L1-python/source/Plotting II.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feuille 2 - UE Projet CMI-L1\n",
    "Reading files with Pandas, ploting and fitting data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "# pandas is a Python package providing fast, flexible, and expressive data \n",
    "# structures designed to make working with “relational” or “labeled” data \n",
    "# both easy and intuitive. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I) Files : reading typical format files\n",
    "we propose to work with some column data :\n",
    "* csv : column data delimited by \",\" or \";\" with headers\n",
    "* txt : column data delimited by spaces with headers\n",
    "* raw : column data delimited by spaces without headers\n",
    "* dat : column data formatted delimited by spaces\n",
    "* xlsx : excel data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a) CSV files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x;y;er\r",
      "\r\n",
      "1;1;0.2\r",
      "\r\n",
      "2;4;0.2\r",
      "\r\n",
      "3;8;0.3\r",
      "\r\n",
      "4;17;0.4\r",
      "\r\n",
      "5;24;0.2"
     ]
    }
   ],
   "source": [
    "!cat data.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   x   y   er\n",
      "0  1   1  0.2\n",
      "1  2   4  0.2\n",
      "2  3   8  0.3\n",
      "3  4  17  0.4\n",
      "4  5  24  0.2\n"
     ]
    }
   ],
   "source": [
    "# read file\n",
    "d = pd.read_csv(\"data.csv\",delimiter=\";\")\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b) Raw files with headers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x y er\r",
      "\r\n",
      "1 1 0.2\r",
      "\r\n",
      "2 4 0.2\r",
      "\r\n",
      "3 8 0.3\r",
      "\r\n"
     ]
    }
   ],
   "source": [
    "# text files\n",
    "!cat data.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    x y er\n",
      "0  1 1 0.2\n",
      "1  2 4 0.2\n",
      "2  3 8 0.3\n"
     ]
    }
   ],
   "source": [
    "# read file\n",
    "dtext = pd.read_csv(\"data.txt\")\n",
    "print(dtext)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c) Raw files without headers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 1 0.2\r",
      "\r\n",
      "2 4 0.2\r",
      "\r\n",
      "3 8 0.3\r",
      "\r\n"
     ]
    }
   ],
   "source": [
    "# raw values\n",
    "!cat data.raw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   0  1    2\n",
      "0  1  1  0.2\n",
      "1  2  4  0.2\n",
      "2  3  8  0.3\n"
     ]
    }
   ],
