{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Step 5 : residuals of SDC sweeps\n", "\n", "📜 _Once we have defined our SDC method after choosing :_\n", "\n", "- _some_ $Q$_-coefficients (underlying time-stepping method, cf. [step 1](./01_qCoeffs.ipynb)),_\n", "- _one_ $Q_\\Delta$ _approximation (preconditioner for SDC, cf. [step 3](./01_qCoeffs.ipynb)),_\n", "\n", "_we need to evaluate the quality of this new time-integration method._ \n", "_For that, we can have a look at the **residuals**._\n", "\n", "\n", "Starting from the SDC sweep formula\n", "\n", "$$\n", "u^{k+1} - \\lambda\\Delta{t}Q_\\Delta u^{k+1} = u_n + \\lambda\\Delta{t}(Q-Q_\\Delta)u^k,\n", "$$\n", "\n", "the residual at sweep $k$ for the Dahlquist problem is defined as :\n", "\n", "$$\n", "r^k = u_n - A u^{k} = u_n + \\lambda\\Delta{t}Q u^k - u^k.\n", "$$\n", "\n", "From an implementation perspective, it can be interpreted as the \n", "**difference of the SDC solution versus the solution obtained with the underlying time-integration method**\n", "defined by the $Q$-coefficients.\n", "\n", "For instance, if the $Q$-coefficients are obtained using a collocation method, \n", "then the numerical solution at node $u_m := u(t_0 + \\tau_m\\Delta{t})$ should satisfy :\n", "\n", "$$\n", "u_m = u_0 + \\int_{t_0}^{t_m} \\lambda u(s)ds,\n", "$$\n", "\n", "where the integral is approximated with the quadrature rule stored in the $Q$ matrix. \n", "Hence if we note $u^C$ the collocation solution, then we have\n", "\n", "$$\n", "u^C = u_n + \\lambda\\Delta{t}Q u^C,\n", "$$\n", "\n", "which means that the SDC residuals for this solution are zeros.\n", "\n", "> ⚠️ **Residuals** and **time-integration errors** are not the same, \n", "> since the underlying method for SDC has its own time discretization error, \n", "> even if the underlying method is usually chosen to be very accurate.\n", "\n", "Let's setup (as before) the Dahlquist problem ..." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# Problem settings\n", "lam = 1j\n", "T = 4*np.pi\n", "u0 = np.exp(1j*np.pi/6)\n", "\n", "nSteps = 12\n", "dt = T/nSteps\n", "times = np.linspace(0, T, nSteps+1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... and the definition of our SDC method :" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from qmat import Q_GENERATORS, genQDeltaCoeffs\n", "\n", "coll = Q_GENERATORS[\"coll\"](nNodes=4, nodeType=\"LEGENDRE\", quadType=\"RADAU-RIGHT\")\n", "nodes, weights, Q = coll.genCoeffs()\n", "\n", "QDelta = genQDeltaCoeffs(\"BE\", qGen=coll)\n", "P = np.eye(nodes.size) - lam*dt*QDelta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We build our SDC loop, and this time store the residuals for each sweeps, time-steps and nodes, \n", "along with the numerical error versus the analytical solution :" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "nSweeps = 4\n", "uNum = np.zeros(nSteps+1, dtype=complex)\n", "residuals = np.zeros((nSweeps+1, nSteps, nodes.size), dtype=complex)\n", "error = np.zeros((nSweeps+1, nSteps, nodes.size), dtype=complex)\n", "\n", "uNum[0] = u0\n", "for i in range(nSteps):\n", "\n", " uNodes = np.ones(nodes.size)*uNum[i] # initial guess\n", "\n", " # Initial residuals & error\n", " residuals[0, i] = uNum[i] + lam*dt*Q @ uNodes - uNodes\n", " error[0, i] = uNodes - u0*np.exp(lam*(times[i] + dt*nodes))\n", "\n", " # Sweeps\n", " for k in range(nSweeps):\n", " b = uNum[i] + lam*dt*(Q-QDelta) @ uNodes\n", " uNodes = np.linalg.solve(P, b)\n", "\n", " # Residual & error after sweep\n", " residuals[k+1, i] = uNum[i] + lam*dt*Q @ uNodes - uNodes\n", " error[k+1, i] = uNodes - u0*np.exp(lam*(times[i] + dt*nodes))\n", "\n", " uNum[i+1] = uNum[i] + lam*dt*weights.dot(uNodes) # prolongation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we take the $L_\\infty$ norm on each nodes ..." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "residuals = np.linalg.norm(residuals, axis=-1, ord=np.inf)\n", "error = np.linalg.norm(error, axis=-1, ord=np.inf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... and plot this versus time for each sweeps :" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "for k, sym in zip(range(nSweeps+1), [\"o\", \"^\", \"s\", \">\"]):\n", " p = plt.semilogy(times[1:], residuals[k], sym+'-', label=f\"$k={k}$\")\n", " plt.semilogy(times[1:], error[k], sym+'--', c=p[0].get_color())\n", "plt.grid(); plt.xlabel(\"time\"); plt.ylabel(r\"residuals & error(--) ($L_\\infty$ norm)\"); plt.legend();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that residuals are a good approximation of the numerical error for the first sweeps,\n", "but we also see some discrepancies for the last sweeps.\n", "While the residuals are relatively constant over time, the time-discretization error increases for the last sweeps,\n", "which is not shown by the residuals.\n", "\n", "This is because we only did 4 SDC sweeps here, so the SDC approach is way less accurate than the underlying collocation\n", "method using 4 Legendre Radau-Right nodes (order 7).\n", "This can be observed more in details by looking at different total numbers of sweeps $K$. \n", "For that, we can use the `monitor` parameter of the `solveDahlquistSDC` function (simplifies the code), \n", "extract the maximum $L_\\infty$ norm over all time-steps,\n", "and plot this versus the sweeps :" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from qmat.sdc import solveDahlquistSDC\n", "\n", "for nSweeps, sym in zip([10, 8, 6, 4], [\"^\", \"o\", \"s\", \">\"]):\n", "\n", " uNum, monitors = solveDahlquistSDC(\n", " lam=lam, u0=u0, T=T, nSteps=nSteps, nSweeps=nSweeps,\n", " Q=Q, QDelta=QDelta, weights=weights,\n", " monitors=[\"residuals\", \"errors\"] # list of data we want to monitor for all nodes, time-steps and sweeps\n", " )\n", "\n", " # Extract maximum residuals and errors over time\n", " residuals = np.max(np.linalg.norm(monitors[\"residuals\"], axis=-1, ord=np.inf), axis=-1)\n", " errors = np.max(np.linalg.norm(monitors[\"errors\"], axis=-1, ord=np.inf), axis=-1)\n", "\n", " p = plt.semilogy(residuals, sym+'-', label=f\"$K={nSweeps}$\")\n", " plt.semilogy(errors, sym+'--', c=p[0].get_color())\n", "\n", "plt.grid(); plt.xlabel(\"sweeps\"); plt.ylabel(r\"max. residuals & error(--) ($L_\\infty$ norm)\")\n", "plt.ylim(1e-6, 2); plt.legend();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here 8 sweeps are required to reach an accuracy below $1e^{-4}$, which is the accuracy of the collocation method.