cooling water

model fitting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# background\n",
    "\n",
    "I wanted to explain fitting data, and thought a nice example would be cooling water.  I heated water in a small pan with a digital thermometer in it.  When the water boiled I started measuring the temperature, I started with every °C change, but got distracted and measurements tailed off…"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import optimize\n",
    "\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set(style='ticks')\n",
    "plt.rcParams[\"figure.figsize\"] = (6, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# load data\n",
    "\n",
    "load the data into a data-frame; pull out time in minutes from the start, and show the last few rows to make sure it's all loaded"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>datetime</th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>2021-04-30 17:40:07.131095</td>\n",
       "      <td>36.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>2021-04-30 17:42:06.586292</td>\n",
       "      <td>35.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>2021-04-30 17:43:22.915849</td>\n",
       "      <td>34.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>2021-04-30 17:46:58.308528</td>\n",
       "      <td>32.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>2021-04-30 18:03:05.450975</td>\n",
       "      <td>27.9</td>\n",
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      ],
      "text/plain": [
       "                     datetime  value\n",
       "46 2021-04-30 17:40:07.131095   36.0\n",
       "47 2021-04-30 17:42:06.586292   35.0\n",
       "48 2021-04-30 17:43:22.915849   34.4\n",
       "49 2021-04-30 17:46:58.308528   32.8\n",
       "50 2021-04-30 18:03:05.450975   27.9"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('temp.csv', parse_dates=[0])\n",
    "\n",
    "time = df['datetime'].values\n",
    "vals = df['value'].values\n",
    "\n",
    "mins = (time - time[0]) / np.timedelta64(1, 'm')\n",
    "\n",