   "source": [
    "# read raw file\n",
    "draw = pd.read_csv(\"data.raw\",delimiter=\" \", header = None)\n",
    "print(draw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### d) Formatted file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         0         1\n",
      "0      0.0  0.894520\n",
      "1    100.0  0.849616\n",
      "2    200.0  0.806313\n",
      "3    300.0  0.763861\n",
      "4    400.0  0.722299\n",
      "5    500.0  0.681680\n",
      "6    600.0  0.642211\n",
      "7    700.0  0.603411\n",
      "8    800.0  0.565199\n",
      "9    900.0  0.528873\n",
      "10  1000.0  0.492817\n"
     ]
    }
   ],
   "source": [
    "# read raw file\n",
    "fwidths = [11,10]\n",
    "dexpe = pd.read_fwf(\"expe.dat\",delimiter=\" \",header = None, widths = fwidths)\n",
    "print(dexpe)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### e) Excel data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  data Unnamed: 1 Unnamed: 2\n",
      "0    x          y         er\n",
      "1    1          1        0.2\n",
      "2    2          4        0.2\n",
      "3    3          8        0.3\n",
      "4    4         17        0.4\n",
      "5    5         24        0.2\n"
     ]
    }
   ],
   "source": [
    "d = pd.read_excel(\"data.xlsx\")\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### More formats\n",
    "see references https://pandas.pydata.org/docs/getting_started/intro_tutorials/01_table_oriented.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"02_io_readwrite.svg\" width=\"800\" height=\"500\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import image module\n",
    "from IPython.display import Image\n",
    "  \n",
    "# get the image\n",
    "Image(url=\"02_io_readwrite.svg\", width=800, height=500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## II) Filling variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   x   y   er\n",
      "0  1   1  0.2\n",
      "1  2   4  0.2\n",
      "2  3   8  0.3\n",
      "3  4  17  0.4\n",
      "4  5  24  0.2\n"
     ]
    }
   ],
   "source": [
    "# read file\n",
    "d = pd.read_csv(\"data.csv\",delimiter=\";\")\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use **headers** or **column numbers** to fill the variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0    1\n",
      "1    2\n",
      "2    3\n",
      "3    4\n",
      "4    5\n",
      "Name: x, dtype: int64 0     1\n",
      "1     4\n",
      "2     8\n",
      "3    17\n",
      "4    24\n",
