{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting Function Models\n",
    "A functional model allows for the creation of data, fitting of experimental data, plotting and symbolic manipulation of mathematical models based on functions. This includes symbolic intergration, differentiation and algebra. This module requires sympy and numpy to work. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Importing pyMez, this should take roughly 30 seconds\n",
      "Importing Code.DataHandlers.GeneralModels\n",
      "It took 0.575 s to import Code.DataHandlers.GeneralModels\n",
      "Importing Code.DataHandlers.HTMLModels\n",
      "It took 0.152 s to import Code.DataHandlers.HTMLModels\n",
      "Importing Code.DataHandlers.NISTModels\n",
      "It took 2.558 s to import Code.DataHandlers.NISTModels\n",
      "Importing Code.DataHandlers.TouchstoneModels\n",
      "It took 0.014 s to import Code.DataHandlers.TouchstoneModels\n",
      "Importing Code.DataHandlers.XMLModels\n",
      "It took 0.155 s to import Code.DataHandlers.XMLModels\n",
      "Importing Code.DataHandlers.ZipModels\n",
      "It took 0.008 s to import Code.DataHandlers.ZipModels\n",
      "Importing Code.InstrumentControl.Experiments\n",
      "It took 0.743 s to import Code.InstrumentControl.Experiments\n",
      "Importing Code.InstrumentControl.Instruments\n",
      "It took 0.019 s to import Code.InstrumentControl.Instruments\n",
      "Importing Code.Utils.Names\n",
      "It took 0.016 s to import Code.Utils.Names\n",
      "It took 4.241 s to import all of the active modules\n"
     ]
    }
   ],
   "source": [
    "from pyMez.Code.Analysis.Fitting import *\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "from ipywidgets import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creation of a new functional model\n",
    "1. Pass parameters as a list or a string separated by spaces\n",
    "2. Pass variables as a list or a string seperated by spaces\n",
    "3. Pass an equation that sympy understands "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "line=FunctionalModel(parameters=[\"m\",\"b\"],variables=\"x\",equation=\"m*x+b\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.12"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now line can be point on any line\n",
    "line(m=1.2,b=3,x=.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2,  1,  4])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# or you can set the parameters\n",
    "line.set_parameters(m=3,b=1)\n",
    "# now any x_list you pass it as an np.array can be calculated\n",
