padgett-work
/
dissertation_work
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
dissertation_work/Programming/Python files/NonUniformFiniteDifference....

1484 lines
116 KiB
Plaintext
Raw Normal View History

First push to the new thing
2024-02-19 17:04:37 +00:00
{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"def f(x):\n",
" return np.sin(np.pi * x)\n",
"\n",
"x = np.linspace(0,1,100)\n",
"x = x**2\n",
"\n",
"h = np.diff(x) # we define the vector h as the difference of successive x[i] using the built in diff function\n",
"\n",
"f = f(x)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"A = np.zeros((len(f),len(f))) #we create the matrix A by initializing to 0"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {},
"outputs": [],
"source": [
"for i in range(1,len(f)-1):\n",
" A[i,i-1] = 2/(h[i-1]*(h[i-1] + h[i])) #we populate the diagonal (minus the extreme ends), the one to the left and right with a,b,c respectively\n",
" A[i,i] = -2/(h[i-1] * h[i])\n",
" A[i,i+1] = 2/(h[i]*(h[i] + h[i-1]))\n",
"\n",
"A[0,0] = 1 # we denote the far corners of our matrix to be 1\n",
"A[len(f)-1,len(f)-1] = 1\n"
]
},
{
"cell_type": "code",
"execution_count": 112,
"metadata": {},
"outputs": [],
"source": [
"u = np.linalg.inv(A).dot(f) # we solve our system"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fb7a088d220>]"
]
},
"execution_count": 113,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAD4CAYAAADhNOGaAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAv70lEQVR4nO3deVxU5fs+8IsdcmMQYRAQyEAhdwXFJRUFxA3XUlNREHC30oL0U7YnpV8zd0c03Jc0QVHZUlEDm1QQFYRRVEYcEFBxAdme3x8WvwyQbWaeGeZ+v173HzOc4VxP6lydWc7RAsBACCFEY2nzDkAIIYQvKgJCCNFwVASEEKLhqAgIIUTDUREQQoiG0+UdoCFyc3Nx584d3jEIIUSt2NjYwMzMrMr9alkEd+7cgbOzM+8YhBCiVsRicbX300tDhBCi4agICCFEw1EREEKIhqMiIIQQDUdFQAghGk4uReDp6Ym0tDRkZGQgKCio2m3WrFmDjIwMJCcno3v37vV6LCGEEMVijRltbW0mkUiYnZ0d09PTY0lJSczR0fGVbby8vNjx48cZANa7d2+WmJhY58dWN2KxuFGZaWhoaDRxanrubPQRgYuLCyQSCTIzM1FaWop9+/bB29v7lW28vb2xY8cOAMCFCxdgbGwMoVBYp8fK01suPeHmN01hv58QQhRFz9AA3kEfQGAhlPvvbnQRWFpaIisrq/K2VCqFpaVlnbapy2P/4e/vD7FYDLFYDFNT0wZl7djfFV4LAmHazqpBjyeEEF76jPfGO1Pfg6CtChaBlpZWlfsYY3Xapi6P/YdIJIKzszOcnZ2Rl5fXoKxnwvagvLQMQ/x9GvR4QgjhQVdfH4N9p0IivoRbF5Pk/vsbXQRSqRTW1taVt62srJCdnV2nberyWHl6kl+AhINH0HPkMJhYtVXYfgghRJ5cxo5EK7M2iN28XSG/v9FFIBaLYW9vD1tbW+jp6WHSpEmIiIh4ZZuIiAhMnz4dANC7d288fvwYMpmsTo+Vt1O/7AarqKD3CgghakFHVxduftOQefkKMi78pZB9NLoIysvLMX/+fERFRSE1NRUHDhzA9evXERgYiMDAQADA8ePHcevWLUgkEohEIsydO/e1j1WkwtwHuHD4KJy9R8DYvOpZ+AghRJX08h4OgYUQMZu2KXQ/3D/SVN9p7MdHjYXmLORSPBu3bAn3tdDQ0NDUNNq6OmzpiV/Zoj2hcvl9Cvv4qDp6JMuBODwSLmNHomWbhn0CiRBCFK3nCE+0trJEtIKPBjSyCADg9607oK2jg8Ezp/KOQgghVWjr6GDILB9Ir99Aavx5xe5Lob9dhRXcu4+Lx07CdeIYtGhtwjsOIYS8otuwIWhj2w4xCvqk0L9pbBEAQJwoDDp6uhjoM4V3FEIIqaSlrY0h/jNwP+Mmrp2KV/j+NLoI8u5KcflEDPq+Nw7NBMa84xBCCACgi/tgCNvbIWbz9hq/ZCtPGl0EABC75RfoGRrgnWmTeEchhBBoaWlhaMAMyG5m4krMKaXsU+OLIDfzDq5E/47+UybgjVYtecchhGi4twcPQFuHtxAn+gWsokIp+9T4IgCAmC2/wLBZMwyY+h7vKIQQDece6IsHt+8i6WSc0vZJRQBAlnETV2JOYcCUiTBs0Zx3HEKIhnJ8px+snDogVhSGivJype2XiuBvMZu3w6hlC/SfMpF3FEKIhvKY7Yu8LCkuHY9S6n6pCP6WfSMDV0/FY+C0STBo9gbvOIQQDdOxfx+06+yEONEOVJQp72gAoCJ4Rcym7XijVUv0mzSBdxRCiIbxmO338ouuR08ofd9UBP8ivZ6G6/HnMchnMvSNjHjHIYRoCAdXZ9h07YS40B0oLytT+v6pCP4jZvN2NBMYo+9743hHIYRoCI/Zfi9Phnkkksv+qQj+4+6Va7hxPhGDZkyBnqEB7ziEkCauvXMP2PXoit9Dd6K8tJRLBiqCakRv3IYWrU3gOnEs7yiEkCbOY7YvHv99wSxeqAiqcTs5BemJYgye+T50DeiogBCiGG/27Ia3XHri1LZdKCsp4ZaDiqAGMZu2oWUbU/QZP5p3FEJIE+UeOBOFeflIPBTONQcVQQ1uXUyCRHwJbr7ToKuvzzsOIaSJsenaCQ6uLji9fTdKi19wzUJF8Boxm7ahlXkb9B43incUQkgT4zHbD08LHiLh4G+8o1ARvI7kz4u4dTEJbn7ToKOnxzsOIaSJaNfZCR3798HpX3ajpKiYdxwqgtrEbN4GY6E5XMaO5B2FENJEeMx5eTRwft9h3lEAUBHUKj1BjNtJKS+PCnR1ecchhKg5605OcBzQF2d27EVJURHvOACoCOokemMoTNpawHnMCN5RCCFqzmO2L549eozzew/xjlKJiqAObvxxAXeSr2LILB86KiCENJiVU0c4DeyHM2F78eL5c95xKlER1FH0plCYWFqg12gv3lEIIWrKY7Yvnj8uxLm9B3lHeQUVQR2lnUvE3ZTrGOI/A9q6OrzjEELUjKWjA94ePABnduzFi2eqczQAUBHUS/TGULS2aoteo4bzjkIIUTMes33xvLAQ5/ao1tEAQEVQL6ln/8Ddq9cxNMCHjgoIIXXWtoM9OrkNRPzO/Sh++ox3nCqoCOopeuM2tLayRM+Rw3hHIYSoCffZvigqfIKzuw/wjlKtRhWBQCBAdHQ00tPTER0dDWNj42q38/T0RFpaGjIyMhAUFFR5/w8//IDU1FQkJyfj8OHDaNWqVWPiKEVq/HlkXUuFe+BMOioghNTKwqE9ugwdhPhd+1H85CnvONVqVBEEBwcjLi4ODg4OiIuLQ3BwcNUdaGtj/fr18PLygpOTEyZPngxHR0cAQExMDDp16oSuXbsiPT0dn376aWPiKA0dFRBC6spjtp9KHw0AjSwCb29vhIWFAQDCwsIwZsyYKtu4uLhAIpEgMzMTpaWl2LdvH7y9vQG8LILy8nIAQGJiIqysrBoTR2munzmHrOtpGOo/A9o6dFRACKle2w726OI+GPG79qOo8AnvODVqVBGYm5tDJpMBAGQyGczMzKpsY2lpiaysrMrbUqkUlpaWVbbz9fXFiRMnatyXv78/xGIxxGIxTE1NGxNbLqI3hMK0nRV6jqKjAkJI9f55byB+137eUV6r1q/JxsTEQCgUVrl/2bJlddqBlpZWlfsYY6/cXrp0KcrKyrB79+4af49IJIJIJAIAiMXiOu1bka6fOYesa6kYGjADF4+dREVZOe9IhBAV0raDPboMHYSo9SKVfW/gH7UWgbu7e40/y8nJgVAohEwmg1AoRG5ubpVtpFIprK2tK29bWVkhOzu78vb06dMxcuRIDBkypL7ZuYvaEIpZ61ei58hhEB+J5B2HEKJCPOb44XlhIeJV+L2BfzTqpaGIiAj4+PgAAHx8fBAeXvVya2KxGPb29rC1tYWenh4mTZqEiIgIAC8/TRQUFITRo0ejSEXOwlcf9AkiQkh1LDs6oPOQv783oOJHA/9gDR0TExMWGxvL0tPTWWxsLBMIBAwAs7CwYJGRkZXbeXl5sRs3bjCJRMKWLl1aeX9GRga7e/cuu3z5Mrt8+TLbuHFjnfYrFosbnFne4/hOP7YqJYG5jBnJPQsNDY1qzMw1K9jX56OYYfNm3LP8e17z3Mk/nBwXw2UW7Q1lS0/8yrR1dbhnoaGh4TuWjg5sVUoCGxo4k3uW/05Nz530zWI5iN4QitZWlnAeTecgIkTTec6Z9fIMo2rw3sA/qAjkIPXsH7hz5RqGBsyk6xUQosGsnDpUnmFUFc8pVBMqAjmJ3rgVJpZ0FTNCNJnH30cDqvwt4upQEchJ2rlE3Em+iqEBM6Cjp8c7DiFEyaycOuLtQf1xOmyPyl1voDZUBHJ0cr0IAgsheo8bxTsKIUTJhs33x7NHj1XyegO1oSKQo/SEP5F5KRlD/H2gq6/POw4hRElsunaC44C+OLV9l9odDQBUBHJ3cr0IxuZm6DNhNO8ohBAlGTbPH0/yC3B+7yHeURqEikDOJH9ehER8CW5+06FrYMA7DiFEwd7s2Q0Ori74fdtOlKjhGRIAKgKFiFovQiuzNuj