      "Name: y, dtype: int64 0    0.2\n",
      "1    0.2\n",
      "2    0.3\n",
      "3    0.4\n",
      "4    0.2\n",
      "Name: er, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# taking values from headers\n",
    "x=d[\"x\"]\n",
    "y=d[\"y\"]\n",
    "e=d[\"er\"]\n",
    "print(x,y,e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0    1\n",
      "1    2\n",
      "2    3\n",
      "3    4\n",
      "4    5\n",
      "Name: x, dtype: int64 0     1\n",
      "1     4\n",
      "2     8\n",
      "3    17\n",
      "4    24\n",
      "Name: y, dtype: int64 0    0.2\n",
      "1    0.2\n",
      "2    0.3\n",
      "3    0.4\n",
      "4    0.2\n",
      "Name: er, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# taking values from colon  .iloc[row,col] or .loc[row,col]\n",
    "x=d.iloc[:,0]\n",
    "y=d.iloc[:,1]\n",
    "e=d.iloc[:,2]\n",
    "print(x,y,e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## III) Plotting data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         0         1\n",
      "0      0.0  0.894520\n",
      "1    100.0  0.849616\n",
      "2    200.0  0.806313\n",
      "3    300.0  0.763861\n",
      "4    400.0  0.722299\n",
      "5    500.0  0.681680\n",
      "6    600.0  0.642211\n",
      "7    700.0  0.603411\n",
      "8    800.0  0.565199\n",
      "9    900.0  0.528873\n",
      "10  1000.0  0.492817\n"
     ]
    }
   ],
   "source": [
    "# read raw file\n",
    "fwidths = [11,10]\n",
    "dexpe = pd.read_fwf(\"expe.dat\",delimiter=\" \",header = None, widths = fwidths)\n",
    "print(dexpe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get x and y\n",
    "x=dexpe.iloc[:,0]\n",
    "y=dexpe.iloc[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb0838ea250>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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exbRqcHXVY9q0aTz88MNcccUVfP7zn+fQQw/lsMMO49Of/jRQHQ088MADjB8/nh//+MdccMEFAFxzzTV85StfYd9992Wvvfbie9/73oZ2GYCRI0dy1VVXMXnyZPbZZx8mTJiwegC8M8cffzw33HDD6kHqiy66iFNOOYVDDz2U7bfffp2veeGFFzJnzhzGjRvHrFmz2HnnnQGYNGkSK1asYJ999uETn/gEEyZMWL3N1KlT2WeffTj99NO7rLchmvad1K3g90FIXXvooYfYY489Wt2MHtlqq61WzyLShin9/CPirsxsK9X3CEKSVGRASNqkefTQOgaEJKnIgJAGmP407qjuW5+fuwEhDSBbbLEFS5YsMSQGmKy/D2KLLbbo0XZeKCcNIKNHj6a9vX31/Yw0cKz6RrmeMCCkAWTIkCE9+kYxDWyeYpIkFRkQkqQiA0KSVGRASJKKDAhJUpEBIUkqMiAkSUUGhCSpyICQJBUZEJKkIgNCklRkQEiSipp2s76IuBJ4G/BUZv5lYf15wOkN7dgDGJmZz0TEo8ALwCvAis6+L1WS1DzNPIK4CpjU2crMvDgzx2bmWOB84CeZ+UxDlYn1esNBklqgaQGRmXOAZ9ZZsTIZmNGstkiSeq7lYxARsSXVkcZ3G4oTmBURd0XE1HVsPzUi5kbEXL8ERZJ6T8sDAjge+FmH00sHZ+Y44Bjg7Ig4rLONM3N6ZrZlZtvIkSOb3VZJGjA2hYA4jQ6nlzJzUf3vU8ANwP4taJckDWgtDYiI+DPgzcD3GsqGRcTwVc+Bo4D7W9NCSRq4mjnNdQZwOLB9RLQDFwJDADLzsrraXwGzMvOPDZvuANwQEavad21m/qBZ7ZQklTUtIDJzcjfqXEU1Hbax7BFg3+a0SpLUXZvCGIQkaRNkQEiSigwISVKRASFJKjIgJElFBoQkqciAkCQVGRCSpCIDQpJUZEBIkooMCElSkQEhSSoyICRJRQaEJKnIgJAkFRkQkqQiA0KSVGRASJKKDAhJUpEBIUkqMiAkSUUGhCSpyICQJBUZEJKkIgNCklRkQEiSigwISVKRASFJKjIgJElFBoQkqciAkCQVGRCSpKKmBUREXBkRT0XE/Z2sPzwinouIefXjgoZ1kyJiQUQsjIhpzWqjJKlzzTyCuAqYtI46t2Xm2PrxfwEiYhBwKXAMsCcwOSL2bGI7JUkFTQuIzJwDPLMem+4PLMzMRzJzOXAdcGKvNk6StE6tHoM4MCLuiYhbImKvumwU8FhDnfa6rCgipkbE3IiYu3jx4ma2VZIGlFYGxK+AXTJzX+CLwI11eRTqZmc7yczpmdmWmW0jR47s/VZK0gDVsoDIzOczc2n9/GZgSERsT3XEsFND1dHAohY0UZIGtJYFRES8LiKifr5/3ZYlwJ3AbhExJiI2A04DZraqnZI0UA1u1o4jYgZwOLB9RLQDFwJDADLzMuDtwFkRsQJYBpyWmQmsiIhzgFuBQcCVmflAs9opSSqL6jO5f2hra8u5c+e2uhmS1GdExF2Z2VZa1+pZTJKkTZQBIUkqMiAkSUUGhCSpyICQJBUZEJKkIgNCklRkQEiSigwISVKRASFJKjIgJElFBoQkqciAkCQVGRCSpCIDQpJUZEBIkooMCElSkQEhSSoyICRJRQaEJKnIgJAkFRkQkqQiA0KSVGRASJKKDAhJUpEBIUkqMiAkSUUGhCSpyICQJBUZEJKkIgNCklRkQEiSipoWEBFxZUQ8FRH3d7L+9Ii4t37cHhH7Nqx7NCLui4h5ETG3WW2UJHWumUcQVwGTulj/W+DNmbkP8Clgeof1EzNzbGa2Nal9kqQuDG7WjjNzTkTs2sX62xsW7wBGN6stkqSe21TGIM4EbmlYTmBWRNwVEVO72jAipkbE3IiYu3jx4qY2UpIGkqYdQXRXREykCohDGooPzsxFEfFa4IcRMT8z55S2z8zp1Ken2trasukNlqQBoqVHEBGxD3AFcGJmLllVnpmL6n+fAm4A9m9NCyVp4GpZQETEzsD1wF9n5sMN5cMiYviq58BRQHEmlCSpeZp2iikiZgCHA9tHRDtwITAEIDMvAy4AtgP+LSIAVtQzlnYAbqjLBgPXZuYPmtVOSVJZM2cxTV7H+vcC7y2UPwLsu/YWkqSNaVOZxSRJ2sQYEJKkIgNCklRkQEiSigwISVKRASFJKjIgJElFBoQkqciAkCQVGRCSpCIDQpJUZEBIkooMCElSkQEhSSoyICRJRQaEJKnIgJAkFRkQkqQiA0KSVGRASJKKDAhJUpEBIUkqMiAkSUUGhCSpyICQJBUZEJKkIgNCklRkQEiSigwISVLR4K5WRsS93djH4sw8opfaI0naRHQZEMAg4Ngu1gcws/eaI0naVKzrFNP7M/N3XTweBT5Y2jAiroyIpyLi/k7WR0RcEhELI+LeiBjXsG5SRCyo101b795JktZblwGRmT8FiIi/6bhuVdmqOgVXAZO62P0xwG71Yyrw5Xq/g4BL6/V7ApMjYs+u2ilJ6n3dHaQ+o1A2pasNMnMO8EwXVU4EvpaVO4AREfF6YH9gYWY+kpnLgevqupKkjWhdg9STgXcAYyKicaxhOLBkA197FPBYw3J7XVYqP2ADX0uS1EPrGqS+HXgC2B74fEP5C0B3Zjh1JQpl2UV5eScRU6lOUbHzzjtvYJMkSat0GRCZ+Tvgd8CBTXjtdmCnhuXRwCJgs07KO2vjdGA6QFtbW6dBIknqmS7HICLipnXtoDt1OjETeFc9m2kC8FxmPgHcCewWEWMiYjPgNJxKK0kb3bpOMR3SYeyho6CaabT2iogZwOHA9hHRDlwIDAHIzMuAm6musVgIvAi8u163IiLOAW6lug7jysx8oLsdkiT1jnUFxOPAL4DOprICLC8VZubkrnacmQmc3cm6m6kCRJLUIusKiOlUp3jeB3wTmJGZ85rdKElS663rQrl/zcwDgTdTXdPw1Yh4KCIuiIg3bpQWSpJaolsXytW31fjHzNyP6rqIvwIeamrLJEkt1a2AiIghEXF8RFwD3AI8DPzPprZMktRS67qS+khgMnAc8Euq215Mzcw/boS2SZJaaF2D1B8HrgU+mpld3VdJktTPrOtK6okbqyGSpE2LXzkqSSoyICRJResag+j3brz7cS6+dQGLnl3GjiOGct7Ru3PSfqNa3SxJarkBHRA33