP55Z4H3u3bP+gbGgp4ANg4W42rMhKJXLP1c8cVbtLBgKWKz+dzOp02mx6fo6WKJEl+vz89PX32y8gjJBaFN4Tdg8f8ljoawNEAy0vRyYDBwGQDDgwzAJvcif7CGx0ZyU/PV59x2PgMO+fz+dLS0rSycyYkSeIiYbUKAshJEQITEwmuMOA7enj4mFzTttEOAJ7AqFZGzk7PeJ/agAiLyDflzB2CMD+0R0gsd3jeFpYmq+Z4KJySooeY8zwvTnl2idFkP4LQD/IIiUWxrYB7Z4e9Y5x97O/Rr+7fnGLb5Oay9MqXOb+cf2cHB+DUv0YmwgzAJ2r46zbwuc65HhnjrHO2P9Hwyv9dE6+gf6PLs3r9Bp7X6Wfi5q0f+Ed7+4fL4wUPzzQdPfX0MxJ8+GXrPv7Rqo/8temFvzQ+B8Bus99z1m0A8tNWJMPaqXxx82c+sf6i7rHe/37tdvnMTR/8Wp7dVZOvd84OQSwMEkJiUWQJ2JLHNamq99bkcFv0GkYIINeJXCcHINWGiTAADAbYvAy48Xs/OO+MD7e93ri9tkDguVe6x57tC/z1pT8nyeCp3H73Peefefr7I92nl2RJjD3XNLA7nPHMI7cn+PD8tLz8tLzfB/8k3xQ4+2q3fv3hABRnFAIQ+PhvHzEi1uRW6tb1myAWCYVGCQ1QeptVZiLbYYwNJxRExa9hZH4PzMjIeO6Pj67Jy3jkQOev3+8vvWjn319/q7i4WHsTZ6CgoOC13XurL73mgYNHf7e/s9KV9sLjD+fkzG8aYstIdJ7wmtxVSbBxblLtKcWZRQAA1uhZbPdwgtAT8ggJDdgTS1e5/XjbuhwDyicAPHWGLfNBKRBB1zgbDsKdcGgUQLi3dcfqoh2ri1LrTnZ/5pqJhBNVtEIQhKu++MWPZ4753n4JQKS3DdUbEn94MBLqHusFwHP8Laf9V5KMnJ2ijILrtn7hG//4LsDRqHrCWpBHSGiAMph+s45B0UnYeWxwcQCYyp4EEbuiSY+CjmMIpxIfTNg1v46jzZ62CIsAKMsqSbHP5yeAptS6o/Y3eVol09RlEcSckBASi6VrgvX7ASBLQGWmYUIIlQzvGZyvEEZDeQ4dpy9NRSiNPrs4z1H1Siiy1mWkkLtSsnNTXQD84UDvxKLGaBCEnpAQEotF2SDcnKfvyIYpbF7YPCbGxJ5oKbqxHqFQUiVPvRB7WlkknPgDlVCkMizeKBQlbh5tM9QQgpgHJITEYtkzFD3QeQzhVBYmhOHBHikwAYDPyLFlGdnYiE/NsLsLALBIONzXkfgDG5UxhLp3GZ2EosQto+3GWkIQiUNCSCwWJQ5puBBucnM2DgAOjTBfwg5VPC660si4qIwyjymUcHQ0wiJKymi1qyIZViWOosRNozSPibAMJITEYtlj0GD6qaTZoy2/IyzaaC0RFMlRRMhA4tuECefLtI92hSIhAAXp+dnOrGRZlhiKR0ihUcJCkBASi8ITRMc4A+C0YY1BhRNqFhAdVSTHUWq8R+goVRJHE/UIG4ejV64yeoMQQFFGgVxHPxYaP+obNNocgkgIEkJiUewZiqbJb3Rxggn+m+KJo4kLYWwovLGZMlEblAqKnhYkVoFgng1CABy46pwK+VgxjCBMjgm+uggro04ZNdYSmfl6hJHRociYBwCfkmbPLUqiZYlhy861ZboASAFfeKg3kYeYJ2VURjGDyuoJq0BCSCwK82wQyhyXGy3hOBCbjzg7SsWeUBwtXTAcoSQqJIlERxlY80ibfGwGjxAqM8gjJKwCCSGxKMyTMirjcmJlBgcgEMHh0bmdwlBMbMwQF5VR8mVCCeTL9I73y2P/spyZK9Ly5rxeB5T+MkfIIyQsAgkhsXD8YRzxMgA2DhvdphBCzDM6qmquZnymjEy80VoCFRRK+HGV2yxCXp5d6rA5APRPDHhDY0abQxBzQ0JILJz9wywsAcCqbC7dNP3b40KYQKM1RWwcJqidkFF801Dn3B6hqTJlZGycrTKnTD5uGqZqQsICkBASC8dsG4Qym3OjB3N6hJJ/PDzcD4Cz2e2FZck2LEHsecV8ShoAaXwk4h2e/WJVpoxZhBy0TUhYDRJCYuGYLWVURjFm79Ac9Qdid7REwV5UwdlM49JynFBcKR/OmS+jardtFo8QqjgtJY4SloCEkFg45vQIV6ZzeSkAMBJC29hsUqgqpTeROwV1vkz3bNFRT2B0yO8BkGJPKc3Ub5LwnKg8QprQS1gAEkJigUQY3vdEZabONJkyMvWJ5cvEm6uZJlNGJl5WP6tHqPSUqXFV8Oao/ZCpyqngOR5Ah7c7EA4abQ5BzAEJIbFADsYaW5dlRD0w85Bg4qhqDKG5PMIEG60diWfKmMv+FLuzJKMIgMQkpSE4QZgWEkJigZgzLiqTSOIoE0PhgS7gmD05k2AvLOfsAoDwcJ/kG5/pMsUjNElPGTVVWeXyAUVHCfNDQkgsELOV0qtReYQzXiP2tsnDb+0rSjhnqj6GJUg8i1U1NHgqJqydUIh3HKV8GcL0kBASC0TlERpryDSsyuYyBADo8bF+//TXmDZTRsZREpvHNEO+zITo6x3vA2DnbRXZK/WzLDFUHiEJIWF2SAiJhcCAfbGBf8eZqXZChuew0RUvopj2GtUYQnNlysjEy+pn2CZs9rRKjAGoyC6TO7mYipqcSg4cgJaR9rAUMdocgpgNEkJiIbSNMU8QAHKdKE03nRAigXlMovm6jKpR5ctM7xGaOS4KIENIz0/PAxCKhDq9XUabQxCzQUJILARFXUzoDsrMkTgqSWJvdO/NbCmjMso0DLG/k4mhqReYbfrSVKi/