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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Calculating the Area of a circle using Monte Carlo" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import matplotlib.pyplot as plt\n", | |
| "import math" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Defining the function for the simulation" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def run_simulation(n_simulations):\n", | |
| " \n", | |
| " # Define parameters and initialise variables\n", | |
| " L = 1\n", | |
| " radius = L/2\n", | |
| " inside_circle_count = 0\n", | |
| " \n", | |
| " # For plotting later\n", | |
| " X_points_out = []\n", | |
| " Y_points_out = []\n", | |
| " X_points_in = []\n", | |
| " Y_points_in = []\n", | |
| " \n", | |
| " for i in range(n_simulations):\n", | |
| " x = np.random.uniform(0,0.5)\n", | |
| " y = np.random.uniform(0,0.5)\n", | |
| " if (np.square(x) + np.square(y)) <= np.square(radius):\n", | |
| " inside_circle_count = inside_circle_count + 1 \n", | |
| " # For the plots\n", | |
| " X_points_in.append(x)\n", | |
| " Y_points_in.append(y)\n", | |
| " else:\n", | |
| " # For the plots\n", | |
| " X_points_out.append(x)\n", | |
| " Y_points_out.append(y)\n", | |
| " area_ratio = inside_circle_count/n_simulations\n", | |
| " square_area = L*L/4\n", | |
| " # As with our ratio we are only calculating the top right quadradnt\n", | |
| " circle_area = 4*square_area * area_ratio\n", | |
| " \n", | |
| " print(\"The area of the circle is {} for {} simulations\".format(circle_area, n_simulations)) \n", | |
| " return X_points_in, Y_points_in, X_points_out, Y_points_out" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Running the simulation" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "The area of the circle is 0.7 for 10 simulations\n", | |
| "The area of the circle is 0.75 for 100 simulations\n", | |
| "The area of the circle is 0.786 for 1000 simulations\n", | |
| "The area of the circle is 0.7844 for 10000 simulations\n", | |
| "The area of the circle is 0.7829 for 100000 simulations\n", | |
| "The area of the circle is 0.786078 for 1000000 simulations\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "simul_list = [10,100,1000,10000,100000,1000000]\n", | |
| "for simul in simul_list:\n", | |
| " X_in, Y_in, X_out, Y_out = run_simulation(simul)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "The real area of the circle is 0.7853981633974483\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "#Same radius as in the simulation\n", | |
| "radius = 1/2\n", | |
| "circle_area = math.pi*np.square(radius)\n", | |
| "print(\"The real area of the circle is {}\".format(circle_area))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Plotting the simulation" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "The area of the circle is 0.79 for 100 simulations\n", | |