\n", "While the residuals decrease is almost identical when $K$ varies, this is not the same for the errors, \n", "that follows the residuals decrease only when $K$ is large enough.\n", "\n", "> 💡 If the time-discretization error of the underlying method is known a priori, then targeting a \n", "> **residual level close to the time-discretization error level** can be an acceptable stopping criterion.\n", "\n", "In practice, residuals can be also monitored to evaluate the quality of a $Q_\\Delta$ approximation. \n", "For instance, if we use the same SDC method, but using a trapezoidal rule for $Q_\\Delta$, \n", "and monitor residuals & errors ... " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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ZTdC4R8mObYDw8HDmzZvHwoUL6d27N61atWLWrFmF7uvn54efn1+x7f3+++/07t27wPY33niD2bNn89RTTwHQvn17Ll68yKJFi6QgKs/UvMrsroEvLyB89RYcMqHGrjCYr0oMIYQQhtJoSn7aqtnDuVeTJcdS+DwiTe7rzR4GrYUpU3L+/Hlu3bqFp6cnnp6ebNiwgaeeeoqWLVsWWqSU5pRZWloaWm3+6csWFhZy2b14MAtLS861daBDeCr14+DCicM0aeOtdiwhhBCmpLXIvbT+v88DdyaP5tHk/vHYhyYvhiD3dJlGo6FTp05A7jyid999l+eee469e/fi6emZb//SnDIbOnQoCxcupFGjRrRr147w8HCWLVvGiy++WNpvo9TkKrMKoN3U91HI/StxYMlUteMIIYQoC22HwZivwck1/3Ynt9ztZbQOUVhYGC1atKBatWp52+bOncuQIUMYNmwYV6+W8LRfCXz66aeMGjWKSZMm0aZNG2bOnMmrr77KggULTHYMY8kIUQXg8dAgdrrMwC0e6p5KUDuOEEKIstJ2GLR+PHdOUcp1cKybO2eoDEaG7vL398ff3z/fNo1GQ2BgoMmPVa1aNVasWMGKFSvybdfr9WRkZJj8eIaQEaIKouHK9eRowfUm7P9lvdpxhBBClBWtBbj3hvajcv8sw2JI3CMFUQXRslMvzjfJ/UtxadNnKqcRQgghKhcpiIqh1s1di5LTM3cydbMjyWSmp6mcRgghhKg8pCAqhq+vL1FRURw6dEjtKABUb9QSAIdM2LZ0kspphBBCiMpDCqIKpP/Tb5Jqm/vYKfgfdcMIIYQQlYgURBWIhaUl59vkrj5a/zpciY5SOZEQQghROUhBVMG0n/4hCrk/uJCFr6odRwghhKgUpCCqYNp0HUDcnQVCG0XEqxtGCCGEqCSkIKqArnVvDoBzChzY/pW6YYQQQohKQAqiCmjwO5+Tc+cnF7PhU3XDCCGEEJWAFEQVkFPNOkT2qQtA/eg0srMyVU4khBCitGJTYom6GVXkV2xKbJkev0+fPkyYMCHfthUrVmBvb8/KlStNdpwrV67w3HPPUatWLezt7enUqROhoaEma99Yci+zCuqx97/j/COPUisZgj6by+OTFqkdSQghhJFiU2IZsnUIWbqsIvextrDm1+G/4uroWuQ+xlIUhYiICMaMGQNAWloar7zyCjt37iQoKIhevXqZ5DiJiYn07NmT/v378/vvv1OnTh3OnTtHjRo1TNJ+aUhBVEHVrF2f6Ja2tIvMIOv37SAFkRBCVFiJmYnFFkMAWbosEjMTy6QgOnPmDLdv38bT05Po6GhGjBiBnZ0dYWFhuLm5mew4ixYtomHDhnz55Zd525o0aYJeryc5OdlkxzGGnDIrRnm7dce/ZTfM/SVteTaHuCvnVE4jhBDifoqikJadVqKvjJyS3ek9IyejRO0pimJQ1tDQUCwsLLh+/Tre3t507dqVPXv2FFoM+fn54ejoWOzX3r17Cz3OL7/8gre3N6NHj6ZOnTp07tyZ9evLxw3LZYSoGL6+vvj6+pKcnEz16tXVjlNA5+ffRP/7RLQK7Jw/gafX7VE7khBCiDvSc9LptrGbSdsc/8f4Eu33zzP/YG9lX+J2w8LCABg1ahSffPIJvr6+Re47ceLEvFNrRalfv36h28+fP8/q1auZMWMGb731FgcPHmTKlClYWVkxfPjwEuctC1IQVWCtO/dltzPUTYBG4XFqxxFCCFFBhYaGMmDAACIjIx84wdnZ2RlnZ2ejjqPX6/H29sbPzw+Azp07c/z4cdauXSsFkSida92bUfe3c9S8DYf/CsT74bFqRxJCCAHYWdrxzzMlu+/kyYSTJRr92fDYBlo7ty7RsQ0RHh7OvHnzWLhwIb1796ZVq1bMmjWr0H39/PzyCpqi/P777/Tu3bvAdldXV9q2bZtvW5s2bfjpp58MylsWSlUQZWdnc+3aNdLS0qhdu7bRFaMw3tB533H+94ew1MPFT/ykIBJCiHJCo9GU+LSVraVtifcz5FRYSZw/f55bt27h6emJp6cnGzZs4KmnnqJly5aMGDGiwP6lOWXWs2dPTp06lW/b6dOnady4sfHfgIkYXBClpKTw3Xff8f3333Pw4EEyM++tgdOgQQN8fHz4z3/+U24nIlc2DtWqc6GhluYX9TQ9l4UuJwcLSxn4E0IIUTKhoaFoNBo6deoE5M4jevfdd3nuuefYu3cvnp6e+fYvzSmz6dOn06NHD/z8/BgzZgwHDx5k3bp1rFmzprTfRqkZdJXZ8uXLadKkCevXr+fhhx9m8+bNREREcOrUKQ4cOMB7771HTk4OAwYM4LHHHuPMmTNllVvcx3JsbqVumw3bPp6mbhghhBAGq2lTE2sL62L3sbawpqZNTZMfOywsjBYtWlCtWrW8bXPnzmXIkCEMGzaMq1evmuxYXbp0YcuWLXz//fd4eHjw/vvvs2LFCp599lmTHcNYBg0l7N+/n127dtG+fftCX+/atSsTJkxgzZo1fP755+zZs4cWLVqYJKgo2qAJ77Hzix9wi4fs/+1TO44QQggDuTq68uvwX0nMTCxyn5o2NctkDSJ/f3/8/f3zbdNoNAQGBpr8WABDhgxhyJAh+bbp9foyOZYhDCqIfvzxxxLtZ2Njw6RJk4wKJIyTPnYwBGzH/XQmt27GUqOW6f/SCCGEKDuujq5lUvCIkpGFGSuJga/6kVANHDLhz0/fUDuOEEIIUaGUavZtRkYGR48eJS4ursBw17Bhw0oVTBjGytqGK+52OB9Np84foTBP7URCCCFExWF0QfTHH3/w/PPPEx8fX+A1jUaDTqcrVTBhOF2D+nD0LC63ICLkZzr1eULtSEIIIUSFYPQps8mTJzN69GhiY2PR6/X5vspjMTRixAhq1qzJqFGj1I5SZoa//x05WtAA51bMVTuOEEIIUWEYXRDFxcUxY8YM6tata8o8ZWbKlCl8/fXXascoU3YOTlxskPsjdT+buyaREEIIIR7M6IJo1KhR7N6924RRylb//v3zrbFQWVk9k7tStV0W/LrydZXTCCGEEBWD0QXRypUr2bx5My+88AJLly7lk08+yfdliJCQEIYOHYqbmxsajYatW7cW2GfVqlW4u7tja2uLl5cXe/fuNTZ6pTbwhbmk3FkB3vqXYHXDCCGEEBWE0ZOqN27cyI4dO7Czs2P37t1oNJq81zQaDVOmTClxW6mpqXTs2JEXX3yRJ598ssDrgYGBTJs2jVWrVtGzZ0/Wrl3LoEGDiIqKolGjRgB4eXnlu43IXUFBQbi5uRn0vWVmZuZrKzk5Gci9d1t2drZBbT3I3fZM2e75VvZ0OJJGw1iF+OtXqO5cx2RtV1Rl0c+iIOln85B+Nh9D+jo7OxtFUfLm04qSUxQl709D+06v16MoCtnZ2VhYWOR7zZC/IxrlbgoD1atXjylTpjB79my0WtMtZ6TRaNiyZQvDhw/P29atWzc8PT1ZvXp13rY2bdowfPjwAqtrFmf37t2sXLmSTZs2FbvfvHnzmD9/foHtGzduxN7etDfVKwvJcefpvGwdFgrsG9yCOn1fUjuSEEJUepaWltSrV4+GDRtibV38bTiE6WRlZXHp0iWuXbtGzr/mzqalpfHMM8+QlJSEk5NTse0YPUKUlZXF2LFjTVoMFXWc0NBQZs+enW+7j48P+/fvL5NjzpkzhxkzZuQ9T05OpmHDhvj4+DywQw2VnZ1NcHAwAwYMwMrKymTt/rR7Ix1DU6h9OprBiwabrN2Kqqz6WeQn/Wwe0s/mY0hfZ2RkcOnSJRwdHbG1Ldnd6++nz8pCY2WV74yLOfXr149mzZrx+eef5237+OOPefvtt1m0aBG+vr4mPd6HH37I22+/zZQpU1i2bBm3b9+mWrVqBn//GRkZ2NnZ0adPnwL9fvcMT0kYXRCNHz+ewMBA3nrrLWObKJH4+Hh0Ol2Bq9nq1q3LtWvXStzOwIEDCQsLIzU1lQYNGrBlyxa6dOlS6L42NjbY2NgU2G5lZVVm//iYuu36oyZA6Cc0O5/DpTPhNG3b1WRtV2Rl+TMU90g/m4f0s/mUpK91Oh0ajQatVmvwYEF2bCzRo0Zj5epK7alTcejV06yFkaIoREREMGbMGLRaLWlpabzyyivs3LmToKAgevXqZdLjHTp0iPXr19OhQwc0Gk3e93q3/wyh1WrRaDSF/owM+fthdEGk0+lYvHgxO3bsoEOHDgUOumzZMmObLtS/fzEURTHol2XHjh0GHzMgIICAgIByua7Sg/Qe8RrByz6hwQ049IEvTTceUjuSEEKIIuQkJKC7eRNdQgKXXnkFWw8PsxZGZ86c4fbt23h6ehIdHc2IESOws7MjLCzM4Hm4D5KSksKzzz7L+vXr+eCDD0zadmkYfb7r2LFjdO7cGa1WS2RkJOHh4XlfERERJgvo