    "line(np.array([-1,0,1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TcBf+oH/bzG4A1gOXh2JdIuLnnGPusi1MnZvFgaJS/jy6H787vTeNGqgtglQsVEfpXFnJ\nrLNC8fgi8nN5ew9xx+xMPs7ZxrDurXnw0qH06xTndVlSx+mbtiIRxOdzvPHDBu6fn0OZz3HnBYO4\n7sRE6qstglSDAl8kQqzdcZCU1HS+W7uLk/q04/5xQ0lo18zrsiSCKPBF6rjSMh8vfLWWRz5cSaMG\n9XhgfBKXJ3fXN2WlxhT4InXY8rx9TEpNJ33TXs4e1Il7Lx5Cp5ZNvC5LIpQCX6QOKiot48lFq3lq\nUS6tmjbkiV8dy/lJ8dqql6Ao8EXqmB837GbSrHRWbTvAuGO78rcLBtGmeSOvy5IooMAXqSMKikt5\neMFKXvx6LfEtm/DidSM4Y0BHr8uSKKLAF6kDvsrdQUpaOht3HeLq43swcUx/4tTsTEJMgS/iob2H\nSrjvveW8tXgjPds3560JxzOql5qdSXgo8EU88mHWVu54J5OdB4u5+bTe/Gl0X5o0VLMzCR8Fvkgt\n276/iKnvZvFeeh4D41vy/LUjSOrWyuuyJAYo8EVqiXOO2f/ZzD3zsikoKuOvv+jHb0/rTcP6anYm\ntUOBL1ILNu85xJTZGXy6YjvHJfibnfXpqGZnUrsU+CJh5PM5XvtuPTPez8EBUy8cxNUnqNmZeEOB\nLxIma7YfICU1g+/X7eKUvu25b1wS3duq2Zl4R4EvEmKlZT6e/WItf1+4kiYN6vHQpUO5dHg3tUUQ\nzynwRUIoa8teJqWmk7l5H+cM7sS0sUPoqGZnUkco8EVCoLCkjMc/WcUzn62hTbNGPH3VcZybFO91\nWSI/o8AXCdKS9buYOCud1dsPMv64btx5wUBaN1OzM6l7FPgiR+lgUSkPLVjBy9+so0urprx8/UhO\n69fB67JEKqXAFzkKn6/czuS0DLbsPcQ1x/fgtjEDaNFYLyep2/QXKlIDewtKmPZeNrOWbKJXh+a8\n/dsTGJHY1uuyRKpFgS9STR9k5nHnnCx2HSzm96f35taz1OxMIosCX6QK2/YXctecLN7P3MrgLi15\n8boRDOmqZmcSecIe+GY2BngMqA8855ybEe51ioSCc45ZSzZx73vLOVRSxsQx/bnplF5qdiYRK6yB\nb2b1gSeBs4FNwA9mNtc5lx3O9YoEa+OuAm6fncEXq3YwIrENM8YPpXeHFl6XJRKUcG/hjwRynXNr\nAMzsTWAsoMCXOsnnc7zyzToeXLACA+4ZO5hfj+pBPTU7kygQ7sDvCmwsd3sTMKr8AmY2AZgAkJCQ\nEOZyRCqXu+0AKanpLF6/m1P7deC+cUPo1kbNziR6eP6hrXNuJjATIDk52XlcjsSgkjIfMz9fw2ML\nV9G0UX0euewYLjmuq5qdSdQJd+BvBrqXu90tME2kTsjcvJeJs9LJztvH+UnxTL1oMB3iGntdlkhY\nhDvwfwD6mllP/EF/BfCrMK9TpEqFJWU89vEqZn6+hrbNG/HMr4czZkhnr8sSCauwBr5zrtTM/gdY\ngP+wzBecc1nhXKdIVX5Yt4tJs9JZs+Mglyd3Y8p5g2jVrKHXZYmEXdj34Tvn5gPzw70ekaocKCrl\nwQ9yeOWb9XRr05RXbxjFyX3be12WSK3x/ENbkdqwaMU2pqRlkLevkN+clMhff9Gf5mp2JjFGf/ES\n1XYfLGbavGzS/rOZPh1bMOvmExneo43XZYl4QoEvUck5x/yMrdw1N5M9BSXcemYfbjmzD40bqNmZ\nxC4FvkSdbfsKueOdTD7MziepayteuX4Ug7q09LosEc8p8CVqOOf49+JNTHsvm+JSH5PPHcANJ/ek\ngZqdiQAKfIkSG3b6m519mbuDkT3bMuOSJHqp2ZnIzyjwJaKV+Rwvfb2OhxesoH49496Lh/CrkQlq\ndiZSAQW+RKxV+fuZmJrOfzbs4Yz+HZg+LokurZt6XZZInaXAl4hTXOrjmc9W88QnuTRvXJ9//HIY\nY4d1UbMzkSoo8CWipG/aw8RZ6eRs3c+Fx3ThrgsH0b6Fmp2JVIcCXyJCYUkZf/9oJc9+sYYOcY15\n9ppkzh7UyeuyRCKKAl/qvG/X7CQlNZ11Owu4cmR3Us4dSKumanYmUlMKfKmz9heWMOP9HF77bgMJ\nbZvx+o2jOLGPmp2JHC0FvtRJn+TkM2V2Jvn7Crnx5J785Rf9aNZIf64iwdArSOqUXQeLuefdLN5Z\nuoV+nVrw1FUncmyCmp2JhIICX+oE5xzvpucxdW4W+wtL+ONZfbnljD40aqC2CCKhosAXz23d6292\ntnB5Psd0a8UDl45iQGc1OxMJNQW+eMY5x5s/bOS+95ZT4vMx5byBXH9yT+qrLYJIWCjwxRPrdx4k\nJTWDb9bs5PhebZlxyVAS2zf3uiyRqKbAl1pV5nO8+NVaHv5wBQ3r1eP+S5L4ZXJ3NTsTqQUKfKk1\nK7b6m50t27iH0QM7cu/FSXRu1cTrskRihgJfwq641MdTn+by5KJc4po05J9XHsuFQ+PV7Eyklinw\nJayWbtzDpFnprMjfz9hhXbjrwsG0bd7I67JEYpICX8LiUHEZj3y4ghe+WkvHuCY8f20yZw1UszMR\nLwX1rRYzu8zMsszMZ2bJh82bbGa5ZrbCzM4JrkyJJF+v3sE5//ic575cyxUjE/jwL6cq7EXqgGC3\n8DOBS4D/Kz/RzAYBVwCDgS7AQjPr55wrC3J9UoftKyzh/vnLeeP7jSS2a8YbNx3PCb3beV2WiAQE\nFfjOueVARR++jQXedM4VAWvNLBcYCXwTzPqk7lqYnc+UdzLYvr+I357aiz+N7kfTRvW9LktEygnX\nPvyuwLflbm8KTPsvZjYBmACQkJAQpnIkXHYeKGLqu9m8u2wLAzrH8ew1yQzt1trrskSkAlUGvpkt\nBDpXMGuKc25OsAU452YCMwGSk5NdsI8ntcM5x5ylW7j73SwOFJXyl7P7cfNpvdXsTKQOqzLwnXOj\nj+JxNwPdy93uFpgmUWDLnkPc8U4mn+RsY1j31jx46VD6dYrzuiwRqUK4dunMBV43s0fxf2jbF/g+\nTOuSWuLzOV7/fgMz3s+hzOe484JBXHdiopqdiUSIoALfzMYBjwMdgPfMbKlz7hznXJaZvQ1kA6XA\nLTpCJ7Kt3XGQlNR0vlu7i5P6tOP+cUNJaNfM67JEpAaCPUpnNjC7knnTgenBPL54r7TMx/NfruXR\nj1bSqEE9Hhw/lMuSu6ktgkgE0jdtpVLZW/YxKTWdjM17OXtQJ+69eAidWqrZmUikUuDLfykqLeOJ\nT3J5+tPVtG7WkCd/dRznJXXWVr1IhFPgy88sWb+bSanp5G47wCXHduXOCwbRRs3ORKKCAl8AKCgu\n5aEFK3jp63XEt2zCi78ZwRn9O3pdloiEkAJf+HLVDlLS0tm0+xDXnNCDiWMG0KKx/jREoo1e1TFs\n76ESpr+XzduLN9GzfXPe/u0JjOzZ1uuyRCRMFPgxakHWVu58J5OdB4v53em9+eNZfWnSUM3ORKKZ\nAj/GbN9fxNS5WbyXkcfA+JY8f+0Ikrq18rosEakFCvwY4Zwj7cfN3DMvm0PFZdx2Tn8mnNqLhvXV\n7EwkVijwY8DmPYe4PS2Dz1ZuZ3iPNjwwPok+HdXsTCTWKPCjmM/nePW79Tzwfg4OmHrhIK45IZF6\nanYmEpMU+FFq9fYDpKSm88O63ZzStz33jUuie1s1OxOJZQr8KFNS5uPZL9bwj4WraNKgHg9dOpRL\nh6vZmYgo8KNK5ua9TEpNJ2vLPsYM7sw9Fw+mY5yanYmInwI/ChSWlPH4J6t45rM1tGnWiKevOo5z\nk+K9LktE6hgFfoRbvG4XE1PTWbP9IJcO78Yd5w+kdTM1OxOR/6bAj1AHi/zNzl7+Zh1dWjXlletH\ncmq/Dl6XJSJ1mAI/An22cju3p2WwZe8hrj0hkdvO6U9zNTsTkSooJSLInoJips1bTuqPm+jVoTn/\n/u0JJCeq2ZmIVI8CP0K8n5HHnXOy2F1QzC1n9OYPZ6rZmYjUjAK/jtu2r5C/zcnig6ytDO7Skpev\nH8HgLmp2JiI1p8Cvo5xzzFqyiWnzsiks9TFpzABuOqUnDdTsTESOkgK/Dtq4q4DbZ2fwxaodjEhs\nw4zxQ+ndoYXXZYlIhFPg1yFlPscr36zjoQUrMGDa2MFcNaqHmp2JSEgEFfhm9hBwIVAMrAZ+45zb\nE5g3GbgBKANudc4tCLLWqJa7bT+TUjNYsn43p/XrwPRxQ+jWRs3ORCR0gt3C/wiY7JwrNbMHgMnA\nJDMbBFwBDAa6AAvNrJ9zrizI9UWdkjIf//fZav75cS7NGtfn0cuPYdyxXdXsTERCLqjAd859WO7m\nt8ClgetjgTedc0XAWjPLBUYC3wSzvmiTuXkvt81KZ3nePs4fGs/UCwfTIa6x12WJSJQK5T7864G3\nAte74v8H8JNNgWn/xcwmABMAEhISQlhO3VVYUsY/Fq7i2S/W0LZ5I/7v6uGcM7iz12WJSJSrMvDN\nbCFQURpNcc7NCSwzBSgFXqtpAc65mcBMgOTkZFfT+0ea79fuIiU1nTU7DvLL5O7cft5AWjVr6HVZ\nIhIDqgx859zoI803s+uAC4CznHM/BfZmoHu5xboFpsWs/YUlPPjBCv717Xq6tWnKqzeM4uS+7b0u\nS0RiSLBH6YwBJgKnOecKys2aC7xuZo/i/9C2L/B9MOuKZItWbGNKWgZ5+wq5/qSe/PWcfjRrpCNi\nRaR2BZs6TwCNgY8CR5V865y72TmXZWZvA9n4d/XcEotH6Ow+WMy0edmk/WczfTq2YNbNJzK8Rxuv\nyxKRGBXsUTp9jjBvOjA9mMePVM453svI4645Wew9VMKtZ/bhljP70LiBmp2JiHe0XyHE8vcVcuc7\nmXyYnU9S11a8euMoBsa39LosEREFfqg453h78UbufW85xaU+Jp87gBtOVrMzEak7FPghsGFnASlp\n6Xy9eicje7blgfFD6dm+uddliYj8jAI/CGU+x0tfr+PhBSuoX8+49+Ih/GpkgpqdiUidpMA/Sivz\n9zNxVjpLN+7hjP4dmD4uiS6tm3pdlohIpRT4NVRc6uOZz1bz+CeraNG4AY9dMYyLjumiZmciUucp\n8Gtg2cY9TEpNJ2frfi48pgtTLxxEuxZqdiYikUGBXw2Hisv4+8KVPPfFGjrENebZa5I5e1Anr8sS\nEakRBX4Vvlm9k8lp6azbWcCVI7sz+byBtGyiZmciEnkU+JXYV1jCjPdzeP27DSS0bcbrN47ixD5q\ndiYikUuBX4FPcvK5PS2TbfsLuemUnvzl7P40baS2CCIS2RT45ew8UMQ987KZs3QL/TvF8czVwxnW\nvbXXZYmIhIQCH39bhLnLtnD3u9nsLyzhT6P78vvT+9CogdoiiEj0iPnAz9t7iDtmZ/JxzjaO6d6a\nB8cPpX/nOK/LEhEJuZgNfJ/P8eYPG7l//nJKfD7uOH8gvzmpJ/XVFkFEolRMBv66HQdJSUvn2zW7\nOKFXO2aMT6JHOzU7E5HoFlOBX+ZzvPDlWh75aAUN69Xj/kuSuGJEd7VFEJGYEDOBn7N1H5NmpbNs\n015GD+zIvRcn0blVE6/LEhGpNVEf+EWlZTy5aDVPLcqlVdOGPH7lsVwwNF5b9SISc6I68P+zYTeT\nUtNZmX+Ai4d14W8XDqZt80ZelyUi4omoDPyC4lIe+XAlL3y1ls4tm/DCdcmcOUDNzkQktkVd4H+d\nu4OUtAw27CrgqlEJpJw7gDg1OxMRiZ7A33uohPvnL+fNHzaS2K4Zb044nuN7tfO6LBGROiMqAj99\n0x5uemUx2/cX8dvTevHn0f1o0lDNzkREygsq8M1sGjAW8AHbgOucc1sC8yYDNwBlwK3OuQVB1lqp\nhLbN6NcpjmevSWZoNzU7ExGpiDnnjv7OZi2dc/sC128FBjnnbjazQcAbwEigC7AQ6OecKzvS4yUn\nJ7vFixcfdT0iIrHIzJY455KrWi6odpA/hX1Ac+Cn/x5jgTedc0XOubVALv7wFxERjwS9D9/MpgPX\nAHuBMwKTuwLflltsU2BaRfefAEwASEhICLYcERGpRJVb+Ga20MwyK7iMBXDOTXHOdQdeA/6npgU4\n52Y655Kdc8kdOnSo+W8gIiLVUuUWvnNudDUf6zVgPnAXsBnoXm5et8A0ERHxSFD78M2sb7mbY4Gc\nwPW5wBWPAatIAAAFeElEQVRm1tjMegJ9ge+DWZeIiAQn2H34M8ysP/7DMtcDNwM457LM7G0gGygF\nbqnqCB0REQmvoALfOTf+CPOmA9ODeXwREQkdnaVbRCRGBPXFq1Azs+34dw0drfbAjhCVE0qqq2ZU\nV82orpqJxrp6OOeqPMyxTgV+sMxscXW+bVbbVFfNqK6aUV01E8t1aZeOiEiMUOCLiMSIaAv8mV4X\nUAnVVTOqq2ZUV83EbF1RtQ9fREQqF21b+CIiUgkFvohIjIiowDezy8wsy8x8ZpZ82LzJZpZrZivM\n7JxK7t/WzD4ys1WBn23CVOdbZrY0cFlnZksrWW6dmWUElgv7mV/MbKqZbS5X23mVLDcmMI65ZpZS\nC3U9ZGY5ZpZuZrPNrMLTltXGeFX1u5vfPwPz083suHDUUcF6u5vZIjPLDrwG/ljBMqeb2d5yz+/f\naqm2Iz4vXoyZmfUvNw5LzWyfmf3psGVqZbzM7AUz22ZmmeWmVSuLQv5adM5FzAUYCPQHPgWSy00f\nBCwDGgM9gdVA/Qru/yCQErieAjxQCzU/AvytknnrgPa1OH5Tgb9WsUz9wPj1AhoFxnVQmOv6BdAg\ncP2Byp6XcI9XdX534DzgfcCA44Hvaum5iweOC1yPA1ZWUNvpwLza+nuq7vPi1Zgd9rxuxf/lpFof\nL+BU4Dggs9y0KrMoHK/FiNrCd84td86tqGBWdc+wNRZ4OXD9ZeDi8FTqZ2YGXI7/dI+RYiSQ65xb\n45wrBt7EP25h45z70DlXGrj5Lf522l6ozu8+FnjF+X0LtDaz+HAX5pzLc879GLi+H1hOJScVqoM8\nGbNyzgJWO+eC+Rb/UXPOfQ7sOmxydbIo5K/FiAr8I+gKbCx3u7IzbHVyzuUFrm8FOoW5rlOAfOfc\nqkrmO2ChmS0JnPmrNvwh8Lb6hUreRlZ3LMPlevxbgxUJ93hV53f3enwws0TgWOC7CmafGHh+3zez\nwbVUUlXPi9djdgWVb3R5MV5QvSwK+bgFfYrDUDOzhUDnCmZNcc7NCdV6nHPOzI76mNRq1nklR966\nP9k5t9nMOgIfmVlOYGvgqB2pLuBpYBr+F+g0/Lubrg9mfaGo66fxMrMp+Ntpv1bJw4R8vCKNmbUA\nUoE/uZ+fUxrgRyDBOXcg8PnMO/jPRRFudfZ5MbNGwEXA5ApmezVePxNsFtVEnQt8V/0zbJVX3TNs\n5ZtZvHMuL/CWctvR1AhV12lmDYBLgOFHeIzNgZ/bzGw2/rdwQb1Qqjt+ZvYsMK+CWWE5W1k1xus6\n4ALgLBfYgVnBY4R8vA5Tnd/ds7O5mVlD/GH/mnMu7fD55f8BOOfmm9lTZtbeORfWRmHVeF68PAPe\nucCPzrn8w2d4NV4B1cmikI9btOzSqe4ZtuYC1wauXwuE7B1DBUYDOc65TRXNNLPmZhb303X8H1xm\nVrRsqBy233RcJev7AehrZj0DW0dX4B+3cNY1BpgIXOScK6hkmdoYr+r87nOBawJHnhwP7C331jxs\nAp8HPQ8sd849WskynQPLYWYj8b++d4a5ruo8L56MWUCl77K9GK9yqpNFoX8thvsT6lBe8IfUJqAI\nyAcWlJs3Bf8n2iuAc8tNf47AET1AO+BjYBWwEGgbxlpfAm4+bFoXYH7gei/8n7ovA7Lw79oI9/j9\nC8gA0gN/OPGH1xW4fR7+o0BW11Jdufj3VS4NXJ7xarwq+t3xn8nt5sB1A54MzM+g3NFiYR6jk/Hv\niksvN07nHVbb/wTGZhn+D79PrIW6Knxe6siYNccf4K3KTav18cL/DycPKAnk1w2VZVG4X4tqrSAi\nEiOiZZeOiIhUQYEvIhIjFPgiIjFCgS8iEiMU+CIiMUKBLyISIxT4IiIx4v8B8xtigiVZuQMAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb545e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# This can be used to plot functions\n",
    "x_data=np.linspace(-10,10,1000)\n",
    "plt.plot(x_data,line(x_data))\n",
    "plt.title(str(line))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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29iyh95PCwo29e3RyHbS19VkIMlwrPS30TFuNph1IJ4bei3RCLS3/sHPmq5Vd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\ng28YhtFGMINvGIbRRjCDbxiG0Ub4P/CsfaFw0t4DAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb890a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# if you have a data set it can actually fit the data using the model\n",
    "x_data=np.linspace(-10,10,1000)\n",
    "# make a line with a little noise\n",
    "y_data=np.array([2*x + 3.5 +random.gauss(0,5) for x in x_data])\n",
    "# now to fit we use line.fit_data\n",
    "line.fit_data(x_data,y_data)\n",
    "plt.plot(x_data,y_data,label=\"Data\")\n",