| "The area of the circle is 0.776 for 1000 simulations\n", | |
| "The area of the circle is 0.7844 for 10000 simulations\n", | |
| "The area of the circle is 0.78328 for 100000 simulations\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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ezHWvBPC7AD4+F+FLiFpa/eG5xdf0rycoB4+D11jGkT52pia/pinO8DaoHOln7+GdfKCg+e6SwzqlcUhLHksKJt1CxgbE4nmMY/59nMSiaE349wN4Kvr9MQCPZa779wD+IYCPzkX4EqKW6nlOx2vneGnhxBq+8KhE4cg+1x9qXtL/k+ZzWuwUxlE+JnNnajP6cwrICzUPkVGToU0SSRdRqqzaN5B1IPyHAHwg+v3tAN6XXPMmAP9t83OR8AE8AuBpAE/fdddd1ikm0aoypWaOJ3CHk2nHVvuq05qdTK2Hn9vJlj5xEjftb+lF6NIn7blQ9jQ/2t0d126Rk3tWoNQOZAnefq2HP32k7Z6dyZQmN8ESElkA4b8tQ/jvjX4/2JD83ZvfZ/PwpfAMx1BznN6n9HJtCeFLdMXieFGyoAxC7W5FIs+UvzTfkc6R1EE8PLwyIpLdHdeuSxivh/fNCWbOJNTUtjaGn5tcabuU8nMTrFHg3FERnQifDOkA+H4AXwXw+c3nWwC+wpH+8fH5rCFBrQ5q51hjzCUkKdUVz+IDi5MjJTIp0cZ80mL37mFEtO265v68yLTUjsRTpia9h1GiqnTi/6fGoGmXa6s0Pq3SxzHkjoR/C8ALAO6JkravJ64XefjA+ctjOD6+7v16n5cewvW5Oz29mSfhdFAyx3GIRbOjlJCkVFc446FZf5617lp55nRBQ84HB/YQteWT293l2i3p9qyhcurmtUrXqlIhTQBJSMOz0iCV17RY0ncMSO4/9Z8y2hGB3Qd8O2Q4VfKRXQS8BcBnN9U6j2/+7wkAD2auVRN+7uP5InvpotY6KnF1l2YHWRon5ax5efganZcWKmicy4LT8vLn8LBsjLXkLO3fOOpDvhL59QzHm8BNhjReTXWyRaVCrrJFQho5BbK+LDqXUJMkxEryUEz0Vj54xRG+p7JLyVLiHdcScvqRvk3KK4bPee1aHdaAG0P6rElOF+I+eupOjafv4Yl3r+CSDFhSkWLdGtcsbs5IceOu2epr+5T2x0o+15rYUcL3UnZpOKRGB63x5WmMEn3hdtg1yefSceK1lUCSe8dj1By3UPLKi3XuCUpVT8D1k4JPTm7ygvTZnd4evvieGs89JUmNR9wiVkUtNg1pUEL3SvKl/XGY6J0l/J4efq0Olu5xeEiT0zRGqb54lHbm1p/n2+1KqH0SWuqUSp4F0PKQdv1b2q/lRVUbnIfiWfLlXaVT4+HHoGQgTQBx3kfaH4eJ3krCn6p0Tk/zsmodw7eG7jT34EIy8d+lRF5L+FNf0vXHPWnfy8On5MQZVU3/PCMNOXla2q/lRdU9OdK0kH0uyUVZX+uASzF8bf8phbIoau6TG3/lRG8l4cd1+FzC3cNB8HYyLPeg/i4l8lax3pLua54oloxf6ziloRavsXvJsTQmz75KwUU6rs2Jd6iFmqAS6dXcPyWN3IC5rV7N5EmTdg2y7ltP+BRahAA94WVIpMnUVu+kKDlo0ntZydwSGvEYu5eHX+KcOd4dog5denpBnLVJ2+Y667FdkyRzrNszrzppA3aa8Fsk+b3gaYw0yVRyEVeOJ9Z9qQ6PYzuC43jBOnbr3KX5S65vLeZJM6Zua0dC4DEkhCkVmKRkyzsZsnr4bQi/e7maAt5xYE0y1RK31sIac+eMg0fxQ7yOpW2WQkWeu420b63DiGn/JGdxNVk7XCJIWq1iWUwtqjIs8cnaewqx04S/ZA/f2xhpkqk9DJ6HoyNNyJbAzb8mlFTrcUs5CvAtCJCgNiTnAupM6HjCJkFKvPycoqcL5fZt2aRoBi6x1rUehBE7TfhLjuH3MEZzGzxO77nKNolxOD0t34Obf6l8PORofdaih75KjVHzvlxclDP9mi1SaYI0lk1iPHJYMumEsNuEH0L/rbEUPfTC4x4t5UdVtmmMAzU+qv/SHZDHTklCqlKv2ntOJLJtcUZVFqXBabZIkzC1yV6N8Shhbi+Lwc4TvgW9jESaxGuxla8ZS2ujpGlfs1a916bHGs6NNX2eQ+Jctqhoksh2dr7iYvzp77myyh7brCUnDsNK+Dcwx47M657ehqqHs6JJmkp39KW1lQub9orhx/cH8gcjSuRtTYZrn9TtylcSJaAGLlUii4evXUirh79dhK+dLw+SbeVBSkmpNIa5k75pn9L/K70UJie3knykuTIvY0rNk2QOJXNi0afYGOU+mqex2Zukk9rL6mpj+BaSXmP420X4lLFP4TW3LWPEnM5SY5jLWZHIdRx1p9wuxfGSVA5RhoUqnfSozhrH/Osjj48rOas0qZqDmDysbtoGteBrrLrnVtuxvZXwE5QeAsq9yayGROI5pB48ks61dZFzO+U5nJWa0EbJE11KaLWWjKljYCwcmkOTw/AsSdceKPXr4GAZXrnzItw7wucIlNLBFNbFK4mZTuGG3HW5igmN8YllwK23krxaOjESDtDKfls8fMt3c/pRwxFNjKM2YdprYqjFuIRQjLP13SvClxjL0qK6886bBGddvKXvpU/AUgs8F+KwhkK1Y6iNh0va4/qklT1V4l0DreGrcdg0JeM1BrmJcaS2ZHPHvMdxngOMJP2iJtmAvSJ8SRhAsm2OCc6iq7X13yVdrCl24IxJ3G7J6bASqrVPUtmXcnWSs+8pWMnbSsZSD7+Wo0oPvVbJi8tWcwLx3lKmWErMLwY14auHz4Mi0Fh/JGeKTDK36KHUg+IWuEUXuZBJOgap912jl9o+xX2TyN7LY5UavlZOoTQUWMuFzcJfVtLukUxaSswvhpSwYjAy3ivClxpM76etU3iFXyy6qE12anNtFhm1XmsezpvG8LV0CtP1bAmjcby7OGe3BxkvsZxSu1gFY9grwqdCYpP+DIOc8Gv0TersjGPek7TqorbsTmP8rDJqvdYsfCH15nOfHqeRWiDVpVb8ao7KcBaoZudgtZ6tQ0zTPTQLQzBxe0X4IcjjzxKC651XqtUvLhGcywmUclnpoWXWfIZ2fBY5aNdNbRirleGqgWa32MIAV7VJEVlNIsWaU+i5G9AovGBrtneEX0rgWRbznEi9Ne5wKwmJcWe2cLrd2unRhMJSY6SRlTaMNRnFJRZ6TNDmgzznsroIhpp471I5SdXQEuP9wn7tHeGHcFOZLWQ/d7WW9mlIyTjj0GDp+txJlh7j8Uq+eiQ2LQ4AdU+v2HcNCWsrvmrvF7fhIptSZ6wJh5rnAhaX5AjieN3WEr6nB6IlfY/tbU3fLdVaEv0+ObnqV2vymqDZHUvWmXQuKYNNOX9U+y09/NooAtXvlgfGcfNhkk28gKxC1y56iZJpBuO9hRI+obmVhH/PPeeuITRNzLbF3Gj7biFkTdLRfYES0KwdybUeFVbc+qHuke68Smf7aFFbAqrghBCCX9SCkpVpzXps4UrtSM+lqF3EXtZUm5QLYTsJ//j43J2MONl5kZ3HQpLMcepAlE6W1Hw8HlZKodkdS9aJh4cfwuU4Dw7yXFLihNPTmw/tVR86FujqMm1pqWP+TwRqPjS6NPX9cyg0aCmNygnEmijSTLLXDkGTlNtgKwkfyBN+bbjBLd5IwKsmnIrhe1aZ5AjPM4avzRVYCii0Y+DayOX1jo7yBkK7jjUy8mhbe0/t/SzJf6qNF0FsGTxDJKW2PEIxHiQg8WxWD79Ohj09/Fivcm/Doqp0tOHJ09MyWbUmGQ9CyLWZVulo1qikoiWdH+o4jlpHgQqLtHr3tWflYW2VTjwfJQ//pdQQtCiTbJ3Y0CwsLnZZ6NdWEr53DF8iQy/9kegM52F6VZmUzgPiPi0St0sqadRWtLR2FErtn5y0LQePw5y5N3RpUOPUxt99GGP4Jq4Puuj1a0vKOC+r5bZHO3Hctq/Q1lYSvneVzoRepYhWvZLqGFdlIrnX4WHfs2KWVOlGyf/4+OZ8tXYUavKLtViCU5t+92GM4XM4Cy9i2PxLLBRL3KjUDrcgrcbFQmDGidlKwj8+Pm/ycI/nNrbmfhzZc0ToVerYSh65cFTvg8i4/uXm4eQknzsphcM8HYUcP/QwkjVEzYW9vLi4mMitsSolwXoYFy8YjMZWEn6ctJU+DS1Fi51DCZR3zekep8PScXAL2lse45iPdx8c2AmhBXLj1uRGevTdK8IQIzXGFodjaieX2E53R5p+TeNNefcdR2P47nFltYX1cXtK+D3JRIitJ3xgGe9QsIALBfQgk967Goo0cyEnqt9e8eW0zdL9OU7ofWia99yVqr8sRqWFMYr7eWOepImg0iRrKx0441LalnDnenD9rERzwgfwAIBnATwH4NHM398F4FMAPgHg9wDcy7eZr9JpoVwtQS0KLs7viZ6OiMdTvK0qe2pr/OfIN3jOnZTzJDKeJSfDTSL1dy5uJP1MpEMJ01IX7OSFNSV8AIcAngfwGgDHAJ5JCR3A90U/Pwjgt/h2ZYQ/59EWMUqLsrd3vQRwxQW1bXDtaB281Dnk6vMt5LuUnT+3g9H0r6WHT4ISpiZ+mXpZkjhXvHgthxdJ+1mB1oR/P4Cnot8fA/AYcf3DAH6Tb/eK8KeqCYt8eiw0idOxhMVeQq8YvuYIAgkxle5dmgupR1qKcR8f3wyH1DzhP4ceeBjjCUsa18uo2XbkBpQr2ZpQsx1suD1qTfgPAfhA9PvbAbwvc93PbnYCXwTw2kJbjwB4+vJzRfhHR7az2Hsp5GyejgO0Oq5pV3NccQqrh0/NhXaeUkNodTqWpB+lGL71eIjFOTNUlYQkdqpRXG47uKMe/tsyhP9e4vqfBvCrfLvnN+SgVa5eC21J9eVaSGK6c3ht1hh+yxJU6zwvTT9qjfGioY3TS56IpJSktB3kDqXa4hi+NqRzAOAbfLvn1Yuj10JrZVh6eE/SdTGXN6qt0uG8cIlMa3IAOSzJw98LxBOorX+2TtbFRZ5wuB3CtlXpALgF4AUA90RJ29cn17w2+vkfSTqU8/C16LXQctvk2iNze4WjJOthTm9UA2u4Is3jleL01jlZSqx7ceGXHpDU3sfKbfUSayp2nNGjLPMtAD67idE/vvm/JwA8uPn5lwB8elOW+ZHUIOTbvPnglRa9FlouSVl7ZK7GWNUs5KV5+DVjKcksfstX7n6SCEBphyA92Gxusu1pdOYe6zVIYpYeHn5NxY4ztvLBK6+jFSzKt4RcAVfLPvWrdiFL1oPXCz441FY7WZwzyfjj+awJ986JnrvdRcmEs+iaGL6lHFSihNZxFfqylYRf+05bKywK2yJXIE2mtnpLktRD9gRFSpJ5sZCa9mn7+J5zxeYtTkwvHlpkviKN2U1VOqWKnZyAJd6ItWJH0/9pW0