DGEVSAiJhWDmlFGZ2YVQHOhioSAAW04en5Gtq2WJwTlT7XnFACBFxL62qReY3CMEDSYkrAMJIbEQzJwyKrPRzTl4AGgaZV5x8r1KBoo5NwhlHLEy/6nVhKIUbh/thDwR3mWu2g8FpbrxCHmEhLkhISQWglKWYKouo2ocPNbkcAAYsH+KUxgvpTflBqGMMHNZfetIuyiFARRnFqYLaXpblhiKR9jkaWGYexIIQRgFCSExbwb86PExAOl21GaZVAgxa3TUhPN4p6I0WpvacdT8cVEA+Wl52c4sAOOhib7xAaPNIYgZISEk5o2iK3W5HG9eHZxNCMWeqJA4zBwaXVkrH4g9rZAk9V3mnL40lZpY2JbyZQgzQ0JIzBvzZ8rIzFRBERkekCa8APi0DJtrhQGWJQafnmXLzgXAQkHx6DEVCErfslUm9ghB85gIi0BCSMwbqwhhfW50IkODhwVVJd0hdaaMmYY2TEWYLl9GYqzZ0yYf15g1U0aG5jERloCEkJg3VhHCLAHVWRyAkISGkbhTGM+UWWneuKhMPHG0Oy4kXWM9/nAAQF6q253qMsayxKAKCsISkBAS82NcRLOXARB4rHOZWggxwzZhPFPGlKX0alSN1uL5MvFMGbOW0iuUZpak2lMADPqHPYERo80hiOkhISTmx94hJjEAWJfDpdiMtmYu4tuEqnlM8SJCE6eMysRbb3c1gUVfQnz6ksnGEE6F57hqV4V8TPkyhGkhISTmRzwuatYKQjVTPUJpwhsZGQTAOZzCilLDLEsMmzufT8sEIPnGIyNH5ZMW8gihUmuKjhKmhYSQmB9W2SCUOS5m5L7hqCOrxBiF4krwFvj/j1cTxiK6TcPRLqlmLiJUiG8TkkdImBULfBEQpuJd0zdXU5OfiqI0ABgX0eRlUGfKmLiCUE18DEV3M4CjvsGR4CiAdCGtMCPfSMsSI544Sh4hYVZICIl5EJJwcIQB4IBNbgsIIaZERy20QSgjHDuPSRUXrZYH/pmcypxygbcD6B7rnRB9RptDENNAQkjMg/eGWUgCgOosLtt0s2CnZ5IQWqK5mhqlLbhsueJXmbyUXkHg7eXZKwEwsJaRNqPNIYhpICEk5oG1Nghl4kI4yFgoED7aDQC8TSisMNCqxBHySzmHE0Bk5Kg04bVWpoyMEh09QtFRwpSQEBLzwFopozKKqe8OMbG7RS5CEApWcoJFXFqeF4qi7WPE7mZFSyyRKSND+TKEySEhJOaBFT3CykwuxwEAgwEMtCobhNbIlJFRorjDHQcHJo4CcNgcK7PMXvuhQPkyhMkhISQSRWLYPxwVwnrrCCEH1MWsHWqxwBjCqThiFRRHeg7Ig/2qcsrtvOnbGcSodlXyHAegfbRDjEyZkkwQRkNCSCRKo5eNiwBQlIbCVKOtmQ+K/8p6lOZq1vIIo9Y2jnXIBxaKiwJIF9KKMgoBiFK4zdtptDkEMRkSQiJR9liqglCNbLCdhXNGOwCA44RiUw9tmIRQVMHZ7ABaIl75jIUyZWQoOkqYGRJCIlGsuEEoIxu8KtBpj4QA2N2FfFqG0UbNA05w2PNLAbSlRc+Yv8voJJQBwjSPiTAh9gSvC4fDd9xxx8svv5yXl3fjjTeuW7du0gV///vf//jHPyo3v//97+fn5wMYHx///ve//+6771ZVVX33u98tKirSynRCZ6wrhGtzuBQb1gejvohVKgjVCKXVE/1tfSkcAJ7jq3LKjbZofqwij5AwMYl6hD/4wQ8ef/zxG2+8cf369R/+8IfHxsYmXbB///4DBw5sieF0OuXzV111VUNDw3e+8x2bzXbOOecwxqasTViDvRasnZCx89jg4jb4LVZKr8ZRUt2Rykc4ACjLKkmxO422aH4oHmGTp1WiLwHCZCTkEYqieM899zz55JMnn3zyKaec8uyzzz722GNXXXXVpMtWr169c+dO9Zmenp4nn3yyvb29sLDwpJNOKioqevXVV0899VTNzCf0omuCHQ0AQJaAykyLCSGAzXncBn/UF7FKl1E1QmlNW3r02HJxUQCulOzcVNeQ3+MPB7rHelZmlRhtEUHEScgj7OzsHBwcPPHEE+Wb27Zt271799TLdu3addlll339619vaGiQz+zfv7+srKywsBAAz/MnnHDCtA8kzI+6lN56MghsdmNtoE0+tqJHKJRUtadFP601ORWG2rJA4vOYqKyeMBkJeYT9/f1ZWVl2e/Ti3NzcxsbGSdesXr36qquuKioqevvtt7du3frKK68cf/zx/f39LpdLuSY3N7evr2+mZ5mYmDjttNOUZznttNO+973vze/VLHv8fr8gCMp7qCH/7rUDNgAbssLj4wHN1082G8X+TGkCwIiQncM7MD4+05WMMZ/PjL2h27MEIAKgJGAfn9l+kzAxMcEd+5OpPKP0LbwD4P2+Q8fnbjbILivh8/lEUbTZLFMwakIkSUpkPy6hb8yMjAy/36/c9Pl8WVlZk67Zvn27fHDppZcGAoE777zzkUceycjICAQC6gdmZmbO9Cypqal33nmnsnJ+fn5GhpVS+8yAzWZLkhC+740AEoDjCx0ZGSmar59sNoT3yNKxL6WmKiUjbeZ3iDHGcZzZ/vciLNLpjH6ea0Mwm3lTYYxNMnJ9wRocAYD2iS7z228GeJ53Op0khItBkiS1eM1EQt+YpaWl4XC4q6urtLQUQEtLS0VFxSzXV1VVvfDCCwDKyso6OjrC4bD81dzS0qLo5VR4nq+rq3O73YmYROiMdVNGZbjeaHO1AylVtR52/AqLvYqO0a4QJAB5QaT09RhtzkJQah+PDFMFBWEuEtojdLlcZ5