diff --git a/notebooks/pdes.ipynb b/notebooks/pdes.ipynb
index bb634bc..7bbf074 100644
--- a/notebooks/pdes.ipynb
+++ b/notebooks/pdes.ipynb
@@ -248,7 +248,7 @@
},
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": 4,
"id": "b3b69c74",
"metadata": {},
"outputs": [
@@ -266,7 +266,7 @@
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0"
]
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- "execution_count": 7,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -278,7 +278,7 @@
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{
"cell_type": "code",
- "execution_count": 8,
+ "execution_count": 5,
"id": "c7af2b38",
"metadata": {},
"outputs": [
@@ -288,7 +288,7 @@
"fill_boundary! (generic function with 1 method)"
]
},
- "execution_count": 8,
+ "execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@@ -321,7 +321,7 @@
},
{
"cell_type": "code",
- "execution_count": 9,
+ "execution_count": 6,
"id": "76888875",
"metadata": {},
"outputs": [
@@ -339,7 +339,7 @@
" 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0"
]
},
- "execution_count": 9,
+ "execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@@ -360,7 +360,7 @@
},
{
"cell_type": "code",
- "execution_count": 10,
+ "execution_count": 7,
"id": "e29f8eaf",
"metadata": {},
"outputs": [],
@@ -370,7 +370,7 @@
},
{
"cell_type": "code",
- "execution_count": 11,
+ "execution_count": 8,
"id": "b75d45cf",
"metadata": {},
"outputs": [
@@ -380,7 +380,7 @@
"visualize (generic function with 1 method)"
]
},
- "execution_count": 11,
+ "execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@@ -402,7 +402,7 @@
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": 9,
"id": "b5a0362c",
"metadata": {},
"outputs": [
@@ -413,45 +413,45 @@
"\n",
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"metadata": {},
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@@ -989,7 +989,7 @@
},
{
"cell_type": "code",
- "execution_count": 13,
+ "execution_count": 10,
"id": "ec0622d6",
"metadata": {},
"outputs": [
@@ -999,7 +999,7 @@
"generate_system_sparse (generic function with 1 method)"
]
},
- "execution_count": 13,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -1045,7 +1045,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 11,
"id": "a5cc7201",
"metadata": {},
"outputs": [
@@ -1064,7 +1064,7 @@
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]
},
- "execution_count": 14,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@@ -1145,7 +1145,7 @@
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{
"cell_type": "code",
- "execution_count": 4,
+ "execution_count": 12,
"id": "0244f525",
"metadata": {},
"outputs": [
@@ -1182,7 +1182,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 13,
"id": "2f70617a",
"metadata": {},
"outputs": [
@@ -1192,7 +1192,7 @@
"jacobi! (generic function with 2 methods)"
]
},
- "execution_count": 15,
+ "execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@@ -1231,7 +1231,7 @@
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{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 14,
"id": "7a8ff556",
"metadata": {},
"outputs": [
@@ -1249,45 +1249,45 @@
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@@ -1801,7 +1801,7 @@
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- "execution_count": 23,
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"id": "67e79b9c",
"metadata": {},
"outputs": [],
@@ -1811,7 +1811,7 @@
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{
"cell_type": "code",
- "execution_count": 24,
+ "execution_count": 16,
"id": "86c8fbb7",
"metadata": {},
"outputs": [
@@ -1822,116 +1822,116 @@
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@@ -1987,7 +1987,7 @@
"source": [
"## Conjugate gradient method\n",
"\n",
- "In this section, we will discuss the implementation of the best known solver, the [Conjugate Gradient Method](https://en.wikipedia.org/wiki/Conjugate_gradient_method).\n",
+ "In this section, we will discuss the [Conjugate Gradient Method](https://en.wikipedia.org/wiki/Conjugate_gradient_method). Combined with the multi grid method, it achieves the best scalability for solving Laplace equations.\n",
"\n",
"\n",
"The idea of the conjugate gradient method is to transform the problem into an optimization problem of the form\n",
@@ -2027,12 +2027,12 @@
"source": [
"### Convergence analysis\n",
"\n",
- "For a first convergence analysis, we will use the implementation of the conjugate gradient method from the `IterativeSolvers` package."
+ "For the following convergence analysis, we will use the implementation of the conjugate gradient method from the `IterativeSolvers` package."
]
},
{
"cell_type": "code",
- "execution_count": 25,
+ "execution_count": 17,
"id": "9f8dbf39",
"metadata": {},
"outputs": [
@@ -2052,45 +2052,45 @@
"\n",
"\n"
],
"text/html": [
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+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using IterativeSolvers: cg!\n",
+ "N = 80\n",
+ "u = zeros(N,N)\n",
+ "fill_boundary!(u)\n",
+ "A,b = generate_system_sparse(u)\n",
+ "x = zeros(length(b))\n",
+ "_,ch = cg!(x, A, b, reltol=1e-5,log=true)\n",
+ "display(ch)\n",
+ "u[2:end-1,2:end-1] = x\n",
+ "visualize(u)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "id": "30c6e04e",
+ "metadata": {},
+ "outputs": [
+ {
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",
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ],
+ "text/html": [
+ "\n",
+ "\n"
+ ]
+ },
+ "execution_count": 19,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Ns = [20,40,80,160]\n",
+ "reltol = 1.0e-5\n",
+ "iters = zeros(size(Ns))\n",
+ "for (i,N) in enumerate(Ns)\n",
+ " u = zeros(N,N)\n",
+ " fill_boundary!(u)\n",
+ " A,b = generate_system_sparse(u)\n",
+ " x = zeros(length(b))\n",
+ " _,ch = cg!(x, A, b, reltol=reltol,log=true)\n",
+ " iters[i] = ch.iters\n",
+ "end\n",
+ "plot!(plt,Ns.^2,iters,xaxis=:log10,yaxis=:log10,label=\"reltol=$reltol (CG)\",marker=:auto)\n",
+ "plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5396554c",
+ "metadata": {},
+ "source": [
+ "The number of iterations needed to converge is much lower with the conjugate gradient method than with the Jacobi method. However, the number of iterations still increase with the problem size, so there is still room for improvement. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "92bfd7d7",
+ "metadata": {},
+ "source": [
+ "### Number of iterations\n",
+ "\n",
+ "We can prove that the number of iterations to achieve a relative error of $10^{-s}$ increases as $O(s \\sqrt{\\kappa(A)})$. As a reminder, the condition number of A $\\kappa(A)$ is ratio between the largest and smallest eigenvalues of A: \n",
+ "$$\\kappa(A)=\\dfrac{\\lambda_{max}(A)}{\\lambda_{min}(A)}$$\n",
+ "\n",
+ "It can be shown that in our example $\\kappa(A) = O(N^2)$. Thus, the number of iterations scales as $O(s N)$ for the conjugate gradient method. Remember that the number of iterations scales as $O(sN^2)$ for the Jacobi method.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1bb8ffe6",
+ "metadata": {},
+ "source": [
+ "### Goal\n",
+ "\n",