n0ZSV8BSwK20LJtcUGpYWsSVL2IoUSKMMpkbHFWGs8/PSec1TfWMY4juW+9q5YW0y4RytIqQIKXjJe3U9mMlfCLyCnfJZF3GobG/fPQkotdLolqBJqqTHSEgo159w955CXp0Mylar26l/LcI/akGgFqSEGT6um8Ug2fVkJP0LszaZzSIVI0mNwrck7K6iEZOn8Jm24Z+74K7WraemhWoxpqb+t5WVxSCiD5g1KJq0MpGketIKcyxsyKOZK+BtI49XcAz+lXZb3y7+5vsf9kRwDIiGHubfc41j26HMG2qN/pbV8csLfs7e8lhJypFCSSasQmGl82jK4k5M8IbT09LiQQ0ExV8LfQHoG+MVF+e9nZ323yDFqigR6OiW1oDzSFmsrZ0yPjm6W2paMek/St8bwl1A508rwmAyJVCiUB3L7dlvBUkRDGJqdInzr4hpHORlyCUyOkOaANA691LLBCdT6ainbVK+k4bA5yNSyBpawc/POZ04wGxKJUCgvsbWiGmNxO0P4NYtLWubIJfEkBiHtc4+FRsX4F1EVkYGk2mwuQyX1GjWGofU8lO6xBLIv5ZmoqjFN4r2Z0ZV4UZySWGG0ZDtD+DVbQm6OYsXiQjbSMree3t9Stu1SaKrNvF8wn+tLSjCUAY2/J1nzPeamdA/LKbPe0IbLLU+tNzNqFGm09vA1Yado8K8CXgi7QPg1SR8qESiRc2oYcmcleTwIVIO5PTkNDNVmKkhlUVpTt2/n+3JwwDsGExdow0M10Ja09go9So3ihJKsJkPbXcepkE4Pa8oNOKPAfxd4MRh5d8EhUtoAACAASURBVFGE38rDp+Q8KWZuTrm5mOPBnG2BpvZdS04aj1pLlHF/LM9HtNIDS1+8oQnRTSSerh+qv7PsYscxfyLflL2f28vKKPD55eSaeNeVxDWfXjF8jky021FL4q8n5tTP+N5SUrIsaM2cWYiSe/CqlSGzjJna2daGSeK/n57mq5pKY89VQXEl0zUOHzUWdk3MTeoUMkLeGcIPwZbQ4Tx1pTyvLfr4PqnCWl+J1wpzxvmpMFkq19q1pdlZ1Xj40jF5GbJYlqmMqBi+5aE1Tldqxg6UnaGDg/L11gfIqLGQ41wy0U/YJQ8/t0Wszd5PSiO18lKvYhuqZHrnFCT31i7eEuL508StKaKUvJeXSvC20AOOvHL3KPWpFFIaR16GNbsbbpeXe7fExYV9t0Lpfelv7znNhHJ6HRurwa7E8O+555z1IKwHY+VK5kweQIQlxetLC3/OPkpDJ4eH+rYl3ib1hCx1aKL0VYAUAXryhMVoa8OSlCwnXbHmLyTHLGhzAdz4pQ+rxp8/R2ELcnKyHA9uwi5U6Rwfn5MTXDvRMbgFIdnZzek9x8jlmCbC2QYP33I8BRWWKcVsvUNb41jWN8/jpS1G2yOJneqK1cOnQkLWPnHjp/S+tGt4STogy1kbnqGiTFtbWYefvuKQU8IaEvbwfGtIxHP+qbI2Sx+9+pa798HBVcz28NB+FpF2/loZPgsZaWHtu3QeKa+Xi+EfHdFVjLmddW2fJOOn9L7Unpjw45tLFpint1Foa6c9/OmTezhDKlsvArCQozcJUzLS9tHbE26VA9POX6vQVo8dVOvEO7VbSvMEVCjMs4+chy9pW5uj+9qB4TRCiQJ4KkmhrfuAbwcj7zYhc8lHEsNPP7mts3SHVUrcacjRQmba+ecWE0f4mv5zi38p0BJMK2JuTcbxfVqFkalCh1zpZWl83lELafGFR9t33BHCxy7GfNaeUhzJ4vP0Ngpt7USVjpT0rZAkiijlti5073AE96Riaey5/lNyXtqxDXPuXKh+tH5PQgtQFTEtDKUErY1cru0P3h7D53EWXsQQPo+z8JF7GVIoCS2uRPCMye2Sh5/W4UuTRF7QzIs2aWi9Twi8gRgzjgl3FgnVf4+FHuvm1ObcZNg4b/by/899jo0WXJVO6bNNBk2C0hHpH7xdEU8NwR7DzU3KyUl2y7WVMfyU8CWKOFc1hGQHUprTkmKVEpgSA6ElMy5RRy1yDhoCWToZ5kCt36VUbmlgrb7ZhjnUrAuJs34D0gnXLlBqUqZM+bZX6ZSOViiN3fuZCA8Pv+a71hi+91jHse4ALi2BLJkMc6Bk51X91XMXZK2vX/oc5tbN8XE+6RwCPb4iJCcqWsBNSiLwnSH8GK0XgoZYpV6sZnfA1VV7jp0ba4schUZGkv57yMPSDjV/tR7+HCEhzkDHDqXnHLaGxPGoKn4oZZY93nvKdT4R+E4Sfg9oE4HTtRqPmPOue3l33L28q5C8vEMvUrS2w81fTd/mCAlpKmK2KWQldTw0BTfX0FIYnEe5Dx7+klG7Oyid5SJ5EcTSoInhc2ei5OC1zqztcLt4raGUVKa19qClfd6mpLTU8eBK6oslyWoLocQ4it8RuRL+DNAs9LgMbnri1FJeuVSUdNVjbXiVNVv65L2LlxrHJXnQpQqsWN975yFK/dTIljplNGvUTFleQadTwQmEubOEvwRFqoWlBn4bIfGwLETm5eFb1qv3Ll4bZ/aGdT1Rnn6vXYCk7/E1p6flo8slxuHGHHsv2ArB7SThb9N2koKlDG7bxhgCH0N1Pk5E3ZZlvXof0cCFcVo6NTVypAxfjzi/te8lI6EJ/7z8vV7WX9DeThJ+z4RRyyoQSxnckrb0UlCLqJbIPObHok8LWuPVqLk3ZfhanVvk1XfNeChn5WMXzh5oheB2kvB7KFII7atAqFg95VlsG5a+I7P0z3tMc8qoZj3N7eF7c4Fl1312FnxjzPvs4efkaJGHZT4k95G0W2rn9LS8yJf4TtwaLD3nYulfi2ci