4uKChYVFgdGguLi4Ml8DydfXl6ioKA4dqpjFRIZD7o+3eWSKykmEEKLqURQFfVpaib6UjIy7bwIgIyqKS6+8QvSTo7j955/oUlNL3JY+LQ1DpweHhoZiYWHB9evX8fb2pmvXruzZs6fQYsjPzw9HR8div4q7EtzX15fHH3+cRx991KCMZc2oEaK7s7bXrl1Ly5YtTRro36ytrfHy8iI4OJgRI0bkbQ8ODuaJJ+TWFMWxHjsWFn2PfRZsWzWLoZMWqR1JCCGqDCU9nVOeXsa9+c6VVplRUVye/H8Gv71VWCgaAy4CCgsLA3LXGPzkk0+KnS80ceJExowZU2x79evXL3T7Dz/8QFhYWLkcaDCqILKysiIyMtJkw3gpKSmcPXs273l0dDQRERE4OzvTqFEjZsyYwbhx4/D29qZ79+6sW7eOmJgYJk6caJLjF6UinzIDGPjiXA59/D2OGWDx0zaQgkgIIUQhQkNDGTBgAJGRkYSGhha7r7OzM87OzgYf49KlS0ydOpWgoCCjJp2XNaPnED3//PN8/vnnfPjhh6UOcfjwYfr375/3/O4VXuPHj+err75i7Nix3Lx5kwULFhAbG4uHhwfbt2+ncePGpT52cXx9ffH19SU5OZnq1auX6bHKyvmWdnQ4mk6jqwopSQk4Vjf8l1gIIYThNHZ2tAorvri4K+PECS4++1zBF7Ra0OuxaduW2v83GYdu3Up8bEOEh4czb948Fi5cSO/evWnVqhWzZs0qdF8/Pz/8/PyKbe/333+nd+/e+baFhoYSFxeHl9e9UTOdTkdISAgrV67k+vXrBmU2tVJddv/ZZ58RHByMt7c3Dg4O+V43ZFJ1v379Hni+c9KkSUyaNMmorFWZ19xVZI16EQsFtr09lqdXyurVQghhDhqNpsSnrTT/HjG5UwjZtm1b5pOrz58/z61bt/D09MTT05MNGzbw1FNP0bJly3xTVe4y9pTZI488wrFjx/Jte/HFF2ndujVvvPFGgUUVzc3ogigyMhJPT08ATp8+ne81tdZQEAU193iI3TWhbiLUP3xZ7ThCCCGKo9GAopilELorNDQUjUZDp06dgNx5RO+++y7PPfcce/fuzfusv8vYU2bVqlXDw8Mj3zYHBwdq1aqFh4eHQWsGlQWjC6Jdu3aZMke5VNHnEN0V+5A7dX+PptYtuHg6gsYtO6kdSQghxH0sa9XCwsUFq3r1zL4OUVhYGC1atMh3A/S5c+cSFRXFsGHDOHjwoMkvvS+PjC6IqoLKMIcIYMTCHzm435vaSXBg3bs0/mib2pGEEELcx6pePZr/tVOVlar9/f0L3AZLo9EQGBhY5sfevXs3QLm491upCqJbt27x+eefc+LECTQaDW3atOGll16q0MVDZWRr78BVL1dq/xVLjbBzascRQghRCK3c/0xVRi/MePjwYZo1a8by5ctJSEggPj6e5cuX06xZs7z1DCq6gIAA2rZtW+QtPiqSTi+9g14Dja8q7Pz+I7XjCCGEEOWK0QXR9OnTGTZsGBcuXGDz5s1s2bKF6OhohgwZwrRp00wYUT0VfaXq+7X2epj4GrmPMz//QtUsQgghRHlTqhGiWbNmYWl576ybpaUlb775JocPHzZJOGFa1xvmrkvR8KpCRlqqymmEEEKI8sPogsjJyYmYmJgC2y9dupRvprooPzq/sxIFsNTDltkj1Y4jhBCVkqH3EROlY6r+NrogGjt2LC+99BKBgYFcunSJy5cv88MPP/Dyyy/z9NNPmyScMK0WHXpwo2buY7eDBYtZIYQQxru7sGBWVpbKSaqWu/1d2oUdjb7K7KOPPkKj0fD888+Tk5MD5N7j7LXXXjPJ7TzKg8qyDtH9Yrs2ps6Oi9S+BScj9tK6U+8HvkcIIcSDWVpaYm9vz40bN7CyskKrNXrMocrR6/VkZWWRkZFhUL/p9Xpu3LiBvb19vik8xjD63dbW1nz88cf4+/tz7tw5FEWhefPm2Btwd93yrrKsQ3S/4f4/cSbYG0s9HPtgCq03hasdSQghKgWNRoOrqyvR0dFcvHhR7TgViqIopKenY2dnZ/A6TFqtlkaNGpV6/aZSL8xob29P+/btS9uMMBNbewdi6mtpekmP+5kMteMIIUSlYm1tTYsWLeS0mYGys7MJCQmhT58+WFlZGfRea2trk4zGlaog2rlzJzt37iQuLq7AKpNffCGXdpdXFk+NhiWBOGRCxN6f6dT7CbUjCSFEpaHVarH9981aRbEsLCzIycnB1tbW4ILIVIwuqebPn4+Pjw87d+4kPj6exMTEfF+i/HrspXlEN8z90Z/8eqnKaYQQQgj1GT1CtGbNGr766ivGjRtnyjzCTFK8W8OlKFwjb6DLycGilJPRhBBCiIrM6BGirKwsevToYcos5U5lunXHv/WbvJgsC6iTCD++PlTtOEIIIYSqjC6IXn75ZTZu3GjKLOVOZbp1x7/Vqd+MW3fWz3Q9eEHVLEIIIYTajD5PkpGRwbp16/jzzz/p0KFDgUlQy5YtK3U4Ubaudm1EnaAYaifCmaP7adGhco/4CSGEEEUxuiA6evQonTp1AiAyMjLfa6VdC0CYx4gPN3Pmz9w1icLfn0yLH8PUjiSEEEKowuiCaNeuXabMIVRga+9AjJuGppcV3M+kqx1HCCGEUI2sK17FaUYPB8AxA/74fJ6qWYQQQgi1SEFUxQ1+1Y9Um9zHuh/+q24YIYQQQiVSEBWjMl92f7/zLXIrohqJCro7N+oVQgghqhIpiIpRmS+7v183v6/IsgDnFNjz3xVqxxFCCCHMTgoiQeOWnTjfPHfZhPhtP6icRgghhDA/KYgEANo+fQFoEZnKmWP7VU4jhBBCmJdJC6LffvuNSZMmMXPmTFauXGnKpkUZe2zSInK0YJsN4R/8n9pxhBBCCLMy6R09V65cybZt27C0tOSRRx5h8uTJpmxelCEbO3suuWlwv6zgfipN7ThCCCGEWZl0hGjSpElMnjyZadOmMWbMGFM2LcxANzL3Jq+OGbDji/kqpxFCCCHMx6QFkVarJS0tDWdnZ1JTU03ZtDCDoZMWkWad+zjnh0B1wwghhBBmZNKCKCAggC+//JK5c+fy+++/m7JpYSZ31yRqdFkhM11OnQkhhKgaTFoQTZ48mZkzZ/L2228zevRoUzYtzKTtm4tRAEs9bH5bfoZCCCGqBpNOqh48eDCDBw82ZZOqCggIICAgAJ1Op3YUs2nXzYeQ6lA7CaofjVY7jhBCCGEWJl+H6PTp0/Ts2dPUzaqiqqxU/W9X+7UGwDlRIT01WeU0QgghRNkzeUGUnZ3N//73P1M3K8xoyFufc9sOqqdC0Jo5ascRQgghypysVC0KcKzuzIXWDrlP/tytahYhhBDCHAwuiCZOnMj69es5fPgwWVlZZZFJlAPOg58EoGW0nh2fy5pEQgghKjeDJ1UfPXqU7777jtTUVKysrGjbti2enp54eXnh6emJViuDTpVB/6ffIGLJ19hnQXbgf+Gl99SOJIQQQpQZgwui/fv3oygKJ0+eJCwsLO9r8+bNJCUlAaDRaEweVJiXhaUl0c2taReVRePLetJTk7FzcFI7lhBCCFEmjLrsXqPR0KZNG9q0acOzzz6bt/3cuXOEhoYSERFhqnxCRS2mv4/yyiws9bD13Wd4etmvakcSQgghyoRJ1yFq1qwZzZo1k/uYVRIdew9jr9MsXJLB9cA5teMIIYQQZcagCT8xMTEGNX7lyhWD9hflzyXPegDUSYTTR/aqnEYIIYQoGwYVRF26dOGVV17h4MGDRe6TlJTE+vXr8fDwYPPmzaUOKNQ1eOFGdBrQAOEfTlc7jhBCCFEmDDplduLECfz8/HjsscewsrLC29sbNzc3bG1tSUxMJCoqiuPHj+Pt7c2SJUsYNGhQWeUWZlKjlit7G2lpflGPZVqm2nGEEEKIMmHQCJGzszMfffQRV69eZfXq1bRs2ZL4+HjOnDkDwLPPPktoaCh///23FEOViPXYsQA0O5/DtZgzKqcRQgghTM+oSdW2traMHDmSkSNHmjpPmbh06RLjxo0jLi4OS0tL3n33XUaPlju5l9Sjz7/FvvXfUycR9qyaxdgP5VSoEEKIyqVKrKJoaWnJihUriIqK4s8//2T69OmkpqaqHavCsLC05EobZwCabz9BSlKCyomEEEII0zLpZffllaurK66urgDUqVMHZ2dnEhIScHBwUDlZxVF75LMo+z/FPgt+mjuMLs+MBTtncO0IWi01bWri6uiqdkwhhBDCKOVihCgkJIShQ4fi5uaGRqNh69atBfZZtWoV7u7u2Nra4uXlxd69xl0CfvjwYfR6PQ0bNixl6qrjytkjVJv7KTl3flvcDt1k7Ml1jA3/kLHbn2bsr2N5fMvjxKbEqhtUCCGEMFK5GCFKTU2lY8eOvPjiizz55JMFXg8MDGTatGmsWrWKnj17snbtWgYNGkRUVBSNGjUCwMvLi8zMgldBBQUF4ebmBsDNmzd5/vnn+eyzz4rNk5mZma+t5ORkALKzs8nOzjb6+yzM3fZM3a4pRYeHUCsNlDvP6ydA9+M6DrTVwp3btGTrszkRfwIXGxf1ghajIvRzZSD9bB7Sz+YjfW0eZdXPhrSnURRFefBu5qPRaNiyZQvDhw/P29atWzc8PT1ZvXp13rY2bdowfPhw/P39S9RuZmYmAwYM4JVXXmHcuHHF7jtv3jzmzy94h/eNGzdib29fsm+kEkk4uIWHfvqnwPaz9SCwr5Yj7hrQaBht9yQdbTqrkFAIIYQoKC0tjWeeeYakpCScnIq/H2epRoiys7O5du0aaWlp1K5dG2dn59I0V6isrCxCQ0OZPXt2vu0+Pj7s37+/RG0oisILL7zAww8//MBiCGDOnDnMmDEj73lycjINGzbEx8fngR1qqOzsbIKDgxkwYABWVlYmbdtU9p79rdDtza7B24F6ztaD7/tp6TTAjkFdB5s5XclUhH6uDKSfzUP62Xykr82jrPr57hmekjC4IEpJSeG7777j+++/5+DBg/lOLTVo0AAfHx/+85//0KVLF0ObLlR8fDw6nY66devm2163bl2uXbtWojb+/vtvAgMD6dChQ978pG+++Yb27dsXur+NjQ02NjYFtltZWZXZX4iybLu0NLcL72fNnT+bX4OJ2/Uke54pt9/DXeW5nysT6WfzkH42H+lr8zB1PxvSlkEF0fLly1m4cCFNmjRh2LBhzJ49m/r162NnZ0dCQgKRkZHs3buXAQMG8NBDD/Hpp5/SokULg7+Bwmg0mnzPFUUpsK0ovXr1Qq/XG3zMgIAAAgIC0Ol0Br+3UilJNysl3E8IIYQohwwqiPbv38+uXbuKHFnp2rUrEyZMYM2aNXz++efs2bOn1AWRi4sLFhYWBUaD4uLiCowamZqvry++vr4kJydTvXr1Mj1WuVbNFSi4QvXdGujuKbNnXFqZO5kQQghhEgYVRD/++GOJ9rOxsWHSpElGBfo3a2trvLy8CA4OZsSIEXnbg4ODeeKJJ0xyDPEAjm75nt4thDTAhoe1/NY1d1I1UhAJIYSooEyyDtHff/9d6CXvJZWSkkJERAQREREAREdHExERQUxMDAAzZszgs88+44svvuDEiRNMnz6dmJgYJk6caIr4RQoICKBt27Ymmw9VUVnWyJ0sf/dyxHP1INw99/HAMD0ud+as2VpVM384IYQQwgRMsg7RoEGDiIiIoGnTpka9//Dhw/Tv3z/v+d0rvMaPH89XX33F2LFjuXnzJgsWLCA2NhYPDw+2b99O48aNTRG/SHLKLFeDTr2ItV/FTad7l9k3joPO0Trq3YIn/9az9jFrWtQ0zXwxIYQQwtxMUhCVdimjfv36PbCNSZMmmew0nDCMe8vOJG3+mZtpiYxF4YX4SCzcErnq/AVuCdD3mEKrKe/TuHoDtaMKIYQQRikXK1WXV3KV2T2dmrSkU96zhwD4MSQUt01HsNTDzc8XQc+hKqUTQgghSsckc4jWrl1b5ld8qcHX15eoqCgOHTqkdpRyadAbq0i9s1xTy8M3SbxxWd1AQgghhJFMUhA1btwYS0sZbKpqHKs7c8azBgB2WRC08D/qBhJCCCGMZJKCaNCgQVy5csUUTYkKptOk99HdWZCx0b5o0lNLvky6EEIIUV6YpCAqZ/eHNRm57P7B2nR5lDPNLABIsYf0lCSVEwkhhBCGM0lBVFnJHKKSsR2Wu0Bm7QRISU5QOY0QQghhOJlULUrNZ8J8rtYGmxz4++PX1Y4jhBBCGMyggujuytH/9swzz+Dg4FBgu8wrqhosLC2J75a7KGOTA1cIfLaryomEEEIIwxhUEHXp0oVXXnmFgwcPFrlPUlIS69evx8PDg82bN5c6oKgYHnn9Y9KtoUYqdAi9zV/fLVE7khBCCFFiBl0rf+LECfz8/HjsscewsrLC29sbNzc3bG1tSUxMJCoqiuPHj+Pt7c2SJUsYNGhQWeU2C1mYseRcXN3Z2d6RDqEpANz+/mt49g2VUwkhhBAlY9AIkbOzMx999BFXr15l9erVtGzZkvj4eM6cOQPAs88+S2hoKH///XeFL4ZAJlUbqun4GXmPm5/N4XDw9yqmEUIIIUrOqNUUbW1tGTlyJCNHjjR1HlGBdfF5mm1NPqD5BT1a4ML6JXgPeFrtWEIIIcQDGXWVWXZ2Nv379+f06dOmziMqON2jffMetzyezpmIvSqmEUIIIUrGqILIysqKyMhINBqNqfOICu7xKcuJd8p9bKWDsBWz1A0khBBClIDR6xA9//zzfP7556bMUu7IStWGs7K24UoXNwCyLMGyaXOVEwkhhBAPZvQdWbOysvjss88IDg7G29u7wDpEy5YtK3U4tfn6+uLr60tycjLVq1dXO06F0WPKEhJ2P4tNDji4NlY7jhBCCPFARhdEkZGReHp6AhSYSySn0qq2Rq08OdjGlnaRGaT/+jO88r7akYQQQohiGV0Q7dq1y5Q5RCXjMno8RK6l+elsvn+5F7buLRnx9hdqxxJCCCEKZXRBBHDr1i0+//xzTpw4gUajoW3btkyYMEFOLwn6jZ3GH2vX0fiqQqd9N4k7fgDdm9lYWFmpHU0IIYQowOhJ1YcPH6ZZs2YsX76chIQE4uPjWbZsGc2aNSMsLMyUGUUFdbt3JwD0QJ1E+HWpr6p5hBBCiKIYXRBNnz6dYcOGceHCBTZv3syWLVuIjo5myJAhTJs2zYQRRUU1aMZKkhzu/ZLZ7diHoiiqZhJCCCEKU6oRolmzZmFpee+sm6WlJW+++SaHDx82SThRsTlWd+ZCp1pA7ihRw1iF4M/nqxtKCCGEKITRBZGTkxMxMTEFtl+6dIlq1aqVKlR5IesQlV7HifPI0d77Rcv8aZOqeYQQQojCGF0QjR07lpdeeonAwEAuXbrE5cuX+eGHH3j55Zd5+unKcf8qublr6bXp8ihnm+dOpFaA5tE6Dmyr3At6CiGEqHiMvsrso48+QqPR8Pzzz5OTkwPk3tLjtdde48MPPzRZQFHx2Q4ZCss2o9fAeXcL6sqVZkIIIcoZo0eIrK2t+fjjj0lMTCQiIoLw8HASEhJYvnw5NjY2pswoKjifCfO5WhssFEhtWo9ujz2vdiQhhBAin1Lf7d7e3p727dvToUMH7O3tTZ1PVAIWlpbEd2sBQP3DV8jOylQ5kRBCCJGf3O1emMUjr39Mqg3UvgU/vTOW/z7tzeVzkWrHEkIIIQC5270wExdXd855OALQYscp2oen8veiySqnEkIIIXLJ3e6F2TQdPwNCF2B754xZk8PXuRUfSw0XV3WDCSGEqPLkbvfCbLr4PM22Jh/Q/IKeNBtwSoMgv/8wZtk2taMJIYSo4uRu98KsdI/2hc92YaHLfe7291ky01KxsXco/o1CCCFEGSr1VWaVmaxUbXqPT1lOfHWwyYF0K6iVBNuXvKZ2LCGEEFWcXGVWDFmp2vSsrG244u0GQNad9Rmd/jyE7s7inkIIIYQa5CozYXY9piwh0xKqp0GyHdxoWoP0lCS1YwkhhKjC5CozYXaNWnlysLUt7SIzuNLAgqc2HFA7khBCiCpOrjITqnAZPR4i19LinI6ToX/R2uthtSMJIYSowuQqM6GKfmOn8ce6dTS+ohAe8C5nOm4j7cQRxq75S+1oQgghqiCj5xAB7N27l+eee44ePXpw5coVAL755hv27dtnknCicrvdqxMATcMTaL76Dzz2xBKxe7O6oYQQQlRJRhdEP/30EwMHDsTOzo6wsDAyM3OXH759+zZ+fn4mCygqr0EzVpLkAE7pcLk2aBU4u1p+d4QQQpif0QXRBx98wJo1a1i/fj1WVlZ523v06EFYWJhJwonKzbG6Mxc61QJyiyGAFpGpXIg8qGIqIYQQVZHRBdGpU6fo06dPge1OTk7cunWrNJlEFdJx4jxytOAWD1ddwFoHB5fOUDuWEEKIKsbogsjV1ZWzZ88W2L5v3z6aNm1aqlCi6mjT5VHOtsgdYUy3z706sWnYTW5evahmLCGEEFWM0QXRq6++ytSpU/nnn3/QaDRcvXqV7777jpkzZzJp0iRTZhSVnO3jQwFocEUhrgY4ZMJffv9RN5QQQogqxejL7t98802SkpLo378/GRkZ9OnTBxsbG2bOnMnkyZNNmbHUbt++zcMPP0x2djY6nY4pU6bwyiuvqB1L3OEzYT67v9mM2w24WdsSvTYHbT1XtWMJIYSoQowuiAAWLlzI22+/TVRUFHq9nrZt2+Lo6GiqbCZjb2/Pnj17sLe3Jy0tDQ8PD0aOHEmtWrXUjiYAC0tL4ru1wO3XM9S+noPXX/9g7+ikdiwhhBBVSKnWIYLcYsPb25uuXbuWy2IIwMLCAnt7ewAyMjLQ6XQoiqJyKnG/R17/mFQbcEmGoDWz1Y4jhBCiiil1QWQKISEhDB06FDc3NzQaDVu3bi2wz6pVq3B3d8fW1hYvLy/27t1r0DFu3bpFx44dadCgAW+++SYuLi4mSi9MwcXVnXMe1QCw2BlCwvVL/DB9MH+smqNyMiGEEFVBuSiIUlNT6dixIytXriz09cDAQKZNm8bbb79NeHg4vXv3ZtCgQcTExOTt4+XlhYeHR4Gvq1evAlCjRg2OHDlCdHQ0Gzdu5Pr162b53kTJNR0/PffPaB1BU5+g4+/RaDf9rHIqIYQQVUGp5hCZyqBBgxg0aFCRry9btoyXXnqJl19+GYAVK1awY8cOVq9ejb+/PwChoaElOlbdunXp0KEDISEhjB49utB9MjMz81beBkhOTgYgOzub7OzsEh2npO62Z+p2K6JO/UfxR5MPaH5Bj0ankG0BDa8q/PnlQvo+92ap2pZ+Ng/pZ/OQfjYf6WvzKKt+NqS9MimIEhIScHZ2NklbWVlZhIaGMnt2/nklPj4+7N+/v0RtXL9+HTs7O5ycnEhOTiYkJITXXnutyP39/f2ZP39+ge1BQUF5c5FMLTg4uEzarWhudGpH8wvHaHY6g5MtLWl/Ioe0/37PdmcPk7Qv/Wwe0s/mIf1sPtLX5mHqfk5LSyvxvqUuiDp06EDv3r2ZMGECXl5enD59miFDhnD69OnSNg1AfHw8Op2OunXr5ttet25drl27VqI2Ll++zEsvvYSiKCiKwuTJk+nQoUOR+8+ZM4cZM+6tlpycnEzDhg3x8fHBycm0Vz9lZ2cTHBzMgAED8t0CparKfvQRQnd1wSUJspyd0JNAi2gdty1u0XngM8a3K/1sFtLP5iH9bD7S1+ZRVv189wxPSZS6IBo/fjyRkZH079+fRx55hL1799KlS5fSNluARqPJ91xRlALbiuLl5UVERESJj2VjY4ONjQ0BAQEEBASg0+kAsLKyKrO/EGXZdkViZWXF5S71cfnzCq6nEzjVXEubs3ouf7mCrkPGm6R96eeyJ/1sHtLP5iN9bR6m7mdD2jJ4UrVer0ev1+c9f/311/nyyy9Zv349P//8M1lZWXz33XeGNlskFxcXLCwsCowGxcXFFRg1MjVfX1+ioqI4dOhQmR5H5Ndz6lIyLcHtBqS3bAxAixMZnDr0l8rJhBBCVFYGF0RPPfUUa9euzbft4MGDvPLKK8yfP59evXqxcOFCkwW0trbGy8urwHnF4OBgevToYbLjiPKjUYuOnG1tC4Dd2Uuca6jhfBMLUm7Fq5xMCCFEZWVwQbRnzx769euX9/zEiRM8/vjjvP/++7z77rvMmTOHTZs2GdRmSkoKEREReae1oqOjiYiIyLusfsaMGXz22Wd88cUXnDhxgunTpxMTE8PEiRMNjW+QgIAA2rZtWyanAEXxXEbnnh5rcTYH17fm88T2SLwGjFE5lRBCiMrK4IIoNTUVCwsLAC5evMigQYNYtGgRU6dOBcDV1ZX4eMP+T/7w4cN07tyZzp07A7kFUOfOnZk7dy4AY8eOZcWKFSxYsIBOnToREhLC9u3bady4saHxDSKnzNTTb+w0LtbXYKmHM99+rHYcIYQQlZzBBVGnTp2YNm0an332GX379mXSpElMmDAh7/U//viD5s2bG9Rmv3798q4Au//rq6++yttn0qRJXLhwgczMTEJDQ+nTp4+h0UUFk9I7t0BuEnGTlKQEju77hf+O787thBsqJxNCCFHZGFwQrVixglOnTrF48WJGjRrFkiVLWLt2Lf/88w9Llixh9uzZ+Pr6lkVWUcU8Nv1Tkhygeips/2gSiTNn0f6fWwT5/UftaEIIISoZgy+79/b25ty5c3nP27dvz5w5c7h27Rp2dnZMnTqV//yncnxg/fuye2FejtWdudCpFh3/vonT/qNc6uJGneCr1Nl7kuyMdKxs7dSOKIQQopIo9b3Mxo8fz5UrV4iNjSUxMRE/Pz9T5CoXZA6R+jpOnEeOFhpfUajZoQe37cAlCbZ/9H9qRxNCCFGJmOTmrhqNhrp162JtbW2K5oTI06bLo5xtkbuwVvqOXznTqToAjkH7URRFzWhCCCEqkXJxt3shimM35AkAmp/MoPGo/+Qu2hin8Oead1ROJoQQorKQgqgYsg5R+TDgxfe4WhtscuDS7xs56ZE7dyh7y88qJxNCCFFZSEFUDJlDVD5YWFoS360FAA0OXaHBuP8jxRZS6jigy8pSOZ0QQojKQAoiUSE88vrHpNrkTqiOP3GIZkHBjPn2Hyxk3poQQggTMLogSk9PJy0tLe/5xYsXWbFiBUFBQSYJJsT9XFzdOedRDQCLP/fgXKeByomEEEJUJkYXRE888QRff/01ALdu3aJbt24sXbqUJ554gtWrV5ssoJpkDlH50nT8dPRA0wt6DgV9jy4nh99Wz+HHmcPVjiaEEKKCM7ogCgsLo3fv3gBs2rSJunXrcvHiRb7++ms++eQTkwVUk8whKl+6+DzN+SZatMD5Dcv5/av5NP14Ky3/OEXMqQi14wkhhKjAjC6I0tLSqFYt9xRGUFAQI0eORKvV8tBDD3Hx4kWTBRTifrpH+wLQLPI2Xj7PEVMPrHPgn0VTVE4mhBCiIjO6IGrevDlbt27l0qVL7NixAx8fHwDi4uJwcnIyWUAh7vf4lOXEVweHTAj55A1u9usAgHvoDRKvX1I5nRBCiIrK6IJo7ty5zJw5kyZNmtCtWze6d+8O5I4Wde7c2WQBhbiflbUNl7vUB8DlnzMMnb6a6zVzC6SdCyeqnE4IIURFZXRBNGrUKGJiYjh8+DB//PFH3vZHHnmE5cuXmyScEIXpOXVp7mrVN+Dv/y7ncvfGALgdOE9maorK6YQQQlREpVqHqF69enTu3Bmt9l4zXbt2pXXr1qUOVh7IVWblU6MWHTnb2haA9F9/xufNNdxygJq34fcPX1U5nRBCiIrI0pCdZ8yYUeJ9ly1bZnCY8sbX1xdfX1+Sk5OpXr262nHEfVxGj4fItTQ/k83NS2c5512Lhkdvore1VTuaEEKICsiggig8PLxE+2k0GqPCCFFS/cZO449162h8ReHImnk8vvi/2NvXwMbOXu1oQgghKiCDCqJdu3aVVQ4hDJbSuzP8EEaTiJtYWdpKMSSEEMJoBhVEhYmKiiImJoas+26yqdFoGDp0aGmbFqJYj03/lGPbelIjFf5Y/n+MmvcdtxKuscP/Vep3eZReY/5P7YhCCCEqCKMLovPnzzNixAiOHTuGRqNBURTg3ukynU5nmoRCFMGxujMXO9Wixt83cdybezr3d9/H6RSextmoaJCCSAghRAkZfZXZ1KlTcXd35/r169jb23P8+HFCQkLw9vZm9+7dJowoRNE6TpxHjhYaX1HYHbiCOqPHowean8smPDhQ7XhCCCEqCKMLogMHDrBgwQJq166NVqtFq9XSq1cv/P39mTKlctxGQS67L//adHmUsy2sAIj/cQOPjJzCqea5v9YX1yxWM5oQQogKxOiCSKfT4ejoCICLiwtXr14FoHHjxpw6dco06VQmN3etGOyGPAFA85MZxJw5gnboEACanUgjOuJvNaMJIYSoIIwuiDw8PDh69CgA3bp1Y/Hixfz9998sWLCApk2bmiygEA8y4MX3uFobbHLg749fZ9jLfpxvAJZ6CFv6ptrxhBBCVABGF0TvvPMOer0egA8++ICLFy/Su3dvtm/fzieffGKygEI8iIWlJfHdWgDQ4NAVdLocbj/SFYCmEQnEx5xVM54QQogKwOirzAYOHJj3uGnTpkRFRZGQkEDNmjVlYUZhdo+8/jEXggfjkgS/fTKdJ6av4u/t3mQ4aLG4cJzqro3VjiiEEKIcK/U6RPdzdnY2ZXNClJiLqzs7ParRIfQ2Fn/uwW6mA+02/oxrw5YAZGdnq5xQCCFEeWZ0QbRgwYJiX587d66xTQthlKbjp6MPXUDzC3oOBX1Pfe8eRMUfB0VBdyWM7IQDnDyehEV9T9BqqWlTE1dHV7VjCyGEKAeMLoi2bNmS73l2djbR0dFYWlrSrFkzKYiE2XXxeZpt7gtpHq0jev0ScuakE+8Ev3lrqXNLYWsPLcqRfXAkd39rC2t+Hf6rFEVCCCGML4gKu9FrcnIyL7zwAiNGjChVKCGMpXukD3y2i+Yn07HLBqdUmLotd/K/dY6ewL5auDPHLUuXRWJmohREQgghjL/KrDBOTk4sWLCAd99915TNClFij09ZTnx1sLszZej+X/AnDyj4faWj43k93LnVDHeulBRCCFG1mbQgArh16xZJSUmmblaIErGytuFyl/pFvt7sGrwdqMdvg4720XqIPWLGdEIIIcoro0+Z/XutIUVRiI2N5ZtvvuGxxx4rdbDyICAggICAALlRbQXTc+pSEnc9hXUhP7a7C0I0j4UXg/UwKMGs2YQQQpRPRhdEy5cvz/dcq9VSu3Ztxo8fz5w5c0odrDzw9fXF19eX5ORkqlevrnYcUUKNWnQk3N2ClmcLVkQK94qi3e01PGsnS0UIIYQoRUEUHR1tyhxCmJSmbz84uzPvuU4DFgqcrwdx1cEuE7Y9pOVZ147qhRRCCFFumHRhRiHKi2Y9BsLn9wqi6HoQ2EfLEXcNaDRo9QqKRoOi0XDp4kn2rp7F6Pd/xMrKWsXUQggh1GJQQTRjxowS77ts2TKDwwhhKva1G3DTBhwy4bYNvPucFp3lvWsI9FoNKJY4WlVn/+uP0zkyi18jPWnjt5rWHXqrmFwIIYQaDCqI/r32UGhoKDqdjlatWgFw+vRpLCws8PLyMl1CIYzg3rIzx9csotakWdRIh1eiHNC4V6eaa3NSG/YBrSUtnBvTwKEeGldXcqIu0vqsjpsv/YcfnunLU9PXqP0tCCGEMCODCqJdu3blPV62bBnVqlVjw4YN1KxZE4DExERefPFFeveW/8MW6rpy9gi1Js9Cb5H73DXiNu91SIeUa3BiH3Bnpeo6vzLm0z84sHkN2Us+pnYi1Fi3h6+OeDJ4yc/Uqd1Qxe9CCCGEuRi9DtHSpUvx9/fPK4YAatasyQcffMDSpUtNEk4IYyXFXaJGKtRIyX3e5goMCL1vQUburVQN0H3kRDpv281pD0e0CnT7XzqHnvJhb9AGFdILIYQwN6MLouTkZK5fv15ge1xcHLdv3y5VKCFK7c4K1Pf/gr8SlLsgY1ErVVdzqcsTmw5x6YUBpFtD7QRoUK+lGUMLIYRQi9EF0YgRI3jxxRfZtGkTly9f5vLly2zatImXXnqJkSNHmjKjEIaLP13oZvcSrFTtM/sTXL7+kvSp43Hv0B0AvU7HyTOHyjSyEEII9Rh92f2aNWuYOXMmzz33HNnZuTeOsrS05KWXXmLJkiUmCyiEUTKTC91scWdg6EErVTfq9BCNOj2U9/yH95+hTvBRQkZ78/L/fYXWwsLkkYUQQqjH6BEie3t7Vq1axc2bNwkPDycsLIyEhARWrVqFg4ODKTMKYTgbp2JfPusKXw7QQglWqlb0euoHR1L/Jjy0/jArfb04f/mEqZIKIYQoB0p9c1cHBwc6dOhAx44dy30hlJaWRuPGjZk5c6baUURZc8k/90enuff4tg0sHKPlmLsWSrBStUarpevmnVxp7oSVDgbszuTQqyMJ3LTA1KmFEEKoxOCFGd9//30cHBweuEhjeVyYceHChXTr1k3tGMIMFI0GDaAnt+qPrgebemoZt1NP/UQYt0thzeO5+5WEXd16PLLtfxz4YAaOP/xBh3OQ8OH3LIkI4pVZW6lRzaUsvx0hhBBlzOCFGe/OF/r3Io3305TwQ8aczpw5w8mTJxk6dCiRkZFqxxFlzL52A2Id4KZT/lt2pNppmP+NjoePKuxvC45WJb9pr0ajoce7y4l7bAxnp/4H54QcBm+6yd9t1/H4M2+V4XcjhBCirBm9MOP9j0srJCSEJUuWEBoaSmxsLFu2bGH48OH59lm1ahVLliwhNjaWdu3asWLFCoMWgJw5cyZLlixh//79Jsstyi/3lp1J+ulnbqYlMhaFcXFHuXwqnAY9OxN2bDXeERlM3J6Dw6vZUPKaCIA6XbrjsvMge18by62smzwhxZAQQlR4Rl9llp6ejqIo2NvbA3Dx4kW2bNlC27Zt8fHxMait1NRUOnbsyIsvvsiTTz5Z4PXAwECmTZvGqlWr6NmzJ2vXrmXQoEFERUXRqFEjALy8vMjMzCzw3qCgIA4dOkTLli1p2bJliQqizMzMfG0lJ+desZSdnZ03QmYqd9szdbsC2tV3px3uAGQ36UBwUl16dx1AQpPeXBwzEpdk2Pn6GEZuMKJItrSkx/qfUPT6vJ9d6L7N/LXNn8GvBNCueVdTfisVhvw+m4f0s/lIX5tHWfWzIe1pFOW+pXsN4OPjw8iRI5k4cSK3bt2iVatWWFtbEx8fz7Jly3jttdeMaRaNRlNghKhbt254enqyevXqvG1t2rRh+PDh+Pv7P7DNOXPm8O2332JhYUFKSgrZ2dm8/vrrzJ07t9D9582bx/z58wts37hxY14BKCq2G//7np5bjqAH/vdMT1w6Di1dg3o9VgFv435ZYZ8HxPb2omOT0SbJKoQQwjhpaWk888wzJCUl4eRU/NXHRhdELi4u7Nmzh3bt2vHZZ5/x6aefEh4ezk8//cTcuXM5ccK4y5L/XRBlZWVhb2/Pjz/+yIgRI/L2mzp1KhEREezZs8eg9r/66isiIyP56KOPitynsBGihg0bEh8f/8AONVR2djbBwcEMGDAAKysrk7Yt7imsn38Z24W2UZlcc4YOW3fiVLO20e0rOh2R78/CZnMQWgWu1oRdg5149eWN1HNpZKpvo9yT32fzkH42H+lr8yirfk5OTsbFxaVEBZHRp8zS0tKoVq0akHtaauTIkWi1Wh566CEuXrxobLMFxMfHo9PpqFu3br7tdevW5dq1ayY7zv1sbGywsbEpsN3KyqrM/kKUZdvinvv7uYv/F8Q+/Sz1EiB41mie+vLv0jSM58KPSXh8H+envoZbYg5jv0/m6ytDaTXKl1GP+proO6gY5PfZPKSfzUf62jxM3c+GtGX0OkTNmzdn69atXLp0iR07duTNG4qLizP5KAoUvHJNURSjrmZ74YUXih0dul9AQABt27alS5cuBh9HlH+NWnlyeXjuz7bdPwmEbFpZ6jade/Sic/BebndqjqUeRu5WyF66ku9/kjWLhBCiPDO6IJo7dy4zZ86kSZMmdOvWje7dc+/5FBQUROfOnU0W0MXFBQsLiwKjQXFxcQVGjUzN19eXqKgoDh2Se1hVVsPf+oJTzS2x1EPmp6tITy38lh+GsKhRgy7f/4L9zKnkWIBrMgzpZ9ycOiGEEOZhdEE0atQoYmJiOHz4MH/88Ufe9kceeYTly5ebJByAtbU1Xl5eBAcH59seHBxMjx49THYcUTVZWFrSev7HpNpAg+sKP78x3CTtajQaGr88kZZbf6H1J59TrVbu/KTUtNus+u/r6HU6kxxHCCGEaZTq1h316tWjc+fOaLX3munatSutW7c2qJ2UlBQiIiKIiIgAIDo6moiICGJiYoDcFbI/++wzvvjiC06cOMH06dOJiYlh4sSJpYn/QHLKrGpo7fUw5wbl/s62CYnlYNC3JmvbpkUL6nndK9y3TBtEo1XbmbakC2dijpnsOEIIIUrH6EnVAHv37mXt2rWcO3eOTZs2Ub9+fb755hvc3d3p1atXids5fPgw/fv3z3t+97Yg48eP56uvvmLs2LHcvHmTBQsWEBsbi4eHB9u3b6dx48alif9Avr6++Pr6kpycTPXqBq7eJyqUUR/8yB9hHWkao+fKYj+y+43GyrrgxPrS0Kem0i40GdtUePG7dNbHjaV1/7FMGPqeSY9jbrEpsSRmJoJej+5KGNkJBzh5PAmL+p6g1VLTpiaujq5qx8zn/szEHoH0hNwb/bp2rBCZK0o/56PXwcX9kHIdHOtC4x6gtVA7VfH0OjQX91E/4QCai07QtE/5zyyMZvRl9z/99BPjxo3j2Wef5ZtvviEqKoqmTZuyatUqfv31V7Zv327qrKq5WxCV5LI9Q2VnZ7N9+3YGDx4sVzCUoZL0c/iun9BMeQebbDgyuClPLfvN9DmuXeP4axOwORENwN62Gk48XJt3x/2Ic/U6Jj9eWYtNiWX4psdJIwuKuMjB2sKaX4f/Wm4+rGNTYhmydQhZuqwi95HMJhb1C/wxC5Kv3tvm5AaPLYK2w9TLVZyKmPmOfWfimbftOPOGtqNXi4pxn8XdJ68xK/Awi8Z60691PZO1a8jnt9GnzD744APWrFnD+vXr833A9OjRg7CwMGObLVfklFnV0rn/k5zsn7tmUMs/z3N0v+kLIqt69ei4aRvVXvsPeg30jlJ44ts4Zn/Sn50HNxGbEkvUzSiibkQSdfQ7ov75NPfPG5FE3YwiNiXW5JlKIzHmDCs+Tcdvg46O5/VQyP9fZemyckc2yonEzMRiCwuQzCYV9Qv893mU+wsLQEmOhf8+n/t6eVMRM9+hKAqLd5zkbFwKi3ecxMgxD7NSFIWlwWe4nq5hafAZ1TIbfcrs1KlT9OnTp8B2Jycnbt26VZpM5YacMqt6Rizawu5j3jSKVTjz/izabRuIhWWpziwXoLGwoMHU6Tj37seZyf+hbkIKr/1Xz7Xet4sebblzL+