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@badly-drawn-wizards
Created November 4, 2019 11:10
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Visualizing power sequence theorem of spectral radius.
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Background\n",
"So I did this while I was trying to visualize the power sequence theorem on the wikipedia page: https://en.wikipedia.org/wiki/Spectral_radius (Last retrieved 2019-04-15). This was a while ago, so I can't remember why I did it. It does look cool though. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"from numpy.random import random\n",
"from numpy.linalg import cond, inv, svd, eigvals\n",
"from scipy.linalg import fractional_matrix_power, block_diag\n",
"\n",
"from matplotlib.transforms import Affine2D\n",
"from matplotlib.animation import FuncAnimation\n",
"from matplotlib import rc\n",
"\n",
"from mpl_toolkits.axisartist.grid_helper_curvelinear import GridHelperCurveLinear\n",
"from mpl_toolkits.axisartist import Subplot\n",
"\n",
"rc('animation', html='html5')\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def rand_mat():\n",
" mat_shape = (2,2)\n",
" while True:\n",
" mat = 2*random(mat_shape)-1\n",
" mat = 0.5*(mat + mat.T)\n",
" try:\n",
" lam = eigvals(mat)\n",
" if np.any(lam < 0.0):\n",
" continue\n",
" rad = np.abs(lam).max()\n",
" except:\n",
" continue\n",
" if cond(mat) < 4.0:\n",
" break\n",
" return (mat, rad)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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GOXpEdzNdA4OLOzs7ezg91jUddv369SxcuFBzKnStYLFYwpYGHggKMow8+dkKXtldz4/fPMgVD2/kdzct5IIZnnkjtLa4QpEGHjUKQcubbbfbaW9vR6fTUVtbO8pPdw+zySZ8amoqa04O8OiH3eRnGPjHbYs4q0wZ9ZraCSZKoBZ1t1JEAu+Cv5CthSWTsrjr+d3c8dcdfP2Cqdx98bRRrl8scG+qphAkSXoKuBJoFkLM9fB9KYN9HwsAJ/CEEOIhpedX42b7Yp2Rw3A6nQ5JkrDb7fT3949gnZHNd3dYbQ6+98p+3tjbwOVzC/jl9fP9So21Wq0Ru+GmFiKRd0EpynJSeO2uFfz4zYM8uu44O2vaefjTi0ZUmprNZs15FyJWIeC72asd+K4QYrckSWnALkmS1gohFPVmMJvNXtuMeWOdcf3ASNYZ+eOaOOMaZquurkaSJEVvtIbOPu58dicHG7q559IZ3LVqit8LLdJ4F9RGOHgX1LYqjYk6fnn9fComZ/P91w9wxcOb+PPtFSwszRyWpybvgi+Eog5Fs2avQohGoHHo5x5Jkg4DxYzRrMW1k3NHRwcpKSm0tbV5DLO5ss64htlMJlNA6bBms1lRgsmOU+189bldWG1O/nJ7BRfNCiwpJVo23AJFtPIueMINS0qYV5zBF/+2g5uf2MJDNy/i0jkFYSHjVTsJKix7CEOKYxGwzf27/v5+1q9fT3NzMx0dHcydOxej0YjFYgEIGeuMO5S8XV7bU8e