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@duetosymmetry
Created January 9, 2025 15:54
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Kartik's toy BVP example
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "fb3dfd16",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%config InlineBackend.figure_format = 'retina'"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "285b1f24",
"metadata": {},
"outputs": [],
"source": [
"import time\n",
"import numpy as np\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import rc\n",
"\n",
"from dedalus import public as de\n",
"import dedalus.core.operators as ops\n",
"\n",
"import logging\n",
"logger = logging.getLogger(__name__)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "ee0f205f",
"metadata": {},
"outputs": [],
"source": [
"ncc_cutoff = 1e-6\n",
"tolerance = 5e-8\n",
"Nx = 20\n",
"my_scale = 1.5\n",
"max_iters = Nx*4\n",
"boundary_width = .04"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "2627a0eb",
"metadata": {},
"outputs": [],
"source": [
"xb1 = de.Chebyshev('x1', Nx, interval=(0, 1 - boundary_width), dealias=my_scale)\n",
"xb2 = de.Chebyshev('x2', Nx, interval=(1 - boundary_width, 1), dealias=my_scale)\n",
"x_basis = de.Compound('x', (xb1, xb2))\n",
"domain = de.Domain([x_basis], np.float64)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "ad019a25",
"metadata": {},
"outputs": [],
"source": [
"problem = de.NLBVP(domain, variables=['f', 'fx'], ncc_cutoff=ncc_cutoff)\n",
"problem.add_equation(\"dx(fx) = f/(1-x**2)**4\")\n",
"problem.add_equation(\"fx - dx(f) = 0\")\n",
"problem.add_bc(\"left(f) = 1\")\n",
"problem.add_bc(\"right(f) = 0\")"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "6a800cfd",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2025-01-09 09:52:42,680 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 1.5e+02/s\n"
]
},
{
"data": {
"text/plain": [
"<Field 140031508310336>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"solver = problem.build_solver()\n",
"x = problem.domain.grid(0)\n",
"f = solver.state['f']\n",
"fx = solver.state['fx']\n",
"f['g'] = 1-x # initial guess\n",
"f.differentiate('x', out=fx)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "9c8d225c",
"metadata": {},
"outputs": [],
"source": [
"logger.setLevel(logging.INFO)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "25cfb336",
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2025-01-09 09:52:42,736 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 2.8e+02/s\n",
"2025-01-09 09:52:42,738 __main__ 0/1 INFO :: Perturbation norm: 2.4280397281905124\n",
"2025-01-09 09:52:42,738 __main__ 0/1 INFO :: rms δf: 0.02127503652376801\n",
"2025-01-09 09:52:42,738 __main__ 0/1 INFO :: rms δfx: 0.1971245411711014\n",
"2025-01-09 09:52:42,759 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 2.8e+02/s\n",
"2025-01-09 09:52:42,761 __main__ 0/1 INFO :: Perturbation norm: 0.07654999079803662\n",
"2025-01-09 09:52:42,761 __main__ 0/1 INFO :: rms δf: 0.00010009551092341636\n",
"2025-01-09 09:52:42,761 __main__ 0/1 INFO :: rms δfx: 0.005014186366196408\n",
"2025-01-09 09:52:42,782 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 2.9e+02/s\n",
"2025-01-09 09:52:42,784 __main__ 0/1 INFO :: Perturbation norm: 0.006010689215542295\n",
"2025-01-09 09:52:42,784 __main__ 0/1 INFO :: rms δf: 1.7099053278718314e-05\n",
"2025-01-09 09:52:42,784 __main__ 0/1 INFO :: rms δfx: 0.00027605946365633473\n",
"2025-01-09 09:52:42,805 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 2.9e+02/s\n",
"2025-01-09 09:52:42,806 __main__ 0/1 INFO :: Perturbation norm: 0.0009673371834044691\n",
"2025-01-09 09:52:42,807 __main__ 0/1 INFO :: rms δf: 1.1268183979164277e-06\n",
"2025-01-09 09:52:42,807 __main__ 0/1 INFO :: rms δfx: 5.1014606427705486e-05\n",
"2025-01-09 09:52:42,828 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 2.9e+02/s\n",