"image/svg+xml": [
"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<svg height=\"248.518125pt\" version=\"1.1\" viewBox=\"0 0 386.845313 248.518125\" width=\"386.845313pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
" <metadata>\n",
" <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
" <cc:Work>\n",
" <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
" <dc:date>2022-04-01T21:45:38.729824</dc:date>\n",
" <dc:format>image/svg+xml</dc:format>\n",
" <dc:creator>\n",
" <cc:Agent>\n",
" <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>\n",
" </cc:Agent>\n",
" </dc:creator>\n",
" </cc:Work>\n",
" </rdf:RDF>\n",
" </metadata>\n",
" <defs>\n",
" <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n",
" </defs>\n",
" <g id=\"figure_1\">\n",
" <g id=\"patch_1\">\n",
" <path d=\"M 0 248.518125 \n",
"L 386.845313 248.518125 \n",
"L 386.845313 0 \n",
"L 0 0 \n",
"z\n",
"\"/>\n",
" </g>\n",
" <g id=\"axes_1\">\n",
" <g id=\"patch_2\">\n",
" <path d=\"M 44.845313 224.64 \n",
"L 379.645313 224.64 \n",
"L 379.645313 7.2 \n",
"L 44.845313 7.2 \n",
"z\n",
"\"/>\n",
" </g>\n",
" <g id=\"matplotlib.axis_1\">\n",
" <g id=\"xtick_1\">\n",
" <g id=\"line2d_1\">\n",
" <defs>\n",
" <path d=\"M 0 0 \n",
"L 0 3.5 \n",
"\" id=\"me5c53ab7b5\" style=\"stroke:#ffffff;stroke-width:0.8;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"60.063494\" xlink:href=\"#me5c53ab7b5\" y=\"224.64\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_1\">\n",
" <!-- 0.0 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(52.111932 239.238438)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 2034 4250 \n",
"Q 1547 4250 1301 3770 \n",
"Q 1056 3291 1056 2328 \n",
"Q 1056 1369 1301 889 \n",
"Q 1547 409 2034 409 \n",
"Q 2525 409 2770 889 \n",
"Q 3016 1369 3016 2328 \n",
"Q 3016 3291 2770 3770 \n",
"Q 2525 4250 2034 4250 \n",
"z\n",
"M 2034 4750 \n",
"Q 2819 4750 3233 4129 \n",
"Q 3647 3509 3647 2328 \n",
"Q 3647 1150 3233 529 \n",
"Q 2819 -91 2034 -91 \n",
"Q 1250 -91 836 529 \n",
"Q 422 1150 422 2328 \n",
"Q 422 3509 836 4129 \n",
"Q 1250 4750 2034 4750 \n",
"z\n",
"\" id=\"DejaVuSans-30\" transform=\"scale(0.015625)\"/>\n",
" <path d=\"M 684 794 \n",
"L 1344 794 \n",
"L 1344 0 \n",
"L 684 0 \n",
"L 684 794 \n",
"z\n",
"\" id=\"DejaVuSans-2e\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_2\">\n",
" <g id=\"line2d_2\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"120.936222\" xlink:href=\"#me5c53ab7b5\" y=\"224.64\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_2\">\n",
" <!-- 0.2 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(112.984659 239.238438)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 1228 531 \n",
"L 3431 531 \n",
"L 3431 0 \n",
"L 469 0 \n",
"L 469 531 \n",
"Q 828 903 1448 1529 \n",
"Q 2069 2156 2228 2338 \n",
"Q 2531 2678 2651 2914 \n",
"Q 2772 3150 2772 3378 \n",
"Q 2772 3750 2511 3984 \n",
"Q 2250 4219 1831 4219 \n",
"Q 1534 4219 1204 4116 \n",
"Q 875 4013 500 3803 \n",
"L 500 4441 \n",
"Q 881 4594 1212 4672 \n",
"Q 1544 4750 1819 4750 \n",
"Q 2544 4750 2975 4387 \n",
"Q 3406 4025 3406 3419 \n",
"Q 3406 3131 3298 2873 \n",
"Q 3191 2616 2906 2266 \n",
"Q 2828 2175 2409 1742 \n",
"Q 1991 1309 1228 531 \n",
"z\n",
"\" id=\"DejaVuSans-32\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-32\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_3\">\n",
" <g id=\"line2d_3\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"181.808949\" xlink:href=\"#me5c53ab7b5\" y=\"224.64\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_3\">\n",
" <!-- 0.4 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(173.857386 239.238438)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 2419 4116 \n",
"L 825 1625 \n",
"L 2419 1625 \n",
"L 2419 4116 \n",
"z\n",
"M 2253 4666 \n",
"L 3047 4666 \n",
"L 3047 1625 \n",
"L 3713 1625 \n",
"L 3713 1100 \n",
"L 3047 1100 \n",
"L 3047 0 \n",
"L 2419 0 \n",
"L 2419 1100 \n",
"L 313 1100 \n",
"L 313 1709 \n",
"L 2253 4666 \n",
"z\n",
"\" id=\"DejaVuSans-34\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-34\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_4\">\n",
" <g id=\"line2d_4\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"242.681676\" xlink:href=\"#me5c53ab7b5\" y=\"224.64\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_4\">\n",
" <!-- 0.6 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(234.730114 239.238438)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 2113 2584 \n",
"Q 1688 2584 1439 2293 \n",
"Q 1191 2003 1191 1497 \n",
"Q 1191 994 1439 701 \n",
"Q 1688 409 2113 409 \n",
"Q 2538 409 2786 701 \n",
"Q 3034 994 3034 1497 \n",
"Q 3034 2003 2786 2293 \n",
"Q 2538 2584 2113 2584 \n",
"z\n",
"M 3366 4563 \n",
"L 3366 3988 \n",
"Q 3128 4100 2886 4159 \n",
"Q 2644 4219 2406 4219 \n",
"Q 1781 4219 1451 3797 \n",
"Q 1122 3375 1075 2522 \n",
"Q 1259 2794 1537 2939 \n",
"Q 1816 3084 2150 3084 \n",
"Q 2853 3084 3261 2657 \n",