+ "The conjugate gradient method provides some improvement to the Jacobi method, since the number of iterations increases more slowly with the problem size. However, the ultimate goal is to find an iterative method whose number of iterations is _independent_ of the problem size."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "956564d5",
+ "metadata": {},
+ "source": [
+ "### Preconditioner\n",
+ "\n",
+ "To achieve this goal, we will apply a [preconditioner](https://en.wikipedia.org/wiki/Preconditioner) to transform the original problem into a format that is easier to solve. \n",
+ "\n",
+ "A preconditioner is simply a linear function $M$ such that \n",
+ "$$M(b) \\approx x, \\text{ with } Ax=b \\text{ for any } b.$$ \n",
+ "\n",
+ "When we have found such a function $M(b)$, we can solve the _preconditioned problem_ $(MA)x = Mb$, which is equivalent to $Ax=b$.\n",
+ "\n",
+ "The way that this preconditioning affects the number of iterations is that it reduces the condition number of $A$: \n",
+ "\n",
+ "$$ \\begin{align}\n",
+ "&M(b) \\approx x, \\text{ with } Ax=b \\text{ for any } b \\\\\n",
+ "&\\rightarrow M(b) \\approx A^{-1}b \\\\\n",
+ "&\\rightarrow M \\approx A^{-1} \\\\\n",
+ "&\\rightarrow M A \\approx I \\text{ (Identity matrix)} \\\\\n",
+ "&\\rightarrow \\kappa (MA) \\approx 1 \\\\\n",
+ "\\end{align}$$\n",
+ "\n",
+ "We mentioned that the number of iterations to achieve a relative error of $10^{-s}$ is $O(s\\sqrt{\\kappa (A)})$. With $\\kappa (MA) \\approx 1$, the number of iterations will scale as $O(s)$. Thus, the number of iterations will be independent of the problem size for the preconditioned problem. \n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "89563cc4",
+ "metadata": {},
+ "source": [
+ "### How to build a preconditioner ?\n",
+ "\n",
+ "Many ways of building a preconditioner can be found in the literature. The solutions range between two extremes: \n",
+ "\n",
+ "1. $M=A^{-1}$. This is the exact preconditioner. The CG method will converge in just one iteration. However, it is exactly as costly to compute the matrix $M$ as it is to find the solution to the original problem. \n",
+ "2. $M=I$. This is the other extreme where we do no extra work to find the matrix $M$. The preconditioned problem is identical to the original problem.\n",
+ "\n",
+ "The solution is to find a good trade-off such that we get a matrix $M$ that is accurate enough to approximate the original problem but also cheap enough to be computed quickly. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4338ee30",
+ "metadata": {},
+ "source": [
+ "### Jacobi Preconditioner\n",
+ "\n",
+ "Next we use the Jacobi method to construct a preconditioner for the CG method. The matrix $M$ is simply computed as the grid values after a certain number of iterations with the Jacobi method. In order for $M$ to be linear, we set a fixed maximum number of iterations in the `jacobi!` function and disable the relative error stopping criterion."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "id": "cd608f2f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "struct JacobiPrec{T}\n",
+ " u::Matrix{T}\n",
+ " f::Matrix{T}\n",
+ " niters::Int\n",
+ "end\n",
+ "function jacobi_prec(N;niters)\n",
+ " u = zeros(N,N)\n",
+ " f = zeros(N,N)\n",
+ " JacobiPrec(u,f,niters)\n",
+ "end\n",
+ "function LinearAlgebra.ldiv!(x,M::JacobiPrec,b)\n",
+ " M.u[2:end-1,2:end-1] .= 0 \n",
+ " M.f[2:end-1,2:end-1] = b\n",
+ " u,_ = jacobi!(M.u,M.f,reltol=0,maxiters=M.niters)\n",
+ " x[:] = @view u[2:end-1,2:end-1]\n",
+ " x\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "46b3883d",
+ "metadata": {},
+ "source": [
+ "Run the following cell for different values of `niters`. The larger the value of `niters`, the more matrix $M$ resembles the exact solution. The fewer iterations we use, the less accurate the approximation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "id": "858ac6ba",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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48IUXXpg0adIDDzwQERFRVFT0yy+/bNq0qV69epZLKj9s+uqrryYkJMie/ZiYmDIBzzw0atRo8uTJWVlZ/fv3z8zMXLp0aWJi4qBBg+QQB8aYt7d3dHT09u3bhw8fPnfu3Nq1ax88ePDtt9+OjIz8559/4FBdunQ5d+7cY489Nnz4cF9f35CQkEceeaT8EQcOHDhixIiffvpp4MCBCxcuvO+++/7444958+ZJkvTGG29QyplqjOseySV4UY3HLi4ufvnll2vVqgU/TYPB0L9/fzl8V/pf/MTmzZvhaLKrJzo6usxRZJ+y5cl3Szz2vHnzoBw9ZMiQO3fulJne0qVLy3ifBUHo1q3btWvXZBs5fgLG8Vn49NNPoWJct27dX375pWvXrowxSyCIJElnz5594IEHLDOR47ElSbpz544cciij1+uXLl2KxWOrXt6DBw+Wf4jovvvu27JlC/qRSJIkSb/++it8Mic4OPjw4cO247GPHTtWXsxv0aLFiRMn4PV88cUXoR4O47F37txZfiaq8RMzZsyYP38+/OwGDBgAI2kkSbpx40a7du0sBl5eXmvXri0fP5Genj5kyBBLyL2NeOzCwsKnn34aHrR27drvvvsuPKglHrvMWcgBhunp6bYvO1H1CBI9XVAduHz5MmMsMjKyzBNEOTk5x44du3btmo+PT1hYWKdOneAjPbdv387NzQ0ODob/dEpLS9PS0nx8fGT3tIVr164ZjcYmTZrIh9i+ffuoUaNmz569cuXKq1evHjlypLi4uH379vCfNaSwsPDo0aPJyckeHh6hoaHt27eH2Sny8/Nv3boVFBSkKtVmZGT8/vvvmZmZ4eHh/fr18/HxuX79eklJiewYgZZGozEjI8NoNPr7+1v+4UqSdOTIkfPnz9euXbtv377h4eE5OTk5OTnwxFNTU00mU9OmTVUvryiKf//997lz54qKikJDQyMiItq1a6d6muXPeu/evTdv3pQTGfn4+KSkpEiSZMnmVFxcfO3aNX9/f8uKIklSfHz8P//8k5mZWadOnWbNmnXq1Ek1r1FWVpbs6pE/FHkzJCSk/C3LP//8YzAYLAe9e/duRkaGfIlSUlIOHTpUXFzcrl27rl27lj8pk8l04MCBpKQkf3//QYMG1atX79atW/n5+WFhYfAJacaY2Wy+efOm/OS07By7du1acXFxs2bNysz/6tWrx44dy8/PDw0N7dOnT5kPPS8vLysrq/yX4caNG8XFxeU/dMLl0DpBqAPXCVfPhSAIV0I6NkEQBGELWicIgiAIW9DzToQ6bdu2ffPNN2WhkiCIexnSJwiCIAhbkN+JIAiCsAWtEwRBEIQtaJ0gCIIgbEHrBEEQBGELWicIgiAIW9A6QRAEQdiC1gmCIAjCFrROEARBELagdYIgCIKwBa0TBEEQhC1onSAIgiBsQesEQRAEYQtaJwiCIAhb0DpBEARB2ILWCYIgCMIWtE4QBEEQtqB1giAIgrAFrRMEQRCELWidIAiCIGxB6wRBEARhC1onCIIgCFvQOkEQBEHYgtYJgiAIwha0ThAEQRC2oHWCIAiCsAWtEwRBEIQtaJ0gCIIgbEHrBEEQRM1BkqTnnnvu6aeftvSkp6ePHTu2TZs2o0aNunr1agXGpHWCIAii5vDll18ePHjwyJEjlp6nnnrK19c3Li6uRYsW0dHRkiRpHVOowD4EQRCEG5Kenj5w4MDY2NjXXnstOTmZMZaYmNipU6dbt275+vqazeaQkJDt27f36tVL07BOv5+4c+fOokWLRo4c2aVLl9u3b6vapKenR0dH169fv1u3br///rulf+PGja1atQoNDZ02bVpJSYmzp0oQBFGtmTZt2pIlS+rUqWPpiY+Pb9Wqla+vL2NMr9d36tQpPj5e67BOXyfu3r2bm5s7bNiwU6dOGY1GVZvJkyc3aNDgypUrzz//fHR0dFFREWMsPj7+hRde+OKLL86ePXv27Nk333zT2VMlCIKovmzcuNFgMDz22GOw89atW3DZCAwMvHnzptaRDQ6YnU1CQ0Pfe++9nJycadOmqRpcv359z549aWlp/v7+EydOXLVq1Q8//PDkk0+uW7du9OjRPXv2ZIzFxsZOnjx54cKF5Xdfu3btnTt3Zs+e7dzTAJz64bgoipIk6fX6KjuoazGZTAaD078qboLJZNLr9YIgOO8Qe9PPO29wrbjhhzsotLWTRpZPtvOj3Z00fsUoEg+K7A6n8apl5+bPnw97Xn755Xfffff27duxsbG//PJLTk5OQUGBKIo5OTkBAQEBAQGFhYUW4/z8/MDAQK0zdP334+LFiyEhIcHBwfJmhw4dLly4wBhLTEwcNmyYpTMtLS0/P9/Pz6/M7llZWXfu8F5ih3Di68NVeTii5jH/5FZXT8Gt8e8yxqnju9s6USjuNkmpnMbZ2cGrVq2aOXNmmf6bN2/q9fqRI0cyxu7evZuVldWlS5ejR482adLkypUrll8Dly5dmjp1qtYZun6dyM7Ohv/9AwICbt26Jff7+/tbOhljWVlZ5deJs2fPbtmyxeKVev755996662qmDdBENWT/Pz8qjycwWDw9va2YSCITKj080RRUVFXrlyR2zt37nz++eflzQYNGgQFBa1fvz4mJubHH3+8c+fOkCFDtA7u+nUiKCiooKDAsnnnzp3GjRszxgIDAy0fZ15eHmOsbt265Xdv165d48aNly9fXiWTJQii2lP+56ZrESRJEB353KmHh4f825oxJgjChg0bnnzyyYULF4qi+NVXX9WqVUvrgK5fJyIjI9PT03NycmSv2fnz5wcMGMAYa968eUJCgmyTkJAQHBxsub0gCIKoMQiSVPn7CcjAgQPPnDlj2ezRo8fVq1dzc3MDAgJ0uoo8u1QV64Q8RcZYSkpKYWFh06ZNGWOff/65j4/P2LFjGzdu3KtXr+XLly9fvnznzp3//POPrNdPnDhxyJAhL774YkRExIoVKyZOnFgFU60IkmqTMWZfCNX61UDtOQZy2LE4zgsdR+MkKvOnw3OtsM8L9ivaYEOUrPZm0G8Srf1FJuuTDllFnpZ2cOAISzvHeMk6jgkobaL1QXBJMoNJwDY6U1ZxkM9XIezDNvi/I1jbggCe8hA8rE299cesh976HE49QytL+1y2r7Xfu9TS9jGI1n111nM0CNa2TtFmqv33IIIgVEC+tlAV68TQoUONRmPTpk2ffPJJxpjsNbt06ZLl7m/t2rXjx4/39/cPCwvbunWr3N+lS5dFixb17du3qKho+PDhCxYsqIKpEgRBVDGC6GC/k8OpinVCfn6pDG+//bal3aRJk8OHVR4imjFjxowZM5w4M4IgCJcjMSbat3IhrtcnCIIg7mUcrk84HFonKguPjxu1R33lGsdHduYbE/Sj31X754WOz3GO6L6YjaTuQ+c5X+wcJXCO0AcA7c0KTcLahppEidnqoy80Wn30t4ut+kQdqZ7V3mB9RrNYsP49ms3W2ChJoVWYwOSsWoUEf5FW5p8O0CEEhfYArznUHvTAxDp/QWc9X73O+lSoh876rJGvroGlHSoFW9oFpdZz9NJbz0ti6v2eYJoeCplWXatwO0Tm5n4nyhdLEARB2ILuJwiCIFyJw+MnHA6tEwRBEC5FlBitEzUdDk0C8dGj2gOXPTa+fd897qPHxucYk2Nu+LHUz51vbth8BNU3oA18xgSeI/ybFTk0CSPUJ0DMRKHR+vd1F+gWBvB3V0uwxgqYdTB5PpgP0ABECSRdVmgVonobvXLg+iCxEUp9AuoQsG2NjdAJVk1Cp/OytD101nP0FqwxE1CnqQ3iv+B1hnqPB2jrFbER1vMFYRVlNAn3/UdMOjZBEARhE7e/nyAdmyAIgrAF3U8QBEG4EtKx7114/OY8OgSmPeA26vaYj55nHM3aiYPmoxhSQs5dYYP1279uokKfUM/dZBahPmG9Fy8F7RKTtX0XtEugfADmoGdWn75BsPr0RQFoD/C2X7RqAxIDWoXAk/cJA+ZlQvI1gf8VME4CahJ6qEkIPpY21GB8WQBoW3M9eSL5l+D/T5Oorg8ZBKjlWHdwb5+/FUFyQF5xp0LrBEEQhEtxe32C1gmCIAiXIjHBvfM7kY5NEARB2ILuJxwJXg1A3b+vfH7fvj3Ps/+V8tdXYj4QzfNB9mWojf25oddHYYPETIhQn1D3iaP6hFm9XQpiGkQwOx34raZj1lgEPfD7SwxoD+CnnfK8QB4kQVv8hKCIpQCxESCPkw7TJASrxgD1FU+htqXtzaw5nXwka64nL6B/GEDgA/wGKM8R+byYetutXTkQSXJzLYXWCYIgCFdC9ScIgiAIm0ikYxMEQRA49FxszYcrboBDkxB5NAmNcQA8Pn2RY85cMR9O0Dy44h6wcThs8JgJ0IaaBKJVlEJNAvQXg4OVMqhPAL0BIDD1+tJQt4BXQlR48q1jClzV0dTzOAlIPQlMO4H6hIdg1R5qMWv8hJfkBfo9gL11DnqkxjWE53vFFPqWW//zrUbQOkEQBOFSKH6CIAiCsIHg9vETtE4QBEG4FHou9p4CzYkEbXie/Uf88lhdBMyGp+YzrlVgc7Nvg2kMmuNFKjVP7PqojwM1CRHRJKBWYZSsPn0jODGoT8CYCSOo7WwWYF1rGDeAaAYMi2mwHleZ+wvz5KvHTAg8MRMM0yRAzASz6hOeCk3Cuq8n0CQMiCahiKBB61qr18yQqqEm4f7PxVI8NkEQBGELup8gCIJwKaRjEwRBEHZw62WC1gmnwVMTAtMb0BgLNL8NpkNUfEyt+gR2XMfFf9ifJ3ruWmMmEN3ChOgWpeAESoAmUQI0CYU+Adow1xOXVgG0BKX0AO215XRS6B+KPE4gZkJRJwPoE7CGhKINNAkwvgc4LoyZgG1BoVUg58KTZwzpdzvcXp+gdYIgCMKliMzN/U6kYxMEQRC2oPsJgiAIVyIwd/eR0TrhSLjyGnHVYLC2UU0C0R647DXnPoJzwzQPx+gHXPYcx8V0COzclTmdmGq/CexrBJ9YqSKPkwm0rfWrjYK1DfUJRW0JLl0B+gDUYyPwcdTrYOvQmAmrPmEAWoUBahWwLYHcTWBMg0KTYKAN4yeYapsrfKK6Q887EQRBELagdYIgCIKwgfv7nUjHJgiCIGxB9xOOBavtrC3XEFcOIlSr0KhPaOyXOI7FoxnwxJFw1bLG7KHewNT7sWsL4ydM4BMzgQMYGczdZD0C1CeMQikYx9pWxk/AXE8wlsKKUnmAznuYAwoRvhS+fp1qW6lJWNt6WHMCahVI2wPs6wHGN3DUmUBjJlCtAskHVR1xkN9pypQpR44cycvLa9asWWxs7KBBgxhjp0+fnjt3rsVm4cKFDz30kNaRaZ0gCIJwKSLjqixljwEDBsyePbtOnTo///zzI488cvny5fDw8Ozs7OvXr3/11VeyTbNmzSowMq0TBEEQLsVBecXHjBkjN5555pnXXntNXicYYz4+Pp07d67MyLROEARB1BCuXLmSnp7+888/N2zYsEePHpbObt26+fv7jxo1asqUKTqdZlma1onKwpNbhq+NxENw6Q3qvnU+7cEx8QeVGQeLjdA+B6baNiPjK/I4gU/DDH7cKfQJRJMwKeIkTKC/VNVGoU9I6voEQ/I+QQTMM6/oVtck0JoTDOZ3QupjAxuDBOMk9MAGi5kAM4NtOH1Mk8BqVFRzBEmb36moqCgnJ8ey6efnZzD83yeyYcOGX3/99cKFC//5z39q1arFGGvSpMkXX3wRGRl5+fLlWbNmZWdn/+c//9E6Q1onCIIgXIrG/E5Llix5++23LZvPPvvsihUr5Pbrr7/++uuvZ2ZmduzYsXnz5sOHD4+MjIyMjGSMtWvXzmg0Lly4kNYJgiCI6oakLX5i6dKlM2fOtGEQHBzcvn37xMTE4cOHw/6AgICioqIKTJDiJwiCIFyK9L9HnnheCDdv3jx8+LDRaBRFcdeuXUeOHOnduzdj7PDhw+np6Yyx5OTkxYsXDxs2rAITpCMEftwAACAASURBVPsJR4LmccJqM2B1HTTqAZgmwRNvYa6EVsEVz+EoG8bs2pgRG6X2gPSDI5gVmoRZvS2o15NQ6hDqmoRZsvaLWC0KxQMwPL821etFY3UsdAzL76RX7ddztaEmYW0rtQee+Al1e1yTwPSbe4ji4uKXX345ISFBp9M1btz4008/7dq1K2Ps6NGjjz32WEFBgZ+f36hRo6DDih9aJwiCIFyKI+LsGjdufPLkScaY2WzW662L97x58+bNm1emUyu0ThAEQbgSQaM+YRvV9aAyiwSjdYIgCMLFaHwutuqhdaLSoD8EsFxPsG1fq8DjBtRtMM1A0S/a1ycqp21UPJ5DYY/ERihteLQHrA01CbN6W1DXJ8xovWv7cRIilt8JiaWQ0KgbdfDa2kgsBcNiKZC2BPuhzqGuSUAdQqFVYG1Mq2A1FAfFYzsPet6JIAiCsAXdTxAEQbgUB+UBdB60ThAEQbgU0ifuKbjyOCFxFQpfPLDnizngqKkg2tcheGy0xm3gNkg/g/3gXJD8S3zag7UtYpqEgOgTiJaA9YsS0q+oM1EZTQKrTIF57zEbqE/wxFhgbcFuG9aTUORuUrS15W5CtQ2Ofd0Ohz7v5AxonSAIgnApbu93Ih2bIAiCsAXdTxAEQbgU8jvVeHg+X0VOJ9AvKmwwe54YC9hWj5Pg0STMldAtzJguwqFP8OVfsq894G11HYJLb8DaiA4hYZqEBLUH9TZPzQkMwcaWtRfJ+4TGVSD1tBU6hHo/1B5gnQmFVsFR4xrVG6qlEIFAOjZBEARhC7fXJ2idIAiCcClu73ciHZsgCIKwBd1POAueOtgKTQLacOV64tEMNGoSPFoFas9Ubaxe/LI26tqDiUuHsJ+LyYzoBFi/sm2dtSRhNlBLwHQIjtgISZsmoaiJrSwebXffsiOptTENQ4f2q4+I5nHCpo/YKE5Xs4hRTSB9giAIgrCF2/udaJ0gCIJwKaRjEwRBELaQBCa5te+M1glHIqEboFuhSSCxEYg9nvcJth2kYUCNAdUtrMc1Yf1IXiaTQpNQ1yFMXDqE/bgHzAbXHjBdAcZPqPcrYiBQ7UFC+tWB/0Lgd0aQrCqA5LD8SOo6BPxHhsdhaDwuh/YgINfHrf+t1jhonSAIgnAppGMTBEEQtiB9giAIgrCBJAkS6RP3JjzVAxiqVcBaFEg/R/0JRf0GLEcToj1gmoSJR5Pg0CGg9qDUJ6xagolDh8D1Caw2tdZcTJhWoa5D4DmagCahtRgyFlCg6IU5wbRpFTzZlVBNAhlFa8yE8qjY9XHvp0crjNv7nSgemyAIgrAF3U8QBEG4FIqzIwiCIGwhMibe8/qEJEnbtm07depUixYtnn76aQ8PjzIGGzZsKC4utmw2b968X79+JSUl69evt3R27NjxgQceqILZOgUslgK2NeZ6Qmtra6ybzRNXgWkSCh1CETNh9bYaUU0CxkMATQLoCmakzadDcNSHQGtTq2sVmPagtKl4nAREQHQpWCtCoUPAL4SgPgfeI5dvVa4SN643aLXR1l9toPsJxthrr732008/xcTErFu3bufOnd98800Zg7Nnz+bn58vtrVu3zpkzp1+/foWFhVOnTp0yZYrc36BBgyqYKkEQRBUjSYJ0j99P5Obmfvjhh6dOnWrVqlVMTExYWFhiYmJUVBS0WblypdxITk5et27duHHjLG999tlnzp4hQRAEYQOnrxMnTpwIDg5u1aoVY8zf37979+4HDx4ss05YWLdu3eDBg++77z5Lz6effqrX63v37t2yZUtnT5UgCMIFUH6n9PT04OBgy2aDBg3S09NVLUVRXL9+/bvvvitvCoLQt2/fS5cu3b59e9asWatWrXr22WfL75WWlnb48OFbt27Jm/3793/88ccdfRK8oBpDZWyQGAulJqFur1Wr4KonodAqrG2lDgH1Cag9AH1CgNqDEdhAXQHRJyR1GzRHk6SuT0ioPlHx2Aj4AaA2CrDERkg1B0ndRFLUstY6Bwz7CoWA2XDleqq4JlEZoBpaBeh0Ok9PT1sWpE8YDAZRBFFUZrPBoH7QvXv3FhYWjhgxQt4MDAw8cOCA3H788cfHjh07ceLE8vv6+PiEhoZ27txZ3gwPD9fr9Q4+B4IgahBV/C9Cp7MTpiaJ97w+ERoaeuPGDcvmjRs3Bg4cqGq5bt26CRMm1KpVq/xbvXv3LigoyMjICA8PL/NWUFBQx44dn3/+eQfOmSCIGkz5Ry4J2zg9HvvBBx8sLi7+/fffGWPXr18/efLkww8/zBjLzMz8+++/LWbZ2dk7duyYMGGCpae0tNTS3rVrV0BAQGhoqLNnSxAEUeUI/ydR8LxcgdPvJ7y9vV9//fVRo0Y9+uije/funTZtmnxPEBcXt2rVqoSEBNls48aNHTp0aNeunWXH1atXb9mypXXr1tnZ2QcOHPjss89qhkOJT6sQ1NuYbsGT6wmNsbDawCoKmCahrCHBo0lY20YOTQL2i1yahHr8BK5DIJqEpK5PKOtJSKr9yjgJptqveAOpa43HTKgPo6gJIcD5Q61CfV+t8Rw88MRMCIJ7e+JdgSSye93vxBibPn16r169Tp06NXbs2J49e8qdI0aM6Nixo8WmX79+w4YNg3tNnjz5/vvvT01NDQgI+Oyzz0JCQqpgqgRBEFUNPe8k0759+/bt28OekJAQ+K8f3knI+Pj49O/fvyomRxAE4UIkpjWDsCpjxow5fPhwfn5+06ZNFy5caHnyc+PGjQsWLMjJyRk6dOhnn33m5+endWTKF0sQBFETmDRp0unTp7OyshYsWPDkk08mJyczxi5fvjxt2rSNGzdeu3YtLy9v/vz5FRiZ8gBWFp7fAUob9efNoT8a1yGYXXuRI8YCy+mkjKsAbUUNCZ56EuqahAloD2asLSH6BKpVQB3C2o/rEPb1CTROAs3jBHs5YgIUJupaFBOwmAl1xaFyuZ60xVhodZGg9mhN7EpQHfUPSXBIHkD5ESHG2KhRowICAlJSUiIiItavXz98+PAHH3yQMRYbGzt06NCVK1diwQkYtE4QBEG4EgfWsztz5kxqaurOnTujoqLkteHixYudOnWS323Xrl1ubu7NmzcbNmyoaVhaJwiCIFyKRh27qKgoJyfHsunj42MJO9u9e/eRI0f++uuvKVOmyDcNt2/ftggSPj4+BoMhOztb6zpB+gRBEIQrkeOxOV+MsSVLljQDLFq0yDLUnDlz4uLi4uPj165d+8MPPzDGgoKC8vLy5HcLCwtNJlO9evW0zpDuJxyLut6g9EEz1TZD+vG4CisiGmOhsYY21C3AEXhiJqAmgeVu4tEktMZPoJoEqkPAKBFMn4B+f9CPPpWizScuoTmRQDwEEm+h+F5Be6ZelwLP7+RefnyOEuBKe6fNxP1ZunTpzJkzbRgEBAS0bt366tWrjLGWLVvGx8fL/fHx8XXq1IEJ9zih+wmCIAhXIv1PouB5YYPcuHHjp59+ys7OLigo2Lp16+HDh/v168cYmzBhwk8//XTs2LGCgoIlS5ZMmDBBq4jN6H6CIAjCxTgizk4Uxffeey8mJsZoNLZq1WrLli1yIHPz5s1Xr149btw4OX7ijTfeqMDgtE4QBEG4Eoc87xQeHr5v3z7Vt8aOHTt27NjKDE7rRFWAubX5tApE2+DK9aRuo9AqGFO1V+R6gloF2MOsqCcB6l2jNa55NAnQ5tAkeHI6MaZe71qpPXDUuJYc5N9X6ApQfAAaA5KYSUDqUsDzEpCYCaVuwVT7lThXw3CGxlAtdQtRJ4luLQG49eQIgiAIl0P3EwRBEK6G8gASBEEQGA6Mx3YStE44Ei5vLsfj7JgbHKuVzfOEvDLvE+hHtQqoSdjXJ/A20Ce4akjY7+eKmeDQJ7TWllCC1JaAIHUm4I9H+DkiqZsUb2D5pgSBI35CMab983KLCAu3/v/pGGidIAiCIGzh/usE6dgEQRCELeh+giAIwpW4//0ErRNVDd+T6uraA2aP19C2X9NC6a2XOPqBPgFiJkQkZgLVISqlScB++3WwmdaYCQmpP6GAw3uP5PgSkJxOirIRCk0C6BCK/E7qmoTAeBQrLMYCw810ixqFIElu7dqhdYIgCMKV0P0EQRAEYQv3Xyfc+maHIAiCcDl0P1F5HP9DgCvXExZjgYyDtpFaFFCTUMZMiMAGts3qbUQzELn0Bo2ahMaYCVyH4Ahm4QLRIaBWAR3TAtQAME1C4ycM5i8J6hqD4hTd+ndtzcT97ye0rRNGo7G4uNhSRY8gCIKoJJLk7jo21+QkSXr//fdbtGjh4+MzcOBAuXP69OmrV6925twIgiBqPvxFilx128G1TsyfP3/27NkPPvjgU089ZemMiIj4+OOPnTYxgiCIewR3Xyfs+53y8vJWrlz5/vvvv/DCC5s3b75w4YLc371797lz55aWlnp6ejp5kjUWRz2HzlNDW3s+KPUcQSKqT0BfP6JVMEyrQGpIcORuwjUJnvgJnpxOHHmcMAT1nE6K+BhBrbfsG/brXcOYCQnRJJRorc7uetzahV+jsX8/cenSpZKSkieffLJMf3BwsCiKWVlZzpkYQRDEPYHEBP6XS2Zo/37C29ubMZafnx8UFAT7r1y5otfr69Sp46ypEQRB3AOIkiBWdx27VatWISEhK1euZCCXQHFx8bJly3r06OHj4+PcCRIEQdRo3F/Htn8/odfr33nnnaeffjo+Pj44OPjWrVsLFy78+uuvr169euDAgSqY4j2OhG5o2xnN+wTMeTQJSbCvT4iSulYBNQOlniGq2ihqWSNjatcksFiKyuQ+soJrDOp1rdEPSYDzh7mhdKr2ivxOldIkKmrBB2kMKrh9/ATXzc5TTz31/fff3759+5tvvrl69erixYv9/f337dvXs2dPZ8+PIAiCcC28cXbR0dHR0dHZ2dm5ubmBgYFltAqCIAiiYrh/PLb9+wlRFOfNm5ebm8sYq1u3brNmzeRF4ty5c8uWLXP6BAmCIGo0ItPxv1wyQ6514q233rpz506Z/osXL37yySfOmVX1QgIvbQjgxWXDswMHkuIlWV48NsqXWOEXk8CLWV8KG+wF9pXACx0HOZZiHGyqAMU4yEtS7mC9tnBLcWnhHOBnwXH5ub57EsfL/p6E85C0SNkumWHFV6fbt28HBAQ4cCoEQRCEG2JLn/jll18OHTokiiJj7K233vL397e8VVhYuH379r59+zp7fgRBEDUbbTcKrrijsLVOHD9+fM2aNXJ78+bNOp315sPX17dbt26kTxAEQVQalwVac2JrnVi8ePHixYtNJpOHh8eZM2caN25cZdOqpvB81I6ycQbKqAGkVgESYyFh8RA89licBBo/oR4DoagzobXmhMIeUgnnPBxeka4JHEvgiaXA5sPTtter3cZloNeheiNKgujezzvZfy7WYDDAtGIEQRCEA3H/52K11SkqKSm5e/euZVOn05GUTRAEUbPhet6poKBg+vTpjRo18vHxCQK0adPG2fMjCIKo2UhMcPP4Ca77iYkTJ+7atWvGjBk7duzo0KFDZGTk9u3bMzMzFy1a5OTp1RAUqX2QtoD6Xt3hhtR+/QM8JxKiJaA2WE0IJBcTmpdJqybBU3OC43PBPi7FroiRom4EHLIyyoJ9rQL/TF2PO3z7nY37+53sr04FBQXbt29fu3bt8uXLw8PDH3roocWLF585c6Znz57Hjx+vgikSBEHUYNy//oT9deLKlSuSJA0ZMoQxZjAYZH1Cr9fPmzdv48aNJSUlTp8jQRBEzUV+3onz5ZIZ2l8nvLy8GGNms5kxFhISkpqaKvf7+/uXlJTIeZ8IgiAId0COjHYs9teJxo0be3t7JyQkMMa6d+++devW06dP5+bmLl26tE6dOsHBwQ6fU3XGmhFHEKwvaCEgL4WNAF4KM8n6Qm3U80FVJjUUlufHRtIikNcI9GL5ixQvmKPJvr0yj5P6dJTzgbmetOZQ4nhx7MuV98nGVbdng+XsItwTiTmgTlFubu7o0aMDAwNr167dpk2b3bt3y/0nT55sBtixY0cFZmhfx/by8po0adKJEyf69Okzbty4999/v3PnzowxnU730UcfCZgiRxAEQXAgMSZWWngoLS3t3bv36tWr69Wrt27dulGjRl27di0wMLC4uNjDw+P333+XzWrXrl2Bwbmed/r444/lhre39x9//LFv377r16/36NGjY8eOFTgkQRAEYUHj807q94jBwcEvvvii3J40adILL7xw5cqVLl26MMb0en1gYGBlZqgtzo4xVrt27ejo6MockiAIgrCg8UEm+77EPXv2+Pn5RUVFyZtJSUkNGjTw9/ePjo5evHixj4+P1hlqWCfy8/NTU1OLi4stPR4eHu3atdN6yBoGX74m9Y9WGUohqPcDeQN6+TAb+DWCY6KxGoofMvbniaPt+X083kLdhu8Zf564Cvtz4Ish0Or6x66zM46lDcHGlrZ9KzqK4/a9F8jOzk5KSrJs1q1bF+bFSElJiYmJ+eijj2QXU7NmzQ4ePBgVFZWUlPTMM88UFRVZ/EP8cK0Tp0+fnj59usXDZaFhw4ZpaWlaD0kQBEFYkDQ+8Lp69erNmzdbNsePH79w4UK5ff369QEDBsyZM2fMmDFyT2hoaGhoKGOsQ4cOb7755oQJE5yyTpjN5hEjRhgMhnfeead58+be3t6Wt2rVqqX1eARBEAREawBdbGzszJkzy/dnZmYOHjw4JibmpZdeUt3RbDbD8hD82F8n/vnnn/T09GPHjvXo0aMCByAIgiBsIEqs8gF0ubm5/fr1a9u27eDBg0+dOsUYi4yMDAgI+PHHH4OCgpo2bXrlypU5c+Y88cQTFRic636CMRYREVGB0e81oN8fSgYCZqNoc+gQDLEH7+jUJQmFRsKli6BHrgQ8moEidxNmrlFXwPblcvvzGGH5mqCJYoPnwHapzIiYJsGRikyzJuHONVfcAYck5MjOzg4LC7t9+/a8efPknjfeeKN79+63b99etGjRzZs3g4OD//Wvf7366qsVGNz+OhEVFdWmTZtdu3ZNmjSpAgcgCIIgnE2zZs327t1bvn/ChAkTJkyo5OBcOva///3v2bNn37hxo0+fPlCfoOedCIIgKolWHbvq4fI7jR07ljEWGxtb5i163okgCKKSuDARLCf21wm9Xq96O8Poeady4FqCta1DdAv4FIJCSxCg9qCuSSh0DsW+iD06Z6026m0UOFHN2kBldAWt8RMcu6Kny6EaOEiqwPUAR2lLDhpHY6mOew05l5k7Y3+dEARh4MCBVTAVgiCIexD3v59wTRU9giAIorqA3k988803X3311axZs/r06YMldKpbt+5///tfZ02NIAjiHqAa69jFxcU5OTmlpaWSJOXk5KjvbNCcRrDmgfqIsVgKsAFjHXQKHQL229cqUBswH+WYSFuhnfDoEOptPv+4Oz9Vz+EtRjUGHp1G43S4BrI/KM9n56j8To6yd9WYVYnEmJv7ndB/9OPHjx8/frzcPnLkSFXNhyAI4t7ChQVNOaEbAoIgCBfj3o874etEenr6jRs3bO9McXYEQRA1HnSd+OKLL+bPn297Z4qzY0xZ1wF2S4gOgeRi0nHpFhJHv3r8BBZ7oYjbUGgV0MZqJSjaHJqEImaCwyeOVtLliEVA7e3X2ED3FZC4Dc1+AkfpNI63d1SsDNdRHeVfcWs/jTaqsd9p7Nix3bt3l9sXL16cN29edHT00KFDg4OD09PTt2/ffujQoXfeeaeq5kkQBFEzcf/4CXSdaNKkSZMmTRhjkiS99NJLy5YtmzFjhuXd8ePHz507d82aNZZqGARBEEQFEJkguvc6YT/OLjEx8fz585ZnnyyMHz/+wIEDd+7c4TnMnTt3kpKS5BTlmsjKykpJSdG6F0EQRLVBYhL3yyXYXydKS0sZY9euXSvTn5qaKkmS0Wi0O8KqVasiIiJGjBjRvHnzc+fOlTdo3ry58D8GDx4sd0qSNGPGjFatWg0YMKBTp04ZGRn2z8YVCOClY5L1JTDkJVleevBS9jPwklRfOsVL/VhwHMU8wb4CeOmYYHkJyEsngRfTWV7o6SLjMOQFNzAb5Qv7NLR+ehxjwjPgORZqAseENvA6wGtVmfmr2yvG5zgv/AOA4yAWHJdBK5XYldCM/XWibdu24eHhEyZMSEhIsHT++eef06dPf+CBB+rVq2d795SUlPnz5x8/fvz8+fM2CvKdOHFCkiRJkvbs2SP37N+///vvv7948eI///zTtm3bRYsW8Z4TQRBE9UH8n+uJ5+WSGdpfJwwGw9dff52SknL//fdHRER06dIlPDy8a9euRqNx/fr1dnffunVr3759W7ZsyRh77rnnDh06pPq4rdFoLCoqgj1btmwZM2ZM3bp1GWPTpk3bsmWL5KqbLoIgCKchSQL/yyUz5Iqz69mz54ULFzZs2BAfH5+RkdGpU6cOHTqMGzfOz8/P7r7JycnNmzeX23Xr1q1Tp05KSkpYWFgZs6FDhxqNxqZNm3744Yf9+/eXdxw9erT8bvPmzfPy8m7fvi0vG5DS0tKMjAy5HixjLDw8vEGDBjwnRRAE4Q5IjImunoNt7K8TKSkpr7766uLFi2fNmlWBAxQUFAQEBFg2fXx88vPzy9jExcVFRUVJkvTRRx89/vjjly9frl+/fkFBgaV2no+PD2MsLy+v/Dpx5cqV3bt3nzlzRt4cMWLEnDlzKjDPCqN4Zhxs6JDn9BUPwIGmCNoSSLQEE9ObgY0ePNdvBm2efhh7oQdzg3eXekVbB2ywWAosrsJ+vAVsS4g9RPkQIfYLC15neHHVr79SIlS8gYyPHIujzRVrUpkxBfvXGdtXay4vpsnCxpko4nuwWu6OoaCgwEEjcWEwGLy8vGwYSMxlNwqc2F8ncnJyvv3223fffbdiBwgODs7NzYWjlf+9HxUVxRgTBGHGjBnvvvvu8ePHR44cCXe8ffs2Y0z1RiEqKiosLGz58uUVmx5BEPcavr6+rp5CNcO+PtGyZcuAgICzZ89W7AAdOnQ4fvy43I6PjxcEITIyEjMuLS3Nz8+X3Vlwx+PHj7ds2VK+qyAIgqhJiFpeLsH+/YS3t/fHH388c+ZMHx+f3r1763TaShuNGjVqzpw5S5cuHTx48Ny5cydNmlS7dm3G2Ny5c319fefPn5+YmBgXF9e9e3eTyfThhx+GhIT06NGDMRYTE9O+ffsvv/yyRYsWsbGxMMqPIAiixuBCgZoT++uE2WxesGDBzZs3+/Xr5+npGRoaqtf/n++6QYMGx44ds727t7f3/v37Fy9evHPnzn79+sXGxsr9TZs2le8PAgICkpKSfvnlF09Pz86dO3/++edy2e2IiIiffvpp5cqVubm5zz333LRp0yp1ogRBEG5JTdCxbdTHrlOnDs8xoqKitmzZUqZz6tSpciMsLOyzzz5T3bFXr169evXiOYQLUeTaU9QjgnogooWCezNoIYFvjQhsDOBHhwgOppfUtWtFfkDEXqFpQx1ekQcQttU1bYW+LVhVcEFSVEtC2jx6KbQXgQXUwBEtV0JsmKRqrz3LM4cWrVWjFireVmraOsRG/frzaNpatWXl9x9raxyU67iEY7C/Tuh0Ouz/OEEQBFFJqnEeQAyTyUTlTgmCIByFKDE3zyvOK0r//PPP/fr1q1+/voeHR2ho6LBhw6gYKkEQROWRtLxcAtedwRdffPHss882bNjwkUceqV+/fnp6+i+//NK3b9+4uLhhw4Y5e4puDlbnRwKfKfytoNAwgA4hYFoF2FBqEtZ+PaI9YG2srhGmVeiRmkU6EI2nbCPxdwJPjJ61LXFpGNAG1hRC4uYUHxKyr8Dz96gtvg+Lg+OJv+OJZ8SuCV/Mo9bYSdBGwhYVV6dSv5VrfrYeSVKE07oh9teJ0tLSV199dcyYMRs2bPD09JQ7CwsLR44cOWvWLFonCIIgajZc9SdycnKWL19uWSQYY7Vr1168ePHFixezs7OdOT2CIIgajqxjc75cMkP79xOiKDLGPDw8yvTLPfK7BEEQRMUQa4DfKSoqytfXd+nSpZ988oklJsBsNr/11lsRERH169d38gzdHZ0i1561Hz4zDn8FmKFOAP28EvTLW1HoE+Ad+MUSkfgJPaJD6JE568H4ejA3Zds6T70ENAmBR7ewtkWF7xvEWzAzaNuPvZCwWApBXXtQXGcoEKF/qHwRAtamNk1CGd+gNb5Em96jOT8jEkNT8WyFfHqG47SN6kL1fy7Wy8tr0aJFr7zyypEjR0aMGFG/fv2MjIzt27cnJSVt3ry5CqZIEARRgxFZ9b+fYIzNnj27Xr16b7/99ptvvskY0+l0nTp1+uGHHx555BEnT48gCIJwMbwRcxMmTJgwYUJBQUFWVlZwcDClbiUIgnAINS0eW87bTosExAB8/R46dT0Aagxm4PPVw3gCxRMBwIcOQwIQfQJqHgaoVcD4CRHRJBRaBfBHw5gPqE8A/76yfpG6DqHM9QR1CNhW98srYilQ3z0WP8HU+4Emocg9BT8vVKxQj8lQ/okj2gPSj+ZZQnQLgafNo2EguZ4ExWeqrlugWoVig6PWEMf/Rq5cUojmUV1woI5tMpkKCgrKZ94rKSkpLCwMCgqq2LC88djbtm3r0aOHn5+fn59fYGBgv379fv3114odkiAIgoBUPh779u3bAwcO9PX1bd68eXh4+LZt2yxvrVq1qkGDBm3atOnatWtaWloFpse1TqxevXr06NEZGRnjx49fuHDhmDFjLly4MGjQoB07dlTgkARBEIQFURL4X+ggojh+/PicnJxbt2699957Y8eOzcrKYoxduHBh4cKFf/zxR3p6eufOnStWFtq+36mkpOS11157+umnv/zyS0sGwPfeey86OvqVV16Jjo6uwFEJgiAIB1KvXr3x48fL7ccff5wxlpKSUq9evU2bNg0fPrxFixaMsZdfxUEeuAAAIABJREFUfvn++++/e/euVu3A/jqRmJh4586dJUuWwDSxXl5eCxcu7NmzZ1ZWVr169TQdsoZRS2f1d3vprc/+6xX6hPVXgAm0S0Xow1W/t5OAD10RJwHMzWAcLH4C5oDSobqFuoYB614oYyn0qm2e+AkYbyExdd1CgrEUQNtQlnWB9uB6Irm2lBKDei0EQcLu77GcUUy9H36mWO0HjvgJHv1G0Q81ITSnlno+Liw3Fx4/AfvVNQkMVNvg2EFrDQx3xuEJ/nbs2BEUFNS6dWvGWFJSUsuWLeX+yMhIs9mclpYmLxv88OrYQrmPsXwPQRAEoRWtdU/T0tJOnTpl2WzYsGFISIhl8+LFi88999wXX3zh7e3NGLtz545capoxptPpfHx8cnNztc6QKx7b399/0aJFa9eutRTHNhqNy5Yta9as2T1+M0EQBFFJtNY9/eabbw4ePGjZfOKJJ+bOnSu3k5KSBg0a9Oabb44YMULuCQ4OtiwMRqOxoKAgODhY6wztrxO1atVasmTJiy++ePTo0WHDhgUHB9+4cWPHjh1paWnfffed1uMRBEEQEEliqKdTjVmzZs2cObN8f2pq6qBBg+bNmzdp0iRLZ5s2bfbs2SO3T506FRgY2LBhQ60z5PI7zZgxIzg4eMWKFR988IEoigaDoXv37mvXrh08eLDW49U8/AwmS9vXUGppQ1+tGWgMpcDPrjdDP7L6+MrYC2tbBGOadfBY1raJQ4fQYbqFIs7DelwDEj8Bcz3pBQOwgTmdoA5hAG2rDqFT6A1AkwBxD0o9A/6FgX2R0tfQmw1zQyl30OouRj48LKYBi41giK4gqMej8OR30iGaBE8+KJ74Ca4q54pYCvU2BNce3Du7hUvJzs7u27dv586dW7RosW/fPsZYhw4dZHF78eLF69ev7969+2uvvfbss8+WT+pqF159YsyYMWPGjCkqKiouLvbx8alVq5bWIxEEQRDlERkTKy3G5+fnd+nShTG2Zs0auWfu3Ln16tWrX7/+zz///Prrr69cuXLo0KGLFy+uwODa4rG9vb1lbYQgCIJwCBLT5ndSJSIi4ptvvlF966GHHtq7d29lBueKs2vdunX5Vei55557+OGHK3NsgiAIQvq/Wwqul0uwfz+RlpaWmJj4xBNPlOn/17/+9fDDD5tMJhhXcQ9yn4/1ITMvvVWfMIlWX3CJ2eoQLDJbywLqFT56K/C3BYzANCO5mwyIJmEAmoRJZ1+rQNuMR6vAYims56gDuoVOsuo6kqCuSSjqVUiwzgSsPW7fx6146BDGMYB+CYmlwH3i6o4CvOYEpkmo52hiPDqEAONRsNxZWI0QJDeXhNnYz+mEthF7iEKrQG1qJlqfi6167N9PpKenM8bCw8PL9Dds2NBoNN66dcsp8yIIgiDcA/vrRGBgIGPs8uXLZfovXryo0+n8/PycMi+CIIh7A/4kgK563sv+OtGsWbOmTZvOnj27oKDA0pmdnR0bG9ujRw850zhBEARRMSTp/1KL87xcgn1pQRCEDz/8MDo6unnz5sOGDQsNDb127VpcXFxpaelvv/1WBVN0N0Z9dQZu1t2SamkXpwZY2gX5oF1svesyGK0PjAmCl6UNC5XAh+TMQBAwKfJEVUKT4NIqmHo/kuvJAHzcJiSWwgy1CtCGeZxgTAOsX40+d488KaKQJBQxE+pP5wuoJsHzp2m/0rOA5W5CNAlMh1BoEogOwWOj48jvpGyD2SPagzKWQj3XFl+tbPV9mcIGUr3jKmpInaJhw4YdPHjw9ddf37RpU0lJia+v76BBgxYvXty2bVtnz48gCKJm48IbBU54H1Xq2bOnHPxdWFhoySpFEARB1Hh469nJ5OXlnTx50mg0Omk2BEEQ9xrur2NrC31ISEjo27dvZmZm/fr1nTShaofU2Orn9SrNs7QFpD6wMjbCuk6bkLZRtO5tBI5hI3DAG3i0h0ppFerxE4q4CkUsBczvZFbtF4FuIUlm0G/VJHQSjCtSz7+kjDzCdAIzhw2IyeCps40UQxCw8bGa2KgmAeNOkLxYGnULnrogeiRmAm1jWoWi375WobnGdTWviQ1x//iJezpEjiAIwuVozSte9dA6QRAE4Uq05hWverTpEwRBEMS9hrb7iW7duhUUFNDzThBzgDV3k0dgkbV919r2MlptTGbrNTeK1nYpyAdl1FnbpTrrWl4KNAAPoCUYgcbApVWgNbSZqr2Oo262AfzmgLEUZhBLYQY+d5FZr4koAA0DahKKmhPq9auhH1xx866QEmCxbG3j89WiQPJHIdEFeCyFut4gMHWtQofEoyjrkEPtQd0G1g6BMRN6VJ+As4fag7omJ6Bahbo9w+xZzcQh+WKdiv37CZPJ1Ldv382bN5eUlOh0OlokCIIgHIjEBJH75ZIZ2l8ndDpdYWHh2LFjw8PDX3nllUuXLlXBtAiCIO4RZH2C8+USuNaJP//8MyEhISYmZt26dS1btuzSpcuaNWuKiors7ksQBEFUd3j1idatW7/55puxsbFbtmxZs2bN1KlT58+fP3HixMmTJ0dGRjp1im6OWAvUTvABPlwfa30Fj7sllrZnibVdy2QtH1tLb61LUSJa/fUeQKvwEK3+dAPQLRSahCIvE9KGNbERHQLWzdZz1c1W1ypM4DtmAHEMoqJt1SoU+Z2wmAYYPwG6dcARDhPmKOpgo20H5XfSqE+geZwU+ZpgnRKDaj9W5wPVJJCYCWX8BOgHp6JTP90y/TxaBWxz6BAcMROYzuHOuDCAjhNtzzv5+vpOnjx5165d48aNy8zMXLFiRcuWLR977LErV644aX4EQRA1G1FioiRwvlwyQw3rhCRJhw4devrpp8PDw7/77rtJkyYdPnz4k08+OXPmzIMPPpifn++8WRIEQdRgakLejuzs7PXr13/++ecXLlxo0aLFsmXLJk6cKNcveuihhx5//PGQkJDTp0/36dPHybMlCIKoabh/nJ39dcJsNjds2NBsNkdHR3/44YcDBgwQlCnh69evf999992zyQElg/WeTKoFfLteVt+33hNoFR7WC+VZam176IANiCfwAM/4G9Ba1tb58MRM6HhqYnO1BdU2rJutjKUAfnMB6hPqNSckLI4BiY2ASXJExbfUeixBoX+A+hbgWHitbAxEk1BoFfbrTyhrWRvs9uuR+Ak9Txt+FqhWAWeMxU9YgRqDsl6Feu0QrfW0sZoT1USGqMZw3U+89tprkydPDgsLwwySk5MdNiOCIIh7CRcKD5zYXyf0ev3ChQurYCoEQRD3IO7/vBPlASQIgnAlEqO84jUeRRABaHsA/6mH1T+u01t1CAPQJAzAX2/QgTaiT+BahTZNAoRhoLEUeEwGnA+o6Q2+9B7AUy3C+hMS1CRgnIR6P176Qb2uOPSQS0AvUdbcRvI7Oag+tlLJw2ImEH0C0SSUeZyscSd6AbRhP6pVYJqEuuYEYyN0yPdKe/wEZoP0I20F1bAuhfvnFad8sQRBEIQt6H6CIAjCldSE52IJgiAI51ETnncibCPB5/eVxaMtCHrgw9UDrQLoEHrYBj50Hr1B0QZz0yG6Ao+vmS/eAo5vP5bCDC4K1CokJKZBAfQ7S4inGvr6Jav2I4G8SRKIpZAQjaRS+Z3QWApEn4D5lJD8TlhshE7g0SGsNgZQZwLGtRiQ/E4KrcJ6JmW+P7BdCa2Cq84HjKdh6u3qCf/thEvOldYJgiAIV6LJ7+SSdYJ0bIIgCMIWdD9BEAThSjTpEy75aU/rRKXB/KQKoQD4Z2HtB9gGmoTSz4v0M3VfMP5su7b8Tkptgye/k3osBYxpMEtYLAXMrcTsYlbUu4Z6ANQk4LGgJgG0CkG9/oRUCX1COX2oQ8C4CvsxEzw5nbC2QaFJwH7YRjQJjlgZxfcNyekkaNUqsDa0R2tXqLerCxSPTRAEQdhCkigemyAIgsCRlGUZ3RDSsQmCIKo9165dGzx4cN26dQVBgFXj/vWvfwn/o379+hUbnO4nqh513zdPrWAB0yTQfrAv+sw71ka0DaxuNoyZUNSvhloFyLOk0APA91BRcwKcABKXICh0CBCfAeInFHmcQB4tCamPXRl9Ap2noo3VnEDyOylyMXHoExLQJ5j9mAkDmBtsYzETqFaBxPFg31tUe+DQIWoSkrKce8WoVavW5MmTFyxY0KtXrzJvffrpp1OnTq3M4HQ/QRAE4Urk+AnOF0ZwcPATTzwRERGhNr5UybrUtE4QBEG4EokJIverAuPPnj07NDQ0LCxs3bp1FZsh+Z0IgiBcidY8gJcuXdq3b59ls2nTpk2bNsWMly5dunnzZoPBsHfv3ujo6KioqB49emidIa0TTgP94CvuiMSfMbffr/ALI7UWKhNvAduiIq7Celz4bRNhTQiGAGMjBHVfv47B/FGg5rYAc0mpaxKK/E5ILQqtCKhWAfM4IfmdsPoTHPqEMncTjJPANAnQRj4vNN8X+p1R3xf77mEaBqbPQe4F3QJj//79ly9ftmw+8sgjM2bMwIybN28uNwYNGvTwww/v3buX1gmCIIhqhtZ8sc8///zMmTMrcKCsrCxfX98K7EjrBEEQhCtxSP0JURS3bduWnZ3NGPv+++/9/Pwee+yxkpKSBQsWDBw40MfH57vvvjt79uzGjRsrMDitEwRBEK5EYkLln4uVJEkWLaZMmXL06NFatWo99thjer3eaDS+9dZbJSUlbdq0OXHiRKNGjSowOK0TlQb8EhBgVCV8NN8MalSIoK3w0QuqbcWhOKajzJ+D6RBY3WP1th7ETJglHn3Cui8sGa48R4Bk/7k7WHNCB8YxKWIOrDETIvgAoD4hKmIpnKtP4DETmD6hrlUoallL6lqFUnvg0SSsc8byOKG5nnTq9ny5xaz7csVPIG3s/6qy272jnP+HQ+Kx9Xr9Z599VqbTYDC8++67lR2anoslCIIgbFMV9xN5eXmLFi3666+/IiMjX3/99bCwsDIGX3/99c8//3z9+vUmTZq8/PLLbdu2ZYwVFhbOmjXLYjNs2LDo6OgqmC1BEERV4v55AKvifuKZZ565evXq8uXLPT09R44cWd7giy++6Nu376JFi0JCQh566KG0tDTGWElJyZo1awb+j2bNmlXBVAmCIKoYUcvLJTj9fiI1NfXHH39MS0urX7/+Aw88EBoaevjw4TIZSPbu3Ss3evfuHRcXd/DgwaefflrueeKJJ5w9w0oimIFn0QTb1qZkBjmIzFbfsVkEz/iLwEayr1Uo5oD1c/l8JdW20qeM6BlIrieoTyjqhytyKCGzlqDvHhwLahIwfgL46xX1twV1TUKhTyCahPb8Tla44icU/VBfAXUgJEyrgHUj7OsQsMa1QZGDi4G2pNqvXXvAdAjYrng9CSzXGUNrm1cTJHav30+cOXOmadOmcp5CvV7ftWvXv/76CzMuKChIS0uDKUomTZoUExPz1VdfSZV/cIwgCML9ECUNL5fg9PuJzMzMwMBAy2ZQUFBGRoaqpSRJ06ZN692790MPPcQY8/DweO211zp16pSdnb1o0aI//vjjww8/LL/XhQsXdu3atXv3bnlz5MiRr776qhPOA1DLucMTBOFUCgoKqvJwBoPBy8urKo/ocJy+Tvj6+hYVFVk2CwsL/f39VS3nzJmTmJi4f/9+edPPz2/ZsmVyu0uXLt26dVuxYoW3t3eZvZo2bTp06NDp06fLm+Hh4RULOOSn0OjU4QmCcC7O/hehFYfETzgVp68TjRo1SklJMZlMBoOBMZaUlDRq1KjyZrGxsfv27du/f7/qKhIREWE2m3Nzc8uvE56eniEhIZ07d3bG5HkQgCYhlAIfdwmou1AKfOgm6zU3A63CBP3swDdtVtRvUI8/0F4hAebYwWIp7Od3gjqEqFPXHhR+f7iDIrZD/Y8Eag+KeSpyOomgDTUemN8J6BMCnKd9fYInlgKbPxY/oZMw3UK9ZrUO0Rv0HDqEst86Nz2HJmHQqX/uPPUnUK2LMfU2Yo/HAzHVNuPodzck1zmUOHG6PtGtW7fAwMCtW7cyxo4fP37lypURI0YwxuLj49evXy/bLFq0aNu2bbt27QoKCrLsmJqaKt8eiqL4zjvvNGvWLDQ01NmzJQiCqGIcUn/CqTh9ndDpdGvWrJk1a1anTp2GDx/+ySefyHcMx48fX7FiBWOstLT09ddfT01NjYqKCgoKCgoKev/99xljv/76a0hISJs2bUJDQ3fs2PH11187e6oEQRBEeaoizm7AgAEpKSnJyckNGzb08/OTO2NiYiZOnMgY8/T0VH2WaeLEiaNHj7527VpgYGBISEgVzJMgCKLqqXABoiqjivI7eXl5tWrVCvYIgiArFjbw9fWNiopy5rwcgK4E1GG+C/zgd61nZyr2tLSNRtA2W+sYG0UOfULRBpNA7ka56lVgtQEUMROYVgHmA/3+ijYyCaauVTCFDgF7oX8f5JsC9iKiW4hgfFHi0Scg6v34nzVWJ8N+vw6JsdAxdb1B0YYaA9aP5m4C/VyahLo9XkObQ3vgiaXgyOmE2bgzoiPyOzkVygNIEAThUtw+bwetEwRBEK7EhQk5OKF8sQRBEIQt6H6isujzrHF3Uq513TXlWyMwS4utYR8lRmt/iRloFaIBtNW1Cizvk9YfI0p/Lo8mwaNVWMdU1HXQIXWw4YYIffdIbAc4dzPURYA9rI0BtQqFPoHGSTDVfmzKEPz5fUyTULfBNAmF3x/sq0N0CKU9oklw6BA8ugVPfifF+SLz5NHPGGJT3dFa97TqoXWCIAjCxbi3jE3rBEEQhEtxYYI/TmidIAiCcCXur2PTOlFZdCnWOgcl6db8YkX5fpb23ZLa1rbRqlUUA32iRASxFBLM+2Q/lkKRTwlxdCrz5CC+ckyTQHzcijgJMJDC1w9/KQEbIGEwAfTrJPttPdQqkHgCpQ6hHneC6xMVh0+rsIL56NG8W8i+UIfAci5hMRNYPIRWrUJzvQqm3s+Tx4knvxPhKGidIAiCcCXunweQ1gmCIAhXQn4ngiAIwhaUt6MGsm1ce7j5UN36lraPodjShvqBEWgPJSCnUwmImSgBtShKQa1sE+KLV/jZNX7JsFw6yuf6EX+3DtEtwC8ihUSis74hgPOCmoQATkAQ1bUTqJfAHE16cO6iwsZ+rQ5lnQx1G+1qhboOwZOzCI0zgP56VKtQ1yF44htQrQLN44S0eWyw3GJoXAVWi4IxtY3qqFVIbn8/QfHYBEEQhC3ofoIgCMKViEwS3TvSjtYJgiAIV0LrRM0n9W6gpR0A9AmDDtY2sGIGPnoYJ1EKcjrB/E4mHq0CjM8XBwB9vsCfjviIdYivXBlLYW3roTsTTk6nLmJATQLqForQC5i7SaFDgCEVWoV6P5wnplXAN7QWuMf95hwxAahWISH9wJ4