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# find and fit function\n",
    "\n",
    "the next thing I did was to try and figure out what function to fit it with\n",
    "\n",
    "I was using this to explain something of the form $\\exp(-t \\tau)$ but wasn't sure what other terms were in there.  I ended up with:\n",
    "\n",
    " * `b` for a \"baseline\" equlibrium temperature, i.e. room temperature\n",
    " * the boiling point; actually slightly above presumably because the metal pan was a bit hotter\n",
    " * $\\tau$, the cooling rate\n",
    " * some exponent; not sure what the physical interpretation of it is but maybe the difference in cooling between metal/water?\n",
    " \n",
    "this gets a reasonable fit using a single significant digit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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H9BoxbvCcxhyp34/SpCsRmUkK+6vA5cul7lOf5Na1C1lSHqDAGkiNvx+lFTJFZCZpIbSrxFsUZNmNH6G8/hCxuA3tHfTaOTQmitmwMsjamtJ0N1FEMpjC/iryVtQQ7+vm5jUQ6hhgVX8E/6pruWHNcq2IKSIzSmF/FRmGgX/5euzBXsoNg/ISMKPHIbYQvLnpbp6IZDDV7K8yw3LjX/FRTJcbADs6RP+R3+AkYhd4p4jI5VPYp4GVk4+/9iMYRrJ0E+/vZuDY6zhOcoSObTscONbKD185rklXInJFqIyTJu7CILnL1jNwcj8A0a5mzPpD+Kpv4Ovfe4N9R8ZufqI7XYnIdE37yj4SibBz505uv/127rzzTr70pS8BcOrUKbZu3crmzZvZunUrp0+fnu63yjje8mp8C69NPR9uPsnbv903IehBk65EZPqmfWX/5JNP4vV6eemllzAMg46ODgB27tzJtm3buOuuu/jpT3/KY489xve///1pNzjT5Cy+Hnuon2hHIwD9Jw8StPyEEgUT9qtv6mF9bVkaWigimWBaV/YDAwM8//zzPPTQQ6n68/z58+ns7OTo0aPU1dUBUFdXx9GjR+nq6pp+izOMYRj4azbgyi8GoCjfy/Xus8w3wxP206QrEZmOaV3ZNzQ0UFBQwO7du9m3bx9+v5+HHnoIn89HWVkZlmUBYFkWpaWltLS0UFRUNOEzwuEw4fDEYAuFJpYxMp1huci77hb63n6V4HyHqtJcnLbTvBFZSq/j58YVZdi2ww9fOc7SygLW1pSqfi8il2RaYZ9IJGhoaGDFihU8+uijvP322/zxH/8xTz311EV/xjPPPMPu3bun04yMYLq95K+6lfChvdy8poJlHQOsHujHv+pD/NvBLh7/532pfdVhKyKXalphX15ejsvlSpVrVq9eTWFhIT6fj9bWVhKJBJZlkUgkaGtro7y8fNJn3Hfffdxzzz0TtoVCIbZv3z6dps1JpjeX/FW30vf2q5SXJCddNTe8weFjLsCX2m90Lfzfu6FSV/kiclGmVbMvKipiw4YNvPbaa0ByBE5nZyeLFy+mtraWPXv2ALBnzx5qa2snlXAAAoEAlZWVE76CweB0mjWnWbkB8q67FcNKTrrq7uxhg7eeXGN4wn5aC19ELoXhOM60kqKhoYEvfvGL9PT04HK5ePjhh7n11lupr69nx44dhMNhAoEAu3btorq6+qI+s7GxkU2bNrF3714qKyun07w5K9bbRv87v6K5tZdfvtXIsOPhjchSBh3vpH13fvomjdQRkfOadtjPBIV9Uqynjb53fsWvD56hsb3/nIG/+pr53H3rMpV0ROScNIN2FnMXlJK/6hZuwaGlLcyZUBia6nkjWs2gM1bDf/tkB2+f7FDHrYick9bGmeXcBWXkX3cLC8rmseG6cpaVebjJ+x75xtCkffcdCfHDfz+uGr6ITKKwnwPchUHyVt6Mabm4eU0Ft68NcndFC/OMgUn7/u+XjqvTVkQmUdjPEe7CIPmrbsV0eSgvyWNlVYAbve9TbPZN2nd0aKZWzBSRUQr7OcQ1r4T86z+O6fYSnO9nUWkO6zynKLe6J+2roZkiMp7Cfo5x5ReSv3ojli+Xm9dUsHpZEas9Z1jiagMmh7pWzBQRUNjPSVZugPzVm3D557GyupjKkjxq3M2scDdhTBH49U09V7+RIjKraOjlHGX5/OSv3sjA0ddSNzA/EwqT03iKQ9FFJLBS+2rFTBFR2M9hpttL3qpbGTj+BuXGWYLz/cTiTXha6zkYWUwEDxtWBllbU4ptOxw83kZ9Y49WzhTJQgr7Oc4wLfzX3oTpy2W44d3UipkfHewlf8VHWXND8k5YutWhSHZT2GcAwzDIXbIay+tnsP4g5SV5lAPG4GFirV7e6fFPeatDrZwpkj0U9hnEu2AZZm4+A8d+ix2L4Dg2Ayf309Gag4GN84H++F+82cgv3mzUVb5IFtBonAzjLigjf81tuPzzUtsWmu3c6HkfD7Ep36PhmSKZT2GfgaycPPLXbMJTshCA4Hw/q4LwUd+JKWfcAvzqrUZ++MpxzboVyVAq42Qow3Ljv/bDWP4Chk8fTnXc1oQ6+PezA9THy3AYK9v84s3G1GOVdUQyj67sM5hhGORUrSBv1e9heXyUl+Rx03VBPragn/Uq64hkFYV9FnAXBgms3Yy7oBTDMLh5TQX/Zf08Pr+6m7rrc6d8j2bdimQWlXGyhOnNIW/VrQyfPcrwmaPJ4ZklML/9LKfcw7wbK59y1q0mY4lkBoV9FjEMk5xF1+EKzGfg+D7s6DDB+X4+XN5DUesJfhddRK+TO2HWrSZjiWQGhX0WGi3rDL73JtGOxlTn7Yf7usmvrmTVR9ZhmgYHjrVOORnr4PE23eBcZI5RzT5LmR4f/tqP4F9+49gNUaqLqaKZgbf3Eu/rpr6xZ8r3qp4vMvco7LOYYRh4g0sIrL0dV2B+ant8oIe+Q69Q4wlhYk96n1bRFJl7FPaSnIS1+uPkVq/GMJOdtI7jsJAWti9uodDsT+07Ws8XkblFNXsBkp23vsprcRdVMHhyP7HedgzDYNP1RaxcMECj7af42nWsXVmpzlmROUhhLxNYufnkXf9xoi31DJ76HSRiI6toRjD7DhBrjeIJLsEwzv9HoYZsiswuCnuZxDAMvAuW4S5ekByx09kMgB2PMnDyAJHQ++QuW4crv2jK92vIpsjso5q9nJPpzSVv5S3krbwFy+dPbY/3ddH31r8zcPIAdiwy6X0Hj7edc/18LbQmkh66spcL8hQvwF1QynDjuww3vItjJ3BwiLTUE2s/i69qBd4F16Q6d881ZFPr54ukj67s5aIYloucRdcRWLcZd1F5arsdjzH4/tuED/wb0bazOI7D0sqC836WFloTufp0ZS+XxMrJJ2/lLcS6mhl6/20SQ8n18RPDA/S/+1tcTSe4fvH1bFgZnFTKGe+9xm4AdeCKXCWG4zizroDa2NjIpk2b2Lt3L5WVlelujpyDYyeItLzP8Nkjk2r3rsIFnIyX8f+O9U1YK39UTVUhx892p56rtCMys1TGkctmmBa+imsIfOg/4au8dsJwzHh3M0v63uIzq4f5vWsDE973waCHsdKObTscONaqu2aJXGEq48i0mS4PudWr8S5YxtDp3xFtO5t6LdbZyP3L4fYlBZyMl7J40QLea+iZFPaQLO38/LenNWRTZAYo7OWKsXx+8q79MPHKWobPHCba2ZR8wYCFnh6qvL14zBhGafGU73cctMqmyAxRGUeuOFdeAXkrbyaw5jbchcHUdsdxiLSeYknvAf5rdQ/5xlDqtQ0rgxhMffU+usqmSjwil09X9jJjXIFi8lfdSry3naHT7