"2025-01-09 09:52:42,829 __main__ 0/1 INFO :: Perturbation norm: 0.00018872220823976349\n",
"2025-01-09 09:52:42,829 __main__ 0/1 INFO :: rms δf: 2.360608760617621e-07\n",
"2025-01-09 09:52:42,830 __main__ 0/1 INFO :: rms δfx: 1.0263371991699937e-05\n",
"2025-01-09 09:52:42,851 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 2.9e+02/s\n",
"2025-01-09 09:52:42,852 __main__ 0/1 INFO :: Perturbation norm: 3.982150073831932e-05\n",
"2025-01-09 09:52:42,852 __main__ 0/1 INFO :: rms δf: 4.920112678379288e-08\n",
"2025-01-09 09:52:42,852 __main__ 0/1 INFO :: rms δfx: 2.1933119236987852e-06\n",
"2025-01-09 09:52:42,873 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 2.9e+02/s\n",
"2025-01-09 09:52:42,875 __main__ 0/1 INFO :: Perturbation norm: 8.45160190376727e-06\n",
"2025-01-09 09:52:42,875 __main__ 0/1 INFO :: rms δf: 1.0521797332229165e-08\n",
"2025-01-09 09:52:42,875 __main__ 0/1 INFO :: rms δfx: 4.646530372618751e-07\n",
"2025-01-09 09:52:42,896 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 2.9e+02/s\n",
"2025-01-09 09:52:42,897 __main__ 0/1 INFO :: Perturbation norm: 1.816810762856955e-06\n",
"2025-01-09 09:52:42,897 __main__ 0/1 INFO :: rms δf: 2.229521345378113e-09\n",
"2025-01-09 09:52:42,898 __main__ 0/1 INFO :: rms δfx: 9.876725377239115e-08\n",
"2025-01-09 09:52:42,918 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 2.9e+02/s\n",
"2025-01-09 09:52:42,919 __main__ 0/1 INFO :: Perturbation norm: 4.0812765848983224e-07\n",
"2025-01-09 09:52:42,919 __main__ 0/1 INFO :: rms δf: 4.733544657318266e-10\n",
"2025-01-09 09:52:42,920 __main__ 0/1 INFO :: rms δfx: 2.108085883656701e-08\n",
"2025-01-09 09:52:42,941 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 2.8e+02/s\n",
"2025-01-09 09:52:42,942 __main__ 0/1 INFO :: Perturbation norm: 1.0999659042071934e-07\n",
"2025-01-09 09:52:42,942 __main__ 0/1 INFO :: rms δf: 1.0030493022935757e-10\n",
"2025-01-09 09:52:42,942 __main__ 0/1 INFO :: rms δfx: 4.717430176480361e-09\n",
"2025-01-09 09:52:42,963 pencil 0/1 INFO :: Building pencil matrix 1/1 (~100%) Elapsed: 0s, Remaining: 0s, Rate: 2.8e+02/s\n",
"2025-01-09 09:52:42,964 __main__ 0/1 INFO :: Perturbation norm: 4.780126764937006e-08\n",
"2025-01-09 09:52:42,964 __main__ 0/1 INFO :: rms δf: 2.1230407159784427e-11\n",
"2025-01-09 09:52:42,965 __main__ 0/1 INFO :: rms δfx: 1.6250406443224893e-09\n",
"2025-01-09 09:52:42,965 __main__ 0/1 INFO :: terminated after iters=11, max_iters=80\n"
]
}
],
"source": [
"pert = solver.perturbations.data\n",
"pert.fill(1+tolerance)\n",
"start_time = time.time()\n",
"cur_iter = 1\n",
"while (np.sum(np.abs(pert)) > tolerance) and (cur_iter <= max_iters):\n",
" solver.newton_iteration()\n",
" logger.info('Perturbation norm: {}'.format(np.sum(np.abs(pert))))\n",
" logger.info('rms δf: {}'.format(np.sqrt(np.mean(solver.perturbations['δf'].data**2))))\n",
" logger.info('rms δfx: {}'.format(np.sqrt(np.mean(solver.perturbations['δfx'].data**2))))\n",
" cur_iter += 1\n",
"end_time = time.time()\n",
"logger.info('terminated after iters={}, max_iters={}'.format(cur_iter-1, max_iters))"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "31c7b9ed",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f5b85a661f0>]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 258,
"width": 380