999r333gugu7v72WefvfTSSwH09vbeeeed8jWHDx+WDwYHBx988MGTTjoJwNatW1esWPHYY48B2L1798GDB88///xkvAwiqXiC6BhnAJw2rMmxmITIyFNtAbyfUq3MFrYQinhU+CVltrC1KMooyHRkABgNeo/6Bo02hyDiJFo+8eMf//jhhx/evHlzfX39Nddcs3HjRgCtra3/8R//IV/whS98oaioqK6urrKycv369ddffz0AjuN++ctffu1rX/vABz5w1lln3X333Tk5OUl6JUTy2DMUjbJvdHGCNXswKOLxXmqV4t1aCCXBpGKCid3NsGAFAgeuOpbmQ/kyhKlIdDNp3bp1jY2Nhw8fLigoyMvLk09u27ZN2QJ85ZVXurq6PB5PeXm5egfxIx/5SFtbW3Nzc1lZ2dSdRcISKMpxnNUqCGUio0ORMQ+AcVtah6PQkkIYq0Mv9zEp4AsP9drzio01aQHUuqv2DrwHoHG45aSS4402hyCizCOrwm63r1+/Xn2G4zilcB5AaWmpvIk4idTU1A0bNizYRMJwrL5BqMRFG5yVErgDw0yUYCHXloE1x2a7V/gkAGJXsyWF0EWDCQkzYp0vA8I4rNtuWyYUi4u2Z1UBCERweNRKTmHveP9YaBxAJudwhwAg1NVksE0LQukvQ6PqCVNBQkjMgT+MI14GwMZho9uSQijGZCNQEO0pY63oqBIXrU2PtupVfFxrUZ5d6rA5APRPDHhDk9s0EoRRkBASc7B/mIUlAFidzc1SfmdmFNnIWBn1SPZYKnFUCSTW5q2WD0KdlvQIbZytMqdMPm4abjXWGIJQICEk5mCPZXtty0iBifBwPwDOZq+ojn4LW9QjXF2yiU9JAyCNj0S8w4YatUBom5AwISSExBxYPlOmK1psYC+qqM8X5JN7h6xUf6DM8Kt1VysjhS1aTbhKGUxI24SEaSAhJObA+kIYjSI6SqtXpnN5KQAwEkLbmDWk0BMYHfJ7AKTYU0ozi4XS6DZnqNuS0VGVR2hJISeWJCSExGyEJbzniQrGJmtmyoS6lTGENQDqY3JulehoY6ynTI2rguc4oSTqUVnUI6zKqeA5HkCHtzsQDhptDkEAJITE7BwaZf4wAJRnRH0py6EIhqOkGiq/1ipCeETJlHFVA3CUWlsIU+xOeRihxKSWkXajzSEIgISQmB2rx0WZGAoPdAEAx8m7a3EhtEjiqOIRyk2r7YXlnF0AEB7uk3xmH8Y0LRQdJcwGCSExG/FSemumjIq9bSwSBmBfUcI5U3GMR2ikYYkTr51wVQHgbHZ7YRkAMCb2WLICQRlDQfkyhEkgISRmQ+URGmvIAlFnysgHq7K5DAEAenysf+45ZQYzIfp6x/sA2HlbRfZK+aSjJJovI1o+X4aEkDAFJITEjDBg37C1Q6PxTJmYePAcNrqir2Wv6bcJmz2tEmMAKrLL5J4sdhhCMgAAIABJREFUAISYqIesuU24yl3NgQPQMtIeliJGm0MQJITEzLSOMU8QAHKdKE23pBAqGSWKeEAV5jV/vsykuKiMKl/Gkh5hpiMjPz0PQCgS6vR2GW0OQZAQEjOjbBBadPoSJEnsje6iOUpUQmidxNF4l1F3XAiF4ipwHACxv5OJIWMsWxwUHSVMBQkhMSNWTxkVB7pYKAjAlpPHZ2Qr560khNN5hJwzNTqDSYqIfW1G2LVYKF+GMBUkhMSMWF4IY7kkygahzAYXJw8jbBplXlF/uxJFlMLto52QZ7u7KtV3OWL9ZSxaTSjXREJVJUkQBkJCSMyI1dttx0vpVRuEAJw2rM3hADBgv4mdwtaRdlEKAyjOLEwX0tR3CRYvq1c8wiZPC4N5/wTEMoGEkJieAT96fQCQbkdtliWFMDRdpoyMJaKj08ZFZZRGaxbtOJqflpftzAIwHproGx8w2hxiuUNCSEzPuzGFqMvleEvqIMSeqJA4jg2NwipCGM+UmSzkjpW18oHY0wpJ0tUsjaiJBXspX4YwHBJCYnqsvkEYGR6QJrwA+LQMm2vFpHstUUGhdCBbNcUj5NOzbNm5AFgoKB61ZAUCzWMizAMJITE98eZq1hTCkDpThpv8Eupzo6caPCxoypJuibFmT5t8XHNspoyMYPl8Geo4SpgFEkJieqzuEc6UKSOTJaAqiwMQktAwYkansGusxx8OAMhNdblTXVMviJfVd1tSSKiCgjAPJITENHhFtIwxAAKPdS5LCuEsmTIyJt8mbDx2+tJUlJqQkDX7y5RmlqTaUwAM+oc9gRGjzSGWNSSExDTsG2ISA4B1OVyKzWhrFsRMRYQKJp/HNGn60lQEdaM1ZsaXMDs8x1XlVMjHlC9DGAsJITENVq8glCa8kZFBAJzDKeSXTHuNdTzC6YXQ7srn0zIBSL7xyMhR/SzTDsqXIUwCCSExDVbfIFSihUJxJfjpXdotMY3fNxx1f01F03C0S+qqKbUTUTguXk1o0XwZN3UcJUwBCSExDVZPGY1nyswQFwWQn4qiNAAYF9HkNZcSHvUNjgRHAaQLaYUZ+TNdZvl8GRflyxCmgISQmExIwsERBoADNrmtKYTKBuEMmTIypo2OxuOisdF90yJYfB5TZU65wNsBdI/1Tog+o80hli8khMRk3htmIQkAqrO4bIfR1iyIOVNGZcwrhDEPaWopvRpV4qglPUKBt5dnrwTAwFpG2ow2h1i+kBASk7H6BiELBcJHuwGAtwmFFbNcadrEUZVHOKsQ5pdyDieAyMhRuY2O5VCio0coOkoYBwkhMRmrp4yK3S1yOYFQsJITZnNplRf4rsk8QkUVZkoZjcLzQlG06YxVtwkpX4YwASSExGSs7hGGupW46IyZMjKVmVyOAwAGA+ieMIsWjoXGByaOAnDYHCuzSme/WIn9WjQ6SvkyhBkgISSOQWLYPxyVhHprCqGSOTJtczU1HFAX3yZMrlWJ0zgcHdFXlVNun6H2Q8FRYu18mWpXJc9xANpHO8SIiackE0saEkLiGBq9bFwEgOI0rjDVaGsWRDxTZubaCQUT5svMWUqvRvF6Q9YMjaYLaUUZhQBEKdzm7TTaHGKZQkJIHIOqgtBYQxYIi4TD/R0AwHFC8TRDGyZhRiEcTihTRkYoquBsdgDhgS4W9CfXsuRA0VHCcEgIiWOweqZMuK+DiSEAdnchn5Yx5/VmFMLYWKKZ2m2r4QSHPb8UABgTe9uSaFbSUMYO0zwmwihICIljWEKZMnOrCIC1sa7i7WNsOJg8uxIlGAl1ensA8BxflVOeyEOsni+zijxCwmhICIlj2GtxIVRyRhIUQjuPDS4OAAP2DRvvFDZ72iIsAqAsqyTF7kzkIVbPl1E8wiZPq2TBMRrEEoCEkIjTNcGOBgAg24GKTIsK4dxdRiehBIHNUFY/r7ioTHxUvTXzZVwp2bmpLgD+cKB7rMdoc4jlCAkhEUcdF7WkDDIm9kSHNiToEcJk24TzypSREUqqwHEAxN42Fgkny7Jkoqg+ldUThkBCSMRRauksGhcND/VKgQkAfEaOLcud4KPMJYTzqZ2Q4VMz7O4CACwshvstWYEQ7y9D24SEEZAQEnHitRPWTBmNx0VXJhoXBbDJzdk4ADg0wnyGOlQRFmkdaZePq10ViT9QsPo2oYsarRFGQkJIxLF8yqiSKVOSaFwUQJodq7I5ABGG9zxGOoUdo13BSAhAQXp+tjMr8Qdavaxe8QiPDFvSfsLqkBASUTxBdIwzACk2rM62pBAq2SKOubqMTsIk0VHFH1qV8AahTHxCrzUrKIoyCjIdGQBGg95Bn2ma3RHLBhJCIsqeoWjq+kY3J1jz/0KcZxGhgkkSRxsTHDoxhXhotLsZFqxA4MBV51TIx0coOkrojjW/8AitGQnh8RZrx0W7Gw+9ebClY9TPpaTZc4vm9VjlJf+zlx0eNUZIusd63+3fLx8nnjIqY8vO5TNdnV7/W83dHe/vS4J1SUd5yf/seMMbHDPWGGK5YTfaAMIUvO9h9x6KyMeWE8LBwcEvf/7K7oZ9qzP43rHAUJi77/IDmzZtSnwFZc7GoVH28wZ2yzweqhnPNr/Y5InWfszXIzx06NDnH/1XJsIlWSl3fvz8vOq19/z2oYKCgiSYmSyUl/xcy0tnVJzygaLNxtpDLCtICInJWEsIGWOXnLf9UwWRM85ZJ59p9kx84sLzXtn1bm5uoo3Dc51wOTlPkAEYCRrjEY6HJuQDp925Ii0v8Qd6vd5Lz/0/P9lWsTo32lv11Y6hi7Z/9J+7dvO8ZUI+Sn8ZgtAfEsLlzjVvRP49wMZUk+Cufj3Cc/jFSbYT8i2giLt3784VvWdUxNtyVrvSr6jO+d0Dv/2Pr309kRVO/1vYKyIQierfMx2swePg+fDL2+1ZQlJsViNK4Wuevx5Az3iffIZJbOf//qedt99z9m2JrPDYo7/fUZahqCCAU8py/7e744033jj55JOTYbO2NI+03frmXQyMAycPYvzJrv/JdGRUuSpuOPGrRltHLAtICJc7jaNs97EZInLmpNciQ1KPHDmyLmvyv/GG3LS/7NuT4Ar7ho9pt+0VsWeYA1hY0srGWWHs8HCs+I8BHEJS6PBwk8AnKsKH9u/d5p48OnJ9pu3QwYOWEEK/GIi/AwBivwkEG307ETphmcgJQUxLdnb2yJQq+GG/6MqdR3TR0uS4cz3ByW+BJ4wcl8sQewjCctBvruXOL06yeUV87d/SP3slAMVp3F/OsgGotUgp4SmnnPLtr3qv3lCQ4Yj+MzPg0ZaRm2+4LMEVXt5uD0u475B03yEJgIPH388IpaWl6RAXBWC32e/7Pz8B8NUXvxUIBwGcUXnqJWsu4JDo+3/+xy/+2pOPfbRqBR9rEOsPR17o9H7z9NOTZLO2VLsq5HfgO/+6tXe8H8Ca3Nr/PP7qVPtkN5cgkgQJ4XJHFryjgWh01OXEFkv1V8vMzLz5lts/8Y1rv7SxaN2KzJ6xwK8ODR131rknnnhigivUuTkA613RVx2SkOtk6/R6Ezhwq9013uCYrIIAKrLKVrvn0RCgvr7+1Asv/exTf9i5JrcsK/Xg4Pg9+3u+8f1b3e5Eu60aS6o9RX69Oc5sWQhHg6PzegcIYpFQaJRAhKHFGxXCDxZaSQVlPn7xJQ987fP7BkZ/+NqRl8Sc7/7q4R/e8bP5LlKWAXds/N+BEb0/F0prsXQhrTizcL4Pv/kHP7z1wcdfZSt+8NrhPX0j9335k5d/8lNa25h0Nq5YKx/0TwyGIiFjjSGWFeQREjgyygIRAChN5+79oM1ocxZCfnD4+m21AFZ89cfOqg0LWGFHOf+vVewnByQA+z38pRobOAdKc7UzKk79SPmHFrDCli1bNv7sZwN3fAWAPTSspXF6cc2Wz73Z806nt1tiUutoBzmFhG6QR0hYfio9i4TDfR0AwHFCceWC11HK6vd79H4flFL6GtfC7ReKKjibHUD4aDcL+rWxTF+UsnrlDSEIHSAhJOJCWJ9oAbq5CPe1s7AIwJ5byKekL3idendMCEf0F8KoR1gzz54yaji7YM8vBY4ZUGwtqmO/A5qo4yihIySEhFoILekRhrqjX5rzmr40lbU5XIoNADonOE9wrqu1IxgJdXp7APAcX5VTPuf1s6B0G1feE2uxShlMOGxJIScsCgkhgX