9L++nJCuZF+9cwtS8wLV1OHkXYlFeqDtRzShI47W7zuELz+zkK8/t4gdXzKbMbte05V+kuwyKIElSKvAKcLcQotv9+66uLu655x4KCwspLi7mzjvvBGDDhg2atvL25e8+tamaB/51iLPLJ/DHW5eQkRzc5AsHL4GWvRWjtbXZWMhJNfDil5Zz9z/28MC/DnHJ5CRWni9CVqrujlDwLmiqECRJSmRQGTwvhHjV0zF5eXns2LFjxO/6+vo093fBcyddIQS/W3uUhz84zqVz8nno5kUYE4O3UsJhbmrV+h0il3chWJiSdDz+mSX85PV9/G17PV99bheP3LIIgz40lqsMh8MRkg1hzXZ4pMGrfxI4LIT4rT9/q7W56S3BxOEU/OCNSh7+4Dg3VZTy2C2LVVEGoA3vgitiPUtRSwWrS5D46tn5fOWsCbx3qImvPLsLq80RUpmhCnFq2ez1HOA24EJJkvYOfVaPccphREKzVbvDyd3/2MtzW0/z5ZXl/PL6eap1NdK6AhAGN9y09Hdj0WVwhcVi4ZaKIh68bh7rqlr40t92hlQphOp+atnstQEIyMZRq5GlUrhPJqdTcM/L+3lrXwP3XjaDu1ZNDam8UMNms4VsM9YboplnUKm84uJiblk2AX2CxPde3c8XntnBX25fiilJ/XsdqvFpWxwQIMJpbgoh+P4blby2p57/umS66srAXZ4W0DqjLhw8g6GOMrjDdY7euLSUX9+wgI9OtHHH09uxDNhVl+fvnHE6ncPh+7a2Nq/HRUXqcjjMzYKCAoQQ/Pztw/x922m+umoKX7tAfWUgy4vlEGA4eAYlSQor78L1S0rQJUh856W93PX8bv58ewWJKrmY8PEzlGtqvJXDy9R1Qggefvhh2tvb6ejogGhu9hqqBBNvkPcsfv+fY/xlUzWfPXsS9146I2QTTOuin/Hgz0dC/89rFxVjGXBw/2sHuO/VA/zfDfP9mkNjcV+0tLQM0+3J3BeuZLS5ubnDSXmydZaWlkZBQUF0N3u12Wyabn7BoIn74s56Hnr/GJ9aUsKPrpoT0rdNOCyE7GxlRVdqyQv3pnAoMVbOyi3LJnKm28rD7x+jIN3If106Y1RNjfuid6WYd20aI9fUGAwGent7WbVqlV/XWVFR4fOYiFcIWj9cu93OwTYnv911iItn5fHL6+f7TaPlL4LhXQgE4XhjjwfeBW81NRfk9HFgkoFH1x2nu+k0F01KUlxT4wmhrEOJeIWg9cOtPN3KY3usTMtL5fc3Lwp51pkv3oVQQOu6gmjnXXCtqfHko3d1deF0OmlraxtVUyN3cn54+nS+9c9DPHu4mXOXzOP8OYH3wgjl/YwrBBd0mAf42j8OkKRP4C+frSDVEPrbE+2NPZQgknkXXDtEeVrwMnWdK8W8K3WdyWTi5MmT5Obm+iw0euyWxdz0xBa+89I+Xv9aKlPzUgMeX6jmTMQrBDUbWY6FAbuTLz+3i+ZeGw9fU05JljaLNBxlz+OBd8FgMIxa4K7/lynm5Q5RrjyVrp2clYQurVarogVqStLxx1uXcOUjm/jKc7t4/WvnBPTSsVgsIeNdiHiFoNWC+cU7h9le3c53V2Rz1hRtqw5jecdfbevAnWLe06e7u5vNmzcPm+/BdHJWAn+svKJME49+ehG3PrmNe1/ex2O3LA6oND9UvAsRrxC08HfXHmrir5tP8bkVk1ma1xP1Ne1jIZJ3/N07OXujrnMPs6Wnp5OXlzesePbs2cOKFStCNiZ3+BsWXzE1h+9dNpNfvHOEJz48yZfP96+KN5RuZkQrBC383YbOPu55eR9zitK5b/VMtmzaqLm/q/WGmxYumAyz2YzJZMJisXj108fq5JyVlTUcT1cSfm5vb9c8DTyQsPidK8vZV9fJ/757hAWlmX61kHM4HCELxUe0QlCbc94ddoeTu1/ci83u5NFbFpM0lEkWyzyDZrOZiRMnqnIuT2E21wUvf6fX62lvbx/hp8udnNXuEBUtSVeSJPGrGxZwuLGH7760j3fuPk9RF2q73R7SJL2IVgihNm8ffv8Y20+18/ubFlKWkxI23gUtFZCSBeNOMe9pscvX7u6nu3dy3r17N9OmTdOsJ6fWvAvB1IWkGvT85sYF3PCHj3jgrUP8+lMLFMkL5ZqIaIUQyiKc3ac7eGTdcW5YUsK1iwaJQrQ238PFMyib754+3sJsqampAVHXhWPTtKAg8Bh/IPKCGd/iiVnctWoqj647zidm53Opj/yEUM/RiFYIoeIZHLA7+e9X9lOQbuTHV88ZIS8azE1PcDqd9Pf3e02