LuxXx/LinearModel.ipynb

## LinearModel.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sympy\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "std = 1\n",
    "N = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_obs = np.arange(N)\n",
    "y_obs = np.arange(N) + np.random.normal(0, std, N)\n",
    "model = lambda x: [1, x, x*x]\n",
    "x_obs, y_obs;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = sympy.Matrix([model(k) for k in x_obs])\n",
    "y = sympy.Matrix(y_obs)\n",
    "gamma = (x.T*x).inv()*x.T*y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = sympy.Symbol('t')\n",
    "A = sympy.Matrix(model(t))\n",
    "mf = lambda v: ((A.T*gamma)[0]).subs(t, v)\n",
    "mf = np.vectorize(mf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1187fa30>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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c+++vaXNIfWZcdzK3D+up0JeDimTO3blm1qnUsvdKPP0vcFHlliUi4RQWOS9+tpZH3luOO9wx7CguP6kTdSthzltJDJVxaHAFMCnMOgfeMzMHnnX3ieFexMxGA6MBUlNTK6EskdpncVYOY6ekszAjh0E9WnHv8F50bKE5b6V8ogp+M7sdKAD+FabJQHfPMrPWwGwzW+buc0M1DP5SmAiBydajqUuktiieQSszO5fG9euyZ18BLRrV46+XHsO5fdpqzlupkAr/bWhmowhc9L3M3UMGtbtnBb9uBqYC/Su6P5FEUzyDVvHQyrv2FmAYN57ZnfP6tlPoS4VVKPjN7GzgVuB8d98Tpk0jM2tS/BgYDCyqaKEiiebBd5YdMINWoTtPz1kdo4qktjho8JvZK8DnQA8zyzCzK4GngCYETt8sMLMJwbbtzGxmcNM2wCdm9i3wJfC2u79bJf8LkVrE3Zn2TSYbd+SFXB9uZi2RSEXSq+fSEIufD9M2CxgafLwG6BtVdSIJZv32Pdw+bRFzV2whuY6RX3jgWdSSM2iJVIQ6/IrUAAWFRcEumitIMrj7vJ4c0iCZ26ctCjuDlkhFKfhFYmxJ1g7GTFnIwowczjiyNfeO6PXjUX1Skh0wg1bJiVVEKkLBLxIjefmFPPnBSp6du4bmDZN58tJjOK9UF83SM2iJVAYFv0gMfL56G7dNTee7rbu5+LgO3D7sKJo1rBfrsiRBKPhFqlFObj4PzFzKq1+tJ7VFQ/511QAGHtEy1mVJglHwi1STdxdt4E/TA6NoXn1qF244szsp9TQFolQ/Bb9IFdu0I487py9i1uJN9Gx7CC+MOp7eHZrGuixJYAp+kSpSVORMmree+2cuZV9BEWPOOZIrT+5MskbRlBhT8ItUgbVbdzNmykL+u2Y7J3RpwQMX9qFzy0axLksEUPCLVKqCwiKe++Q7Hpu9gnp1k3jgwt6MPL6jBlSTGkXBL1JJFmflcOvkhSzK3MHgnm24d0Qv2miic6mBFPwiUcrLL+Sv/1nJhI/W0LxhPZ6+7FjO6XWYjvKlxlLwi0Thq7XbuXXyQtZs0Y1YEj8