3D1hbC+NCJxQmhnccGFweAqd4THWgZaYuwCICyrJIUu3PO62fhmDEUFkRptNbkaZEsOEaDsCgkhMud7gnW7weALAGVmdYWQkfJwuOKMvVGDCZUpi8tJi4qo7wDFhVCV0q2O9UFwB8O9Iz3Gm0OsVwgIVzu7I0lGNbncpaUQdV+2CI9QgB1MSHcp6MQapIpIyOU1IDjAIi9bZAii1zNEGri24QUHSV0goRwuWP1DcLwcL/kGwfAp2fZchbbVs2QUfULnr40FT4tw5azAgATQ+JA12ItMwJKHCX0h4RwuWN1IRRjWSGOUg3KzurcHM8BQMNItLYy2UiMtYy0ycfVi/YIAThKrb1NqHiESsSYIJINCeFyx/pCqGTKLNadApAhoDqLAxCW0ODRwynsGuv2hwMA8tJyXSnZi19QlS9jSSGpiXuElrSfsCIkhMuaMREtYwyAg8e6HKsLoTaTXZVqwr26JI42xuOiGriDUP0gCHVZ0iMszSxOtacAGPQPewIjRptDLAtICJc1+4aYxABgnYtzWrK3WvzrXishrIu1qt6ryzZhUywAWOvSxn6rV1DwHFftqpCPaZuQ0AcSwmXNHovHRaUJb2TkKABOcAj5JZqsqbwVOglh7Lte+fZfJHZXPp+WAdWbYzmU6GgjRUcJXSAhXNYoZeN1bksKobINJhRVgtfGpd2sqqDQQQmV7/rFp4xG4Tih2NrVhFRBQegMCeGyxurttkPKBmGpNnFFAEVpyE9hALxifDpVkhjye+RtsHQhrShj3tOXZkKJjoa6LOlRUQUFoTMkhMuXsIT3PQwAB2yyqkeoZcqowiZXVP+SXU2oJEZWuyp57foZWL2/TFVOuY2zAej0dskptQSRVEgIly9KqVxFJudaVIdLw4gXEWqUKSOzMUeSD5LdcVTVXE2blFEZq1dQOGyOsqwSABJjrSPtRptDLH1ICJcvVq8gZGExLDdP4TihqELDlTflxDzCwSR7hCOa9ZRRYy8s4wQHgPBwn+Qf13Bl3aB8GUJPSAiXL1YXQrG3lUXCAOz5pZwzVcOVldDo3iRPek+SR8jZ7PaCMsDCgwlr3JQvQ+gHCeHyJS6E7tkvNClil2ZDJyZRk8kyBADonmADSZv0rgxYsHG2iuyV2i6uxIpFa5bV11J/GUJH5iGEt99++5o1a9atW3f33XdPvff111+/+OKLV69evWnTpptuuikYjA42/X//7/+dGePCCy/UxmpCC6w/hjBWO1GssRDyXHQwIZK5TdjkaZVH7lVkr3TYHNourmQPiT2WFBJFCJs9bRKTjDWGWPLYE7zuiSee+PnPf/63v/0tHA5v3769urr6nHPOUV/w/vvvn3322T/84Q+9Xu//b++845sq1zj+nMymM+neu4xaOhgXLsiQKUqRIYKAIIo4ipelooyr18UVJwoqIOpFxcEQ2QKCRaZSaUtbRjc0nWmTtGnSrPPeP057GtpCT0LWSd/vH3zehPfNeXKac37nfd9nPPHEE3q9/p133gGAvLy8xMTE9PR0AODz+Vb/AhjLKFehBi0AgJ8QIj1ZKYTthemtkW67A2l+xPlaBADZ9WhcmE3ODz3Xife1spDDLaXqWTkj9BZ6Bbj716llWqPuZqM0ytozZgzGFKZCuHnz5mXLliUlJQHA4sWLN2/e3EEIFy1aRLczMjK++uor+mXv3r3Hjh1rDWsxVoPtG4SAED3XsW7sBEWK7fPLWLEMYWf4obFAEICQoaocGQ0El+mV7jwkSGLr1DIAKJKXYiHE2BSmS6N5eXn9+/en2v379y8oKLhD5zNnzvTr149+uWnTpiFDhsydO/fy5csWG4qxLmxPrmaQVSKtBgC43r5cL4nVPz/N9kJo/ZwyJnDc3Hl+wQCAjAZDNSsjEBLa/GWw4yjG1jB9Tqyvr/f29qbaPj4+tbW1t+u5a9euw4cP5+TkUC9nzpz59NNPi0Siffv2DRs2LCcnJyam6+ffpqam2NhYoi2seOLEiVu2bGH6PTAAAKDRaPh8Po/X/Z81q4ZPPQb18dCqVOzbg9EX5VMNTnC0SmXNCAGEkFqtjhECjyM0kHBNiWoVKndrT6iMyFiquAEABBDBggDrfgUKIigKZFUA0FRyReATZPXPvzPNzc3E3aUICBeFUo1rsiJbnB/nR61W6/V6Lped6fCdA5IkEYNUiUyvb4lE0tTURLWbmpr8/Py67HbkyJGMjIzDhw+HhIRQ70yZMoVqDB48+MKFCzt37nzppZe6HOvp6ZmVlSWRtD7di0QiNzc3huZhKLhcLkMhvKw0ACAAGBIm8mThHqGyXko13KJ6eXp6WvGTEUIEQXh6evbyNhQokBFBqc5jsLVrVJUqynVGHQAEeQSESKyWXM0UMqq3Pv88AHBkFdY9RUxACN3lQZNC+lKNEmW5/e13BjgcjlAoxEJ4N5AkqdF07/nNdGk0Li7u6tWrVPvKlStxcV0k8vjtt9/mz5+/d+/eAQMGdPkhYrH4DjYRBCEWiyVtYBW0HQod3FAhABByobcP+1QQTHPKWNtllKa9DIUNHEfb10Vt4ClDwfZEayGeQZ4CDwBQaJUydb2jzcG4MkyFcP78+Zs2bWpqalIoFJs3b543bx71/tKlS4uKigAgMzNzxowZW7du7dOnj1wuVyqVAGA0Go8cOaLT6RBCBw8ePHTo0IQJE2z0TTDMudRWV6GfhOCzM5RUb4N02x2waT2m9upLYut7ylDwTUMJ7VFIw8oQQMSJo6l2IQ6rx9gSpnfBJ598ctCgQeHh4VFRUaNHj54zZw71/r59+2QyGQAcOXJEIpEsW7Zs4MCBAwcOpOIlEEIvv/yyp6enp6fn0qVLN2/ePGTIEBt9Ewxz2O4ySqoUxsYGACCEIp5/qI2OYlMhtMOMkCv253iKAYBsURsaamx0FJsSj8PqMXaB6R4hj8fbunXrZ599RhCE6Zp1SUnrD3TdunXr1q3rPCo7OxshpNPphEJ25nV2RdguhLqbRVSjNUjANvT3b/3k3AZkRMC16nGK5WVUI8EGsRM0grDYlmt/A4BeWkw5kbKLBFyYEGMXzFsX4/F4FuzcEgSBVdCpYLsQ0uuiVk+uZoqfEMI8CABQG6BQac1JYU1znVLbCACeAo9AjwArfnIH2vPLsLMMBZ1qAEdQYGwKOzeIMHeB1ghXFAgAOARryxDSofQ22yCkSGtzjrbu6ig9v0mQxBJgwz+BST0mVvrLRPtE8jk8AKhsqm7Wqx1tDsZlwULY48iXIz0JABDvTXixM+edrsIm9Xg7YyPH0aL2DULbCrlJqXpWCiGfw4vyiQQABKhEUeZoczAuCxbCHgfbc8ogXYuhTgoAwOHyg6NteqxUX5v4y9A+kPFtXpE2gh8YTgiEAGBU1JHNjTY9lo2gtwmvN+DVUYytwELY46DLKaSwdV20lAoG4AdFUOVnbQf9rHDJykujNky3fQscDv2swNJtwrg2ISzG/jIYm4GFsMdB39PT2DkjpMsp2HpdFABivQkfAQBArQYq1dbRQpWuuVpVCwB8Dj/K2+a5pNlehiIB+8tgbA8Wwp4FAshl+dJoexnCMNtusAEAAe3+RNlWym1SJC9BgAAgVhzF49g8exaf5fll4sUxlD9RqeKGgTQ62hyMa4KFsGdR3Iga9QAAgSIIcXe0NRZhUpje5kIINgirL7Rl9aXOtJeqZ+fSqKfAI9gzEAD0pL688aajzcG4JlgIexbZLF8XBZLUV5dRTTssjYINhLC4XQjtYT8/NBY4HADQ19xEep0djmh12vPLYH8ZjG3AQtizYLsQ6msrkE4LAFxJIMfD2w5HbHcctVIEhUlyNXvMCAmBkBcQBgBAGulnCHaB88tgbA0Wwp4FLYRsdRmVtiZXs2lOGVOSfAkBBwCgSNm6qnw36ElDufImABBAxNo4doKmvQwFO6MJ6Rkh9pfB2AgshD2L7IbWBvaUYYiAA33FBAAggMt3PSksU97QkwYACPUK9uDbaZOWH8ryRGttM8LCNj8jDMa6YCHsQchaQNqMAMCDBwnsLENoklPGTkIIVo0mpHe5EuyyQUjBD4+nGiyNoAjyCPARegOAStdc21znaHMwLggWwh7E32338WRfwrq1FOyG3o5BhDQpbUKYc9dCaGeXUQpBuInjKAsLE4LJ6cL5ZTC2AAthD4LtRSeMChmVJ4wj8uT5BtntuGlWnBHSOWXsOCPkeIq53r5AZaeTVdrtuFYkHvvLYGwJFsIeRA7LhdBkOhhjuzKEnUn1az1YXlu+cstAgNrrTtg6udqt3FKtnoXQzw3FCiyEGOuDhbAHwfZ027p2T5l4ex5XLIAoLwIAtEa4qrB8UlilqqFqCYmFPv4iX6vZxwDWJ1rDS6MYW4KFsKegMcB1JQIALgFJElYKoUM2CCmsEk1YSHvK2Hc6CAACljuORvqEC7gCAKhprm3UNTnaHIyrgYWwp5DbgIwIAKC3D+HOc7Q1FmFSmN5+LqMUVskvQy/r2dNThoIfzu4KvVyCGyOOpNrF8jKH2oJxQbAQ9hToqUyaPyung2SL2lBfDQAEl8cLjrTz0VOtUaq+0BGxExQ8/1BCKAIAY2ODsVFu56NbhQQcVo+xGVgIewrszylTTLn+80KiCK69p7SmjqMWK6FDYidaIQiTsHpWTgqx4yjGdmAh7CmwPXaC3tyy/7ooAER6Ev5uAAByLdxUWSKFjdqmOrUMAIRcQYR3mHXNY4KA7fWYcOptjM3AQtgjIBHkydk+I7R3crUO0IUJLYsmpBf04iTRHMIB1137NmElK4UkXhLDIQgAKFPe1BlZWUYD47RgIewRXFcilR4AINyDCBQ52hqL0LWl27a/yyiFib+MJcPbi05IHCPk9HnTsTOUUMRzC/MKBQAjMpYpcWFCjDXBQtgjMIkgdKwhFoKMBkP1DQAAgnACIbRkRljU0LqzFSeJtpZJZsEPiaH2Vg11UqTVOMSGu8Q0+7ZjLcG4GFgIewQ5DezeIDRU30AGPQDwfIM5bh4OseEuQwmLHD0jJHh8XmA4AABC+qoyh9hwl7RvE2J/GYxVwULYI7gkaxNCtm4QtoXShztGRQCgr5hw4wIAlDchuda8sVqj7kajFAA4BCdWHGUD6xjhMvllCrG/DMaqYCHsEbB9RtieXC3UMeuiAMDjwD2S1sKEOWZOCksUZUZkBIAI7zA3ntAm9jGA/YUJ2zOOkuwso4FxTrAQuj6ValSjAQDw5kOsNyuFsD2nTLjDhBBMognN3SYscmAEoQkClqfe9hNJJG5iAFDrNVWqakebg3EdsBC6PrSXY4qfHUs2WBGEaI9/O6fb7kDKXQuh/XPKmEL7GemrSoE0OtASi8H5ZTC2AAuh60PftdPYuS5qkNeSahUAcDy8uWJ/B1pi8YyQ3tNy7IyQ4+HNlQQCANLr9LVSB1piMXS+cuwvg7EiWAhdn/bkauwUQnodz1Gh9DQpvgSHAAAoUKAWxhMqEqESRRnVdqwQwi35ZYoca4llxLUnWsMzQozVwELo+rSn22apELatiwoc5zJK4cmHOG8CAPQkFMiZTgormio1hhYA8Bf5UltcDqS9Qi87/WVMlkbxjBBjNbAQujgqPRQ3IgDgcyBRzE4hrHBwThlTLIgmbI8gtHsZws7QQsjS/DLhXqEinhsAyNT18haFo83BuAhYCF2c7HpEIgCARDEh5DraGovQOTrLqCkW5JcxcRl1BiFkd+ptDkHEiqOpNt4mxFgLLIQuTjbLIwhJtcqoqAMAgi/gU4lRHIoFQkj7Nzp8gxAAeL5BHHdPACCbG40KmaPNsQRcjwljdbAQujjsr75URJUh5IdEA8fxU1o6WWsO48KEThI70QpB8ENbhYSlk0J6hRlHUGCsBRZCF4ftQkhvZfHDHRlBSBPqTgSJAAAa9VDS2L0U1mvkDRo5ALjzRSGewbY2jwl0LCZLtwnxjBBjdbAQujIGEvLlCAAI9pYhrHR8crUOmLU6SnvKxIlby+k5nPZtQnYWJowVR3MJLgDcbJS2GMzM+orBdAUWQlfmSlu4W5QXIXFYhsu7gg4idHjsBE27EDJwHKW9/BN8Hb9BSNGeaI2dS6NCriDCOxQASESWKModbQ7GFcBC6MqwPYIQGfSG2goAAILgh0Q72Jo22iMozJkROoPLKAUvOJLg8QHAUF9NtjQ72hxLoEtZ4bB6jFXAQujKtOeUYem6aFUpMhoAgBcQRghFjjanFXpGeIlBqXonSbdtCsHl8YIjAQAQYmlYPV3cGG8TYqwCFkJXJpvlhenp27TACSIIaXr5EJ58AABpM6q9Y6X3FkOLtKkSALgEN8Yn0i7WMULgOvllWGk/xtnAQujK5LJ8adQky6izrCsCAIeAJEnr+bxzYcIieRlVNi/KJ1zAFdjDOGbwWb5N2Mu31f4SRRmJSMcag3EBsBC6LOUqJGsBAJAIIcKTlULoVDllTGHoOFoob5WZBF/nsp9+sGBpqXpvoVeAuz8AtBi0NxtZWUYD41RgIXRZTKsvsVIGETJUte4AsVQI2zcI27KCOQn8sDggCAAwVJVTu7CsIwFHE2KsBxZCl4Wux8vSUHqDrJJsUQMA10vC9ZY42pxbYOg42p5TxslmhBw3d55vMAAgo8FQfcPR5lgC7YWLhRBz92AhdFnYnlOG9uNwkpwypiT7EjwOAMA1JVLfZkJFIrJM2aoxcU42IwQAfji7twlpL1zsL4O5e7AQuizt6bbZGTtBb185lacMhYgHvbwJADAiyLtNYcJy5U0q70mgWQbnAAAgAElEQVSQR6C30Muu9jGAztSjY6njKJ1xtIGV9mOcCiyErolCB+VNCACEXOjD0jKETiyEcEs0YddC2J5TxmkiCE0RhLO7HlOIZ5AH3x0AFFqlTNPgaHMw7AYLoWuS3VYbIUlC8Nn5RzZJruZ0S6NgIoQ5txFCJ8wpYwqdelsvLQGmhTScCAKIuHZ/GTwpxNwV7LxHYrrjUj27IwhJlcLY2AAAhMCN5x/qaHO6oNsZoRPmlDGFK/bneHgDAKlRGRpqHG2OJbSH1ePVUczdgYXQNaGnKSnsFEKdaSi9U0Z/9PdvtSq3ARm7kkITl1FnnBHCLWH1rBQSXI8JYy2wELom2SyfEdIbVwKn3CAEAD8hhHkQAKA2QKGyoxLWqmVKbSMAeAo8gjwCHGAfA+iCHiytx0Q/YWAhxNwlWAhdEB0JVxStZQj7sdNl1MRTxrki8ExJ9W1tdI4mpHetEiSxBDjpn6C9MGFFkWMtsYxon0g+hwcA0qaqZr3a0eZgWAwWQhckrwHpSACAeB/Cm+9oayzCaZOrmZLWtjrauTAhvWuV4JSeMhT0uWVpBAWfw4vyiQAABKhEUeZoczAsBguhC8L2CEKk0xrqpAAAHA4/OMrR5tyWlNvnl6EX6+Kc0lOGgh8YQQiEAGCU15LNjY42xxLaw+ob8OooxnKwELogrM8pU1kKJAkmd2rnJO32jqN0uhOn9ZQBuOU5g6XbhCaJ1lhpP8ZJwELogrBdCHXS1i0rOg2YcxLrTfgIAABqNVBlskXVrFdXq2oBgM/hRXqHO8g6RtDp62g3XXaBU29jrAIWQlcDmZQhZHs9XjoNmHNCACT7djEpLJSXIEAAECOOorw5nBb6DLN3Rkj5IpUoyg2k0dHmYNgKFkJXo7QJlDoAgEARhLqzckbYXpjeKXPKmNJlPaaiBqcOpTelPYKCnTNCOjpFT+pvNFY42hwMW8FC6GqwPYIQSFLfXobQqWeEcDshdO7kaqbwQ2OofAX6mptIr3O0OZZAl7jC24QYi8FC6GrkyFsbLN0g1NdWIJ0WALjiACoHmDPTXpiwwXRp1KnTbZtCCNx4AWEAAKRRX13mYGssIl4STTUK8TYhxlKwELoaOW2J+FkaO8GKUHqaJF9CwAEAKFKiRj0AgJ40lCtvwK1ZoZ0ZAcsTrSVI8IwQc7dgIXQ1shta9Y+tM0I6uZpzu4xSCDitVa4QwOUGBADlyht60gAAoV7BVJ0gJ8ckvwwrtwlNQglbfZQwGHPBQuhSNOgIaTMCAHceJPiwVAjpnDLOvsFGkXbrNiErcsqYwvb8MkEeAT5CbwBo0qlqm+scbQ6GlWAhdCku1bc2kn0JLit10DS5GjuEJOVWISxS0Dlloh1lklkIItoKE1aysjAhmJxqvE2IsQwshC5Frpzd66JGZT2pUgAAx82d5xvsaHMY0WFGSMdO0HtXTg7HU8z1lgAA0moMskpHm2MJOL8M5i7BQuhSsF0I2z1lwuOcswxhZ1L9Wg29LEc6EhW3ZX92fpdRmluq1bMQnF8Gc5dgIXQp2oWQnS6jJvV42TGdAgCxAKK8CADQGuFMZXWTTgUA3kIvf3fW5PWhV6F1Upb6y+BS9Zi7Aguh66AxQGETAACXYG8ZQhZUX+oM/dhxui0VQC9fNtlvEkHBSiGM8gkXcAUAUNNcRz2IYDBmgYXQdbgsRwYSAKC3D+Hu1Bkub4u+Ld220