    "plt.plot(x_data,line(x_data),\"rx\",label=\"Fit\")\n",
    "plt.title(str(line))\n",
    "plt.legend(loc=4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# this works with even more complicated functions\n",
    "gaussian=FunctionalModel(parameters=\"alpha x0 delta\",variables=\"x\",equation=\"alpha*exp(-1*(x-x0)^2/(2*delta**2))\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha*exp(-(x - x0)**2/(2*delta**2))\n"
     ]
    }
   ],
   "source": [
    "print(gaussian)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xbfd0198>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KpF9r9xClkSIaF5dl/NjNGusuAZr1dz93Hzezh4DngAjwpLsfNLMHY8sfc/dDZvZtYB8w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\nIYW7iEgeUriLiOQhhbuISB76/53juMltTiusAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xba680f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# it also has a latex form\n",
    "x_data=np.linspace(-1,1,1000)\n",
    "plt.plot(x_data,gaussian(alpha=1,x0=.1,delta=.1,x=x_data))\n",
    "plt.title(\"${0}$\".format(gaussian.to_latex()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xb8cfd68>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FtGwUE7S2Q2317sM8OHM9KenHmTCwPY9e0Tei/n5/UxeQiA+WpmTRPa4xbZrWD2q71w+J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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc05d780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now you have the ability to add functions \n",
    "gauss_line=line+gaussian\n",
    "x_data=np.linspace(-1,1,1000)\n",
    "plt.plot(x_data,gauss_line(alpha=1,x0=.1,delta=.1,m=1.2,b=.1,x=x_data))\n",
    "plt.title(\"${0}$\".format(gauss_line.to_latex()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-alpha*(2*x - 2*x0)*exp(-(x - x0)**2/(2*delta**2))/(2*delta**2) + m\n",
      "3*alpha*exp(-(x - x0)**2/(2*delta**2))/delta**4 - alpha*(2*x - 2*x0)**2*exp(-(x - x0)**2/(2*delta**2))/delta**6 - alpha*(2*x - 2*x0)*(8*x - 8*x0)*exp(-(x - x0)**2/(2*delta**2))/(8*delta**6) + alpha*(2*x - 2*x0)**4*exp(-(x - x0)**2/(2*delta**2))/(16*delta**8)\n",
      "alpha*(x - x0)**2*exp(-(x - x0)**2/(2*delta**2))/delta**3\n"
     ]
    }
   ],
   "source": [
    "# we can take a derivative\n",
    "print(gauss_line.d())\n",
    "# or a higher order one\n",
    "print(gauss_line.d(order=4))\n",
    "# or with respect to a parameter\n",
    "print(gauss_line.d(respect_to=\"delta\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xbacca58>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rCL0n6LA7FY0XSz7bD6Un+Ty7p4PP/Pdz7Gjt48KTF/KJC9dwxtKq0I8r0ROp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\npJ2Sj4iIpN3/B1ClKon3ZO+CAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc05da58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we could even plot/fit using the derivative of any order\n",
    "gauss_line=line+gaussian\n",
    "x_data=np.linspace(-1,1,1000)\n",
    "gauss_line_d3=gauss_line.d(order=3)\n",