U/CIVsGtvAQ+9u4yXP19Hh+Yp/OPK/pzSrVXItsWzaGm8HakpFPwiESgZ3i0a1aPQnZzcfK4Y2Jk/DO5Oo/qhf5SKZ9EqHmEzMzuXsVPSART+EjPqUCxyECWnQHRg2+595OzJ5/rTu3HneT3Dhj7A+FnLD5hFKze/kPGzlldx1SLhRRT8ZvaCmW02s0UllrUws9lmtjL4tXmYbUcF26wMztMrElceevfAKRAdeGN+xkG3DTdblmbRkliK9Ij/ReDsUsvGAB+4ezfgg+Dz/ZhZC+AuYACBidbvCvcLQqQm2rQjj6ycik+BGG62LM2iJbEUUfC7+1xge6nFw4GXgo9fAkaE2HQIMNvdt7v7D8BsDvwFIlLjuDuvfbWeMx/9KGybSML7liE9SEnefyA2zaIlsRbNxd027r4BwN03mFnrEG3aA+tLPM8ILhOpsdZv38NtU9P5eOVW+nduwVlHteHR2SsqNAVi8QVc9eqRmqSqe/WEuoPlwNmjATMbDYwGSE1NrcqaREIqKnJe/nwtD81ajgH3jujFZf1TSUoyWjWpX+Hw1ixaUtNEE/ybzKxt8Gi/LbA5RJsMYFCJ5x2AOaFezN0nAhMB0tLSQv5yEKkqq7fs4tY3FjJv3Q/8pHsr7r+wN+1LnMpReEttEk3wzwBGAQ8Gv04P0WYWcH+JC7qDgbFR7FOkUhUPqvbo7BWkJNfh4Yv78tNj22u4BanVIgp+M3uFwJF7SzPLINBT50HgNTO7EvgeuDjYNg24xt2vcvftZnYv8FXwpca5e+mLxCIxsWzjDm55fSHpmTkMOTowqFrrJhpUTWo/c695Z1XS0tJ83rx5sS5Dapniu28zs3Np0qAue/YV0iwlmXuGH82w3m11lC9xzczmu3taJG01ZIMkhNJDJ+zMK6COGTee1Z1z+7SLcXUi1UtDNkhCCHX3baE7z8xZHaOKRGJHR/wSVyoy0uX8dT9EdfetSG2j4Je4Ud6RLnP3FfLIe8t5/tPvqGNGYYjrWRo6QRKRTvVI3CjPSJdfrNnGOU/M5blPvuOyAancd0EvDZ0gEqQjfokbkYx0uTs4QcpLn6+jY4sU/v3rAZzUtSUADZLraOgEERT8EkfaNUshM0T4F5+u+WzVVv44eSEZP+Ry+Umd+OPZPWhY73/f4rr7ViRAp3okboQb6fJ3px/B7VPT+flzX1A3yXjt6hO5+/yj9wt9Efkf/WRI3Ag10uX5fdvx1/+sIisnl6tO7swfBvcgpV6dg7ySSGJT8EtcKT5dsyMvn/vfXsozH62mS6tGvHHNSRx3uOb4EYmEgl/izpzlmxk7JZ1NO/K4+idduPHM7jRI1lG+SKQU/BI3cnLzue/tJbw2L4MjWjdm8m9O4phUHeWLlJeCX+LCh8s3M3ZyOpt35vGbQV35/RnddJQvUkEKfqnRSh7ld2vdmAm/GEi/js1iXZZIXFPwS42lo3yRqqHglxpHR/kiVavCwW9mPYBJJRZ1Ae5098dLtBlEYErG74KLprj7uIruU2q/Ocs3M0ZH+SJVqsLB7+7LgX4AZlYHyASmhmj6sbufW9H9SGLYkZfPfW8tZdK89Ryho3yRKlVZp3rOAFa7+7pKej1JIHNXbGHM5IVs3JHHNT/pyg1n6ihfpCpVVvCPBF4Js+5EM/sWyAJudvfFlbRPiXM78/K5f+ZSXvlyPV1bNVK/fJFqEnXwm1k94HxgbIjVXwOHu/suMxsKTAO6hXmd0cBogNTU1GjLkhruk5VbuXXyQjbk5HL1qV248SzdfStSXSrjiP8c4Gt331R6hbvvKPF4ppk9bWYt3X1riLYTgYkAaWlpB06VJLXCpC+/Z9xbS9i9r5C6ScbvTu/GjWd1j3VZIgmlMoZlvpQwp3nM7DAzs+Dj/sH9bauEfUocGj9rGWOmpLN7X2AWrYIiZ+LcNUz7JjPGlYkklqiC38waAmcBU0osu8bMrgk+vQhYFDzH