nz5KDtApUw+D5/nDEUuD1UWA/olVAG6Tf3XB/fYLWCYIgCFciSqIoufVKQTo2QRAEYQu6nyAIgnAlImNm0idqNvkm6zWUmLW2hCdIYAR9qTD/EszXZJSgDoFoEkh9bAmJFYDgz/Jjvmz1Nqx/oHDpI5qEMk4CtIGNiOR3EhX1JNTjJxRxEora17AfzJPZbzPEngdH6RMCFjOB2CjjEjANgKn3c+gZeiROAovVwHM9qZ8LGjMB5sxTc6K6aBIQUZBgeXk3hNYJgiAIVyIxUXRvJZvWCYIgCFdiZpLZvdcJ0rEJgiAIW9D9RGWBuZjumkGNa+CAh75ahU8ciYcwgYf/TUjNCTR/EYefE30+HcYrIL5jxbGgPxqOD35+mBFNQhknoa43KNqwVoSkrlUoNQn71xzL44ReQg7xR+uz/FgcAJdWgYyjQ8asTFxF5WIv4JyReXLEW/BobNUR0XF+J6PRWFBQUKdOHRgXZTKZEhISAgICIiIiKjYs3U8QBEG4Elmf4HxhgyQnJ3ft2tXPzy8oKKigoAD2t2rVKiYmpmfPnjExMZLWpKGMMVonCIIgXIvIRJGZOV/YIH5+fkuWLDlx4kSZ/gULFjz88MMnT548f/78vn379u3bV4EZ0jpBEAThShxyP1G3bt3BgwfXrVsXdoqi+O233z777LOMsYCAgNGjR2/durUCMyR9orJA/QBqFSLib4V+VXgHKCriJBhoq/dr1SQgmJ9Xh+goesy5Dk9MVPcjK46L1JwQsbgQpm4jIXEVPJqEQofQHCeBnZn63lprJGA6BJrXiKtGBaYB8MReqI/DF2+BHQvRTjhiJjA9A2tXy2AKh5KZmVlcXNykSRN5s2nTpnFxcRUYh9YJgiAIVyL7nfjtz5w58+2331o2o6Ki2rZtq2pZWFjIGKtVq5a86eXlBaULfmidIAiCcCW2hYfy/P333/ICIDNkyBBsnQgJCWGM5eTkhIaGMsays7PlHq3QOkEQBOFKJCZpei52woQJM2fO5LGsXbt2q1atjh49Onr0aMbYsWPHunXrVoEZ0jpRWaDf3KTwd1ud8bB2AqZPwGf/oY/ezBU/UfH8TkpNAsmJhOgWCoCjWlHvGsvXhOaqsq89KM8d0xsqo0kg1xMTglDtwb5ugeUs0qxVIP2YNobGLnDljFIfhy+XlLZ+PGai5qD1fkJ9EFFcu3ZtTk4OY+zLL7/09fV95plnGGMzZ86cO3du7dq1ExMTDx069Omnn1ZgcFonCIIgqj2SJJ06dYoxNmXKlISEBIsmMXXqVIPBsHr16sDAwAMHDpDfiSAIovohMVGq9P2EXq//7LPPVN+KiYmJiYmpzOC0ThAEQbgSyhdb88FiICDQz47losH0CUXdBeS4PM/+o/mC4NwU+Z3UdQvFmDz+d9BGwi2UOZoQ7UGrJoHlJ8CuFRZj4Sigf1/Rj9pDm4rngMJs+OpYMNBfiZxRijlXXP/AcjphmlB10TC0Phdb9VA8NkEQBGELup8gCIJwJRIzV16fcCq0ThAEQbgSSZIkifSJGo2E1EhgqCah7jXFYiC01sGG8NRCwHzNeKSHuokyTsJ+G9Mq8BrX9nM3KXQLOE80rkLdyFHqBI9/XPHdwOIkYFsxaMVjLNB61IpYCvVxNGsbGmMyeM4dPV9W/ZAcET/hVGidIAiCcCUan4t1gahMOjZBEARhC7qfIAiCcCUSEyUN8RMu+HFP60RlUWgJyBsC5njG6knANkcdbD6tAvqgrWPqUO0E6Yf+bkQb4ImZQM9FYcORewqJpUBzNHFoGBj2VSYboDmgsH51zQCz54qlQPfliM9A4yHUj6tZqwBjonUmOOJIqiOSJEoSv9/JBf+0aZ0gCIJwJRrvJ1wArRMEQRAuRdv9hAsgHZsgCIKwBd1PVBaljxvEUiA+Xz4/OKJJKKywnEtIG4l1UPxSQOIn0HxQiK9fBw4GczdBf7QiHgLYY7oL1CEYptkwprrFUz8cj6twDFguLIUNhw6B2aO5tlB9gif2QqM9aOMaA2KDHBer713dczpByO9EEARB2ILydhAEQRC2oLwdBEEQhG3MjO4n7k0U9Qw4nKaYD11rHieFwoBpEmAD1rfQKXZWj11QPCMPzEWF9gCPpT43VIfguA48WgUGHjOhrV4FBpd/XKsOodjSGFfx/9u786imrvwB4DckLAFU9jUKgoBLEdlVdpAoWqSO0g6WGSooxVq16mhrZ+rY2qHHOSBo9YwzuA0qWo9LxRlFQRErsiggimyVAQphC/tmgCT398c9fb8YktcgEKD9fg5/vHfffTf35YV88+597145GxSb02Js9lVovusRjzelSD3B2IA4AQAAEwkjaHcCAABAB+53AgAAQANjBNcTvx1yR0oaYSO33OwKlCO/LVt2R8Hr82BLlvPL8zpIdsGoSPYTyCkTy+5WeL3GCoxb9Xq3giLzRsh+sbGaZ2Kk5Leby3kGQs6KYv0ZEuny5q4Y4WvJGxtKXh1G9QyH3HIUqP8UgbEInscGAAAwhcH1BAAATCwxgv4JAAAA8sBzdr9+iszeMFblK0TuOE4KjKf0WheGvOcJ5IytxJDdsSCvP+O1MuW8iQr1T8jZIG+sp6lCXj+BAskK5VGkX0GR+sjvG1BkXCY55YywH2Wqzz8B1xMAAABoTfr7naAfGwAAAB24ngAAgIkE48X+toxq/mQ55ShC7mvJa9d+be4Hea/LkJlHkecVFOqHkP1SIz720TxrMvmenxhZppF+xuT1H7yWZxSvq9hzG7LrMJp+Efl1mCL9Ulg8ydudIE4AAMDEmuz9ExAnAABgYk32+52gHxsAAAAduJ4YL+PdMipvbmqGnJbb17oYFGjnlff8hDwK5ZbbD6FAx8VY1WGyNVmPQz/E6xSYl3sUpY/HfBujeq2pOFf2pL8vVhlxAmN8//79+vp6Dw8PKysrmXkqKiry8/MtLS29vLyoxMHBwYyMjM7OzoCAAGNjYyVUFQAAlAxj8SR/HlsZ7U7vv//+1q1bs7Ky3N3dU1NTh2c4f/68l5fXgwcPNm3atHnzZpI4MDDg6+sbGxublpa2YMGCoqIiJVQVAACUTjySP7nq6+v/97OGhoYxrN+4X088efLkzp07L1++1NHRCQgI2Lt37+rVqyUziESizz///NSpU2+//Tafz7eystqxY4etre3ly5f7+voKCgpYLNb+/fu/+uqra9eujXdtAQBA2TAe8dwDsqxatYrP57PZbISQs7PzpUuXRl8mMe5x4saNG4GBgTo6Ogihd955JyIioqqqytramspQXFzc0dERFBSEEDI0NPTx8fnPf/6zc+fOGzdurFmzhsViIYRCQ0NjY2NFIhGTyRzvCk9qCrXzjm97tHIbfSdbZwIAk1pKSoqvr++YFzvucYLH43E4HLLMZrP19PR4PJ5knKivrzcxMaECgLm5OY/HIzsGBASQRA6HMzQ0xOfzTUxMpMpvb29/9uzZ8ePHyaq9vf3ixYvH9YgAAFOaSKTUh58ZDIaKCm0L/9j1Y7e0tJSWllpbW6urq49JgcS4xwm+BqsMAAAUp0lEQVSRSCT5HrFYrKGhIakMklcJVAbJdLIgtSPR19fX2Nj45MkTsjp9+nRnZ+exPggAwK+HzG+S8aOioqKmpkabZWyex1ZRUdm3bx9CqKmpKSEhYcOGDaMvkxj3OGFqatrY2EiWRSJRa2urmZmZVIaWlhZqtbm52cXFRSq9ublZRUVl+MUEQkhbW9vMzMzNzY2s9vb2Jicnj8eBAAB+HZT8FcFkMsPDw2l+4GOE8Uies8vJydHU1KRWHRwc3N3dEUL37t3T1dVFCN25cyckJMTb21uy5WY0xj1OeHt7x8TECIVCFov14MEDfX19GxsbhFB/fz+DwWCz2QsXLsQYP3nyxMXFZWBgICsra9euXWTH1NTUzz77DCGUnp6+dOlSVVXV4eXb2tqWlpYWFBSM94H8vxmora2tr69v1qxZynvRCVVUVOTo6DjRtVCS6upqXV1d0qP2q9ff319XV2dnZzfRFVGS58+fz5s3j1Wg1OfGmEzm2rVraeJE4Y0UxUu7c+fOlStXJL/xpk2bRuIECRIIIS6Xa2Njk5+fP1ZxgoHHop+dhlgsXrx4sZmZmb+/f2Ji4ieffLJt2zaEUHh4+IwZM44dO4YQOnDgwPnz57ds2XLz5s2hoaGMjAyEUGdn58KFC4OCgmxsbL755puzZ8+uXLlyXKsKAAC/Av39/RYWFhcuXFi2bNmYFDjucQIh1Nvbe/LkSR6P5+vrS33X37t3T01NzdPTk6xeu3YtJyfHwsIiMjKS3NeFEGpqajpz5kxXV1dISAj0TgMAgDzl5eWHDh3y9PQUi8WnTp169erVo0ePZLbBvAFlxAkAAADjqrOz8x//+Ed5eTmTyXR0dIyKipLswxgliBMAAADowHixAAAA6MB4sTIIhcJjx45lZ2dzOJw9e/bIvB83PT09OTmZyWRu2rTJw8ODJPb29sbFxZWWls6bN2/37t3a2trKrfgbKikpOXLkSE9PzzvvvPPee+9Jbe3o6Lh06VJOTo5IJPLy8tqwYQNp9Lx//35aWhqV7bPPPpsS9wh1dHT8/e9/r6qqcnR03LFjh4aGhlSGpKSkqqoqsmxoaEjuvkMI1dbWxsXFtbS0+Pv7b9q06ReenJo00tLSzp8/z2KxoqOjlyxZIrX11q1bWVlZkimxsbEqKirJycmlpaUkZfr06Z9//rmSqjsKzc3NP/zww7NnzywtLSMjI2Xmqa6ujo+Pb21tXbZsWVRUFOPnmfbOnj178+bNGTNm7Nix47dz95fipsZnXcn+/Oc/nz9/Pjw8vL+/39/ff/jTmw8ePAgNDV22bNmSJUuCgoKePXtG0sPDwwsKCiIiIp4+fbp+/XqlV/xNNDc3e3t7W1parl279k9/+tO5c+ekMty6dSsjI8PLyysoKOjIkSNbtmwh6bm5uZmZmbo/myrfmyEhITU1NX/84x/v3r0bExMzPMOFCxd4PB45qBkzZpBEgUDg7e2tpqa2fv36o0ePHjx4ULm1fkOZmZlhYWFcLtfNzW3FihUvXryQysBms6kzWFBQkJ6eTs7j1atXq6qqpN6ESe7s2bPHjx+/f/++vHGN+vr6vLy8tLS0wsLC4uPjDx06RNL/9a9/7du3b926daampl5eXu3t7Uqs9RSBwet6enqmT5/+9OlTjLFYLLa2tk5NTZXKs2bNmq+++oosf/LJJ1FRURjjiooKDQ2Nrq4ujHF3dzebzS4vL1du3d/E3/72t+DgYLJ87ty5RYsWSWUQi8XUclZWlra2Nkn55ptvoqOjlVbPMZGXl6ejozMwMIAxbmhoUFdXb2hokMrj5+d3+fJlqcTk5GRHR0eynJWVZWJiMjg4qIQKj1JwcHBsbCxZ/vjjj2NiYmgyOzs7Hz16lCyHhIScOnVq3Os3DhISEpYvXy5z04kTJ9zd3clyeno6h8MRCoUYYzs7O+qMc7ncQ4cOKaeqU8jU+A2oTOXl5QwGw8HBASHEYDA8PT3z8/Ol8uTn51PzZHh5eZEMjx8/tre3nz59OkJo2rRpixYtevz4sXLr/iby8/O9vb3Jsre3d3Fx8cDAgGQG6tocIcTj8YyNjamUgoKCjz76KDY2tr6+XmkVHo28vDx3d3cyiIKpqamlpaXM8epTUlK2bt16/PjxV69ekRTJM+7h4cHn82tra5VW7TcmeXKpD6pMz58/f/HiheRF8NWrVz/++ONvv/22r69v3CuqFFL/tjwej8fjdXV1VVRUDP93BpIgTkhramrS09OjVg0MDKhxRwiMcXNzM5WHytDc3Kyvr09l09fXl9pxcpI8XgMDA4xxU1OTzJx8Pn/Pnj0HDhwgq1ZWVsHBwfb29j/++OP8+fPLysqUVONRUOQceXt7e3h42Nranjt3bunSpSRqSr5LTCZTV1dX3rs0eQiFQj6fP/yDKtOJEyd+97vfUQ/0Ll682MfHZ+7cudevX3d2dv51hArJk6iurj5t2rSmpiZyHqlPBf279JsF/djSNDU1JX9QCwQCqe5oBoOhoaFB5aEysNlsqR21tLSUUuVRkTxegUCAEJJZ7c7OzuXLl//hD38ICwsjKe+++y5Z2Lx5s0gkio+PP3HihFKq/OYUOUf79+8nC9HR0XZ2dqmpqaGhoWw2e3BwkMrz6tWryX9yWSyWurr68A/qcIODgykpKRcvXqRSyHg5CKGYmBh7e/uLFy9GRUWNd4XHm8yzT57qHRgYIE8b0LxLv2VwPSGNw+G0trZSP6Bqa2vNzc2l8sycOZNqdqipqSEDp3M4HMm2iNraWmpA9clM6ljYbLbkL26iu7t7xYoVPj4+sbGxMgtZsGDBlPgVJnmwYrG4rq6O5hypq6vPmTOHHJfkjq2trf39/cM/FZOQ5GeS+qAOd+3aNW1tbT8/v+GbWCyWnZ3dlDi5v2jmzJk//fQTWW5oaBgaGjI3NzcxMVFVVaXeJZn/7wD6sWVwcHBISkrCGNfW1mpra1dVVWGM6+rqLl68SDJ88cUXwcHBYrFYKBR6eXklJiZijPv7+3V1dR88eIAxzs7O1tHR6evrm7iDUFRqaqq1tXVPTw/GePv27eHh4ST9v//9b2lpKca4t7fX29t748aNkh3aGGMej0cWuru7nZyc9u/fr9yKv4nW1lZNTc1nz55hjFNTU8m8JhjjwsLCu3fvYowFAkFbWxvJ/Pz5cy0trUePHpEMenp6TU1NGOO4uDgfH5+JOoQR2bt375o1azDGQ0NDS5cuPXbsGMZYLBafOXOGz+dT2bhc7pdffkmtDg0NNTc3k+Uff/xRR0cnLS1NuRV/c8P7samDzc3NNTQ0JMuxsbGBgYEkw9q1a/fs2YMx7urqmjVrVnp6utJrPdlBnJAhMzPT0NAwICDA2Nh43759JDE1NZU032OM29raHBwcnJ2d7e3tPT09e3t7Sfq///1vfX39wMBAfX39M2fOTEztR0goFK5bt87KysrLy8vCwuLly5ck3dXVlcQ/Mlbj7NmzrX7W2dmJMXZ0dJw3b56Pj4+ent7bb789JYIixvjIkSMGBgbkHF27do0k7t27l9