    "plt.plot(x_data,gauss_line_d3(alpha=1,x0=.1,delta=.1,m=1.2,b=.1,x=x_data))\n",
    "plt.title(\"${0}$\".format(gauss_line_d3.to_latex()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pv/zPgibbuMdfD7zzXVYk8CLr6hsI1jewxu5JuPDxmXwWpXu4udOijU8snJsz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\nUsIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc05dfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Qp5WEF877LBrvh1c/3cAs14szsG+poSjGKaFZtkF8SYw3TNc/vRXSiyMcj72z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\nUioiWUHr7hKRtSLyrYgMdbX3E5Hl9rp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      "text/plain": [
       "<matplotlib.figure.Figure at 0xb69f470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# or create data and fit it\n",
    "gauss_line=line+gaussian\n",
    "x_data=np.linspace(-1,1,1000)\n",
    "output_noise=np.random.normal(0,100,len(x_data))\n",
    "gauss_line_d3=gauss_line.d(order=3)\n",
    "y_data=gauss_line_d3(alpha=1,x0=.1,delta=.1,m=1.2,b=.1,x=x_data)+output_noise\n",
    "plt.plot(x_data,y_data)\n",
    "plt.title(\"${0}$\".format(gauss_line_d3.to_latex()))\n",
    "fig=gauss_line_d3.plot_fit(x_data,\n",
    "                           y_data,\n",
    "                           **{\"title\":\"Fit of Noisy Data\",\"initial_guess\":{\"alpha\":1,\"x0\":.1,\"delta\":.1,\"m\":1.2,\"b\":.1}})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LjkwbmodrzuuBCSYlIKwWUlI/2hy+rzVyOIfPjHDAZ2H31692K4EYcPVAT5zV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\n8f8BCcSi20zfPM4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcaa2978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TvviJhev3+x1nMLdYb/rRBzSoLLM8NuoVrqphzJAOnjVffUt3mrpLKwd3aeXZ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\n3LhrsWRTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd0564e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# now we can create a DataSimulator object to change the output noise on any FunctionalModel and fit it\n",
    "model=line+gaussian\n",
    "model_2=line+gaussian\n",
    "model.set_parameters(m=.5,b=3.4,delta=1,x0=10.,alpha=20)\n",
    "simulated_data=DataSimulator(model=model,output_noise_type=\"normal\",output_noise_width=2.,output_noise_center=0.)\n",
    "simulated_data.set_x(-25,25,1000)\n",
    "plt.plot(simulated_data.x,simulated_data.data)\n",
    "fig=model_2.plot_fit(simulated_data.x,simulated_data.data,**{\"title\":False,\"initial_guess\":model.parameter_values})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# now we can create an interactive plot\n",
    "# By passing a keyword set of parameters we can change which parameters that we interact with\n",
    "def plot_fit(**options):\n",
    "    defaults= {\"output_noise_type\":\"normal\",\n",
    "              \"output_noise_width\":2,\n",
    "              \"output_noise_center\":0,\n",
    "              \"m\":.5,\n",
    "              \"b\":3.4,\n",
    "              \"delta\":1,\n",
    "              \"x0\":10,\n",
    "              \"alpha\":20,\n",
    "              \"x_min\":-25,\n",
    "              \"x_max\":25,\n",
    "              \"number_points\":1000}\n",
    "    fit_options={}\n",
    "    for key,value in defaults.items():\n",
    "        fit_options[key]=value\n",
    "    for key,value in options.items():\n",
    "        fit_options[key]=value\n",
    "    line=FunctionalModel(parameters=[\"m\",\"b\"],variables=\"x\",equation=\"m*x+b\")\n",
    "    gaussian=FunctionalModel(parameters=\"alpha x0 delta\",variables=\"x\",equation=\"alpha*exp(-1*(x-x0)^2/(2*delta**2))\")\n",
    "    model=line+gaussian\n",
    "    model_2=line+gaussian\n",
    "    model.set_parameters(m=fit_options[\"m\"],b=fit_options[\"b\"],\n",
    "                         delta=fit_options[\"delta\"],x0=fit_options[\"x0\"],alpha=fit_options[\"alpha\"])\n",
    "    simulated_data=DataSimulator(model=model,output_noise_type=fit_options[\"output_noise_type\"],\n",
    "                                 output_noise_width=fit_options[\"output_noise_width\"],\n",
    "                                 output_noise_center=fit_options[\"output_noise_center\"])\n",
    "    simulated_data.set_x(fit_options[\"x_min\"],fit_options[\"x_max\"],fit_options[\"number_points\"])\n",
    "    model_2.fit_data(simulated_data.x,simulated_data.data,**{\"initial_guess\":model.parameter_values})\n",
    "    parameter_text=\"${0}$\\n\".format(sympy.latex(model_2.equation))\n",
    "    for key,value in model_2.parameter_values.items():\n",
    "        parameter_text=parameter_text+\"{0} = {1:3.2g} \\n\".format(key,value)\n",
    "    fig, (ax0, ax1, ax2) = plt.subplots(nrows=3)\n",
    "    ax0.plot(simulated_data.x,simulated_data.data,label=\"Data\")\n",
    "    ax0.plot(simulated_data.x,model_2(simulated_data.x),\"ro\",label=\"Fit\")\n",
    "    ax0.legend()\n",
    "    ax1.text(fit_options[\"x_max\"]+7,\n",
    "             .1,\n",
    "             parameter_text,\n",
    "             fontsize=12)\n",
    "    residuals=simulated_data.data-model_2(simulated_data.x)\n",
    "    ax1.plot(simulated_data.x,residuals)\n",
    "    ax2.hist(residuals)\n",
    "    plt.show()\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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s3s+A085kwGlnAtClazcmzlzkXZdf6Ca7oIgm9atn4SC97vwnwFBgiVLKLSJr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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcfd5160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.plot_fit>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interact(plot_fit,\n",
    "         x0=(-20,20,1),\n",
    "         alpha=(-100,100,1),\n",
    "         m=(-2,2,.1),\n",
    "         output_noise_width=(0,10,1),output_noise_type=[\"normal\",\"uniform\",\"triangular\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Use case of electronic circuits\n",
    "We can build electronic circuit models\n",
    "<br/>\n",
    "$Z_{L}=i 2 \\pi f L $ <br/>\n",