xDrbU++YEDddV7WBwdojhkUX3M9a2649pzDMZdWFGhWrsg06cpeZpxrXgn5qzcSWL0xNUbfMAzKS/JYtwAWD/yO/t+9ynXFETasmFiuGV1l81yzcjVeX+TiXLEr+927d/N3f/d3vPjiiyxfvpxDhw7x2GOPEYlEqKio4Mknn6S4eOparWQH17wS8ueVEO/rZrjhKLGOJhySpZh4uIN4uIM/WZnLJ64t4+RAPtUL56fG35/vRiqj9XwtviZyblck7I8cOcKhQ4eoqKgAwLZt/uzP/oxvfOMbrF+/nm9/+9v8zd/8Dd/4xjeuxLeTOc6VX0jeio+SGAwz3HCMaNsZRqd7ONFBFnGGxX43Xk8UJ5oHPv85Z+WOvzH6B8s8NVWFrK8tY9lCBb/ItMs40WiUr3zlK/z1X/91atvhw4fxer2sX78egD/4gz/g5z//+XS/lWQYKzeAv2YD8268k5yFtZguT+o1JxFjuOkE4Td+Rv+R37Cq1D5niQemXnzt+Nlunn3pXb783df5+vfeUIeuZLVpX9k/9dRTbNmyZcJM15aWFhYsWJB6XlRUhG3b9PT0UFBQMOH94XCYcDg8YVsodO5p9pJ5TG8OOUuux1e1gmjraYabTqSWYXBwiHY2Ee1s4rPX+amrKeHkQD5LqkonXK2fq8wzavwQTpV7JBtNK+zfeustDh8+zCOPPHLZn/HMM8+we/fu6TRDMoRhufAuWIanfCnx7haGm04Q625NvW5HBqhigEW5Jm6jn0SfgREowTCMCy6+Bsn6/tqaUo3qkaw0rbDfv38/9fX1bNq0CUhekd9///3ce++9NDc3p/br6urCNM1JV/UA9913H/fcc8+EbaFQiO3bt0+naTKHGYaBu2gB7qIFJAbDRFrqibaewo7HAHAcm2jbWaJtZ7Fy8vEGl7BmcdUFF19bWlFw3lE9mrglmWxaYf/AAw/wwAMPpJ5v3LiR73znOyxbtowf/ehHHDhwgPXr1/Pcc89xxx13TPkZgUCAQCAw5WsiVm6A3KU3kLN4FdH2BiIt9cT7OlOvJ4b6GDz1O4xT7/D59WXUr6jieNjDgWOdkxZaW1tTyv/Ze2LK7zM6qkclHslUMzKpyjRNnnjiCXbu3Dlh6KXI5TIsF97gErzBJcT7uomE6pOjeBJxIFnbj/eEWESIJXlu6u5YyIn+Ek52GSytLEyF9vlG9WjilmSyKxr2r776aurx2rVrefHFF6/kx4sAyaGbrvz15FavJtrRRLT1FLGesclVdjxGtPV9FgNL5/lx+xZiD3ow/Mkr9Q+Wey5m4pau+mWu03IJMmcZlhtv2WK8ZYtJDA8QbT1NtPUUieGB1D6J4QESDcnbKVo5+XhKq3j0k9fydsNi6pt6WFpRcFETt87Vsbvjv32IQyfbdQKQWU9hLxnB8vnJWbQSX9UK4uF2oq1niHU0pDp1IVnfHzpzBM4cYXleIdfVLMRdnJsK5/OVeM511b/j6d9M6Bu4cUUZm29azKnmXoW/zCoKe8kohmHgnleKe14pzrK1xLpDRNvPEutsTtX3AeL93cT7u+HU77ByA3jmV3L9ggVsWFHGvqNjwz0v1LH7wXX53zjayhsfeL9q/jIbKOwlYxmmhae4Ak9xBU4iRqyrhWjbWWJdLTiOndovMRhm6OxROHuUP1mZw53V+bw/mMvCJYtYe23wvB27F6JhnTJbKOwlKxiWG09JFZ6SKux4lFhHE7HOJmLdIRw7kdrPiQ6x0BpiYT6YPS0MngjiLixnTXVwUsfuVLdXnMr4xdpGqbNXrjaFvWQd0+VJDeN0EjFi3a3EOhqJdTVPqPHb8Whq8paBwefWFFK3rIj3+31ULV7ImuWlfPP7+887kQvGFmtLfe55hngCOgnIjFDYS1YzLDee+ZV45lfi2Anive3EOpJr8djRsTtpOTgk+ruoAqrywAw3E6kP8sgnyjn8oQXUtw5SvWAeP//tGd44OnlY53jn6ux9891WXnr9jMb5y4xQ2IuMMEwLd2EQd2GQnGVrSfT3EOtuJtbVQiLclVp7H8CODhNpPQ2tp1mKwfKiAly+Mq6/ayHv3FRJfUv/hGGd451riOevDzVpKQeZMQp7kSkYhjEyeauQnKqV2LEI8e4Qsa4WYt0h7Fgkta+DMza6h3dZapjUlBTjyo1j91sYeYUYppXa/1I7e6eq+YtcKoW9yEUw3V48pYvwlC7CcWwSfd3EupqJ9bSS6OtK3XwFkgu1xXrbifW2M3TmMIblxhUoxjVvPq55JdxwTfGUs3hvXl3BL95snPS9P1jzvxjqAJYPUtiLXCLDMJPhHSgmh1U48Rix3jbiPW3EultJDPZO2D/ZCRwi1h1Kvf9zNxRSt7SA031uKhdXsXZF8i5v51rK4VJojR+ZisJeZJoMlzs1nh/Ajg6lgj/W04odGZywf/Ivg06qDKgKgNHVSP+hAlyB+TzyiSBH1pXyXltkwgJul0LLOMtUFPYiV5jpyRlX8nGwhweSN1TvbSfe2566C9eoiTX/kywBlub7cNnFRBo7k39F5BVhuNwX9f0v5ubskn0U9iIzyDAMrJw8rJw8vGWLgZEr/96R8A93kOjvmTDSJ7nPMNHOJuhsSn4OBpY/gJVfjCu/GCu/ECs3MKHjd9SFbs4u2UlhL3KVmZ4cPCUL8ZQsBJKTtxLhDuLhzuRXXxdOIjbhPQ4O8YFe4gO9RELvA8mholZuACu/CFdeIVZeIZZ/3nmXcZbspbAXSTPT5cEcuQ0jkCz9DIaJ9yXDP9HXSWIgPOnq37ETqfLP6EBQwzCwcufx8EcKOFkT5HQPLFxcydraBeqczXIKe5FZxjAMLP88LP88vMFqIDmiJ97XTaIveeWf6O+esG7/KMdxiA/0wEAPi4BF+UDnafoO+LH8BanPtXLnYebmYxjmVT02SR+FvcgcYFhu3AWluAvGSjF2LJIM/f4e4v3dJPq7SAz1T/n+xPBA8uQw0gcAI2WgnPzkSSAveQKw/AUYHh+Gob8CMo3CXmSOMt1ezJHlHUbZ8SiJ/p6Rk0CyxGMP9U2Y9DXKsRPEB3qSfwm0jftclwczNx8rJ4CVG0g9NnP8+ktgDlPYi2QQ0+XB/MBfAI6dIDEYJjHQO/LVQ2KwFzsyNOVn2PEo9khn8XiGYWLm5GPl5idPAjnJf63cfAzr4oaFSvoo7EUynGFauPIKceUVTthuxyIkBntJ9Pcm/x3oSXYEf2Ak0CjHsZP7fWCGMIDp8WH6kkNMzZw8LF8+5shj0+WZkeO6GjJp2QmFvUiWMt1ezJFbOI5yHAcnOpT8S2CwD3soPPY4OvVfApCcF2BHh4mHO6b+PuNOAFZOHqYvD9Pnx3B7Z23/QKYtO6GwF5EUwzAwvLmY3twJfQEATjyWDP6hvmQZaLCPxGAYe7h/yj6BUXYsklw19ANlIUj+1WH6/Jg+P5bXP/I4F3PkcTpPBpm27ITCXkQuiuFypxaAG89xbOzhQezhfhJD/dhDfeMe90+43+8HpfoTBsNMVTwaPRlYvrzkScDnx/TkYnpzkiclj2/KWcRXQqYtO6GwF5FpMQwztSSEe2K3AI5j40SGSAwngz8x1I89nDwhJIYHz9k/kHr/uJPBlN8bA8Pjw/TmYHpzMT05yZPCFTghZNqyEwp7EZkxhmFijJRpKJh4New4Dk48mvyrIDKAPTzyNfL4ok4GJPsY7OgQ9HVN3QYMDI935GTgw/DkJDuUPTnJE8XI8+T8grGhpZm27ITCXkTSwjAMDLcX0+2F/MJJr5/zZBAdwo4MYkeGcKLDk5aRmPQ5ODgjHcjnbQ8Ghtsz4STwhY/5OFFTxtnOKAsrSlh1bQWGHccxXLO2Y/lcFPYiMitd6GQAyTKPHR3GGQl/Ozryb2Twkk4IMHJSGOlMZtxKFIuARQXAQAt9b/4u2TbTSrXN8PgwXd7kXw9uX3K7x4vh9iVfd3sxrPRHbfpbICJymQzTwvL5wec/5z6OnUhe2UcGR4aIDo1c6Q8lTxQj/46/r/CFOHZi5AQzeOGdAcNyjQS/L3kicHnHThZuz9hjlxfT65uRSWoKexHJaIZpjfUbnIdjJ5JX9uc5IYy+7tiJS2qDk4iTSMRhisXrJrXXcuFf/iE8JVWX9D0uRGEvIsLISWFkjsH5OI4Ddhw7Ghkp+wzjRCM48cjYCWFkmx2L4MSGzzsPYdLnJ+JE2xsU9iIi6WQYBlhurBw35ORdcH/HcXASseQJIZYsFznRYex4FCcWwYlFsePJf514BMNy46tYfsXbrbAXEZlBhmFguDzg8gD5aWuH1isVEckCCnsRkSygsBcRyQIKexGRLKCwFxHJAgp7EZEsMCuHXiYSydlpoVDoAnuKiMgHBYNBXK6J8T4rw769vR2A7du3p7klIiJzz969e6msrJywzXAuZR7vVTI8PMzhw4cpKSnBsi7tpgOhUIjt27fz7LPPEgwGL/yGWSpTjgMy51gy5Tggc44lU44DruyxzJkre5/Px/r166f1GcFgcNKZbS7KlOOAzDmWTDkOyJxjyZTjgJk7FnXQiohkAYW9iEgWUNiLiGSBjAv7QCDAZz/7WQKBQLqbMi2ZchyQOceSKccBmXMsmXIcMPPHMitH44iIyJWVcVf2IiIymcJeRCQLZFTYnzp1iq1bt7J582a2bt3K6dOn092ki7Zr1y42btxITU0NJ06cSG2fa8fU3d3NZz7zGTZv3sydd97JZz/7Wbq6ugA4dOgQW7ZsYfPmzfzRH/0RnZ2daW7t+T344INs2bKFu+++m23btnHs2DFg7v1MRu3evXvC79dc+3kAbNy4kTvuuIO77rqLu+66i1//+tfA3DuWSCTCzp07uf3227nzzjv50pe+BMzw75aTQe69917n+eefdxzHcZ5//nnn3nvvTXOLLt7+/fud5uZm5+Mf/7hz/Pjx1Pa5dkzd3d3O66+/nnr+zW9+0/mLv/gLJ5FIOLfddpuzf/9+x3Ec5+mnn3Z27NiRrmZelHA4nHr8yiuvOHfffbfjOHPvZ+I4jnP48GHn/vvvT/1+zcWfh+M4k/7/cBxnTh7L448/7nzta19zbNt2HMdx2tvbHceZ2d+tjAn7jo4OZ926dU48Hnccx3Hi8bizbt06p7OzM80tuzTjf5kz4Zh+/vOfO/fdd5/z9ttvO5/4xCdS2zs7O501a9aksWWX5ic/+Ylzzz33zMmfSSQScT75yU86DQ0Nqd+vufrzmCrs59qx9Pf3O+vWrXP6+/snbJ/p361ZuVzC5WhpaaGsrCy1lo5lWZSWltLS0kJRUVGaW3d55vox2bbND37wAzZu3EhLSwsLFixIvVZUVIRt2/T09FBQUJC+Rl7AX/7lX/Laa6/hOA7f/e535+TP5KmnnmLLli0TpuDP1Z8HwCOPPILjOKxbt44//dM/nXPH0tDQQEFBAbt372bfvn34/X4eeughfD7fjP5uZVTNXmaXxx9/nNzcXD71qU+luymX7Wtf+xq//OUv+cIXvsATTzyR7uZcsrfeeovDhw+zbdu2dDflinj22Wd54YUX+PGPf4zjOHzlK19Jd5MuWSKRoKGhgRUrVvAv//IvPPLII3zuc59jcHBwRr9vxoR9eXk5ra2tqbXwE4kEbW1tlJeXp7lll28uH9OuXbs4c+YM3/rWtzBNk/Lycpqbm1Ovd3V1YZrmrLzymsrdd9/Nvn37CAaDc+pnsn//furr69m0aRMbN24kFApx//33c+bMmTn58xj97+zxeNi2bRsHDx6cc79b5eXluFwu6urqAFi9ejWFhYX4fL4Z/d3KmLAvLi6mtraWPXv2ALBnzx5qa2tn7Z/WF2OuHtPf/u3fcvjwYZ5++mk8Hg8A1113HcPDwxw4cACA5557jjvuuCOdzTyvgYEBWlpaUs9fffVV5s2bN+d+Jg888AC/+c1vePXVV3n11VcJBoP80z/9E5/+9Kfn1M8DYHBwkL6+PgAcx+Ff//Vfqa2tnXO/W0VFRWzYsIHXXnsNSI7A6ezsZPHixTP6u5VRM2jr6+vZsWMH4XCYQCDArl27qK6uTnezLspXv/pVXn75ZTo6OigsLKSgoICf/exnc+6YTp48SV1dHYsXL8bn8wFQWVnJ008/zcGDB9m5cyeRSISKigqefPJJ5s+fn+YWT62jo4MHH3yQoaEhTNNk3rx5PProo6xcuXLO/UzG27hxI9/5zndYvnz5nPp5QLLW/bnPfY5EIoFt2yxdupS/+qu/orS0dE4eyxe/+EV6enpwuVw8/PDD3HrrrTP6u5VRYS8iIlPLmDKOiIicm8JeRCQLKOxFRLKAwl5EJAso7EVEsoDCXkQkCyjsRUSygMJeRCQL/H9SmDebWpIThQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b = 20\n",