5pBRja7NHcP3NipUaarZCbOUa+1jDJ8qW9TIQyI/TcglPrtG0g+qnZIuLN0rXnEd1JqWVLP07E96XZrABHRlwJKxL+EhSU2bmvg+aVy8kwwMtprwKQFr5MFNlDbkMn1PqgBWL2TpXvG2ooVnXnp0n/IQSw811ULDMdTuc1vQy6CauLtzcmarCZ/aRmnAeeqWkIuk3Qmrt94G1jBMr/OINB9NHziC03AMFa7YJlDRgFnDbr0Sjhs0J3wADwB4FsBzAB7N/P3nAHwGwCcB/DaAM67NifCnV+Cln4MDnRC4BWAJuUjajbF6674ysBJ3i4ohj0PHpE5fbtzp+DUcQ8ljm3S0NI4W55m5dGwbPXwAhwCeB/AaAMcAngFwb3LNjwO4Y/PzBYAPce16e/gcOdSEXLbZc+9phLxlZZ2zFs8EeHj4UqePu5e2OmYcy21ZwzpzODcao9uCa4tj7kwSrQn/fgBPRb8/BuAx4vo3AfifXLvehB8Cn1iyzsm2eu69jZWno0ORFEeaUnLWzCXldWs+EllIKka0c+u9zuZwgjRG1zOaUqqouzbmjiTRmvAfAvCB6Pe3A3gfcf37APx84W+PAHgawNN33XVXCKHvmTK95mQpBqLzTtMtlMmRK9d/6pwUctEK+lXj6XNVZpPOSN9EptEzDeFz7fbWq7hf0nJKr75wunh6KpgDZ0JoTfhvyxD+ewvX/gyAjwN4BdduXJa5C6dGTmjl/Vh0pnMuyY0IKFK1PCzFfbT9o4yJ9Ohha5+tuiR1rCT621uv0v7F60Bbvq2F1sDfuHcDQlhESAfATwD4EwB/XXJj7sGrpWIO78c7ednKE/PSbYpQaxK2pY+WqEr3sL45jGuvpgxRsivRVv/MoVfUmqvhD+671UejNBBWa8K/BeAFAPdESdvXJ9e8aZPYfa30xtt4PPJc3s82JZwli6+l0exxdlFJrlaD0spjpkIgpcoWSV966lXLe0narnYgGkxuj7LMtwD47IbUH9/83xMAHtz8/GEAfwbgE5vPk1ybNYSfJlFOT/vE4yUeXA05l0iwRmda75607UsWWc0ipxYodWSux7itxxe08pgtO5HSd9JYtXftu3YMHrsJSdulcNvpqXC+t83Db/WxEn4u5g/4v+R8upcktlrr/XDfaWFEPAyBZazSsVj7x+WEWhnAi4v8uCi9jMMtLWrJLbud3JweHd2U6TYc+ubVdklnRPq/bTH8Vh8r4VMenHcMUVPeF0NLKhwJehsRLx20GCLPBZyT8zje9OK1zkAuMcjFkEvjKlWbUeEWL0OkDUdML4NJxz/nIX9ze/gcRGt9m6p0Wn2shE95Ld5VAhIPSUuUubmXxk29jAi1bfeQDzUPXgu4ZLRqyUmyq9PEeUuy6JH41OYagHw7c1flzBnDXyJ2ivCtCb0WHgcVA7XEMluRVA7UIq2pgpHIh+p3692Flnit7cZjpORZkkUvEs2tJ+28tTROHkn+1vdfGnaG8HMPzOQSel4xfEm5F0VOWvKiPGtLyMZa6eJlNLl4ubXvEmjj09JxSduNibkkz+mJ2Bx6ePglaPW2lSe8rR52Dj0Nx04QPhXayMXIa6t0pMpWihNbSJPy6uL7TBUAVkPEXTOOMiKTyDCNlx8c0H2n5KqBp/GUtEvNcSkef3FRvs/cZKeVfwtCm9PoeUKcvNUKsPCdnSB8Sxy0BpJwTWl7ycVBa+K2EuXxqHTxiHVzRwBQRrSW7DiDZiUnSwx/+p7Teu6Gue/vnbtqNZ6a3fTLDThWXewE4VNbadF5FUpYE7ISD7BEml5k7hH/rSFdCSlSRlRq+Kyx3dqFn36/V815D8Tyb1EKGt+DkxenB5pdOHu4WcVYrA9bAsKBKoWzE4RPEWmLGmDp1v3wUD65AJ9L4BaDhMy9tsJWYtQmTNO5K/1tGqO3MdJ8dwnE3tJT5Qx1bThFkoej+qN9/oQbk2bHmpO5pA/Uejg9DeElGDw0ggh2gvBLcdA776xXzFIcXuqlSpQwnuAaeIV9WsLyQE/84Z5YrjFo1u/OLdMe/ZAY6prwqSYPF3+nZNxqnB/NeCiZS8NO1Jr4wlDo5D57+JPg0smvDV9IY71cPHry9DlDUfsA0elpvvIlTYTO6Y2WdHEY8hVUuQ9FajVzbv3uUhKILfshMdQ1Dot3Hk4S8uHGU+skSOeD6sPDGMM3scbw+ZlgJsPz+5pkHZWwtIRVco+yTwTvef5LfM/aGHeNEY1j+bk+tPDwuTzQnA8X9eqHxMOvIXzL8wgUOD3j1qu0VJurnpPsuDjZPowxfA5n4UUM4Rs4CS8Om3e7Hh6Wy7kKi2SnCb92i6tZQBSRp4rrtfXmyM3b48v1O7eDkLQjSapaZOQdwz8+vmk007LJffDwJSTJGZZ0NxrrTanyi3oegdMjbWzdYrwkOwkuiS8NEb8XF+Gl3B+oGt4EO034OYFrSFVbfqgJ2XiEVTiD5O3xSRaKZ+zaKiPp90r5mfj/JERUMjIXF/1OZqX64RXGm9rgHBpp37SGVTpWDpLwlEfYV3PtOJZ1bfp8FwWPcjrISICdJ3wrxvGmAqbKXZrUgwP9grCgt4cvTbj29mwtkC5Uaagh9V5PTvLf8TyZVWKwKA/SaoAsZCv1qjlvmGtPkuCVPANSW9ihkUFJj9J+Zr376SPESvgFWL3ZkqFo8erFceSP89U+xUlBIpPpHnNA48VKCYNLJua27K3LF6exSkmXGoN1B6C9XutVc+PjDLG1qk5ivKzQ9Dkng9XDbwirN0sl/ryRMy6pB6mpbZbcT7Jw5vDwtV6nNNw1juVrc0cxeIYL0n5IQk052XN9qj1SQgKJsxD