v04519/H8tefgWAx59dxvnX3wdgSEga8Ab0KaaLb12wOhxWWfbyK1x864IWtUiSNh0DOiAWPbusR+WSNJAM6IDYccTQHpVL0kAyoAPivKN3Z+iQQWuUDR0yiPOO3r1FLZKkTceAHqReNRDtLCZJWtuADgioQqIVgeD0WkmbugEfEK3g9FpJfcGAHoNoFafXSuoLDIgWcHqtpL7AgGgBp9dK6gsMiBZweq2kvsBB6hZweq2kvsCAaJFWTa8Fp9hK6h4DYoBxiq2k7nIMYoBxiq2k7jIgBhin2ErqLgNigHGKraTuMiAGGKfYSuouB6kHGKfYSuouA2IA8g62krrDgNBG4fRaqe9p6hhEREyKiAURsTAiphXWnxcR8+rH/RHxSkRsW697NCLuq9fNbWY71XxOr5X6nqYdQUTEIOBS4EigHbgzImZm5oOr6mTmxcDFdf3jgb/NzGcadjMxM59uVhu18Ti9Vup7mnkEsT+wMDMfyczlwHXAiV3UnwzMaGJ71EJOr5X6nmYGxCjgsYbl9rpsLRGxJTAJ+G5DcQKzIuKuiJja2YtExNSImBsRcxcvXtwLzVYzOL1W6nuaOUgdhbLspO7xwM86nF46ODMXRcRrgR9GxPzMnLPWDjOnA9MB2traOtu/WszptVLf08yAaAd2algeDSzqpO5pdDi9lJmL6n+fiogbqE5ZrRUQ6ju8g63UtzTzFNOdwG4RMSYiNqMKgZkdK0XEnwFvBr7XUDYsIoaveg4cBdzfxLaqH1s1xfbxZ5eRvDrF9sa7H29106RNWtMCIjNXAOcAtwIPAd/KzAci4gMR8YGGqn8FzMrMPzaU7QD8NCLuAX4J/Edm/qBZbVX/5hRbaf009UK5zLwZuLlD2WUdlq8CrupQ9giwbzPbpoHDKbbS+vFmfer3nGIrrR8DQv2eU2yl9eO9mNTvOcVWWj8GhAYE72Ar9ZwBITWJd7BVX+cYhNQkTq9VX2dASE3i9Fr1dQaE1CROr1VfZ0BITeL0WvV1DlJLTdLK6bXOnlJvMCCkJmrF9FpnT6m3eIpJ6mecPaXeYkBI/Yyzp9RbDAipn3H2lHqLASH1M86eUm9xkFrqZ1p9c0JnUPUfBoTUD7Xy5oTOoOo/PMUkqdc4g6p/MSAk9RpnUPUvBoSkXuMMqv7FgJDUa5xB1b84SC2p17R6BpV6lwEhqVf59a79hwEhqc9zem1zOAYhqc9zem1zGBCS+jyn1zaHASGpz3N6bXMYEJL6PKfXNoeD1JL6vFZPr+2vM6gMCEn9gjco7H2eYpKkDdCfZ1AZEJK0AfrzDKqmBkRETIqIBRGxMCKmFdYfHhHPRcS8+nFBd7eVpE1Bf55B1bQxiIgYBFwKHAm0A3dGxMzMfLBD1dsy823rua0ktdR5R+++xhgEbLwZVM0eHG/mIPX+wMLMfAQgIq4DTgS68yG/IdtK0kbTqhlUG2NwvJkBMQp4rGG5HTigUO/AiLgHWAR8NDMf6MG2RMRUYCrAzjvv3AvNlqSeacUMqq4Gx3urLc0cg4hCWXZY/hWwS2buC3wRuLEH21aFmdMzsy0z20aOHLm+bZWkPmVjDI43MyDagZ0alkdTHSWslpnPZ+bS+vnNwJCI2L4720rSQLYxBsebGRB3ArtFxJiI2Aw4DZjZWCEiXhcRUT/fv27Pku5sK0kD2ca4vUjTxiAyc0VEnAPcCgwCrszMByLiA/X6y4C3A2dFxApgGXBaZiZQ3LZZbZWkvmZjDI5H9XncP7S1teXcuXNb3QxJ6jMi4q7MbCut80pqSVKRASFJKjIgJElFBoQkqciAkCQVGRCSpCIDQpJUZEBIkooMCElSkQEhSSoyICRJRQaEJKnIgJAkFRkQkqQiA0KSVGRASJKKDAhJUpEBIUkqMiAkSUUGhCSpyICQJBUZEJKkIgNCklRkQEiSigwISVKRASFJKjIgJElFBoQkqciAkCQVGRCSpCIDQpJUZEBIkoqaGhARMSkiFkTEwoiYVlh/ekTcWz9uj4h9G9Y9GhH3RcS8iJjbzHZKktY2uFk7johBwKXAkUA7cGdEzMzMBxuq/RZ4c2b+ISKOAaYDBzSsn5iZTzerjZKkzjXzCGJ/YGFmPpKZy4HrgBMbK2Tm7Zn5h3rxDmB0E9sjSeqBZgbEKOCxhuX2uqwzZwK3NCwnMCsi7oqIqZ1tFBFTI2JuRMxdvHjxBjVYkvSqpp1iAqJQlsWKEROpAuKQhuKDM3NRRLwW+GFEzM/MOWvtMHM61akp2traivuXJPVcM48g2oGdGpZHA4s6VoqIfYArgBMzc8mq8sxcVP/7FHAD1SkrSdJG0syAuBPYLSLGRMRmwGnAzMYKEbEzcD3w15n5cEP5sIgYvuo5cBRwfxPbKknqoGmnmDJzRUScA9wKDAKuzMwHIuID9frLgAuA7YB/iwiAFZnZBuwA3FCXDQauzcwfNKutkqS1RWb/OW3f1taWc+d6yYQkdVdE3FX/Yb4Wr6SWJBUZEJKkIgNCklRkQEiSigwISVKRASFJKjIgJElFBoQkqciAkCQVGRCSpCIDQpJUZEBIkooMCElSkQEhSSoyICRJRQaEJKnIgJAkFRkQkqQiA0KSVGRASJKKDAhJUpEBIUkqMiAkSUUGhCSpyICQJBUZEJKkIgNCklRkQEiSigwISVKRASFJKjIgJElFTQ2IiJgUEQsiYmFETCusj4i4pF5/b0SM6+62kqTmalpARMQg4FLgGGBPYHJE7Nmh2jHAbvVjKvDlHmwrSWqiZh5B7A8szMxHMnM5cB1wYoc6JwJfy8odwIiIeH03t5UkNVEzA2IU8FjDcntd1p063dlWktREg5u47yiUZTfrdGfbagcRU6lOTwEsjYgF3W7hmrYHnl7Pbfsq+9z/DbT+gn3uqV06W9HMgGgHdmpYHg0s6madzbqxLQCZOR2YvqGNjYi5mdm2ofvpS+xz/zfQ+gv2uTc18xTTncBuETEmIjYDTgNmdqgzE3hXPZtpAvBcZj7RzW0lSU3UtCOIzFwREecAtwKDgCsz84GI+EC9/jLgZuBYYCHwIvDurrZtVlslSWtr5ikmMvNmqhBoLLus4XkCZ3d32ybb4NNUfZB97v8GWn/BPveaqD6jJUlak7fakCQVDfiA6K+39IiInSLivyLioYh4ICL+pi7fNiJ+GBG/rv/dpmGb8+v3YUFEHN261q+/iBgUEXdHxE31cr/uL0BEjIiI70TE/PrnfWB/7ndE/G39O31/RMyIiC36Y38j4sqIeCoi7m8o63E/I2J8RNxXr7skIkqXEZRl5oB9UA2A/wZ4A9XU2nuAPVvdrl7q2+uBcfXz4cDDVLct+X/AtLp8GvCP9fM96/5vDoyp35dBre7HevT7XOBa4KZ6uV/3t+7L1cB76+ebASP6a7+pLpj9LTC0Xv4WMKU/9hc4DBgH3N9Q1uN+Ar8EDqS6vuwW4JjutmGgH0H021t6ZOYTmfmr+vkLwENU/7lOpPpAof73pPr5icB1mfmnzPwt1cyy/TdqozdQRIwGjgOuaCjut/0FiIitqT5IvgKQmcsz81n6d78HA0MjYjCwJdU1Uv2uv5k5B3imQ3GP+lnfumjrzPx5VmnxtYZt1mmgB8SAuKVHROwK7Af8Atghq2tNqP99bV2tP7wX/wL8HbCyoaw/9xeqo9/FwFfrU2tXRMQw+mm/M/Nx4J+A3wNPUF07NYt+2t+CnvZzVP28Y3m3DPSA6PYtPfqqiNgK+C7w4cx8vquqhbI+815ExNuApzLzru5uUijrM/1tMJjqNMSXM3M/4I9Upx4606f7XZ9zP5HqNMqOwLCIeGdXmxTK+kx/e2CDb1tUMtADoju3A+mzImIIVThck5nX18VP1oed1P8+VZf39ffiYOCEiHiU6lThWyLiG/Tf/q7SDrRn5i/q5e9QBUZ/7fdbgd9m5uLMfBm4HjiI/tvfjnraz/b6ecfybhnoAdFvb+lRz1T4CvBQZv5zw6qZwBn18zOA7zWUnxYRm0fEGKrv6PjlxmrvhsrM8zNzdGbuSvVz/HFmvpN+2t9VMvO/gcciYve66AjgQfpvv38PTIiILevf8SOoxtf6a3876lE/69NQL0TEhPr9elfDNuvW6pH6Vj+obvXxMNWo/9+3uj292K9DqA4l7wXm1Y9jge2AHwG/rv/dtmGbv6/fhwX0YKbDpvYADufVWUwDob9jgbn1z/pGYJv+3G/gk8B84H7g61Qzd/pdf4EZVOMsL1MdCZy5Pv0E2ur36jfAl6gvkO7OwyupJUlFA/0UkySpEwaEJKnIgJAkFRkQkqQiA0KSVGRASJKKDAipF9S33P5g/fzwiHguIrr8RsT6duxLI6LXv2xe6g0GhNQ7RgAfbFi+LTOP7WqDzJxIdYGbtElq6ndSSwPI54A/j4h5VFe+PrlqRX3PnG8CW1P9nzsrM29rRSOlnvAIQuod04DfZOZY4LwO694B3Fqv25fqtifSJs8jCKn57gSurO+ue2Nmzmtxe6Ru8QhCarKsvhnsMOBx4OsR8a4WN0nqFgNC6h0vUH3391oiYheqLzO6nOoW7OM2ZsOk9eUpJqkXZOaSiPhZRNwPLKNhkJrq9uPnRcTLwFKqe/JLmzwDQuolmfkOqK6DAD7aUH41r37RvNRneIpJ6n3Lgb/szoVywBuopsVKmxy/MEiSVOQRhCSpyICQJBUZEJKkIgNCklRkQEiSiv4/BjBDWkIJhl0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "fig = plt.figure(figsize=(6,6)) # s\n",
    "ax = plt.subplot() \n",
    "ax.plot(x,y,\"o\",label=\"Experimental data\")\n",
    "ax.set_ylim([0,2])\n",
    "ax.set_xlabel(\"t[s]\")\n",
    "ax.set_ylabel(\"V[t]\")\n",
