340 lines
276 KiB
Plaintext
340 lines
276 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"import scipy as sc"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Exercise 1 - Simple FFT"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# using sc.fft\n",
|
|
"\n",
|
|
"def f(x):\n",
|
|
" return np.exp(-np.pi * x**2)\n",
|
|
"\n",
|
|
"n_segments = 2**13\n",
|
|
"# FFT works best with 2**n segments\n",
|
|
"x = np.linspace(-10, 10, n_segments)\n",
|
|
"# plt.xlim([-5, 5])\n",
|
|
"fx = f(x)\n",
|
|
"\n",
|
|
"plt.plot(x, fx)\n",
|
|
"plt.show()\n",
|
|
"fk = sc.fft.fft(\n",
|
|
" fx,\n",
|
|
" # norm = 'ortho'\n",
|
|
")\n",
|
|
"k = sc.fft.fftfreq(n_segments, 2/n_segments)\n",
|
|
"plt.scatter(k, np.abs(fk))\n",
|
|
"# plt.xlim([-5, 5])\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Exercise 2 - signal analysis"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 16,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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pl8SL9egJ11kYEADlvcgCYwxdPHcwi3XIhU4kntSrzYjChMSLwXTl4K4GgCatqqVnKIJonKpVrCSXkAOQ7nmhg89qTg1kny8BkPdMFvqHY/o+mI0HzOtyoqbUAyCV8EsUJiReDEY/+LK02qtKPPC6HGAsZfkT1tCZQ8gBoINPJnIJOQDA1Aoql5YB7jmrLvHA48rumGpKCx0RhQuJF4PJddNUlNTtxbTorCV3z0ux9v4R6vViIeFYQm8rn021EUChP1nIJVmXw/dRallQ2JB4MZjOHMr7ODw+T4vOWjqDueVL1JR64XIoSDL1ck7CGvgaLHJn3qCOM0VPnKfQn5XkakAA5Hk5VyDxYjCd+VgMWt4Lb7BFmA9jLKf+EgDgdCj6vJMAtY5072e21SbpVvtElZKEWPLZR6n44dyAxIvB5ON54YuO7jeyjoG0RME6f+Z9ejjcUuykjdMyugdVr1dtWe7zNxxNYJBuJraMrhxzB4E0I5A8LwUNiReDyStWS4vOcni4p6LYDa/LmfX7SbxYTz7ipdjjgt+nhpq6aA4tozPL6znS4WGjDtpHCxoSLwaSSDL0aomCdTlsnOTutB794MvwWoAz4ZZiJ1WMWQYXoLmsQYByz2SAG4G5eD/5Pto1GKHE+QKGxIuB9A9HkUgyKIpa+pwtusVAOS+WkY/VDlClgwzkO4fkPbOeHl2AZu95qS1TE+cTSYbTg5Q4X6iQeDEQvmlWFXuyuhOHw8NGA8MxjEQTho6NyAzjDj4SoFZB3jN7E08kdQ92TVn2RuDoxHlah4UKiRcD4dZCrgef3+fWrxSgiiNr4CGHmhwPPvK8WM9pgwQozaE19A1HwRjgUIDqktzmkHcsP0nFDwULiRcDyddqB9IOP1p0lpC/50WLtwfDSCap1NYKjAr9kffMGnQPdokHTkduFytS0m7hQ+LFQPiiy9VqB4BG3mCJNk5LyDfkUFfmhaIAsUQqeZswj0SSoS+Ue74EkLpNvDNI+RJW0DOkhYzy2Ucp6brgIfFiIPmGjQCgiTwvlpLvHLqdDl34UMKn+fSGIkhqIYdckuYB8rxYTY8BHuwGrUqJ7okrXEi8GEjK85Lbpgmk+sN0DdKiswJDQ390+JkOn7/qUm/OIYdGv2q19w/HEI5R4rzZ5Jt3BgB12j5K1UaFC4kXA+HuznwOPt7X4DS5rE0nlkiibzj/OdQFKFl9pnM6z7AfAPiLXPC51a2R5tB8egwxAsnzUuiQeDGQVL5EbrF2AKgv4xYDLTqz6QupVQ5Oh4LK4tw3Tqo4sg4jPGfqDe+UM2EVRoTfeb7T6WCE7qgqUEi8GIju7syhNwGHPC/WoYcc8qhyAFIVR5TzYj5GiBcgrdcLzaHpGBM2Ut8bTSQRGIkZMi5CLki8GEQskUQ/Dznkseh4yKF7KIIEldqailEHH/e8UMWY+fQYcPABac0GKexgOj2D+YduvS4nKordAIAuMgQLEhIvBmFUyKG6xAOHwu9JokVnJkaUugNp3jNKFjSdXr3MNvc1CKQ1qqM+IaZjhOcFSIXgKe+lMCHxYhDpjZUceYQcXE4HqkspdGQFvC9LdY4lthweb++m+TOdPm0Ocy2T5tSXkQC1gniaB5uMCGIiSLwYhH4XR54LDkhlylPSrrnw5mb5Hnx80xyMxOmOKpPpNUi8UKmtNXAPdj59ejh15HkpaEi8GETq4HPn/bPSM+UJ8+gLqYl9VXmGHMq8qVJbEqDmwtdhrnficOrKyICwAt5uIp+rATi6EUjipSAh8WIQ+sGX56YJpPcoIPFiJqmDLz/xoihKSoCS5W4ajLFU2ChPAUqlttZgVNgPSO+3RGuwECHxYhBGHXwAUMvdnWT1mQrfOPNJuOboljttnKYxGIkjllCFRr7rkFe6ROJJDEbieY+NyAzeJNKINUjh98KGxItBGHnw1VOvF0vQE3bztNqB9GRB2jjNok8LORR7nPC5nXn9rCKPE2VeFwBah2bSb6DnRTcCaf4KEhIvBmGUuxpIc1nTwWcqqY0z/9AfhY3Mx0irHQBqSYCajlEJ10DKCOwepNBfIULixSB08UKeF1sSjiUQ0iqDjLH6aA7NhntejPCcAanQXzcJUNMw1vOS6rI7MExddgsNEi8GYazFQF12zYaLT5dDgd/nyvvn8Y2TN9wixGNksidAVX9WYOQcel1OVPIuu+Q9KzhIvBhEv4H5EtUlHijUZddU9JylEg8UJb8STSA9YZc2TbMw0oAASIBagdEClCqOChcSLwaQSDIMaJd/GRFvdzkderM7svrMwajuuhy9yy6FHEzDyIo/gASoFfDuuoZ5z3izQZrDgoPEiwEMDKtdIQHobsp8oSZZ5mJkrB1IVRv1hqKIJZKG/ExiYnoNTLgGqL28FfQaWLUJ0DUPhQyJFwPgrs7yIjdcTmP+Sev9FG83E6NDDlXFHri0DqE9FHYwhT5B3jM6+MyBMSbMiKArAgoPEi8GYHTIAUh5XihWaw5GhxwcDoVCfyZjfMIuhY3MJBiOI64VKBid80JrsPAg8WIARlsLQCpWS1ny5pCesGsUFHYwl94h43otASnPSzAcRzhGF2yKhu+jRjQZ5OhGIO2jBQeJFwPoFXHwUZ8QUzE65ABQ3pLZGD2H/iIXPC51i6TEa/EYHboF0irGaP4KDqHi5bXXXsMnPvEJNDU1QVEUPPPMM5O+Z/PmzTj//PPh9XoxZ84cbNy4UeQQDUHkwUdlmubQZ3CyJ5BqT04CVDwj0QRGYsY1GQTUCzZrS8l7ZhYiPNi1peoa7BmiLruFhlDxEgqFsGzZMjz66KMZPd/a2oqrrroKH/7wh9HS0oKvf/3r+Nu//Vu88MILIoeZN0bH2gGgRhMvPbRpmoIIq6+OKh1Mg/dD8jgdKPXm32SQU6e3mCfvmWj6DC6TBoCaMvVnhWNJDNEFmwWFcat8DK688kpceeWVGT//2GOPYebMmfje974HAFiwYAHeeOMNPPLII1i/fr2oYeaNCPHCLb5uzWIwonEaMT4i5pAOPvNInz8j1woJUPMw8ooVTrHHhRKPE6FoAj1DUZT5jGllQViPVDkvW7Zswbp160a9tn79emzZsmXc90QiEQSDwVFfZiNEvPB7OeJJBMNkMYgknkgioDUZNNbzQqW2ZiHCcwbQFQFmIiJsBFDeS6EilXjp7OxEfX39qNfq6+sRDAYxMjIy5nseeOABlJeX61/Nzc1mDHUUIipVfG4nyjT3N/UJEcvASMzwJoMAXexnJgMCQg4AzaGZiCh8AEi8FCpSiZdc2LBhAwKBgP7V3t5u+hhEJOwCtOjMol9Ak0EgPWwUQZIu2BQKvzW43EDxCaTdDk6hP+GI8rzwfktkBBYWQnNesqWhoQFdXV2jXuvq6oLf70dRUdGY7/F6vfB6jasQyRbGmJ5oZlRLa05NqRdHe0K06ASTupfK2IOvWqtcimt3Xxm9KRMp+ofFzCH16jEPEQm7ABmBhYpUnpfVq1dj06ZNo1576aWXsHr1aotGNDkjsQSicfXuGlp09kT3vBgsPj0uh36Y0hyKJaAdfBVFYnJeaP7EIyJ3EEgrfqA5LCiEipehoSG0tLSgpaUFgFoK3dLSgra2NgBqyOe6667Tn//yl7+Mo0eP4q677sKBAwfwwx/+EL/5zW/wjW98Q+Qw84K7q91OBcUeY7pCcmq0TqHkeRGLKM8LQIefWXDPS4WgsFFvKIoEhf6Ewo0Io9eh3naC9tGCQqh42b59O1asWIEVK1YAAG6//XasWLEC99xzDwCgo6NDFzIAMHPmTPzpT3/CSy+9hGXLluF73/se/uu//kvqMmk91l5kbIkmQJ4Xswjwg6/IePFCORPmwAVohcHeM7X0GkgkGfo17w5hPIkk06sqjZ7D9LYTROEgNOfl0ksvnbCr4Vjdcy+99FLs2rVL4KiMZWBEc1cLsNpTiWa0aYokNYfG56SQADWHVNjI2HXodjpQVexBbyiK7sGIviYJYwlq4hMwfg6p4WdhIlXOix0xw2qng08s/br3jObQrugJuyU0h3aEe7XKvC5DK/6AtPmjKwIKChIveZKKtZPVblcCgipVAHJZmwXv81JucMIuQOvQDHjYz+hSdyCVOxhLML0ZJWF/SLzkiRlho94Q9QkRCYWN7E08kUzLlyABakcCghKuAcDrcsLvo4afhQaJlzwRGTaqJovBFPpD4qw+uhtHPOnXZ1D41p7oBoQAzxmQnjhPc1gokHjJkwHBFgPPwyCLQRwBvVSaPC92ZEBgvgRAc2gGojokc2gOCw8SL3nCLQajG5xxaNGJZ0BQpQqQmr/ASAyReMLwn0+k5Z0JSNYFaA2awYBADzZAlZuFCImXPBHVlpzDk80o3i6GaDyJUFQVFSK8Z+VFbridav8f2jjFEDAt5EC9ekQRGBHnwQZIgBYiJF7yJJXzImrjpA6tIuGeM0UB/D7jN05FUag9uWB4zpKog49ulhbPgKD74Th0OWPhQeIlT0RWGwFU6SCaQFqPF4fD2A7JnFo/CVCRiOquy6ktVecvGI4jHKPQnwj0UmlBYSPyvBQeJF7yZEBggzMAqCnT7jcapJCDCPoFx9qBlAClsIMYRHXX5fiLXPBoicBkuYtBZL8sgMRLIULiJQ/CsQQi2o3S5HmxJ3pzM0GbJkAbp2hE550pikJzKBhdgAreR0l8Fg4kXvKAe11cDgWlXjHXRNG9HGIReaM0hw4+saS6s4oToDU0h0LRQ3+Cw0Z0O3jhQOIlD/rTrAWjb5TmkOdFLCLLpDkkXsRiyhzSOhRGMplqwimqzwvdDl54kHjJA9H5LkDq4Osji0EIA4Jj7UBatQodfEIYEHgpI4cEqDgGw3Hw+xJF7aVup0OvZKLQUWFA4iUPAgLvxOGQxSCWAcH9JQA6+ESjN4oU1K4AoDkUCZ+/Yo8TXpdT2O+hlgWFBYmXPBDdFRJQLYYqTRzRojMeM0MOpwcjYIy8Z0YzEKK8JTuje84EGoFAag7J81IYkHjJA9H9JTjUYEkcZoSN+KYZjSdHXSJI5E8skcRghN8oLXAOKedFGKJ7vHD0buUkQAsCEi950C+4vI9DVp84RF6syfG5nSjzqdVoNIfGkn7but8npuIPoDUokgHaR4kcIPGSBwETwkZAymIgz4vxpDZOc1zWtHEaCxeffp+YG6U56VcEUOjPWMwwIAC6nLHQIPGSB2YtOjr4xCG6vwSHKo7EYEbSPJBagxEK/RlOqmqTDAgic0i85IFe5WBazgtZDEYSiScwLPBG6XT4BZung3RFgJH0m5CsC1DoTySi74fjkHgpLEi85MGA4LbkHFp0YuBhP1E3SqdDCZ9iMKO7LofWoRjMC79T4UMhQeIlD1Kl0lTiZ0fSqxxE3SjNoYNPDDxnSbQBAZAAFYUZvZaAtIafw1HEE0mhv4sQD4mXPDDL3VlDzZWEYEafHg6JFzGY0eWaQ3MoBrOS5iuLPXA6FDCmdiwn7A2JlxwJxxIIx1T1Luo+Dg5ZDGIwa9MERlerEMYRDJN4sTtmJc07HQqqStS1fprm0PaQeMkR3l/C6VBQJuhGaU5lsQcOBWQxGIxZzbEACv2JImDBHJJ4MZaACY0iORT6KxxIvORIurta1I3SHKdDQXVai3nCGIIWHHy9IfKeGQmfQ9EJ1wAdfCJgjJmW8wKQAC0kSLzkiJkWH0CZ8iLQD74isZ4zYHS8vZe8Z4bBe674yfNiSwYjcSSSatM/8p4R2UDiJUdSB5854oUWnfHoB58JVrvToaC6hO5WMZqAiQKU1qDx8JCR1+WAzy3uRmkOzWHhQOIlR/RNU+B9KunUUqM6wzEzbATQxikCU8NGPHE+FNG9BUR+mO3BptBf4UDiJUfMrHIAgJoystqNJmCy94wqjozHzMOvusQLhwIkGdAbojk0ArP30To/rcFCgcRLjph98JHFYDxmb5zccj89SFcEGEE4lkAkriY/m7EO1VJbOvyMxPTwO/XMKhhIvORIcMS8fAkgPeRAB59RBEwMOQAUNjKaQS1nSVEgvF0BJyVAaQ6NILWPmjt/tAbtD4mXHDE9VkuLznD0jdOEZE+AvGdGw9dgmdcl/HoHDoX+jMUq7+dQJI7hKN0ObmdIvOQIX3RmHXx1/FZi2jQNw/yNU51DOviMQZ8/E/qDcMiIMBazw++lXhd8bvXY6xmk4gc7Q+IlR6zyvAyG4wjHEqb8zkImlkhiOKr+O5oVNqJkQWMxO+wHkHgxGjOrxQBAURTdEOweohC8nSHxkiNmLzq/zwWPS50u2jjzh88fAJSZXO5O82cMZq9BgEJ/RsN7LZllBAJpeUtBmkM7Y4p4efTRRzFjxgz4fD6sWrUK27ZtG/fZjRs3QlGUUV8+n8+MYWbFoMmLTrUYKFnQKLjVXup1weU0R8PzTTMUTSAUoXh7vpjdpwcgz4vRmNlkkEMCtDAQvmv/+te/xu233457770XO3fuxLJly7B+/XqcPn163Pf4/X50dHToX8ePHxc9zKwxO1YL0MZpJKnuuuZtmiVeF4o9ahdRmsP8SV0NYOLBxy/YpPkzBBKgRK4IFy8PP/wwbr75Ztx4441YuHAhHnvsMRQXF+OJJ54Y9z2KoqChoUH/qq+vFz3MrIgnkhiKmH/41VG5tGGY3V+Co2+cZPXlDR189ofylohcESpeotEoduzYgXXr1qV+ocOBdevWYcuWLeO+b2hoCNOnT0dzczOuvvpq7N27d9xnI5EIgsHgqC/R8JARQJ4Xu2KF5wygUlsjsfLgG4zEMRKlxPl8SVVt0j5KZIdQ8dLT04NEInGW56S+vh6dnZ1jvmfevHl44okn8Oyzz+L//b//h2QyiTVr1uDEiRNjPv/AAw+gvLxc/2pubjb8c5wJX3DFHifcJuVLAEBtKc+Sp0WXL2aXSXNo4zQOK0qly7wueLXEebrhPX94ryUz1yHlDhYG0lUbrV69Gtdddx2WL1+OtWvX4qmnnkJtbS1+9KMfjfn8hg0bEAgE9K/29nbhYzS7TJrDS20pSz5/rLDaAao4MhIr5lBRFOqyaxDReBIjMXPbFQBkQBQKQhM2ampq4HQ60dXVNer1rq4uNDQ0ZPQz3G43VqxYgcOHD4/5fa/XC6/Xm/dYs8HsqwE4lCVvHFZYfADdb2QkZndI5tSWeXGif4QOvzzhnjMAKDUxd1BPuh6KIJlkpnVnJoxFqOfF4/Fg5cqV2LRpk/5aMpnEpk2bsHr16ox+RiKRwHvvvYfGxkZRw8waqz0vtGnmj9kdkjlk9RmHVeuQjAhj4AnXZT4XnCYKiGrtcs14kmEgrd8TYS+Eh41uv/12PP744/jZz36G/fv349Zbb0UoFMKNN94IALjuuuuwYcMG/fn77rsPL774Io4ePYqdO3fif//v/43jx4/jb//2b0UPNWNkOPiSSWbq7y40LAsbUbWRYejr0Ko5DJL3LB+sWoMelwOVWp4UGRH2Rfjp+9nPfhbd3d2455570NnZieXLl+P555/Xk3jb2trgcKQ0VH9/P26++WZ0dnaisrISK1euxFtvvYWFCxeKHmrGWNHZEwBqSkdbDFUlHlN/fyFhRZktkLqjijbN/GCMWT+HJEDzItWnx9z5A1QB2j8cQ/dgBPMaykz//UT+mOI6uO2223DbbbeN+b3NmzeP+v9HHnkEjzzyiAmjyh2rymzdTgeqSjzoC0VxejBM4iUPrNo4U/H2KMXb82AoEgd3PlrWq4cEaF6kxKe5HmxAFaDvdw1R7pmNka7ayA5Y0ZuAQ9UqxmCV1V5V4oGiAIkkQ98w3WqbK1x8elwO+NxOU383iRdjsCpsBNAcFgIkXnIgYFGlCkBJu0YRtOBOFUDznhWrHjOaw9wJDNPBZ3es6rUE0BwWAiReciCV82K+u5N7XqjHRO4wxsjqszlWJc0Do5OuGaPE+VyxKvwOUMVYIUDiJQesKtEEgFryvOTNSCyBuJYwQVafPbEq7AcANaWq5yyWSIlgInus6pcF0BosBMw3WwoAGXJerPK8DEfj+P6mQ2hpG8Al59XilktmmXpFghHwTdPpUPRbns3E6nLptt5hPPzSQfSGovjCqum4YnFmDSNlwkrPmdflRHmRG4ERtVqlotj8xPk3D/fg8dePosTjwtfXzcXcevtVzKTCRtZ5z6zaR5NJhifebMXL+7swv8GP2y8/z5K/ZTtD4iUHrCqVBtItBvOz5JNJhr/92Xa8daQXALC1tQ8n+ofxwKeXmj6WfEj3nCmK+dU+Vlp9pwZG8Nkfb0FHQP37ef1QD/79cyvwyWVNpo8lH3jCrhWeF0CdQy5ezBYOm/Z34Uv/vUP3Hr5+qBt//MrFmF5dYuo48sWqm90B6y9I/e7zB/Cj144CAN4+2od3Twzg17eshsdlL0PQSuhfKkvU/hLaxmnihXAcK/uE/Pfbx/HWkV4Ue5z46kfmQFGAX21rx9ajvaaPJR9Szc2s0e5Wes/ueXYvOgJhzK4twafPnwIAuO+PezEUiU/yTrkIWJRwzbEqZ2IwHMM3f/8e4kmGyxfWY9nUcgTDcXz7T/tNHYcRyGAEBkZiiMTNvR38rSM9unD58trZKC9yY1fbAH659bip47A7JF6yJBJPIppIArAoYdcid2c4lsD3Nx0CANx95Xzcfvk8XPuBaQCAh19639Sx5IteqWKh1Q6Y7z1751gfXt7fBadDwY++uBIPfnopZtaUoGcoip++0WrqWPLFyoMPsM579vjrregZimBWTQn+4/Pn43ufWQ6HAry0rwst7QOmjiVfdO+ZBUZgeZEbbqfqde0ZMq9lAWMMD7+o7pefXzUNd185H3eunwcA+OHmIwjHzBVSdobES5Zwi8+hAKVeC5oraQm7g+G4qX/oT+08ib5QFFMqivD5C1XR8tXL5sChqOGjo91Dpo0lX6ws0QSs855tfPMYAOAzF0zFnLoyeFwOfOUjcwAAv97ebqsrJ6xM2AWsES+ReEK3zu+4fB48Lgfm1JXiU8tVD9qT29pMG4sRWJm3pCiKJT2zdrYNYPvxfnhcDnztsrkAgM9c0IzGch9OD0bw8v6uSX4CwSHxkiXpcVor8iXKvC54tbiomYvuyXfUjfHGD86AS0vQbSwvwqXz6gAAv91xwrSx5Mu5aLV3D0bwwt5OAMB1q2for1+5uBFlXhdO9I/g7Vb7hP+sTJoHrJnDF/d2oWcoinq/F+sX1euv/68LpgIA/vReh20s9/TrHSwL/XEvtol3VP1uRzsA4ONLG1HvV40Yj8uBv1qhCtBnW06ZNha7Q+IlS6wskwY0i8Hk0FFrTwi7TwTgdCj6IuNcvVxN9NxkI4uBNxm0+uALmug9e35PB+JJhmXNFVjQ6NdfL/I4ceUStdropX32mcOghY0iAWvylv60uwMA8L9WTtUNCAC4aGY1Gst9GAzH8cahHtPGkw9WtysAgFrNA2rWHIZjCfzPu+ocXrOyedT3rta8Z68e7MZgmMrvM4HES5ZYdZNtOnUm50z8abdqDXxwTg2qtU2bs/a8WjgdCt7vGkJ737Ap48kXKxucAWquFK8q6DEp4fNFTZhcOUZZ9Efmq96zVw92mzIWI7Ay5ACY73kJxxJ49X11fq5c3Djqew6Hos/ha4fsMYd8/lwOBUUmX+/AqddC8F0meV62tvZhMBJHvd+LVTOrRn1vXkMZZtaUIJpIYssR+3hArYTES5ZYXeUAAA3lqsXQGTBn0f3lwGkAYx98FcUerJxeCQDY/L69Nk6rDr70eLsZVl8wHMPbWkXYRxfWn/X9D86pgcuh4GhPCG299hKgluUt+c2tNnrt/W6MxBKYUlGERU3+s75/yXm1ANTSdzuQ7jmzIvwOAA1+k/dRzTv9kfl1Y17IevGcGgDAG4ftMYdWQ+IlS6x2VwPQY6WdQfEbZ2A4plcxrNU2yDPhi25ba5/w8RiB1cmegLmW+6sHuxFLMMyqLcHs2tKzvl/mc+P8aaoA3XLUHhun1UYEF599oShiWvWhSLjn7KML68c87NfMrobLoaC1J4QT/fILUCuvBuDUcyPQBM8LYwybNCPwI/PPNiAA4OK5mnixiQC1GhIvWWK11Q6kWwwjwn/XG4d7kGTA3LpSNFUUjfnMBTPUg++d1j5b3PVidbInYG6TrFe0TfOjC8beNIHUHG4/1i98PPkSSyQxHFVzhaxah5XFHjg167lXcKktYwyva+GgsTxngCpAuUdmx3H559DK++E4fB81I2x06PQQTvSPwONy4INzqsd85qJZ1VAU4GhPCL1059KkkHjJEhms9gYTLYbXtFDQJeN4XQBgeXMFXA4FncEwTg6IF1T5YuWt4ByzPC+MMT1k9KG5488hFy92OvgAoMyiw8/hUPQ7jkTPYWtPCF3BCDwuhx6iHYvzte/tahsQOh4jkMGAMDP8zvfRi2ZVo9gz9t9seZEbczTPqN169lgBiZcskWHR1esWg3h1zuOvE4mXYo8Li6aUA7DX4Wel1WfW/UYn+kdwKhCGy6Hg/OkV4z7Hw0Z2sPp4c7NSr2tU1Y3ZpOZQ7OG3RROfK5or4JsguZXP4c42+degFGEjbR8NhuMYiYqt+uMh9dWzxva6cFZMqwBgDwFqNSReskSGRdeYZjGIDNOcHBjByYEROB0KPjBjfIsPAJZMUV3W+04FhY3HKKy8U4WT6jEhVijwg29Zc8W4Fh+gJl7PqlHvxtkj+RzK4P0E0sqlBc/h20e1g2/2xAcf97zsOxWUvt+LlTdKc/w+l17pJNKLnUwyvHNMncMLz6gyOpMVNhKgVkPiJUtSi846q51bDCOxhD4eEWzXFtziJv+EBx8ALGpSPS/7OuQ++BJJhsGIBGEjk+7G4SGji2ZNvGkC0Pu/7Jd8DrkBYVXIiGOGB5QxppfOTma1N5X7UFnsRjzJcPi03B2vra4WA9SqPzNCR4e7h9A/HIPP7cASzUM9Hkunqt/fczJgi/xBKyHxkiUyeF58bicqtPtARFoMPAS0cvrkB9/CxpTnReZFNxROiT1Le/VoB1+P4HwJ7q5eNXPigw8AFjbZQ7zIcPAB6bln4vK82vqG0TOk5rss10IK46EoCuY32GMOra4W45iRtMvX4PnTKie9NXpOXSmcDgXBcNyUnEY7Q+IlS6TZOP3ik3bf0SpPJgsZAWqTJadDQW8oakouTq7wTbPI7bT0+vn0hF1RYq93KIIT/erBumKSgw8AFjSWAZA/9CeDAQGkwrcdAq32904GAAALGsrgdU3ezC3lPRsUNiYjsPqKDo4ZxQ+ZhowAwOtyYnatGr49IPkcWg2JlyyRoVQaSC26LkEbZzAcw4FO9RBbmYF48blTi25fR0DImIzA6u66HF6pEk0k0T8sph04z12ZVVOCsgz+XvnBd7QnJHXOhAz5EgDQUK62DhAZcuDiZfEk4QbOfE2A8rUrK7IYgfUmNKp774Q6hzyfZTLmad6zA50kXiaCxEsWJJMMQxLkSwApz4soq++9EwEwBjRXFem3IE9GeuhIVmSx+Lwupy5gOgT169mjHXyLMjz4GvxqzkQiyXCoS96cCVkOPjM8L3tPqmspU/GyIC1sJHP41ur7xTgNgq8IGAzHcLQnBEDNHcyE+Q32EKBWQ+IlCwbDcfD9wGrLvV5w2IgffEunVGT8nlTOhLwWg9UXa6bTqFnuHQNi5zDTTVNRFFsk7UqTL6GJl8BIDMNR4xPnGWO652WyRE/O3PpSOBSgfzhm6qWR2SJLxZjosBE35JrKfWfdCzcePHx7kDwvE0LiJQu4xedzOzKKP4tEDxuJEi/aols0JbODD1CTzQDgSLf8VrvVFh+QbrkL8rycyu7gA6AnfB7sknfjlOXgK/O6UOLRSm0FeF9O9I8gMBKD26lgbv3Z1zqMhc/txCyt0ZnMlX8y9FoC0irGBHnP+D6aqecMSIWNDp8eQjQu/uoJu0LiJQtkyXcBxHeH3Ktb7ZkvOn5vTmtPCMmknC5ruTwv4sIOgeEY2vtUUbQoizmcpeUtHZVYgMqyDkWX2nLP2bwMk3U552lC54ik5dLp7QqsNiL4/J0ejAjZs/ZmmbMEqF6aMp8L8STD0R4551AGSLxkgQzNzTgiq42GInE9TjvWDbbjMbWyGB6nA5F4UtprAmTo08Np1O6KEiFeuNdlWlUxyosz/3vl4qVVm38Z4R12ZViHeuhP4Bxm4zkDgJk1cs+hLO0KALXfkkMB4kmGnpDxYTY+h4uz8GAriqJ7z45JOocyQOIlC2RJFARS4qUvFEUkbmxlCM93yCZOCwBOh4Lp1cUA5A0dyTSH3PNySoDQ0/Ndstg0gZT3rL1/RFqXtSxhI0BszsR7WrJuNp4zAJhZk/KAyogs7QoAwOV0oEbb47oCxoqX4WhcbxaYjQcbgN7t+qikcygDJF6yICBJnBYAKord+sI3uj05P/gWZrnggPSwg5yLTpYeIYBYqz3bEltOXZkXJR4nEkmGtj455zAoScIuIC5viTGmr8NC87zI0q6AI0qA7u8YRJKpPZ14U8pMmVGtzaGk+6gMkHjJgqAEtxFzFEURVi69Ry/PzM5qB1KWu6yxWllKpQGxd1Tt5YmCWQrQdJf1EQk3TsaYVN4zUTkvHYEw+kJRuBwK5mmls5nCrfaOQFhIFVS+yOQ5A8RVbu49lV21XzozNSPwWK98a1AWSLxkgUxWOyDOYkgtulw8L5p4kfDgA+Saw3q/D4qiNqrrDUUN+7nBcEy3urP1vAByW+4jsQRiCVXoySRAjTYguOdsbn3ZhDdJj0VliQeVWp7TsZ5hQ8dlBLIkXHMaBFUc5eo5A1ICVMY1KAskXrJAJosPELPowrEEDvE4bS6LTrMY5M154cme1rusPa5UvN3IXi+8t8SUiiJUlXiyfr/MFUfc++lyKCj2WNuuAAAa/GK67O7NskfPmcgsQGVqVwCkjMBTBof+uAc70yaR6czQ5q9nKKr/exGjIfGSBbJZDNzqM7Ky50DnIBJJhppSD+r9mSfrcrjF0BWMYCQqX4t52VzWTQJyJnJN1uXI7D1L95wpimLxaFJrsDcUNfRKBb053dTsDz4gPWlXXgEqyxqcWqkK0JP9xq3BcCyB97VeSbkYgaVel37/GVUcjQ2JlyyQKVEQSFt0BooXvaV8U3lOh0N5kRtlWkLziX5yWU+GiKTdPTn06ElnhlYxdrxPvvnTrXYJkuYBNXHeqyXOG9kwUm8SmeMcypw4L1PhA5DaR08YKF7e7xpEPMlQWezWDZRsmVktr/dMBki8ZAEPOchjMaiHjJGLbq++aeZmtSuKgmlV6rjaJDv8wrEEIlr5byG7rHPp6plOs/Z31T0Yke6CRtk8Z4qioKnCWCOiKxhG92AEDiV1X1i28DXYLqEBIVv4fUqF+m/VGQwjnjCmPcCetDupcvUQzqhRxyWjAJUBEi9ZIJvVnnJ3GrdB6cm6OR58QOrwa5dMvPBNU1HU1u4y0FShhY0MynkJReJ6vlGuc1hR7Nb/fWTznsmUcM0x2nLntxDPrStDUY55Pc1cvPTJ1yxStjmsK/PC7VSQSDLDih/2GLCPcgFqpHFaSJgiXh599FHMmDEDPp8Pq1atwrZt2yZ8/re//S3mz58Pn8+HJUuW4LnnnjNjmJMiU4ddAJiibZrBcFzfEPIhlkjigHapYq4hBwCYVs09L3ItOh5rL/O64HBYny8BpIeNjPm3Um8TBur9Xj1mni2KomCqpIefbGsQSPOAGiTW+cGXzb1iZ9Ks7Q1dg2HDm1jmi0ztCgDA4UjznhkkFHK5XuVMmnXxIpcBIQvCxcuvf/1r3H777bj33nuxc+dOLFu2DOvXr8fp06fHfP6tt97C5z73Odx0003YtWsXPvWpT+FTn/oU9uzZI3qokyLTvTgAUOxx6dUkRiy6Q11DiCaSKPO50FxVlPPP4RunbGEj3V2dRbt80Ri9aeZTnpkOn0PZwg4B/XoHeeaQrxWjLGQj5rCqxIMitxOMGZuIagQyXe/AMdJ7Fksksb+TJ+vmLkBF5OIUEsLFy8MPP4ybb74ZN954IxYuXIjHHnsMxcXFeOKJJ8Z8/vvf/z6uuOIK3HnnnViwYAHuv/9+nH/++fiP//gP0UOdEBnzJYD0P/D8D5k9af1d8qnkkNVikC3sB6QOvo5g2JB2/Lm2lD97XJr3rFeuOZQtXwIwPvcsPV8iVxRFMVxUGUVAssIHQG0rABiTt3SoS70Nuszn0kM/ucDD7x2BEcQMysUpJISKl2g0ih07dmDdunWpX+hwYN26ddiyZcuY79myZcuo5wFg/fr14z4fiUQQDAZHfYlAxnwJwFh1vjfPEltOc1rCrtGdY/NBNnc1oF4M53M7wJgxdxztzfEyvzOR1/Mi38Fn5L9V92AEncEwlDySdVPjkjNpV8Z1mBKgxhmBi5r8eRmBNaVeeFwOJJmxfaDy5UT/MP7h6ffww82HLR2HUPHS09ODRCKB+vr6Ua/X19ejs7NzzPd0dnZm9fwDDzyA8vJy/au5udmYwZ8Bz5colShfAjDWYsi3PDN9TIoCDEcT6DOwc2y+yFapAmj5JQYdMvk2GExH1oRPmQ++TgO8Z/zgm1VTgpI8jSRp51BC75mR++heg0K3DodiqGfdKE70j+AXW9vwux0nLB2H7auNNmzYgEAgoH+1t7cL+T3+Ihe+vm4ubrp4ppCfnytGWQyJJNNvk87X8+JzO/XuvzLlvcjUXTedZoO8Z/s7glqDQW9ODQZHjUnSUlsZD76aUo9h3rM9J4w5+ICUV1amOYzEEwjHZA6/G2cE5mtAADDMsDESWQwIobt4TU0NnE4nurq6Rr3e1dWFhoaGMd/T0NCQ1fNerxdeb34bdSbUlfnw9XXnCf892WLUomvtCWE4mkCR26l358yH5spidATCONE/ghXTKvP+eUYgo+cFSLeQ89ug0jvr5tt9lv9dDYbjCAzHpEly1hN2JZpD7j07fHoIJ/pH9NbuuZDrbeBj0SxhqS33YMsWfueVm6cGRpBMspy964kk06/nyNeDDciZtCtLwrVQz4vH48HKlSuxadMm/bVkMolNmzZh9erVY75n9erVo54HgJdeemnc5891jEoW5LkSC5v8cBoQFmusML7tfb7ImLALpFvIeVrtJ3O7SXosij0uVGuVbDJafbIJUKPc+3sNtdq1MUnl/VTnT6Z2BYB6T5zToSCWYDg9GMn55xztHsJILIFij1O/XyofmgU0Is2XoCQdkoWHjW6//XY8/vjj+NnPfob9+/fj1ltvRSgUwo033ggAuO6667Bhwwb9+a997Wt4/vnn8b3vfQ8HDhzAP//zP2P79u247bbbRA/VlnCLITASw2AeF3jtyfMiuDPh/UtOSZRoJtuFcByjmvoZ0RgrnZQAlWgOJdk4z8SI5Ni+UFTPuci1w3U63LDpDUWluWdMtgZ1HJfToYe6Tw7kPod8DS5sNMYI1A0bCQWo1XMoXLx89rOfxUMPPYR77rkHy5cvR0tLC55//nk9KbetrQ0dHR3682vWrMEvf/lL/PjHP8ayZcvwu9/9Ds888wwWL14seqi2pNTrQoXm0s8n2SyfG1DHoklCz4tsF8JxjCgtj8TTL4IzVoB2SjKHiSTDYEQOl/WZGOHe5wbEzJoSlBngHfT7XCjROvTKsg5l9ZwB6UIh/33UKAMiPZwlC0FJei2ZYr7cdttt43pONm/efNZr11xzDa655hrBoyocmiuLMTAcQFvvMOY3ZH9wMcZGlfcZgYyeFxnLbIGU1d4zpFrIubSEf79zCLGEehEcr5zIlyb93iU55jDds2j1xnkmRuQtGZnvAqi5OA3lPhzpDqEzENZvC7cSWUO3ADC9uhhbW/twrDf3u4T2GDyHTeW8U3IEiSQzxJuTLynPS4GHjQjx8ATBXBdde98IBsNxeJwOzK0rM2RMUnpeJKxUAdSOvzwMcrwvtzlMP/jyTdblNGoiqEMSq49bfEVuJzwuubYuI/KW9HvFDDIggFQHZ1kEqKwVf0DaPprjLc7JJEvLWTJmDmvLvHA61HuXuvPIxTESLkCN8A7mg1w7AJETM7W7hHK9Op1vmvMaygw7FLjF0DMUleZuFZmtvpmaVZzrxml0vgsANErmeZFVfALA9Cr14OsejCCkhbay5T2D+oOkw+dQHgEq7xzOrFbnsDXHrtLH+4YxFInD63JgjkFeLqdDQb12R5kshqAsc0jipQCYWasuulyvTuebplEhI0C9mdjnVv+8OiU4/BhjUl7qx5mlWX1HcxWgBlwEdybcapdl05Q17Aeo3jNenZWLETEwHNVzLYwoseXoF38adFtyvgQlsdrHgu+jrd1DOXUG5yGj+Y1+uJzGHa0NmgCVYR8FUt4zEi9E3vC+LLmGjbh4WTq1wqghQVEU3fsiQ95LKJpAUtuPrF50Y6GLlxwEaPpFcCKs9s5AGMmk9dc8yGLxjcfMPAQoDzc0VxUZ2lNHOs+LDbxnwXAc/cPZV26+Z3DFJqdRttCfJBV/JF4KAO7u7Apm77JmjGH3CS5ejDv4gFSprQyZ8txq9zgd8EqWLwGkWX05HHwHOwcRjSfhz/M28DOp9/ugKEAswdATsj7eLkusfTxm6R7Qoazf++6JAQDGGhBAWt6SJAdfQGIBWuRx6mIvl3W4W5vDZUbPoZ8bEdbvo4A8RoR8uziRNeXFblRpLutsvS/tfSMIjMTgcTpwXr0xyboc7nmRIewQTAs5GJXQaiTcas9t00x5zoz8bG6nA3U83i6B90xmqx2AXs2Ti/dsd7s6h8sMNiD0ijEJDAggrcxWwtAfAMyozi1pN5lkepn00majjUB5PC8ytSsg8VIg5Hr47T45AABY0Ghcsi5HpkUna3MsDt80+0JRDAxnd5nlbt1qN3bTBNJyJiQQoDJb7UB63lL2nhc+h0umVBg4olS+RDAczzmR2EhkF6C5Vm4e7QlhKBKHz21csi6nUaKcF5naFZB4KRBytRje4xfBCTj4miSKt8vi6hyPEq9L7/CZrQBtaR8AYHzIAUiVvMuQt5RqjiWn1c49L63doawSPrsHIzgVCENRjF+HZT63foeQDKEjmSv+gNxzz97TjMBFTeWGJusCcuUtydSugMRLgcDj7YdPZ2f16SEHgy0+QK54u+ybJpCW8JnFxjkSTeCQNufLmysMH5OMnhdZvWfTqorhdCgIRRNZ3Y/DD77ZtaUoFXBZoUz3jMluRMypUwUo71adKaLyBoHUGuSN6qxEpoo/Ei8FwjwtX+VAZ+aLTo3Tive85HNtgVHIUt43EXzjPJSFAN17KoBEkqGuzKuHCIxEpl4vstypMh4elwPNWrO6I1nM4bvt4g4+AGjgAtRi7xljTJobicdjXoO6jx7tCWXVn0qkeElvVNczZG3ivExhPxIvBcL8RnXRHekeQiyRzOg9rb0hDGpNlebWGd86nHteBsNxDFkcb5fJYhgPPof7O4IZv+fdE8aXuafTJFGXXdlzXgDoSe/7szAieImt0VUqHD18a7EADUUTuudA1jlsLPehzOdCIslw5HRmHtB4Iqk3+jQ6ZwkY3ajO6sRrmTzYJF4KhCkVRSjzuhBLsIzDDrvaBgCozemMjtMC6qWRPN7eZXGTLNnd1QD0e6kOdGYhXrR8F6OrVDiNkhx8QHp/CXnncEGjOoeZClC1VcEAAHGeF1lCf7K3KwDU/lTzNe9LpqGj97uGEI4lUep16TkzRsMNQauTdmVq9CnnXxCRNYqi6C7PTA+/Hcf7AAAXzKgSNq46v2oxnA5a7O60wcHH568rGEFfKLOKI70/iIB8FyBVrdI9GLG8UZ0dQn/Zipf2vhH0DEXhdir6e41G77ckzcEnZ7sCTmofzUy88H10xbQKOARdnNggSfiWwkaEELJddNuP9QMAVk6vFDamujJ10Z0epEU3GaVeF6Zr91QdyODwOx0M43jvMBRFTLIuANSUeqEoQDzJ0JdlCbfR2CH0x6/YONSVWfh22zH14Fs6tQI+d/a3iWcCr2I7LYn3UwarfSJ4/uDBDI3A7cfF76O8UZ3V4duAJN11ARIvBcV8zXLL5OALDMf0xFCRi65e87xYHTaSvVKFw13W+zKYQ37wzW/wCxNlbqdDv7PHyjkMxxKIxlUxILMAnVqphm+jiSSOZNBpd/sx7v0UaEBw76fFtxLLlC8xEfO08O3BLI3ADwj0YHPPi9VzyEulZViDJF4KCH7w7e+YfNHtbFMX3MyaEtSUeoWNqV6zGLosDxvJs+gmgocOMvGevdOqHnwXCjz4gDTvmYVzyK12hwKUeKy3+sZDUZSsEq+5AP3AdHEHX702f32hqC4ArcAOYT8g5cE+FQhPGr49OTCCkwMjcDoUYd5PAKjT91EyAjkkXgqIhY1+OBSgMxie9I/8HW3TFOl1ASRcdJJbfVy88BL2idjGLb6Z4g4+IN1yt24O08ukReUVGAWfw32nJhYvvUMRPblepOelotgNj5aQ321hqa1MB99ElBe59cRbnlM2HtxztqjJjxIBPXo4/JqObqs9L2F59lESLwVEidell2rySqLxePNILwBgleCDr16WhF0b5LwAwArNejvYNTiqFfeZBEZiemL2hQLd1UDKcrfSe2YX8QmkbvaebA1yA+K8+lJUFHuEjUdRFNSWWR++TVX8yes543AvSsskc/j2UXUfvUCg5wxIiRerjUCZ8pZIvBQYK6apFtyu9v5xnxkYjurlmZecVyt