33bp7zel6SVbTQ33ccSStZUCtz3jef+VkjeG7Qbqgcp8YPSs2JAkjr4qgCWnowrsKyNIPCQHWEGbJaGp0pEb2Gg81p2fSnZmXjsT9pnSF0htuHZV2r5rxeazJ0k4nzndMazAnA+2zB+Hi4voLi5Xb9ZXwg7w6o6Q0NbHFGmhLwloYIGprX5M85e6pIcDc9do3MeX6aHmIzBLD1xB2Ts+0IQ0PHSmtqbhkmPKqtfFui1HzMGilZH1J3mlVm1T2Hkn3EMJK+CHQYZjYQ5EoTk31gFe/z874BdAiKZV+R3qWSYsEoEQWtecsSbfo8f08q7HSD2ewSmfGtHinQq3j46kXd97ZZk2W7ictz6bacOWUaAHfB3w7GHnX9CWPjzfhS7aPc1hjDqV3oeZCEFZlsZb6eSRFS7LTEiCXLLPOD+Xhec6/p8GSVvHUEqJHaNOy8ys9rX3nnf5xessOL5WBRPZVxjO5wTkQgpF33Ylc+unl4U+K0aPqwrvflPehUXaKbDyOOOAWjebJxBIBcrH2GnJrYdwllT/eu0bvccz1LltqrkvJUOt4PTx8SV+qjGfSyZXwA21lufDBHIdkTdDG8C191XoxXBWFxsMvfSe3g5l+zy0YSXJ1LqOdoteuoSVy1WNAm9LkFJKKJK+1UXIGT07KO40WT9S/3JmcgiQCWQl/A6G8bgjcWt6o3armrucUoaUXU/pQVRTSGD7lyUiuTz05Tb/nRs+kfyuUxnByMt+9U9L3knEpNzKdaQVcefw1fEGuJYXHuhI+A+8FqPUuuBh6j61+7h6SRaOt0qEM6wSpAZpCIdv2dHDPst5WoGTe2sMv5bVaGv0eRppcS4qY9Er4DLxJVascPbx4Dr0SfZI2NSEmj+qW3thlD7/HOLQ7Uo++zW6kpVUn+1ql4xVSsdxP613MrkwEeiQspQnb9FM6z2j69Hiy0oIeu7bWoMJoLat0QpAZea7gQHvf2Y20wivcO8LvvaAkMWdKOWZXpoVBIk/uRSpLl12vst6W9/N40b1lnUocgmmHmhuz5b4lnWx9OirZgULcd+9COr1DJBIF1MbwLWfQx+1tS7VHCbmyxfh3qionfTJ63+BZ8knpUq1jZXV0JA4B1Yea+7Z6GboIwsqOvSN8z1LGONlYysRzYRxtSKnm/JqaRbhNhoKSufWk0FosQX65+Vef5UK0lepSzZhrQplcsp4aW81959qNk3Le97JMalI0E0Z5ErHieytBqb3pbJL4d2n822Nxc9/vSXaUjObo61Li8pqEJkdwEl2iwiacjFt6+NTYatbrHPk2Vrf22cPntl2aCeMWz6Qg1PEHFmiqVNKDuqwKWbMIvMlOQhYlT5aTeStilsrP29ik7Un1RjK3ksIQ6cFiXmcshSAbJzW2Gh2gHI1WxQ3sGPc1hi9JrGgWJqdUk+KX2jw4sCmAdeGOo/2o5KVsczWLUfoegJgUvY+SniCRXwvDKA3fSOQ0tSmVVWneNTJuUaUjkSmXmyj9Ladz2lNZJVDvYvaxSke6BZXEJTVVNxKPXFMSJr1/PPHS8JNWdtM4qe9bjIUw/3RD1lrylsqydksu0b1eob8cuUuObZDISnKWUisZc+OW6CoHrhgmVx1WetVljRNRs4vZyuORj4/P1d6xlHg4wpUIWxLDLymjdLsrrUo5PKTf+CNN2FKljpTRoDw9bXWHNuFe+nDbYc/FyY1pgnf8l0taatePdh49PPwSOA+8Vb6EMsp33inXp5p5DaFuF9Oc8AE8AOBZAM8BeDTz9x8D8EcAvgfgIVmb5+rJ9PKgOGHnFFCqADWJKq72nFM6bhFxL4Mp9VHrGVJETJGFhsA1svIiC6sj4e3hW9vTGqTSvOcOFtMWALSsDqLuq11flvUiQc0upinhAzgE8DyA1wA4BvAMgHuTa+4GcB+AX7MQvlR4XpbfspCkpzXWeHmlhLRE6TjZSMhUGqIpkfZUQaMNBXDev+VT8lpbwtMz5YoTLKD0vkSwpX5MB4t55rBqd2EUOKeFOw55jiNISmhN+PcDeCr6/TEAjxWu/RUr4Uu3Rx6W3yJsTmGm72ti1KX+S4lPUzoqaVO64Ki2pKGWHCFrk9kSufRGK/0ErooTrPco6T1XdTPHTsPbw6d0i9u9TnJvseMotkn8sTXhPwTgA9HvbwfwvsK1JOEDeATA05cfvYfvCcsExt8pvc+TSwpJDE1JOanSMG4RcWQqyTNIiLmUx6AWd3w/aVUKd/9tBjX/tbuI3JxanQVrDFviFKVj5HYU3HqucVLite1hzNk2mEluTfhvyxD+ewvXmjz8OT2yFtASZWrsLDHOUihoCrNQZFpaQKU6eCoWGtdwc4ZBIjvqZdJW0ls6KHJq8RYqq7OQ09vpWur8eI/wY1oVx60Xi5GJn/vwCNeJ22A6u5UhHUuVzpJRE6opebuaKoajoxBu3brZdvzglsZDKencVE0jJR5pLT0n29z9KIM1Fzy8QEtoS5ojsuzYJA9aUbu63HxfXFwZhcPD6w/UScc86ZrEIFmcKInB0LxuVBwaY4iiNeHfAvACgHuipO3rC9eKCb/nefitURuq0XpnFBlb2s8pOlcSKF1Alqdlc32a6/2qGmi9QCpRqiV8yRyX+sadWyOp8+eMlIZ8uQRqauS8yrUpcPKRtCV2+Ob08C/bx1sAfHZTrfP45v+eAPDg5ucfBvAlAH8F4GsAPs21uS2EL1ESz1CNBJ4PxJT6xJ1WKZGN1cBJcgCSsfWGZrycLmiqtWoevMsd5GeZM808cXKSjnvKaXF/94gkaAyato0b350zht/q05rwvRIsEoL2CtVIQW0vtcpIEYF1xzDBmuzThDTm9vDj+dQYJUtMudR2bseU6plUnpoxxPeSPNsyobbAALh8DoAyVLm/S46bKK1Jbj6kITWxw5fGMaPzY1bCT+DlSUstsleoRorS+CznolOLrzb+bpWLpSx1DkhJOTdeTWmitn0qQW/9WJyG0jxxesGFmNJTZXPtSEOAGq4Yx/qnjMUOH9GxlfATeBGw1EP1Pk0zh1z1Sin+SymUNjZesyOxGl5q1yHxxLy28Ry01SSS72qMQ0kfpTkeadjM6jRM49FU6UiMqMTTlq5dLVd4OZMsiI6thJ/Aq254KR6+l5Ll2tFsfa191xBwqSJH0qdui3EDLoxDjVfTV238mOrX9J7gqW8lg685Cdai/5aKofhjPelTKisuhNXcqSAmcSX8BF4E3CKGP+d4ajznHih5d6X3is5dyVM7L1Li4Kp2tBUzx8fXd4TpuTjx36Xj8DK0mtATdU9phVjvcKwYxDbtVcALYSX8K3gqoGeVjhVeBqWVYfLyeGqrXEqfVpU8VKzc23ByD9Zx/aJkqpk/qpS0pQ7k+s/d8/btvJGIr/PcPbs6TUQmfG/Ow9egZyy3dSihtYdfY5h6eHeaKpfe3lqcWK19wIy7j7bG39sI9jBw0hi+JLwnrTKr5Ypm678ggK1/41Vrr0ELbeJzSjZJt+faMbWM4dcqpqcR8UxkWsdn1bkeoQFt3yij6Dk/OVnXJvslBQrWvtY8lay5V/XcFxreag+/REKWEkMPcKRYQ5q13/Uwft5G1DNM5JHIrMlH1MwPZYA0DoEnxjFfq66N0U+QGNlpbHOsXWlfOSLW9r9ZDq/Qka2O4ZcWbqt3k3LgrDXnNc3iCTBoSTbeY9LslJa0W6H0ovadqLXecuH5HTUkYTTqQa+eiVAi52neGZX6z11ftf4yX97qKh3PYwJqQcU9ufreWT0BZkwtva05vbkl7VY0SWQNAS7BW5760eMlQJ79tZ7jpH1yvvRqxNu328zfVhO+l4ffIvESf6ZqCImXY/UEWmCJseWlolZWXKLUQoC9dIaaQ6kxm4hsCR4+NyYK0v5zchmGNqXCW034HjF8DyvKETl1rrx0Ic/hrS3B29JCslBbGJkeeqRd9D3mjxu3NJTjeXb8nJD2XzPXJZlZdHerCX8ScE2VDlWjLCUFzePrlBfDLeRW3nCp3aV4W1JIFltLQmmxU6yJ4beYv3SMnBcqDbvGfaLWtCWn0HsXKbmfNhxd+mh1d+sJvwaabTQlWM5a5xZYyduvSYxZQBHgtnlbEoJbuhHLkYWVsLznT5NrmJwc6VHN3K5jHG8avskgUuPppcPxHJVeYRpD4uGfnsrkrdHdvSZ87baKygGUJoZ7wMV69osXmlYJNEKpT5IQRs0ZNtsIz/nTrJfpPJ3p/J1a0rLuinvloShizq1n7juTIeMiAhJjGWMrCf+ee85dlNizyieeGOqdnCnm9jg9lKgnKI+txsOfy+BuE7zCEBZ5c4a6xgmohbYYI8cV6efWreuhLMo47LyHf3Bwfm3A1gWqeTNQKxKeMzE6jvJHyJcCitStMfzc5/BwngfVlrijmlCbaKyRL3XvXOijZ9WPxBBO61kTFpNU9+1FDB84d5nAEuGfnMiIw2NhliazxymUpfGnD5gsiYQ4A6mt0pEsPC4sF99vepR/6pOmnbnDexw0ZGWVJ3XvUgyfShz3iOFrPHyt0QyBfxJbg50hfItHTFljijg8lSjXVutz5qf7cormPVYPeHts0gWoSbx7t7Ok3VbJMHEfrx1TrkrHwwmogSaGrw2LhcDvajVj2xnC1ypUTTjDQjqcAdGUunlAmgSbO8eQQmuAuAUhJe2cQ2EJcVjaWVI+xWLkWjsIvRKznB5JqnQ0OkM9v2M9M2wrCT+N4VsUrCR4yXkZ2ri7lqR6xPWl28QlPnwl9Wqkco/b0zylbUliWtqZ08OXOiMUaXElirVo/ZrQ1jv6o6ObepeWm+Z03mLotpLw4yod60Fp1CLjFFMr6NbXW0DlDnr3pRUsO6WSB5t7PkLr4WtP76whFg/UxOytHqgFmhe8WOC9BnLkbQk7WZyxrST8uA7fGr/jFivlCU7tSxW59Y7AAqlXtLQYvhRUjkLykI8kgcrlQWI90e5EgJvvkO0NbfjBwwO1gOpXDbh8Re9drkfod+sJ31qmJ/Fe0trZ3Al6kgVpqcRpnWjSLMYlVelIIc1RaL+ffpfTH6ms0hhwzZHIXqitYuoVDmxB+OOYfx9AS8PF9cfj2I2tJ3yK1LlFS12TKmaNt6KpxInL+jQPcGmxxNi8Jyiy8jzmtoUXuxRjbHFUrOOoQYuQjiUC0BLUXGjOF9p6wg+hrPSei7aWIKXbsdJ9etUOb0NsXoJeHn6LkJdU11qH22rbt3zfYsBy3jh3xg4HbnezpN2WRsY7QfgleC5ab4K0Pqbu5cV5kMVSQj2lJFhJhhIjrZGPlaRK35Hq2hLKET2/X6OT3rpY6zB4Q1sgUOrjThO+56L19qa0E9jCi6tZJJw8ehkDqh+1zzN4E7mkz5K/T+DOl/GUe4/5bGnAtP0vxfCt7/SthbZiquTU7DThT4LyUlTvtkpJ4BoL3gvWZPmu9iME+f0khkiiaxKnwSOE0kuOrfJK1v6nTkPvo8tz/ZE6invp4S8d6WLL1S1rLXgvUIuTSjD17EcIfcNOEg+1NtQU4+JC5iSUFr+UCLnwhpdMtR6+1FhZn9VZKrg539sY/jYituIlRV2CslKL0/Owp5p+9IbEQ/WKDWu2+DlDoiFCiVHx8H61Idjak1HndpqsqDHAK+EvFDHxax7y6tk/bTlsCyKeI2xTk2z1MoaaHJCkSIEiQum9PORekm/6/5KwGNfvnFyWUITAQavz8biA+74dVsJfFqj4PrUIeisotTh7elVLSBBL/h6CX7ir5qEoCxFKdxNWg07NYSmByukXV8rI7QZ6O1baiibJtTfHdR7CSvjLApeILP19CZ7/hB4nfvaGNEbfo9qLMhwcEUiIMJdfkhycZjHonEw0B7ZJPPzDw5tkP3ecv5XBuSmDlfAXB81DFksl1J4ekzR5V7sLoOZFU83h0Zca+XJEWGpbQrwW/eMMqZTsc157evRAWla5lDh/q8T4TZ1tTPgAHgDwLIDnADya+fsrAHxo8/ffB3A31+auEz61IFt4WK3QI9RiTd55etW5T+2TnukYJXFt6f04eWjG6WHQuWQ3Z2Co3RT3BK42vNUKNZU3FLp6+AAOATwP4DUAjgE8A+De5Jp/DuA/3LCOwQAABTBJREFUbH7+KQAf4trddcIvLUjJoluKh98LkjCLVyUPlVtpNRetdkqUsbA8BV5j0Ln5sZ6VU5tE7xkilRhZiz51jeEDuB/AU9HvjwF4LLnmKQD3b36+BeCrAAaq3V0n/BDyC5JTimFYTgy/FySlkJ4P9KTzws1HLeYoO6XyA62MD5cM50IzOdSUyaZx/taQJMat+uRVpTOES5IuYhiGhwA8EEJ45+b3twP40RDCu6Nr/nhzzZc2vz+/uearSVuPAHhk8+vfAfDH5M13Eq/6AeCuM2A4yP/9a38BfP5P+/Zpbtz3BuDo+Ob/f/c7wCc/Jb/G+/5e7Z+fl//2h39IfPFVuHSeDMjpWXgJ+NMvXP78N159Oebvfgf4ypeBr37ddp/0nlS73N9zkMw7NVaPcWkQjzEHD33C3w4hvNLyxVuCa4bM/6VWQnINQgjvB/B+ABiG4ekQwpsF9995rLK4wiqLK6yyuMIqiysMw/C09bsFL/MavgTgh6Lf/yaAr5SuGYbhFoDvB9DZsq5YsWLFCgoSwv8DAK8dhuGeYRiOcZmUfTK55kkA/3Tz80MAfidwsaIVK1asWNEVbEgnhPC9YRjejcvE7CGA/xxC+PQwDE/g8kyHJwF8EMB/GYbhOVx69j8luPf7K/q9a1hlcYVVFldYZXGFVRZXMMuCTdquWLFixYrdgCSks2LFihUrdgAr4a9YsWLFnqA54Q/D8MAwDM8Ow/DcMAyPZv7+imEYPrT5++8Pw3B36z7NBYEsfmwYhj8ahuF7m+cfdhYCWfzcMAyfGYbhk8Mw/PYwDGdz9LMHBLJ41zAMnxqG4RPDMPzeMAz3ztHPHuBkEV330DAMYRiGnS3VFOjFO4Zh+IuNXnxiGIZ3so1an9iSfNDoWIZt/AhlcTeA+wD8GoCH5u7zzLL4cQB3bH6+2HO9+L7o5wcB/Nbc/Z5LFpvrXgngdwF8HMCb5+73jHrxDgDv07Tb2sP/EQDPhRBeCCF8B8CvA3hrcs1bAfzq5uffAHB7GIbcg1zbDlYWIYTPhxA+CeClOTrYERJZfCSE8H83v34cl89/7CIksvg/0a8nyDzUuCOQ8AUA/BsAvwjgWz071xlSWajQmvBfDeCL0e9f2vxf9poQwvcAfAPAaeN+zQGJLPYFWln8MwC/2bRH80Eki2EYfnZzZMkvAvgXnfrWG6wshmF4E4AfCiH8j54dmwHSNfKTm7DnbwzD8EOZv19Da8J3O5ZhB7Av45RALIthGH4GwJsB/NumPZoP0mNJfjmE8LcA/GsAP9+8V/OAlMUwDAcA/h2Af9WtR/NBohf/HZdH0d8H4MO4ipQU0Zrw12MZriCRxb5AJIthGH4CwOMAHgwhfLtT33pDqxe/DuAfN+3RfOBk8UpcHrr40WEYPg/g7wF4ckcTt6xehBC+Fq2L/wSAOKTvEq0Jfz2W4QoSWewLWFlstu7/EZdk/+cz9LEXJLJ4bfTrPwDwvzv2rydIWYQQvhFCeFUI4e4Qwt24zO08GEIwHya2YEj04gejXx8E8Cdsqx2yzW8B8FlcZpwf3/zfE7icKAD4awD+Ky7flvW/ALxm7gz5jLL4YVxa9r8C8DUAn567zzPK4sMA/gzAJzafJ+fu84yy+CUAn97I4SMAXj93n+eSRXLtR7GjVTpCvfiFjV48s9GL13FtrkcrrFixYsWeYH3SdsWKFSv2BCvhr1ixYsWeYCX8FStWrNgTrIS/YsWKFXuClfBXrFixYk+wEv6KFStW7AlWwl+xYsWKPcH/B2Hajs7a1J0iAAAAAElFTkSuQmCC\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "simul_list = [100,1000,10000,100000]\n", | |
| "for index,simul in enumerate(simul_list):\n", | |
| " fig = plt.figure()\n", | |
| " plt.axis([0, 0.5, 0, 0.5])\n", | |
| " X_in, Y_in, X_out, Y_out = run_simulation(simul)\n", | |
| " plt.plot(X_in,Y_in, 'o', color = 'blue')\n", | |
| " plt.plot(X_out,Y_out, 'o', color = 'red') \n", | |
| "plt.show()" | |
| ] | |
| } | |
| ], | |
| "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": "3.7.3" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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