"Q 3669 2231 3669 1497 \n",
"Q 3669 778 3244 343 \n",
"Q 2819 -91 2113 -91 \n",
"Q 1303 -91 875 529 \n",
"Q 447 1150 447 2328 \n",
"Q 447 3434 972 4092 \n",
"Q 1497 4750 2381 4750 \n",
"Q 2619 4750 2861 4703 \n",
"Q 3103 4656 3366 4563 \n",
"z\n",
"\" id=\"DejaVuSans-36\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-36\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_5\">\n",
" <g id=\"line2d_5\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"303.554403\" xlink:href=\"#me5c53ab7b5\" y=\"224.64\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_5\">\n",
" <!-- 0.8 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(295.602841 239.238438)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 2034 2216 \n",
"Q 1584 2216 1326 1975 \n",
"Q 1069 1734 1069 1313 \n",
"Q 1069 891 1326 650 \n",
"Q 1584 409 2034 409 \n",
"Q 2484 409 2743 651 \n",
"Q 3003 894 3003 1313 \n",
"Q 3003 1734 2745 1975 \n",
"Q 2488 2216 2034 2216 \n",
"z\n",
"M 1403 2484 \n",
"Q 997 2584 770 2862 \n",
"Q 544 3141 544 3541 \n",
"Q 544 4100 942 4425 \n",
"Q 1341 4750 2034 4750 \n",
"Q 2731 4750 3128 4425 \n",
"Q 3525 4100 3525 3541 \n",
"Q 3525 3141 3298 2862 \n",
"Q 3072 2584 2669 2484 \n",
"Q 3125 2378 3379 2068 \n",
"Q 3634 1759 3634 1313 \n",
"Q 3634 634 3220 271 \n",
"Q 2806 -91 2034 -91 \n",
"Q 1263 -91 848 271 \n",
"Q 434 634 434 1313 \n",
"Q 434 1759 690 2068 \n",
"Q 947 2378 1403 2484 \n",
"z\n",
"M 1172 3481 \n",
"Q 1172 3119 1398 2916 \n",
"Q 1625 2713 2034 2713 \n",
"Q 2441 2713 2670 2916 \n",
"Q 2900 3119 2900 3481 \n",
"Q 2900 3844 2670 4047 \n",
"Q 2441 4250 2034 4250 \n",
"Q 1625 4250 1398 4047 \n",
"Q 1172 3844 1172 3481 \n",
"z\n",
"\" id=\"DejaVuSans-38\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-38\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_6\">\n",
" <g id=\"line2d_6\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"364.427131\" xlink:href=\"#me5c53ab7b5\" y=\"224.64\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_6\">\n",
" <!-- 1.0 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(356.475568 239.238438)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 794 531 \n",
"L 1825 531 \n",
"L 1825 4091 \n",
"L 703 3866 \n",
"L 703 4441 \n",
"L 1819 4666 \n",
"L 2450 4666 \n",
"L 2450 531 \n",
"L 3481 531 \n",
"L 3481 0 \n",
"L 794 0 \n",
"L 794 531 \n",
"z\n",
"\" id=\"DejaVuSans-31\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"matplotlib.axis_2\">\n",
" <g id=\"ytick_1\">\n",
" <g id=\"line2d_7\">\n",
" <defs>\n",
" <path d=\"M 0 0 \n",
"L -3.5 0 \n",
"\" id=\"m952bd28186\" style=\"stroke:#ffffff;stroke-width:0.8;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"44.845313\" xlink:href=\"#m952bd28186\" y=\"212.146067\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_7\">\n",
" <!-- −0.10 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(7.2 215.945286)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 678 2272 \n",
"L 4684 2272 \n",
"L 4684 1741 \n",
"L 678 1741 \n",
"L 678 2272 \n",
"z\n",
"\" id=\"DejaVuSans-2212\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"242.822266\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_2\">\n",
" <g id=\"line2d_8\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"44.845313\" xlink:href=\"#m952bd28186\" y=\"173.133581\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_8\">\n",
" <!-- −0.08 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(7.2 176.9328)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"242.822266\" xlink:href=\"#DejaVuSans-38\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_3\">\n",
" <g id=\"line2d_9\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"44.845313\" xlink:href=\"#m952bd28186\" y=\"134.121095\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_9\">\n",
" <!-- −0.06 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(7.2 137.920314)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"242.822266\" xlink:href=\"#DejaVuSans-36\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_4\">\n",
" <g id=\"line2d_10\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"44.845313\" xlink:href=\"#m952bd28186\" y=\"95.108609\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_10\">\n",
" <!-- −0.04 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(7.2 98.907828)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"242.822266\" xlink:href=\"#DejaVuSans-34\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_5\">\n",
" <g id=\"line2d_11\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"44.845313\" xlink:href=\"#m952bd28186\" y=\"56.096123\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_11\">\n",
" <!-- −0.02 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(7.2 59.895341)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"242.822266\" xlink:href=\"#DejaVuSans-32\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_6\">\n",
" <g id=\"line2d_12\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"44.845313\" xlink:href=\"#m952bd28186\" y=\"17.083636\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_12\">\n",