    "ax.set_title(\"Temporal Evolution of Volume\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IV) Fitting data : linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import curve_fit\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(x, a, b):\n",
    "    return a * x + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([-4.01437909e-04,  8.87155318e-01]), array([[ 1.96723961e-11, -9.83619802e-09],\n",
      "       [-9.83619802e-09,  6.88533863e-06]]))\n"
     ]
    }
   ],
   "source": [
    "popt= curve_fit(func, x, y)\n",
    "print(popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "[a,b]=popt[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb083cadf40>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6,6)) # \n",
    "ax = plt.subplot() \n",
    "ax.plot(x,y,\"o\",label=\"Experimental data\")\n",
    "ax.plot(x,func(x,*popt[0]),label=\"Linear model\")\n",
    "ax.set_ylim([0,2])\n",
    "ax.set_xlabel(\"t[s]\")\n",
    "ax.set_ylabel(\"V[t]\")\n",
    "ax.set_title(\"Temporal Evolution of Volume\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## V) Fitting data : non linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.102</td>\n",
       "      <td>0.319</td>\n",
       "      <td>0.565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.204</td>\n",
       "      <td>0.452</td>\n",
       "      <td>0.672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.306</td>\n",
       "      <td>0.553</td>\n",
       "      <td>0.744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.408</td>\n",
       "      <td>0.639</td>\n",
       "      <td>0.799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.510</td>\n",
       "      <td>0.714</td>\n",
       "      <td>0.845</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       0      1      2\n",
       "0  0.102  0.319  0.565\n",
       "1  0.204  0.452  0.672\n",
       "2  0.306  0.553  0.744\n",
       "3  0.408  0.639  0.799\n",
       "4  0.510  0.714  0.845"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read raw file\n",
    "fwidths = [6,6,6]\n",
    "dexpe = pd.read_fwf(\"power.dat\",delimiter=\" \",header = None, widths = fwidths)\n",
    "dexpe.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get x and y\n",
    "x =dexpe.iloc[:,0]\n",
    "y1=dexpe.iloc[:,1]\n",
    "y2=dexpe.iloc[:,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb083dbd130>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "fig = plt.figure(figsize=(6,6)) # s\n",
    "ax = plt.subplot() \n",
    "ax.plot(x,y1,\"o\",label=\"Experimental data 1\")\n",
