lmfit strange example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# lmfit strange example\n",
    "## Yoav Ram, 24 Sep 2015\n",
    "\n",
    "I found a strange bug or bad behaviour in lmfit - probably going down to stuff that lmfit wraps, but I'm not sure.\n",
    "\n",
    "I generate random data (with same seed, so it's always the same), and save it to a csv file.\n",
    "I then fit the same model with the same guess to the generated data and to the data loaded from the csv file.\n",
    "The first fit fails and the second succeeds.\n",
    "\n",
    "4/9 update: Matt Newville suggested to check if this happens with only one replicate per time point.\n",
    "24/9: Matt suggested to check what happens if I don't use panda's aggreagation and instead give lmfit all the points (incl. duplicate time points)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import pandas as pd\n",
    "import lmfit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y0 = 0.1\n",
    "r = 0.7\n",
    "K = 1\n",
    "nu = 2\n",
    "q0 = 0.001\n",
    "v = 1.4\n",
    "reps = 30 #1 4/9 update\n",
    "noise = 0.02\n",
    "\n",
    "def ode(y, t, r, K, nu, q0, v):\n",
    "    alfa = q0 / (q0 + np.exp(-v * t))\n",
    "    return alfa * r * y * (1 - (y/K)**nu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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zLKRiFDBEqlKpH375Wd3xiXrl7NEtMjLqe79BkSpVupl1oOiM2ZBaFEQOiGoYIlXJCZPw\n8rO6VxF2iEtO1Js9+/BKZ0zqmAKGSFVqJrkLHoTgsYv4RL0lS86rdMakjqlJSqQqFTc/hYl6nwRm\nRo9PRtuIilSGahgiVamP4nWiBtAe05KlTGsYZrbQzJ4ys6fNbHWJ56eZ2UYze9TMfmJmF2SQTZEM\njKewiOCG6O89tLSsJgSKzmidqAszzKPUm8wChpk1Al8HFhJmJ51vZm9LJVsKbHb3k4A2YL2ZqVYk\nY9K6deuYOvUYpk49BuglBIZF0aMTcO6+u5P29g20t28Y8zvCSfXJsvA9FXjG3Z8HMLM7gQ8CT8bS\nbKGwW8xk4HV3769kJkUqYd26dVx55RcpbKW6hORKtDuZM2eGNvmRTGW2NIiZ/T5wprt/Ijr+CPAO\nd780lqYB+CfgN4BJwB+6+72p+2hpEKl5kycfyfbtpwKPRmdOAr4LHAzAnDlTeOYZzeiWkVNrS4OU\nU8r/KfCou7eZ2Rygy8z+l7tvjydas2bN3r/b2tpoa2sbyXyKjLodO14H7qVQob4Xs/EMDLyeYa5k\nLOnu7qa7u/uA7pFlDeM0YI27L4yOLwcG3P2aWJp7gHXu/s/R8QPAanffFEujGobUPLNJhLkX10Zn\nVgK9pH4biYyY4dQwshwltQk41syONrNm4DwK+0rmPQXMBzCz6cBbgZ9VNJciFdEEnAFcHT3OQKPe\npdpk9o10934zWwrkgEbgFnd/0