" <!-- 0.00 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(15.579688 20.882855)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"159.033203\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_13\">\n",
" <path clip-path=\"url(#pe25664bbd7)\" d=\"M 60.063494 17.083636 \n",
"L 60.094549 17.146987 \n",
"L 60.187712 17.33704 \n",
"L 60.342983 17.653795 \n",
"L 60.560364 18.097248 \n",
"L 60.839853 18.667395 \n",
"L 61.181451 19.364224 \n",
"L 61.585157 20.187712 \n",
"L 62.050972 21.137824 \n",
"L 62.578896 22.214504 \n",
"L 63.168929 23.417672 \n",
"L 63.82107 24.747215 \n",
"L 64.53532 26.202984 \n",
"L 65.311679 27.784779 \n",
"L 66.150146 29.492346 \n",
"L 67.050722 31.325364 \n",
"L 68.013407 33.283436 \n",
"L 69.0382 35.366078 \n",
"L 70.125102 37.572705 \n",
"L 71.274113 39.902621 \n",
"L 72.485232 42.355004 \n",
"L 73.758461 44.928892 \n",
"L 75.093797 47.623169 \n",
"L 76.491243 50.436548 \n",
"L 77.950797 53.367557 \n",
"L 79.47246 56.414523 \n",
"L 81.056232 59.57555 \n",
"L 82.702112 62.848507 \n",
"L 84.410101 66.231007 \n",
"L 86.180199 69.720388 \n",
"L 88.012405 73.313699 \n",
"L 89.90672 77.007671 \n",
"L 91.863144 80.79871 \n",
"L 93.881676 84.682868 \n",
"L 95.962317 88.655826 \n",
"L 98.105067 92.712878 \n",
"L 100.309926 96.848908 \n",
"L 102.576893 101.058372 \n",
"L 104.905969 105.335281 \n",
"L 107.297153 109.673182 \n",
"L 109.750446 114.065139 \n",
"L 112.265848 118.503719 \n",
"L 114.843359 122.980977 \n",
"L 117.482978 127.488439 \n",
"L 120.184706 132.017093 \n",
"L 122.948543 136.557373 \n",
"L 125.774489 141.099155 \n",
"L 128.662543 145.631744 \n",
"L 131.612705 150.143873 \n",
"L 134.624977 154.623697 \n",
"L 137.699357 159.058797 \n",
"L 140.835846 163.436177 \n",
"L 144.034443 167.742273 \n",
"L 147.29515 171.962964 \n",
"L 150.617965 176.083582 \n",
"L 154.002888 180.088927 \n",
"L 157.449921 183.963294 \n",
"L 160.959062 187.690493 \n",
"L 164.530311 191.253882 \n",
"L 168.16367 194.636399 \n",
"L 171.859137 197.820605 \n",
"L 175.616712 200.788728 \n",
"L 179.436397 203.522712 \n",
"L 183.31819 206.004279 \n",
"L 187.262092 208.214985 \n",
"L 191.268102 210.136293 \n",
"L 195.336222 211.749646 \n",
"L 199.466449 213.036547 \n",
"L 203.658786 213.978648 \n",
"L 207.913231 214.557842 \n",
"L 212.229785 214.756364 \n",
"L 216.608448 214.556893 \n",
"L 221.049219 213.94267 \n",
"L 225.552099 212.897609 \n",
"L 230.117088 211.406421 \n",
"L 234.744186 209.454745 \n",
"L 239.433392 207.02928 \n",
"L 244.184706 204.117917 \n",
"L 248.99813 200.709887 \n",
"L 253.873662 196.795897 \n",
"L 258.811303 192.368283 \n",
"L 263.811053 187.421151 \n",
"L 268.872911 181.950529 \n",
"L 273.996878 175.954515 \n",
"L 279.182953 169.433418 \n",
"L 284.431138 162.389909 \n",
"L 289.741431 154.829154 \n",
"L 295.113832 146.75895 \n",
"L 300.548343 138.189856 \n",
"L 306.044962 129.135307 \n",
"L 311.60369 119.611729 \n",
"L 317.224526 109.638632 \n",
"L 322.907471 99.238702 \n",
"L 328.652525 88.437863 \n",
"L 334.459688 77.265337 \n",
"L 340.328959 65.75368 \n",
"L 346.260339 53.938791 \n",
"L 352.253827 41.859911 \n",
"L 358.309425 29.559591 \n",
"L 364.427131 17.083636 \n",
"\" style=\"fill:none;stroke:#8dd3c7;stroke-linecap:square;stroke-width:1.5;\"/>\n",
" </g>\n",
" <g id=\"patch_3\">\n",
" <path d=\"M 44.845313 224.64 \n",
"L 44.845313 7.2 \n",
"\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
" </g>\n",
" <g id=\"patch_4\">\n",
" <path d=\"M 379.645313 224.64 \n",
"L 379.645313 7.2 \n",
"\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
" </g>\n",
" <g id=\"patch_5\">\n",
" <path d=\"M 44.845313 224.64 \n",
"L 379.645313 224.64 \n",
"\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
" </g>\n",
" <g id=\"patch_6\">\n",
" <path d=\"M 44.845313 7.2 \n",
"L 379.645313 7.2 \n",
"\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <defs>\n",
" <clipPath id=\"pe25664bbd7\">\n",
" <rect height=\"217.44\" width=\"334.8\" x=\"44.845313\" y=\"7.2\"/>\n",
" </clipPath>\n",
" </defs>\n",
"</svg>\n"
],
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt #we plot the result\n",
"\n",
"plt.plot(x,u)"
]
},
{
"cell_type": "code",
"execution_count": 115,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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
"image/svg+xml": [
"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<svg height=\"288.921094pt\" version=\"1.1\" viewBox=\"0 0 427.102557 288.921094\" width=\"427.102557pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
" <metadata>\n",
" <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
" <cc:Work>\n",
" <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
" <dc:date>2022-04-01T21:46:20.461457</dc:date>\n",
" <dc:format>image/svg+xml</dc:format>\n",
" <dc:creator>\n",
" <cc:Agent>\n",
" <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>\n",
" </cc:Agent>\n",
" </dc:creator>\n",
" </cc:Work>\n",
" </rdf:RDF>\n",
" </metadata>\n",
" <defs>\n",
" <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n",
" </defs>\n",
" <g id=\"figure_1\">\n",
" <g id=\"patch_1\">\n",
" <path d=\"M 0 288.921094 \n",
"L 427.102557 288.921094 \n",
"L 427.102557 0 \n",
"L 0 0 \n",
"z\n",
"\"/>\n",
" </g>\n",
" <g id=\"axes_1\">\n",
" <g id=\"patch_2\">\n",