z0xePxtLS0XFxclixZoq2tTd3VhjHetm2bmZmZn5+fiYlJfn7+xNR+hPh8vr29vYuLy4IFC3x8fMg5EgqFCKG8vDySp66uTlVVtaamhtqru7tbU1PTycnJw8NDW1ubfIdOfjdu3LCystLX12ez2VZWVrt27cIYk5vac3NzSZ6YmBgOh+Pn52dqalpYWEgSy8rKOBwOuTs8PDxc6vcQwBjDuB2ydXd3FxcXW1hYUIOHDwwMdHV1GRkZkVWRSFRUVMRisRwcHCTvCGppaamoqLCzs6NyTgllZWWdnZ1OTk7U6MdtbW1sNpv0XvT390tm1tHRYTAYQqGQ7DV79uwp0cJGaWhoqKqqWrBgAdWr2dPTIxQKSS9uT09PWVmZWCy2s7Oj+nWJ6urq+vp6Jyenyd85QRGJRIWFhWpqagsXLqQ+qI2NjQYGBuR5yaGhof7+fqmHJPr6+srKyoaGhuzs7CRv65jMBgcHJfvb1dTUyGmSPFiEUFVVVWNjo5OTk+TwRwKBoLCwUF9fHx6ykwniBAAAADrQjw0AAIAOxAkAAAB0IE4AAACgA3ECAAAAHYgTAAAA6ECcAEAhxcXFPB6PLPP5fJkDCALwqwRxAgCFLFu27MiRI2T57NmzTk5OQ0NDoy/2xYsXjx49Gn05AIwfGAcQgBGzs7N79913x2Rqpri4uJycnPLy8tEXBcA4gTgBwIitWrVq1apVE10LAJQE2p3AhKmvr1+xYsXhw4eplPLyci6Xe/r0aXm7iESiw4cPu7u7GxkZ2drarl+/nprLuqura+fOnWTElKVLl0qOko0Qam9v3759u42NjbGxsaen55UrV6hNT58+DQwMLCoq+vTTT+fMmWNlZYUQwhgnJCTMmzfP1NQ0ODi4oqJCsrSrV68uX76cmhB35cqVycnJKSkpzs7OZmZmXC5Xcq6boqKijRs32tvbm5qaurq67tq1q6enh2z64osvbt++XVdXFxgYGBgYGBERQdIFAsGBAwccHBz09fUdHR0PHz4M4yaACQTXE2DCcDgcT0/PnTt3vvXWWwEBAQKBICwsbHBw8L333pOZH2McFhZ2+fLlyMjILVu2CASCzMzMiooKa2vrwcHBwMDAkpKSPXv2WFlZXblyJSwsrKWlZdu2bQihV69e+fv7v3z58tNPP7WwsPjuu+/WrVv3z3/+Mzo6GiHU3t6ekZHx/vvvczicbdu2kUk4vv7663379kVGRnK53MLCQi6XS81thxCqqam5c+eOWCxmMpkIoXv37tXX14tEoujoaFVV1bi4uJCQkKqqKjKCUEZGhkAg+Oijj/T09MrKyhITE0tKSm7fvo0Q8vT0vHv37v/+97/Q0FCEEJkMUSgUrly5srCwcPv27XPnzi0qKtq9e3ddXV1cXNx4nxEAZJvQUQjBb51IJOJyucbGxo2NjZs2bdLQ0CAzk8uUmpqKEIqLixu+6eTJkwih7777jqyKxWIulztt2rTu7m7885C3169fp17U19dXV1e3v78fY3z37l2E0PLly6mBQtva2jQ0NCIiIqjyycQb1Mip8fHxCCFqimx1dXUzMzPyWhjj7OxshNDwSbaJS5cuIYQqKirI6gcffGBnZyeZISkpicFgPHz4kEqJj49nsVjDp/IGQDmg3QlMJBUVleTkZBUVFR8fn6SkpGPHjpGZyWVKTU1ls9lbt24dviknJ8fAwGDdunVklcFgfPjhhz09PeQrOycnx9zcPDg4mHrR6Ojojo6OvLw8qoQNGzZQw6kWFRUJBALJGdx+cTa31atXT5s2jSy7urqqqKjU1NRQW/v6+m7evJmUlHTw4EFyQ61UQ5ak77//3sbGZv78+R0/8/f3FwqFxcXF9HUAYJxAuxOYYMbGxn/5y1+2bNni4+MTGRlJpYeGhpJf+gihmJiY2NjY+vr6WbNmqampDS+kurrawsJC8gYka2trhBCZiK26utrS0lJy+HfSCSE5TZvk0OhkdjNqSHmEkJGREf1Y4sbGxtSyqqqqqqoqNcb11atXo6OjxWLx/PnzqflTW1tb5RX1008/VVZWDh/Nm5qLDQAlgzgBJlh7e/vBgwf19PSys7Ozs7M9PDxIenR0NHVP0fz58xFCmpqaXV1dMgthMpnd3d2SKSQnmf2YyWR2dHRIbiWZyVaCxfr//wXST0D1NiOEBgcHJfsnFIcx/vDDD319fS9cuECmQKisrCQNTfJ2UVdXd3NzS0tLk0qXnC8BAGWCdicwkTDGUVFRvb29T5488fb2/v3vf9/W1kY2BQYGfvAzNzc3hJCLi0tzc/Pz58+Hl+Pg4EAmEaJSsrKyEEKLFi0iWysrK5ubm6W2ymvjIpPVSD7+lpOTIxaL3+AAm5qaWltbV69eTc2T8/DhQ8kM6urq5AqD4ubmVlJSMjQ0pPs6agopAJQM4gSYSImJidevXz99+vTs2bOTk5MFAgHpPZaZOSoqSk9PLyIigroXtqSkhCxHRkaqqKjExMT09vYihHJzcxMSEvz8/ObOnYsQ2rhxo0gk2rx5M5mY7+HDh99++21QUNDs2bNlvpC9vb2rq+vXX39dWVmJEOLz+bt27Xqzp+oMDQ21tLS+//57EgyePn26f/9+yQxWVlb19fV5eXkdHR3kGmj79u0IofXr11PDhHR2dh49elRysjYAlGpCe9HBb9rjx4/V1NR2795Npdy8eZPBYCQkJMjb5dGjR6QjYebMmUZGRgwG49atW2RTSkqKtra2urr6zJkzEUKOjo51dXXUjqdPn9bU1NTQ0CC7u7q6NjY2kk2kF4SaQpmoqKggHR5z5sxRVVXdu3evgYEBzf1Of/3rXyV3V1dX//LLL8ny8ePHWSyWnp6etbW1hoZGYmIiQujkyZNka2trq5OTE/lntLa2Jonp6elmZmYMBmPWrFmmpqYIIRMTE+p+KgCUDOY9BROmpqamra1t4cKFVJsMQujFixdisdje3l7eXgKB4IcffqipqdHV1XVxcbG0tKQ2tbW1ZWZmdnZ22tjYeHp6kocbKHw+PzMzs6enx9bW1sPDg7o+6OnpqaysnDt3rlRPdX9//+3bt8m04Q4ODsXFxQYGBubm5qQoHo9HGrUQQoWFhSYmJmZmZtS+hYWFpqam5CseIfTy5cvc3Fwmk+nj42NkZESmXjcwMKDyNzU1NTU1sVist956i6QMDAw8fPiwurpaW1t7zpw5Tk5OYzJMCABvAOIEAAAAOvALBQAAAB2IEwAAAOhAnAAAAEAH4gQAAAA6ECcAAADQgTgBAACADsQJAAAAdCBOAAAAoANxAgAAAB2IEwAAAOhAnAAAAEAH4gQAAAA6ECcAAADQgTgBAACADsQJAAAAdCBOAAAAoANxAgAAAB2IEwAAAOhAnAAAAEAH4gQAAAA6ECcAAADQgTgBAACADsQJAAAAdCBOAAAAoANxAgAAAB2IEwAAAOhAnAAAAEAH4gQAAAA6ECcAAADQgTgBAACADsQJAAAAdCBOAAAAoANxAgAAAB2IEwAAAOhAnAAAAEDn/wCHUtJZL7UxrwAAAABJRU5ErkJggg==",
+ "image/svg+xml": [
+ "\n",
+ "\n"
- ]
- },
- "execution_count": 25,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "using IterativeSolvers: cg!\n",
- "N = 80\n",
- "u = zeros(N,N)\n",
- "fill_boundary!(u)\n",
- "A,b = generate_system_sparse(u)\n",
- "x = zeros(length(b))\n",
- "_,ch = cg!(x, A, b, reltol=1e-5,log=true)\n",
- "display(ch)\n",
- "u[2:end-1,2:end-1] = x\n",
- "visualize(u)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 26,
- "id": "30c6e04e",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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",
- "image/svg+xml": [
- "\n",
- "\n"
],
"text/html": [
- "\n",
- "\n"
- ]
- },
- "execution_count": 26,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "Ns = [20,40,80,160]\n",
- "reltol = 1.0e-5\n",
- "iters = zeros(size(Ns))\n",
- "for (i,N) in enumerate(Ns)\n",
- " u = zeros(N,N)\n",
- " fill_boundary!(u)\n",
- " A,b = generate_system_sparse(u)\n",
- " x = zeros(length(b))\n",
- " _,ch = cg!(x, A, b, reltol=reltol,log=true)\n",
- " iters[i] = ch.iters\n",
- "end\n",
- "plot!(plt,Ns.^2,iters,xaxis=:log10,yaxis=:log10,label=\"reltol=$reltol (CG)\",marker=:auto)\n",
- "plt"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "5396554c",
- "metadata": {},
- "source": [
- "The number of iterations needed to converge is much lower with the conjugate gradient method than with the Jacobi method. However, the number of iterations still increase with the problem size, so there is still room for improvement. "
- ]
- },
- {
- "cell_type": "markdown",
- "id": "92bfd7d7",
- "metadata": {},
- "source": [
- "### Number of iterations\n",
- "\n",
- "We can prove that the number of iterations to achieve a relative error of $10^{-s}$ increases as $O(s \\sqrt{\\kappa(A)})$. As a reminder, the condition number of A $\\kappa(A)$ is ratio between the largest and smallest eigenvalues of A: \n",
- "$$\\kappa(A)=\\dfrac{\\lambda_{max}(A)}{\\lambda_{min}(A)}$$\n",
- "\n",
- "In our example, it can be shown that $\\kappa(A) = O(N^2)$. Thus, the number of iterations scales as $O(s N)$ for the conjugate gradient method. Remember that the number of iterations scales as $O(sN^2)$ for the Jacobi method.\n"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "1bb8ffe6",
- "metadata": {},
- "source": [
- "### Goal\n",
- "\n",
- "The conjugate gradient method provides some improvement to the Jacobi method, since the number of iterations increases more slowly with the problem size. However, the ultimate goal is to find an iterative method whose number of iterations is independent of problem size."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "956564d5",
- "metadata": {},
- "source": [
- "### Preconditioner\n",
- "\n",
- "To achieve this goal, we will apply a [preconditioner](https://en.wikipedia.org/wiki/Preconditioner) to transform the original problem into a format that is easier to solve. \n",
- "\n",
- "A preconditioner is simply a linear function $M$ such that \n",
- "$$M(b) \\approx x, \\text{ with } Ax=b \\text{ for any } b.$$ \n",
- "\n",
- "When we have found such a function $M(b)$, we can solve the _preconditioned problem_ $(MA)x = Mb$, which is equivalent to $Ax=b$.\n",
- "\n",
- "The way that this preconditioning affects the number of iterations is that it reduces the condition number of $A$: \n",
- "\n",
- "$$ \\begin{align}\n",
- "&M(b) \\approx x, \\text{ with } Ax=b \\text{ for any } b \\\\\n",
- "&\\rightarrow M(b) \\approx A^{-1}b \\\\\n",
- "&\\rightarrow M \\approx A^{-1} \\\\\n",