/yQw0j3ExKdSq+3ZV8DdMxbztw9XU/rDDzd1oohUnahO9bj7HuDQUssmlHj8FPBUNPuQ+PbV2u3c/Pq3rNu2J2ybcFMqikjV0AxcUiXy8gv581tLuOTZzykscl759Qm0D06RWFq7MMtFpGoo+KXSLVifzbAnP+a5T77jsgGpzLrhVE7semjYqRNvGdIjRpWKJCaN1SOVZm9BIU+8v5IJH63msEMa8M8rB3Byt5Y/rg81deItQ3poAnSRaqbgT1DTvsms1ABelJnDza9/y7KNO7kkrQN3nNuTQxokH9CueOpEEYkdBX8CmvZNJmOnpJObH+hWmZmdy9gp6QDlDuX8wiKe/nA1f/3PSlo0qscLl6dx+pFtKr1mEak8Cv4ENH7W8h9Dv1hxt8pIgr/4r4XM7FyS6xj5hc6Ifu24+/yjadawXlWVLSKVRMGfgMJ1n4ykW+W0bzIZM3kheQVFAOQXOvXqJDGoR2uFvkicUK+eBBSu+2Qk3SofmLn0x9Avtq+wSDdhicQRBX8Cqki3yqIi5+XP17Jp596Q63UTlkj80KmeBFTebpWZ2bn88Y1v+XTVNurXTWJvqSN+0E1YIvFEwZ+gIulW6e68MT+DcW8uocidBy7sTYO6Sdw2ddF+F4d1E5ZIfFHwS0ibd+Zx25RFvL90EwM6t+Dhi/vSsUVDAMxMN2GJxDEFvxxgZvoGbp8aGD75jmFHccXAziQl2Y/rdROWSHxT8MuPsvfs464Zi5m+IIs+HZry6CV9OaJ1k1iXJSKVTMEvAMxZvplbJy9k26593HRWd34zqCvJddTpS6Q2UvAnuN17C7hv5lL+/cX3dG/TmOdHHU+v9k1jXZaIVCEFfwKbt3Y7N732Let/2MPoU7twkyY8F0kIUQe/ma0FdgKFQIG7p5Vab8ATwFBgD3C5u38d7X6l4vYWFPLo7BVMnLuGDs1TmDT6RPp3bhHrskSkmlTWEf9p7r41zLpzgG7BfwOAZ4JfJQaWZO3gptcWsGzjTi7tn8rtw46icX394SeSSKrjJ3448HJwkvX/mlkzM2vr7huqYd8SVFBYxLNz1/D4+yto1lDDJ4skssoIfgfeMzMHnnX3iaXWtwfWl3ieEVy2X/Cb2WhgNEBqamollCXF1m7dzU2vLeDr77MZ1rstfx7Ri+aNNJKmSKKqjOAf6O5ZZtYamG1my9x9bon1FmIbP2BB4BfGRIC0tLQD1kv5uTv/+uJ77nt7Kcl1jCdG9uP8vu0IXHYRkUQVdfC7e1bw62Yzmwr0B0oGfwbQscTzDkBWtPuVsm3akccf31jIRyu2cEq3ljx0UR/aNtVAaiISZfCbWSMgyd13Bh8PBsaVajYDuM7MXiVwUTdH5/er1lsLs7hj2iLy8gsZN/xofnHC4TrKF5EfRXvE3waYGgyVusC/3f1dM7sGwN0nADMJdOVcRaA756+i3KeEkbMnnztnLGL6giz6dmzGY5f0pUurxrEuS0RqmKiC393XAH1DLJ9Q4rED10azHzm4T1Zu5ebXv2XLrr3ceGZ3rj2tK3U15IKIhKAO3HEuL7+QB99ZxoufraVrq0ZM/OVJ9OnQLNZliUgNpuCPYwszsrlx0gJWb9nN5Sd1Ysw5R2rIBRE5KAV/HCooLOLpOat58oOVtGpSn39eOYCTu7WMdVkiEicU/HHmu627uXHSAhasz2Z4v3aMO78XTRsmx7osEYkjCv444e78+8vv+fNbgZuxnrz0GM7v2y7WZYlIHFLwx4HNO/O49Y2FfLg8cDPW+Iv6cljTBkz7JlNz34pIuSn4a7hZizcydko6u/cWcNd5PRl1YieSkoxp32Qydko6ufmFAGRm5zJ2SjqAwl9EyqTgr6F27S3gnhmLeX1+Br3aH8LjP+u33/y342ct/zH0i+XmFzJ+1nIFv4iUScFfA321djs3vbaAzB9yufa0rvz+jO7Uq7v/zVhZ2bkhtw23XESkmIK/BtlXUMTj769gwker6dC8Ia9dfSJpnULPjNWuWQqZIUK+XTMNxCYiZdM9/TXEyk07ueDpT3l6zmouOq4DM39/StjQB7hlSA9SSt2slZJch1uG9KjqUkUkzumIP8aKipyXP1/LA+8so1H9ujz7i+MYcvRhB92u+Dy+evWISHkp+GNo0448bn79Wz5euZXTerTiLxf1oXWTBhFvP+KY9gp6ESk3BX+MvLtoA2OmpJOXX8ifR/TisgGpGjNfRKqFgr+a7czL5543l/DG/Ax6t2/K4yP70VVj5otINVLwV6P567Zzw6RAN83fnX4E15/RjWSNmS8i1azCwW9mHYGXgcOAImCiuz9Rqs0gYDrwXXDRFHcvPTVjrZdfWMSTH6zkbx+uon3zlP26aWrYBRGpbtEc8RcAf3D3r82sCTDfzGa7+5JS7T5293Oj2E9c+27rbm6YtIBv12dz0XEduOu8njRpEBhNU8MuiEgsVDj4gxOmbwg+3mlmS4H2QOngT0juzqtfrWfcm0uoVzeJpy87lqG92+7XRsMuiEgsVMo5fjPrBBwDfBFi9Ylm9i2QBdzs7osrY5812bZdexkzJZ3ZSzZx8hEtefjiwGiapWnYBRGJhaiD38waA5OBG9x9R6nVXwOHu/suMxsKTAO6hXmd0cBogNTU1GjLipk5yzdzyxsLydmTzx3DjuKKgZ1JSgrdTVPDLohILETVpcTMkgmE/r/cfUrp9e6+w913BR/PBJLNLOQcge4+0d3T3D2tVatW0ZQVE3n5hdw1fRGX//0rWjSsx/TrBnLVKV3Chj5o2AURiY1oevUY8Dyw1N0fDdPmMGCTu7uZ9Sfwi2ZbRfdZUy3OyuGGVxewcvMufjWwE7eeHdmk5xp2QURiIZpTPQOBXwDpZrYguOw2IBXA3ScAFwG/MbMCIBcY6e4exT5rlKIi57lP1vDwrBU0bZjMS1f05yfdy/fXioZdEJHqFk2vnk+AMscYcPengKcquo+abGNOHn94fQGfrtrG4J5tePCnfWjRqF6syxIROSjduUv5b6J6Jz0wzs6+giIeuLA3I4/vqHF2RCRuJHzwl+cmqt17Cxj35hImzVtPnw5NefzvT0BrAAAIjElEQVRn/eiicXZEJM4kfPBHehPVgvXZ3PDqN6zbvodrT+vKDWd21zg7IhKXEj74D3YTVWGRM+Gj1Tw2ewWtm9TnlV+fwAldDq3OEkVEKlXCB39ZN1FlZudy46sL+HLtds7t05b7RvSmacPkGFQpIlJ5Ej74bxnSY79z/BC4ieqMo1pz9uNzKSpyHr64Lz89tn3IC7gaXVNE4k3CB3/pm6gOa9qADs1TePnzdRyT2ozHf9aPww9tFHJbja4pIvFIVycJhPSnY05nym9Pol7dJOav+4HrTz+C168+MWzoQ9kXhkVEaqqEP+KHwAXcZ+as4rH3V3LYIQ2YdPWJHB+cKKUsGl1TROJRwgd/ZnYuN05awJffbef8vu24d0QvmqZEdgFXo2uKSDxK6FM9by3M4pzH57I4M4dHL+nLEyP7RRz6oNE1RSQ+JeQR/+69Bdw9YzGvz8+gX8dmPDEy/AXcsmh0TRGJR7Um+CPtVvnt+mx+H7wD93enH8H1Z3SL6g5cja4pIvGmVgR/JN0qi4qcZ+eu4ZH3ltO6SX1e/fUJDNAduCKSgGpF8B9svJ2NOXnc9NoCPlu9jaG9D+OBC/roDlwRSVi1IvjL6lY5a/FGbp28kL35RTz00z5cnNZBQyiLSEKLds7ds81suZmtMrMxIdbXN7NJwfVfmFmnaPYXTrjukw3r1eHqf8ynQ/MU3r7+ZC7RuPkiIhUPfjOrA/wNOAfoCVxqZj1LNbsS+MHdjwAeA/5S0f2VJVS3SgN27ytk9KldmPKbgRo3X0QkKJpTPf2BVe6+BsDMXgWGA0tKtBkO3B18/AbwlJlZZc+7W3wB96F3l5GVkwdA4wZ1+dvPj+XUcs6