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@pietromarchesi
Created April 28, 2018 12:17
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Comparing PCA and TCA with component plots\n",
"We begin by generating the data in the same way as is done [here](https://github.com/ahwillia/tensortools/blob/485ad985b9f11c71244df6f34891a5f193639d61/examples/neuro-demo.ipynb)."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"np.random.seed(2902)\n",
"import matplotlib.pyplot as plt\n",
"import tensortools as tt\n",
"from sklearn.decomposition import PCA\n",
"import seaborn as sns\n",
"\n",
"\n",
"# dimensions & params\n",
"N = 5 # neurons\n",
"T = 100 # time points\n",
"K = 50 # trials\n",
"R = 2 # number of latent factors\n",
"\n",
"lgc = lambda x: 1 / (1+np.exp((N/2-x)*0.3))\n",
"A = np.array(([lgc(n) for n in range(N)], [lgc(n) for n in range(N)[::-1]])).T\n",
"B = np.array(([np.exp(-(t-T/3)**2/100) for t in range(T)], [np.exp(-(t-2*T/3)**2/100) for t in range(T)])).T / 1.1\n",
"C = np.array(([k%2 for k in range(K)], [int(k>=K/2) for k in range(K)])).T\n",
"\n",
"time = np.arange(T)\n",
"\n",
"# generate the toy dataset from latent factors\n",
"X = np.einsum('ir,jr,kr->ijk', A, B, C)\n",
"#X += .1 * np.random.randn(N, T, K)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We then plot the factors:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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MFZt30Jdp0trEG5bA6JlQ6iPOUXs7v5vSck1LXpDEC9u4jKO+VXLcWLzdIO8Z\njhaocXYCZ7zMUmwl1AmOE65R46IssioVG99qxT6uukbUeFzsS2nH7Vy/3PhGj3lCOS72ptNfpUgk\nHD/z3u+A334Slj5c7xUZGpQb//YG1zzyGmcePoXPvGtWvZfTXw4HliqllimldgO3AycFjlGAVyet\nEzA1GDWs3roTW8HUUWUI5jFDsRW8sWl7FVdWRTaWWCHDY6QrmLe8Xp31GKpOXLe5wmxknKc1eqw/\ndoPS/LnF7AaF59q2wtNc5Zary7d1jhf/uvGkcjLMWjFoYl/wWmz5vJjYm01/lSTVCqffAmP2hzvO\nhdVP13tFhgbj/n+t5Yr7XuBd+4/jaycd2Mxd/CYBK30/r3Jf83MFcI6IrALuBz6tm0hEPiYii0Vk\n8YYNG6qx1obGE73TRw8t+ZymrpSxewdsXVn6hj+AIaOcJicmw9y0xNc1js9y5ptcxIiropng6PGy\nN57FZK4LhK1O8MU8+s+UkHWNGk+oLBaJftSUbsDYl+Dz1o0PJPZxXwy8rHPSWDIqTFuHU6N5yF5w\ny6mw6bV6r8jQIDyxbBOfueOfHDplBD8689CKPt5pUM4EFiqlJgPvBW4SkdCbVkr9TCk1Tyk1b8yY\nIl3fBiErNjkb2aaVkWHe2xXXyzc14Sa4LW8ACvaaUd55o/aGzSbD3KyU4uuFYuXWYqwTMRvEnONi\nBGqM3UD32L/AxhAYt+z495KNffTvjNkaf262QAyGz01gkSVVRJxWJ/Zxdg1nvLzYx23sK/SlF44X\nr/0c55t2XtPF3hPYaVMlowoMHw8fvgeU7XQD3LbnZc0Mhbzc1cNHfrmYKSPbue68+bS3NH0Xv9XA\nFN/Pk93X/FwI3AmglPo70AaMrsnqmojlm3bQnk4yZnhryecMaUkxelgLKzc3oWDeutz5feT08s4b\ntY+xZDQxsY/2C7KGcd7T6IxjsY1ncf5drcc2dqNctDAryNjGisF4P3Hw/RQTgzlLRswXh2rFXr9J\nsf+xjxO2BZaM0JeK/sc+GzdvzsNsMszVYfQsOOtO6O2CW06BXU346NRQEdZs3cmC6xfRnk5y4wWH\nM3JoS72XVAkWAbNEZG8RacHZ1Hdv4JgVwDEAIrI/jmA23x4DLN+0nWl7DSnbnjNl1BBWNKNg9ipd\nlCuYR+7tWDmsJm8JvocSK1aKCJ341s6l2Q2C40qpItnp6OobBRvPrGCWs4gAjfniUCgGA/MW8Ron\nlUWWZPnwAaV5AAAgAElEQVRCsRFjH1dyrlqxj4mvFyOz6a+aTJkPpy6Ern/Bneea/+j3QLbu2M25\n1z/J9l1ZbrzgcCaPLP2xeyOjlMoCnwIeAF7CqYbxgohcKSInuod9HvioiDwL3AYsUMoUKg+yfPOO\nsjb8eUwZOYSVW5pRMC+H9FDHtlYOo/YGZcHWFdVZl6GqZGKFYolCp9yKFAXZ3sLxYpng2I1nMRUg\nilWHiK0THFNruZjXOInbuCQmvk0T+xgxXb3YR8c3V4fZeJirzL7Hwfu/D6/9H/z2U6axyR5EX8bi\nIzcuZsWmHfzvuYex/4SO4ic1EUqp+5VSs5VSM5RSV7mvXa6Uutf984tKqSOVUgcrpQ5RSj1Y3xU3\nHratWLF5R1kb/jymjhrCmq192g+VhmbLG052udwNr6P2cc83toxmxMso6jyixeslxwidWC9s/t4I\nPt4v5jWOb6McvaGtaEvomGYf2Zg1Fa43IsOskrHvpXliH23JqEfsTR3mWjL3XPi3/wfP3e7UaTYM\neixbcfFtz/DUii189/SDOWKGse4awnT19LE7a/cvwzyqHctWrO3uq8LKqsjW5TByWvnneaXlzMa/\npiTWexrz+N5/fKwIKpo1DGQ5i1VUyJV4ixdX4Y1nA/cE684t1ukviWvJKGaPaIrYq9BxuvVXNPYx\n5+Y2/RlLRo14xyUw7wKnE+A/flrv1RiqiFKKy3/7PA++uI7LT5jDCQdNrPeSDA2KV+Vi+l7lZ5in\nuCK7qTb+KeVYMsr1L4OzmTrVbgRzkxLX7CMTM+b3u8a1bo4bc67fT6FYpj+36Ka/WH9u9LmFdoPw\ne00RXYe56WIfU9KvarGP8XJ7MTCb/mqFCLz3O7DfCfDHS+H5e+q9IkOV+PGflnLLEyv4+FH7cP6R\ne9d7OYYGZrlbg7mcLn8eU1w/fFNt/Nu+ETLbYUQ/Mswibmm5ZZVfl6HqxD0uj/OeluxLLbKhLfyY\nPfrRvn88riW0Mx5XVi56c1lcC+vg+pyf4+0GKWVhkYyNke7cSsS+3EoixWIf35kwzpJha4/LrSkm\n9nF1rr11mDrMtSSRhJN/AVPeDL/+OLz+aL1XZKgwdyxawf889AofOnQSX3zPfvVejqHBWb55B6mE\nMKGzrexzJ3S2kUpIc238629JOQ9TWq5pKVmYxdTWjbMFWLYiuKc4zhZQLGObF4PxwjZcVi46swr5\ncnX6dtGliUFdHJJYboa5iGCuQuyzmtgXttwuL/YZq7TYx36pKDP2cfH1xowlo9ak2+HM2xw/3u1n\nQdfz9V6RoUL830vr+NKvn+fts0bz7VMOIlHBb6OGwcmqLTuZOKK9X+WKUskEE0e0s2LzziqsrErk\nSsr1I8MMTmZ66wqzeboJifOIxlaHKFJOLROTrYwbK1kMFhFX4YoKKnIM4huixFaAiBGKACnXwxxX\n6UJ3bkPGvsROfxWNfYzYNpv+6smQUXDOr6BlmFOj2ZRJanqeXrGFT976NHMmdPCTcw6r6DdRw+Bl\n9ZYdTBrR3u/zp4xqby4PsyeYR0zt3/mdkyGzA3ZsrtiSDLUhzl8aJwZL9RrrxrMxWc7ibZRjNv3F\n1UuO8QT7x4uXlSt905+ybdJS2qa/Zoh9zmvcILHP1WE2nf7qxIgpjmjevcPpBmg+AJqW1zZs48KF\nixjX0cb1C+YzrDVV7yUZmoQ1W/uYNLL/gnnqqCHNJ5iHjoWW8jc5As7/mwDdKyu2JENtKPCXxmYy\no60I+s1lfjEY5yeOFor6NspxGeZSLQ7xNoaoMd14XEtoK+v0eIgqK1eL2MeJ17JjX0IpO91646qB\n+OeL803rxr33Yjb91ZNxc+DMW51d47edAZkmerRqAGB9Tx/nXvckCRFuPP/wstobG/Zsdmdt1vX2\nMXEAGebJI4ewaftutu/KVnBlVaS/JeU8Oic7vxvBXDYicpyILBGRpSJyqWZ8qog8IiLPiMhzIvLe\nSl7fKlHYltsSukCYhaomxFRqKLV1s9YbXaLdoOw21f73GszKxsTIE8yktFnZWsS+nA2DxWKfb4hS\nJPaBcwveS5mxz5QQ+3StBXMJN+0CEdkgIv90f33EN2b5Xg+24W1Opr8NTv45rHwS7r4ArCb54DPQ\n05fhvBsWsWXHbm44f36/mk8Y9ly6uvtQCiYPQDB79ZubZuPfluX9q5Dh0elaObpXVWY9ewgikgSu\nAY4H5gBnisicwGFfxunYeShOq/trK7mGOPFa6kauuFJhznjcuXEb2uL9uaGNfTHCrCBjG+PBLduf\nGxe/zG7n94gqGU0X+5gnA1WLfYzlJZdhrqUlo8SbFuAOtzPYIUqpX/he3+l7/UTNec3JnJPg+Kth\nyf1w/+fNhpYmYFfW4qKbnuLVdb1ce/ZcDpo8ot5LMjQZq7c6T5QGYsnwzl2ztQmeTtkW9Kzuv38Z\nnP0f6SGw1WSYy+RwYKlSaplSajdwO3BS4BgFeO1IO4E1lVxAbMWKUjeexXiNg9coNhZXJ9gZL/6I\n3rlGdFY2OKaUim3KUcrGs+D1ASxXMFskIjb9NVnsYzP4dYi9O1ety8qVctPumbz5Y/C2z8FTC+Ev\nV9d7NYYYbFvxhbue42+vbeLbJx/E0fuOrfeSDE2IJ5gHYsmY2OkJ5ibo9rdtPdhZ6JzU/zlEHFtG\nt9koXSaTAP+3jFXua36uAM4RkVXA/cCndROJyMdEZLGILN6wYUPJC4itiRwzZsU82i82blnRojdT\nLMtZwiYw55pBi4Ot/XNwrcUsDqGsrB0tBj1LRoaU1p8bl7GtVOzjfMrlxj5uw2CcbaXQN11e7Atq\na0dkxGtdVq6UmxbgZNdDdbeITPG93ubeqP8QkQ8MZLENyTGXw8FnwZ+/4QhnQ0Ny1f0vcd+za/ji\ncftx8mGT670cQ5OyeosjmPtTg9ljzPBWUglpjgyzZ6PonBJ/XDE6pxhLRnU4E1iolJoMvBe4SURC\nn+tKqZ8ppeYppeaNGTOm5Mmztp3zgEbV+00nJSRW8m2JJaLygYqe1/aNRTQYSSclUgx65+rEYP6a\nejGYTkpk2TNvLOTP9V8zIiubTkpozMo6GWYl+jrMVg1ir2vg0t/Y++eNi32x+MaN9Sf2jbjp7z5g\nulLqIOAh4Ebf2DSl1DzgLOD7IjIjeHJ/v/02BCJw4g9h5rHwu8/Cy/fXe0WGAD//6zKue+x1Fhwx\nnYuO2qfeyzE0Mau37mDM8Fba0sl+z5FMCOM725pEMLu5ks4BfskcMcVYMspnNeD/pjLZfc3PhcCd\nAEqpvwNtwOhKLSBrqdy/9bCYsRGBlmQi0orQltaLwYxl5+bV1QKOG/PmjfLnxq03N2+EuGpLh2si\ne2vwztWJwfx6g+I1f25o417GyTBLqiWyTFtTxd4X31rFvnC9EV8qalxWruhNq5TapJTa5f74C+Aw\n39hq9/dlwJ+BQ4MX6O+334YhmYZTF8KEQ5xNgCufrPeKDC6/eWY1V93/Eu970wS+csIcRExjEkP/\nWbN1YBUyPCZ2trOmuwksGT3uf/UdA7BkgCO4d2x0SnIaSmURMEtE9haRFpxNfcGN8yuAYwBEZH8c\nwVyxrFPGsmmPFCuKdCJBKpmItAy0p/Ub2ixb5ebVZTkjxZWVnzeqjXJ7jICKG8utN8J/2x4hJLO+\nawaFordGXRy8DHMimYpoU1392Ovi29/YZ+34+Obfi/5LRX9iX/jvSC/EkzXOMBe9aUVkgu/HE4GX\n3NdHikir++fRwJHAi5VYeMPROgzOvgs6JsCtp8GGV+q9oj2eR1/dwCV3P8ub9x7F/5x2cEXN/4Y9\nk9Vbdw6oQobHxBHNkmFeBS3Doa1zYPN4lTJ6gglSQxRKqSzwKeABnM/UO5VSL4jIlSLibaD/PPBR\nEXkWuA1YoILPrQeAX7zqNp6lkuI+Ltf7UtvSSX2DESs645ixFC3JBAnR2TX82ciweFKKmExmXMbW\nl5WNqEgRnXktLcMcHLNdD3Mi2RK5gbHqsQ+VYrNrH3ururGvaae/Em/ai0XkBfemvRhY4L6+P7DY\nff0R4FtKqcEpmAGGjoZz7oFECm7+EPSsrfeK9lieX93NRTc9xYwxw/jZufMG9AjdYABn4+jqrTsH\nVCHDY+KIdrq6+7SZpYaie5WTHR7okxmveYnpkFoWSqn7lVKzlVIzlFJXua9drpS61/3zi0qpI5VS\nB7uVqB6s5PUdQeLIBJ0ISiaEZCLsac0L0HAG1BvPzavJ2KaSQiqRiBG2Cc3GMjs3ppvXEYrOWNTG\ns7Z0ItxgxHdN/7H+8cgYWflzQ2NZz5Khr8OcrUHswxlx1a/YZ6zSYx+Ob/9j71g94mNfyU1/JbU3\nU0rdj7MD1//a5b4/XwZcpjnvb8CbBrjG5mLU3nD23bDwfU4L7fPvH3h2xlAWKzbtYMENixgxpIWF\n5x9OZ3u63ksyDAI2bd/N7qzNxAFs+POYMKKdrK3YuG0X4zoGPl/V6F41sAoZHrnmJWbjXzPh2A1a\ncn8OjqWTCUdcRWw8a4/IchbYIzR1hFMJIZWUyBrD7ekkW3dmIsei5o16fO+3BYTHCm0BuvE4u4YI\ntKQSoTHbtWSkkmmUcsSh/yloU8Xerk/sC202YTuMSO3LyhnKZeIhcPpNsOFluP1syO4qfo6hImza\ntotzr3+CjGVz4wXzGV8BcWMwgL8G85ABzzVpRFvBnA2Ll2EeKMMngiRNt78mI2spWqPEoCuu0kmJ\nLG3WGrHxLGvb0fPmxKBEbjxr1Ty+935ujRBXlu17L5ox79woT7B3rm68NUoo2q7XOBHOytqWI5gl\nFSGKaxB73Sa6/sTeKiP24fjl561k7DO2qqgdA4xgrh4z3gknXQtvPAq//jhoHrkYKsv2XVkuWLiI\ntd19XHfePGaOHV7vJRkGEV5JuUkV8TA3QfOSzE5no14lBHMyBR0TTaWMJsPvPdU9+k9F2AIKvbuB\nzKqtsFW0LzVrOZnWVDLuEX3YE+z32PqPza3JtmlN6S0ZGd+54U2IhfPGblLUbFpLJoRUQiNss06H\n4KSXRY7x/VYr9sFqF16Wu9zYZ8qIfVwljHJjn42p6pG17Ip2+YMSLRmGfnLw6bCtCx66HIaNh+O/\nVe8VDVqyls2nbn2af63u5qfnHMa86aPqvSTDIGNtt9e0pAKWDLd5ydpGbl7S4zaN66hQ3fLOyWbT\nX5ORtWzac35X3cazBOlktJ+4PR3uYpfxjXnzFI4rUl6WMygGc4/+NZ5g35j/Ovn15rOyUd3m2tNh\n60TGKpxXl3ltj/DRZizXE6ypXexZMpKptPbcpoq9Va/Yq6KxryRGMFebIy6G3i74x7XOxpe3frLe\nKxp0KKX48m+e55ElG7jqgwfy7gPG13tJhkHI2u4+2tPJinjiO9pSDGtNNbYlo1I1mD06JsKaZyoz\nl6EmZOxoj2jG9onBSBGUxFZOZjORkNAY6HypNumEuGIwPOadG7XxLKpkWsYVmalEWEh6P7emNLWA\ny/FGR3iN08kE29yMsodXJSPtCuaQF9nEvnjs/SX9NBlxY8loNkTg3VfB/ifCA/8PXvhNvVc06Ljm\nkaXcvmgln/y3GZz95mn1Xo5hkNLV3ceEzraK1PIWkcYvLZfr8ldBwdyzBipX9cxQZYrZDTx/btiH\nnH/MDoViJjim6/TnicFwNYv8uVFtndsixJXXxS4V0VEuHSFAg3YDnec6yjrhiTZdxlbZjmD2LBnh\n9xNvN6hE7HUx7E/sreDfaUzsdeK/v7GPrdltOyK9khjBXAsSCfjQz2DK4XDPx2DFP+q9okHDPU+v\n4jsPvsIHD53EF969b72XYxjErO3eWdFNpBM621nbyM1Lur2mJRMrM1/HJMj2wY7NlZnPUFWUUgFB\nEhZByZwYjK4F7B1bypg3nkokSCY0j+/9ftciQlEnJJOJhNZPnC14L8XEYPjcllS0ZcDxGuuqZDgZ\n55QrmP1Z25DPu0qx1/nA+xf7Yl8q8rHXxbe/sc9YKu+N1sQ+bTLMTUq6Hc64zcnW3HYGbFxa7xU1\nPY8v3ch/3v0cb91nL7598kGmi5+hqqzt7st5jyvBxBHtDZ5hXgnDxkGqtTLzed0CjY+5KQg1jdCI\nlXSEPzcTEDr+jG4oA6rb0JYU0jGP7/VtlOPFYMa1G+g2tGW8jG3EWMF6tf7cBGltKTbPaxwe8ywZ\nqXRrbh5/DAreS4PHPtxgpFaxt32ea40lw2SYm5ihe8E5dzvllW45GbZVrIPpHseSrl4uuukp9hkz\nlJ9++LDcN3yDoRpkLZv1vbuYUMEM88TONjZt301fxqrYnBWlZ/XAW2L7yQnmNZWb01A18pvHov25\nuY1nEY1AdN7TsN81LL5SiUQRMZjI+XPz1yzmz/XEoMaSUWSscL1hf27abfYR7TUOjym3rFyLptay\nib1+Xt2aorzcGcs2HuamZ9Q+cNYd0LsObjsddm+v94qajq7uPhbc8CTtLUluMI1JDDVg47bdWLaq\nqCXDm2tdT4PaMnrWVM6OAfm5ekzzkmbA39kN8rV2PTy7gbZkWuBcv5gJjoVLm7kCVCMys64I8rq3\n+cdD3ea02VM3k6kpbeaNRdUJjupU5/dch8qiWU4dZkcMFo4py7FkpFvSmvdSm9hrvdH9iH0oRjGx\n18W3v7G3bC++mmohVaiSYQRzPZg8D065ztkx/quPgN2gGaYGpLcvw/kLF9GzM8MN58+vSE1cg6EY\nXkm5SmaYc6XlGtXH3LOmshnmYWMhkTIZ5iYh1wgkFSVsHUGS1LRRDj+i14lB12OrETo5T6tGIHkt\noZ157YKxwmvq/LnevHoxmNII2/Bmwvy5ns872htt59YbHFOWWyVDY8nINR+pcuxjvdFlxL74Rs74\n+A4s9kJS08DF82NXEiOY68V+74Pjr4Yl98Mfvmh2jpdAxrL5xC1P88q6Xq495zAOmGhajhtqgydq\nK+lh9jLMXY0omPt6YFdPZTPMiSQMn2AEc5Pgiakoj6i3OS/Kuwv6R/9Bu4GuMoLXbU4nBr0x72f/\nWOE1NY/+I+wG/ixxVNWJdo0Y9MY8f65+vfoxTzC3tLS6x/rmbbrYx5eVq0bsvet7dpioyieVxNRh\nrieHfxS2Loe//QhGTIUjL673ihoWpRRfuudfPPrqRq4++SCOmj2m3ksy7EHkBXPlLRkNmWHuXev8\nXskMM7il5cymv2bAy2p6m8vCbZTzYjC6pXEid2xuzIoeA8d+4D363xnw9zuP7/O2gIIKELkWy1HW\nCb/XOGyr8Mq0WbZCKZXbRJ5vCR22G3h/TiUd20XUxrN0MpyxxS0r51ky/O+lVrGPbrldXuwtOzhv\nXOw1HvB+xN67ZtSmSu9JRSUxGeZ6864r4YAPwkNfgefvqfdqGpYf/t9S7npqFRcfM4vT5k+p93IM\nexhd3TtpTSUYMaRyfvlhrSmGt6Ua08Oc6/JXwQyzN1+3EczNgOebTbliJpzBs90x0W5KSxb4XWMe\n32u7zXltn/Wb0nK2gIKsbJEKEK6ASuvqMPtaWPvXqJu3wOLgvq900rEF6MSgM2+4O57nYc5nmP3X\ndDPMtY695Qj8asU+pfnikKv93M/YpxIxm/5MlYxBRiIBH/gpTH0r/PrjsPxv9V5Rw3HX4pV87+FX\nOHnuZD77rln1Xo5hD2RtBZuW+Bnf0ZbzRzcUOcE8obLzdkwyzUuahJwgSUYIHVuRTOrr53qZyry4\nCovBuKYcnt0glH22vY1nbgayIMNc+PjenwFVSuU2nun8xJ5Q9ASWLpOZrwDh8027xyUTbik2TbY3\nHRE/XEtGa6vrYdYI22rHPi6+5cQ+aMmIir12vZ4HvMzY57L7CX3muhqWDCOYG4F0G5xxK4yYBred\nCRteqfeKGoZHX93AZff8i7fNHM03P/QmU2vZUBe6KlyD2WN8Z1tjepg9wTy80hnmSZDdCTu3VHZe\nQ8XJC5KILKfbGCLau5vICRbdxrO0l0WOzDhqrBO+MefnsO+3vUUjrkJeY71lIC8GfV5Zu3Bev6DL\nf6nw/Ll6r3Fcp7+21pbQvE0Xe0/Y1jD2RX3etjKb/gYtQ0Y5NZqTaadGc++6eq+o7ry4pod/v/lp\nZo4dxrXnzDW1lg11w8swV5oJnW2N6WHuWQ1D9nK+zFeSXGk5Y8todDJWPsOc1rZKzjflCI5Zrt9V\nJ668rGE6JuOY9gSopq6xN+Yd6x8DaEuFM9chv6uu6oTPkmFpxKs3b2HnPJ8YjNl45pVpU74nKxKw\nZOhK5FU99lGb/sqMfbaM2Gvbcfcn9gU+b92XClOHeXAzcjqcdSds3wi3nrZH12he272TCxYuYlhr\nihvOn09Hm6m1bKgPlq1Y19NX0RrMHuM729mwbVco61J3etdW3r8MpnlJE5ETOgnPT6wXg7qxjCdA\ntcLW+bfu+WzDj9LzfuJwq2Q79wgego/vC2v2WjoBGvH4PuO14056Zdx0vt/wmF8MprTC1vVNe2LQ\nb1Wws1hKSKdS7rE6YVu92Ee1ok71I/Z5q0d87JOJhLatdipZfuy96ycT+i8Opg7znsCkuXDKDdD1\nHNx1PrjfQvckevoyLLh+Edt2Zbnh/PlVeRS+pyIix4nIEhFZKiKXRhxzmoi8KCIviMittV5jo7Fp\n2y6ytqpahlkp2NC7q+JzD4hKd/nzMBnmpiHrsxs4HeV03lOJ7Dbn2Qmcn3VZ2fDmMqWUYynw2ihr\nNp4lfWLQ/0UzWGNY63fN+X714soTtrGea005taj6zpmcGAyLV+wMWVIRfmxP2FYv9sH4erFP9SP2\n4U1/+tjrKonkKnOUG3v/hsuY2FcSI5gbkX2Pg/d+B159AP5wyR61QWZ31ubfb36K1zZs4yfnzGX/\nCR31XtKgQUSSwDXA8cAc4EwRmRM4ZhZwGXCkUuoA4DM1X2iD4VkmxlfDw9zRoKXletY4NZMrzfDx\nIAlTKaMJyPldE3qRmbGi/bk5v6vGl5oN2A38YjD4+D4kFC070p/rraEllSAhxbzGmqxsxKa/Uvy5\nqWSEP9cV/+lEInSu2FksElrrRLPF3rtGTWPv83nrOv152fJKYuowNyrzL4StK+Dx7zs1mt/22Xqv\nqOoopbj0nud4fOkmvnPqwbx9lqm1XGEOB5YqpZYBiMjtwEnAi75jPgpco5TaAqCUWl/zVTYY1ajB\n7NGQzUsyfbBjU3UyzIkkDBufr/NsaFgK7Qa6Vslhf663KdvzIad1WU6/9zRRmMksEKAJfY1hvz/X\nKnh87y8zltBaJ9KaMW+etK8CRGGDjMIsp95u4AjJXRl9HeacPcIXB7GzZCWl9wRbtYm9pRnrT+z9\n9p1isQ9vJuxf7PNPQJwvB7uzusy1yTDvORzzVTjwFHj4Cnjurnqvpup876FXuOfp1Xz2XbM55bDJ\n9V7OYGQSsNL38yr3NT+zgdki8riI/ENEjtNNJCIfE5HFIrJ4w4YNVVpuY+DVSR7XUR1LBtBYpeV6\nq1SD2aPDdPtrBjyxkozIcvpbQns/e/hbQjtjYWGb9CwZmo1cnm86ro2ys8aoyhKi3TzmvRfdxrPC\nts+FmVcRtJnVQp93lDdaX2MYO0uWpN46EfIaVyf2Or9wf2KfKSP2ug2X/Ym9v6yc1pJh2aas3B5F\nIgEfuBamvQ1++wl447F6r6hq3LFoBT/801JOmzeZi4+ZWe/l7MmkgFnA0cCZwM9FZETwIKXUz5RS\n85RS88aMGdxPArp6+kgnhb2GtlR87s72NG3pRGM1L+nxuvxVSTAPn2AyzE1Azu8a0bY443Vviyhf\nVlCzVyuuxO3QFvas5ts+azaIRdTsLcg4BgSUJ/6c6hDhJiIZy86N+Y/31ptOJLS2itx78fy5mnrJ\nnl3Dv0YAcT3MKU1mtelib9U+9kGPfTD2lm02/e15pFrhjJth5N5w+1mw/uV6r6ji/HnJer706+d5\n+6zRXPVBU2u5iqwG/G0SJ7uv+VkF3KuUyiilXgdewRHQeyxd3X2MHd5GosJ+OAARYUJne2N5mHNN\nS6pgyfDmNRnmhidvcXAES7ChhFL5Mef4wvG035eqe0SfsxtoavZGtH3OBPy5hY/vfeI14CfO20u8\nphx6ceWJzMLScU6ZtkRCSEh4LP9edH7ivNfY+bnQkmGTjLBO1Cb2lh0W0/2JfdYuPfZRXyrKj33Q\n563L7htLxp5H+0inRnOqDW45BXq76r2iivH86m4+ecvTzB43nGvPnptr52moCouAWSKyt4i0AGcA\n9waO+Q1OdhkRGY1j0VhWy0U2Gl3d1Skp5zGuo7XBBLP7HarSXf48OibArh7Y1Vud+Q0VwS9eg00u\n/HWCda2S8y2hddaJQruBzlbh2Q10bZ+9GsL+4/1/drKghQLKn1nVt1EutAUUrMm3eSxYa9lvY0hp\nNp5553qfawWb/pRFVpK+ChqaTX9Vj70+Y1ut2GtL5FmFLbfLjX2uWkhE7CuJUSfNwoipTo3mHZvh\nllNh17Z6r2jArN7q1