" <path d=\"M 7.2 281.721094 \n",
"L 416.943182 281.721094 \n",
"L 416.943182 15.821094 \n",
"L 7.2 15.821094 \n",
"z\n",
"\"/>\n",
" </g>\n",
" <g id=\"matplotlib.axis_1\">\n",
" <g id=\"xtick_1\">\n",
" <g id=\"line2d_1\">\n",
" <defs>\n",
" <path d=\"M 0 0 \n",
"L 0 3.5 \n",
"\" id=\"m682a89f269\" style=\"stroke:#ffffff;stroke-width:0.8;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"25.82469\" xlink:href=\"#m682a89f269\" y=\"148.770523\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_1\">\n",
" <!-- −10.0 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(10.502034 163.368961)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 678 2272 \n",
"L 4684 2272 \n",
"L 4684 1741 \n",
"L 678 1741 \n",
"L 678 2272 \n",
"z\n",
"\" id=\"DejaVuSans-2212\" transform=\"scale(0.015625)\"/>\n",
" <path d=\"M 794 531 \n",
"L 1825 531 \n",
"L 1825 4091 \n",
"L 703 3866 \n",
"L 703 4441 \n",
"L 1819 4666 \n",
"L 2450 4666 \n",
"L 2450 531 \n",
"L 3481 531 \n",
"L 3481 0 \n",
"L 794 0 \n",
"L 794 531 \n",
"z\n",
"\" id=\"DejaVuSans-31\" transform=\"scale(0.015625)\"/>\n",
" <path d=\"M 2034 4250 \n",
"Q 1547 4250 1301 3770 \n",
"Q 1056 3291 1056 2328 \n",
"Q 1056 1369 1301 889 \n",
"Q 1547 409 2034 409 \n",
"Q 2525 409 2770 889 \n",
"Q 3016 1369 3016 2328 \n",
"Q 3016 3291 2770 3770 \n",
"Q 2525 4250 2034 4250 \n",
"z\n",
"M 2034 4750 \n",
"Q 2819 4750 3233 4129 \n",
"Q 3647 3509 3647 2328 \n",
"Q 3647 1150 3233 529 \n",
"Q 2819 -91 2034 -91 \n",
"Q 1250 -91 836 529 \n",
"Q 422 1150 422 2328 \n",
"Q 422 3509 836 4129 \n",
"Q 1250 4750 2034 4750 \n",
"z\n",
"\" id=\"DejaVuSans-30\" transform=\"scale(0.015625)\"/>\n",
" <path d=\"M 684 794 \n",
"L 1344 794 \n",
"L 1344 0 \n",
"L 684 0 \n",
"L 684 794 \n",
"z\n",
"\" id=\"DejaVuSans-2e\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"211.035156\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"242.822266\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_2\">\n",
" <g id=\"line2d_2\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"72.386415\" xlink:href=\"#m682a89f269\" y=\"148.770523\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_2\">\n",
" <!-- −7.5 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(60.245009 163.368961)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 525 4666 \n",
"L 3525 4666 \n",
"L 3525 4397 \n",
"L 1831 0 \n",
"L 1172 0 \n",
"L 2766 4134 \n",
"L 525 4134 \n",
"L 525 4666 \n",
"z\n",
"\" id=\"DejaVuSans-37\" transform=\"scale(0.015625)\"/>\n",
" <path d=\"M 691 4666 \n",
"L 3169 4666 \n",
"L 3169 4134 \n",
"L 1269 4134 \n",
"L 1269 2991 \n",
"Q 1406 3038 1543 3061 \n",
"Q 1681 3084 1819 3084 \n",
"Q 2600 3084 3056 2656 \n",
"Q 3513 2228 3513 1497 \n",
"Q 3513 744 3044 326 \n",
"Q 2575 -91 1722 -91 \n",
"Q 1428 -91 1123 -41 \n",
"Q 819 9 494 109 \n",
"L 494 744 \n",
"Q 775 591 1075 516 \n",
"Q 1375 441 1709 441 \n",
"Q 2250 441 2565 725 \n",
"Q 2881 1009 2881 1497 \n",
"Q 2881 1984 2565 2268 \n",
"Q 2250 2553 1709 2553 \n",
"Q 1456 2553 1204 2497 \n",
"Q 953 2441 691 2322 \n",
"L 691 4666 \n",
"z\n",
"\" id=\"DejaVuSans-35\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-37\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_3\">\n",
" <g id=\"line2d_3\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"118.94814\" xlink:href=\"#m682a89f269\" y=\"148.770523\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_3\">\n",
" <!-- −5.0 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(106.806734 163.368961)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-35\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_4\">\n",
" <g id=\"line2d_4\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"165.509866\" xlink:href=\"#m682a89f269\" y=\"148.770523\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_4\">\n",
" <!-- −2.5 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(153.368459 163.368961)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 1228 531 \n",
"L 3431 531 \n",
"L 3431 0 \n",
"L 469 0 \n",
"L 469 531 \n",
"Q 828 903 1448 1529 \n",
"Q 2069 2156 2228 2338 \n",
"Q 2531 2678 2651 2914 \n",
"Q 2772 3150 2772 3378 \n",
"Q 2772 3750 2511 3984 \n",
"Q 2250 4219 1831 4219 \n",
"Q 1534 4219 1204 4116 \n",
"Q 875 4013 500 3803 \n",
"L 500 4441 \n",
"Q 881 4594 1212 4672 \n",
"Q 1544 4750 1819 4750 \n",
"Q 2544 4750 2975 4387 \n",
"Q 3406 4025 3406 3419 \n",
"Q 3406 3131 3298 2873 \n",
"Q 3191 2616 2906 2266 \n",
"Q 2828 2175 2409 1742 \n",
"Q 1991 1309 1228 531 \n",
"z\n",
"\" id=\"DejaVuSans-32\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-32\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_5\">\n",
" <g id=\"line2d_5\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"212.071591\" xlink:href=\"#m682a89f269\" y=\"148.770523\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_5\">\n",
" <!-- 0.0 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(204.120028 163.368961)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_6\">\n",
" <g id=\"line2d_6\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"258.633316\" xlink:href=\"#m682a89f269\" y=\"148.770523\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_6\">\n",