    "x = np.linspace(0, mins.max() * 1.1, 301)\n",
    "y = b + (110-b) * np.exp(-x**0.7 / 6)\n",
    "\n",
    "plt.plot(mins, vals, 'o', markeredgecolor='none')\n",
    "plt.plot(x, y, lw=3, alpha=0.5)\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# fitting the model\n",
    "\n",
    "the above gave me a reasonable model, so lets get the computer to find a better set of parameters\n",
    "\n",
    "I drop the first value because things were changing quickly and I don't trust it, I also drop the final five values so we can evaluate its prediction on them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 23.291  103.620  7.206  0.750]\n",
      " [ 24.596  104.127  7.428  0.769]\n",
      " [ 25.901  104.633  7.650  0.787]]\n"
     ]
    }
   ],
   "source": [
    "def fn(x, baseline, maxtemp, tau, nonlin):\n",
    "    return baseline + (maxtemp - baseline) * np.exp(-x**nonlin / tau)\n",
    "\n",
    "mu, cov = optimize.curve_fit(\n",
    "    fn, mins[1:-5], vals[1:-5], \n",
    "    bounds=(\n",
    "        (10, 90,    0, 0.1),\n",
    "        (30, 120, 100, 1.0),\n",
    "    ),\n",
    ")\n",
    "\n",
    "sd = np.sqrt(np.diag(cov))\n",
    "\n",
    "# mean and 95% confidence intervals\n",
    "ci = mu + np.r_[sd] * np.c_[[-2,0,2]]\n",
    "\n",
    "# print CI to 3 decimal places\n",
    "with np.printoptions(formatter={'float': ' {:.3f}'.format}):\n",
    "    print(ci)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# plot fitted model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, mins.max() * 1.1, 301)\n",
    "y = fn(x, *mu)\n",
    "\n",
    "plt.plot(mins[:-5], vals[:-5], 'o', markeredgecolor='none', label='train')\n",
    "plt.plot(mins[-5:], vals[-5:], 'o', markerfacecolor='none', label='test')\n",
    "plt.plot(x, y, lw=3, alpha=0.5, label='model')\n",
    "plt.legend()\n",
    "sns.despine()"
   ]
  }
 ],
 "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": "3.9.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}

temp.csv