swuip6/EfgL4DYz+zEhuH3G3bdmlWeR0dMDdFHo9F4G7M4uOyIl\naD8MkSpg1gp8heR2qyvQ7yMZLbXWJCUiIjVEjaQiVWEn6e1W1SQl1UZNUiJVwGwiYXb3wdGZXwHN\nuO/ILlMyptXaPAyRupbL5Vi//qboaA9hNdr8woLLCAFEpHooYIhkIJfLsWjRH9Pb+6XoTH6EVHz/\ni8sqnzGRfVCnt0gGLr/8C1GwWBw93lyUZs6cWZXOlsg+qYYhkoEXXngpdeb3iHd6NzV1cP31d1Q0\nTyL7o4AhkoEpU8azdWt8VNTNzJhxCMcfHxY76Oi4Q6vSStXRKCmRDEya1MqOHTuBQ6MzrzJx4gS2\nb9dEPakMTdwTqRE7dvSVdU6kmqhJSiQTfYRtWNdGx5qoJ9VPAUMkEy3AdSSH0S7PKC8i5VGTlEgm\nSjUdD6k5WaTiVMMQycRuYFXseBVqkpJqp4AhUgHxZUA6Oi4EBoDtwJVRiu2ohiHVTsNqRUZZLpfj\n7LMX09MTdh9uaVnN7t07GRhoJPRjACynoWGAPXt+lVk+pb5o8UGRKrR+/U1RsAgd3D09ENaJSnZ6\nDwxo7SipbgoYIhXxOHBu9PcsSo83aaxcdkSGQQFDZJTNm3cyXV1fJL5f98SJB7FjR7LTe8aMQzLI\nnUj5FDBERtlddxUvXT59+np27nyegYEbAGho2M1tt/2fbDIoUibNwxAZZWFl2nyT1LnA47zxxk7u\nuefvaG+fSXv7TO655++02KBUPY2SEhllM2cexZYtrwEnRmceY8aMabz88gtZZkvq3HBGSSlgiIyy\nxsbJDAyMp7D96ioaGnazZ8+2LLMlda7mVqs1s4Vm9pSZPW1mqwdJ02Zmm83sJ2bWXeEsihywgYEm\nQrDI76735eicSG3J7FtrZo3A14H5wM+BfzezDe7+ZCzNIcD1wJnu/pKZTcsmtyIHolQNWLViqT1Z\n/sw5FXjG3Z8HMLM7gQ8CT8bSfAi4y91fAnD31yqdSZED1wesjB2vjM6J1JYsA8bhwIux45eAd6TS\nHAuMM7MHgUnAV939byqUP5ERsgfYBdwQHe8irCUlUluyDBjl1MnHAScD7wMmAP9iZv/q7k/HE61Z\ns2bv321tbbS1tY1cLkUO2DjgQuC56Ph04KbssiN1qbu7m+7u7gO6R2ajpMzsNGCNuy+Mji8HBtz9\nmlia1UCLu6+Jjr8JbHT378TSaJSUVDWzVuCjFALGLOBW3LV/t2Sn1hYf3AQca2ZHAy8D5wHnp9L8\nA/D1qIN8PKHJ6toK5lFkWOLLmUMPcDPxpUGgN5N8iRyIzAKGu/eb2VIgR1h17RZ3f9LMLoqev9Hd\nnzKzjcBjhEbfm939iazyLFKO9HLmcD/ppUHCarUitUUT90RG2IIF59LVtYhCgDiUwjwMgE5aWj7L\nzp1bMsmfCNRek5TIGPY94OrYcXJY7cyZh1c4PyIHTgFDZITNnDkJ+DsKa0e9Bnwc2BAdL2H27OdK\nXSpS1dQkJTLCGhsPZmCgmcLaUcuif0Ond0vLau6+u1Or00qm1CQlUgXCXt3xPguApbS3hxpGR4eC\nhdQmBQyREVdqFncj9913V8VzIjKSFDBERtwuCs1QRH/vzigvIiNHfRgiIywssnw8kF/B5ljgJ7j/\nMrtMiaRoAyWRKmB2EGFhgvjM7t2478ouUyIp6vQWqQoTgK+Q7PRekVFeREbOfnfcM7NlZjalEpkR\nEZHqVc4WrdMJu+F9O9pSdUhVGJF6sG7dOqZOPYapU48BdhKaoTqjx7LonEhtK6sPw8wagAXABcAp\nwLcJiwU+O6q5K4P6MCRr69at48orv0ihz+Ki6N9Do39fBRpwV9CQ6jGcPoxyahi4+wDwC+AVwvZh\nU4DvmNmXhpxLkTHm2mtvo7Aa7WJCh3djLEUjDQ3NWWRNZETtt9PbzC4D/gR4HfgmsMrd+6Jax9PA\np0c3iyK1ZgrwBnBEdLyNWbOOzDA/IiOjnFFSrcA57v5C/KS7D5jZB0YnWyK14wMfeDednfGJeq9G\n1f1w1NRkXH+9KuNS+zQPQ+QATZ06g61b3yDeZzFx4gTe+c4zAOjouFBrR0nV0cQ9kQyEUefXEd8g\nCZbj/kZ2mRLZD03