" <!-- 2.5 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(250.681754 163.368961)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-32\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_7\">\n",
" <g id=\"line2d_7\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"305.195041\" xlink:href=\"#m682a89f269\" y=\"148.770523\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_7\">\n",
" <!-- 5.0 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(297.243479 163.368961)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-35\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_8\">\n",
" <g id=\"line2d_8\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"351.756767\" xlink:href=\"#m682a89f269\" y=\"148.770523\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_8\">\n",
" <!-- 7.5 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(343.805204 163.368961)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-37\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_9\">\n",
" <g id=\"line2d_9\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"398.318492\" xlink:href=\"#m682a89f269\" y=\"148.770523\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_9\">\n",
" <!-- 10.0 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(387.185679 163.368961)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"127.246094\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"159.033203\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_10\">\n",
" <!-- x -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(413.983807 177.047086)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 3513 3500 \n",
"L 2247 1797 \n",
"L 3578 0 \n",
"L 2900 0 \n",
"L 1881 1375 \n",
"L 863 0 \n",
"L 184 0 \n",
"L 1544 1831 \n",
"L 300 3500 \n",
"L 978 3500 \n",
"L 1906 2253 \n",
"L 2834 3500 \n",
"L 3513 3500 \n",
"z\n",
"\" id=\"DejaVuSans-78\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-78\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"matplotlib.axis_2\">\n",
" <g id=\"ytick_1\">\n",
" <g id=\"line2d_10\">\n",
" <defs>\n",
" <path d=\"M 0 0 \n",
"L -3.5 0 \n",
"\" id=\"m4c14de641f\" style=\"stroke:#ffffff;stroke-width:0.8;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"212.071591\" xlink:href=\"#m4c14de641f\" y=\"268.065611\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_11\">\n",
" <!-- −0.100 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(168.063778 271.864829)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"242.822266\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"306.445312\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_2\">\n",
" <g id=\"line2d_11\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"212.071591\" xlink:href=\"#m4c14de641f\" y=\"238.241839\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_12\">\n",
" <!-- −0.075 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(168.063778 242.041058)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"242.822266\" xlink:href=\"#DejaVuSans-37\"/>\n",
" <use x=\"306.445312\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_3\">\n",
" <g id=\"line2d_12\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"212.071591\" xlink:href=\"#m4c14de641f\" y=\"208.418067\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_13\">\n",
" <!-- −0.050 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(168.063778 212.217286)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"242.822266\" xlink:href=\"#DejaVuSans-35\"/>\n",
" <use x=\"306.445312\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_4\">\n",
" <g id=\"line2d_13\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"212.071591\" xlink:href=\"#m4c14de641f\" y=\"178.594295\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_14\">\n",
" <!-- −0.025 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(168.063778 182.393514)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-2212\"/>\n",
" <use x=\"83.789062\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"147.412109\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"179.199219\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"242.822266\" xlink:href=\"#DejaVuSans-32\"/>\n",
" <use x=\"306.445312\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_5\">\n",
" <g id=\"line2d_14\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"212.071591\" xlink:href=\"#m4c14de641f\" y=\"148.770523\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_15\">\n",
" <!-- 0.000 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(176.443466 152.569742)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"159.033203\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"222.65625\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_6\">\n",
" <g id=\"line2d_15\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"212.071591\" xlink:href=\"#m4c14de641f\" y=\"118.946751\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_16\">\n",
" <!-- 0.025 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(176.443466 122.74597)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"159.033203\" xlink:href=\"#DejaVuSans-32\"/>\n",
" <use x=\"222.65625\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_7\">\n",