xam7xJ6IbpAxjKXUQo+yxOtcQlujDgSABCgYrw6ijEfLISuwyWWF50gW9SG+moAILg8nhOXIewMndy8qok1WUZN4fmHEkIRABgbG4xN8m77OyH0k8d17C+DMR8shK5DTpsQprBTCGn3fV5wFMFl05SWfvLQ6ViTZfQWCIIf2qrcLPWXiRO32o9nhBgLME8I9Xr9nTuQJGk0dlEMpduBmLuH7em26XU5dq2LAkCUJ+HvBnxo4hP1ACDkCiK8Qx1tlHnQ55yl24R0AWTsOIqxAKbP3dXV1bNnz7548aJQKHzvvffmz5/foQNCaMWKFV988QUAPPLII59//jmPxwOA/Pz82bNnl5aWSiSSbdu2jR071rpfgOKFH7+8UH4KEEqLGPbx7EXmDi+XVs7b9aa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      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = (I - w * A) * T\n",
    "plot(x, P[:, 3:5], marker=:auto, xlims=(-1,-.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "59f3d561",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": ""
    }
   },
   "outputs": [
    {
     "data": {
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   "source": [
    "Sc = P * ((P' * A * P) \\ P') * A\n",
    "w = .67; k = 1\n",
    "E = (I - w*A)^k * (I - Sc) * (I - w*A)^k\n",
    "scatter(eigvals(E), ylims=(-1, 1))"
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    "* Eigenvalues are closer to zero; stronger smoothing (larger `k`) helps.\n",
    "* Smoother can be made stronger using Chebyshev (like varying the damping between iterations in Jacobi)"
   ]
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   },
   "source": [
    "# Multigrid in PETSc"
   ]
  },
  {
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    "## Geometric multigrid\n",
    "\n",
    "* `-pc_type mg`\n",
    "  * needs a grid hierarchy (automatic with `DM`)\n",
    "  * `PCMGSetLevels()`\n",
    "  * `PCMGSetInterpolation()`\n",
    "  * `PCMGSetRestriction()`\n",
    "* `-pc_mg_cycle_type [v,w]`\n",
    "* `-mg_levels_ksp_type chebyshev`\n",
    "* `-mg_levels_pc_type jacobi`\n",
    "* `-mg_coarse_pc_type svd`\n",
    "  * `-mg_coarse_pc_svd_monitor` (report singular values/diagnose singular coarse grids)"
   ]
  },
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    "## Algebraic multigrid\n",
    "\n",
    "* `-pc_type gamg`\n",
    "  * native PETSc implementation of smoothed aggregation (and experimental stuff), all `-pc_type mg` options apply.\n",
    "  * [`MatSetNearNullSpace()`](https://petsc.org/release/docs/manualpages/Mat/MatSetNearNullSpace/)\n",
    "  * [`MatNullSpaceCreateRigidBody()`](https://petsc.org/release/docs/manualpages/Mat/MatNullSpaceCreateRigidBody/)\n",
    "  * [`DMPlexCreateRigidBody()`](https://petsc.org/release/docs/manualpages/DMPlex/DMPlexCreateRigidBody/)\n",
    "  * `-pc_gamg_threshold .01` drops weak edges in strength graph\n",
    "* `-pc_type ml`\n",
    "  * similar to `gamg` with different defaults\n",
    "* `-pc_type hypre`\n",
    "  * Classical AMG (based on C-F splitting)\n",
    "  * Manages its own grid hierarchy"
   ]
  }
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