cE8mEAY8D50bHs6JzImOLahgiB0hLgUgtUg1DJBMtJJukAJZnlBeR0VPWPAwR\n2Zc9ZZ4TqW2qYYgcMAdWxY5XRedExhb1YYgcILOpwBnAo9GZk4AHcX89u0yJ7MeoLQ0yWqLFDJ8y\ns6fNbPU+0v22mfWb2TmVzJ9IebYDXcCfRY+u6JzI2JJZwDCzRuDrwELgOOB8M3vbIOmuATaisYpS\nBeIr065bt47Gxokk15L6WnROZGzJsg/jVOAZd38ewMzuBD4IPJlKdynwHeC3K5o7kRLSK9NeeeUy\nSv1v5N5YdE6k1mUZMA4HXowdvwS8I57AzA4nBJH3EgKGOiskU9dccxOF2kTeUmBl7HglGiUlY1GW\nAaOcwv864LPu7tHGTSWbpNasWbP377a2Ntra2kYifyJFduzYDnwPuDo6cxKwGxgAbojO7WL69GkZ\n5E5kcN3d3XR3dx/QPTIbJWVmpwFr3H1hdHw5MODu18TS/IxCkJhG2LbsE+6+IZZGo6SkYsyaCRP1\n4rO6Hfgr4mtJzZ17G4880l35DIqUqdZmem8CjjWzo4GXgfOA8+MJ3H12/m8zuw34XjxYiFTeBODj\nQP5r+Ang1qJU06ZNrWCeRCojs4Dh7v1mthTIEbYnu8XdnzSzi6Lnb8wqbyKD2wPcTBjYB3A/0EtL\ny2p6esKZlpbVdHR0ZpM9kVGkiXsiQ2A2kdAk9eXozCqgh40b72L9+psA7X8htUH7YYiMsrD3xceA\n56Izs4BbtPeF1BwFDJFRZvYmQj9GvIaxE/dfZ5cpkWGotU5vkZqQy+X2NjeF/2W+THIexrLii0TG\nIAUMkX3I5XIsWvTH9PZ+KTrzYIlUmtUt9UFNUiL7cPLJbWzevIRCjeIQYBzxJqnm5gF279bKtFJb\n1CQlMsKeeea51Jnjgc0UZnXv5Pzz/6CymRLJiAKGyD7s3v0rkn0UPwU+SWGU1Om8/HI6qIiMTQoY\nIvvQ29tHmKyX31FvADiBQpNUJ4XgITK2KWCI7NMAMJ5CgPgU8RqHZnVLPVHAENmnFuArpJczb28P\na0l1dHRqVrfUDQUMkSEbx3333ZV1JkQqTgFDZJ96SHZ6LwN6M8qLSLYUMERi4rO6OzouJAQHB66M\nUuwG+rLJnEjGNHFPJJLL5TjrrLNxD3tZmL2OezPwVeKbI8FluP8yo1yKjAxN3BM5AB/60AW49wO7\nAKK/DyqRUkuBSH1SwJC6Fm+C2rr1dZJ7XeT7K1bFrliF+jCkXilgSN3K5XKcffZienry28g/CLwX\nuDo6bge+S+jDKCwFMn/+uyqbUZEqoT4MqVsLFpxLV9ciCv0TLUAz8LXoONQw5s9/N/ffvxmA+fPn\n0tXVVfG8iow09WGIDMFrr6VXmD0IuI7kJL3lChAiEQUMqVsvvPAE2vxIpHxqkpK6ZdYKHAc8HZ3Z\ngbZflXqhJimR/Uhut9oDPE6hz+IyQnPUhuh4MfDNymZQpIqphiFjVvGsbVi06I/o7f3NKMVTJPss\nJhE6va+NjlcCfbhvq1SWRSqm5moYZraQ8H9sI/BNd78m9fyHgc8ABmwHPunuj1U8o1Jz0kNmH354\nMTNnvpne3oF9XOWESXv5IbS7aG5WJVwkL7P/G8ysEfg6MB/4OfDvZrbB3Z+MJfsZ8L/d/VdRcLkJ\nOK3yuZVas379TVGwCLWHnh547rnLCF/5i6NUl5CclDceOAN4NDo+i4kTH0VEgix/Pp0KPOPuzwOY\n2Z3AB4G9AcPd/yWW/kfAEZXMoIwtAwMQmpvyTVCXkuyzeBtwL3BidHwvK1f+aSWzKFLVsgwYhwMv\nxo5fAt6xj/QfA+4Z1RxJTYv3WcybdzIPPfRpeqNVPJqbP01vb0PqigHgVsIGSQBLiddAmpo6OOWU\nU0Y/4yI1IsuAUXZPtZmdAXwUOL3U82vWrNn7d1tbG21tbQeYNak1uVyORYv+mN7eLwHw4IOX0d+/\ng9BxDb29vwLGARdRWKq8mfC1ytcwjiY0UYUaSH9/aNrSjnoyFnR3d9Pd3X1A98hslJSZnQascfeF\n0fHlwECJju8Tgb8HFrr7MyXuo1FSwsknt7F58ynAc9GZjYTfQ/FlPnYT+iny5y5KHS8nOWqqk/b2\nDdpdT8akWhsltQk41syOBl4GzgPOjycwsyMJweIjpYKFSN7TT/8X8FMKk+4epHgv7mWE4JA/t4r0\nqKgwFyNoaVlNR0fn6GVapMZkFjDcvd/MlgI5wrDaW9z9STO7KHr+RuBzwBTgG2YG0Ofup2aVZ6le\nZk3AuyisNFtKeh+L/FLmhRpFa+sVvP3toYmqo6NTzVEiMZq4J2PCzJmz2LJlK4XmpSWEiXjxJqkB\nwgKD+VrICpK1kE4mTfoc27a9UJlMi2RoOE1S6WEjUsdyuRwLFpzLggXnksvlRu2+w3mdCy64gHHj\npjNu3HQuuOCCoudff70H+AShA3sDofbQQ+j0Xhn9vRvYSWiCuoGwN/cqwrarncAq3LVft8ig3L2m\nH+Et1Le1a9d6a+scb22d42vXrh3WPTZu3OgtLdMdbne43VtapvvGjRtLpmtvP8fb28/xjRs3Fh2X\nSt/UNHXvfRsaJnlz86FDep358+c7TN57DUz2xYsX+5w5cxxao8dEh2mxNAc5THA4LXpMiNKMj9JN\ni85NjqWZ7HPnnj6sz0+k1kRl59DK26FeUG2Peg8Ya9euLSpM165dW1bBHi9wW1reHF3v0eN2nzPn\nuEQgSgeV5uZD9lv4z5lzUuq+pxW9Tnv7OYmgt3jx4sTrwJSia6AhFRAmp9KkA8i0KE2HwznR49zE\nPZqbDykZvETGouEEDPVh1LgJE2bS0/MuCstZnERz84M0No7bu45Sc/NyBgYa6e9fHx1/mqlTm9iy\n5dckV2r9KoX2/N8Huoj3AcyZM5tnn10eS/NOwtSY/FDWWbS3P5cYhjpu3HT6+78Yu+YE4nMdoJMZ\nM9ak+h/Sw1unkpyh3UmYZBfvj0hf00qYY1HIG1xPeke9pqZ+zjhjIRAWKFQnt9SL4fRhKGDUOLOD\nSM4lyG8IFB8+egJwJsnCMz/DOZ/mbYTRzcdFx/9JusBtbLydPXvaKASnnYR+gML+ETNmTGD37nEA\nrFy5hM9//i/p6xugsNzGY4Sus+Oj45/Q0NDMwEA8IBxJGO2UPzZgcuo9Nqby9z1Cv0U+zaeizyU/\ni3sFsIfQz1F4Ty0td7Bz5xZE6o0CRh0KmwAlR/qE2sLHKRSMDxAm1ueDwROEAje+eVC+szdfwF5C\nKGCnRccfyiCJAAALrUlEQVSvRcfxQrlUreT7wKHR8auYjcM9vmT4xRTvm91EGNWUz+99JJcZXxrl\nb1J0vD3Kf3yzo0ui99gaHW8jGTQ70agokYJam7gno2Y3cDOFQjlHKOjzq7SuIgSA+OZB6UltFxNq\nAvn1HrcSmoDeR2GuQzPhl33+uPiXuvs4wgqw+TQTSDYvQfjVH8/vfcCvSa4kO4nkTnj9JOdQLI3e\n49roeEVRXgqjovJWccwxby2RTkRKUcCoeTtJ7ku9jFBwHkfYSgRCwR4vXKG4zT9dwDYRAkQ8yOwg\nuZrrf5Ps57iYYjtTaZaXSDOBZE0lv2RHvH+iVP7jxqXSrCIdHA46qJmBgX56e8PM7ubmfr7whT8r\nkR8RKUUBo+a1AL9FITicQFgJPl57KFVIp2uivSQL2HEUb1d6Y+qaiSSbePIFff5X/jJCLSUemD5F\nMjitoHg60ITUfUvlP53f9MZIbwU2U1j2YyfnnfcHnH/++bFd+Naok1tkCBQwat4uQsGY/9W/mVCQ\nf4xCYd9LcSG9i2SBa4TaQH4l193AbSS3K3WSTVvpWkm6oC+VZk/qdXYSmpeWMbh+8qvOFvLSTDKg\nNafu8VPgLOKbIb388nbOPPNMBQmRYVLAqHmNFPdP7CJZ2P8jIQDkf23vJgSI3ti5fkKhm68dXEZx\nX8MKks0+HyVZSJcafLAjlWYcoakr/zqrCEEkvsz4ttQ1fYQaRHyRwAZCR3a+2eoBCjO9IfS9fAD4\nTnTcGXtORIZDAaPmpdvuIRS28cJ+BckhqKcThtXGzz1BstO7VDNQutknvvwGFDcTrQLeRLK2Uyq/\nKwhNafnCvxV4L4WO8nHRa7+Uyks84DWk7rGKeNDRyrMiB04BY0xK9wn0kvw1vqrEuQdS1/RTXPin\nm4YMOJhk53S63+ObJAvyg0vkN10L6QUeil2zjLD9e3yI7MVRfvLSI6A6OeigJt7zHq08KzJSFDBq\nXEODMzCQ7p9IF56NFP+qv4TkL/TdFPcjxJ/vJQSiJRQCQlPqvpdQ3O+RDjIDlO70/nUsXfq+HRSb\nQJhsmJ9H0koYKlzo5L7yyj/liiuuKHGtiAyHAkaNa25uZNeu+CZAu6N/0801aeMITUX5Jqn8zO58\nMOgjuX9EP6Gwj8+XeIAwGuvcWLp0h/Z4kkHGUq/zUcLoq/z8DCjuKJ9IurbT2jqOrVuT80jmz38X\njzwS3s/KlQoWIiNNAaPGHX74kan1nToJTUPxYPATSjcvxWsDD5BsOpoUpcn3GwwQ+izSQSUeQO4h\n2XG+jDArO57mH1PH+aG38dFVS0nWdl6N/g0BsKmpj6OO+i22bl1CvNZktoHXX9fGjCKjRQGjxs2e\nPZtnn02f7aM4GKT7Fr5GcuRRH8mmo0bCvIr4+lPp/ojDgGsoFNorKR5ZtZLkTO9TCLvzhlqIWR+H\nHfYWtiQmiR9NmEeRv+Ys5sz5L2bPngmE+RP5uRQiUjkKGDVu3ryT6epKzvRubZ3E1q3bKASDHaR/\n1S9e/CEA7rjjXgDa2t7FD36wae8s6KamftxvZc+er0THHRx66BS2bIm/1q5UbqYU5a+5uYne3uTw\n1jlztjF79rFAWCH28suvZsuWeLB6HrMXcf9qdI9Pc/31f1PUaf3ww4vp6Ql/axSUyOjT4oM1bsGC\nc+nqmkW8JjB37r/y+OOP0t8fCvCmpjdoa3sn3d2PAfDhD5/F7bffXnSvXC4XmwV9IUDieP36m+jq\nMgqT4Q7D7Ke4Xxe9zmW4NySCzFFHzeTZZ7cQH6E1d+5beeSRh/f7HqZNm773tUuNcErnV6OgRMqn\n1WrrUChsFxHvw2hv37C3gIeRK0xzuRxnn7147z4bLS2rueKKS3nooUf2vg6UCjLJYJDeM6PUfe++\nW8NgRUbTcAJG5jvmHeiDOt9xr9ytVUfy9fa1Jetw8zfU+4rIgUE77tWnam+aqfb8idQjNUmJiEhZ\nhhMwSs3oqhgzW2hmT5nZ02a2epA0X4ue/7GZza10HkVEJMgsYJhZI2GBoIWE3X7ON7O3pdK8HzjG\n3Y8FLgS+UfGMiogIkG0N41TgGXd/3t37gDuBD6bSLCJMXcbdfwQcYmbTK5tNERGBbAPG4cCLseOX\nonP7S3MEIiJScVnO9C63pzrdKVN03Zo1a/b+3dbWRltb27AzJSIyFnV3d9Pd3X1A98hslJSZnQas\ncfeF0fHlwIC7XxNLcwPQ7e53RsdPAfPc/ZVYGo2SEhEZolobJbUJONbMjjazZuA8ivfQ3AD8CewN\nML+MBwsREamczJqk3L3fzJYCOcLSqLe4+5NmdlH0/I3ufo+Zvd/MniHssLMkq/yKiNQ7TdwTEalD\ntdYkJSIiNUQBQ0REyqKAISIiZVHAEBGRsihgiIhIWRQwRESkLAoYIiJSFgUMEREpiwKGiIiURQFD\nRETKooAhIiJlUcAQEZGyKGCIiEhZFDBERKQsChgiIlIWBQwRESmLAoaIiJRFAUNERMqigCEiImVR\nwBARkbIoYIiISFkUMEREpCyZBAwzazWzLjP7LzO7z8wOKZHmLWb2oJn91Mx+YmbLssiriIgEWdUw\nPgt0uftvAA9Ex2l9wAp3/y3gNOASM3tbBfNYc7q7u7POQtXQZ1Ggz6JAn8WBySpgLAI6o787gd9L\nJ3D3X7j7o9HfO4AngZkVy2EN0v8MBfosCvRZFOizODBZBYzp7v5K9PcrwPR9JTazo4G5wI9GN1si\nIjKYptG6sZl1AYeVeOqK+IG7u5n5Pu4zEfgOcFlU0xARkQyY+6Bl9ei9qNlTQJu7/8LMZgAPuvtv\nlkg3Dvg+cK+7XzfIvSr/BkRExgB3t6GkH7Uaxn5sABYD10T/fjedwMwMuAV4YrBgAUN/wyIiMjxZ\n1TBagW8DRwLPA3/o7r80s5nAze7+O2b2buAHwGNAPpOXu/vGimdYRESyCRgiIlJ7xsRMbzNbY2Yv\nmdnm6LEw6zxVmpktNLOnzOxpM1uddX6yZGbPm9lj0Xfh37LOTyWZ2a1m9oqZPR47t9+JsmPRIJ9F\nXZYVg02EHup3Y0zUMMzsKmC7u1+bdV6yYGaNwH8C84GfA/8OnO/uT2aasYyY