FrubE+z8Pz5DDe1lquKUioLfAp4AHgJuFMp9YKIXCkiJ7qHPQBsEpEXgUeA\nS5RSm+qz4sagq0o1mD0mdLY31qa/njXQMhxah1dn/lwtZmPLaGQKvKfJQmHr9+7qHv3nN6WFs4aF\nmUwJjPkf7SdQKpxVTPprARdkT21EyI0XeqPzGdvgRkNvPO2WcHOuUygkvWxtsJtfsIW1tilHMuHz\nE+fHE3YGS1JaYWvZtYm9zhPsxa+c2GdLjL1e2NoFXypKjX3+34q+3bkX+0piBHMzMfEQOO1GWPcC\n3LWgqWs0d+/McP4NT7IzY3HD+YdXZUOVIYxS6n6l1Gyl1Ayl1FXua5crpe51/6yUUp9TSs1RSr1J\nKXV7fVdcX5RSToa5iv8+x3W0sb63DzvwH37d6F1TPf8y5MvV9RpbRiPj954GPaLBKg4QFlCFtYCj\nMpmJQJazUND51+GNF7RRLihfpnIWhVQymJX1CVvNBrF822f95rJ8ljMoMguFeKhNdbDtc8iSkfIJ\nRQ4uE+gAACAASURBVL3vtylib9Uj9oXrDXdZrNOmv2LNDkRkgYhsEJF/ur8+4hs7T0RedX+dV8nF\n75HMOhZO+C4sfQh+/9mmrNG8K2vx8ZsW8/rG7fzvOYex7/gqZbIMhgHS05dlZ8aqqmAe39FKxlJs\n3rG7atcoi5611bNjgK95ickwNzKFZcYCj9l9TSO0j+gDvtQoG0Nwc5lVkI2M8LT6Np7p/K7e3EHf\nr7Ner2FHUFwFfb8BMei+HhSvhb7pQqFo+7zGuqxsQmWxJEkyIYgEq1nUJvY6P3Z/Yu+14/bmjo29\ntppF+bHPvxfX5x2Iva3IZfYrRdE6zL5mB8fibAhaJCL3KqVeDBx6h1LqU4FzRwFfBeYBCnjKPXdL\nRVa/p3LYAti6Eh79jmPVeMcl9V5RySil+OLdz/GPZZv53ukHc8TM0fVeksEQSVeuaUkVBbPbEKWr\nu4/Rw1qrdp2S6VkDM/6tevN7GWbT7a+h8XtEox7fe55V//HeuFeT1xnTNZzwHt9rBKhbps1/vDfu\nz0YGKyp4Ain46N/v3XWacoRrAft9v2FbgOTO123OSycTobF8ww5/xtaXYVYWtiRz7zcTlbmuUuxD\n6y3wTVcn9toui3ZhubpyY+/FV/+lovaWjFyzA6XUbsBrdlAK7wEeUkptdkXyQ4C2rquhTN75ZTjo\ndPjT1+HZO+q9mpL5zoNL+M0/13DJe/blg4eaWsuGxqarpxaCuYGal9gWbFtXnS5/Hi1DoG2EKS3X\n4OQqQGh8vwVNQrSd6uzc5jHn+IiNZ1Fi0NdRLtgEw9u4F5zXqw7hzV3g3Q1sYFSKAgtUxlaRwtZr\nQ+2cX2i78HuN04HsafCLgf948DLMKfeYiAYu3peKKsQ+2FY7/17Kj723IdCbOyr2qaRgB2KftRXJ\nfsS+ML5RXypqb8kopdkBwMki8pyI3C0iXumqks7dk5ogVAwROPHHMP3t8NtPwrK/1HtFRbn1iRVc\n88hrnHn4FD5x9Ix6L8dgKMo6L8NcVUuGK5gboRbztvWgrOpaMsCxZRhLRlGK2SHdY04TkRdF5AUR\nubVS186L17BH1D8W9eg/yjKQccdEou0G/o5ywayi5791xoLeXdcWkExEZmxzFSsCLaMLNv1pxrx1\naatZ5NpUR3mNw9nThJ1FeRnmmPg2Rez9XuOaxd5f0k//haPSloxK5avvA6YrpQ7CySLfWM7Je1IT\nhIqSaoHTb4a9ZsId58C6oEumcXjk5fV85bfPc/S+Y/jaSQeaWsuGpsAr9za2o3pWiTHDW0kmpDEy\nzNWuwezRMdFYMorgs0MeD8wBzhSROYFjZgGXAUcqpQ4APlOp6/sfa6cDrZKDm8cg6GktLBXmFzPe\nmHe+rmZvusBuEGxk4W+jHOF3DYrXgCfYWZPzmud39Y8Fq0MU+HN1YjApYaHo8xrnM7b58aTKYrsZ\n5nSwJnKNYq/dRNeP2HsecOf84rH31juQ2PvrO6eSektLPSwZRZsdKKU2KaV2uT/+Ajis1HMNA6R9\nBJx9F7QMdWo0N2BDgH+t6uaTtz7N/hOGc81Zcyte6sVgqBZdPX3sNbSF1lSyatdIJoQxw1obI8Ps\nVa6opiXDm99YMopRih3yo8A13r4gpdT6Sl3ca2+cTAjJyMyq5OoIZwLZv1TCyWSmA2LGGwPcjXKF\nY9419fV+7YIybcGxZC7LGexi5/f9FmZPg/YH//tz3le+PFnQHpEJiMGoLKcuK5vAylkygrWWC7zG\nVYp9OCPuzzBXJ/bBWsv+Lwb9jX0yIW5zF71IrySlKJeizQ5ExP+/64k4NV7Bqen6bhEZKSIjgXe7\nrxkqyYgpTo3mvm645TTo66n3inKs3LyD8xcuYuSQFq4/bz5DW4vuMzUYGoZ1PX01KXk4rrOtMdpj\nV7sttkfHRMf+YWWqe53mphRL42xgtog8LiL/EBHtHqH+2B4zPiGZTuhrAXtiBYICKp8ZDHpaC8cS\noTHId5uDwCN6O9AIJDiWy0YGKypoxKD7WkHGVmOdsAqsHoEKEIHNeX5/bs4y4M/2BjzMdiLtHiMh\nW0U+vtWJfSjD7P/iUGbsMyXGPlhrOVhv2j/mjEfHPhuIb1TsK0nR2UpsdnCx6596FrgYWOCeuxn4\nGo7oXgRc6b5mqDQTDnJqNK9/Ee46ryE+iLp3ZFhww5PszlosPH8+Y02tZUOTsba7jwlV3PDnMaGj\nrTG6/fWshkQahlS5ek3HREANqq6ldSKF07r+aOBM4OciMiJ4UH9sj1lfpjLcRtnvH9W3Sk7lHtGH\n6/2mfI/v9W2UE6R1m9bswkoNVkAoFvpdi9kNNBnmCKuH35+rFZl+Mei+ZunGfOtNqizkPMzBLw61\nib1e2JYfe6vM2Fs5Ydv/2AdbbvvP9QvxSlKS/C6h2cFlSqkDlFIHK6X+TSn1su/c65VSM91fN1R0\n9YZCZr4L3v8DeO1P8LvP1LVG866sxUdvWszKzTv52bnzmDXO1Fo2NB/revoYVwPBPL6zLbfBsK70\nrnXsEhXOzIQYPjF/PUMUpVgaVwH3KqUySqnXgVdwBPSAsfxZw2SwjbJGrAQ2iKVjMoNRY7nubf4s\npzuulAr5c4OeYX+WMxNYT269uUf/dsH8nl/YW2PBeiNEZnDTn/9a+RrNemGbVBZ2IhUZ39rHXpNh\nrlbsvS8r/gYt/Y29poGLvz52JTFm0sHG3A/DUV+EZ26Gv1xdlyXYtuILdz3Hk69v5r9PPYi37LNX\nXdZhMAyEvozF5u27q1ohw2NcRxu9u7Js21Xn7p09a6pfIQN8zUvMlpYYitohgd/gZJcRkdE4Fo1l\nlbi4k93z/KPRbZRzNXsDHlzv9WSoVbLKeW91Y1BoncgJW18mOF/lIWwZ8I6xNOLKqz8M+Sykv9Ra\nUpPltHylzZIhe4Tv3EQwc+0v/xYWtkksVK6sXNj3W4vYa1tu9yP2BZngEmKvs2SUG/tgfWf/uf76\n2JXECObByNGXwcFnwZ+/Af+sWJWhkrn6gSXc9+wavnjcfpx0SJV32xsMVWJ9j7OPuZo1mD0mNEot\n5p4qt8X2MN3+ilKiHfIBYJOIvAg8AlyilNpUiesHs4aWrVAqLEjy4qowU+xlP51ufoWb0rxsYrA7\nXj7DrLFO+DK2zu9hIVkwphFX/mxvfuNZ3jedzz4XZl7z7yUREoq5c4ObCXUZ24IMc97DrPP9NlXs\n3ZJzubFaxL5gs2bhF5Jq1WE2O7AGIyKONaN3Ddz7aRg+Hma8syaXvukfy/npX17jnLdM5aKj9qnJ\nNQ2GarC2eydATTzM3sbCdT19zBw7rOrX06KUY5GYXYPeUu0jIdVmMsxFUErdD9wfeO1y358V8Dn3\nV0XxZ5j9HlF/O2v/JrBQaTOfpSCYNSzYIKbJcqY1tYD9LaEBtzJCoVDMV99IhDYEemsJ1vu1cu/F\n77EN1nfOi8FgibdkzmtcmD3N5t5L3hPsF4MpLEgkc+8p7N2tfuyDHnDveuXG3l+HuZTYB7P7/Ym9\ntyHQ83n756tnlQxDM5JqgdN+CaP3hTvOha7nq37Jh19cx1d/+zzH7DeWK95/gKm1bGhqcl3+amDJ\naIhuf33dkNlRG0uGiCkt1+BYdj5TGWyV7N94lgw8vldKOY/+PcEX2HiW8VkG0kF/rs9uEPT9BrOG\nwXJrhVUygm2Uo7ORhQ07NI1AArWAQ2M+K4IzX9jqERR04JSVU26GOdT22ap+7J3axfpNf9WKfXC9\nfq9xf2Kf7wKoj70ntiuFEcyDmbZOp0Zz63C45VTorl4259mVW/n0bc9w4KROfnTWoabWsqHp8cRr\nLSwZDdHtL9e0pAaWDHCaozRg3XiDg16QhL2nwY1nucyqz3sazMrmxWCwjXLYbpCf1xWgvrq8wVJs\n/myktsFInN0gkUBEwjWRC7zRQetE4RjkM9Z+MagrK5dSWVRu01+4gUu1Y1/Ol4qisbfskmIfVc2i\nP7H3N6pJxsS+khhVM9jpnOSI5l29jmju6674JVZs2sGFNy5ir2EtXHfefIa0GKePofnp6uljWGuK\n4W3pql+rvSVJZ3u6vhnmXNOSWgnmiUYwNzBOG+X8xjPwZ2V9j+8DFoew3zUorsKlwnL+XI3dIFTN\nwickwxUV/FYPvdc42EQk592NEpJWvD/XP+bEprC+czoZForgWTLS+fdS8MWhuWLv9xrXLPY+n3fU\nlwqz6c9QPuMPhNN/CRuXwJ3nQnZ3xabesn03CxY+ScZSLDz/cMYMr14LYYOhlnR19zGuii2xg0zo\nbKtzhtlrWlIDS4Z3nd61dS1/aYjGqwUMaISZL2sYWaHAJ65CG9rypcIKz80LvmDNXt3Gs1BTjoRe\nXHkZW7/X2BNyft+083tCI15LG/OvU9dB0C8k/R7mVLCaRQ1jn6+JHLZklBr7wpbbxWMf/PvuT+wL\nnihEeK7rUofZMAiY8U448Uew7M9w38UV+ZDqy1h89JeLWbVlJ784b179NisZDFWgq6ePCZ3tNbve\n+M62+maYe2qdYZ4E1m7YUZGiDoYKk/XZAiKrEPjtBoEx/7lRG8RCbar9dZgDnuDgxrNUIlHY9tm2\nc6XJghvPMrbtszgEBGhOXHmP98OZ61SJYxDOyqYS4WoWyrZJSz7DrC3TFpFhrlTsg2Xc/OK1WrEP\nCtug17j82Oc3NzpxC2bETYbZ0F8OOQuO/hI8exv8+ZsDmsq2FZ+/81kWL9/Cd087mPnTR1VokQZD\nY9DV3VcT/7LHhM46d/vrWQ1DxzobhmuBqcXc0PibRoSErc97mgo8vs9vostn/wq8p7ZGDObEq38T\nWHQbZe/cwjbKKtq7axWO+a+Vbz6Sz8pmApnMZIlj/nVmfXaDREJISH7Mspx66yqZzh1TmJXVZJgr\nHPtgA5eCNtVlxj4Y36jYh20rhZsJy4p9YEOgf53ZgNWjUhjBvKdx1H/CoefAX74NT/+y39N88w8v\n8ft/reVL792PEw6qUUbKYKgRlq1Y37urJhUyPMZ3tLNx2y52Z+3iB1eDWtVg9vAy2cbH3JD4Kx8E\nPaIF3dsiNtGV2m3Of06uAoR/c15gLP/oX+PPLWi57ffn2iGhGM7Y+kRmUAxG+HODY/7Y+L3GufV6\n8cs4tkhJJENjXiybK/Z2zWNf4PMOPTUoFOKVwgjmPQ0ROOH7jkXjvs/A0ofLnmLh46/z80df57y3\nTuOjbze1lg2Dj43bdmHZquYZZnBqMdeFnjWOTaJWdBjB3Mj4m1zkKkCEsrKJ0Fi+Y5xPXEXWCXaz\nnL7NWgmBRMJfLzkgBn1CsrCjnF0gTv1r8WoYO2OeGAwLUO/32KYcMWP+2Hhry9VT9tkjst4+omRL\nbqygWkgNY++Pb39jXxjf4rG37GBGvPzY+7PwwTrX2UCmvVIYwbwnkkzDqTfC2Dlw53mw9rmST33w\nhS7+63cvcuyccVxuai0bBimeNaKmGebOOpeW61ld2wzzsLEgSSOYG5RgW2Lwe0R1tYsDlQ98YibY\nbc4vIp358mIw6AkOeo09EeSUINM/vteVjouu2VuYjfT7fpVSTgWICE9wYUvoYL3kgI3B16nOymSc\nCdyyckldI5BkdWMftMNkfOK0WrEPermDXuNyY++PrX++TODvtFIYwbyn0tbhlJtrG+GUm9u6sugp\nz6zYwsW3P8NBk0fwwzMOrfgOVIOhUahlDWYPL8NcFx/z7u3Qt7W2gjmRdLqQmuYlDUnGCtsCgj7a\nZCLvzw15bCNqLfvtBt5niN97mrtmoFVyUNgGm3JktWIwv2ktL8S9DGhADPrsBt5r3rKTmjFv3alg\n5jpQ4s1fHi63Hs+SkcyXlSt4LxpvdKVjH9xMaPnEf7mx1wvxcOyD1gnv76DgS0WJsfd77EMCPxD7\nSmEE855MxwRHNGd2OqJ559bIQ5dv2s6FNy5m7PA2rjtvHu0tyRou1GCoLV01bIvtke/2t7Nm18yR\nKylXQ0sGuLWYzaa/RsRpchEUOsFH9H4xExRXidwxwW5+/jHwZU/9jSoCj++DvtRwm2qNn9i3aS2d\njMhyBr3GvkxmsE5wOpBZLcyWF2Y5LZ3dwB2zs06GWZKp3Fi4wUhtYu+vktHf2Ftlxj6YCe5P7HU+\n72DsTVk5Q2UZNwdOvwk2LYU7zoHsrtAhm7fvZsENi1BKsfD8+YweZmotGwY3XT27aEkmGDW0RhUj\ngOFtaYa2JOuTYfZEa61qMHsMn5AX64aGQtf22e/7FdFXTchnbGN8qVGP7zW2gExIQOXHw62SPTEY\nfvQfKisXVYrNt96gmE4mEihVWJ84HciW5ywOIauHb9OfK5jxqmSEsuXVj30yMG9Gk7GtdOx1f9/+\necuNfcgOE4i9d26lMILZAPscBSddA288Cr/9VEGN5r6MxUduXMTqrU6t5X3GmFrLhsFPV/dOxnW2\n1tyjX7dazLm22LXOMJv22I2K9vG9b+OZv8Ztgd3AVyfYGYv256YSgQyz3xYQIWwLG1kU1vsNbjzL\nCyh/xjYobO3cfN6aQn7hROG5GZ9ATUUJxYAYTPsyzJa76S+R9NVhDm76C5Xeq2zsdcI2laxy7EOd\n/jRfKqoQ+0phehgbHA4+HbpXwJ++DiOmwjFfwbIVn7n9nzyzcivXnjWXw6aZWsuGPYOunj4mdNSu\naYnHhM72+maYh9c4w9wxEXb3Ql+Ps6/C0DAUeIID1gnL14wCCh/9Z0MCtLDbnE4M+itA+LOcIv6N\nZ4FMsO/xvW0rlMqLq1BDjxjvbtD36xe2ujH/61lb0ZYuFIrBahb+jK43Zgc8zM6GwEKLQ3BDW+Vj\nHy7F5o9fqbG3yoh9UNhaA4h9xsrHPuSFr1JZOSOYDXne/gVn89+j34HOyVy19s388YUuvnLCHI5/\nU40/SA2GOrK2u4+DJo+o+XXHd7bx2Ksba35detZA+0hoGVLb6/pLyxnB3FDoNv35xaC/KYTf02oF\nxIquVXK4Q1vee+qfN+1rGZ1v+5z34Po3lvnn0wnbqI1n/kYg3u+hltDBEm/+rGyoAkRhsw//enNj\nlmPJSLge5mAL61rGvtAOU37sg2X5Sol9qMFIP2LveKMjvPCmSoah6ojA+74LM4/F/v3nWfb3ezj/\nyOlc+La9670yg6FmKKVY293HxBpu+POY0NnG+t6+glJQNaHWNZg9vGv2rKr9tQ2xOJ3z9J5W/6Y0\n8B6le+I1mBkMVFSwVUEbZfA9ovdlVr3rZiNEUNxY8NF/QRvlUGmzsO83E7BrBCth+MeDdZizATHo\nvR2/P9fKbfpryb0XWzmZ8lx8qxz7cJtqVSAwqxr7CK9xubGPLmVnNv0ZakEyxR/mfJMXrCn8b+uP\n+PIhddixbzDUkU3bd7M7a9e0QobH+M42bAUbtoU331aVWtdg9uh0BXO3qZTRaGRtOyxsfQ1G/GIk\n5cuQBrOG4VbJYTHozzgW+HOT4hOKgYyjbizC9xvfRjno+y20G/jPCYrMgoxtzuKQF6/ppOT2QSR9\nGVvPwywpr6ycmyH1x7fKsdc1cEn1J/ZW+bEPxjfK6uE/JyTwbd2GS33sK4URzIYC/vbaRv7jV0v5\n4birSHeOI3nbabDptXovy2CoGWu3/v/2zjtOjupK28/tMEFplHMWkpCQQAIhghcMGBtwEMaAyWCC\nsb3G2d7PXntZx7XZ9TqwxosxFkbkbLREG4xxREKAEEICFEAoZ2kkTepwvz+qqrvCreqemaqu7pn7\n/H4wmr5d1afPTPe8feq95xge4lED4/Awx9SLudJjsS36jwKEbi1XhbiHRkBRrNjXrHXP0AhH1bDo\nNc5L7+X7jEJcGesJrxi09Wl2r3k2nhUqr4qevYWqtsv3a/cEK7o4GM/R5vu1beqzn9fuATfiLVZl\nrbZyCbPCHJTfas99MX8Vzr2ypV/xQ4U992GhBbOmwKotzXxq0UtMGNKHH195BonLHjEW7jgHDmyP\nNziNpkJsMfsgj26qvGAeaW40rGinjEwbtOyKx5KRTBvDS3SFuerI2uwG3lHJxTVr3V4BtR+TTiRs\nVUznmufyvU2AGuvFCqnbbmD37qoqoMYxdgFl3CaEMAaFWNVe91AO23mLY6j9/MT5orB1d5bIe73G\nxT7MRoU5mUo5j1XkN+rcF8dUdy33uS7k3ts3uvO5d2zkTLo/VBRtIGGiBbMGgE17W/jEbUvpW5/i\n9qvm09QnDUOmwMUPwKGdcPf50H4g7jA1msjZus8cWjIwHg8zwJZ9FbRCWZP2Kt0hw2LAGO1hrkLs\ngyy8lUGnGEwm7N0N3NPbiv5c1Ro4/bkpV/XU7TW2j1H29AlOCMd97JXXpN1uYBOSlhgsjgFXDAIp\nVEhdGwYVdoOMfc3dzcJck7ks4Gwr55ffqHLv8UbbxL87v2Hm3j5W2+017nTuXS0IM4qfS5howaxh\n76EOrli4lLZMjtuvms9o+6XoscfAxxfBtpVw32VgfjLWaHoqW/e3UZdKMKSCQ0ssBvZJ05BOVNaS\nsd8Uq01jK/eYdprG6ApzFaKq4Nmrsg5hm0wU1oqVQa+nVdV3F1wdIFzntV9mB4qb1hRrHpFpsxTY\nh1ikXKItlSj6XdMJ4bUFJIpr9udojLB2tcizi/+kUygW2srlzD7M6TpH3Flb1dbTSSTk3Ht6LXu8\n0eXl3u0BL5V7+1ht60NZ13LvHXLjl/uw0IK5l9PakePq219k495Wfn35PKaP7O+909T3w4L/gfXP\nwaOfBVv7G42mp7FlfxujmhoqPrQEjEuWowc2srWS47Et/3DTuMo9pp0BY40YbAOTNPEipXT4QC0B\nlvPZIJZOiMKlfe9I6GJl0G0ZcA8RsbcKs9bdQznsm9a8AzvcfmKbAHWf17HmtE54rB6u51JcL4rB\nQsXWViF1VmyL3SzyWavCnHI8p2xexpb7bC7fpdy7N1yWk3uVrUK1pnou9nW3z9vhx47LkiGEOFMI\n8aYQYq0Q4usB9ztXCCGFEPPM7ycKIVqFEMvN/24OK3BN98nm8nzunld4ZeM+brxwDsdNHuJ/57mX\nwGn/Bq/dD8/8e+WC1GgqzNZ9rbF0yLAY3dTI5n2VrDBvNL7GsekPjApzpgVa98bz+BoP7nZfSVcF\n1Bgw4rQFZHIu8apo4+a+BG8JMPulf0eV0243cLcZs1eJPSOhnZfvM26rh833a1S17ZXghMJu4KzY\nOicTGmtCCJxjqoudLqxcWmvS7MOcNLtk2G0Xlcq9aoCLQ7xGlHt3ftPdyH0yIPexWDKEEEngJuAs\nYCZwkRBipuJ+/YEvAEtcS+uklHPM/z4dQsyaEJBS8m+PruSZ1dv57oIjOHNWGf7Fk74Cx34S/n4j\n/OOX0QepCZ2ufvjtTRg9mCu/4c9i9MCGgo+6IuzfDH2GVH5oiUWhF7MekV0tFNt9OaucqsvhYG48\nc480dm9ay+ULFUB73137MW4xmHJ0Y/DaOXJmRdbbC9jtz3X5ie3+XPfADkebNp947Zv+3Bv78mox\nmLIN+8hbg0tS9Y7zZnJFr3Ehf5Hl3iVsXR8cIst90tnDuRK5D4tyzjgfWCulXC+l7ADuBc5W3O97\nwA1ADHNdNZ3l58+u4Z6lG/nsqVO47ISJ5R0kBJx1A8xYAE9/A157MNIYNeESwoffHk8uL9ne3BbL\nhj+L0QMb2XmwnY5shaxP+zfF51+G4mPr1nJVg7dVmFPYGtU9tVhxX0q391r2TnZziiCP3cDW79ca\nCV3wuzpEptpu4JyOZ6tkuroxeISib59gS7yqeyKnbce6xaB9TLU028ql0s4+zNl83tbxI9rcuz3B\nOVcluNzcW7koN/fueL2bMcvLvbci7jw2rk1/Y4CNtu83mbcVEEIcDYyTUj6uOH6SEOIVIcTzQoiT\nVA8ghLhWCLFMCLFs586d5cau6SJ3L3mXnz2zhvOOGctXPzC9cwcnkvCxX8OE98Ajn4b1z0cTpCYK\n9IffEuw62E42LxkZZ4W5qREpYXtzhdLfvNnwEceFZQXZrztlVAt+VUO70PFUgl1DLqwKn73fr58v\n1e9SeirpHJXstlWASwwm/YSt/8Yzz5qtyukWg/bWZlJKbxs8e4U07xbitjHVLkuG3R5R6dw78tuF\n3Ls3XJaTe/uGy67m3t1rOeU41inEw6LbZxRCJICfAF9RLG8Fxksp5wJfBu4WQgxw30lKeYuUcp6U\nct6wYcO6G5ImgD+s2s63fvcap0wfxg8/NrtrG5vSDXDhXTDkMLj3Eti6IvxANVHQ3Q+/9vv1yA+5\nVju3OMZiW1hdajZXypYRd4W53whIpHSFuYpw2wKEEGY7MPVQjpRrDbyVwWwubxOD7o1namGWtHVN\nMOwazscEoxpuVUIL3mjXxjNlVdZnzdmmzacDhL2q7ePPdVs9jKEcpiUjb2z6S6a8XTLctoqocl9s\nK1f0GtvzG1XuHWO1A1vklc69swWhM/fpmCrMmwH79umx5m0W/YFZwJ+EEO8AxwOLhRDzpJTtUsrd\nAFLKl4B1wLQwAtd0npc27OG6u19m9pgmfnnJ0Y4XQKdpHASXPgQNA+Cu82DvhvAC1cRCiQ+/Dnrq\nh1yrnduoGCvMlh2kIp0y2vZDe3NxRHUcJJJGD2jdWq5qcFc5rX87ps35DOVwb1qz+3MzrkqwatOf\n05/r3FzmtjhYsWbzbluAd+OZU/A5/bnO7hCJQrcK98azQr9fuwB1x+vYEKiunnorzP5eY+u5hp77\nEh9WIst90n/TX1S5D4tyFNOLwFQhxCQhRB1wIbDYWpRS7pdSDpVSTpRSTgReABZIKZcJIYaZvkmE\nEJOBqcD60J+FpiRrdxzg6tuXMXpgIws/cSx96lLdP2nTGEM0Z9vgznPh0O7un1MTJV3+8FuxCGOm\nUGGO08NsivUtleiUYYnUOCvMYA4v0YK5WlALkqLQ8Xh3bUM5si6/q73XctYlBoseW7t4ddsNnD17\nC2s2O4fH9+u2MXgsBd4+zIXnYjs25z6vvRLs6g5hrdunAHr6MJv5K3TJSHs3/eUKFdtoc6+ev8F3\nIQAAIABJREFUstiF3JeykAR8cPB6wMvLvdtjX8ivQ+DHYMmQUmaB64CngdXA/VLK14UQ3xVCLChx\n+MnACiHEcuBB4NNSyj3dDVrTObY3t3HFwhdJJRLcfuV8hvSrD+/kw2fARfcZranuuQA6WsI7tyZs\nuvzhN55wK8/W/W00ppM0NaZji6GxLsmgPunKTPuzRGqcHmYwh5doD3O1oBIkhhi0tQpzj1G2tydz\niUgwBGShT7DbY2vfrJXwqTDnvBsCrccrdlRwbSbM+XiNXZf+U64KqBWLeyhHQWQq1sD0RueLz8Xp\nzy0KW6vCnE6nHHHnfMRgFLn3CltvfsvKvXvDZRm5998QWF7u3ePMi/lVi/SwKKvMKKV8AnjCddv1\nPvc9xfbvh4CHuhGfppvsb81wxcKl7Gvp4L5PncD4IRG0jppwApx7K9x/OTx4JVxwFyRDqGBrQkVK\nmRVCWB9+k8BC68MvsExKuTj4DD2fLftaGT0wnqEldkYPbKyMYLZ6MMddYW4aC6v/zxiKFMFmHU3n\nKFb3nELHdyhHUviKFbu4cvcJdvtzM64+zA5Pa87td00Ubvd4d22X792VSmu92M/XO47bOjbjthvY\n+yW7fN7FeIvV8j5+m/7yOeP+poe5OPTE6zW2jg0794mEICEIyG9EuXdM+vNOYLSOLSf3Sc+HIFvu\n9aQ/TWdoz+b41B3LWLfzIDdfdgyzxjRF92AzPgIf/DG89RQ89kU9tatKkVI+IaWcJqWcIqX8gXnb\n9SqxLKU8pTdVl8HYaDdmUEz9iG0YgrkSloxNIJLQf2T0jxVE0zjIdcChHfHGUWXE1Tc94xJB4LxE\n75nelnD2AnavGceovafOMdVuf67dbuD0Ghc7QOQ9dgN7RwX35jFrPWjanBWLry3AtpZ2CXFHBwjF\nmpQSmbcqzPXmOWwC1DWtz53fUHMfkN9yc+/2XJfKvWfKoqIiXir3hSsKZeY+LLRg7qHk85Iv3/cq\nL6zfw4/PP4qTplZgY9axV8PJX4NX7oA//TD6x9NoQmbT3lbGDopvw5/F6KYGtlRi09/+zUZbt0Qy\n+scKYuAE4+u+d+ONo4qIs2+6e2gEOH2/GXdV1tVbV1019BOD7jHVNmHm8qW6Bbx1TNZlNyh0VLBb\nBtwT5RwVW68twFmVdW48s1sykq6KrlPYevOQy0tEPkNOChLJpCMfDmHrk98wc5922DnyHj9xObl3\nWz1K5d4ubDPujh9l5r7Yyk5dYY6zD7OmxpBS8t3HVvH4a1v51w8eztlzKrgD/tRvwtxL4fkbYNnC\nyj2uRtNNWjqy7DnUwZiBVSCYBzZyoC3LgbZMtA8Ud0s5i4HmXlQtmO3E1jfd3VYOVL5ftej1tnCz\nX75X2yOKl9K9Y5TtHSDcLeeM2xWtzWy9gN2WAWPd3trMO47but3d3zlpW3P3CbbW/cWgzTOcy5Kj\n+CFVLWyjz70Vr9GVQnpa5EWRe2cbPPWHinJzH/yhQlsyNGXwqz+v57d/f4er/2kSnzxpcmUfXAj4\n8M9h6hnw+Fdg9WOVfXyNpotYnuFqqDCPMkW71eYuMpo3FUdTx0mTKZj3bwy+X+8itr7pvsLW5jV2\nVwbtbcRUQtGwTjirkWBOlDOrhlIq1mx2A5UtwHGJ3ly3+3PdrdasmBxi0LdlmtNSYG+Dp7R6OPy5\n0rNm5Y58lqxdMNtasRXirUjuE06vcbICube3yFNsCCycN8Tch4UWzD2Mh1/exI+efIOPHDWab35w\nRjybl5IpOP82GD0XHroa3n2h8jFoNJ1k415DMFdDhdmKYfPeCG0Z+ZxhyaiGCnN9P6O3u64wl02U\nfdPVgyHso5Jdm8vMNSml14dsWRF8BJTVbs3dJ9j6t3OMsqJ6mrd1gHD7fvN+FduiyMzm3WJQ0e/X\nPWhF0U7NWndOx3NWn63ciXyGrChujLdXmN0joa31KHJvfXDIqh6zzNz7eq59cm+JdOO5uMdxl5d7\nd49mK3a/3IeFFsw9iOff2sm/PLiCE6cM4cfnH0kiAtN72dT1hYsfMP4Y330B7Hgjvlg0mjKwxOnY\nKtj0N86scm/aG2GbxgPbIJ+BQROie4zOMHA87NMVZhux9U0vilen0HGOUfZ6T/NSvSkNLGGr8p4a\nm8sKm+j8egG7xGDaVo0sVmWd1dUgYRvUoxmK3mgh7B0g7P5cr2izD+Vwd4BwtNDLOy0ZjrZyFc69\nszVc53Of7ULu/Udul5d75e9KUjhyH9fgEk0NsGLTPj5z50tMHdGfX112DPWpmDfxAPQdYgw2SdUb\ng030JC9NFbN5XyvppGB4/xD7lHeRof3qqUslClXvSNi3wfg6cHx0j9EZmsZpS4aT2PqmqwSJY1Sy\nSww6Pa3uqmFRKKq8p2mryqkY2OHooOGyGzg3l1ltxtxeWZ9ODTZ/rsoTXIzXtSHQ1s2isCnN85hF\nkelXlU3kMw5LRnHsc1FkViL3KXOISFZRsY0q90lbtTyTc09g7Fzu3QNc/LzRYaEFcw/gnV2HuPK2\nFxnUp47brzyW/g3xDV3wMGgiXPKAMYL3rvOgdV/cEWk0SjbtbWVUU2O8V2ZMEgnB2EGN0VaYLfvD\nwInRPUZnGDjeiEm3pAS6PTSsW6gFiSi0+1J5jaHYGcFpq7Bfvle1GTOEjnpgh2vjmeK89o1nnkEW\nObUYdPtzUyphZgpJt9gTwrkpzS34siXEYDYnIZ8jZxuDYRe2fj7vSHJvxqu2a0SUe4cdxjtdsBBv\niLkPCy2Ya5xdB9u54ral5KVk0dXzGT4gvpG+vow6Ci68E3atgXsvhkwF+stqNJ1k896WqtjwZzF2\nUB82RVphNgVzNXiYwRDMmRZo0cNgLeLqm57NqwRJItCzCkV/qbtSaaxJ/0qmo4uDe0OgrVWYonrq\n6InsHkWdD/BN5/3EoF28OqvEYG0uU3uN0/ZewH49hvMSIbNkhXrTn29FPILcuzf9JbuQe/emPysn\nfrm3b7j0VuHLy73SY2+z2bjjDQstmGuYQ+1ZrrztRbY3t/GbTxzLlGH94g7Jn8mnwDk3w4a/wSPX\nFiYdaTTVwuZ9rVWx4c9i7KBGNu6JsMK8dwP0GwnpKvmQXeiUoTf+xU2Q71e1Zq9yukdCp1wVUPv9\nHef1EYNSGnMFMj5DOYyYnH5X4zGcwlYlFMEcYe1as253bwi04sspBnYUnoujU4PKUmBYMvLC21bO\nL79R5t7pm+587nP5zufebvXoSu6LHypcH+hsk/7sFpGw0IK5Rsnk8nzmrpdZtbWZmy4+mqPHD4o7\npNLMPg8+8ANY9Sg89XV96VVTNbRnc2xvbmdMFVWYxw3qw96WDAfbs9E8wL4N1bPhD3Qv5iqiKK4C\nKsGOiqKz369qyIXdn+ted3ZFUFQcTZGkFoOGeHVXFC1/bibAY2sdb19z+4nd57U8uKqKrd2f6x65\nbbddCOm0ZNgrwar+zlHl3hrg4iemIfzc28eHq8Zx2+MtnXufTX85pxAPCy2YaxApJf/voRX8+a2d\n/Mc5s3jfjBFxh1Q+J14HJ1wHS2+Bv/407mg0GgC2mmOoq63CDBF2yti3oXo2/EGxwqw7ZcSOcuCE\nWZVVe41tG888bdpsG7kUVo/Cpj+fgR1GPFLhNfZfs9b9uzg4/blplbA1LQXuKqe1uUy16c/y5+bz\nkrz0sU7k84h8lpytrZxDKPr4vCPJfcLqZqG2yhgxhZ17UajOu73GUeU+LLRgrkH+8+k3efjlzXz5\n/dO44Ngq+oNXLu//Hsw+H579Diy/O+5oNBo276uelnIWBcG8JwIfcy5rdK2pJsHcOAjq+utOGVVA\nRiHa0uble7V31/i3ta6aCpfLy8IYZvd6zl7lVHaWkB5PcNq95hJIwb7fYjcLv1ZsObO/s9tHm0o4\n8+AeFOJ4LvZKsM0ekZBZhyVDCGF8cLAd685vFLlPuR7TPajGijfM3KcTxRZ5uby6Il5u7t359ct9\nWKRK30VTTfz2b2/zv39axyXHjedzpx0WdzhdI5GAs38Jh3bCo9dB3+Ew9fS4o9L0YqwqbjVt+hs3\n2BDvkVSYD2wBmYOBVWTJEMKwZWhLRuwUuhC4ukdkbX5XZcsvs/rn7iEMxqX9jFLwJTiYzSrtBsXN\nZXnP5Xv3EBGV39W5Kc15bN7hz1VvPMsoxKDlz1WKQfdawikUjXgldTJLXjjlV6EncoVzf6i98rk3\nun1489vp3CsGuBTa3OlNf72bx1ds5TuPreIDM0fw3bNnxTPFLyxSdfDxO2DETLj/ctj8UtwRaXox\n7+5pIZkQjGyqkg1wwJC+dTSkI+rFvHeD8bWaKsxgCPi978QdRa+nUMl0VWUdXmOf3sVu76738r1w\n/O0qtjbziiB3v1+nd7d4+T6rqkYmE4U14/5qIenpZuHwBHu9sJYHVzUsxb2m6gCRzeVJyBw54ZyV\nUCq/UeQ+aXq5MwrxH1Xu3fH69VouJ/eeEeE+be7CQgvmGuEf63bzpfuWc8z4Qdx40dxIPj1VnIYB\ncMlD0Hco3PVx2L0u7og0vZQNu1sYM7Axkst4XUUIYbaWi6DCXOjBXGWCefAkQzDrDcGx4j85z8dr\nnLQJHZfFwe3P9Vy+t3r2qmwgCWe/X4fX2NFOzblmrLvFlVpkGjYG5/MEq9+vKl7Dg1vw/boqpPY1\nP39uIq+oMJv5VXmNI8u91aZN8fOOLPdmfB25vNfnHVHuw6J6/jpofFm9tZlrFy1j/JA+3HrFPBrS\nVTDFLyz6j4BLHwYk3PkxOLgj7og0vZB397QwYUj1+Jctxg1qZGMUHuZ9GwBR3GhXLQyaZPRiPrg9\n7kh6NWpB4hyjrO4xnDdbhRXXhBDFyW856akaWr5UVR9m+6hkw+/qv5ZKKqqRfn5XM772TM5cU1sn\n3NVnaz3n0wvY8ufmFOLfij2Xz5Mki/QIZiO/OWV1Oprcpwtt2lSbPKPJfcqVez/bSlm5d1Xa/Xze\nYaEFc5WzeV8rn7htKX3rU9x+1XwG9qmLO6TwGXoYXHy/IZbvOg/aD8QdkaaXsWF3C+MHV59gjrTC\nPGC0YY2qJgZPMr5qW0asZFTCLCEKlT/VGhT7CHsv0Rd7Lbv74xbFoL8twBrt7PDCFiqg0jMSGsyO\nCuYwD/u5rDWAtqzXMpB0CVC1GLR1llAM7OhQtT2zPZeEzJJPuD3MZlW2grlPurtZVCD31n2t3Dvy\n19ncu+wc9tynk1ow9yr2Hurg8t8soaUjx+1Xza+qllehM3YenH87bFtpeJqzHXFHpOkl7G/JsL81\nU50V5sGNNLdl2d+SCffEezdU14Y/i0GmYN7zdrxx9HKsDgVOr3EioE+w8/K9W+ikzV7LmZzT/mCs\nufy5ym4MXkuBe+OZ6vK9fdiHqhVba4eqwmwXiooqZ9LaXKbuJALQllFP1TPilSRlTm3JyPv5vCPK\nfTJh+ri94jW63BvntXLv3rhnPJdwcx8WWjBXKW2ZHNcsWsbGPa38+vJ5TB/ZP+6QomfaB2DBjbDu\nj7D4OjBfxBpNlGzYcwiA8YP7xhyJlwlDjJisGENjz3oYPDncc4bBwPEgErBXC+Y4UQ2NMMRKXnnJ\n2zEqOZ/3VPcKLb9yirWEc9qc6vK9Nf5auXms0PbMpxdwQH/nNoUtoOgJzpt2A1VF3Oa5VhxbOK9y\nE12epMwiXRVmS9i6W60ZOYkm996x5OoNg8G5D+jDrBTi3c+9esOlf+7DQgvmKiSby3Pd3a/w8rt7\n+dmFczh+8pC4Q6occy+F074FK+6DZ78ddzSaXsCG3YbloRorzBNNwfz2rhAFc/tBOLitaH+oJlJ1\nMGCsrjDHjGpoRHGMsnqwBhT7/XoFVHFUsnrTn9r3m3YJUJU/1/LgesWgU9g6+jt7xJVq01+poRz+\nwz4K8SrbtEmS5BQe5mJ+K5l7hze6S7mXFc99TtnSzy3EdR/mHo+Ukn979HWeWb2d7yw4gg/OHhV3\nSJXnpK/CgW3wt59D/1Fw/GfijkjTg3l3jyGYq9HDbIl4S9SHglW9HTIlvHOGyeCJusIcM7l83iOu\nkgmn11hVCbamzXn75xb9uV5bgDVGWT3UBGyX2VWe1lyAd9dWPVVtaCtevld7gg3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OJ5IcRJqgcQQlwrhFgmhFi2c6fi8mIErN95kEtuXUJ9KsHdnzyO0QMbK/K4mhpmzDFGn+bmzbDo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\njUaj0Wg0Afx/aK8cQHmOBsIAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x103f5a128>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f, ax = plt.subplots(1, 3, figsize=[12,4])\n",
"ax[0].plot(A)\n",
"ax[1].plot(B)\n",
"ax[2].plot(C)\n",
"ax[0].set_title('Unit factors')\n",
"ax[1].set_title('Time factors')\n",
"ax[2].set_title('Trial factors')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We then suppose that we have two trial types, A and B, with the first half of the trials belonging to type A and the second half to type B. Thus, the second trial factors (plotted in yellow in the figure above) perfectly corresponds to the trial type. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"trial_type = ['A' if int(k<K/2) else 'B' for k in range(K)]\n",
"trial_types = ['A', 'B']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot trial averages"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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qzTuvot4lBVKFEGKduDgSotRuod4zd9zn//wGHH8YTBbQafixB97zlTmntVa7ZKZrFchj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uN+cNu5a1jSbXLQunIG0RV76WwcoL1+5Pdi3FPcwnLtFFa9iyJXHzdXRyECAqizJxIYaiI5Z3Ks\nyXgx0/JjcNhcDCy8EWNJNTGOAD6KSWGTuYSPyyf3IuiXooqucSA1SX1xJ5G9ZTTmRBASEsmstkpO\nBSzBrUlumffZBf4nlyWZkYQHGXljaB7BUrI8KJlPU21EWY/Q2ThAX4fN1yEqinKZXA43lafaibNX\nIVJjOWFp40aCwTlIeerdHK7u5JGVGRj9ZOHPR6/JRCcEPzqtg+xryTn5O/Kj5vCbme3ENX6KQadR\nsLd+xK/3dkETXzbv5a2oBIJceuKPVCHXbKa+tIfZ1yRNmgVRLyZlViTmYCONpmyQktvbM/jIpGOa\no5ShDit1nYO+DtEnJvdvfYJot/Zj63cS0XCCDzIHWG2IRIfgubZZzE4KJTsuxNchjimjXse1uXFs\nrwxAi5zGxoEBPkkeILqjEPCs8aMoin+pKezAYXMRU7yLU/khhASEsrHsY0hZwjMlFkLMBu5ePPGW\nibiYxPBAHliWxhunGqjP+zoM9/CQLoLjwW04c+JI6jpB5fG2EQ2o7xiw01JZQL5WxLvBQTxSl47s\n6aUh/Vr0Rh1zVk/uD9oAer2O7IVx1Nc6ISWTxUV2Wt1DnDMZuU5/nI/KpmZvlyq6xkHdWc8ltMie\ncxzMdLC2tYahpOV81GLklnnJPo5ufNy+IIVBh0ZZxBpWWwtpitUjLDZCZC81Z6bmm09R/FnZ0RYC\njU4iesrZnlTN1qh8ArtqaJ/5ALvONnPf0jRCzP61BtXja7OwmAz8y6kAmHETa8/sYHbEDF6d009S\n6Q6k1Dizz/qFr7OzsJl7dXvYFxxKt2OIZR+1oVuwnKoqNzOWxhMYMvGWzxgLOUvicbs0+lbeheVM\nFRED8FF0KrcGnGR/2dQc16WKrnFQd7aTUHsz3ZmBuIMDWNJRx0cB69DrBFvyEn0d3rhYlB5BRrSF\nX/fkE+ZyssSSwuFcPZENR2mq7GF40OnrEBVFGaGhPgf1xZ3EtR6jd3YKzaEad7Q1QHAc/68lF4NO\nx0N+MID+syIsJh5bnckHJa2U5Pw1wt7H3+hjeD+tBy3BRHzvWUo+acQ+dPF85XJrvH6omFsNn/Bs\nXAI3V0dhaOumbem9uN0aeev9p/fvasWmhxAWG0iDIQs0jTvrE9hjCWKOVkJZVfWUvCWQKrrGWF+H\njdaaPqIbj7M7o5eNxigC9AH8pHEGK7OiiQmZXAuiXowQgjsWJvNqYyT2qFw29rSzK3uQmLYCpMZV\n399MUZTxU3G8FalBbOV+3pwzxOKo2WRWHqB/1n38/mQrty1IIjbU7Oswr8jDKzOIDQngmwc0tNxb\nWHb6TeZHz+Z/VjtILnsHp12jcH/DRb//ncImFvbs4sNgPTXuIW49KhAz8iirNZA+J5qIeMs4no1v\nCSHIWRJPi3UYmbeM5YVOKl29nDMZWCOPsafkyhad9Weq6BpjZUc9f1Rxbcc5OM3Jzc1VtCdtoKJX\ncOv8yX9d/0K3z09Gr9NxIHgT65rKaYjTQWgfAdoQ1Wpcl6L4BSklpZ82Eya7CAyysSe1mzuHXGAw\n89P+1QA8sS7bx1FeuSCTgX+9eTalzX28aPkKQm/iyfZWDiX2M5Alie0q4uSuWnpah/7ie11ujZc+\nPMnjprf4WXQs91YlYLS2UrPoYZw2N0u3ZvrgjHwrZ4ln9mr7nC0E1rQwrdPIW9EJ3Bxwkj+ebvRx\ndONPFV1jSEpJ2ZEWIoetdCa5CI6KZEFvB78dWkp0cIBfTKUeTbGhZtbmxPAfjXMIF0auMcWwP8dB\ndPNx6go71CVGRfEDjeU9dDYOEF++i08XBRMdFMW60r30zbqXFwsGuXtxCknhgb4O86pcOyueLXmJ\nfP/TXpqWfYd59af4UkQ+P1jcSlb5KwiXg/0vn0Nq8n993zuFTdzX9zw7QvVo3S42v9PO0LItVFsN\n5F+bSlTS5FyP8VJCowNJmx1FVXckmiGAe+oSec9sYA5FnC2voq3/8lf692eq6BpDrTV99LbbiK39\nmHdyBtnq0KEFxfKsNZX7l6YRYJicqxFfyp0LU6gaMNGUsJ47W2r4YPowic2f4nbLP/UKKooycZ3Z\na8WkcxLXcYrtWc18SReFUafnJ0Ob0OsEj6/N8nWIo+K7W2YRFmjk4dNZuKZdy9cKPyA0I4OdKxxk\nlf2BpooeSj9t/tPxA3YXB3e/RnzwCZ4NC+WfdlvAHExpwmZCYwJZdEO6707Gx/LWp2AbdNGzchuz\njrVjczo4EBjA7bqP2FHQ5OvwxpUqusZQ2dEWdLiJGCzmUC5sqS9kf+hWdHoT9y5N9XV4PrF+ZhyZ\n0RZ+1ruc5b2dmOIi6YvqIczRQsnBJqSUX/wiiqL4RE/rELVFHSRZP6Zqbgi6yHBuO/cJPTl38Zuz\ndh5Ylkacn47l+qxIi4kf3pFHRfsgXx96CIMlmu9XFbFjKTTEnyG8u5wDvyultqgDTZP8x/Z3uNn9\nLP8QGcM39lmIrrdx7trv0tvlYM09OZP2lj8jkTwjgshEC3URixHdfdxUEcrbMck8FLCft0+NfO2z\nyUAVXWPE7dKoONZCdHsBR+dI8gPDScTEtxuXsDU/kejgqTGA/rP0OsFjqzP5XXs6wyHp3DFo4+3Z\nQ8TX7KWraZDWmj5fh6goykWc2WdFh0ZC3V6en9fF/fooAqXGtzs3EGI28ldrJkcv13lrc2L5/m1z\nebdG8u3IH5BuDOH51i5e3mQksOfXBPVaee/ZAl76wYvEdXyL50QA33kZ8k7bKb7uX2lp17HugRmk\nzIz09an4lBCCvHUpdHdLBueuZ/NxOMwwTl0H0a0HKWsZ+Ur//k4VXWOk4kQrdpubhOYj/HH2EPc3\n13I29kaanUE8vDLD1+H51M3zkogLDeI3+lu5uamSo7MMhA+XoJdOig9Ora5mRfEXtgEH5z5tJq7t\nJA2zA+lJsHB36QFqM+5hR52Rb12XQ6Rl8q0/dfuCZP7xhhlsL5Xc5/4OObowXq4rY8fNA9SZ/5uQ\n3ioGazMIPfsdtn1yEz3xj/Dp2h/RZQ9h4yOzmLl8aiwL9EWmL47DHGykIWcLwY3dzKvR8UJ0HA8a\nPuSlw7W+Dm/cqKJrDEhNcur9OoKHW+mIrCEkPpxrBgZ4qnEV62fEMjMh1Nch+lSAQc+XV2Xwo5Z8\nLIEJrBMm3s+zEdd8lIpjLZdcA0dRFN848V4tLqeblNrd/Gx+Bw86jFjM4XzVuoHchFDuWTx5h0w8\nes00fvnAQmqdkcxp+x7P6r7BNzuD2ZDZRXf2C5i1XehjQqlPu5a+5PlMX5rILX83n+yFk/em1pfL\nYNKTvyGFpnYD/ekLebAogrcDTeQYizhy4iRtfVNjQL3B1wFMRjVnOuhuGSK3eicvrbLzlbZeysNW\nUdoWw082zfB1eBPCtsWpPLu/kpcNt/Bo03Pcn5fI+oJDNCWupGCvlSWbp97UakWZqHrbhzj7cSOJ\nbceonjaATIrgwfIidqd+i7IyA6/dMwu9Tvg6zDG1ITeO5VlR/OpQLZVtafzEdj3RwSaeWJtNalQQ\nAI5hFwajbtLfV/FKzV2XQtFHjVTP2sbcnd8ke76B7eGhPNL2Ni8cXMLTN8z0dYhjThVdo0xKycld\nNQQ6unCaSumcYWFDdTObHTdxx4IUpk/y+yyOlCXAwDevzeFf3hrk3vBI1pmDODatiYSO05z5QMfc\nNclT5lYZijLRHXmrGuF2klbzDk/dP8Q/dA6hhWXzRPlcti1OZVH61BizFGQyXHJ2psms/pd6KUaT\nnsWbM9i//Rxd2Wv4mwMFfPMeHTu7D/DgkcP0rskiLMi/bh11uVQ5PsoaSrtpqx8gteZ9Xlw1zMNt\njRwK3UyNLpVvbJzu6/AmlG2LU5mWEM0zrlv4q8YK3l0qSKt/D6fDzanddb4OT1EUoKW6l8qTbaTU\n7mHPYhtpseGs7WziyaFHSI4M4Z9unPy9E8rombEsgchEC9XZtxFhHWBJkZvnoiJ5XP6eX39a6+vw\nxpwqukaR26XxyavnCHD00GU5iT49kOuHdTzZuonHrplGfNjkmEo9WvQ6wfe2zuK5gVVgnsk6g4M9\nc1uJbzlK0X4rgz12X4eoKFOay+Fm329KCHD1E2I7yNtLJE/XlbIn8j72DaTy47vysQSo3h1l5HQ6\nwYrbs+gf0lG/5GEeOmhihzGA5KACDh/YRUP3X670P5moomsUnd5TT3frMNPLf8/L17j4dmMtP3Xd\nRnJSEk+sm1xTqUfLovRIbpmXwpe77+PRjg4+XmYksnsPmsvNwdfKfR2eokxph/9YRXerjZnFv+Zn\n6/v5xsAgwebpPNG4nifXZzM/NcLXISp+KDU3ilmrEqk252Ejia8cCOB7MbH8vfg133vrzKRer1EV\nXaOkp3WI4+9WE9t2imPpxawOGkKKmbzg3MhP7szHqAZWXtR3t85iMHwGu7iRf+xsZvuKdjJqdlJ5\nsp3yY2qVekXxBWtJF4X7G0hu2MeR7AoSk4zc3G9jW+fDbMpL5W/UB0nlKiy/LYvQmEDKFv01S09r\nRFXA6fA25lY9x86i5i9+AT+lKoFR4HZp7H2hEJ3ThqX3jxxYredLvS4e7H2Uv78+l2w1eP6SQs1G\nnr1nPt+330qmM5mkJCfNQR8S2lvNR9tL6O+aGlOJFWWi6GkdYs//nMEy1ILm3sXetQa+3dTAo8Nf\nJyQplx/ePhchJvdsRWVsmcwGNj6Ui80dQMnSr/NXe/S8KsJZEPw+77z1Ki29kzPvq6LrKkkp2feb\nYlrqh5hW+Qq/vKGf/2pr4m8HH2PNwjweWpHu6xD9wuykMJ7anM+2/q/xeI+THddBdOt2tGE7u392\nCqfD7esQFWVKGOi28/aPjuPu7ye19n/45RY3P2+08u+OL9MYsYjnH1iA2Th1b2mjjJ74zDDW3DuD\nDmMK1VkP8PSbBr4XHMOXdT/lH17cyYDd5esQR50quq7SsR1VlB9vJ6PmHf648BTfdLXysm0bxpyN\n/Nsts9Wnwctw75I07li/lL8e+Bo/7mrjxZu6yKx6mVarjZ3PnMDlVIWXooylwR47b//nUWzdQ2SV\n/4xnN3fwo+4GXrLfy9mYG3nl0aXEhqgJQcroyV2ZyJItGbREzacv4ha+9argB6EBPNH/NP/3pT24\n3JqvQxxVqui6QlKTfPraOU7sqie++TB7Zu5hbXw3+/pu51zaffx023wMahzXZfvGhmxWrr2Bfx58\nku8Md/LKNQVkVb5MY9Ugu545rnq8FGWMtNb08ep3D9HXNkh61S94bmsD/9fVxs8GHuVs8jZ+95Wl\nRE3Re8YqY2vBpnTyN6TQkLCKzsRH+fIbQfwwyMANrX/LU7/aRf/w5LlLiZhoswQWLlwoT5w44esw\nLskx7GL3T49RXzVMQtNBjqa9xoaUDg723oFz4Vf43pZZauD8VZBS8sLBGt5/fwd/Z/kxz8lgbjuw\ngrqMbYSFwg1fX0JkosXXYSqja9J0CftDDruQ5tYo/LCWw3+sxmTrIqr5F7x7bSPfGLbzb0NfZf7q\nm/n6hmz1IVIZc2c/buDAK+UEDrWRWfkybyyvZnnsEOfkYzz0yNdIi5qweX/E+UsVXZdBapLSj2v5\n9PUy7C4DSdbX+WDBx9wS6OIF2xPccMNW7luapi4pjpKTdV18/+WdPOZ6hveMvaw4MJuOxAdxm4JY\nsD6R/M0z1ArQk8ekedNM5Bx2ISklDSUdHHjxFD2DRiI7i2kK2I57QRvTu6fxq5An+dbNy1iVHePr\nUJUppKGsmw9fKGKwz0VC82EG5U5KFraTITIxzHuKbddeQ6Bpwo0pHN2iSwhxPfAMoAd+KaX8j888\nHwC8BCwAOoG7pJS13ueeBh4B3MDXpJS7L/WzJmLCsttclLx3ljMf1THoDCG0rxa78zX6F5QSOjiP\nkqyv8c2tS0kMD/R1qJNOr83Jz/eX4Tz8c5JCdtJWHkd6zzY6o+diwMacRRHM2pJHWMyE/QSkjMyY\nFV3jmb9gYuawC9kGHJTvLaNgbw0DjmAChruxdL1O4dyTLA0084HrHvLX3sEDy98RdMMAAArWSURB\nVDMwGVTvljL+HMMuTrxbTcGHVqTUiG0voF93iM7Uc4iYVBKnP8yadVtIjAjydajnjV7RJYTQA+XA\nRqABOA5sk1KWXHDMXwNzpZRfFULcDdwipbxLCJEL/B5YDCQCHwLTpZQXHZgzERLWUI+NxoIqqk+U\n0FJlY9Adj9QZsQw0IB176cn5lABTFp1pT7Bl7QryUsJ9Gu9U0Nhj4+V9BRiKf4lRfoy+Yjphjhvp\njfDcgiRQNhOVoJG5YDqpi2YSGhuCmOQ34J1kxuSXNd75CyZGDjtPc2v0tfZTe6yY+jPVdDbDkIwH\nocMy0Aj2j2hPPUxoRDit5puZvupObp6fomYnKhNCX6eNwt3VFB9sxKUZMLiGCO05h01fgyOkDmeE\nk4CMmeTk30jW9IUkRoX76krTqBZdy4DvSimv824/DSCl/PcLjtntPeawEMIAtAAxwFMXHnvhcRf7\neZeTsN780Q8Z7h70bnnOQ8rz/wGpefdqnkuDSJBuAW6JdOu8DwNoAUgtEE2E4taH4zb8udckaLAR\n4SxjOOQY/UkDWGI2EL/gXlbPTleDSn3A7nKzv7iB+lO76Gt6g8BGG4E9C9CLuQxaUpE6z/8shObA\n6OxCyD6EGETo7Ai9CwxuhE4i9BKhA6EHdHjeqAKEwPP2Ob99/gf/r7eUZ0NdRb603I3XkLdq3UgP\nH6uia1zzF4w8hx3e+RY1Rwq8WxfkYe+Xnlzm2XH+a6lJpOZ5UrqFN58JpKZDuvXgNiFlAFJa0HQh\nuAyRf35PSDdBg41I91nswYUMJPYTFL2GsBlbWTl/zkQeL6NMcU6HG+vZdso+KKGhZgAHwX96zuAa\nwmjvRsg+JAMghpE6O+jdoHd7crwehF4HOoFOLxA6gdDpQAhv7pcIIRAIpDexhyZEsvnxJ0ca4ojz\n10gGxCQB1gu2G4AlFztGSukSQvQCUd79Rz7zvUl/Ea0QjwKPAqSmpo40droLIxgOXDDi4/+Shh47\nejmIThtCr3Wid1WhubpwB3Uho13oc+aSnL6JaTlPkRplUeO1fCzAoOf6vDTI+ypSPkZ7v53yqiqs\nFR9iq96OaHChHwpF54xGyAg0EYrUJ+MiEDeBSE0PGjD5ln+ZcIr3fHw5RddYGfP8BVeWw8reP8qg\nc+OIjh0JHXb02NBpNnRaPzpXHXrXaTRjN25LHyQaMaTnkTrtPlLTs0iNsqBTvcGKHzCa9GTOjydz\nfjwAg712mgutNBRV0FrVxFCfG7c7CI0YNJ0ZTRf4pw8bgGdwwGVOfB+2FsDjo3cO502IUchSyueB\n58HzKXGk3zftpkBsvWV/2hZC9+d/vRUteh16nQ690YDOaMQYGIgp0ExgWDjBEVEEh0QSFBSMyaBX\nBZWfEUIQG2omdt4smDfrosc53RrDw8P09bUz2N2Fra8H+8AAzmEHLrsDt9uF2+X09IBKiXRLpNQ8\nvQmSz70P2ESbgDIRzVxxm69DGDdXksOW3H8TNWfOXLDnz/lHnP8ErvPkM533U7reYEBv0KMzGDGa\nAzCaTZhDwwkKDyM4NJpgSzgmkxG9KqaUScwSFkDWqiyyVl38VlRut4ZzwMZQby8D3R309fZgHx7C\nPjSI2+XC5XSguTWkpqFpGlK60bQ/dzOHx2WMSewjKboagZQLtpO9+z7vmAZv93wYngGpI/neK7bm\njntH66WUScyo12G0BBFiSYOENF+Ho4yvCZu/Zi5ewczFK0br5RRFuYBer0MfZsEcZiEyNdHX4fzJ\nSKamHAeyhRAZQggTcDew4zPH7AAe9H59O7BPeroCdgB3CyEChBAZQDZwbHRCVxRF+UIqfymKMmF8\nYU+Xd4zDE8BuPFOuX5RSFgsh/hk4IaXcAbwAbBdCVAJdeBIb3uP+AJTgGUXz+BfN/FEURRktKn8p\nijKRqMVRFUWZCCbNICSVwxRlyhlx/lIr3ymKoiiKoowDVXQpiqIoiqKMA1V0KYqiKIqijANVdCmK\noiiKoowDVXQpiqIoiqKMA1V0KYqiKIqijANVdCmKoiiKooyDCbdOlxCiHai7jG+JBjrGKJyx5q+x\n+2vc4L+x+2vcMLLYO6SU149HMGPtMnPYZP+9TlT+Gru/xg3+G/uo5q8JV3RdLiHECSnlQl/HcSX8\nNXZ/jRv8N3Z/jRv8O/ax5s9to2Iff/4aN/hv7KMdt7q8qCiKoiiKMg5U0aUoiqIoijIOJkPR9byv\nA7gK/hq7v8YN/hu7v8YN/h37WPPntlGxjz9/jRv8N/ZRjdvvx3QpiqIoiqL4g8nQ06UoiqIoijLh\n+W3RJYS4XghRJoSoFEI85et4LkUIkSKE2C+EKBFCFAshnvTujxRCfCCEqPD+G+HrWD+PEEIvhDgt\nhHjXu50hhDjqbftXhRAmX8f4eYQQ4UKI14UQ54QQpUKIZX7U5t/w/q2cFUL8XghhnqjtLoR4UQjR\nJoQ4e8G+z21n4fHf3nMoFELM913kvuUvOczf8xeoHDbeVP66OL8suoQQeuBZYBOQC2wTQuT6NqpL\ncgHflFLmAkuBx73xPgXslVJmA3u92xPRk0DpBdvfB34ipcwCuoFHfBLVF3sGeF9KOQPIw3MOE77N\nhRBJwNeAhVLK2YAeuJuJ2+6/Bj67Rs3F2nkTkO19PAr8fJxinFD8LIf5e/4ClcPGjcpfX0BK6XcP\nYBmw+4Ltp4GnfR3XZcT/NrARKAMSvPsSgDJfx/Y5sSZ7/+jWAe8CAs9CcYbP+11MlAcQBtTgHbd4\nwX5/aPMkwApEAgZvu183kdsdSAfOflE7A78Atn3ecVPp4c85zJ/ylzc2lcPGN26Vvy7x8MueLv78\nSz2vwbtvwhNCpAPzgKNAnJSy2ftUCxDno7Au5b+Avwc073YU0COldHm3J2rbZwDtwK+8lxV+KYSw\n4AdtLqVsBP4TqAeagV7gJP7R7uddrJ399r07yvyyHfwwf4HKYeNK5a9L89eiyy8JIYKBN4CvSyn7\nLnxOesrmCTWVVAhxE9AmpTzp61iugAGYD/xcSjkPGOQz3fATsc0BvOMHtuJJuomAhb/s/vYbE7Wd\nlcvjb/kLVA7zBZW/Ls1fi65GIOWC7WTvvglLCGHEk7B+K6V807u7VQiR4H0+AWjzVXwXsQLYIoSo\nBV7B0z3/DBAuhDB4j5mobd8ANEgpj3q3X8eTwCZ6mwNsAGqklO1SSifwJp7fhT+0+3kXa2e/e++O\nEb9qBz/NX6BymC+o/HUJ/lp0HQeyvbMhTHgG6e3wcUwXJYQQwAtAqZTyxxc8tQN40Pv1g3jGSkwY\nUsqnpZTJUsp0PG28T0p5L7AfuN172ISLG0BK2QJYhRA53l3rgRImeJt71QNLhRBB3r+d87FP+Ha/\nwMXaeQfwgHcW0FKg94Ju/KnEb3KYv+YvUDnMR1T+uhRfD2C7ioFvNwDlQBXwf3wdzxfEuhJP92Qh\nUOB93IBnbMFeoAL4EIj0dayXOIc1wLverzOBY0Al8BoQ4Ov4LhJzPnDC2+5vARH+0ubA94BzwFlg\nOxAwUdsd+D2esRtOPJ/OH7lYO+MZxPys931bhGeGk8/PwUft5hc5bDLkL+95qBw2fnGr/HWRh1qR\nXlEURVEUZRz46+VFRVEURVEUv6KKLkVRFEVRlHGgii5FURRFUZRxoIouRVEURVGUcaCKLkVRFEVR\nlHGgii5FURRFUZRxoIouRVEURVGUcaCKLkVRFEVRlHHw/wFYdJjyvhRCigAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x103dc3390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"A_trials = np.sum([X[:, :, i] for i in range(K) if trial_type[i] == 'A'], axis=0) / K\n",
"B_trials = np.sum([X[:, :, i] for i in range(K) if trial_type[i] == 'B'], axis=0) / K\n",
"\n",
"f, ax = plt.subplots(1, 2, figsize=[10,5])\n",
"ax[0].plot(A_trials.T)\n",
"ax[1].plot(B_trials.T)\n",
"ax[0].set_title('Trials A')\n",
"ax[1].set_title('Trials B')\n",
"sns.despine(fig=f, right=True, top=True)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## PCA\n",
"Below, we apply PCA on per-trial-type trial-averaged PCA. That is, we compute the trial average separately for each trial type, and then concatenate the averages. "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"A_trials = np.sum([X[:, :, i] for i in range(K) if trial_type[i] == 'A'], axis=0) / K\n",
"B_trials = np.sum([X[:, :, i] for i in range(K) if trial_type[i] == 'B'], axis=0) / K\n",
"Xp = np.hstack((A_trials, B_trials)).T\n",
"pca = PCA(n_components=R)\n",
"Xt = pca.fit_transform(Xp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot PCA components"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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5UpHOP7LUv3RZ0CVfKSdzAO10r9yjyZeKOOXlsHu3u8lXhw72UZMvFalW25V8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\no1076HRGfY69sC1JrZuE/o9vtfHLL25bouXLYeVKt0Tzhg1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"text/plain": [
"<matplotlib.figure.Figure at 0x109a1b2e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f, ax = plt.subplots(1,R, figsize=[10, 5])\n",
"\n",
"for comp in range(R):\n",
" ax[comp].plot(time, Xt[0:T, comp], label='A', c='r')\n",
" ax[comp].plot(time, Xt[T:, comp], label='B', c='b')\n",
" sns.despine(ax=ax[comp], right=True, top=True)\n",
" ax[comp].set_title('PCA Component {}'.format(comp))\n",
"\n",
"ax[1].legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From this, we can tell that both components, but predominantly the first one, captures the difference between trials of type A and trials of type B, corresponding to the second peak in activity which is only present in trials of type B. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot PCA components by trial type\n",
"We can also see how each trial type is reconstructed as a combination of the two components."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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EECK4Kt3tvj9HSPLcKzurZOqKT0lSFuGOtthJirOSmuC/knSjPGUxHH67hhBC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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x109c66e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f, ax = plt.subplots(1, 2, figsize=[10, 5])\n",
"ax[0].plot(time, Xt[0:T, 0], label='1st component')\n",
"ax[0].plot(time, Xt[0:T, 1], label='2nd component')\n",
"ax[1].plot(time, Xt[T:, 0], label='1st component')\n",
"ax[1].plot(time, Xt[T:, 1], label='2nd component')\n",
"sns.despine(ax=ax[0], right=True, top=True)\n",
"sns.despine(ax=ax[1], right=True, top=True)\n",
"ax[0].set_title('Trials A')\n",
"ax[1].set_title('Trials B')\n",
"ax[1].legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## TCA\n",
"\n",
"Here, we show two possible ways of generating components plots similar to the PCA ones shown above. This of course in a sense __defeats the purpose of TCA__, which is the ability to caputre trial-to-trial modulations in neural responses. Thus, they could only be applied if the trial factors differ across trial types but undergo no significant changes otherwise (e.g. no change over the course of sessions or recording days). In this example, this is true for the second trial factor, which is solely determined by the trial type but other than that remains stable across trial, but it is not the case for the first component. Here, we consider this purely as an example.\n",
"\n",
"Regardless of the crucial caveat of throwing away trial-to-trial variations, even in this case I would say that TCA does a better job at extracting clear and interpretable components, possibly to the nonnegativity constraint. Let's first fit a tensor decomposition:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\r",
"iter=1, obj=0.3298, variation=0.8344\r",
"converged in 22 iterations."