" <g id=\"line2d_16\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"212.071591\" xlink:href=\"#m4c14de641f\" y=\"89.12298\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_17\">\n",
" <!-- 0.050 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(176.443466 92.922198)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"159.033203\" xlink:href=\"#DejaVuSans-35\"/>\n",
" <use x=\"222.65625\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_8\">\n",
" <g id=\"line2d_17\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"212.071591\" xlink:href=\"#m4c14de641f\" y=\"59.299208\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_18\">\n",
" <!-- 0.075 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(176.443466 63.098426)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"159.033203\" xlink:href=\"#DejaVuSans-37\"/>\n",
" <use x=\"222.65625\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_9\">\n",
" <g id=\"line2d_18\">\n",
" <g>\n",
" <use style=\"fill:#ffffff;stroke:#ffffff;stroke-width:0.8;\" x=\"212.071591\" xlink:href=\"#m4c14de641f\" y=\"29.475436\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_19\">\n",
" <!-- 0.100 -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(176.443466 33.274655)scale(0.1 -0.1)\">\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n",
" <use x=\"95.410156\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"159.033203\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"222.65625\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_20\">\n",
" <!-- f(x) -->\n",
" <g style=\"fill:#ffffff;\" transform=\"translate(161.984091 24.442187)rotate(-90)scale(0.1 -0.1)\">\n",
" <defs>\n",
" <path d=\"M 2375 4863 \n",
"L 2375 4384 \n",
"L 1825 4384 \n",
"Q 1516 4384 1395 4259 \n",
"Q 1275 4134 1275 3809 \n",
"L 1275 3500 \n",
"L 2222 3500 \n",
"L 2222 3053 \n",
"L 1275 3053 \n",
"L 1275 0 \n",
"L 697 0 \n",
"L 697 3053 \n",
"L 147 3053 \n",
"L 147 3500 \n",
"L 697 3500 \n",
"L 697 3744 \n",
"Q 697 4328 969 4595 \n",
"Q 1241 4863 1831 4863 \n",
"L 2375 4863 \n",
"z\n",
"\" id=\"DejaVuSans-66\" transform=\"scale(0.015625)\"/>\n",
" <path d=\"M 1984 4856 \n",
"Q 1566 4138 1362 3434 \n",
"Q 1159 2731 1159 2009 \n",
"Q 1159 1288 1364 580 \n",
"Q 1569 -128 1984 -844 \n",
"L 1484 -844 \n",
"Q 1016 -109 783 600 \n",
"Q 550 1309 550 2009 \n",
"Q 550 2706 781 3412 \n",
"Q 1013 4119 1484 4856 \n",
"L 1984 4856 \n",
"z\n",
"\" id=\"DejaVuSans-28\" transform=\"scale(0.015625)\"/>\n",
" <path d=\"M 513 4856 \n",
"L 1013 4856 \n",
"Q 1481 4119 1714 3412 \n",
"Q 1947 2706 1947 2009 \n",
"Q 1947 1309 1714 600 \n",
"Q 1481 -109 1013 -844 \n",
"L 513 -844 \n",
"Q 928 -128 1133 580 \n",
"Q 1338 1288 1338 2009 \n",
"Q 1338 2731 1133 3434 \n",
"Q 928 4138 513 4856 \n",
"z\n",
"\" id=\"DejaVuSans-29\" transform=\"scale(0.015625)\"/>\n",
" </defs>\n",
" <use xlink:href=\"#DejaVuSans-66\"/>\n",
" <use x=\"35.205078\" xlink:href=\"#DejaVuSans-28\"/>\n",
" <use x=\"74.21875\" xlink:href=\"#DejaVuSans-78\"/>\n",
" <use x=\"133.398438\" xlink:href=\"#DejaVuSans-29\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_19\">\n",
" <path clip-path=\"url(#pa1e400c603)\" d=\"M 25.82469 148.770523 \n",
"L 30.466094 234.026188 \n",
"L 31.625276 249.048353 \n",
"L 32.740708 259.901121 \n",
"L 34.152545 267.978922 \n",
"L 35.35413 269.560685 \n",
"L 36.669363 265.626596 \n",
"L 37.848171 257.221337 \n",
"L 38.867093 246.495985 \n",
"L 40.039074 230.622286 \n",
"L 48.142125 78.256283 \n",
"L 49.327049 60.16881 \n",
"L 50.61639 44.51573 \n",
"L 52.044194 32.936467 \n",
"L 53.253888 28.342527 \n",
"L 54.69749 29.401937 \n",
"L 56.327122 39.04063 \n",
"L 58.158183 59.64063 \n",
"L 60.11461 90.906815 \n",
"L 66.120587 208.18627 \n",
"L 67.649369 233.06551 \n",
"L 68.914239 249.496688 \n",
"L 70.351889 262.593576 \n",
"L 72.037925 269.432947 \n",
"L 73.670305 266.81832 \n",
"L 75.378466 254.571683 \n",
"L 76.660071 239.572359 \n",
"L 78.145161 216.961401 \n",
"L 85.488145 76.665421 \n",
"L 86.820671 56.857749 \n",
"L 88.184025 41.384151 \n",
"L 89.457996 32.023469 \n",
"L 90.781121 27.990269 \n",
"L 91.626983 28.550977 \n",
"L 92.599271 32.210621 \n",
"L 94.206984 45.040957 \n",
"L 95.869961 66.273095 \n",
"L 97.702325 97.054043 \n",
"L 104.187644 222.093987 \n",
"L 105.795225 245.153126 \n",
"L 107.330353 260.616802 \n",
"L 109.029815 269.010828 \n",
"L 110.581599 268.106764 \n",
"L 111.847338 261.328619 \n",
"L 113.306973 247.197609 \n",
"L 114.856894 225.719508 \n",
"L 116.183365 203.118741 \n",
"L 122.245323 84.958603 \n",
"L 123.69303 62.032284 \n",
"L 125.202807 43.622831 \n",
"L 126.528323 33.022039 \n",
"L 127.97914 28.035414 \n",
"L 129.44481 30.303201 \n",
"L 130.865913 39.385385 \n",
"L 132.378321 55.90338 \n",
"L 133.758656 76.260403 \n",
"L 139.910303 195.202663 \n",
"L 142.420044 236.948718 \n",
"L 143.722833 252.84942 \n",
"L 145.245459 265.047819 \n",
"L 146.550161 269.448776 \n",
"L 147.911094 267.836392 \n",
"L 149.406932 258.870554 \n",
"L 150.65493 246.017507 \n",
"L 152.201114 224.218545 \n",
"L 153.695161 198.288159 \n",
"L 159.168716 90.696867 \n",
"L 161.60322 53.206842 \n",
"L 162.838198 39.966812 \n",