0PDIk7MYSSQxH1YZTMid7AqqnamplERhLNS8biy1HesGYGvbj3i1RyJC3ZJewH5Cq3tt9MjBho7NX3+8BAKyZXSN8TDJU/dlJgC7TxMtEnhfGGF7T5vBDc8XOIV/joWjC0juqZEqaJ/FSYKyYVgEA2Hl8fPHyxuEeMKZm1debdvBFsrrvxUi4tQCod73IzvmaAOV5SWPxyoHTAIBL54kVnwBQ67c+WVCmTXMyZlQXo7rEg2g8qd80fCaMMbx6UJ3DtSbMYb0ERoTsHZLTSd9Hx2vJf6Q7hJMDI/C4HFg1S6znpdTrQolHrUazch3KlLdE4qXA4CGElvaBcRX66yZZC0DK8zISS+hXqZsNP/jKvC44Jc+XAFL5D9wlfSaMMbyiHXwfnlcnfDy8u6eVpbZ2CfsBapjmfC2XjIeGzuTQ6SGcCoThcTlw0cxq4WOqk8J7Zp85XNjoR5nXhWA4rnfPPZPX3u8GoO65xSYkkddLkD8ok/eMxEuBMb26GFMrixBLMGxrPXvjTCYZXtUW3YcEh4wAoMjj1HsCWHX4yX6fyplcPEcVlduP9WM4erbg29cRxOnBCIrcTlwoOGcJSG2alnpehuXZNDNhzWxVkPAD7kxePai+ftGsahR5xPR3SUefQ0srxvit4PLPocvpwKpZ6hy+eXhsI4Lvo5ecJ94IBKDnLVm1DtPbFciwl5J4KTAURdEPv9cP9Zz1/Z1t/egMhlHqdQlP1uXUWVwubZcqB87MmhJMrSxCNJHE1qNnC9CX96lelw/OqRbW2Cyd9D4hVnXZtZPnBQAu1Txi7xzrG/Nerxf2dqrPmWBAAKmDr8vSkIO95vCDc1Tx8vqhswXowHAUbx1R99ePzBfv/QRS+6h1RqA6f4oC/doXKyHxUoDwPIgX9naelWfyP7s7AACXL6w35eAD0iqOLIq3B2xU5QCoApQnUr+4r2vU9xhjeKblJABg/aIGU8bDu+wmkgy9GV5bYDR2FKDTq4sRSzC8ccbh1943jO3H+6EowFVLG00ZT70EXXbtlLcEpETJ20d70XtGifnzezoRSzDMbyjDnLoyU8ZTb7HnJZgWfpehXQGJlwLk0nl1KPW6cHJgZFTS50g0oR98H19mzqYJWF9qa4d7jc7kqiXq/Pxp9ymEY6mKlZ1tA2jtCaHI7cSVS8yZQ7XLrrUCNBVysMfBB6TE5e93nhz1+u93ngCghpZEJ8xz6iw++AB75bwAwPTqEiyZUo4kA/68p3PU9367Q53DTy5vMm08VuctBXjFX7Ec80fipQDxuZ24fFE9AOBX29r1159pOYmB4RimVhZh7XnmuDoB6xvVBWy2aQJqLkSD34dgOK6HGADg8deOAgA+tqQRpSa6bvXDj0J/GXPNyqkA1MowLvrCsQT+e8txAMBnLmg2bSxcJFnVZTeWSCLE2xXYyIj4uOYZ++XWNt2LvautHzuO98PjdOB/nT/VtLFYnbckmxFI4qVA+eJF0wEAT+86idaeEIYicXz/5UMAgOtXzzC16sbqRnV2KtHkOB0Krr1QPdy+v+kQ4okkWtoH8LwmZL68dpap47G614sd53BufRlWTq9EPMnw75vUtfeTN1rRG4piamWR7l0zg8piN9xOdc1b0WV3MJzK+ymzkffsMxc0o9jjxL6OIF7efxrJJMODfz4AQPW6iO6xlE4qYdfiNUjihRDJimmVuHReLRJJhi/993Z85Zc70RkMY1pVMb64erqpY6krs9bzYjd3Neemi2eistiNo90h3PHbd/GVX+0EAFy9vAlz682Js3Osrjiyo/cMAO5aPw+Aarl/50/78G8vvw8A+Ma68+Bymrf9KoqSdkeV+euQz1+p12Xq586XyhKPvl9+8/e78c3f78bW1j4UuZ342mVzTR2L1XeMybaP2ueviMiab39qMWrLvHi/awivHOyG26ngwb9eYlqiLke32ilfIivKfG788ycXAQCebTmF9r4RNFcV4b6rF5s+Fqvbk8vmss6UVbOq8dkLmpFkwOOvtyKWYLhqSSM+ff4U08eSuiLA/MMvNX/2WoMA8PXLzsOiJj/6QlE91+UfP74AzVXFpo6D76ODkfiYLRREI1vCtRyjIIQwtbIYv77lIjz6yhGE4wn8zQdnCr+IcSzSY7WMMSiKuZnqutUuSaJZNly9fArKfC48ua0ddX4vvvKRuZZYPnUWel6SSaY3OJTF6suG7/zVYsypK8VbR3pwwYwq3PyhWaavASB1+HVbYETYMezHKfI48d83rcK/bzqEkwMj+PSKKaYly6dT6nWhyO3ESCyB08EIZtSYe3zL1F0XIPFS8MyqLcX3PrPM0jFwiy8STyI4EjddRMgWq82Wj8yvx0fm11s6BitLbQcjcfCKf1msvmxwOR24+ZJZuPkSc/OUzqTOwqo/OyZcp1NV4tG9oFahKArq/V4c6x3G6cEIZmg3X5uFbI0iKWxECMfndqJCEyxWhI7smi8hE3UShBx8bge8LnNDnoWElUnXdrpYU2asvOhWNu8ZiRfCFKzMmZDpGne7wj0v3UPmd9mV6T4VO2Nl6I/m0Bhq/dYZEbIZgSReCFPgoaNukzdOxph0sVo7UlPqsazLrt3aysuKpQYEzaEhWHk7eMrzIkfolsQLYQq1perG2WNyj4lQNKFfaU9WX+64nA5Ul3gAmC9AyXNmDFaWu8tWqWJX6izsmSVb6I/EC2EKVnle+KbpcTrgc9Ofez7UaALU7CZnsm2adoWvwf7hKGIJc7vs2rXUXTaszFuSLfRHuzlhCjW658XkkEOaxWdFeWohwQ+/HosEqB17hMhEZbEHTocCxtRrAsxEtnwJu8ITds02ApNJhsFzKWG3r68PX/jCF+D3+1FRUYGbbroJQ0NDE77n0ksvhaIoo76+/OUvixwmYQJWe15kWXB2ptYqzwvlSxiC06GgyqrQn5Z3RuswP/R91OQ1OBSNg+fpy7IOhZoyX/jCF9DR0YGXXnoJsVgMN954I2655Rb88pe/nPB9N998M+677z79/4uLze1kSBiPVeKF3NXGUWO150WSTdPO1JZ60T0YMf3wGyTPiyFwA2JgOIZIPGFa64BgWvjd65IjYCNMvOzfvx/PP/883nnnHVxwwQUAgB/84Af42Mc+hoceeghNTeNfJV5cXIyGhgZRQyMsoMaihF1yVxuHZZ4XmkPDqCnzAh1WekAp9JcPFdoFm7EEQ89QFFMqikz5vfoVK0VuacLvwiTUli1bUFFRoQsXAFi3bh0cDge2bt064Xt/8YtfoKamBosXL8aGDRswPDw87rORSATBYHDUFyEf3PPSZ3KyILmrjcPy0B95z/LGiqo/tV0BCVAjUBQlZUSYuA5lFJ/CRtLZ2Ym6urrRv8zlQlVVFTo7O8d93+c//3lMnz4dTU1N2L17N775zW/i4MGDeOqpp8Z8/oEHHsC3vvUtQ8dOGA9PFkwkGfpCUb1sUzQpz4s8i86uWOU9SwlQmsN8sUKAjsQSiCWoXYFR1JZ5cSoQNvWqDhmvWMna83L33XeflVB75teBAwdyHtAtt9yC9evXY8mSJfjCF76An//853j66adx5MiRMZ/fsGEDAoGA/tXe3p7z7ybEYVWyIOW8GIflnhey2vOmplRdg2ZW/fGQg9OhoNhD1zvkS21Zqtu1WcgYfs/alLnjjjtwww03TPjMrFmz0NDQgNOnT496PR6Po6+vL6t8llWrVgEADh8+jNmzZ5/1fa/XC6/Xm/HPI6zDimRBypcwjlSfkBhiiSTcTnMS90iAGkdKgJpntacffLLkS9gZK4wIGRtFZi1eamtrUVtbO+lzq1evxsDAAHbs2IGVK1cCAP7yl78gmUzqgiQTWlpaAACNjeZfQU4YS60FyYKyXSZmZyqK3Hror3coioZys0N/NIf5UmtBv6VUyIHCfkbAr3kws1Ny6ooVeeZQmOm0YMECXHHFFbj55puxbds2vPnmm7jttttw7bXX6pVGJ0+exPz587Ft2zYAwJEjR3D//fdjx44dOHbsGP7whz/guuuuwyWXXIKlS5eKGiphElbkTNDBZxwOh6KHHcwSoOFYApG4muBNAjR/rLTaaQ0ag6WeF4m8n0L9vr/4xS8wf/58XHbZZfjYxz6Giy++GD/+8Y/178diMRw8eFCvJvJ4PHj55Zdx+eWXY/78+bjjjjvw13/91/jjH/8ocpiESViz6Ki1vJGkmmSZE3bgVruiAGVeeaw+u8LnLzCi9gkxA8pZMhYKG6kI3Q2qqqombEg3Y8YMMMb0/29ubsarr74qckiEhVix6KjM1lh079mgOWEHLj7LvC44HJQvkS/lRak+Ib1DUTSZ0CdExoPPztRZuI/KZATK0SqPOCdIVTqYn/Mi06KzM2Y3qtM3zWKaPyNQFCV1waZJh1+ANzgjA8IQ0o3AdONfJAVRKk0QuWK25yWWSGI4qrrGqUeIMZg9hzJumnbH7NwzMiCMhc9fNJHUxb1oBobV31MhkRFB4oUwDbPdncG0hV1Gh58h1JjseaFkT+MxW4DK2J3VzvjcTn09mD2HMq1DEi+EafCDLxiOm5IsyBdcmdcFJ+VLGILpnhfKWTIcs8O3utVe5DHl950LmLkOGWMYGCHPC3EOw5MFAXP6TNC9RsZjdshBRovP7pjveVHXukwHn93huWdm9HoJx5KIau0KZFqHJF4I00hPFuwxYdFRiabxmH3w6VZ7Cc2hUZiddJ3yvNAcGkWd37x1OKCJT6dDQalE7QpIvBCmYubhNzCsWXy0aRoGn7/BcBzhmPjQn+6uppCDYdSUmVvuThVjxmOmAE0XnzJd70DihTAVMxddQMI4rd3x+1zwaHcamRE6krHKwe6YuQZH50uQADUKbkSYcbO0rOKTxAthKmaGjejgMx5FUUz1nun5EuQ9M4yU58XcfAmaQ+PQw0Yme15kgsQLYSqp9vLmLbpyCjkYSo2poT85rT47o4f+InGMRMWG/ni+hNupoNjjFPq7ziVqS9VLUU01ICTznJF4IUzF1JwXqnIQQq1eais+Z4JyXoynzOuCx2VO6C9lQMiVL2F3ak28WTp9DmWCxAthKmaW2ga0RVdJ4sVQzBKgjDF9DkmAGoeiKKblvch68Nkd3vBzYFj8BZsDkrYrIPFCmIq5nhcKG4kgdfCJTRYciSUQTcjXX6IQMGsdyhpysDvpPbN6BXtAZS18IPFCmIolpdKSLTq7Y1apLbfaKV/CeMzygMqa7Gl3HI5UzyzRoaOApHNI4oUwFd6aPBRNYDgaF/q7ZLUY7I75IQcP5UsYjFlGxICkZbaFgFl3xQ1I6j0j8UKYSqnXBZ9bSxYUaLkzxuhOFUGYd/CR50wUtSbdb0RrUByppF2x4VtZK/5IvBCmMqpPiMCciaFIHPEkA0CHn9GYFXKQ1V1dCJiX80LeT1HUlplTLi1r0jWJF8J0+OHXLdDzwhec1+WAz035EkbCD77haAKhiLjQn4w32RYKqTVoVsIuzaHRmCVAgyNyGhEkXgjTMSNngiw+cZR4XXoCrUjvCzUZFAc/+ET36pHVai8EzOj1EkskMagZKJTzQpzzmGExUKxdLGZY7pTzIg7T8pZIvAjDjIRd7nUB1HvNZILEC2E6ZuRM8INPtiSzQsGMw49yXsTB1+BITGzoL0CXMgrDFCNQm78ynwsup1xyQa7REOcE5npe6OATQY0J1Sp0saY40kN/YtchXawpito07ydjTMjvkHkNknghTMcUq51yXoRijtXHvWdktYtAtAc0Gk8ipF38SOvQePgajCaSCI6I8Z7xhGsZw34kXgjTSSULirf4KungE4J+q60ZnhcJN85CQLQA5QaEogBlPppDo/G5nXoeiqi2EwGJL0Yl8UKYTm1aW2vR7k7KeREDec/sj+iqP261+31uOB3UIVkEesVRUMwcyryPknghTEd3d8aTCIbFuDsHJLYYCgGqGLM/NWVa3pKgOZQ5X6JQqCsT6wGV2ftJ4oUwHZ/biTLu7hS2cVKZrUhEi5dwLIGRmJovIaPVVwiIDv0FJG1uVkiYFfqTcR8l8UJYguhFJ7PFUAikrngQE/rj/SUcClDmlau/RKHAPS+iOl2nQg7kOROF6EZ1qWox+eaQxAthCaLj7XSbrVh4qXQswXTrzEj0+Styw0H5EkIwbQ2SASEM0Y3qAhLPIYkXwhJEel4YY6kGZ2T1CcHrcuquZBFzOEDzJ5waXvUn6uCjHi/CEX2ztMxGIIkXwhJEipeRWALRRBIAbZwiSa8aMxrurpbR4isU0j0vIkJ/dLGmeITnvEgcfifxQliCyEXHrXa3U9G7iBLGI3QO6eATzqiqPwFNzuheI/Ho1Uaicl4kvt6BxAthCSLj7em3ESsK5UuIQqR4kdniKxRENzmT+eArFPga7B+OIRpPGvqzk0lGOS8EcSZ1fnEWA91GbA5CBag+h3TwiURkk7MAhf6EU1HkhtupGmhGdywfDMeRSKrhxMoS+eaQxAthCalLxYy3+MhqNwczQn908IlFZJOzfm0OqyQ8+AoFh0PR76gyeh32aeKz1OuC1yVf+J3EC2EJ/ODrDUURTxjr