VyNwqQcIsaqeCUCm8H6jnrmv9munn0evUy/ltJs0jm0tPrckdZUPj3+KEGBdDAH7Oh9ePl51RURcx8n5Az8Ry9nATA0ctJhJyJp29L4xedNYeQM/Ecu5J7he+xK8mqZTb6X3pXV1fOnj1LkyZN8m3ft28fTZs2LW0uIVRhY2dPtenTyZ6zjBbROn6a/xxj3v+hTI5l79kZjz92cv7N14l3zqFxnWaseD2deKciigrujQKYoyDS6XJISkngZtJ1klMSSE5LICUtEb2i44m+r+TuFH8auDfU7H6tiMIo9gjU9mD+109zNeMSAEq+/ypo0LLuP/vyjr/gm2e5mH4u93UF0Nz/Dgh4/i/sbR0A+OCb5ziTdirvNTR39rvzf5rLxvxC7ZpuAHy77XUoyedY7BEWBa/gyO2iR7znPLKK9s0fyj1G4GQOJRV9X7xp3RfRrf0AAFb+NJN9N/8qct9XPd+lv3fuyvzrf36H7dd/hhJMabu0+wt0Z4vOa/nwHNp0GwhA5L5fUPYuK7qxntNp3+cJAE4eDCZ758Iid9V1nUinR54C4OyRfaRvfwcAB/1tmmZfLfJ9oEDyFc77dyVVW63Aq5ntnsJ7WO7FM1fOHychsOgFTtNbDqfrk9MAiLsSzfWvXyxy37Smg+g2dhYAt+KvcWn9U3mvlTTzwlWfc8K2Y75XujerhW//5gDo9ArjvzhYZCuejWoww6dV3vMXvjxIjq7wkZF2bk7MGdwm7/l/vj5MWlbBK1UVReHktdtoNaBXQKuBKd+H4+HmVOi6fQ2d7fEf2T7v+cwfj3AtKaPQDHWcbFg2plPe87e2HCPmZlqh+1a3tyLgGc+85/O3HefM9ZRC97Wx1HIjJTNf5qVBp+jTwsWotQZLw+iC6NVXX2Xq1Kl88cUXaDQarl69yoEDB5g5c2aR9wgToiLoMewVftj2DR333qDJr0c4M+pvWnTsWSbHsnByovnqdTQHTvy9zeDRFr1OR3JqIonJN7iVEs/t1ERupyeSmp6EpaUVI/vfW//ow40vkZARR5Y+gyx9JllKFvqcHDRZOVhZ2bBm8j8A5MTH875/P27pFeyywDYL7LLuPM6EI224VxCdi87//dz59/z+wuj7vlponQDAqfRTHLMt/GaLFv8aJj+fdoZQ2/Qi+06vv/eBcDH9PGG2hf9DDpCRee+1uOwbJSuI0hO4lhZTZF6AlLR7p6iup14k0qbofW+lxN/LcPsix4vb9/b1e/smx3C2pPP7k6/QPjO8yJfDbsXlPc64dQ3vYvY9fOteUZB+6zqdi9n3n4TL9/ZNullshsI0zT5b6PYDN7vlPc5IvV1suwdu3vtgz0pPLXbf/8U3z3uck5VpcF6A61cvsk9fP9+2mg7WeY8VRWHf2fh/vy2PrVX+X8L9Z2+SpSt8hE8h/9+N/52/SXJGzgMz6hVISs/m73M3C329db38RWjYxUTOx6cWum/jWvnv4xkRc4uo2MLXbatdLf8v7LHLSRy+WPjpXDsrLenZ9/2bpqg3smV0QfTmm2+SlJRE//79ycjIoE+fPtjY2DBz5kwmT55syoyqCQgIICAgAJ2sGVPlDF22jf8Nfgi3GxA59zVa/Hy0zI6V939B/xptaRpbSGEEeaMtuqQkXv24O+k6zX2FC3ceK1xoqskriNLCwui8bj/a7Hv72WbdK2C+H3BvfkrmmTM89VvRv/Opte77h9zGsdB97rbbPBZeDNbDSGcAetcZQKvki3kFnua+kxL3L98B0NdtCC1unQWNJm8/Td5jDVaW9z58HmkyihY3T97bD01ev2o0GmpUc87bt3vth/jn9t4iv788ds4MbPM8Ta+GFrmLu5tH3uMBbZ+jweV/ity3bRPve3nbP0vt6JAi923f7N5Vuv3aP432WAob9WceGNmxiTeH6zxc5OsN2nbPe+zm0ZfDyuIi93Xz6HvvcdvuHM4sZt8295aWcG3ZmcNJuftWu32OVqfXPjD3qZavcrtaswLb6zW7N8rgUr8Zh72KzlCn8b2CqEad+sXuW6th27zHjjVq5du3pJnH9Pfmkdqd8m2rX8Mu77FWo+Hjp/K/fr+6Trb5nn80pmORc2dcHPMXGP4jO5Dzr9OjufNwTnMlMR39fc1oNNCgph2vD2hZYMTFyTb/BSZvDW5DalbhhZa9df5y4Y3HWpGcXnhRb2OZ/+/y1EdbkJBacA6coigsCz7D5cS0fJnVGiUy6iqz7OxsfHx8WLt2LQ0aNCAqKgq9Xk/btm1xdCz8H8iKTK4yq/iM6ee/Nn5E3fc/R6vAyRd6M2L2ujLNGBU4F817PxbYfmfWAnpga3cNIya+Rttu/0dyUBBXpkwtsr3fH7VhxsoIAFL37ydmwktF7hszzIuBi3PXX8o8c4bzb81CY2+HtVMNbGo4Y+lYDa2DA1oHB+y9vbFrn1sIRP21Cc2kdwu0p9PkFkV3R4je8Q2kbW2PAvupIepGJGO3P/3A/QIHfy+ZS0uvI+OjtlinXkNbyOeaXoEsB1dsZx4vP/NxKmJmYM/pG8WeotswoWu5m0tkjsyGfH4bNUJkZWVFZGQkGo0Ge3t7vL29H/wmISqYh5+ZSeAfP9LhYDL1Nu3lytgo6ru3ffAbjWVT+F/Wu/8ma4F+R5Xc9XIAy5o10bjWRevggFU1Jyyq3StaLBwcmDhw4L2m27ShQcDKvNfzfdnb0+a+0RmbFi1o8+PmEkVWbGzyTTy9WwhF18t/uk8x81yA4pQ0i2QuPUWjZbnFBGbhlzc/5K67IwLLLV5ktkZbYAKzWipkZkVhadApNJpCL/REo+K8nKKUx8xGnzJ7/vnn+fzzz/nwww9NmUeIcsVn6WaODnuUOolw4M1nGfWj4XMNSsylZaGb9RrQKnChNnzfT8ts19yJnPZdutB61+4SNW1ZsybVHnnEVEnz2Fs6kkHu6JWWgoUQAIoljlbl5ypNR6vqoFiCppg5GJLZJLJ0en5K9+RC9jTes/oaNxLyXrtGLeZnjyMs3YsZOj02luVjtKWiZr56K73QwgJyC47YWxlkSeZiGV0QZWVl8dlnnxEcHIy3tzcODg75Xl+2rJirF4SoIGrWrk/q+BGwYgvtjmXw68qZDJn8UZkcS9FoCh1tOV+OR1saNG7DmZo1yapVg4SnR2Dtpqf/6QjGNelMVp0OoNHSqEZtGldvoHbUPI2rN+Abn81cSroBih67+EgsMhLR2dYk3cWjQmS2jjvK5VPhNGhVfvsZwMbSgl8m9yIhtSsJ+qlkXjuIZVocOfZ1SK3Xlf/TWlDL0brcfEhDwcxpVw5wLmIvzTr1JqN+93Keuei1qsp75pycHPbt20evXr2wvLPUibkzG10QRUZG4umZO+Ht9OnT+V4rL0NypSWTqgXA4Il+/LjrDzyOpFP9m99IGD0V57oNTX6cijjaYlWvHq337EZjZYVGo8mdq5W8nYd7lu85cZ3c3Onk5n7n2UOqZimp+zNnt/Bie1Ldct/PAG417HC7O9m44WPqhimh+zNn1/Ph+PUcGnv5lOu+ztfPFUS+fs7O5qJj7hIDavWz0QXRrl27TJmjXJKFGcVdvRZvJHrUCFySIPj1Jxn7bdETAY3179EWuwbwUuatcj1yAaC1tn7wTkIIUc6ZdgleISop18at+Wdsf2p+tguP0Nv8+bUfjz7/lkmP8e/RFiGEEOZj9L3MhKhqhs9cxYk21mgVsFj7DSlJCQ9+k4G01tZSDAkhhAqkIBLCAJ0WrifZHurdhF9nPKF2HCGEECYiBZEQBmjatiuXhuVeTNDuQDx7t6xWOZEQQghTkIKoGAEBAbRt25YuXbqoHUWUIyPe2cDpZhZY6iH940/JTC/8BodCCCEqDimIiuHr60tUVBSHDh1SO4ooRywsLWk5bwVpNtDwmsLmN4apHUkIIUQpmbwgevTRR2natKmpmxWiXGnT5VHO+uSuLN1m9xUO7/xB5URCCCFKw+QF0YgRIxg/frypmxWi3Bnl/xPnG2qxyYG4D99Hl1PMbRWEEEKUayYviHx9fXnvvfdM3awQ5Y6FpSX1Zs8j0xLcL+nZNHuk2pGEEEIYyeiC6M8//yzytbVr1xrbrBAVitcjoznZL3fl6OZBZzj+T5DKiYQQQhjD6ILo8ccf5/XXXycr697N5G7cuMHQoUOZM2eOScIJURGMWPIzl+ppsM+Cc/NnyKkzIYSogIwuiEJCQti2bRtdunTh+PHj/Pbbb3h4eJCSksKRI0dMmVE1ctm9KAkbO3vsp08jRwstzuvY/P7zakcSQghhIKMLom7duhEeHk6HDh3w8vJixIgRvP766/z11180bGj6O4GrQS67FyXV64n/cLyHCwCNfwnnfJTpb/4qhBCi7JRqUvWpU6c4dOgQDRo0wNLSkpMnT5KWJovUiappyNKfiXWBaukQ8dYrascRQghhAKMLog8//JDu3bszYMAAIiMjOXToUN6I0YEDB0yZUYgKwbG6M/r/jEOvgTYns9i6ZKLakYQQQpSQ0QXRxx9/zNatW/n000+xtbWlXbt2HDx4kJEjR9KvXz8TRhSi4nj0+beI9KoGQJ3/7iH24kmVEwkhhCgJowuiY8eOMWjQoHzbrKysWLJkCUFBcumxqLoGLP2JGzWg5m3Y9+YzascRQghRAkYXRC4uLkW+1rdvX2ObFaLCc67bkORxQwDwOJLOb6tlGQohhCjvLEvbQFRUFDExMfnWIwIYNkxueCmqriG+S/hx9048jqVTbcNWEkdNpmbt+mrHEkIIUQSjC6Lz588zYsQIjh07hkajQVEUADQaDQA6nc40CYWooHos/paLo5+k9i0ImjGSsd/8o3YkIYQQRTD6lNnUqVNxd3fn+vXr2Nvbc/z4cUJCQvD29mb37t0mjChExVTfvS3XR/cBwONwMju/W6xyIiGEEEUxuiA6cOAACxYsoHbt2mi1WrRaLb169cLf358pU6aYMqNqZKVqUVojZq3lRCsrtApoVn9JSlKC2pGEEEIUwuiCSKfT4ejoCOROsL569SoAjRs35tSpU6ZJpzJZqVqYQscP1nDbDlzj4deZw9WOI4QQohBGF0QeHh4cPXoUyL2Nx+LFi/n7779ZsGABTZs2NVlAISq6Zu17cGFIRwDa7r/B/l/Wq5xICCHEvxldEL3zzjvo9XoAPvjgAy5evEjv3r3Zvn07n3zyickCClEZPPnet5xxt8BKB7eXLyczXW5xI4QQ5YnRBdHAgQMZOXIkAE2bNiUqKor4+Hji4uJ4+OGHTRZQiMrAwtKSpu8tId0aGsUqbHlzuNqRhBBC3KdU6xBlZGRw9OhR4uLi8kaL7pJ1iITIz+OhQQQOCKDDb+dovfsS4bt+onP/J9WOJYQQglIURH/88Qfjxo3j5s2bBV7TaDSyDpEQhRjp/xPBRzrjflnhvP9cOvR+AgvLUq+PKoQQopSMPmU2efJkxowZQ2xsLHq9Pt+XFENCFM7K2obab75LliU0jdHz09uj1Y4khBCCUhREcXFxzJgxg7p165oyjxCVXhefpznRxw2AZn+c5MShP1VOJIQQwuiCaNSoUbIitRBGemLJFi7X1WCfCafnTUeXk6N2JCGEqNKMnrywcuVKRo8ezd69e2nfvj1WVlb5Xq8sq1ULURbsHJyw+b9J5MwNoOW5HLb4TWDU3K/VjiWEEFWW0QXRxo0b2bFjB3Z2duzevTvvpq6QO6laCiIhitdn1GR+2P49Hfcn0HDrIS6MPkyTNt5qxxJCiCqpVAszLliwgKSkJC5cuEB0dHTe1/nz502ZUYhKa/DSLVyrBU5pEPr2y2rHEUKIKsvogigrK4uxY8ei1RrdhFlZWlrSqVMnOnXqxMsvywePKB+catYh+5Vn0ANtozL5een/qR1JCCGqJKOrmfHjxxMYGGjKLGWqRo0aREREEBERwWeffaZ2HCHy+LzwLse97twoOfBPrsWcUTmREEJUPUbPIdLpdCxevJgdO3bQoUOHApOqly1bVupwQlQVD3/0X04MH4xLEoS8+RRjfghVO5IQQlQpRo8QHTt2jM6dO6PVaomMjCQ8PDzvKyIiwqC2QkJCGDp0KG5ubmg0GrZu3Vpgn1WrVuHu7o6trS1eXl7s3bvXoGMkJyfj5eVFr1692LNnj0HvFaKsubi6k/TcYADaR6TxzUpfoo5+R9Q/n+b+eSOSqJtRxKbEqpxUCCEqJ6NHiHbt2mWyEKmpqXTs2JEXX3yRJ58seG+nwMBApk2bxqpVq+jZsydr165l0KBBREVF0ahRIwC8vLzIzMws8N6goCDc3Ny4cOECbm5uREZG8vjjj3Ps2DGcnJwKzZOZmZmvreTkZACys7PJzs42xbec5257pm5X5FcR+tnD52lurd2OTQ64f/UXz9nuJtvqzv+zhOf+Ya21ZsvQLbg6uKoXtBgVoZ8rA+ln85G+No+y6mdD2tMoiqKY9OilpNFo2LJlC8OHD8/b1q1bNzw9PVm9enXetjZt2jB8+HD8/f0NPsagQYN4//338fYu/BLnefPmMX/+/ALbN27ciL29vcHHE6Ikki9G4L3qBxRAAyQ6wKohWo64a+C+ZS0mOU7CzdJNtZxCCFFRpKWl8cwzz5CUlFTkIMhd5f6ukllZWYSGhjJ79ux82318fNi/f3+J2khMTMTe3h4bGxsuX75MVFQUTZs2LXL/OXPmMGPGjLznycnJNGzYEB8fnwd2qKGys7MJDg5mwIABBeZhCdOpCP18Yr8e+IG7pU+NVHg7UM9ZVwjsc68w6tmjO21c2qkZtUgVoZ8rA+ln85G+No+y6ue7Z3hKotwXRPHx8eh0ugL3TKtbty7Xrl0rURsnTpzg1VdfRavVotFo+Pjjj3F2di5yfxsbG2xsbApst7KyKrO/EGXZtrinPPezZeK5fM/vFkbu1+4VRt/31WJ54zhWrp3Mns8Q5bmfKxPpZ/ORvjYPU/ezIW2V+4LorvtXwgZQFKXAtqL06NGDY8eOGXzMgIAAAgIC0Ol0Br9XCINlFv5/MhZ3Tmo3j4UXg/UwKMGMoYQQomoo96squri4YGFhUWA0KC4ursCokan5+voSFRXFoUOHyvQ4QgBgU/jp2LuT/M66wpcDtGBX9OimEEII45T7gsja2hovLy+Cg4PzbQ8ODqZHjx4qpRKiDLi0zPdUd2cAVAPsawNvjbfgmLsWXDuaP5sQQlRy5eKUWUpKCmfPns17Hh0dTUREBM7OzjRq1IgZM2Ywbtw4vL296d69O+vWrSMmJoaJEyeWaS45ZSbMSdFo0AB6cv9PJboehDfVMPpvha5nwPk2JDjl7ieEEMK0ykVBdPjwYfr375/3/O4VXuPHj+err75i7Nix3Lx5kwULFhAbG4uHhwfbt2+ncePGZZrL19cXX19fkpOTqV69epkeSwj72g2IdYCbTvddVQZ4XNTR5jKM3atn9WAbHK3kd1EIIUytXBRE/fr140HLIU2aNIlJkyaZKZEQ5ufesjNJP/3MzbRExqLwQnwkFhmJXBgYCp8foe9RhVpDR9O4egO1owohRKVTLgqi8kpOmQlz69SkJZ3ynj2U+4cPbAnpQOsz2dh/9x2Me0udcEIIUYmV+0nVapKrzER50XDaW+RoofkFPds+mfHgNwghhDCIFERCVADejzzFiY4OANj9+DvZWQXv2yeEEMJ4UhAJUUF4v7uKNGuofwO2zH9O7ThCCFGpSEFUjICAANq2bUuXLl3UjiIETdt25XSP3MVI6wdFknjjisqJhBCi8pCCqBgyh0iUN4+9/x0J1XLXJNoxd5zacYQQotKQgkiICqRm7fpcGZB7p/sW+2O5cOKwyomEEKJykIJIiArmiXe/5mptsM+Egx+8pnYcIYSoFKQgEqKCsbGzJ23UQADahKdweOcPKicSQoiKTwqiYsikalFeDZ26gnONtVjq4dLHfmrHEUKICk8KomLIpGpRnjm98hp6oPXpbIK++kDtOEIIUaFJQSREBdVn1GROtrMBQPfNRnQ5OSonEkKIiksKIiEqsFZv+JNlCU2uKPy8ZKLacYQQosKSgkiICszjoUGc8KoBgPO2v0lPTVY3kBBCVFBSEBVDJlWLiqD3vM+5bQd1E+Dnd59WO44QQlRIUhAVQyZVi4qgvntbzvVpDID77vNcizmjciIhhKh4pCASohIYumAjN2qAUxrsnveC2nGEEKLCkYJIiErAsbozNwbnntptfSiBE4f+VDmREEJULFIQCVFJDH/rC2JcNdhkw/HFb6gdRwghKhQpiISoJCwsLeHZ0QC0icxg38/rVE4khBAVhxREQlQiA1+ez6nmlmgVSFjzidpxhBCiwpCCSIhKxnXyG+g00CJax2+rZqkdRwghKgQpiIoh6xCJiqjbY89zooM9ANaB28jOylQ5kRBClH9SEBVD1iESFVWntz4h3RoaXFfY+sELascRQohyTwoiISqhFh17cuqh2gC4/hFBcmKcyomEEKJ8k4JIiEpq4PvfccsRaiXD9nfklh5CCFEcKYiEqKSc6zbk0iOtAWi+7yoxp8JUTiSEEOWXFERCVGJPzPuOWBdwyIQD709UO44QQpRbUhAJUYnZ2Nlze8TDALQJv034ni0qJxJCiPJJCiIhKrkhUz/mfCMtVjqIXj5P7ThCCFEuSUEkRCVnYWmJ3YsTAGhzMoud3y1WOZEQQpQ/UhAJUQU8/PTrnGhjDUDmlxvQ5eSonEgIIcoXKYiKIStVi8qk6YwFZFmA+2U925ZPVjuOEEKUK1IQFUNWqhaVSafeT3DS0wmA6lv3kJ6arHIiIYQoP6QgEqIK6THvc1Jsod5N+GXeOLXjCCFEuSEFkRBVSMNmHpzr1QCARn+dJj42WuVEQghRPkhBJEQVM/j974ivDjVS4c93n1c7jhBClAtSEAlRxTjVrMP1QZ4AtDwYz6mIEJUTCSGE+qQgEqIKGvHOBi7V1WCXBUf9p6kdRwghVCcFkRBVkIWlJdlPPQFAm6Pp7P/tS5UTCSGEuqQgEqKKevw1f840tcBCgRurlqodRwghVCUFkRBVWO1J09FpoOU5Hb+ve1vtOEIIoRopiISowroPeYkT7e0AsNi4RW7pIYSosqQgEqKK6zBnGRlW0PCawpYPXlA7jhBCqKLKFETR0dH079+ftm3b0r59e1JTU9WOJES50KpzP051dQGg7u+hpCQlqBtICCFUUGUKohdeeIEFCxYQFRXFnj17sLGxUTuSEOXGwwu+IskBXJLg13eeUjuOEEKYXZUoiI4fP46VlRW9e/cGwNnZGUtLS5VTCVF+1KnfjAv9mwPQbO8lLp2LVDmREEKYV7koiEJCQhg6dChubm5oNBq2bt1aYJ9Vq1bh7u6Ora0tXl5e7N27t8TtnzlzBkdHR4YNG4anpyd+fn4mTC9E5fDE/O+45gyOGbB//stqxxFCCLMqFwVRamoqHTt2ZOXKlYW+HhgYyLRp03j77bcJDw+nd+/eDBo0iJiYmLx9vLy88PDwKPB19epVsrOz2bt3LwEBARw4cIDg4GCCg4PN9e0JUSHYOThx64k+ALQOTeLo39tUTiSEEOZTLs4bDRo0iEGDBhX5+rJly3jppZd4+eXc/2tdsWIFO3bsYPXq1fj7+wMQGhpa5PsbNGhAly5daNiwIQCDBw8mIiKCAQMGFLp/ZmYmmZmZec+TkpIASEhIIDs727Bv7gGys7NJS0vj5s2bWFlZmbRtcY/0c8n0fGEBIb/3ofEVhZP+c6i/oYdB75d+Ng/pZ/ORvjaPsurn27dvA6AoygP3LRcFUXGysrIIDQ1l9uzZ+bb7+Piwf//+ErXRpUsXrl+/TmJiItWrVyckJIRXX321yP39/f2ZP39+ge3u7u6GhReiIjsLuLionUIIIUrt9u3bVK9evdh9yn1BFB8fj06no27duvm2161bl2vXrpWoDUtLS/z8/OjTpw+KouDj48OQIUOK3H/OnDnMmDEj77lerychIYFatWqh0WiM+0aKkJycTMOGDbl06RJOTk4mbVvcI/1sHtLP5iH9bD7S1+ZRVv2sKAq3b9/Gzc3tgfuW+4Lorn8XIoqiGFScPOi03P1sbGwKXJZfo0aNEh/LGE5OTvKXzQykn81D+tk8pJ/NR/raPMqinx80MnRXuZhUXRwXFxcsLCwKjAbFxcUVGDUSQgghhDBGuS+IrK2t8fLyKnBVWHBwMD16GDbhUwghhBCiMOXilFlKSgpnz57Nex4dHU1ERATOzs40atSIGTNmMG7cOLy9venevTvr1q0jJiaGiRMnqpjaNGxsbHjvvfdk5ewyJv1sHtLP5iH9bD7S1+ZRHvpZo5TkWrQytnv3bvr3719g+/jx4/nqq6+A3IUZFy9eTGxsLB4eHixfvpw+ffqYOakQQgghKqNyURAJIYQQQqip3M8hEkIIIYQoa1IQCSGEEKLKk4JICCGEEFWeFEQqWrVqFe7u7tja2uLl5cXevXvVjlTp+Pv706VLF6pVq0adOnUYPnw4p06dUjtWpefv749Go2HatGlqR6l0rly5wnPPPUetWrWwt7enU6dOxd7LURguJyeHd955B3d3d+zs7GjatCkLFixAr9erHa3CCwkJYejQobi5uaHRaNi6dWu+1xVFYd68ebi5uWFnZ0e/fv04fvy4WbJJQaSSwMBApk2bxttvv014eDi9e/dm0KBBxMTEqB2tUtmzZw++vr7873//Izg4mJycHHx8fEhNTVU7WqV16NAh1q1bR4cOHdSOUukkJibSs2dPrKys+P3334mKimLp0qVlvpJ+VbNo0SLWrFnDypUrOXHiBIsXL2bJkiV8+umnaker8FJTU+nYsSMrV64s9PXFixezbNkyVq5cyaFDh6hXrx4DBgzIu0lrmVKEKrp27apMnDgx37bWrVsrs2fPVilR1RAXF6cAyp49e9SOUindvn1badGihRIcHKz07dtXmTp1qtqRKpVZs2YpvXr1UjtGpff4448rEyZMyLdt5MiRynPPPadSosoJULZs2ZL3XK/XK/Xq1VM+/PDDvG0ZGRlK9erVlTVr1pR5HhkhUkFWVhahoaH4+Pjk2+7j48P+/ftVSlU1JCUlAeDs7KxyksrJ19eXxx9/nEcffVTtKJXSL7/8gre3N6NHj6ZOnTp07tyZ9evXqx2r0unVqxc7d+7k9OnTABw5coR9+/YxePBglZNVbtHR0Vy7di3fZ6ONjQ19+/Y1y2djuVipuqqJj49Hp9MVuBdb3bp1C9yzTZiOoijMmDGDXr164eHhoXacSueHH34gLCyMQ4cOqR2l0jp//jyrV69mxowZvPXWWxw8eJApU6ZgY2PD888/r3a8SmPWrFkkJSXRunVrLCws0Ol0LFy4kKefflrtaJXa3c+/wj4bL168WObHl4JIRRqNJt9zRVEKbBOmM3nyZI4ePcq+ffvUjlLpXLp0ialTpxIUFIStra3acSotvV6Pt7c3fn5+AHTu3Jnjx4+zevVqKYhMKDAwkG+//ZaNGzfSrl07IiIimDZtGm5ubowfP17teJWeWp+NUhCpwMXFBQsLiwKjQXFxcQUqY2Ea//d//8cvv/xCSEgIDRo0UDtOpRMaGkpcXBxeXl5523Q6HSEhIaxcuZLMzEwsLCxUTFg5uLq60rZt23zb2rRpw08//aRSosrpjTfeYPbs2Tz11FMAtG/fnosXL+Lv7y8FURmqV68ekDtS5OrqmrfdXJ+NModIBdbW1nh5eREcHJxve3BwMD169FApVeWkKAqTJ09m8+bN/PXXX7i7u6sdqVJ65JFHOHbsGBEREXlf3t7ePPvss0REREgxZCI9e/YssGzE6dOnady4sUqJKqe0tDS02vwfjxYWFnLZfRlzd3enXr16+T4bs7Ky2LNnj1k+G2WESCUzZsxg3LhxeHt70717d9atW0dMTAwTJ05UO1ql4uvry8aNG/n555+pVq1a3qhc9erVsbOzUzld5VGtWrUC87IcHByoVauWzNcyoenTp9OjRw/8/PwYM2YMBw8eZN26daxbt07taJXK0KFDWbhwIY0aNaJdu3aEh4ezbNkyJkyYoHa0Ci8lJYWzZ8/mPY+OjiYiIgJnZ2caNWrEtGnT8PPzo0WLFrRo0QI/Pz/s7e155plnyj5cmV/HJooUEBCgNG7cWLG2tlY8PT3lUvAyABT69eWXX6odrdKTy+7LxrZt2xQPDw/FxsZGad26tbJu3Tq1I1U6ycnJytSpU5VGjRoptra2StOmTZW3335byczMVDtahbdr165C/00eP368oii5l96/9957Sr169RQbGxulT58+yrFjx8ySTe52L4QQQogqT+YQCSGEEKLKk4JICCGEEFWeFERCCCGEqPKkIBJCCCFElScFkRBCCCGqPCmIhBBCCFHlSUEkhBBCiCpPCiIhhBBCVHlSEAkhhBCiypOCSAghhBBVnhREQgghhKjypCASQpR7mzZton379tjZ2VGrVi0effRRjhw5glarJT4+HoDExES0Wi2jR4/Oe5+/vz/du3fPex4VFcXgwYNxdHSkbt26jBs3Lu/9AIqisHjxYpo2bYqdnR0dO3Zk06ZNea/v3r0bjUbDb7/9RseOHbG1taVbt24cO3Ysb5+LFy8ydOhQatasiYODA+3atWP79u1l2T1CCBOQgkgIUa7Fxsby9NNPM2HCBE6cOMHu3bsZOXIkTZs2pVatWuzZsweAkJAQatWqRUhISN57d+/eTd++ffPa6du3L506deLw4cP88ccfXL9+nTFjxuTt/8477/Dll1+yevVqjh8/zvTp03nuuefyjnHXG2+8wUcffcShQ4eoU6cOw4YNIzs7GwBfX18yMzMJCQnh2LFjLFq0CEdHx7LuJiFEaSlCCFGOhYaGKoBy4cKFAq+NHDlSmTx5sqIoijJt2jTl9ddfV1xcXJTjx48r2dnZiqOjo/L7778riqIo7777ruLj45Pv/ZcuXVIA5dSpU0pKSopia2ur7N+/P98+L730kvL0008riqIou3btUgDlhx9+yHv95s2bip2dnRIYGKgoiqK0b99emTdvnuk6QAhhFpYq12NCCFGsjh078sgjj9C+fXsGDhyIj48Po0aNombNmvTr149169YBsGfPHt5//32io6PZs2cPSUlJpKen07NnTwBCQ0PZtWtXoaM1586dIykpiYyMDAYMGJDvtaysLDp37pxv2/2n4ZydnWnVqhUnTpwAYMqUKbz22msEBQXx6KOP8uSTT9KhQweT9okQwvSkIBJClGsWFhYEBwezf/9+goKC+PTTT3n77bf5559/6NevH1OnTuXs2bNERkbSu3dvzp07x549e7h16xZeXl5Uq1YNAL1ez9ChQ1m0aFGBY7i6uhIZGQnAb7/9Rv369fO9bmNj88CcGo0GgJdffpmBAwfy22+/ERQUhL+/P0uXLuX//u//StsVQogyJHOIhBDlnkajoWfPnsyfP5/w8HCsra3ZsmULHh4e1KpViw8++ICOHTvi5ORE37592bNnT775QwCenp4cP36cJk2a0Lx583xfDg4OtG3bFhsbG2JiYgq83rBhw3x5/ve//+U9TkxM5PTp07Ru3TpvW8OGDZk4cSKbN2/m9ddfZ/369WXfSUKIUpGCSAhRrv3zzz/4+flx+PBhYmJi2Lx5Mzdu3KBNmzZoNBr69OnDt99+S79+/QDo0KEDWVlZ7Ny5M28b5E52TkhI4Omnn+bgwYOcP3+eoKAgJkyYgE6no1q1asycOZPp06ezYcMGzp07R3h4OAEBAWzYsCFfpgULFrBz504iIyN54YUXcHFxYfjw4QBMmzaNHTt2EB0dTVhYGH/99Rdt2rQxU28JIYwlBZEQolxzcnIiJCSEwYMH07JlS9555x2WLl3KoEGDAOjfvz86nS6v+NFoNPTu3RuAXr165bXj5ubG33//jU6nY+DAgXh4eDB16lSqV6+OVpv7T+H777/P3Llz8ff3p02bNgwcOJBt27bh7u6eL9OHH37I1KlT8fLyIjY2ll9++QVra2sAdDodvr6+tGnThscee4xWrVqxatWqsu4mIUQpaRRFUdQOIYQQFcHu3bvp378/iYmJ1KhRQ+04QggTkhEiIYQQQlR5UhAJIYQQosqTU2ZCCCGEqPJkhEgIIYQQVZ4UREIIIYSo8qQgEkIIIUSVJwWREEIIIao8KYiEEEIIUeVJQSSEEEKIKk8KIiGEEEJUeVIQCSGEEKLK+3/4dFjA0r5XogAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "QDelta = genQDeltaCoeffs(\"TRAP\", qGen=coll)\n", "\n", "for nSweeps, sym in zip([10, 8, 6, 4], [\"^\", \"o\", \"s\", \">\"]):\n", "\n", " uNum, monitors = solveDahlquistSDC(\n", " lam=lam, u0=u0, T=T, nSteps=nSteps, nSweeps=nSweeps,\n", " Q=Q, QDelta=QDelta, weights=weights, monitors=[\"residuals\", \"errors\"])\n", "\n", " residuals = np.max(np.linalg.norm(monitors[\"residuals\"], axis=-1, ord=np.inf), axis=-1)\n", " errors = np.max(np.linalg.norm(monitors[\"errors\"], axis=-1, ord=np.inf), axis=-1)\n", "\n", " p = plt.semilogy(residuals, sym+'-', label=f\"$K={nSweeps}$\")\n", " plt.semilogy(errors, sym+'--', c=p[0].get_color())\n", "\n", "plt.grid(); plt.xlabel(\"sweeps\"); plt.ylabel(r\"max. residuals & error(--) ($L_\\infty$ norm)\");\n", "plt.ylim(1e-6, 2); plt.legend();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... we can see that with this preconditioner, the SDC iteration converges **way faster to the collocation accuracy** (only two sweeps), and this is visible in some residuals value that decrease very quickly.\n", "\n", "Comparing the residuals evolution for different types of approximations can then give some first insights on the efficiency of different SDC variants, for instance when we compare the Backward-Euler sweep from the original SDC methods,\n", "the Trapezoidal rule and the `MIN-SR-NS` diagonal approximation from [[Caklovic et al., 2024]](https://arxiv.org/pdf/2403.18641>) :" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nSweeps = 4\n", "for qDelta, sym in zip([\"BE\", \"TRAP\", \"MIN-SR-NS\"], [\"o\", \">\", \"s\"]):\n", "\n", " QDelta = genQDeltaCoeffs(qDelta, qGen=coll)\n", "\n", " uNum, monitors = solveDahlquistSDC(\n", " lam=lam, u0=u0, T=T, nSteps=nSteps, nSweeps=nSweeps,\n", " Q=Q, QDelta=QDelta, weights=weights, monitors=[\"residuals\", \"errors\"])\n", "\n", " residuals = np.max(np.linalg.norm(monitors[\"residuals\"], axis=-1, ord=np.inf), axis=-1)\n", " errors = np.max(np.linalg.norm(monitors[\"errors\"], axis=-1, ord=np.inf), axis=-1)\n", "\n", " p = plt.semilogy(residuals, sym+'-', label=f\"{qDelta}\")\n", " plt.semilogy(errors, sym+'--', c=p[0].get_color())\n", "\n", "plt.grid(); plt.xlabel(\"sweeps\"); plt.ylabel(r\"max. residuals & error(--) ($L_\\infty$ norm)\");\n", "plt.ylim(1e-6, 2); plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the `MIN-SR-NS` coefficients require $K=4$ sweeps to reach the collocation accuracy, \n", "which is better than the `BE`-based sweep, but still twice larger as the `TRAP`-based SDC.\n", "\n", "However, measuring the number of iterations to a given accuracy is **not sufficient** to assess the efficiency of\n", "a SDC variant. Here for instance, since the `MIN-SR-S` approximation is diagonal, this enable some parallelism across\n", "the sweep update that can improve the time-to-solution.\n", "\n", "Also, we looked at convergence only for one $\\lambda$ value, and only considered the accuracy. \n", "While this is interesting for a first look, analyzing other numerical aspects of SDC variants is critical\n", "for a fair comparison. \n", "This is especially true for numerical stability, which is the subject of the next tutorial (incoming ...)" ] } ], "metadata": { "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 2 }