"L 163.974689 31.929307 \n",
"L 165.357917 27.939028 \n",
"L 166.838012 30.919898 \n",
"L 168.330487 41.323769 \n",
"L 169.788654 58.03779 \n",
"L 172.265066 98.236073 \n",
"L 177.556516 202.56312 \n",
"L 179.773129 238.381296 \n",
"L 181.047968 253.626268 \n",
"L 182.383981 264.410319 \n",
"L 183.796125 269.444822 \n",
"L 184.997177 268.36443 \n",
"L 186.375627 261.107809 \n",
"L 187.548066 250.152924 \n",
"L 189.337651 226.002225 \n",
"L 190.905689 199.009698 \n",
"L 196.31439 92.560023 \n",
"L 197.815059 67.553136 \n",
"L 199.172972 49.348816 \n",
"L 200.451153 36.944743 \n",
"L 201.595919 30.218988 \n",
"L 202.889239 27.928385 \n",
"L 204.138573 31.156112 \n",
"L 205.905516 44.525376 \n",
"L 207.396538 63.029921 \n",
"L 210.672256 120.50448 \n",
"L 214.255162 192.290303 \n",
"L 215.939636 222.156385 \n",
"L 217.689899 246.926358 \n",
"L 219.314718 262.353635 \n",
"L 220.815082 269.085707 \n",
"L 221.852593 269.264233 \n",
"L 222.834908 266.039555 \n",
"L 224.509799 253.22564 \n",
"L 226.486961 227.560612 \n",
"L 228.453015 193.423534 \n",
"L 232.789547 106.973428 \n",
"L 234.596558 74.863561 \n",
"L 236.192425 52.088919 \n",
"L 237.733937 36.68801 \n",
"L 239.328967 28.692782 \n",
"L 240.190459 27.956178 \n",
"L 241.130748 30.058056 \n",
"L 242.025104 34.824175 \n",
"L 242.968114 42.649937 \n",
"L 244.785202 65.055016 \n",
"L 246.648749 96.114377 \n",
"L 251.952707 200.682448 \n",
"L 253.376807 225.161379 \n",
"L 254.893404 246.377609 \n",
"L 256.646722 262.918691 \n",
"L 258.303826 269.455085 \n",
"L 259.498674 268.356328 \n",
"L 260.874251 261.10884 \n",
"L 262.352121 246.630825 \n",
"L 264.008176 223.276293 \n",
"L 268.995691 127.473836 \n",
"L 272.266097 68.276362 \n",
"L 273.718704 48.807315 \n",
"L 275.247146 34.786014 \n",
"L 276.724922 28.387658 \n",
"L 278.198437 29.416929 \n",
"L 279.716907 38.147859 \n",
"L 281.43942 56.738413 \n",
"L 284.234364 102.366333 \n",
"L 287.573035 169.116343 \n",
"L 290.599146 224.733324 \n",
"L 292.01456 244.812925 \n",
"L 293.528369 260.235109 \n",
"L 295.043965 268.434082 \n",
"L 295.946444 269.63473 \n",
"L 296.833305 268.091163 \n",
"L 298.200485 260.521122 \n",
"L 299.63543 246.223192 \n",
"L 301.207312 224.080249 \n",
"L 302.683545 198.458031 \n",
"L 305.598588 140.549202 \n",
"L 308.64513 82.332458 \n",
"L 309.884043 62.829697 \n",
"L 311.325885 44.89079 \n",
"L 312.89134 32.362371 \n",
"L 314.438631 27.907457 \n",
"L 316.105383 32.263836 \n",
"L 317.73816 45.407969 \n",
"L 318.949686 60.274607 \n",
"L 320.277509 80.771303 \n",
"L 323.246581 137.10309 \n",
"L 326.339231 198.606735 \n",
"L 329.117563 242.971849 \n",
"L 330.347359 256.550599 \n",
"L 331.431209 264.701179 \n",
"L 332.551805 269.063183 \n",
"L 333.897574 268.635484 \n",
"L 335.207254 262.31202 \n",
"L 336.798548 247.253269 \n",
"L 338.066948 230.12847 \n",
"L 339.554127 205.392232 \n",
"L 345.926086 81.795597 \n",
"L 347.301568 60.453937 \n",
"L 348.646065 44.160203 \n",
"L 349.87681 33.925862 \n",
"L 351.199633 28.43268 \n",
"L 352.580917 29.065407 \n",
"L 353.970995 36.232392 \n",
"L 355.392487 49.925603 \n",
"L 357.027173 72.599456 \n",
"L 364.544043 215.631129 \n",
"L 366.286633 241.937266 \n",
"L 368.168982 261.32169 \n",
"L 369.802668 269.066133 \n",
"L 370.740616 269.419972 \n",
"L 371.644086 266.910703 \n",
"L 373.185479 256.371868 \n",
"L 374.984392 235.00341 \n",
"L 376.574147 209.480289 \n",
"L 382.221312 98.785556 \n",
"L 384.534639 60.681296 \n",
"L 385.659101 46.65666 \n",
"L 386.955249 35.060215 \n",
"L 388.267906 28.835272 \n",
"L 389.769565 28.900111 \n",
"L 390.914634 34.108582 \n",
"L 392.085155 43.837996 \n",
"L 393.421941 59.907401 \n",
"L 395.049274 85.443536 \n",
"L 398.318492 148.770523 \n",
"L 398.318492 148.770523 \n",
"\" style=\"fill:none;stroke:#8dd3c7;stroke-linecap:square;stroke-width:1.5;\"/>\n",
" </g>\n",
" <g id=\"patch_3\">\n",
" <path d=\"M 212.071591 281.721094 \n",
"L 212.071591 15.821094 \n",
"\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
" </g>\n",
" <g id=\"patch_4\">\n",
" <path d=\"M 416.943182 281.721094 \n",
"L 416.943182 15.821094 \n",
"\" style=\"fill:none;\"/>\n",
" </g>\n",
" <g id=\"patch_5\">\n",
" <path d=\"M 7.2 148.770523 \n",
"L 416.943182 148.770523 \n",
"\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
" </g>\n",
" <g id=\"patch_6\">\n",
" <path d=\"M 7.2 15.821094 \n",
"L 416.943182 15.821094 \n",
"\" style=\"fill:none;\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <defs>\n",
" <clipPath id=\"pa1e400c603\">\n",
" <rect height=\"265.9\" width=\"409.743182\" x=\"7.2\" y=\"15.821094\"/>\n",
" </clipPath>\n",
" </defs>\n",
"</svg>\n"
],
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.plot.Plot at 0x7fb7e0e91eb0>"
]
},
"execution_count": 115,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sympy import *\n",
"import math\n",
"\n",
"init_printing(use_unicode=False, wrap_line=False)\n",
"x = Symbol('x')\n",
"\n",
"plot(integrate(integrate(sin(pi*x),x),x))\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"interpreter": {
"hash": "a7b5a1112396ad393f5588006c146c6954be07cba002f50e558ad6b83bb9990c"
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 2
}