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(solver.perturbations.field_dict['δfx']['g'])"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "13cdb4a0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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5nD9YL3+sgZxzz0rqIylW0g2S7pPUT9J6SSOPnPqCyJYYH6vXBrRVz+bVg7VP52zQkPfnKDMn18POAAAAik5xrIMe2NBdx5ybYGb3SPpE0khJDSQlSWoj/4ow75nZf4/nD3TOtTnaS9KSgnwB8E58rE/Drmily9rWCta+/XWrrh85S2mZOR52BgAAUDRCEdAP3iFPzud8uSPed1Rm1k3S45K+cM7d6Zxb5ZxLd87NkdRb0kZJdwUeSkUUifGZHrukuW44o16wNmnFDl31+nTtTs/ysDMAAIDQC0VAXxo45jfH/OTAMb856gf9KXAcd+QJ51y6/Our+yS1OtEGUfKZme6/sKn+2uPQ/2Zz1+3W5a9M07Z9BzzsDAAAILRCEdAPBuoeZvab8cysrKTOkjIkTTvGOAmBY35LKR6sc8s0SpmZbul+sh65+JRgbcmWfer30lStT033sDMAAIDQKXRAd86tlH+VlbqShhxx+mH555G/7ZxLkyQzizOzJoHdRw83MXC80cxqHH7CzC6QP+gfkDSlsD2jZBvQsa6euaylYnz+xxvW7kxX35emaPnWfR53BgAAUHihekh0sKRtkoaZ2ZjA8og/SbpD/qktDxz23hqSFkv68YgxPpF/nfOqkhab2Vtm9riZfSHpK/kfNr3PObczRD2jBOvdqqZeuqqN4mP9/wtv3ZupS1+eqgUbdnvbGAAAQCGFJKAH7qK3lX/1lfaS7pJ/FZZhkjoeT6gObHJ0ofyhfpH8D4beJf8GR19LOs8591wo+kVkOLdZVY289nQlxcdIknalZ+vKV6dr6kr+DgcAAEoui6bt081sduvWrVvPnj3b61YQQvPW79Y1b87Q7vRsSf6lGV/8S2ud3bSqx50BAIBo1aZNG82ZM2dOYKnvE1Ic66ADReq0WuX10U0dVaWs/znjrJw83fTObH0+b6PHnQEAAJw4AjoiQqOqZfXJoE6qnZIoScrJc7p91Dy9M22tx50BAACcGAI6Ikbtion6eFBHNapaRpLknPT3Mb9o+LgViqapXAAAoGQjoCOiVC1XSqNu7KiWtcoHa098u1SPfbOEkA4AAEoEAjoiToWkeL03sL06NagYrL08fpXuH/2LcvMI6QAAILwR0BGRyiTE6o1rTte5zQ6t5PLBjHW67cO5ysrJ87AzAACAP0ZAR8QqFRejF//SWn1aHdqY9ssFm3XjO7OUkZXrYWcAAAD5I6AjosXG+PRkv5a6umOdYO3npds14I3p2nsg28POAAAAjo6Ajojn85n++edTNLR7w2Bt5ppduuKVadq5P9PDzgAAAH6PgI6oYGa6s0djPdizabD266a96vfyVG3aneFhZwAAAL9FQEdUGXhGff33khbymf/jVdvTdMmLU7Rs6z5vGwMAAAggoCPqXHp6Lb1wZWvFxfhT+uY9B9TvpamavTbV484AAAAI6IhSFzavrjevaaek+BhJ0p6MbF356nT9sGirx50BAIBoR0BH1OpyciV9eGNHVSoTL0nKzMnTTe/O1qiZ6zzuDAAARDMCOqJa85rJ+vTmTqqdkihJys1zuvfThXrhp+Vyjl1HAQBA8SOgI+rVqZikT2/upFNOKhesPfndMv3zi1+Vm0dIBwAAxYuADkiqXDZBH97YQZ0bVgzW3pq6VkM/mKvMHHYdBQAAxYeADgSULRWnN645XT1bVA/Wvlq4Wde8MZNdRwEAQLEhoAOHSYiN0fOXt9I1neoGa1NX7dTlL0/Ttn0HvGsMAABEDQI6cASfz/TQRc10z/mNg7VFm/fqkhenaPWONA87AwAA0YCADhyFmWlwt4b6b98WiglsO7o+NUN9X5yiBRt2e9scAACIaAR04A9c2raWXunfRqXi/N8qO9OydPkr0zRh2XaPOwMAAJGKgA4cw9lNq+q9gR1UPjFOkpSelavrRs7U5/M2etwZAACIRAR04Di0qVNBnwzqqJOSS0mScvKcbvtwnl6buMrjzgAAQKQhoAPHqWGVsvp0cCc1qlomWPu/rxbr0f8tZtdRAAAQMgR04ARUTy6tj2/qpLZ1KgRrL49fpbs+nq/s3DwPOwMAAJGCgA6coOTEOL07sL3OaVo1WPtszkbd8PYspWfleNgZAACIBAR0oABKxcXopata64p2tYK1n5du1xWvTldqWpaHnQEAgJKOgA4UUGyMT//p3VxDuzcM1uav362+L03Rhl3pHnYGAABKMgI6UAhmpjt7NNa/Lj5F5t/PSKu2p+mSF6doyZa93jYHAABKJAI6EAL9O9bV8CtbKz7G/y21dW+m+r00VdNX7fS4MwAAUNIQ0IEQubB5db11XTuVTYiVJO07kKP+b8zQN79s9rgzAABQkhDQgRDq2KCiRt3UUZXLJkiSsnLyNPi9OXp32lqPOwMAACUFAR0IsWYnldNnN3dSvUpJkqQ8Jz045hc9+8MyNjQCAADHREAHikCtlER9MqijWtRMDtae/WG5Hhjzi3LzCOkAACB/BHSgiFQsk6APbuigro0qB2vvT1+nwe/N1oHsXA87AwAA4YyADhShpIRYvTagrXq3qhGsffvrVg14fYb2ZGR72BkAAAhXBHSgiMXH+vRUv5a64Yx6wdqMNam67OWp2rr3gIedAQCAcERAB4qBz2d6oGcz3X9hk2BtyZZ96jNiilZs2+9hZwAAINwQ0IFidGPXBnr60paK9fm3Hd24O0P9Xpqiuet2edwZAAAIFwR0oJj1aV1Tr13dVonxMZKkXenZuvLV6Rq3dJvHnQEAgHBAQAc80K1xFb1/QwelJMVLkjKyczXwrVn6dPYGjzsDAABeI6ADHjmtVnl9MqijapQvLUnKzXO66+P5enn8SjY0AgAgihHQAQ/Vr1xGnw3upCbVygZrj/5viR75chEbGgEAEKUI6IDHqpYrpY8GdVT7einB2puT12jwe7OVkcWGRgAARBsCOhAGypWK01vXtdOFzasFa9/+ulWXvzpNO/ZnetgZAAAobgR0IEyUiovRC1e0/s2GRvPX71bvEZO1cjtrpQMAEC0I6EAYObih0SMXn6LAUulan5qhPiOmaMbqVG+bAwAAxYKADoShAR3r6pX+bVU6zr9W+p6MbF312nR9Pm+jx50BAICiRkAHwtQ5zapq1E0dVKlMgiQpKzdPt304T8PHrWAZRgAAIhgBHQhjLWqW1+jBndSwSplg7Ylvl+r+0QuVnZvnYWcAAKCoENCBMFcrJVGfDuqkDvUPLcP4wYz1uv6tWdqfmeNhZwAAoCgQ0IESIDkxTm9f1159WtUI1iYs265+L03V5j0ZHnYGAABCjYAOlBDxsT49dWlLDT375GBt8ea96j18ihZv3uthZwAAIJQI6EAJYma689xG+m/fFooNrMO4Ze8B9XtpqiYs2+5xdwAAIBQI6EAJdGnbWhp5bTuVTYiVJO3PzNG1I2dq1Mx1HncGAAAKi4AOlFBdTq6kj2/uqJOSS0mScvOc7v10oZ78dinLMAIAUIIR0IESrEm1cho9pLOaVS8XrL0wboVuHzVPmTm5HnYGAAAKioAOlHBVy5XSR4M66qzGlYO1z+dtUv/XZ2h3epaHnQEAgIIgoAMRoExCrF4d0FZXtq8drM1YnapLXpyi9anpHnYGAABOFAEdiBCxMT79u9epuu+CJsHayu1p6j1isuat3+1dYwAA4IQQ0IEIYmYadGYDPX9FK8XH+r+9d+zP0uWvTNV3v27xuDsAAHA8COhABLqo5Ul6b2B7lU+MkyQdyM7TTe/O1puTV3vcGQAAOBYCOhChTq+bos9u7qQ6FRMlSc5JD49dpIfH/qrcPJZhBAAgXIUsoJtZTTN7w8w2mVmmma0xs2fNrEIBxjrDzD41s82BsTab2XdmdmGo+gWiQf3KZfTZzZ3Uqnb5YO3NyWt087uzlZHFMowAAISjkAR0M2sgabakayXNkPSMpFWSbpM01cwqnsBYD0qaIKmrpG8kPSVprKQKkrqFol8gmlQsk6APbuigC06tFqx9t2irLn91mnbsz/SwMwAAcDShuoM+QlIVSUOdc72cc/c557rLH9QbS/r38QxiZv0k/UvSD5LqO+eudc7d75y70Tl3uqQHQtQvEFVKxcVo+JWtdcMZ9YK1+et3q/eIyVq5fb+HnQEAgCMVOqCbWX1JPSStkTT8iNMPSUqT1N/Mko4xjk/S45LSJV3pnNt35Hucc9mF7ReIVj6f6YGezfTIxafIZ/7a+tQM9RkxRdNX7fS2OQAAEBSKO+jdA8fvnHN5h58IhOzJkhIldTjGOJ0k1ZP0taRdZtbTzO41s9vMrGMI+gQgaUDHunqlf1uVjouRJO3JyFb/12fo83kbPe4MAABIUmwIxmgcOC7L5/xy+e+wN5L04x+Mc3rguFXSHEnNDz9pZhMk9XXObT9WQ2Y2O59TTfKpA1HlnGZVNeqmDrpu5Czt2J+prNw83fbhPG3YlaHB3RrIzLxuEQCAqBWKO+jJgeOefM4frJc/xjhVAsdBkkpLOkdSWUmnSvpW/odGPy5wlwB+o0XN8ho9uJMaVikTrD3x7VL97bOFys7N+4PPBAAARak41kE/eCvuWAsvxxz2/r7OuR+dc/udc79K6i1pg6Qzj2e6i3OuzdFekpYU9IsAIlGtlER9OqiTOtRPCdY+nLle1781S/szczzsDACA6BWKgH7wDnlyPufLHfG+/OwKHFc55+YffsI5lyH/XXRJanfCHQLIV3JinN6+rr36tKoRrE1Ytl39XpqqzXsyPOwMAIDoFIqAvjRwbJTP+ZMDx/zmqB85zu58zh8M8KWPry0Axys+1qenLm2poWefHKwt3rxXvYdP0eLNez3sDACA6BOKgD4ucOwRWCoxyMzKSuosKUPStGOMM0FSjqSTzSz+KOdPDRzXFLxVAPkxM915biP9t28LxQbWYdyy94D6vTRV45cd89lsAAAQIoUO6M65lZK+k1RX0pAjTj8sKUnS2865NEkyszgzaxLYffTwcXZIGiX/VJl/HH7OzM6VdJ7802S+KWzPAPJ3adtaGnltO5VN8C/ytD8zR9eNnKlRM9d53BkAANEhVA+JDpa0TdIwMxtjZo+a2U+S7pB/asvhO4DWkLRYR19y8U5JKyQ9YGYTzOxJM/tY0v8k5Uq6wTm3O0Q9A8hHl5Mr6eObO+qk5FKSpNw8p3s/Xagnv10q5471vDcAACiMkAT0wF30tpJGSmov6S5JDSQNk9TROXdc2xQ657YFPv8ZSbUkDZV/I6SvJJ3hnGOZRaCYNKlWTqOHdFaz6uWCtRfGrdDto+YpMyfXw84AAIhsodioSJLknFsv6drjeN8aHVp68WjnU+W/k35nqHoDUDBVy5XSR4M66tb352jcUv889M/nbdLmPQf0Sv82Kp94tMdFAABAYRTHOugASrAyCbF6dUBbXdm+drA2Y3Wqeo+YopXb93vYGQAAkYmADuCYYmN8+nevU3XfBU2CtdU70tR7+GRNXM4KLwAAhBIBHcBxMTMNOrOBhl/ZWqXi/D869h7I0TVvztRbU9bw8CgAACFCQAdwQnq2qK6Pb+qkquUSJPlXeHnoi1/14JhflJ2b53F3AACUfAR0ACesec1kfXFLF7WsmRysvTd9na5+Y4Z2p2d52BkAACUfAR1AgVQtV0qjbuqoi1qeFKxNWblTvYZP1optPDwKAEBBEdABFFipuBgNu/w03XVuo2Btzc509R4xWROW8fAoAAAFQUAHUChmplvPPlkv/qW1SsfFSJL2HcjRNW/O0JuTV/PwKAAAJ4iADiAkLmheXR8P6qjqyaUkSXlOenjsIt0/modHAQA4EQR0ACFzao1kfT6ks06rVT5Y+2DGOvV/fbp2pfHwKAAAx4OADiCkqpQrpQ9v7KCLTzv08Oi0VanqNWKyVmzb52FnAACUDAR0ACFXKi5Gz152mu4+r3GwtnZnunoPn6Kfl27zsDMAAMIfAR1AkTAzDTmroV66qs2hh0czc3TdyJl6fRIPjwIAkB8COoAidf6p1fTJzR110mEPj/7ry0X622cLlZXDw6MAAByJgA6gyJ1yUrLG3NJZrWqXD9Y+nLle/V+frlQeHgUA4DcI6ACKRZWypfTBDR3Uu1WNYG366lT1Gj5Zy7by8CgAAAcR0AEUm1JxMXr60pa65/zGMvPX1qWmq8+IKfppyVZvmwMAIEwQ0AEUKzPT4G4N9fJVbZQY7394dH9mjq5/a5Zem7iKh0cBAFGPgA7AEz1OqaZPb+6kGuVLS5Kck/7vq8W699MFPDwKAIhqBHQAnmlavZzGDOmsNnUqBGsfzdqgq16brp37Mz3sDAAA7xDQAXiqctkEvX9De/Vpfejh0RlrUnXx8MlauoWHRwEA0YeADsBzCbExeqpfS/3tgibBh0c37MpQnxGT9eNiHh4FAEQXAjqAsGBmuunMBnqlf1slBR4eTcvK1cC3Z+mVCSt5eBQAEDUI6ADCyrnNqurTwZ1Us8Khh0f/8/US3f3JAmXm5HrcHQAARY+ADiDsNKlWTp8P6azT6x56ePST2Rv0l1enawcPjwIAIhwBHUBYqlgmQe8ObK9+bWoGa7PW7tLFL0zWki17PewMAICiRUAHELYSYmP0374t9MCFTYMPj27cnaFLRkzR94t4eBQAEJkI6ADCmpnphq719frVbVUmIVaS/+HRG9+ZpRd/5uFRAEDkIaADKBG6N6mqzwZ3Uq2UQw+PPv7NEt318XweHgUARBQCOoASo1HVsvp8SBe1q5sSrH02Z6OueGWatu/j4VEAQGQgoAMoUVKS4vXuwPa6rG2tYG3Out3qNXyyFm3i4VEAQMlHQAdQ4sTH+vTYJc31YM+m8h328Gjfl6bo21+3eNscAACFREAHUCKZmQaeUV+vX3O6ygYeHk3PytWgd2dr+LgVPDwKACixCOgASrSzGlfRZ4M7qXZKoiT/w6NPfLtUd340XweyeXgUAFDyENABlHgnVy2rMUM6q329Qw+Pjp67UVe8Ok3b9h3wsDMAAE4cAR1AREhJitc717fXFe0OPTw6d91u9Xphsn7dtMfDzgAAODEEdAARIz7Wp//0bq6HLmoWfHh0054D6vviVH25YJO3zQEAcJwI6AAiipnp2s719MZhD49mZOfqlvfn6j9fL1ZObp7HHQIA8McI6AAiUrfGVTR6SCfVq5QUrL0yYZUGvDFDO/ezqREAIHwR0AFErIZV/A+PntO0SrA2ZeVOXfT8JC3YsNu7xgAA+AMEdAARLbl0nF7p31Z3nttIdvi89Jem6qOZ671tDgCAoyCgA4h4Pp9p6Nkn642rT1fZUv556Vk5ebrn0wV6YPRCZeUwLx0AED4I6ACixllNqmjsLV3UuGrZYO296et02StTtWUP66UDAMIDAR1AVKlbKUmjh3TSRS1PCtbmrtutPz0/STNWp3rYGQAAfgR0AFEnMT5Wwy4/TQ/2bKqYwILpO/Zn6spXp+nNyavlnPO4QwBANCOgA4hKZqaBZ9TXO9e3U8WkeElSTp7Tw2MX6a6P5isjK9fjDgEA0YqADiCqdWpQSWNv7aKWNZODtc/mbtQlL07R+tR0DzsDAEQrAjqAqHdS+dIadVNHXda2VrC2aPNe/en5SRq/bLuHnQEAohEBHQAklYqL0eN9W+g/vZsrLsY/L31PRraueXOGho9bwbx0AECxIaADwGGubF9bo27qqKrlEiRJzklPfLtUg96drX0Hsj3uDgAQDQjoAHCE1rUr6Mtbz1C7einB2re/blWv4ZO1Ytt+DzsDAEQDAjoAHEXlsgl6b2B7Xde5XrC2cnuaeg2frG9+2eJhZwCASEdAB4B8xMX49I+LmunZy05TqTj/j8v9mTka9O5sPfHtEuXmMS8dABB6BHQAOIZerWro05s7qVZK6WBt+LiVunbkTO1Oz/KwMwBAJCKgA8BxOOWkZI29pYu6NqocrE1Ytl0XvTBJv27a42FnAIBIQ0AHgONUPjFeb15zum45q2Gwtj41Q5e8OEWj527wsDMAQCQhoAPACYjxmf56XmO93L+NyiTESpIOZOfpjlHz9c8vflV2bp7HHQIASjoCOgAUwHmnVNOYIZ3VoHJSsDZyyhr95dXp2rbvgIedAQBKOgI6ABRQwypl9PktXXT+KdWCtRlrUnXR85M0e+0uDzsDAJRkBHQAKIQyCbF68arWuuf8xvKZv7Z1b6Yuf2Wq3pu+Vs6xFCMA4MQQ0AGgkMxMg7s11Mhr26l8YpwkKTvX6YHRv+jeTxfoQHauxx0CAEoSAjoAhEjXRpU19pYuala9XLD20awNuvTlqdq4O8PDzgAAJQkBHQBCqFZKoj69uZP6tKoRrC3YsEcXPT9JU1bu8LAzAEBJQUAHgBArHR+jpy5tqX9e1EyxgYnpqWlZuuq16Xp1wirmpQMA/hABHQCKgJnpms719P4NHVSpTIIkKc9J//56sW79YK7Ss3I87hAAEK5CFtDNrKaZvWFmm8ws08zWmNmzZlahEGP2NzMXeA0MVa8AUFza1UvRV0O7qHXt8sHalws2q/fwKVqzI827xgAAYSskAd3MGkiaLelaSTMkPSNplaTbJE01s4oFGLOWpOcl7Q9FjwDglarlSunDGzvqqg61g7WlW/fpohcm6aclWz3sDAAQjkJ1B32EpCqShjrnejnn7nPOdZc/qDeW9O8TGczMTNKbknZKeilEPQKAZ+Jjffq/Xs31374tFB/r/9G770COrhs5S8/+sEx5ecxLBwD4FTqgm1l9ST0krZE0/IjTD0lKk9TfzJJ0/IZK6i7/HXn+DRhAxLi0bS19MqijTkouFaw9+8Ny3fD2LO3JyPawMwBAuAjFHfTugeN3zrm8w0845/ZJmiwpUVKH4xnMzJpKekzSc865CQVpyMxmH+0lqUlBxgOAUGpRs7zG3tpFnRocmv3345Jt6jV8spZu2edhZwCAcBCKgN44cFyWz/nlgWOjYw1kZrGS3pG0TtL9hW8NAMJTxTIJevu6drqpa/1gbfWONPUeMVlfLtjkYWcAAK/FhmCM5MBxTz7nD9bLH8dY/5DUSlIX51yBt91zzrU5Wj1wF711QccFgFCKjfHpbxc2VfOaybrnkwVKz8pVelaubnl/rhZs2KN7zmus2BhWwwWAaFMcP/ktcPzDJ6DMrJ38d82fcs5NLfKuACBM/KnFSRo9uLPqVkwM1l6ZsEp/eW26tu494GFnAAAvhCKgH7xDnpzP+XJHvO93DpvaskzS30PQEwCUKI2rldXnt3TR2U2qBGvTV6fqgucmavyy7R52BgAobqEI6EsDx/zmmJ8cOOY3R12SygQ+v6mkA4dtTuTkXwlGkl4N1J4tbMMAEI6SS8fp1QFtdee5jeQL/NtjalqWrn5jhh7/ZolycvP+eAAAQEQIxRz0cYFjDzPzHb6Si5mVldRZUoakaX8wRqak1/M511r+eemT5P/LANNfAEQsn8809OyTdXrdFN324Vxt25cpSXrx55WauTpVw65opZPKl/a4SwBAUSr0HXTn3EpJ30mqK2nIEacflpQk6W3nXJokmVmcmTUJ7D56cIwM59zAo70kfRF421uB2qjC9gwA4a5jg4r6+rYzdMbJlYK1WWt36cJhE/XjYnYfBYBIFqqHRAdL2iZpmJmNMbNHzewnSXfIP7XlgcPeW0PSYkk/hujPBoCIVKlMgt66tp3uOb+xYgJzXnanZ+v6t2bp318tUlYOU14AIBKFJKAH7qK3lTRSUntJd0lqIGmYpI7OuZ2h+HMAINr4fKbB3Rrqwxs7qPphu4++OnG1Ln15qtanpnvYHQCgKIRsmUXn3Hrn3LXOuerOuXjnXB3n3G3OudQj3rfGOWfOubrHOe4/A+9/LVS9AkBJc3rdFH019Ax1P2yVl3nrd6vnsIn65pctHnYGAAg1dsAAgBIiJSlerw1oqwcubKrYwJSXvQdyNOjd2frnF78qMyfX4w4BAKFAQAeAEsTnM93Qtb4+GtRRNQ5bzWXklDXq++JUrd2Z5mF3AIBQIKADQAnUunYFfT30DPVoVjVYW7hxj3oOm6QvF2zysDMAQGER0AGghEpOjNPL/dvooYuaKS7GP+Vlf2aObnl/rh4YvVAHspnyAgAlEQEdAEowM9O1nevp05s7qXZKYrD+3vR16j1iilZt3+9hdwCAgiCgA0AEaFGzvL4c2kUXNq8WrC3evFd/en6Sxszd6GFnAIATRUAHgAhRrlSchl/ZWv/qdariY/0/3tOzcnX7qHm695MFyshiygsAlAQEdACIIGam/h3qaPTgTqpXKSlYHzVrvS4ePknLt+7zsDsAwPEgoANABDrlpGSNvbWLLj7tpGBt2db9+vMLk/XxrPUedgYAOBYCOgBEqDIJsXr2stP0+CXNlRCY8pKRnau7P1mgOz+ap7TMHI87BAAcDQEdACKYmemy02vri1u6qEHlQ1NePpuzUX9+YZKWbNnrYXcAgKMhoANAFGhcrazG3tpFl7SuGayt3J6mi1+YrA9mrJNzzsPuAACHI6ADQJRIjI/VU5e21JP9Wqp0XIwkKTMnT3/7bKGGfjhP+w5ke9whAEAioANA1OnbpqbG3tpZjauWDdbGzt+ki56fpF827vGwMwCAREAHgKjUsEpZfX5LZ13RrlawtmZnuvqMmKJ3pq5hygsAeIiADgBRqlRcjB7t00LPXX6akuL9U16ycvP0989/1ZD352hPBlNeAMALBHQAiHIXn1ZDY2/tombVywVrXy/coj89P1Hz1+/2rjEAiFIEdACA6lcuo88Gd1L/DnWCtfWpGer70hS9Pmk1U14AoBgR0AEAkvxTXv7V61QNv7K1yibESpKyc53+9eUi3fD2bO1Oz/K4QwCIDgR0AMBv9GxRXV8NPUMtaiYHaz8s3qqewyZp9tpdHnYGANGBgA4A+J3aFRP18aCOurZz3WBt4+4MXfbyVL08fqXy8pjyAgBFhYAOADiqhNgYPXTRKXq5fxuVK+Wf8pKT5/To/5bo+rdmKjWNKS8AUBQI6ACAP3TeKdX09W1nqFXt8sHauKXbdeFzEzVjdap3jQFAhCKgAwCOqWaFRH10U0fd2LV+sLZl7wFd8eo0DR+3gikvABBCBHQAwHGJi/Hp/gub6o1r2qpCYpwkKTfP6Ylvl+rqN2do+75MjzsEgMhAQAcAnJDuTarq69vO0Ol1KwRrE5fv0IXDJmrKih0edgYAkYGADgA4YdWTS+uDGzpoyFkNZOavbd+Xqb+8Pl1PfrtUWTl53jYIACUYAR0AUCCxMT7dfV4TvXVtO1VMipckOSe9MG6Feo+YrOVb93ncIQCUTAR0AEChdG1UWV/fdoY61q8YrP26aa96Pj9Jr09azQOkAHCCCOgAgEKrWq6U3hvYXg/2bKr4WP+vlqycPP3ry0W66vXp2rg7w+MOAaDkIKADAELC5zMNPKO+vry1i5pVLxesT1m5U+c/O0Gj526Qc9xNB4BjIaADAEKqUdWyGjOks4ac1UC+wAOk+w7k6I5R8zXk/TnaxQ6kAPCHCOgAgJCLj/U/QPrxoI6qnZIYrH+9cIt6PDtB45Zu87A7AAhvBHQAQJFpUydF/7vtDF3Rrlawtn1fpq59c6YeGL1Q6Vk5HnYHAOGJgA4AKFJJCbF6tE8LvX51W1UqkxCsvzd9nS58bqLmrNvlYXcAEH4I6ACAYnF206r69vYzdN4pVYO1NTvT1ffFKXrqu6XKzmVzIwCQCOgAgGJUsUyCXrqqjZ7s11JlEmIlSXlOev4nNjcCgIMI6ACAYmVm6tumpr65/Qy1r5cSrP+y0b+50RtsbgQgyhHQAQCeqFkhUR/c0EEPXNhU8TGHNjd65MtF6v/GdG1icyMAUYqADgDwjM9nuqFrfY29tYuaHra50eQVO