7iR3tTnU+cWLF/KeiUWkAO0P0f1iZiCq10sfnz9JxSeJF8ISqko8cCgAY6lFYhT95K42Bd6hVUSZJv+bqCqhg08kdYIOvkg8gcGImgRMcygWUb1euPisklR8ChMv3/nOd7BmzRoUFxejoqIio/cwxnDPPfegsbERRUVFWLduHQ4dOiRqiISFOB0KqgWV2uqLTlKLoVAQarUPk3gxA1FzyD1nTocCP90oLRRRc8jDRpWSrkFh4iUajeKaa67BrbfemvF7/uVf/gX//u//jsceewxbt25FSUkJ1q9fj3BYTAMewlpEJXz2hdSNU9ZFVyiIrHTopZCDKQg7+PT5ow7Jokn1WzL2nDxnPS/f+ta38I1vfANLlizJ6HnGGP7t3/4N//iP/4irr74aS5cuxc9//nOcOnUKzzzzjKhhEhYiauPkVns1iRehVBS54dIOpt6QcXPIGNM3zupSmkOR8IRdUQcfiU/x1Aqq3OwblrviT5qcl9bWVnR2dmLdunX6a+Xl5Vi1ahW2bNky7vsikQiCweCoL8IeiBIvZLWbg6hKh8FIHHFeoklzKJRzNeRQSIjyYMsefpdGvHR2dgIA6uvrR71eX1+vf28sHnjgAZSXl+tfzc3NQsdJGIcwzwtZ7aYhYg75/BV7nPC55SvRLCREhf5kDzkUEqJ69cgefs9KvNx9991QFGXCrwMHDoga65hs2LABgUBA/2pvbzf19xO5Iy7nhTwvZiGiWoU8Z+YhqsmZ7AdfIaFXGxl8R5WeNC/pOnRl8/Add9yBG264YcJnZs2aldNAGhoaAABdXV1obGzUX+/q6sLy5cvHfZ/X64XX683pdxLWIsJqj8QTGKISTdMQ6Xkhz5l4eOivIxBG92AETRVFhvzcVLWYnCGHQuLMO6qMugFaz1uSdB/NSrzU1taitrZWyEBmzpyJhoYGbNq0SRcrwWAQW7duzapiibAP3GLoMfTgoxJNMxEhXshzZi61Zap4MdJ7RnNoHj63E2U+FwbDcXQPhY0TL5K3KxCW89LW1oaWlha0tbUhkUigpaUFLS0tGBoa0p+ZP38+nn76aQCAoij4+te/jm9/+9v4wx/+gPfeew/XXXcdmpqa8KlPfUrUMAkLEdEZkko0zUWI50XyTbPQENHkTK/4I++ZKRgdvk0kmd6pXFYBmpXnJRvuuece/OxnP9P/f8WKFQCAV155BZdeeikA4ODBgwgEAvozd911F0KhEG655RYMDAzg4osvxvPPPw+fzydqmISF8INvKBLHcDSOYk/+f47UmdVcROQt9dIcmooIAdo7RJ4XM6kt8+JId8iwOQyMxMDTZ2S9okOYeNm4cSM2btw44TNnJhcpioL77rsP9913n6hhERJR6nXB53YgHEuiZzCKadUGiJdh2jTNRGTOC4kXc6gV0OuFvGfmwufQqHXIjUC/zwW3U5qi5FHIOSrinEBRlNThN2TMxknJnuaS3uTMqEoHvVKFBKgpGC1AGWOU82IyRof+7CA+SbwQllJrcJMzKrM1l5oy9d85HEvqVV750qd166VKFXOoNfiOsZFYAhGtZ4zMh18hYXT+YJ/klUYAiRfCYoy2+ijkYC7FHhdKvWq4zzirT/W8VJVQCwQzqPMbuwb5wedxOVDsoSaDZmC458UGTQZJvBCWYrR4oYRd8xE3h+R5MYP0pGsjQn+8XUFVsQeKQhV/ZmD4GrTB9Q4kXghLqS3VEs0MqlYh8WI+RlYcxRNJBCQv0Sw0zmxyli99NsiXKDRSYSNjcwdlnkMSL4SlkOfF/hh5twoPGSmKvLfZFho+txN+nxb6MyBx3g4HX6HBE+eNuqPKDknzJF4ISxHm7pR40RUatWXGeV54lUNFkRtOajJoGkYmfNoh2bPQqChyw+Uw7o6q/uFUs09ZIfFCWApPNOsywGpnjFGptAUYKUDp4LMGEXNYJfHBV2jwO6oAY+awd4hX/Mm7Dkm8EJZS70/lvCSS+SULBsNxxLWfQZ4X8zDSatfFp8SbZiFSZ2CTs14SoJZgZNVYj9YhuaZM3oo/Ei+EpdSUeuBQ1Ls0ekP5LTp+8BV7nPC5qUTTLLgAPR3MP1+CH3yU72IuRgpQHrbgngDCHIzq18MY0+ewVuI5JPFCWIrL6dA3ua5AfouOGtRZQ4MmXjoNEC908FlDvWa1dwZoDu2KUaG/oUhcbzIoc/idxAthOQ3lxhx+PE4rs6uzEOEH38BwDOFYIq+flbL45N00C5F6AwUov5Sxtozm0EzqDLpqhc9fscdpyGW5oiDxQlgOj7d35blxdtPBZwnlRW54XepWkvccDpIAtQLuPct3/oCUAK2mDsmmYlTLArt4zki8EJbTUM4rjvLbOHsGtSQzyRddoaEoiu49y7dqjCcKyhxrL0R072cgvws2h6NxDEdV7xsJUHMxqmWBLj4lNwJJvBCWo+dM5Blv10MOtGmajlFhhx4K/VkCn79IPNXhOBe4AeFzO1BC9xqZSq1BFWN6pZHkBgSJF8Jy6rjLOs9Fp4ccJF90hYgedshXgNIcWoLP7USF1pclHwHanRZyoHuNzKUurWIsH+8ZhY0IIkMMO/jI82IZRiRdj0QTCPGQg+Qu60LECA+oXQ6+QmTUHVXh3O+o6tU9L3KvQRIvhOUYVW3UTRunZRgRNuIHn9flQKlX3iqHQqXegKTdlHiR++ArRHxuJ8r4HVV5eLHtIkBJvBCWU6/FagMj+ZXapkIOtHGaDS+Xzsd7dnqQQg5WkvK85H7w9dokX6JQMeJ2aUrYJYgM8Re54HPnV2o7HI3rIQcKG5mPEY3qKFnXWuoN8IDaxWovVGoNuN/ILgKUxAthOYqi5B1v51UOFHKwhtQVAbknC1KDOmsxotcLhY2shRc/5CNe7BJ+J/FCSEG+FUdU5WAtXLxEE0n0D+dWassFKHnOrKGx3ICE3UH5L/QrZPL1vETiCQxqyb6yC1ASL4QU5FtxRJVG1uJxOfSboHP2ntnE4itUjEzYpe661pDvzdL8fR6nA+VFbsPGJQISL4QU5FtxRD1erCffw4/Ei7XwNdgbiiISzy1xnq9DMiKsgXteunJM2OUdsuv88nuwSbwQUlCfb84LeV4sJ18BepoEqKVUFrvh0e6oyuV+nFAkjsGIGnLgfwuEuTRVFAEATg3kuAa1tcv3Y5kh8UJIwZQKdbGcCozk9H7d4pM8TlvI8A2vI0cByoUrv+uKMBdFUVIl7zkIUP6eEo+TkuYtYoomXk4OjOSUON+lixf51yCJF0IKuMVwsj838cIPvnqy+CxDF6AD2c8hY0zvTWEHq69QafSr6zAXAco9brQGraOh3AdFUbvs9oaiWb+fF0zUlck/hyReCCngFsPpwUhO8Xa+cTbQwWcZUypzF6B9oShiCdVStMPGWag0aQL0ZA4ClIea6mn+LMPjcuh3HOViRHRR2IggsqOqxKM3qssl78VOi65QmVJRDCC3g4+Lz5pSj553QZhPPgKUr0HKd7GWfLzYugClsBFBZIaiKDkvumg8qV/j3kgbp2Xwg68jMIJkMrt4Oz/4yOtiLVyAnugfzvq9XIDW2eDgK2Sa0vJesqXTRkYgiRdCGqbkuOh4roTH6UBVCSXsWkV9mRdOh4JYgumVQ5nCSzTJareWqZW5H3zcaqfQrbVMyaPiiBJ2CSIHchUvXWkWn+y9CQoZl9OhH1wnB7Kz3PWEazr4LCU9bJRttYqdrPZCJiVesttHh6NxvbuuHeaQxAshDVNyDBvxW3DJ4rMe/fDL0urrooRrKeBrMBRNYCDLax7sZLUXMrmGjbjnrNgmpe4kXghp4Adftr1eOrTnqUTTeqbmKkD1ZE86+KzE53bqTQKzOfwYY2nJnrQOraQpx5YF6UUPdvBgk3ghpCHXhF2y2uUh5XnJLWxUR3NoOXwOT2SxDvuHY4gmkgAo6dpqpmpJ172hKMKxzNtOpHq82MOAIPFCSEN6olk21SqdlCgoDbkKUJ7gS3NoPVNzCDtwA6K6hErdrcZf5EKJxwkgO+8Lf9YuFZvC/sq+853vYM2aNSguLkZFRUVG77nhhhugKMqoryuuuELUEAnJaCj3waEA0UQSPaHMq1W69Lby9lh0hUwuSdeReAJ9WjdQEi/Wk/K8ZO494wcfrUHrSW87kU3FETc4+PzLjjDxEo1Gcc011+DWW2/N6n1XXHEFOjo69K9f/epXgkZIyIbb6dDj5dlY7p3UHEsacqlW4RtskduJimK3sLERmTE1h0Z1PMTUXFksZExEdqSSdjMXoNzg4L1+ZEdYSvG3vvUtAMDGjRuzep/X60VDQ4OAERF2YEpFEToCYZwaCGPFtMmfTySZnrDLFyxhHenVKoGRGCqKJ++7wy38qZVFtkgULHRy8Z7xObSL1V7o5JK3ZLc5lC44uXnzZtTV1WHevHm49dZb0dvba/WQCBPhVl9bX2YWQ2cwjFiCwe1UKOQgAWq1iipYMt04+XNTbbJpFjpTcmhUR3MoFzOqVe/J8d7M9lHGmO5ps8scSiVerrjiCvz85z/Hpk2b8N3vfhevvvoqrrzySiQS42dMRyIRBIPBUV+EfZleXQIAON4byuj5dk3kNFUUwekgq10Gpmqhg/YMBSh/rrnKHu7qQod7XgaGYxgMZ9brJSVeaA5lgO+jxzLcRwMjMYSi6jk7xSYe7KzEy913331WQu2ZXwcOHMh5MNdeey0++clPYsmSJfjUpz6F//mf/8E777yDzZs3j/ueBx54AOXl5fpXc3Nzzr+fsJ4ZNerm19qTnXihWLs8zKxRN87WDDdOstrloszn1q/ZyNRy514amkM5mKGJl9aeUEa5Z3wN1pR64HM7hY7NKLLKebnjjjtwww03TPjMrFmz8hnPWT+rpqYGhw8fxmWXXTbmMxs2bMDtt9+u/38wGCQBY2Nm6J6XDK12nihYRZumLOgbZ3em4oXnvJAAlYWZNSXoC0XR2hPC4inlEz4bisT1ajG75EsUOtM0L+ZgOI6B4RgqJ7nzjYsXu3hdgCzFS21tLWpra0WN5SxOnDiB3t5eNDY2jvuM1+uF12uPpjrE5HCrvTMYxkg0gSLPxFbAiT46+GSDe88ydVlTpYp8zKwpwY7j/TiWgQeUe13Ki9zw+6haTAaKPE40+H3oDIZxrDc0qXhJec7sswaF5by0tbWhpaUFbW1tSCQSaGlpQUtLC4aGhvRn5s+fj6effhoAMDQ0hDvvvBNvv/02jh07hk2bNuHqq6/GnDlzsH79elHDJCSjotiD8iJ1AzzeN/nG2d5P+RKyoYeNeib3noVjCb1BHYUc5CE1h5OvwfRqMUIepmeRtGu3Hi+AQPFyzz33YMWKFbj33nsxNDSEFStWYMWKFdi+fbv+zMGDBxEIBAAATqcTu3fvxic/+Umcd955uOmmm7By5Uq8/vrr5Fk5x5ihbZyZWH3tfdxqt8+iK3T4/PUMRSZN+OQWX4mHerzIBBcvRzMSL/YLOZwLzMgiaVcvk7bRHArr87Jx48ZJe7ykJxIVFRXhhRdeEDUcwkbMqC7Gu+0DODaJxRCJJ9A1qDY4I8+LPPh9blSXeNAbiuJ47/CEORN6yKiqmHq8SAQXL5kcfO0UupWS6TWZe174M9xbYwekKpUmCCDNYpjE6lO7uKqdWasniekS5pKp5d6mHY4UcpALvgYHhmPo15Jxx4OHlmbW2OfgOxfgczjZGkwmmV4ZyNetHSDxQkjHrFpt0U1SrcKtwunVZLXLRqahvyPaHM+qLRU+JiJzijxONGnXbUx2+B2lOZSSOXXqfBzuGpywXPpUYATReBJup2KrsBGJF0I65taVAQAOdAYnXHRHTqub5uw62jRlgwvQQ6eHJnzuSLf6/dm19rH4zhW4AD3aPf4cxhJJvRv2LJpDqZhZUwK3U0Eompiw2/UxLbF+WlUxXE77SAL7jJQ4Z5hdVwKnQ0EwHNcvXRyL1MFH4kU2FjT4AQAHOibueM2tdppD+TivXjUiDnYOjvtMe98w4kmGIrcT9WV0PYdMuJ0OfV293zX+HLb2qPvozBp7rUESL4R0eF1O3RI/0DH+ojusWfVzyPMiHQsaVfFytCeEcGzs6z2Go3G92ohCDvKxUJvD/Z3jC1AuPmfWlMBB13NIx7wG7sUefx890m3PnCUSL4SUzOOW+4SLjkIOslLv96Ki2I1Ekuki80x4omdlcaodPSEPXIDuOzV++PawtgYpZCQnmXjPuFeGP2sXSLwQUjK/IZX3MhY9QxH0D8egKMAsm7k7zwUURdFDR/vHCR1xrxp5zuRkbn0pnA4F/cMxdAUjYz7D55YLHUIu+D46XtiIMWbbOSTxQkgJX3TjWQz7TqkLbmZ1yaRXCBDWML9RncP944T+9mmb5qKmie/OIazB506Fb/d1BMZ8hq/DBY32strPFbg35Uj3EGKJ5Fnf7x5UjUCHYj8jgsQLISXzNSvg8OkhROJn50zsOaVuposmuTSOsA5uyY3nPdurzeHCJntZfOcSet7LGAI0HEvoZdQLG2kdysjUyiKUeV2IJdiY3pf9mnE4q7bUNrdJc0i8EFLSVO5DVYkH8STD3lNnH