]
}
],
"source": [
"model, info = tt.cp_direct(X, rank=R, nonneg=True, options=dict(tol=1e-8))\n",
"\n",
"unit_factors = model[0]\n",
"time_factors = model[1]\n",
"trial_factors = model[2]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. Plot time factors weighted by averaged trial factors\n",
"Here we average the trials factors for each component separately for the two trial types, and use these to weigh the time factors returned by the decomposition."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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1JWO7lmTnFGWsvp6q3UuPe08REcm9rnY/R6cpU99TBk/JWBFqboZTToHRm5Zn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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x109e86f28>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"trial_factors_A = trial_factors[0:int(K/2), :].mean(axis=0)\n",
"trial_factors_B = trial_factors[int(K/2):, :].mean(axis=0)\n",
"\n",
"f, ax = plt.subplots(1, R, figsize=[10, 5])\n",
"for comp in range(R):\n",
" ax[comp].plot(time, time_factors[:, comp] * trial_factors_A[comp], label='A', c='r')\n",
" ax[comp].plot(time, time_factors[:, comp] * trial_factors_B[comp], label='B', c='b')\n",
" ax[comp].set_title('TCA Component {}'.format(comp))\n",
" sns.despine(ax=ax[comp], right=True, top=True)\n",
"ax[1].legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see from this plot that the first component captures the first peak which occurrs in both trials types, while the second component captures the second activity bump which occurs only in trials of type B."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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JXGtNq40nOmqiO0XpKppnmbEYsWAsgYVCSn17X1TbWrjczFgoZD1nTGBNtofi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\n0xjjuTdr2qmqLETivO3PRbMLyEhL8V/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efTKTf+b99oryMhncN5OlO2J8MV5jTFyt2VVH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\nxhgPWTFmjDHGGOMhK8aMMcYYYzz036xNTiLyLeJEAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1093bdf60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f, ax = plt.subplots(1, R, figsize=[10, 5])\n",
"ax[0].plot(time, time_factors[:, 0] * trial_factors_A[0], label='1st component')\n",
"ax[0].plot(time, time_factors[:, 1] * trial_factors_A[1], label='2nd component')\n",
"\n",
"ax[1].plot(time, time_factors[:, 0] * trial_factors_B[0], label='1st component')\n",
"ax[1].plot(time, time_factors[:, 1] * trial_factors_B[1], label='2nd component')\n",
"\n",
"sns.despine(ax=ax[0], right=True, top=True)\n",
"sns.despine(ax=ax[1], right=True, top=True)\n",
"ax[0].set_title('Trials A')\n",
"ax[1].set_title('Trials B')\n",
"ax[1].legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From this plot, we clearly see how the two time factors combine to generate the prototypical population activity across the two trial types."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Projecting weighted trial averages using unit factors\n",
"Here, to generate component plots in a similar style to the previously shown component plots of PCA, we average trials _per type_ using the trial factors as weights. Then, we project the resulting two average trials onto the different components (i.e. the different unit factors)."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"tdict = {t : {c : [] for c in range(R)} for t in trial_types}\n",
"\n",
"for comp in range(R):\n",
"\n",
" # trial average per trial type weighted by trial factors of each trial\n",
" for trial_index in range(K):\n",
" weighted_trial = X[:, :, trial_index] * trial_factors[trial_index, comp]\n",
" tdict[trial_type[trial_index]][comp].append(weighted_trial)\n",
"\n",
" # project the weighted trial average onto the nth component\n",
" for type in trial_types :\n",
" tdict[type][comp] = np.matmul(np.mean(tdict[type][comp], axis=0).T,\n",
" unit_factors[:, comp])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot TCA components"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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wci78NhtjjOk6b7Rh/PjOfZ8XrOy6H7wOg5WI5ADfB24CJgB3iciEVseMAR4CZjrnLgQ+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\ncMEFFqz85pyb75wb65wb7Zz7Ruq5R5xz81J/vt4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"text/plain": [
"<matplotlib.figure.Figure at 0x10929fda0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f, ax = plt.subplots(1,R, figsize=[10, 5])\n",
"for comp in range(R):\n",
" ax[comp].plot(time, tdict['A'][comp], label='A', c='r')\n",
" ax[comp].plot(time, tdict['B'][comp], label='B', c='b')\n",
" sns.despine(ax=ax[comp], right=True, top=True)\n",
" ax[comp].set_title('TCA Component {}'.format(comp))\n",
"ax[1].legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we can confirm that the difference between trials of type A and B is by both TCA components."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot TCA components by trial type"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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o9JI2RwIrMXNore+Y4HUN/HWEpiNE8MLVasE0suWCBFYhI0uBUaLO1RuWVgum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\nQgghhBAB8r9SV7WZZ0buiAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x109c16048>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f, ax = plt.subplots(1, 2, figsize=[10, 5])\n",
"ax[0].plot(time, tdict['A'][0], label='1st component')\n",
"ax[0].plot(time, tdict['A'][1], label='2nd component')\n",
"ax[1].plot(time, tdict['B'][0], label='1st component')\n",
"ax[1].plot(time, tdict['B'][1], label='2nd component')\n",
"sns.despine(ax=ax[0], right=True, top=True)\n",
"sns.despine(ax=ax[1], right=True, top=True)\n",
"ax[0].set_title('Trials A')\n",
"ax[1].set_title('Trials B')\n",
"ax[1].legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plotting neural trajectories in PCA space\n",
"Here, we add some noise and refit both PCA and tensor decomposition so that the trajectories will not overlap exactly in the plots. Then we plot the neural trajectories (the lower-dimensional projections) in the space identified by the first two components of both PCA and TCA."
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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KJk2axJVXXunynJza4tScUWRkZTPYlIMp/gJ7Y8VR/GQl2+t683lqG3uWFz4EPr1g/rXw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\nzSvQYYz/ZodhERI7OnOIlMubuhwi63l3ruwMqVe6e5W0Uz7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XO8K8aZJbfv4LcM9WuPAl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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x109dee828>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.einsum('ir,jr,kr->ijk', A, B, C)\n",
"X += .1 * np.random.randn(N, T, K)\n",
"\n",
"A_trials = np.sum([X[:, :, i] for i in range(K) if trial_type[i] == 'A'], axis=0) / K\n",
"B_trials = np.sum([X[:, :, i] for i in range(K) if trial_type[i] == 'B'], axis=0) / K\n",
"Xp = np.hstack((A_trials, B_trials)).T\n",
"pca = PCA(n_components=R)\n",
"Xt = pca.fit_transform(Xp)\n",
"\n",
"f, ax = plt.subplots(1, 1, figsize=[5, 5])\n",
"ax.plot(Xt[0:T, 0], Xt[0:T, 1], label='Trials A')\n",
"ax.plot(Xt[T:, 0], Xt[T:, 1], label='Trials B')\n",
"sns.despine(ax=ax, right=True, top=True)\n",
"ax.set_title('PCA trajectories')\n",
"ax.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plotting neural trajectories in TCA space\n",
"We do the same thing now for TCA, using the two methods outlined above to determine the components. Of course, we should be aware that TCA axes, contrary to PCA axes, are not constrained to be orthogonal."
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\r",
"iter=1, obj=0.5992, variation=0.5543\r",
"converged in 8 iterations."
]
},
{
"data": {
"image/png": 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GvroTEpfDFa9D41j34vMQbyZjjmOt1y3Os89pyW6FopTyjhnAdc6oyrOBFGPM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\nIQvGjDHGGGNi6P8BnPU/eeuFdy8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x109c93358>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"model, info = tt.cp_direct(X, rank=R, nonneg=True, options=dict(tol=1e-8))\n",
"\n",
"trial_factors_A = trial_factors[0:int(K/2), :].mean(axis=0)\n",
"trial_factors_B = trial_factors[int(K/2):, :].mean(axis=0)\n",
"\n",
"unit_factors = model[0]\n",
"time_factors = model[1]\n",
"trial_factors = model[2]\n",
"\n",
"tdict = {t : {c : [] for c in range(R)} for t in trial_types}\n",
"\n",
"for comp in range(R):\n",
" for trial_index in range(K):\n",
" weighted_trial = X[:, :, trial_index] * trial_factors[trial_index, comp]\n",
" tdict[trial_type[trial_index]][comp].append(weighted_trial)\n",
"\n",
" for type in trial_types :\n",
" tdict[type][comp] = np.matmul(np.mean(tdict[type][comp], axis=0).T,\n",
" unit_factors[:, comp])\n",
"\n",
"f, ax = plt.subplots(1, 2, figsize=[10, 5])\n",
"\n",
"ax[0].plot(time_factors[:, 0] * trial_factors_A[0], time_factors[:, 1] * trial_factors_A[1], label='Trials A')\n",
"ax[0].plot( time_factors[:, 0] * trial_factors_B[0], time_factors[:, 1] * trial_factors_B[1], label='Trials B')\n",
"ax[0].set_title('TCA trajectories, method 1')\n",
"\n",
"ax[1].plot(tdict['A'][0], tdict['A'][1], label='Trials A')\n",
"ax[1].plot(tdict['B'][0], tdict['B'][1], label='Trials B')\n",
"ax[1].set_title('TCA trajectories, method 2')\n",
"\n",
"sns.despine(ax=ax[0], right=True, top=True)\n",
"sns.despine(ax=ax[1], right=True, top=True)\n",
"ax[0].legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we can see how neural activity evolves over time in the space constructed by the first two TCA components. In both cases, it is clear that while neural activity in trials of type A only move along the direction identified by one component, in trials of type B both components are 'recruited'. \n",
"\n",
"Interestingly, with the first method, we get exactly the same trajectories as we obtained with PCA (with the only difference that the PCA trajectories were rotated in PCA space and perhaps a bit more noisy).\n",
"\n",
"This type of plot can of course be extended to a 3D plot. "
]
}
],
"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": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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