3XesxM0Zu5GNjcCEHUI6AAAzzWuVlZjhnTSzd1+u7nR7aPm6Zb357K5EYCoQkAHAISFhNgY3Xt+E3100283N/pq4Wad9+wE/czmRgCiBAEdABBW2tZN0ddHbG60bV+mrnlzph4cw+ZGACIfAR0AEHbKBDY3em1AW1UqEx+svzttnXoOm6S5bG4EIIIR0AEAYeucZlX17e1d1aPZoc2NVu9IU9+XpuppNjcCEKEI6ACAsFaxTIJe7t9GT/RtEdzcKDfPadhPK9RnxBSt2MbmRgAiCwEdABD2zEz92tbS/247Q+0O29xo4cY96jlskt6czOZGACIHAR0AUGLUSvFvbnT/hU2Cmxtl5uTp4bH+zY0272FzIwAlHwEdAFCixPhMN3ZtoC9u7fz7zY2emaDP57G5EYCSjYAOACiRmlQrpzFDOmnQmQ1kgc2N9h7I0W0fztMtH8zV7nQ2NwJQMhHQAQAlVkJsjO67wL+5Ua2U0sH6Vwv8mxuNX7bdw+4AoGAI6ACAEu/0uin6321ddVnbQ5sbbd2bqavfmKG/j/mFzY0AlCgEdABARCiTEKvH+7bQqwPaqmLSoc2N3pm2ls2NAJQoBHQAQEQ5t1lVfXtHV517tM2Nvl/G5kYAwh4BHQAQcSqVSdAr/dvov31bKCk+RlJgc6Mfl+uSF6doxbb9HncIAPkjoAMAIpKZ6dK2tfTN7V3Vru6hzY0WbNijnsMmaiSbGwEIUwR0AEBEq5WSqA9u7KC/XfDbzY3+OXaRBrwxg82NAIQdAjoAIOLF+Ew3ndlAn9/SWU2qlQ3WJ63YofOemaAxc9ncCED4IKADAKJG0+rl9PktnXXTmfV/s7nR7aPm6eo3Z2p9arq3DQKACOgAgCiTEBujv13QVB/e0EE1Kxza3GjCsu0695nxemXCSuWw0gsADxHQAQBRqX39ivrm9q66plPd4N30A9l5+s/XS/TnFyZrwYbdnvYHIHoR0AEAUatMQqz++edT9NnNnX4zN33R5r3qNXyyHhm7SGmZ7EIKoHgR0AEAUa9V7Qoae2sX3Xt+EyXE+n815jnpjcmr1eOZCfppyVaPOwQQTQjoAABIiovx6eZuDfTdHV3VpWGlYH3j7gxdN3KWhrw3R9v2HvCwQwDRImQB3cxqmtkbZrbJzDLNbI2ZPWtmFY7z8yua2UAzG21mK8wsw8z2mNkkM7vezPjLBACgyNWpmKR3rm+npy9tqZSk+GD9q4WbdfbT4/X+9HVscASgSIUk9JpZA0mzJV0raYakZyStknSbpKlmVvE4hukn6VVJ7SVNl/SspE8lnSrpNUkfmR18jAcAgKJjZurTuqZ+uPNMXdK6ZrC+70CO7h+9UJe+PFXLt+7zsEMAkSxUd6VHSKoiaahzrpdz7j7nXHf5g3pjSf8+jjGWSfqzpJrOub845/7mnLtOUhNJ6yVdIqlPiPoFAOCYUpLi9dSlLfXewPaqWzExWJ+1dpcuHDZRT3+/TAeycz3sEEAkKnRAN7P6knpIWiNp+BGnH5KUJqm/mSX90TjOuZ+cc2Odc3lH1LdIeinwYbfC9gsAwInq3LCSvrm9q4ac1UCxPv8/5mbnOg37cbkuHDZR01bt9LhDAJEkFHfQuweO3x0lXO+TNFlSoqQOhfgzsgNH1roCAHiiVFyM7j6vib4c2kWtapcP1ldtT9Plr0zTvZ8s0O70LO8aBBAxQhHQGweOy/I5vzxwbFSQwc0sVtKAwIffHOfnzD7aS/7pMgAAFFiTauX0yaBO+tfFp6hMQmywPmrWep3z9Hh9MX+TnOMhUgAFF4qAnhw47snn/MF6+QKO/5j8D4p+7Zz7toBjAAAQMjE+U/+OdfXDnWfqvFOqBus79mdp6Adzdc2bM7U+Nd3DDgGUZMWxdOHBlVdO+HaCmQ2VdJekJZL6H+/nOefaHO0VGAcAgJCollxKL/dvq5f7t1G1cqWC9fHLtqvHMxP06oRVysnN+4MRAOD3QhHQD94hT87nfLkj3ndczGyIpOckLZJ0lnMutWDtAQBQtM47pZq+v7Orru5YRwcXBM7IztW/v16si4dP1sINJ/QrEECUC0VAXxo45jfH/OTAMb856r9jZrdLekHSL/KH8y0F7g4AgGJQtlScHr74VH16cyc1rlo2WP91015dPHyS/vXlIqVlstYBgGMLRUAfFzj2OHK3TzMrK6mzpAxJ045nMDO7V/710+fJH863haBHAACKRevaFfTl0C665/zGSoj1/1rMc9Lrk1arxzMT9NOSrR53CCDcFTqgO+dWSvpOUl1JQ444/bCkJElvO+fSJMnM4sysSWD30d8ws7/L/1DobElnO+d2FLY/AACKW1yMT4O7NdR3d3RVl4aVgvWNuzN03chZGvL+HG3bd8DDDgGEs9hjv+W4DJY0RdIwMztb0mJJ7SWdJf/UlgcOe2+NwPm18od6SZKZXS3pEUm5kiZKGmoHJ/IdssY5NzJEPQMAUKTqVEzSO9e30+i5G/WvLxdpV7p/W4+vFmzWxGXb9bcLm+qytrXk8/3u9x2AKBaSgO6cW2lmbeUP2OdLulDSZknDJD18nA941gscYyTdns97xksaWahmAQAoRmamPq1rqlvjKvq/rxbpszkbJUl7D+Tob58t1GdzNujRPs3VsErZY4wEIFpYNG2mYGazW7du3Xr27NletwIAiFKTlu/QA2MWau3OQ+ukx8WYBndrqMFnNVBCbIyH3QEIlTZt2mjOnDlzAkt9n5DiWAcdAAAEdDm5kr69vasGd2ug2MDUluxcp+d+XK4Lnpuo6at2etwhAK8R0AEAKGal4mJ0z/lN9OXQLjqtVvlgfdX2NF32yjTd9+kC7QnMVwcQfQjoAAB4pEm1cvr05k565OJTVCbh0GNhH85cr7OfHq+x8zcpmqaiAvAjoAMA4KEYn2lAx7r6/s6u6tGsarC+Y3+mbv1grq4dOVPrU9P/YAQAkYaADgBAGKieXFqvDGirl65qo6rlEoL1n5duV49nJui1iauUk5vnYYcAigsBHQCAMHL+qdX0w51nakDHOjq4HUhGdq7+76vF6jVishZu2ONtgwCKHAEdAIAwU7ZUnB65+FR9enMnNa56aH30Xzbu1cXDJ+nvY37Rzv2ZHnYIoCgR0AEACFOta1fQl0O76O7zGis+1v8rO89J70xbq25P/KwXf16pA9m5HncJINQI6AAAhLG4GJ+GnNVQ393eVV0aVgrW92Xm6PFvlujsp8br83kbWe0FiCAEdAAASoC6lZL0zvXt9NqAtqpfOSlY37g7Q7d9OE+9RkzRrDWpHnYIIFQI6AAAlBBmpnOaVdW3t3fVIxefopSk+OC5+et3q+9LUzX4vdlauzPNwy4BFBYBHQCAEiYuxqcBHevq57u76aYz6ys+5tCv868XbtE5T4/X/325iN1IgRKKgA4AQAlVrlSc/nZBU/1415m6qOVJwXp2rtNrk1brzCfH6Y1Jq5WVw/rpQElCQAcAoISrlZKo569opdGDO6lNnQrB+u70bD3y5SL1eGa8vvllCw+SAiUEAR0AgAjRqnYFfTKoo0b8pbVqpZQO1tfsTNegd2frslemacGG3d41COC4ENABAIggZqYLm1fXD3eeqQcubKqypWKD52asTtWfX5is2z+cq427MzzsEsAfIaADABCBEmJjdEPX+ppw91m6plNdxfoseG7MvE3q/uTPeuLbJdqfmeNhlwCOhoAOAEAEq5AUr3/++RR9d0dX9WhWNVjPzMnT8HEr1e2JcXpv+lrl5PIgKRAuCOgAAESB+pXL6JUBbfXhjR10ao1ywfqO/Vl6YPQvuuC5iRq3dBsPkgJhgIAOAEAU6VC/or4Y0kVPX9pS1ZNLBevLt+3XtW/O1IA3Zmjx5r0edgiAgA4AQJTx+Ux9WtfUT3d10197NFJSfEzw3MTlO9Rz2ETd+8kCbdt7wMMugehFQAcAIEqVjo/RLd1P1ri7u+mKdrV18DnSPCeNmrVe3Z78Wc/9sFzpWTxIChQnAjoAAFGuStlSerRPc/3vtq46s1HlYD09K1fP/LBM3Z8cr09mb1BeHvPTgeJAQAcAAJKkxtXK6q3r2unt69qpcdWywfqWvQf014/n66IXJmnKyh0edghEBwI6AAD4ja6NKuvr287Qo32aq1KZhGD91017deWr0zXwrZlauX2/hx0CkY2ADgAAfifGZ7qiXW39fHc33dq9oUrFHYoMPyzepvOemaCHPv9FqWlZHnYJRCYCOgAAyFeZhFjd1aOxxv21m/q0rhGs5+Q5vTV1rc58YpxeHr9SB7JzPewSiCwEdAAAcEzVk0vr6UtP05e3dlGH+inB+r4DOXr0f0t0ztPjNXb+JjY6AkKAgA4AAI7bqTWS9cENHfTqgLaqXykpWN+wK0O3fjBXfV6cotlrd3nYIVDyEdABAMAJMTOd26yqvr2jqx7+8ymqkBgXPDd33W5d8uIUXf3GDE1btZM76kABENABAECBxMX4dHWnuvr57rN0Y9f6io85FCvGL9uuy1+ZpktenKIfFm1lDXXgBBDQAQBAoSSXjtP9FzbVD3eeqYtaniSzQ+fmrNutgW/P0vnPTdDouRuUnZvnXaNACUFABwAAIVG7YqKev6KVfrqrmy4/vZbiYg4l9WVb9+uOUfN11pM/6+2pa1j1BfgDBHQAABBS9Sol6bFLWmjiPd11wxn1lBgfEzy3YVeG/vH5r+r82E8aPm6F9mRke9gpEJ4I6AAAoEhUSy6lB3o205T7uuvOcxv95mHSnWlZeuLbper82E969H+LtW3fAQ87BcILAR0AABSp8onxGnr2yZp8X3c9dFEznZRcKnhuf2aOXh6/Sl0eH6f7Ry/U2p1pHnYKhAcCOgAAKBaJ8bG6tnM9jb/nLD3Zr6UaVikTPJeVk6f3p6/TWU/+rFs/mKtFm/Z62CngrVivGwAAANElLsanvm1qqk+rGvp+8VaN+Hml5q/fLUnKc9LY+Zs0dv4mdWtcWYO7NVS7eil/PCAQYQjoAADAEz6f6bxTqqlHs6qaumqnXvx5pSYu3xE8//PS7fp56Xa1rVNBN3droO5NqsgOX8MRiFAEdAAA4CkzU6cGldSpQSUt3LBHL45fof/9skUHNyGdtXaXrn9rlhpXLaubuzXQn1pUV2wMs3QRufi/GwAAhI3mNZM14i9t9OOdZ+qytr9dS33p1n26fdQ8dXvyZ73DWuqIYAR0AAAQdupXLqPH+/rXUh/Y5fdrqf/981/V5XH/Wup7D7CWOiILAR0AAIStasml9OCf/Gup33HOb9dS37E/sJb6oz/psf8tYS11RAwCOgAACHvlE+N12zn+tdT/8admqn7YWur7MnP00viV6vL4OD0weqHW7Uz3sFOg8AjoAACgxEiMj9V1Xepp/N1n6Ym+LdSgclLwXFZOnt6bvk7dnhynoR/M1eLNrKWOkomADgAASpz4WJ/6ta2l7+84Uy9d1UYtayYHz+U56Yv5m3TBcxN13ciZmrkm1cNOgRPHMosAAKDE8vlM559aTeedUlVTV+7UiJ9XatKKQ2up/7Rkm35ask1t61RQ/4511KNZNZU+7IFTIBwR0AEAQIlnZurUsJI6NaykBRt268WfV+qbX3+7lvqstbuUFB+jC5pXV59WNdShfkX5fGx8hPBDQAcAABGlRc3yevGqNlq5fb9eHr9So+duVHauP6mnZeXqk9kb9MnsDTopuZQublVDfVrV0MlVy3rcNXCIuYN/tYwCZja7devWrWfPnu11KwAAoJhs2XNAn87ZoE/nbNCq7WlHfU/zGsnq3aqG/nzaSapUJqGYO0QkatOmjebMmTPHOdfmRD+XgA4AAKKCc04LNuzRZ3M2aOyCzUpNy/rde2J8pjMbVVaf1jV0TtOqKhXHfHUUTGECOlNcAABAVDAztaxVXi1rldcDPZtp/LLtGj13g35YtE1ZuXmSpNw8F3ywtGxCrHq2qK7erWro9LopzFdHsSGgAwCAqBMf69O5zarq3GZVtSc9W18t3KzRczdo5ppdwffsy8zRhzPX68OZ61WjfGn1aV1DvVvVUP3KZTzsHNGAKS4AAAAB63ama/Tcjfps7gatzWdH0tNqlVef1jX0pxYnKSUpvpg7REnBHPTjREAHAADHwzmnOet267M5G/Tlgs3ak5H9u/fE+kxnNamiPq1qqHvTKkqIZb46DmEOOgAAQAiZmdrUqaA2dSroHxc107gl2/TZnI0at3RbcMnGnDyn7xdt1feLtiq5dJx6tqiuS1rXUOvaFWTGfHUUHAEdAADgDyTExuj8U6vr/FOra1dalr5csEmfzd2ouet2B9+zJyNb709fp/enr1OdionqdVoN9WldQ3UqJnnXOEosprgAAAAUwKrt+zVm7kZ9NnejNuzKOOp72tSp4J+v3vwkJSfGFXOH8BJz0I8TAR0AAIRaXp7TrLW7NHquf776vgM5v3tPfIxPnRtWVIf6FdW+fkWdelI5xcb4POgWxYU56AAAAB7x+Uzt6qWoXb0UPXTRKfpx8TZ9NmeDxi/brpw8/43QrNw8jVu6XeOWbpckJcXHqE3dFLWv53+1qFle8bEEdvgR0AEAAEKkVFyMeraorp4tqmvn/kyNne+fr75gw57fvC8tK1cTlm3XhGXbA5/nU+vaFdS+XkW1r5+i02qVZxfTKEZABwAAKAIVyyToms71dE3nelq7M01TV+7U9NWpmr5qpzbtOfCb9x7IztOUlTs1ZeVOSf4pMafVKq/29VPUvl5Fta5TXonxxLZowZUGAAAoYnUqJqlOxSRd3q62nHPasCtD01bt1IzVqZq+OlXrUn+7KVJWbp5mrEnVjDWpel4rFOszNa+ZHLzD3rZOBZUtxUOnkYqADgAAUIzMTLVSElUrJVH92taSJG3ek6Hpq/xhffrqnVq1Pe03n5OT5zR33W7NXbdbL41fKZ9Jp9ZIVru6KWpfv6La1U1hlZgIErKAbmY1JT0i6XxJFSVtljRG0sPOuV3FPQ4AAEBJUT25tHq1qqFerWpIkrbtO+C/u74qVTNWp2rp1n2/eX+ekxZs2KMFG/botUmrZSY1qVYu+NBp85rJqp5cWjE+NkwqiUKyzKKZNZA0RVIVSZ9LWiKpnaSzJC2V1Nk5t7O4xvmD8VlmEQAAlDipaVmB6TA7NX1VqhZv2atjRbhYn6lGhdKqVSFRtVJKq2aFRNUO3LmvVaG0UpLi2fG0CIXDMosj5A/VQ51zzx8smtnTku6Q9G9Jg4pxHAAAgIiRkhSv80+tpvNPrSbJv3PprDWpwYdOf9m0V7l5v03sOXlOa3ema+3O9KMNqaT4GNVKSVTNQICvnZIYCPP+j3ko1TuFvoNuZvUlrZS0RlID51zeYefKyj9FxSRVcc6lHXWQEI5zjF65gw4AACLO/swczV67S9NX7dSsNbu0akeaduzPLNSYlcrEB8L7oTvuifGxSkqIUVJ8rJISYlUmIVaJCTH+Y7y/7mNajSTv76B3Dxy/OzxUS5Jzbp+ZTZbUQ1IHST8WwzgAAABRpUxCrM5sVFlnNqocrKVn5WjDrgytT03X+tR0rUvN0Ppd6cGP07Jy/3DMHfuztGN/luat331CvZSOi1FSwqEgnxDnU6zPFBN8Hfaxmcykop5pU7NCou6/sGnR/iEhFIqA3jhwXJbP+eXyB+tG+uNgHapxZGb53SJv8kefBwAAECkS42PVqGpZNapa9nfnnHPalZ7tD+u70rUuNV3rUzO0IfDfG3dlBHdBPVEZ2bnKyM7Vjv2F/QpCp2n1cl63cEJCEdCTA8c9+Zw/WC9fTOMAAADgD5iZUpLilZIUr5a1yv/ufG6e05a9B7Rupz/Ab9yVob0HspWemau0rBylZeYoLStXaZk5Ss/K1f7MHKUHaii84pj9f/AfLQq7XMxxj5PfXJ/AnfXWhewDAAAgosX4TDXKl1aN8qXVURWP+/Py8pwysnN/E+CzcvOUm+eUk+v8x7zAx3n+j0OwoOAxlS1Vsh54DUW3B+9sJ+dzvtwR7yvqcQAAAOABn88C889LViAON74QjLE0cGyUz/mTA8f85paHehwAAACgxApFQB8XOPYws9+MF1gesbOkDEnTimkcAAAAoMQqdEB3zq2U9J2kupKGHHH6YUlJkt4+uHa5mcWZWZPArqEFHgcAAACIRKGaIDRY0hRJw8zsbEmLJbWXdJb8U1IeOOy9NQLn18ofxgs6DgAAABBxQjHF5eDd77aSRsofqO+S1EDSMEkdnXM7i3McAAAAoKQK2SO2zrn1kq49jvet0aElEws8DgAAABCJQnIHHQAAAEBoENABAACAMEJABwAAAMIIAR0AAAAIIwR0AAAAIIwQ0AEAAIAwQkAHAAAAwggBHQAAAAgjBHQAAAAgjBDQAQAAgDBizjmveyg2ZrazdOnSKU2bNvW6FQAAAESwxYsXKyMjI9U5V/FEPzfaAvpqSeUkrSnmP7pJ4LikmP9cFC+uc3TgOkc+rnF04DpHBy+vc11Je51z9U70E6MqoHvFzGZLknOujde9oOhwnaMD1znycY2jA9c5OpTU68wcdAAAACCMENABAACAMEJABwAAAMIIAR0AAAAIIwR0AAAAIIywigsAAAAQRriDDgAAAIQRAjoAAAAQRgjoAAAAQBghoAMAAABhhIAOAAAAhBECOgAAABBGCOgAAABAGCGgF4CZ1TSzN8xsk5llmtkaM3vWzCp4MQ6KRmGvj5lVNLOBZjbazFaYWYaZ7TGzSWZ2vZnx/RcGiuL70Mz6m5kLvAaGsl8UTCivs5mdYWafmtnmwFibzew7M7uwKHrH8Qvh7+eegWu6IfCze5WZfWxmHYuqdxwfM+trZs+b2UQz2xv4OftuAccK2xzGRkUnyMwaSJoiqYqkzyUtkdRO0lmSlkrq7JzbWVzjoGiE4vqY2SBJL0raLGmcpHWSqkrqIylZ0qeS+jm+CT1TFN+HZlZL0kJJMZLKSLrBOfdaKPvGiQnldTazByX9S9IOSV/K//1dSVIrSeOcc/eE/AvAcQnh7+fHJd0jaaekMfJf64aS/iwpVtIA51yBAiEKz8zmSWopab+kDZKaSHrPOXfVCY4T3jnMOcfrBF6SvpXkJN16RP3pQP2l4hyHV/heZ0ndJV0kyXdEvZr8Yd1JusTrrzWaX6H+PpRkkn6QtFLSE4ExBnr9dUb7K4Q/t/sF3v+9pLJHOR/n9dcaza8Q/dyuJilX0hZJVY44d1ZgnFVef63R/Apch5MDP2+7Ba7Ju178/1KUL+6gnwAzqy//L941kho45/IOO1dW/jspJv83dVpRj4OiURzXx8zul/RvSS84524tdNM4YUVxnc3sNknPyP9Lo7ukh8QddE+F8Oe2T9IK+f8VrK5zbntR9o0TE8Lr3F7SNElfOOcuPsr5vfLPPigb2q8ABWFm3eT/F+oTuoNeEnIYc2BPTPfA8bvDL6YkOef2SZosKVFSh2IaB0WjOK5PduCYU4gxUDghvc5m1lTSY5Kec85NCGWjKJRQXedOkupJ+lrSrsAc5XvN7DbmJYeFUF3n5ZKyJLUzs0qHnzCzrpLKyv+vZCjZwj6HEdBPTOPAcVk+55cHjo2KaRwUjSK9PmYWK2lA4MNvCjIGQiJk1zlwTd+Rf+rS/YVvDSEUqut8euC4VdIc+eefPybpWUlTzGy8mVUuRJ8onJBcZ+dcqqR75f+XkkVm9oqZPWpmH0n6Tv7pTTeFoF94K+xzWKxXf3AJlRw47snn/MF6+WIaB0WjqK/PY5JOlfS1c+7bAo6Bwgvldf6H/A8JdnHOZRSyL4RWqK5zlcBxkKTVks6RNF1SHUlPSTpP0sfyT29C8QvZ97Nz7lkzWyPpDUk3HHZqhaSRzrltBewR4SPscxh30EPLAsfCTuwP1TgoGgW+PmY2VNJd8j8t3j+UTSHkjus6m1k7+e+aP+Wcm1rkXSHUjvf7Oeaw9/d1zv3onNvvnPtVUm/5V5M4k+kuYeu4f26b2T2SPpE0UlIDSUmS2khaJek9M/tvEfWI8OF5DiOgn5iDf6NKzud8uSPeV9TjoGgUyfUxsyGSnpO0SNJZgX9KhXcKfZ0Pm9qyTNLfQ9caQihU38+7AsdVzrn5h58I/KvJwX8Na3fCHSIUQnKdAw8dPi7/Q6J3OudWOefSnXNz5P+L2EZJdwUeMkTJFfY5jIB+YpYGjvnNSTo5cMxvTlOox0HRCPn1MbPbJb0g6Rf5w/mWAneHUAnFdS4T+Pymkg4ctjmRk38FF0l6NVB7trANo0BC/XN7dz7nDwb40sfXFkIsVNf5T4HjuCNPOOfSJc2QPzu1OtEGEVbCPocxB/3EHPyG7WFmvqMsy9NZUob8SzQVxzgoGiG9PmZ2r/zzzudJOtc5tyO07aKAQnGdMyW9ns+51vL/Ep8k/y8Dpr94I1TfzxPkX3XpZDOLd85lHXH+1MBxTeFbRgGE6jonBI75PfB7sH7k9UfJEvY5jDvoJ8A5t1L+p7jrShpyxOmH5Z+n9vbBNTPNLM7MmgR2qyrwOCheobrOgXN/lz+cz5Z0NuE8fITiOjvnMpxzA4/2kvRF4G1vBWqjivyLwu+E8Of2Dkmj5P8n8X8cfs7MzpX/IdE9YmUmT4Tw5/bEwPFGM6tx+Akzu0D+4HZA/h0oEeZKcg5jo6ITdJStYRdLai//zlbLJHVyga1hzayu/E/7r3XO1S3oOCh+objOZna1/A8Z5Up6Xkefy7bGOTeyiL4MHEOovp/zGfufYqOisBDCn9tV5F8fuaH8QW6G/Ku49Jb/YbIrnXMfF/1XhKMJ0c9tn/zPE5wjaZ+k0fLvKtpU/ukvJul259xzxfJF4XfMrJekXoEPq8n/l+NVOvSXqx3Oub8G3ltXJTWHFcX2pJH+klRL0pvy7zSVJWmt/A//pRzxvrry/9BeU5hxeJXM6yzpn4H6H71+9vrrjPZXqL6fjzLuwes/0OuvkVdIf26nyL8V+OrAODvl/+XeweuvkVdorrOkOEm3yz+9Ya/8U5u2yb/2fQ+vv8Zofx3H79Y1h723xOYw7qADAAAAYYQ56AAAAEAYIaADAAAAYYSADgAAAIQRAjoAAAAQRgjoAAAAQBghoAMAAABhhIAOAAAAhBECOgAAABBGCOgAAABAGCGgAwAAAGGEgA4AAACEEQI6AAAAEEYI6AAAAEAYIaADAAAAYYSADgAAAIQRAjoAAAAQRgjoAAAAQBj5f2kR2NrLOfadAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 248,
"width": 372
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"f.set_scales(1)\n",
"plt.plot(solver.domain.grids(scales=1)[0],f['g'])\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "66156fd3",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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