2XPA2919a9Z5qTQz\new+wA/hrdz8hOvdF4DV3/2L0Y2KKu5eaLDumDPJZ1GVZYWaHAYe5+6PRyNP/IMx/W8IQvhtjooYR\nqefO71OBZ9z9eXfvA+4EPphxnrJWl98Hd/8h8Ebq9H4nyo5Fg3wWUIffjUEmQh/OEL8bYylgXGpm\nPzazW+qlyh1zOPBi7Pil6Fy9cuB+M9tkZp/IOjNVYEgTZetAPZcV6YnQQ/pu1EzAiNrZHi/xWAR8\nA5gFnARsAdZnmtnKq/12xZF1urvPBc4irEH2nqwzVC08tEHX8/elrsuKqDnqLsJE6O3x58r5bmQ1\nD2PI3L29nHRm9k3ge6OcnWrzc+AtseO3EGoZdcndt0T/vmpmdxOa7H6Yba4y9YqZHRabKPs/WWco\nK+6+973XW1kRTYS+C/gbd8/PfRvSd6Nmahj7Er3RvLOBxwdLO0ZtAo41s6PNrBk4jzA5su6Y2QQz\nmxT9/SZgAfX3fUjLT5SFQSbK1ot6LSv2MRF6SN+NsTJK6q8JVUwHngMuirXL1QUzOwu4DmgEbnH3\nL2ScpUyY2Szg7uiwCbijnj4LM/sWMA+YRmiT/hzwD5SYKJtVHiulxGdxFdBGHZYVg02EBv6NIXw3\nxkTAEBGR0TcmmqRERGT0KWCIiEhZFDBERKQsChgiIlIWBQwRESmLAoaIiJRFAUNkFJjZwWb2yazz\nITKSFDBERscU4FNZZ0JkJClgiIyOvwTmRJv0XJN1ZkRGgmZ6i4wCMzsK+H5+4x6RsUA1DJHRUXeb\n9MjYp4AhIiJlUcAQGR3bgUlZZ0JkJClgiIwCd38d+OdoV0h1esuYoE5vEREpi2oYIiJSFgUMEREp\niwKGiIiURQFDRETKooAhIiJlUcAQEZGyKGCIiEhZFDBERKQs/x9j30ctgr9gAgAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b0983c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(0)\n",
    "t = np.linspace(0, 16)\n",
    "y = odeint(ode, y0, t, args=(r, K, nu, q0, v))\n",
    "y.resize((len(t),))\n",
    "y = y.repeat(reps).reshape((len(t), reps)) + rng.normal(0, noise, (len(t), reps))\n",
    "y[y < 0] = 0\n",
    "df1 = pd.DataFrame({'y': y.flatten(), 't': t.repeat(reps)})\n",
    "df1.plot('t','y', kind='scatter');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Save data to file and load it into a different data frame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RWKq8mfC1ytcwjiY0UYUaSH9/aNrSjnoyFnR3d9Pd3X1A98hslJSZnQascfeF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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a64d550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df1.to_csv('tmp.csv', index=False)\n",
    "df2 = pd.read_csv('tmp.csv')\n",
    "df2.plot('t','y', kind='scatter');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two data frame are very similar:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(df1, df2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function creates a model and tries to fit it to the average of the data, using the standard deviaiton for weights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def fit(df):\n",