BKyJS20Vzqqc9sL7E84zgspBt3L0AyAGqpCvNuX3aclTbQwA4rUcrPrx5kEJfRCSEaI74Q50sL30kH0mbQEOz0cBogNTU1HIXU7dOEl1aNeLkbj25/KROOpcvIhJGNMGfAXQs8bwDkBWmTYaZ1QWaAttDvZi7TwQmAqSlpVXoVNDtw0pfYhARkdKiOdXzFdDNzDqbWT1gJDCjVJsZwKjg44uA/1T2+X0RESmfCh/xu3uBmV0HzALqAC+4+2IzGwfMc/cZwPPAP8xsFYEj/ZGVUbSIiFRcVDdwuftMYGapZXeWeJwHXBzNPkREpHIl9LDMIiKJSMEvIpJgFPwiIglGwS8ikmAU/CIiCcZqYrd6M9sCrKvg5i2BrZVYTmVRXeWjuspHdZVPbazrcHePaJyaGhn80TCzee6eFus6SlNd5aO6ykd1lU+i16VTPSIiCUbBLyKSYGpj8E+MdQFhqK7yUV3lo7rKJ6HrqnXn+EVEpGy18YhfRETKELfBX1Mmei+1z45m9qGZLTWzxWb2+xBtBplZjpktCP67M9RrVUFta80sPbjPeSHWm5k9GXy/FprZsdVQU48S78MCM9thZjeUalMt75eZvWBmm81sUYllLcxstpmtDH5tHmbbUcE2K81sVKg2lVzXeDNbFvycpppZszDblvmZV0Fdd5tZZonPamiYbcv82a2CuiaVqGmtmS0Is21Vvl8hsyFm32PuHnf/CAwDvRroAtQDvgV6lmrzW2BC8PFIYFI11NUWODb4uAmwIkRdg4C3YvCerQValrF+KPAOgVnTTgC+iMFnupFAX+Rqf7+AU4FjgUUllj0EjAk+HgP8JcR2LYA1wa/Ng4+bV3Fdg4G6wcd/CVVXJJ95FdR1N3BzBJ9zmT+7lV1XqfWPAHfG4P0KmQ2x+h6L1yP+Hyd6d/d9QPFE7yUNB14KPn4DOMOqeD5Gd9/g7l8HH+8ElnLgPMQ11XDgZQ/4L9DMzNpW4/7PAFa7e0Vv3IuKu8/lwNnhSn4PvQSMCLHpEGC2u2939x+A2cDZVVmXu7/ngTmsAf5LYPa7ahXm/YpEJD+7VVJX8Of/EuCVytpfpMrIhph8j8Vr8Neoid5DCZ5aOgb4IsTqE83sWzN7x8yOrqaSHHjPzOZbYH7j0iJ5T6vSSML/QMbi/QJo4+4bIPCDC7QO0SbW79sVBP5SC+Vgn3lVuC54CuqFMKctYvl+nQJscveVYdZXy/tVKhti8j0Wr8FfqRO9VzYzawxMBm5w9x2lVn9N4HRGX+CvwLTqqAkY6O7HAucA15rZqaXWx/L9qgecD7weYnWs3q9IxfJ9ux0oAP4VpsnBPvPK9gzQFegHbCBwWqW0mL1fwKWUfbRf5e/XQbIh7GYhlkX1nsVr8JdnonfsIBO9VyYzSybwwf7L3aeUXu/uO9x9V/DxTCDZzFpWdV3unhX8uhmYSuBP7pIieU+ryjnA1+6+qfSKWL1fQZuKT3cFv24O0SYm71vwAt+5wGUePBFcWgSfeaVy903uXujuRcD/hdlfrN6vusCFwKRwbar6/QqTDTH5HovX4K+RE70HzyE+Dyx190fDtDms+FqDmfUn8Blsq+K6GplZk+LHBC4OLirVbAbwSws4Acgp/hO0GoQ9EovF+1VCye+hUcD0EG1mAYPNrHnw1Mbg4LIqY2ZnA7cC57v7njBtIvnMK7uukteELgizv0h+dqvCmcAyd88ItbKq368ysiE232NVcQW7Ov4R6IWygkAPgduDy8YR+GEAaEDg1MEq4EugSzXUdDKBP8EWAguC/4YC1wDXBNtcBywm0Jvhv8BJ1VBXl+D+vg3uu/j9KlmXAX8Lvp/pQFo1fY4NCQR50xLLqv39IvCLZwOQT+AI60oC14Q+AFYGv7YItk0Dniux7RXB77NVwK+qoa5VBM75Fn+PFfdeawfMLOszr+K6/hH83llIINDalq4r+PyAn92qrCu4/MXi76kSbavz/QqXDTH5HtOduyIiCSZeT/WIiEgFKfhFRBKMgl9EJMEo+EVEEoyCX0QkwSj4RUQSjIJfRCTBKPhFRBLM/wcZErgueOp/GgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x.col(1), y)\n",