eGRgYQAiBxWLh8OHDowhp/Qmz+Xtdsc67kJOTE9Q5vnnRNNZVNXP/qwdYMimLnFTv3Z9CPUcjXiGo2chSxh/Wn+BoUy9PfW5k8lG4eRc8wVOYzd1PF0J4pJh3D7N1dnZSU1PDwoULNRnfeOBdUMOKTdIn8LubFnLlI5u4/9UD/Om2JV7dyFDP0YhWCKHYVDzW1MOj645x9YIiLpw5MtxnNpspKSlRVZ43CCHo6enBYDDQ0tLi8c3u3slZ9tU9dXJWgnDwLmgpLxy8C2qxXU3PT+O7n5jOL945wtpDTVzixXUYty5DKBp7OJ2C772ynxSDnh9eNXvU92pNYNd0WE8fOcxmtVrJyMjAarViMBiC6uSsBHHeBXWhNu/C588t45XddTzwr0OsnJ7rka8z1A1lI1YhhIJn8O/bT7P7dCe/vXGBRz/NV4KJ7Kd7W+iunZzdzXc5zGYymYY7OW/cuJGKigrNTFytez/EQq/DsaB2yDhRl8AD18zl5ie28vj6E3znE9NHfK9FVCpiFYLak6nbauO3a4+yrCyb6xaNpB+XN9sAmpubPZrv8sNwX+juYTZ/HpbD4Yg6f9cfxDrvQigU0PLyCVy9oIg/bjjB9YuLmTTh4/NrkbOiZrPXy4CHAB3wFyHELz0c823gi4AADgB3CCGsns6n1s2WWWd++95R2s0D3D4/lcrKylHpsJIkYbPZaGlpwWQyDbPOyItdbd/UbreHhWdQ67JnrfcsYoF34X+umMX7h5v4yVuHeOpzS4d/r4VLpIpCkCRJBzwGfAKoA3ZIkvSmayNXSZKKgW8Cs4UQfZIkvQTczGCT2FHwlWDiiXXGdQfetZNzjzOR53e2cfHUNBaUZo14w8shsYaGBnp6epgxY4Yat8QntH5bh4t3IZT+rjuinXdBRn66kW9dPI0H1xzhw6MtrJw+KEOL8allIZwFHBdCnASQJOlF4BpGN3LVAyZJkmxAMoPU7KPQ09NDVVUVTqeThQsXjvLTxwqzyRlzrumwd7+4h4SEBB64YSlFmZ5NrljfAIvzLqgPf3gX/MVnV0zmmY9q+M3ao5w3LQdJkjCbzSGvQ1FLIRQDtS7/rwOWuR4ghKiXJOnXwGmgD3hPCPGe+4kaGhpYtmwZ6enpTJo0ifnz548IsxmNRr8m2f66Tl7f28DXLpjiVRlAeIp+YnnDbbzwLoRqjAa9jm9eNJXvvXKA9w83c/HsfCwWC6WlpSGRJ0MtJ9bTUxAjDpCkLAathjKgCEiRJOlW9z8qKiri0KFD/PKXv+Qf//gH5eXlFBYWDle9+fvAf7f2KNkpSXzFR4lprC/QaCn6CRRaWwehCIu745OLS5g8IZnfrD2K0yk02ZNRazR1gKvqKmG0O3AxUC2EaBFC2IBXAY9F62o1sjzY0MW6qha+cG4ZaT4qybSuK4j1BRrJvAtqQIv5kqhL4O6Lp3O4sZt3Ks9o0o5ALYWwA5gmSVKZJElJDG4Wvul2zGlguSRJyUONXy8CDns6mVobbo+vP0GaQc+ty8dOfx4v/q7WFkksW1xaybtqQRHT81P5zXtV6DSoCVFFIQgh7MDXgX8zuMhfEkIchI+bvQohtgEvA7sZDDkmAE94Op8a2v5kSy9rDjRy69mTyDCNbR2EmnfBHeHyd2NZAcWqRaJLkPjmRdM42WrmUFfo60LUbPa6Bljj4ferXX7+EfAjX+dSYzL9acNJknQJfP6cMp/Haj2ZwuHvAprmPYQjilJcXOz7QJWgJe/CZXMKyE9LZM1xK18JsayIzFQMtqb9TJeVV/fUcctZE8lN8x0Hj3XzNhy8C6HecHNHOLIUteLC1OsSuGZWBk9sb+VgQxdzipQxLnurqRlrHyIiFUKwC/SF7aexOwVfOLdc0fFa5/jHQortWAhFHYovhIN3Qct7urIkkWf3JPDXzaf4vxvmj1k856mmxmAw8NOf/pTm5ma5+3P0NHsNJr5rdzh5aWct503LZeIEZYsuHOZtpPEuqIlwtN+LBd4FV+o693qanrYmVhQm8PruOs5Lbyc/w+R3Tc3dd98dvc1eA91wW1/VQmOXlR9dNcf3wUMIRwhQK94FGByfljyDsb6hGAjvglxT443oRq6pSUxMHEVGm5ubS1tbG/ddX8H7v9vIKV0J1yyf5vd1R2WzVyFEUPnvf99+mtw0AxfNylMsT2t/NxwKSGuewVgOcbo+P281NfKCd62pcSWjNRgMZGZmjqqp8QQ5/2BqfjrnTJ3AK7vr+OZFU0MSpYo4heBwOAJ+uPWdfayvauauVVNJ1Clb4DabLSz+rpYmbjhcIq33ZNRWCN46OVutg81d+/r6WL9+vceaGpmMVi2KeVcX+rpFJfzXP/exq6aDisnql5ZHnEJwOp0BP9x/7qxFADctVZ7vrfXbLNDGHsFAa57BcLgMSnkXfHVydqWuc+/kLNfUNDc3YzAYQlbY5A7X+3nZ3AK+//oBXt1TP34UQqBvs7f3N3LW5GxKs5X//XjYcIt13gX5nnoKs7kufF+dnJVS19XV1YWtEC7VoOeyOQW8vb+RH101G4NeXUszIhVCIAv0WFMPx5p7eeAa5ZuJoH1jj1j3r0PBu+CNuk5e7G1tbWzZsmXYT5d9dYPBQHp6+gg/XY1rCzfvwnWLS3h9bwPrjjRz2Vx1CWEiTiE0Nzfz4YcfcuWVV/r1d+9UnkGS8Nnowh3haLYayxaJP/LkMNtY5rvMfeFqvptMJrKzs4c357Zs2cIFF1wQ4pF9jHDzLpwzZQK5aQZe21Mf+wphYGAgIN9szYFGKiZlkZ/u34MKxw71eOBd8OWne+vkLIfZ5De8L3dHa4UXCbwLel0Cl87J59Xd9fTbHaq6DRGnEOx2O+XlyjIMZZxs6eXImR5+eOVoanVf0DrKEI4FqmaOv8PhGGG+uy/63t5eJEmivb3dYydnJWE2fzBeeRcunJnHc1tPs+1k+zDFmhqIOIWQm5vrt8b/98EmYHAH1h+oxbvgDyKVd2GsMFtfX9+IdFjXBq8Gg2EEGW1VVRUFBQWahR1jtcpRhrf5cnZ5DgZ9Ah8caY59heAvNqaLQFAAACAASURBVB1vYWZB2pgUaZ4Qrg03rc1NnU5Hd3e314XuLczmmjijlGI+7oJpI8+UpGPFlAmsq2rmR2K2anMq4hSCv7DaHOw81eGTBMUTtNb2anPwORyOMf10m81Gb28vO3bsGBVmC6STsxKEg3ch1DyD7vIyMzM1kzfWHL1wZh7r3jjIyVYzU3JTVZEX9Qph9+kO+u1OVkzx/y0RqTn3Sjo5AyPCbJ46Odvtdvbt28fy5ctDPTQgzrsQCowVFr9gZh68cZB1R5rjCkHGlhNt6BIkzirzP2srHCFHg8FAV1eXV/NdaSdnJSZiV1fXuOBdiPU0cG9ztCQrmYnZyew81cEXz1NHXtQrhM3HW5lfkuGTRNUT1LQQ5LJVb8kzchGM0Wikp6dneHGnp6eTl5fndydnJYjzLqgPh8Ohaeq5r3u6ZFIWm463Dr9IgkVUKwRzv519dV185Xz/wpQylPj0cpjNm/kuV7Pp9foRITbX5Bk5HXb79u3Mnj2b1FR1zDtfiPMuqItI5F1YPCmL1/bUU9fR51fKvjdo2ttx6DgdsBOoF0L4l47ohkON3TicgsUT/Z/0TqcTp9NJZ2enYtaZsTo5K4HWZK5x3gX15UUa78KSobm/q6YjchSCkt6OLvgWg8zM6cHKrazvAmBu8cccc66sM54SZ+R0WDnufurUqeEa9WA6OftCnHchNPIiIQQYKih5fjMK0khJ0rGrpoNrFwW/2alpb0dJkkqAK4CfA9/xV4g768zWI3VkGhOoObKfo/39I1hnPKXDunZybmtro66ujgULFgQ5dGUYD7wL4UgS0pJ3IRLJeHUJEosmZrGrpkMVmZr1dhzC74F7Aa92pd1up6qqirq6OhobGykvL/cYZjOZTJxoH2B2QRqzZ8/2Ox02Eh+umggH74LD4Yj5NHClvAtqQKmFN6conb9uPoXd4USvkBjIG9SaMUp6O14JNAshdkmStMrbiVpbW7npppvIz8+npKSET33qUx7DbP12B6c6jnLJvOKANunMZjMZGcrorNVArKfYjifeBa1gNpspLPRdzTglL5UBh5Pajj7KcoJTkGopBCW9Hc8BrpYkaTVgBNIlSXpOCDGi4WtBQQE7d+70KfDomV7sTqGYo94dZrOZoqKigP42EMS6RRILvAu+0N/fHxTfp79Q+gyn5g2+EI839watEDTr7SiEuE8IUSKEmDz0/QfuysAfnGztBWBafmAhvPHQbDXSNsCiWV44yp6VVla6KoRgoVlvRzXkuKKuow+AkqzAagO0TjAJJzOwFoj1EKDadSi+4I8CSjcmkpdmUEUhaNrb0eV364H1wcirbbeQk5pEcpL/QwhHgkmcd0FdxLoLZrVa/XJPpualcrwlQiyEcKCuo4/irMDeEFq/PeO8C+pjPLhE/oxv0oRk6jssio6VrQ9PiNrU5doOC/OKA99Q1HIyaZ2hKPMbRKK/qxbCYQFFMu9CbpqRNvMAfdZ+7LaBUcl4FouFBx98kJaWFrq6uiCaejv6gsMpaOjsY/W8wAgmY73oR2sFFC6eQa0V0MSJEzWTZ7FYRoTFvXVylj+djRaEgP9s2kZhZvJwvk5ycjJZWVmYTCbuu+8+SkpKorO341hoNw9gcwgK/CRUlRHrRT9aK7xw8AxCbPAuuFLXuabZ19XV0dLSQlVVFTB2TY3RaKQ3o42/HdpN2awFI1L5XaGEFyMqFUK3dbDCMDM5sE26cPifWub4x/qGW7h4F/xRQEpraoBRCz0rK4szZ86wePFikpOTFVleuUMvx+YeKxB4wl10KoS+QYWQHgAHAoQnwURrF0XrHP9YdsHceRc8dXJ2XfjuNTUyGa2nmhpvOHLkiH97CKmD87mlpz/AUQ4iOhWCdbAlV7rJ/8uPBF79UMNsNjNpkv8ck8HIiwUXzFsn5+7ubnp7e1m/fj0wmrrOZDKRkZExXDUbbH5LIGHxCamDFlO72RaU7KhUCF1BWAiRnGCiFuK8CyMhhGBgYMCr+e6Lui4xMZH09HRmzZqlyXMMxKI0DjVrsdocQcmOSoUguwwZJv8VgtbmrdbuyXjiXZA7OXvz0ZV0clZCXdfV1UVGRoZmSj2QPaCEBIkkXQL9dmdQsqNSIZj7B12GFIP/lx/rO/6xwrswVpjtzJkzdHV1IUkSiYmJGAyGYXPd307OSqA170Kgc9SgT6DfPg4tBDnPKiEAja11gkms7/j7y7vgrZOzUuo6k8lEd3c3q1at0uyNHS28C4bEcWohBAOLxaJ5Y4/xwLugNMzm3slZDrPJb3hfFPMOhwOdTqfpnky08C609g5Q02YOSva4VAha+7vRzrswlp/e3d2NzWZjw4YNQXdyVgKt39bRxruw+XhbULLHnULQmmcwHAooLy9P0bHuYTb3BS9TzMthNvkt7trJub6+nuTkZM2srjjvwtgoz40MxqSoQLh4BrXmXTCZTGPmvVutVgCPYTbXxJnExESfE9NqtUbFhlugiKb+nzmpBpaVBbc/FtUKQeC9jNMTtJ5MavMuyGG2sRq8dnV1sWXLFo9htoKCAtUp5sOx4aalCxZNTFf9dgcGfWSQrGqKlKTBRWbud/hFkBLJRKeuYTZPC95uHwy1ulPMy2E2uWnMli1bOP/880M5rBEIB++C1gtUy/6fwVgk/XYnhsRxqBDShxKSuq02ctOUb76EYzIlJyePWODui92VYt41nu7eyVlJbkFPT0+cd0FlRAvvghCCAbsTgz44izQ6FcJQyrKcsagUZrOZnJwcVa7BPR3W2ychIYGurq4Rm3KBdHJWAq0VXpx3QX2YzeaANmjl/INx6TLIRU1dASgEJQvGWydn+SNXs3kKs7l2cq6srKS4uFizRKhY33CL8y54R4dl0NIMlBJAhqbNXpU2hPWFYQthqOpRKQYGBrDZbPT29nr00z11cnYNs8nxdKVRg3CYm/HeiuohXLwLgWxEy2XPeWnBKUzNmr362RB2TMhFTbKF4Mo6M1Y1m9lsprKycoSfHmgnZyXQurApHHskWoccxxPvgj+QFYI/e2qeoGWzV0UNYV3hng4rf3otfUjAzgNVlFqrgY+r2bx1crZYLBw8eJCzzjpLpSGPjfHAuxCOJKFY4F3whmDuZ3OEKQQlzV4VNYTt7+9n/fr1NDc309HRwdy5c0eY76mpqeTk5FCQ0YKUNoFVqxYpusBwEJ3GOu9COLIwI5l3IVgEM0dlCyEnNTgXR7NmrwqPoauri3vuuYfCwkKKi4u58847PU7y0uwU6jv7FF9gNGn7QBDnXVAf0bQn09xjJTM5MWLCjkqavSo5hry8PHbs2OFTYGlWMpuPtyq+wGipaQ9GXpx3QV2EI5Et0Dla295HUUbwFqlmzV4VHqMYpdkmmnqsigkhYn1HPM67oD4cDkfUtN873tw73PQ1GGjW7HWsYwJBSVYyQkBDp1XR8bG+4RbrFkk42u9p6Q5B4LwLlgE79Z19qigETZu9ejsmEJTlDE6OE829lOWMvRDGi78b7bwLYyHWLbxgeBdOtgySokzJjRALIRyYWZCOJMHBhm6fx4YjwWQ88C7E8iZtNMmT28CPZSE4nU76+vro6Oigrc07iUpUpi7DIMFqWU4KlQ1dPo8dL/6u1rwLWiugQHgGg5EXDQpPCMGRxk4SJEh29FJT0z4iQU9OygN46KGHaG9vp6OjA2Kp2auMOUUZ7K7p8HlcrL891eZdUAKteQbDsUALCwNrJhwIPI1PaU3NtqoBClN19HR1eKypkV3l1NRUCgoKYq/Zq4y5Rem8ta+BDvMAWSneJ6fZbNY0wSSazM1A4HA4NOcZ1NrtC6UCcjgcoxq81tXVodfrqa+v91lTI/9fr9cjhODbH67l4lmFzJ49e0y5FRUVPq8tqhXCnKJBNuODDd2cO817WbPWJBexvgGmtQKKFt4F95oa97oad4p5V/6LhIQEpk6dSlZWliLqOhnVrWY6LDaWTFInpTuqFcLc4nQA9tZ2jKkQwrEjrhbvghKEwyIZT7wL3mpqXBe7/Deu1HXub/SxqOtOnjxJbm6u35GwXUMuc1whAJnJScwsSOOjE218/cJpXo+z2+1Rk2ASqLzi4mJN5cWKReKpk3Nvby9Wq5VNmzZ5pa6Ta2rkhR7MHk4wvAu7T3eSbtSrEnKEKFcIAOdMzeHZrTVYbQ6MiaMfSjgSTIIpYw0E4Vigke6CyR2ivBHSulLXuTNPA+Tm5jJ//nxNnmMw+yO7azpYNDGLhAR13KkYUAgTeHJTNbtrOlgxdbSZHg5/NyEhQVN/V+vCpnBYQHKOvzfqOnnh++rkrIS6rqamhszMTM2UeqD3s623n6PNPVw5X71oSNQrhKWTs9ElSHx0os2jQoiXPauPUIzRtZOz+yJvbGykpaWFQ4cGqTNcqetMJhPp6ekew2yBIlp4F9ZXtSAEnD9DvaK9qFcIacZEFpRk8NGJVmDGqO9jPQchGhTQWJ2cPVHXuXdybm1t5ZxzztH0jR0NvAsfVDWTm2ZgbpF6vUOjXiHA4D7C4+tPeMxHMJvNYU8wCSXCybsQbCdnJdR1cg2Klnsy0cC7YHM4+fBoC5fPLVBt/wBiRCFcOqeARz44ztpDTdy4dCSFtdYhsljgXRirk3NPTw89PT2sX7/eaydnJWE2pYjzLnjGrpoOeqx2LpyprI+nK5qamrx+FxMKYU5ROqXZJtZUNo5SCOHg1Z88ebKm8vyheffmp7unw7qH2eROzh0dHeTl5TF9+vRQDWkExksdir9Kb92RZhJ1EudO8//lc/z4cQCPiTIxoRAkSWL13EKe2lxNl8VGxhA3faxsuI0Fi8VCaWnpqE7O7ovdvZOzbK57SocdC83NzWRkqOez+sJ4SAP3dxNUCMG/D55hWdkEUg3+L+Guri4Aj2+RmFAIAJfPK+RPH57kP4ebuH7J4IZQOBp7qM27IIfZvMXTW1tb6enp8ein+9vJWQnizVbDL29PbSen2izcdcFUv+U5nU7ZZej39H3MKIQFJRkUZRh5p7JxWCFore39STBxD7N5WvByDr+nTs75+fkYjUa2bt3KBRdcEMphjUA4Ntzy8vz3kwNFNFgkr+2ux6BP4PK5/hPAWiwW2UKIbYUgSRKr5xXyzJZTtPX2MyHVEDZt7ynM5rrg5XRYvV4/ommMHGaT/+9rYyscG25x3gX15fkzRwfsTt7a38AlcwpIM/r/7C0WC5/4xCcAGj19HzMKAeDGpaX8ZVM1r+yu486VUzCbzWRmZqp2fm9hNnmxm81mnE7ncHNX15h6enr6CD9dLfM9zrugLiKdd2FdVTOdFhufXBRY7Yqv8cWUQpien0bFpCxe2F7Ll84rx2KxKCr6UdLJWU6Hda9my87OHi5jra6uJj09XTMfOxrM22AQDM9goIh03oXXdteTk5rEeWNU9/qSN5YLplZvR0VNXIf6O+4E6oUQV6oh2x23LJvId17ax5aTbdjNZpKSkrw2d/XVyTk3N3e4wauSjUKLxRI1jT2iQV6cd2EkmrutvH+kidvPnoxeF9jGta+8nKAVgp9NXL/FIAV7erBy3cNs8oIvsPeRkijx0Fs7uXWKjR07dozw0/0Ns/mDOO+CughHGng4eRd84bmtNdidgtuWTwpYpsViGTMsrsZqUNTEVZKkEuAK4OfAd8Y6YU9PDzU1NdTV1TFz5sxR1WwwmA7r2uDVYDCQm5tLaamRGxoM/H1HLbfPTee8885TYYjKEA7eBa0XaCzzLmh9P/2xDqw2B89tO81FM/OZ7KPtgDco4V1QQyEoauIK/B64FxiziqOhoYFly5aRm5tLYWEhv/jFL8jMzCQ/P3944fvSqLetmMwzW0+zoUFwhZ+DCRTh4l2IZH83WGjNuxDJvSbe3NtAu3mAz587OWB5SuaLIoUgSdJ/AE/O8f+goImrJElXAs1CiF2SJK0aS1ZRURE7d+5UclleMTUvjZXlGaw53sMP++0BZXP5izjvgvoIJ++CVvKUzBkhBE9trmZmQRpnlytPU/ckz9f9VPRKE0JcLISY6+HzBsqauJ4DXC1J0ingReBCSZKeUzqQQPCpuRn0Djh5YdvpUIoZhtbmZjSUPQeLWG+/p9Qi+ehEG0fO9PD5c8uCuv+qKQQf8NnEVQhxnxCiRAgxeej7D4QQt6og2ysmpjg5a2I6f954EqtNWUPYYBDJ5qYasFqtMa+AwrFp6kueEIKH/nOMvDQDVy8ILpytZHxBKwQljV6DlREILBYLd62aQnNPP6/srgu5vFgPAWptAWntnoSr/6evZ7jpeCvbT7XzjQuneuQM9QdaWQgIIdYIIaYLIaYIIX7u8vvVQogGt2PXhyoHwRX9/f2snFnAgtJM/rjhBAN2Z0jlxXqSUKznIEQi74IQgl//u4riTNOosv5AoESpR22z17HgGl65++Jp1Lb38fy2mpDK1NrfHQ8WSSzLU8K78J/Dzeyr6+JbF03DoPffOnA4HJjNZtra2qivr8disVBVVcWRI0e8/k1MpS7LcF2cq6bncu7UHB56/xifXFQyzJWgJsbLhltpafBvKaUwm82kpwedv6YYkWbhOZ2C37xXxeQJyXxycbHbd96p6/r6+oYp5l1L4pOSknjkkUew2Wy0trZCLDZ79QZXbS9JEvevnsUVj2zksfXHuX/1LNXlxQLvgi+Ew0WJZS5MT/Jca2pe21PPkTM9fG9lPgcrD4xZU2M0GsnOzh6TYr67u5ubbrqJCy64IHabvXqDu680uyidGxaX8PTmU9y2fBKl2epO7EjmXVALWvMMhiNqE0reBZn7Qs64ra+vx+l0smPHjlE1NU5dEg9taGVGrpEr5xeSkmzyq6bGEywWCxUVFT7ZpGNSIVgsllE8g9+9ZAb/2t/IL989wmO3LFZVXqzv+IeLZzAaeBdcOzl7Irrx1snZ4XBQVFQ0zGrlOtaf/usQnVYHT39+OaUl6pTvK52jMakQzGYzEydOHPG7ggwjd64s56H3j/Hppa1jNof1FxaLRXOewXCbt6FEJPAueOrk7LrovdXUuFLMj0Vd19zcTFFR0ajQatWZHp7+6BQ3Ly1lQal6XB5KeRdiUiF40/ZfXTWFN/c1cN9r+3nv7vMxJakz6cLBMxhIY49AEWkbbsFApq5zfZP39fXR19fHtm3b6O/v90pdl5mZqRrFvCe3TwjBD9+oJM2o555LZwY1TneMawvB24abMVHHLz45j5uf2Mpv11bxP1fMVkVeOBZMpDdbDYc8mbrOG/eFt07Oer2e9PR05s2bF3QnZyXwxrvwxt4GtlW38/Pr5pKdou4ekdKN75hTCL46Ly8vn8Cnz5rIk5uquWpBEfNV8NG09nfDsUDDybsQTCfnjIyMEea7JzQ1NZGVlaWZUvfEu9DUbeVHbx5kYWkmNy+d6OUvA4M/YfGYUwhK3tb3rZ7JB0eauPfl/bz1jXNJDJB9BsLj72rNuxAqC8gbdV19fT16vZ7q6uqgOzkrQbg3hYUQ3PvyfvrtDn574wJ0KrZmA//C4jGnEJQ83HRjIj+9Zi53PruLRz44znc+EXgXIq13/KOFd8G1FZwnZivZbHanrktPT6epqYn58+eTnp6uyVjDzbvw/LbTbDjawgPXzKE8N1V1ef4ovHGpEAAumVPA9YtLePSDY5xdPoGzpwRWZx6O3pHhIDqV38BymM2b+e4pzGYymUhOTh6RPDOWVVVVVUVGRoZmmZ/h5F041Wrm528f5rxpOdy6LHBqNF/ylM6ZmFMI/jRbfeCaOeyp7eBbL+7hnW+dx4RU/6vrYqXoRw6zuS90maB2/fr1QHCdnJVeB8R+GnhycjJ2h5PvvLQXvU7iVzfMV7WLs7u8rKwsRcfGnELwZ4GmGPQ88ulFXPf4R3z3n/t46rNL/X4oZrNZ8c1WA/4qIPdOzp524eVF6L7Qs7KyMBgMJCUlMX/+fE0W6XjiXfjFO0fYfbqTh25eSGFG6MastB0BxKBC8LeMdU5RBt+/YhY/fOMgT26q5ksry/2SF44kITnBxL2Ts/ti99XJWf7/WH76qVOnSE9P19R8Hw+8C2sqz/DnjdXctnwS1ywMLXHtuN1DcPd3leK25ZPYfLyV/333CPNLMljmB29dKCaUp07O8qepqYmWlhYSEhK8htnkjDk1QqGRyjOoFsLBu9BkTeAnL+9n8cRMfnClOrkwY8GfOpSYUgiBPlxJkvjVDQu47vHNfOW5Xbz+tXOYNMG3RvXX3HQNs3nalOvv7/caZsvJycFoNNLZ2cmqVas0izSYzWYmT56siSzwz99VA1rvAZ1p7+KhXRaSk/Q8/pklJOlD+xz9rUOJK4QhZJgSefKzS7n2sc184ZmdvHrXCtJ9NNOUN6PcOzl7WvBKOjn7qmaTMzC1DDuGg/jFV0We2vK04l1wOAX3v3GEM70OXvjSUgoyQl8y7++aiCmFEKy2L8tJ4Y+3LuG2J7fx9b/v4anPViAhvMbTe3p6sFqtbNiwYTjMJpvr/nZyVgKr1ToueAa1dhm04F0QQvDAWwfZVN3N3SuL/XJLg4G/a0Kz3o6SJH0b+CKDPRsOAHcIIaxqyJdhNpsVJ5gI4XmhG61W7phv4s97W/jKn9Zy+1yTxzCbyWSipaUFIQRTpkxRcxheofUG5njgXdDKZfjDhhM8s6WGq6en8LkVk0MuT4bmFoKS3o6SJBUD3wRmCyH6JEl6iUE69qeDle8KeUNqLD9dCevMf8024kw9wZObqlk8u4i7zprqUV5tbe0o3oVQItwptqFGrPIuvLKrjl+9W8XVC4r4VKn27feys7MVH69Zb8chWSZJkmxAMqObufiELz+9s7OT7du3j1rogXRyvn/1LFp7+/nVu1UkJ+r43Dllo47xxLsQSsR5F9SFFnUo66ua+d4r+1kxZQL/96n5bNm0MaL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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
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},
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"\">\n",
" Your browser does not support the video tag.\n",
"</video>"
],
"text/plain": [
"<matplotlib.animation.FuncAnimation at 0x23d930ceb88>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mat, rad = rand_mat()\n",
"fig = plt.figure()\n",
"trans = Affine2D(block_diag(mat, 1))\n",
"grid_helper = GridHelperCurveLinear(trans)\n",
"\n",
"ax = Subplot(fig,1,1,1,grid_helper=grid_helper)\n",
"ax.set_aspect(1)\n",
"ax.grid(True, zorder=0, animated=True)\n",
"ax.set_xlim((-1.1*rad, 1.1*rad))\n",
"ax.set_ylim((-1.1*rad, 1.1*rad))\n",
"fig.add_subplot(ax)\n",
"\n",
"vs = rad*np.exp(1j * np.linspace(0,2*np.pi,100))\n",
"xs = np.real(vs)\n",
"ys = np.imag(vs)\n",
"circle, = ax.plot(xs,ys)\n",
"\n",
"trace_xs = [np.sqrt(2)*rad]\n",
"trace_ys = [np.sqrt(2)*rad]\n",
"trace, = ax.plot(trace_xs, trace_ys)\n",
"\n",
"duration = 5\n",
"fps = 25\n",
"frames = fps * duration\n",
"\n",
"plt.show()\n",
"\n",
"def init():\n",
" trace.set_data(trace_xs, trace_ys)\n",
" return ax, circle, trace\n",
"\n",
"def animate(f):\n",
" t = 5*f/frames\n",
" ani_mat = np.real_if_close(fractional_matrix_power(mat, t))\n",
" \n",
" [[tx],[ty]] = np.dot(ani_mat,[[rad],[rad]])\n",
" trace_xs.append(tx)\n",
" trace_ys.append(ty)\n",
" trace.set_data(trace_xs, trace_ys)\n",
"# npoint = ani_mat*point\n",
"# trace.set_data\n",
" \n",
" trans.set_matrix(block_diag(ani_mat, 1))\n",
" grid_helper.invalidate()\n",
" return ax, trace\n",
"\n",
"anim = FuncAnimation(fig, animate, init_func=init,\n",
" frames=frames, interval=1000/fps, blit=False)\n",
"anim"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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