357T6qvLaaDT1r4wbfnZADJ5OicCcaYbrUvojmUFi4sudBM51DXEBJJhspiN+r9dIWLjCiKgmXNFQCAnW0DZ32fzytP7LUTJF4IKVEUBedPqwQA7DjWf9b3uedlotbzhLXMbyhDsceJYDh+Vr+XE/0jCIbjcDsVva8PIR9LplQAAHYc7z8rabelXV2Xi5rKqUmkxJw/rQIAsKvt7H1053H1tRWawLETJF4IaVk5XRMvx0cvutODYRzvHYaiAIspX0JaXE4HVmgb57ZjfaO+t7VV/f/FU8rhcdE2JCsrplXA43SgKxg5646cbZpR8YEZVVYMjciQFdo+uusMzwtjTN9b+V5rJ2jXIKTlghnqgtp+vG9U2GHLkV4AaliinG4ilhp+sL3TOlq8vH1UncNVM6tNHxOROT63E8uaVQNhW9ocMsb0Of3ATPsdfOcS5zdXQlHU1gQdgVSn3aM9IfQPx+B1OWyZNE/ihZCWZVMrUOp1oWcoit0nUzF3fvCtnkUHn+xwcfL6oW7E06odtrZq4mUWWe2yc+FMdY5eP9yjv9bWN4zOYBhup4IVzSReZKa82I3lWljolQPd+utvafO5bGqFLb2f9hsxcc7gcTmw9rxaAMDL+7oAqDegvnpQXYCrZ5N4kZ0PzKhERbEb/cMxvKOFGQ52DqK9bwRup4ILbOiuPte4bEE9AOAv+7v0bskv7O0EoIYbqFWB/HxkXh0A4C8HTuuvvbBX3VM/sqDOkjHlC4kXQmrWLVQX1h93n0IiyfD20V6cCoRR5nPhg3NqLB4dMRkupwPrtMPvT++dAgA803ISAHDpvDqU+SjsJzsrmivQVO5DKJrAZs1w+NPuDgDAVUubrBwakSFcoLz2fjd6hiIYGI7qHuz1ixqsHFrOkHghpObyhQ3w+1w43juMl/Z14pfb2gAAn1zWZLu+BOcqn1o+BQDw2+0n0N43jKd2nhj1OiE3iqLgE8tUkfKfrx7BnpMBvHsiAIcCXLnYngffucaipnIsa65ANJHEL95uw6+2tSOeZFjQ6MfMGnte7UDihZCaEq8L162eAQD42pMt+B/N4vvchdMsHBWRDR+cU40V0yoQiSex7uFX0RWMoLHch8ts6q4+F7npQzNR5Hbi3fYBfPo/3wIAfGJZE2pKqb+LXfibD84AAPzgL4fwvRcPAgBuunimhSPKDxIvhPTcfMkszKguRiSuJnze+MEZ1N/FRiiKgns+vhAelwOReBIOBbj/6sXkObMRdWU+3HH5eQCAaDyJmlIPNly5wOJREdnwiaVN+NDcGsSTDPEkwwfnVOPTK+zr/VTYeNeF2pRgMIjy8nIEAgH4/dS5s1DoD0Xx1K6TqPd78bHFjXA4qCmW3TjYOYi/HDiN1bOr9eoHwl68cuA0Dp0exCeWNaGxvMjq4RBZEo4l8PQuNefsr1ZMkc6AyOb8JvFCEARBEITlZHN+U9iIIAiCIAhbQeKFIAiCIAhbQeKFIAiCIAhbQeKFIAiCIAhbQeKFIAiCIAhbQeKFIAiCIAhbQeKFIAiCIAhbQeKFIAiCIAhbQeKFIAiCIAhbQeKFIAiCIAhbQeKFIAiCIAhbQeKFIAiCIAhbQeKFIAiCIAhb4bJ6AEbDL8kOBoMWj4QgCIIgiEzh5zY/xyei4MTL4OAgAKC5udnikRAEQRAEkS2Dg4MoLy+f8BmFZSJxbEQymcSpU6dQVlYGRVEM/dnBYBDNzc1ob2+H3+839GfLQKF/PqDwPyN9PvtT6J+RPp/9EfUZGWMYHBxEU1MTHI6Js1oKzvPicDgwdepUob/D7/cX7B8lUPifDyj8z0ifz/4U+mekz2d/RHzGyTwuHErYJQiCIAjCVpB4IQiCIAjCVpB4yQKv14t7770XXq/X6qEIodA/H1D4n5E+n/0p9M9In8/+yPAZCy5hlyAIgiCIwoY8LwRBEARB2AoSLwRBEARB2AoSLwRBEARB2AoSLwRBEARB2AoSL2l85zvfwZo1a1BcXIyKioqM3sMYwz333IPGxkYUFRVh3bp1OHTo0Khn+vr68IUvfAF+vx8VFRW46aabMDQ0JOATTE62Yzl27BgURRnz67e//a3+3Fjff/LJJ834SKPI5d/60ksvPWvsX/7yl0c909bWhquuugrFxcWoq6vDnXfeiXg8LvKjjEm2n6+vrw9f+cpXMG/ePBQVFWHatGn46le/ikAgMOo5K+fv0UcfxYwZM+Dz+bBq1Sps27Ztwud/+9vfYv78+fD5fFiyZAmee+65Ud/PZE2aSTaf7/HHH8eHPvQhVFZWorKyEuvWrTvr+RtuuOGsubriiitEf4wJyeYzbty48azx+3y+Uc/YeQ7H2k8URcFVV12lPyPTHL722mv4xCc+gaamJiiKgmeeeWbS92zevBnnn38+vF4v5syZg40bN571TLbrOmsYoXPPPfewhx9+mN1+++2svLw8o/c8+OCDrLy8nD3zzDPs3XffZZ/85CfZzJkz2cjIiP7MFVdcwZYtW8befvtt9vrrr7M5c+awz33uc4I+xcRkO5Z4PM46OjpGfX3rW99ipaWlbHBwUH8OAPvpT3866rn0fwOzyOXfeu3atezmm28eNfZAIKB/Px6Ps8WLF7N169axXbt2seeee47V1NSwDRs2iP44Z5Ht53vvvffYpz/9afaHP/yBHT58mG3atInNnTuX/fVf//Wo56yavyeffJJ5PB72xBNPsL1797Kbb76ZVVRUsK6urjGff/PNN5nT6WT/8i//wvbt28f+8R//kbndbvbee+/pz2SyJs0i28/3+c9/nj366KNs165dbP/+/eyGG25g5eXl7MSJE/oz119/PbviiitGzVVfX59ZH+kssv2MP/3pT5nf7x81/s7OzlHP2HkOe3t7R322PXv2MKfTyX7605/qz8g0h8899xz7h3/4B/bUU08xAOzpp5+e8PmjR4+y4uJidvvtt7N9+/axH/zgB8zpdLLnn39efybbf7NcIPEyBj/96U8zEi/JZJI1NDSwf/3Xf9VfGxgYYF6vl/3qV79ijDG2b98+BoC98847+jN//vOfmaIo7OTJk4aPfSKMGsvy5cvZ3/zN34x6LZM/etHk+vnWrl3Lvva1r437/eeee445HI5RG+x//ud/Mr/fzyKRiCFjzwSj5u83v/kN83g8LBaL6a9ZNX8XXngh+/u//3v9/xOJBGtqamIPPPDAmM9/5jOfYVddddWo11atWsW+9KUvMcYyW5Nmku3nO5N4PM7KysrYz372M/2166+/nl199dVGDzVnsv2Mk+2vhTaHjzzyCCsrK2NDQ0P6a7LNISeTfeCuu+5iixYtGvXaZz/7WbZ+/Xr9//P9N8sEChvlQWtrKzo7O7Fu3Tr9tfLycqxatQpbtmwBAGzZsgUVFRW44IIL9GfWrVsHh8OBrVu3mjpeI8ayY8cOtLS04Kabbjrre3//93+PmpoaXHjhhXjiiScyutbcSPL5fL/4xS9QU1ODxYsXY8OGDRgeHh71c5csWYL6+nr9tfXr1yMYDGLv3r3Gf5BxMOpvKRAIwO/3w+UafbWZ2fMXjUaxY8eOUevH4XBg3bp1+vo5ky1btox6HlDngj+fyZo0i1w+35kMDw8jFouhqqpq1OubN29GXV0d5s2bh1tvvRW9vb2Gjj1Tcv2MQ0NDmD59Opqbm3H11VePWkeFNoc/+clPcO2116KkpGTU67LMYbZMtgaN+DfLhIK7mNFMOjs7AWDUocb/n3+vs7MTdXV1o77vcrlQVVWlP2MWRozlJz/5CRYsWIA1a9aMev2+++7DRz7yERQXF+PFF1/E3/3d32FoaAhf/epXDRv/ZOT6+T7/+c9j+vTpaGpqwu7du/HNb34TBw8exFNPPaX/3LHmmH/PLIyYv56eHtx///245ZZbRr1uxfz19PQgkUiM+W974MCBMd8z3lykrzf+2njPmEUun+9MvvnNb6KpqWnUQXDFFVfg05/+NGbOnIkjR47g//7f/4srr7wSW7ZsgdPpNPQzTEYun3HevHl44oknsHTpUgQCATz00ENYs2YN9u7di6lTpxbUHG7btg179uzBT37yk1GvyzSH2TLeGgwGgxgZGUF/f3/ef/eZUPDi5e6778Z3v/vdCZ/Zv38/5s+fb9KIjCfTz5gvIyMj+OUvf4l/+qd/Out76a+tWLECoVAI//qv/2rI4Sf686Uf5EuWLEFjYyMuu+wyHDlyBLNnz87552aKWfMXDAZx1VVXYeHChfjnf/7nUd8TOX9Ebjz44IN48sknsXnz5lEJrddee63+30uWLMHSpUsxe/ZsbN68GZdddpkVQ82K1atXY/Xq1fr/r1mzBgsWLMCPfvQj3H///RaOzHh+8pOfYMmSJbjwwgtHvW73OZSBghcvd9xxB2644YYJn5k1a1ZOP7uhoQEA0NXVhcbGRv31rq4uLF++XH/m9OnTo94Xj8fR19envz9fMv2M+Y7ld7/7HYaHh3HddddN+uyqVatw//33IxKJ5H3/hVmfj7Nq1SoAwOHDhzF79mw0NDSclSnf1dUFAIbMoRmfb3BwEFdccQXKysrw9NNPw+12T/i8kfM3HjU1NXA6nfq/Jaerq2vcz9PQ0DDh85msSbPI5fNxHnroITz44IN4+eWXsXTp0gmfnTVrFmpqanD48GHTD758PiPH7XZjxYoVOHz4MIDCmcNQKIQnn3wS991336S/x8o5zJbx1qDf70dRURGcTmfefxMZYVj2TAGRbcLuQw89pL8WCATGTNjdvn27/swLL7xgacJurmNZu3btWVUq4/Htb3+bVVZW5jzWXDDq3/qNN95gANi7777LGEsl7KZnyv/oRz9ifr+fhcNh4z7AJOT6+QKBALvooovY2rVrWSgUyuh3mTV/F154Ibvtttv0/08kEmzKlCkTJux+/OMfH/Xa6tWrz0rYnWhNmkm2n48xxr773e8yv9/PtmzZktHvaG9vZ4qisGeffTbv8eZCLp8xnXg8zubNm8e+8Y1vMMYKYw4ZU88Rr9fLenp6Jv0dVs8hBxkm7C5evHjUa5/73OfOStjN528io7Ea9pMKgOPHj7Ndu3bppcC7du1iu3btGlUSPG/ePPbUU0/p///ggw+yiooK9uyzz7Ldu3ezq6++esxS6RUrVrCtW7eyN954g82dO9fSUumJxnLixAk2b948tnXr1lHvO3ToEFMUhf35z38+62f+4Q9/YI8//jh777332KFDh9gPf/hDVlxczO655x7hn+dMsv18hw8fZvfddx/bvn07a21tZc8++yybNWsWu+SSS/T38FLpyy+/nLW0tLDnn3+e1dbWWlYqnc3nCwQCbNWqVWzJkiXs8OHDo0oz4/E4Y8za+XvyySeZ1+tlGzduZPv27WO33HILq6io0Cu7vvjFL7K7775bf/7NN99kLpeLPfTQQ2z//v3s3nvvHbNUerI1aRbZfr4HH3yQeTwe9rvf/W7UXPE9aHBwkP2f//N/2JYtW1hrayt7+eWX2fnnn8/mzp1rqpDO5zN+61vfYi+88AI7cuQI27FjB7v22muZz+dje/fu1Z+x8xxyLr74YvbZz372rNdlm8PBwUH9rAPAHn74YbZr1y52/Phxxhhjd999N/viF7+oP89Lpe+88062f/9+9uijj45ZKj3Rv5kRkHhJ4/rrr2cAzvp65ZVX9Geg9cPgJJNJ9k//9E+svr6eeb1edtlll7GDBw+O+rm9vb3sc5/7HCstLWV+v5/deOONowSRmUw2ltbW1rM+M2OMbdiwgTU3N7NEInHWz/zzn//Mli9fzkpLS1lJSQlbtmwZe+yxx8Z8VjTZfr62tjZ2ySWXsKqqKub1etmcOXPYnXfeOarPC2OMHTt2jF155ZWsqKiI1dTUsDvuuGNUqbFZZPv5XnnllTH/pgGw1tZWxpj18/eDH/yATZs2jXk8HnbhhReyt99+W//e2rVr2fXXXz/q+d/85jfsvPPOYx6Phy1atIj96U9/GvX9TNakmWTz+aZPnz7mXN17772MMcaGh4fZ5Zdfzmpra5nb7WbTp09nN998s6GHQi5k8xm//vWv68/W19ezj33sY2znzp2jfp6d55Axxg4cOMAAsBdffPGsnyXbHI63R/DPdP3117O1a9ee9Z7ly5czj8fDZs2aNepM5Ez0b2YECmMm17MSBEEQBEHkAfV5IQiCIAjCVpB4IQiCIAjCVpB4IQiCIAjCVpB4IQiCIAjCVpB4IQiCIAjCVpB4IQiCIAjCVpB4IQiCIAjCVpB4IQiCIAjCVpB4IQiCIAjCVpB4IQiCIAjCVpB4IQiCIAjCVpB4IQiCIAjCVvz/6aljqc4+ErUAAAAASUVORK5CYII=",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"1024 1024\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