    "$Z_{C}=\\frac{- i }{2 \\pi f C} $ <br/>\n",
    "$Z_R=R$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xcdbe748>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SUuNCbPB1kYRkbm4uI0aMaPDcfD4fbre7yeOA/8NHrV23JRZj/+np6aEF5FTH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcaba7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We can use these models for simple electronic circuits\n",
    "Zc=FunctionalModel(variables=\"f\",parameters=\"C\",equation=\"-1*I/(2*pi*f*C)\")\n",
    "Zl=FunctionalModel(variables=\"f\",parameters=\"L\",equation=\"I*(2*pi*f*L)\")\n",
    "Zr=FunctionalModel(variables=\"f\",parameters=\"R\",equation=\"R\")\n",
    "# now for frequencies\n",
    "frequency=np.linspace(0.1*10**3,1*10**9,10000)\n",
    "\n",
    "z_total=Zc**-1+Zl**-1+Zr**-1\n",
    "# a RLC circuit\n",
    "z_total=Zr+(Zc*Zl)/(Zc+Zl)\n",
    "# voltage across the resistor\n",
    "Vr=Zr/z_total\n",
    "\n",
    "# plot of voltage across a resistor\n",
    "Vr.set_parameters(C=10**(-10),L=10**-8,R=complex(50,0))\n",
    "plt.plot(frequency,abs(Vr(frequency)),label=\"Voltage Across R\")\n",
    "plt.text(2*10**8,.5,\"${0}$\".format(sympy.latex(Vr.equation)),fontsize=34)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda2\\lib\\site-packages\\numpy\\__init__.py:1: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"\"\"\n",
      "C:\\ProgramData\\Anaconda2\\lib\\site-packages\\numpy\\__init__.py:1: RuntimeWarning: invalid value encountered in true_divide\n",
      "  \"\"\"\n",
      "C:\\ProgramData\\Anaconda2\\lib\\site-packages\\numpy\\core\\numeric.py:482: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xca7a080>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4xTsTVhfl0qqxl8178mu8i6zd+eQWldK1eWpgXwCMekXHaFdKhUzTIpziyyat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\n1P1D/yYYbZZRSoWfhns0OMG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      "text/plain": [
       "<matplotlib.figure.Figure at 0xc398668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# again we could create a simulated data set with output noise\n",
    "Vr_simulated_data=DataSimulator(model=Vr,\n",
    "                                output_noise_type=\"normal\",\n",
    "                                output_noise_center=0,\n",
    "                                output_noise_width=.01)\n",
    "plt.plot(frequency,abs(Vr_simulated_data(frequency)),label=\"Functional Model\")\n",
    "Vr_simulated_data.set_x(0,10**9,1000)\n",
    "plt.plot(Vr_simulated_data.x,Vr_simulated_data.data,label=\"Simulated Data With Output Noise\")\n",
    "plt.title(\"Simulated Voltage Data\")\n",
    "plt.legend(loc=4)"
   ]
  }
 ],
 "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": "2.7.13"
  },
  "widgets": {
   "state": {
    "52d211924b04457984a3a14d03f3d311": {
     "views": [
      {
       "cell_index": 17
      }
     ]
    }
   },
   "version": "1.2.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