    "plt.plot(np.linspace(0, N, 100), mf(np.linspace(0, N, 100)))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
	{
	"cells": [
	{
	"cell_type": "code",
	"execution_count": 1,
	"metadata": {},
	"outputs": [],
	"source": [
	"import numpy as np\n",
	"import sympy\n",
	"import matplotlib.pyplot as plt"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {},
	"outputs": [],
	"source": [
	"std = 1\n",
	"N = 20"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 3,
	"metadata": {},
	"outputs": [],
	"source": [
	"x_obs = np.arange(N)\n",
	"y_obs = np.arange(N) + np.random.normal(0, std, N)\n",
	"model = lambda x: [1, x, x*x]\n",
	"x_obs, y_obs;"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 4,
	"metadata": {},
	"outputs": [],
	"source": [
	"x = sympy.Matrix([model(k) for k in x_obs])\n",
	"y = sympy.Matrix(y_obs)\n",
	"gamma = (x.Tx).inv()x.T*y"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 5,
	"metadata": {},
	"outputs": [],
	"source": [
	"t = sympy.Symbol('t')\n",
	"A = sympy.Matrix(model(t))\n",
	"mf = lambda v: ((A.T*gamma)[0]).subs(t, v)\n",
	"mf = np.vectorize(mf)"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 6,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"[<matplotlib.lines.Line2D at 0x1187fa30>]"
	]
	},
	"execution_count": 6,
	"metadata": {},
	"output_type": "execute_result"
	},
	{
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"needs_background": "light"
	},
	"output_type": "display_data"
	}
	],
	"source": [
	"plt.scatter(x.col(1), y)\n",
	"plt.plot(np.linspace(0, N, 100), mf(np.linspace(0, N, 100)))"
	]
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python 3",
	"language": "python",
	"name": "python3"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.7.3"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 2
	}