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"image/png": 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5nE6nhg4dqq1bt+o73/mOJGn58uWKjY3VpEmTVF1drezsbL3++uv++p06ddKmTZs0c+ZMud1ude/eXdOmTdOSJUtat1cAAKDDavF7btoC77kBACD6tPv33AAAALRHhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYJKtwUFBTo61//unr27Knk5GRNmDBBJ0+eDChTVVWl3Nxc9erVSz169NCkSZNUUVERUKa0tFQ5OTnq1q2bkpOTtWDBAl27dq3lvQEAAB1eUOFm586dys3N1Z49e7Rt2zZdvXpVY8aM0ZUrV/xl5s6dq40bN2rDhg3auXOnysrKNHHiRP/y2tpa5eTkqKamRrt379Zbb72lwsJCLVq0qPV6BQAAOqwYY4wJtfKXX36p5ORk7dy5Uw8//LC8Xq/69OmjdevW6YknnpAknThxQoMGDVJRUZFGjhypzZs367HHHlNZWZlSUlIkSatWrdLChQv15ZdfKi4u7qbb9fl8cjqd8nq9cjgcoTYfAABEUKSu3y165sbr9UqSkpKSJEnFxcW6evWqsrKy/GUGDhyotLQ0FRUVSZKKioo0ZMgQf7CRpOzsbPl8PpWUlDS6nerqavl8voAJAACgMSGHm7q6Os2ZM0ff+MY3NHjwYEmSx+NRXFycEhMTA8qmpKTI4/H4y1wfbOqX1y9rTEFBgZxOp3/q169fqM0GAACWCznc5Obm6ujRo3r33Xdbsz2NysvLk9fr9U9nz54N+zYBAEB06hxKpVmzZmnTpk3atWuX7rjjDv98l8ulmpoaXbx4MeDuTUVFhVwul7/Mvn37AtZX/22q+jI3io+PV3x8fChNBQAAHUxQd26MMZo1a5bef/99ffzxx0pPTw9YPnz4cHXp0kXbt2/3zzt58qRKS0vldrslSW63W0eOHFFlZaW/zLZt2+RwOJSRkdGSvgAAAAR35yY3N1fr1q3Thx9+qJ49e/qfkXE6nerataucTqemT5+uefPmKSkpSQ6HQ7Nnz5bb7dbIkSMlSWPGjFFGRoamTp2qZcuWyePx6MUXX1Rubi53ZwAAQIsF9VXwmJiYRuevWbNGP/jBDyR99RK/+fPn65133lF1dbWys7P1+uuvB/yX05kzZzRz5kzt2LFD3bt317Rp07R06VJ17nxrWYuvggMAEH0idf1u0Xtu2grhBgCA6BMV77kBAABobwg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWCTrc7Nq1S+PHj1dqaqpiYmL0wQcfBCw3xmjRokXq27evunbtqqysLH322WcBZS5cuKApU6bI4XAoMTFR06dP1+XLl1vUEQAAACmEcHPlyhUNGzZMK1eubHT5smXLtGLFCq1atUp79+5V9+7dlZ2draqqKn+ZKVOmqKSkRNu2bdOmTZu0a9cuPffcc6H3AgAA4P/FGGNMyJVjYvT+++9rwoQJkr66a5Oamqr58+frRz/6kSTJ6/UqJSVFhYWFevrpp3X8+HFlZGRo//79euihhyRJW7Zs0Xe/+12dO3dOqampN92uz+eT0+mU1+uVw+EItfkAACCCInX9btVnbk6fPi2Px6OsrCz/PKfTqczMTBUVFUmSioqKlJiY6A82kpSVlaXY2Fjt3bu30fVWV1fL5/MFTAAAAI1p1XDj8XgkSSkpKQHzU1JS/Ms8Ho+Sk5MDlnfu3FlJSUn+MjcqKCiQ0+n0T/369WvNZgMAAItExbel8vLy5PV6/dPZs2fbukkAAKCdatVw43K5JEkVFRUB8ysqKvzLXC6XKisrA5Zfu3ZNFy5c8Je5UXx8vBwOR8AEAADQmFYNN+np6XK5XNq+fbt/ns/n0969e+V2uyVJbrdbFy9eVHFxsb/Mxx9/rLq6OmVmZrZmcwAAQAfUOdgKly9f1qlTp/yfT58+rcOHDyspKUlpaWmaM2eO/umf/kn33HOP0tPT9ZOf/ESpqan+b1QNGjRIY8eO1YwZM7Rq1SpdvXpVs2bN0tNPP31L35QCAABoTtDh5sCBA3rkkUf8n+fNmydJmjZtmgoLC/UP//APunLlip577jldvHhR3/zmN7VlyxYlJCT467z99tuaNWuWRo8erdjYWE2aNEkrVqxohe4AAICOrkXvuWkrvOcGAIDoE5XvuQEAAGhrhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGCVzm3dAKA11dYZ7Tt9QZWXqpTcM0Ej0pPUKTamrZsFdAgcf2gvCDewxpaj5Vq88ZjKvVX+eX2dCcofn6Gxg/u2YcsA+3H8oT2JMcaYtm5EsHw+n5xOp7xerxwOR1s3p8MK5be0YOvcavktR8s1c+1B3bgz15d84/sPttoJ1pbfTm3pR7jZ8nMKZz9CPf7CdT5oaR2ET6Su31F952bf/17QI0N7tvnB0B63Ee42hfJbWrB1brV8bZ3R4o3HGpxYJcnoqxPs4o3H9J0MV4tPaqH+dhqJ8Qt3P9jPvxKOuxHh7nc4+xHq8Reu80FL63TE/Tyi2/jfC82us7W06Z2blStX6uWXX5bH49GwYcP02muvacSIETetV5/8+s1Zr9uTk9r0YGiP2wh3m0L5LS3YOsGUL/r8vCb/ck+j/breOzNGyn1Xr5uWa0qov51GYvzC3Q/28z9r7buBkfg5hbMfoRx/4TwftLROR9vPI72N31de0Nmffy/sd27a7NtS7733nubNm6f8/HwdPHhQw4YNU3Z2tiorK4Naj8dbpZlrD2rL0fKA+fU79vU/+ObKh1KnPW4j3G262W9p0le/pdXWmZDrBFu+8lJVIyUbutVyjQml31Jkxi/c/WA/D9TceAcr3P2ORD+CPf7CfT4ItU5H3M/behvh1Gbh5tVXX9WMGTP07LPPKiMjQ6tWrVK3bt30q1/9Kqj1tNXB0B63EYk27Tt9odkd1Egq91Zp3+k/33oMtk6w5ZN7JjRZ9nq3Wq4xofQ7EuMXrGD7wX7euMbGO1iR6Hck+hHs8Rfu80EodTrqft7W2winNgk3NTU1Ki4uVlZW1p8bEhurrKwsFRUVNShfXV0tn88XMF2vLQ6G9riNSLQplLskwdYJtvyI9CT1dSaoqf/pjdFXt0tHpCfd0nqb21Yw5SIxfsEKth/s581ryd3ASPQ7Ev0I9vgL9/kglDoddT9vD9sIlzYJN3/4wx9UW1urlJSUgPkpKSnyeDwNyhcUFMjpdPqnfv36NbreSB4M7XEbkWhTKHdJgq0TbPlOsTHKH58hSQ1OsPWf88dntOiB3FD6HYnxC1aw/WA/b15L7gZGot+R6Eewx1+4zweh1Omo+3l72kZri4o3FOfl5cnr9fqns2fPNloukgdDe9xGJNoUyl2SYOuEso2xg/vqje8/KJczsD8uZ0KrPPgZSpsiMX7BCrYf7OeNa427gZHodyT6IQV3/EXifMB+Hn3baG1tEm569+6tTp06qaKiImB+RUWFXC5Xg/Lx8fFyOBwB0/Xa4mBoj9uIRJtCuUsSbJ1Q78SMHdxXnyx8VO/MGKlfPH2/3pkxUp8sfLRVvtESSpsiMX7BCrYf7OfhuxsYiX5Hoh/1bvX4i8T5gP08erYRLm0SbuLi4jR8+HBt377dP6+urk7bt2+X2+0Oal1tdTC0x21Eok1SaHdJgq0T6p2YTrExct/VS4/ff7vcd/Vq1XfDBNumSIW6cPaD/Tx8dwMjGfrD2Y/r3erxF4nzAft5+99GOLXZe27ee+89TZs2TatXr9aIESP085//XOvXr9eJEycaPItzI95z0/Ztktrvi6XCLdwvUGuPL45jP28/L1SM1IskI6G9vWiuo+7nNr7npk1f4vev//qv/pf43X///VqxYoUyMzNvWq8+3Gw7dFqPDO3fPt662M62wWvK25eOGOpCqdNR93Mb9g9bdNT9PFLb+O3vzug7D6TbHW5Cxd+WAgAg+kTq+h0V35YCAAC4VYQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqndu6AaGof6myz+dr45YAAIBbVX/dDvcfR4jKcHP+/HlJUr9+/dq4JQAAIFjnz5+X0+kM2/qjMtwkJSVJkkpLS8P6w2lvfD6f+vXrp7Nnz3aov6lFv+l3R0C/6XdH4PV6lZaW5r+Oh0tUhpvY2K8eFXI6nR1qp6jncDjodwdCvzsW+t2xdNR+11/Hw7b+sK4dAAAgwgg3AADAKlEZbuLj45Wfn6/4+Pi2bkpE0W/63RHQb/rdEdDv8PY7xoT7+1gAAAARFJV3bgAAAJpCuAEAAFYh3AAAAKsQbgAAgFXaZbj553/+Z40aNUrdunVTYmJio2VKS0uVk5Ojbt26KTk5WQsWLNC1a9eaXe+FCxc0ZcoUORwOJSYmavr06bp8+XIYetA6duzYoZiYmEan/fv3N1nvL/7iLxqUf/755yPY8pb72te+1qAPS5cubbZOVVWVcnNz1atXL/Xo0UOTJk1SRUVFhFrccl988YWmT5+u9PR0de3aVXfddZfy8/NVU1PTbL1oHO+VK1fqa1/7mhISEpSZmal9+/Y1W37Dhg0aOHCgEhISNGTIEP3mN7+JUEtbR0FBgb7+9a+rZ8+eSk5O1oQJE3Ty5Mlm6xQWFjYY14SEhAi1uHW89NJLDfowcODAZutE+1hLjZ+/YmJilJub22j5aB3rXbt2afz48UpNTVVMTIw++OCDgOXGGC1atEh9+/ZV165dlZWVpc8+++ym6w32/NCYdhluampq9OSTT2rmzJmNLq+trVVOTo5qamq0e/duvfXWWyosLNSiRYuaXe+UKVNUUlKibdu2adOmTdq1a5eee+65cHShVYwaNUrl5eUB09/+7d8qPT1dDz30ULN1Z8yYEVBv2bJlEWp161myZElAH2bPnt1s+blz52rjxo3asGGDdu7cqbKyMk2cODFCrW25EydOqK6uTqtXr1ZJSYmWL1+uVatW6R//8R9vWjeaxvu9997TvHnzlJ+fr4MHD2rYsGHKzs5WZWVlo+V3796tyZMna/r06Tp06JAmTJigCRMm6OjRoxFueeh27typ3Nxc7dmzR9u2bdPVq1c1ZswYXblypdl6DocjYFzPnDkToRa3nvvuuy+gD5988kmTZW0Ya0nav39/QJ+3bdsmSXryySebrBONY33lyhUNGzZMK1eubHT5smXLtGLFCq1atUp79+5V9+7dlZ2draqqqibXGez5oUmmHVuzZo1xOp0N5v/mN78xsbGxxuPx+Oe98cYbxuFwmOrq6kbXdezYMSPJ7N+/3z9v8+bNJiYmxvz+979v9baHQ01NjenTp49ZsmRJs+W+/e1vmxdeeCEyjQqT/v37m+XLl99y+YsXL5ouXbqYDRs2+OcdP37cSDJFRUVhaGFkLFu2zKSnpzdbJtrGe8SIESY3N9f/uba21qSmppqCgoJGy3/ve98zOTk5AfMyMzPND3/4w7C2M5wqKyuNJLNz584myzR1/osm+fn5ZtiwYbdc3saxNsaYF154wdx1112mrq6u0eU2jLUk8/777/s/19XVGZfLZV5++WX/vIsXL5r4+HjzzjvvNLmeYM8PTWmXd25upqioSEOGDFFKSop/XnZ2tnw+n0pKSpqsk5iYGHDHIysrS7Gxsdq7d2/Y29wa/vM//1Pnz5/Xs88+e9Oyb7/9tnr37q3BgwcrLy9Pf/zjHyPQwta1dOlS9erVSw888IBefvnlZv/bsbi4WFevXlVWVpZ/3sCBA5WWlqaioqJINDcsvF7vLf2BuWgZ75qaGhUXFweMU2xsrLKyspocp6KiooDy0lfHe7SPq6Sbju3ly5fVv39/9evXT48//niT57f27LPPPlNqaqruvPNOTZkyRaWlpU2WtXGsa2pqtHbtWv3N3/yNYmJimixnw1hf7/Tp0/J4PAHj6XQ6lZmZ2eR4hnJ+aEpU/uFMj8cTEGwk+T97PJ4m6yQnJwfM69y5s5KSkpqs0968+eabys7O1h133NFsub/+679W//79lZqaqt/97ndauHChTp48qf/4j/+IUEtb7u///u/14IMPKikpSbt371ZeXp7Ky8v16quvNlre4/EoLi6uwTNaKSkpUTO+Nzp16pRee+01vfLKK82Wi6bx/sMf/qDa2tpGj98TJ040Wqep4z1ax7Wurk5z5szRN77xDQ0ePLjJcgMGDNCvfvUrDR06VF6vV6+88opGjRqlkpKSm54D2ovMzEwVFhZqwIABKi8v1+LFi/Wtb31LR48eVc+ePRuUt22sJemDDz7QxYsX9YMf/KDJMjaM9Y3qxyyY8Qzl/NCUiIWbH//4x/qXf/mXZsscP378pg+b2SCUn8W5c+e0detWrV+//qbrv/45oiFDhqhv374aPXq0Pv/8c911112hN7yFgun3vHnz/POGDh2quLg4/fCHP1RBQUHUva48lPH+/e9/r7Fjx+rJJ5/UjBkzmq3bXscbjcvNzdXRo0ebffZEktxut9xut//zqFGjNGjQIK1evVo//elPw93MVjFu3Dj/v4cOHarMzEz1799f69ev1/Tp09uwZZHz5ptvaty4cUpNTW2yjA1j3d5ELNzMnz+/2eQqSXfeeectrcvlcjV4err+WzEul6vJOjc+kHTt2jVduHChyTrhEsrPYs2aNerVq5f+8i//MujtZWZmSvrqTkBbXuxasg9kZmbq2rVr+uKLLzRgwIAGy10ul2pqanTx4sWAuzcVFRURH98bBdvvsrIyPfLIIxo1apT+7d/+LejttZfxbkzv3r3VqVOnBt9ia26cXC5XUOXbs1mzZvm/zBDsb+RdunTRAw88oFOnToWpdeGXmJioe++9t8k+2DTWknTmzBl99NFHQd9FtWGs68esoqJCffv29c+vqKjQ/fff32idUM4PTQrqCZ0Iu9kDxRUVFf55q1evNg6Hw1RVVTW6rvoHig8cOOCft3Xr1qh4oLiurs6kp6eb+fPnh1T/k08+MZLMf//3f7dyyyJn7dq1JjY21ly4cKHR5fUPFP/7v/+7f96JEyei7oHic+fOmXvuucc8/fTT5tq1ayGto72P94gRI8ysWbP8n2tra83tt9/e7APFjz32WMA8t9sdVQ+Z1tXVmdzcXJOammr+53/+J6R1XLt2zQwYMMDMnTu3lVsXOZcuXTK33Xab+cUvftHochvG+nr5+fnG5XKZq1evBlUvGsdaTTxQ/Morr/jneb3eW3qgOJjzQ5PtCap0hJw5c8YcOnTILF682PTo0cMcOnTIHDp0yFy6dMkY89XADx482IwZM8YcPnzYbNmyxfTp08fk5eX517F3714zYMAAc+7cOf+8sWPHmgceeMDs3bvXfPLJJ+aee+4xkydPjnj/gvXRRx8ZSeb48eMNlp07d84MGDDA7N271xhjzKlTp8ySJUvMgQMHzOnTp82HH35o7rzzTvPwww9Hutkh2717t1m+fLk5fPiw+fzzz83atWtNnz59zDPPPOMvc2O/jTHm+eefN2lpaebjjz82Bw4cMG6327jd7rboQkjOnTtn7r77bjN69Ghz7tw5U15e7p+uLxPt4/3uu++a+Ph4U1hYaI4dO2aee+45k5iY6P/249SpU82Pf/xjf/lPP/3UdO7c2bzyyivm+PHjJj8/33Tp0sUcOXKkrboQtJkzZxqn02l27NgRMK5//OMf/WVu7PfixYvN1q1bzeeff26Ki4vN008/bRISEkxJSUlbdCEk8+fPNzt27DCnT582n376qcnKyjK9e/c2lZWVxhg7x7pebW2tSUtLMwsXLmywzJaxvnTpkv/6LMm8+uqr5tChQ+bMmTPGGGOWLl1qEhMTzYcffmh+97vfmccff9ykp6ebP/3pT/51PProo+a1117zf77Z+eFWtctwM23aNCOpwfTb3/7WX+aLL74w48aNM127djW9e/c28+fPD0jHv/3tb40kc/r0af+88+fPm8mTJ5sePXoYh8Nhnn32WX9gas8mT55sRo0a1eiy06dPB/xsSktLzcMPP2ySkpJMfHy8ufvuu82CBQuM1+uNYItbpri42GRmZhqn02kSEhLMoEGDzM9+9rOAu3I39tsYY/70pz+Zv/u7vzO33Xab6datm/mrv/qrgGDQ3q1Zs6bR/f76G6y2jPdrr71m0tLSTFxcnBkxYoTZs2ePf9m3v/1tM23atIDy69evN/fee6+Ji4sz9913n/n1r38d4Ra3TFPjumbNGn+ZG/s9Z84c/88oJSXFfPe73zUHDx6MfONb4KmnnjJ9+/Y1cXFx5vbbbzdPPfWUOXXqlH+5jWNdb+vWrUaSOXnyZINltox1/XX2xqm+b3V1deYnP/mJSUlJMfHx8Wb06NENfh79+/c3+fn5AfOaOz/cqhhjjAnuP7IAAADar6h8zw0AAEBTCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsMr/AWwljN2t2d6oAAAAAElFTkSuQmCC",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"def signal(x, A=1, B=1):\n",
|
|
" return A * np.sin(2 * np.pi * 2 * x) + B * np.sin(2 * np.pi * 4 * x)\n",
|
|
"\n",
|
|
"n_segments = 2**10\n",
|
|
"\n",
|
|
"domain = [-1, 1]\n",
|
|
"x = np.linspace(domain[0], domain[1], n_segments)\n",
|
|
"\n",
|
|
"fx = signal(x)\n",
|
|
"plt.plot(x, fx)\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"## decompose signal\n",
|
|
"fk = sc.fft.fft(fx)\n",
|
|
"# fk = np.fft.fftshift(fk)\n",
|
|
"k = sc.fft.fftfreq(n_segments, 2/n_segments)\n",
|
|
"print(k.size, fk.size)\n",
|
|
"plt.xlim([-10, 10])\n",
|
|
"plt.scatter(k, np.abs(fk))\n",
|
|
"# plt.plot(np.abs(fk))\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Exercise 3 - Gibbs phenomenon"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 43,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
|
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]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
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},
|
|
{
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"data": {
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"image/png": 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",
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
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},
|
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"def step_function(x, L=1):\n",
|
|
" def heaviside(x):\n",
|
|
" ret = np.zeros_like(x)\n",
|
|
" ret[x >= 0] = 1\n",
|
|
" return ret\n",
|
|
" return 2 * heaviside(x / L) - 1\n",
|
|
"\n",
|
|
"n_segments = 2**8\n",
|
|
"length = 5\n",
|
|
"x = np.linspace(-length, length, n_segments)\n",
|
|
"fx = step_function(x, length)\n",
|
|
"plt.plot(x, fx)\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"# fourier space\n",
|
|
"fk = sc.fft.fft(fx)\n",
|
|
"k = sc.fft.fftfreq(n_segments, 2/n_segments)\n",
|
|
"plt.scatter(k, np.abs(fk))\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"# reconstruct signal\n",
|
|
"fx_reconstructed = np.zeros_like(fk)\n",
|
|
"for i in range(fx_reconstructed.size):\n",
|
|
" fx_reconstructed[i] = np.sum(\n",
|
|
" fk * np.exp(1j * k * x[i])\n",
|
|
" ) * 2 / n_segments\n",
|
|
"\n",
|
|
"fx_reconstructed_easy = sc.fft.ifft(fk)\n",
|
|
"plt.plot(x, fx_reconstructed_easy)\n",
|
|
"plt.plot(x, np.abs(fx_reconstructed))\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Exercise 4 - derivatives"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
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"data": {
|
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"image/png": 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",
|
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
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"data": {
|
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"image/png": 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",
|
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
|
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]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"def f1(x):\n",
|
|
" return np.exp(-x**2)\n",
|
|
"\n",
|
|
"def f2(x):\n",
|
|
" return np.sin(x)\n",
|
|
"\n",
|
|
"def f3(x):\n",
|
|
" return 1/x\n",
|
|
"\n",
|
|
"def f4(x):\n",
|
|
" return np.cos(x) * np.exp(-x**2)\n",
|
|
"\n",
|
|
"\n",
|
|
"def fft_derivative(f:callable):\n",
|
|
" def derivative(x):\n",
|
|
" fk = sc.fft.fft(f(x))\n",
|
|
" k = sc.fft.fftfreq(x.size, 2/x.size)\n",
|
|
" df_dk = 1j * k * fk\n",
|
|
" df_dx = sc.fft.ifft(df_dk)\n",
|
|
" return df_dx\n",
|
|
" return derivative\n",
|
|
"\n",
|
|
"n_segments = 2**7\n",
|
|
"x = np.linspace(-10, 10, n_segments)\n",
|
|
"\n",
|
|
"\n",
|
|
"f1x = f1(x)\n",
|
|
"df1_dx = fft_derivative(f1)(x)\n",
|
|
"plot = plt.plot(x, f1x)\n",
|
|
"plot = plt.plot(x, df1_dx)\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"f2x = f2(x)\n",
|
|
"df2_dx = fft_derivative(f2)(x)\n",
|
|
"plot = plt.plot(x, f2x)\n",
|
|
"plot = plt.plot(x, df2_dx)\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"f3x = f3(x)\n",
|
|
"df3_dx = fft_derivative(f3)(x)\n",
|
|
"plot = plt.plot(x, f3x)\n",
|
|
"plot = plt.plot(x, df3_dx)\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"f4x = f4(x)\n",
|
|
"df4_dx = fft_derivative(f4)(x)\n",
|
|
"plot = plt.plot(x, f4x)\n",
|
|
"plot = plt.plot(x, df4_dx)\n",
|
|
"plt.show()"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "projects-X-9bmgL6",
|
|
"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": "3.12.7"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|