    "    def model_func(t, y0, r, K, nu, q0, v):\n",
    "        At = t + (1./v) * np.log((np.exp(-v * t) + q0)/(1 + q0))\n",
    "        return K / ((1 - (1 - (K/y0)**nu) * np.exp( -r * nu * At ))**(1./nu))\n",
    "    model = lmfit.Model(model_func)\n",
    "    params = model.make_params(y0=0.01, r=0.1, K=1, nu=1, q0=1, v=1)\n",
    "    params['y0'].set(min=1e-10)\n",
    "    params['K'].set(min=1e-10)\n",
    "    params['r'].set(min=1e-10)\n",
    "    params['nu'].set(min=1e-10)\n",
    "    t = df.t.unique()\n",
    "    y_mean = df.groupby('t').y.mean()\n",
    "    y_std = df.groupby('t').y.std() # 4/9 update\n",
    "    if not np.isfinite(y_std).any(): # 24/9 update\n",
    "        w = None\n",
    "    else:\n",
    "        y_std[~np.isfinite(y_std)] = y_std.min()\n",
    "        w = 1./y_std\n",
    "        assert np.isfinite(y_std).all()\n",
    "    fit = model.fit(y_mean, t=t, params=params, weights=w)# 4/9 update\n",
    "    #fit = model.fit(df.y, t=df.t, params=params) # 24/9\n",
    "    return fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fit fails terribly on the generated data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Xj4yMjNOSQPF+hGeeeYZLL72Uhg0bEhMTQ0ZGBocPHy7z7xMMlhCMMUE3cMIEpsTGnrZt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ad40198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit(df1).plot_fit();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "~~but somehow succeeds on the loaded data, although they are almost the same according to the process we did and the `np.allclose` result:~~\n",
    "\n",
    "4/9 update: when using a single replicate the fit is the same (terrible that is):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vcIypc9Wdh2DXyKbJWb9iBQ/Gx3N/M7j+zbbs2/iVv0MyJiBYk5FpUsrd8+Do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\nLCEYY4wB4P8DmSpJL7SSRDIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1adcc208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit(df2).plot_fit();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}