    "ax.plot(x,y2,\"o\",label=\"Experimental data 2\")\n",
    "ax.set_ylim([0,2])\n",
    "ax.set_xlabel(\"t[s]\")\n",
    "ax.set_ylabel(\"V[t]\")\n",
    "ax.set_title(\"Temporal Evolution of Volume\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### log-log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "fig = plt.figure(figsize=(6,6)) # s\n",
    "ax = plt.subplot() \n",
    "ax.plot(x,y1,\"o\",label=\"Experimental data 1\")\n",
    "ax.plot(x,y2,\"o\",label=\"Experimental data 2\")\n",
    "ax.set_xlabel(\"t[s]\")\n",
    "ax.set_ylabel(\"V[t]\")\n",
    "ax.set_title(\"Temporal Evolution of Volume\")\n",
    "ax.legend()\n",
    "ax.loglog()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's because\n",
    "$$ y = x^a + b $$\n",
    "gives\n",
    "$$\\log(y) = a \\log(x) + \\log(b)$$\n",
    "a linear function en log-log scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(x, a, b):\n",
    "    return a * x + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "popt= curve_fit(func, np.log(x), np.log(y1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.500\n",
      "-0.000\n"
     ]
    }
   ],
   "source": [
    "popt[0]\n",
    "a=popt[0][0]\n",
    "b=popt[0][1]\n",
    "print(\"%.3f\" % a)\n",
    "print(\"%.3f\" % b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "fig = plt.figure(figsize=(6,6)) # s\n",
    "ax = plt.subplot() \n",
    "ax.plot(x,y1,\"o\",label=\"Experimental data 1\")\n",
    "ax.plot(x,x**a+b,\"-\",label=\"Model 1\")\n",
    "ax.set_xlabel(\"t[s]\")\n",
    "ax.set_ylabel(\"V[t]\")\n",
    "ax.set_title(\"Temporal Evolution of Volume\")\n",
    "ax.legend()\n",
    "ax.loglog()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### VI ) Error bars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   x   y   er\n",
      "0  1   1  0.2\n",
      "1  2   4  0.2\n",
      "2  3   8  0.3\n",
      "3  4  17  0.4\n",
      "4  5  24  0.2\n"
     ]
    }
   ],
   "source": [
    "# read file\n",
    "d = pd.read_csv(\"data.csv\",delimiter=\";\")\n",
    "print(d.head())\n",
    "# taking values from headers\n",
    "x=d[\"x\"]\n",
    "y=d[\"y\"]\n",
    "e=d[\"er\"]\n",
    "#print(x,y,e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb0828c64f0>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6,6)) # s\n",
    "ax = plt.subplot() \n",
    "ax.errorbar(x,0.1*y,e*2, marker='.', linestyle=\"none\", label=\"data\")\n",
    "ax.set_title(\"with error bars\")\n",
    "ax.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}