- "&\\rightarrow M A \\approx I \\text{ (Identity matrix)} \\\\\n",
- "&\\rightarrow \\kappa (MA) \\approx 1 \\\\\n",
- "&\\rightarrow \\text{ Conjugate gradients will be fast when solving } (MA)x = Mb \\Longleftrightarrow Ax=b.\n",
- "\\end{align}$$\n",
- "\n",
- "\n",
- "\n",
- "\n"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "89563cc4",
- "metadata": {},
- "source": [
- "### How to build a preconditioner ?\n",
- "\n",
- "- $M=A^{-1}$ (exact preconditioner, but as costly as solving the original problem)\n",
- "- $M=I$ (no extra work, but slow convergence)\n",
- "- We need a trade-off (maths + computer science problem)\n"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "4338ee30",
- "metadata": {},
- "source": [
- "### Jacobi Preconditioner"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "id": "cd608f2f",
- "metadata": {},
- "outputs": [],
- "source": [
- "struct JacobiPrec{T}\n",
- " u::Matrix{T}\n",
- " f::Matrix{T}\n",
- " niters::Int\n",
- "end\n",
- "function jacobi_prec(N;niters)\n",
- " u = zeros(N,N)\n",
- " f = zeros(N,N)\n",
- " JacobiPrec(u,f,niters)\n",
- "end\n",
- "function LinearAlgebra.ldiv!(x,M::JacobiPrec,b)\n",
- " M.u[2:end-1,2:end-1] .= 0 \n",
- " M.f[2:end-1,2:end-1] = b\n",
- " u,_ = jacobi!(M.u,M.f,reltol=0,maxiters=M.niters)\n",
- " x[:] = @view u[2:end-1,2:end-1]\n",
- " x\n",
- "end"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "id": "858ac6ba",
- "metadata": {},
- "outputs": [
- {
- "data": {
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",
- "image/svg+xml": [
"\n",
"\n"
- ],
- "text/html": [
- "\n",
- "\n"
]
},
- "execution_count": 16,
+ "execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
@@ -3769,8 +4211,10 @@
"u = zeros(N,N)\n",
"fill_boundary!(u)\n",
"A,b = generate_system_sparse(u)\n",
- "M = jacobi_prec(N,niters=10)\n",
+ "# Generate preconditioner\n",
+ "M = jacobi_prec(N,niters=1000)\n",
"x = zeros(size(b))\n",
+ "# Compute solution as x=b/M\n",
"ldiv!(x,M,b)\n",
"u[2:end-1,2:end-1] = x\n",
"visualize(u)"
@@ -3778,185 +4222,267 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 35,
"id": "1750ecb1",
"metadata": {},
"outputs": [
{
"data": {
- "image/png": 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",
+ "image/png": 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- "execution_count": 17,
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"metadata": {},
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}
@@ -3971,6 +4497,7 @@
" A,b = generate_system_sparse(u)\n",
" M = jacobi_prec(N,niters=100)\n",
" x = zeros(length(b))\n",
+ " # Provide preconditioner to conjugate gradient method\n",
" _,ch = cg!(x, A, b, Pl=M, reltol=reltol,log=true)\n",
" iters[i] = ch.iters\n",
"end\n",
@@ -3978,248 +4505,368 @@
"plt"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "26f7e342",
+ "metadata": {},
+ "source": [
+ "Observe that the Jacobi preconditioner achieves that the CG method needs fewer iterations. However, the number of iterations still increases with the problem size. "
+ ]
+ },
{
"cell_type": "markdown",
"id": "43fb5082",
"metadata": {},
"source": [
- "### How can we improve the Jacobi method?"
+ "### How can we improve the Jacobi method?\n",
+ "\n",
+ "We can optimize the Jacobi method to obtain a better preconditioner for the CG method. Run the following code cell again with a grid size of $N=10$ and $N=100$. "
]
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 38,
"id": "db9397dd",
"metadata": {},
"outputs": [
{
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",
+ "image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
]
},
- "execution_count": 18,
+ "execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "N = 10\n",
+ "N = 100\n",
"u = zeros(N,N)\n",
"fill_boundary!(u)\n",
"A,b = generate_system_sparse(u)\n",
@@ -4545,17 +5302,29 @@
"visualize(u)"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "bf76a64b",
+ "metadata": {},
+ "source": [
+ "The main reason that the preconditioner performs badly for larger problem sizes is that it takes more time to update the interior values of the grid. The larger the grid, the longer the Jacobi method needs to propagate the values from the outer boundary to the interior of the grid. "
+ ]
+ },
{
"cell_type": "markdown",
"id": "c04df158",
"metadata": {},
"source": [
- "### Multi-grid method\n"
+ "### Multi-grid method\n",
+ "\n",
+ "The [multi-grid method](https://en.wikipedia.org/wiki/Multigrid_method) is the second building block of the fast solver for our Laplace equation. \n",
+ "\n",
+ "The multi-grid method achieves a faster convergence of the Jacobi method by starting to solve the coarse problem first and then stepwise increasing the grid resolution. On each resolution level, a few steps of the Jacobi method are performed (only 2 steps per level in this example). Next, the resolution of the grid is increased and the Jacobi method is run again. This process is repeated until we reach the desired grid size. Since the Jacobi method converges after a few iterations on very small grids, the values are propagated to the center much more quickly than without using the multi-grid method."
]
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 39,
"id": "ee7679f4",
"metadata": {},
"outputs": [
@@ -4565,7 +5334,7 @@
"prolongate! (generic function with 1 method)"
]
},
- "execution_count": 19,
+ "execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
@@ -4593,7 +5362,7 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 40,
"id": "260bbcb0",
"metadata": {},
"outputs": [
@@ -4613,7 +5382,7 @@
"Plots.AnimatedGif(\"C:\\\\Users\\\\gelie\\\\Home\\\\TeachingInnovationProject\\\\XM_40017\\\\notebooks\\\\a2.gif\")"
]
},
- "execution_count": 20,
+ "execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
@@ -4638,211 +5407,288 @@
"id": "6122ac8b",
"metadata": {},
"source": [
- "### Multi-grid preconditioner"
+ "### Multi-grid preconditioner\n",
+ "\n",
+ "Let's see what happens when we use the CG method in combination with a multi-grid preconditioner. In the following code cell, we use a multi-grid preconditioner from the package `Preconditioners`."
]
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 41,
"id": "8a5e1031",
"metadata": {},
"outputs": [
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mPrecompiling Preconditioners [af69fa37-3177-5a40-98ee-561f696e4fcd]\n"
- ]
- },
{
"data": {
- "image/png": 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",
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}
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},
{
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- "id": "ab13519f",
+ "id": "63c406e0",
"metadata": {},
"source": [
- "### Number of iterations\n",
- "\n",
- "\n",
- "- The number of iterations to achieve a relative error of $10^{-s}$ increases as $O(s)$\n",
- "- The cost of each iteration is proportional to the number of grid points\n"
+ "The number of iterations is now constant for different problem sizes. Thus, we have finally achieved to build an algorithmically scalable solver by combining the conjugate gradient method and the multi-grid method!"
]
},
{