diff --git a/source/Plotting II .ipynb b/source/Plotting II .ipynb
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--- a/source/Plotting II .ipynb
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-{
- "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": [
- ""
- ],
- "text/plain": [
- ""
- ]
- },
- "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": [
- ""
- ]
- },
- "execution_count": 17,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "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": [
- ""
- ]
- },
- "execution_count": 22,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": 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4+umnGT9+PIMGDWLEiBFlFeBVGTduHDNmzCirpL7//vu59tprOffcc2nfvv0R3/O+++5j7ty5ZGVlMXv2bLp16wbA2LFjKSoqYtCgQfzwhz9kxIgRZftMnDiRQYMGccMNN1S73bGI25jUiaDxIESqt3LlSvr165foYtRKq1atyloRybGJ+v2b2UJ3z47aXlcQIiISSQEhIvWarh4SRwEhIiKRFBAiIhJJASEiIpEUECIiEkkBISLHVatWrQ5bNnnyZJ599tkElKZuTJgwoexhvmPZpr5RVxsiknC33nprXI9f2vlcUpL+Jq4NfVoiknD3338/P/vZzwA4//zzufvuuxk+fDh9+vThnXfeAaC4uJi77rqLM844g0GDBvHb3/4WCJrBXnjhhWVdcJc+Ub1hwwb69evHt771LbKysti4cWOF9+zRowf33nsvI0eOJDs7m0WLFjFmzBh69erF5MmTgSBY7rrrLk4//XQGDhzISy+9VLb89ttvp3///lx++eVs3bq17LgLFy7kvPPOY9iwYYwZM4bNmzfH98OLI11BiDRWr0+CT5fV7TFPHgiXHvvobUVFRXzwwQe89tprPPDAA7z55ps89dRTtGnThgULFnDgwAHOPvtsLrnkErp27cqMGTNo3bo127ZtY8SIEWUDBK1evZrf/e53PP7445Hv07VrV+bNm8d3v/tdJkyYwHvvvcf+/fsZMGAAt956K9OnTyc3N5clS5awbds2zjjjDEaNGsW8efNYvXo1y5YtY8uWLfTv37+s/6g77riDV155hQ4dOvDSSy/xgx/8gKlTpx7zZ5IICggRqXdiu9TesGEDEAzis3Tp0rL7+Lt27WLt2rVkZmZy7733MnfuXJKSkigoKCgboKd79+7V9ktUGiQDBw5kz549pKWlkZaWRvPmzdm5cyfvvvsu48ePJzk5mU6dOnHeeeexYMEC5s6dW7a8S5cuXHDBBUAQSMuXL+fiiy8Ggquezp07x+UzOh4UECKNVR38pR8vUV1quzu/+tWvGDNmTIVtn376aQoLC1m4cCEpKSn06NGjrKvr6rr9jn2fqrr+rq6vuqjuud2dAQMGMG/evBqcZf2nOggROSGMGTOG3/zmN2VdXK9Zs4YvvviCXbt20bFjR1JSUnj77bf5+OOP6+w9R40axUsvvURxcTGFhYXMnTuX4cOHM2rUKF588UWKi4vZvHkzb7/9NgB9+/alsLCwLCAOHTrEihUr6qw8x5uuIETkuNq7d2+FwYDuvPPOGu13yy23sGHDBrKysnB3OnTowMyZM7nhhhsYN24c2dnZDBkyhNNOO63Oynr11Vczb948Bg8ejJnx05/+lJNPPpmrr76at956i4EDB9KnTx/OO+88AJo2bcrLL7/Mt7/9bXbt2kVRURHf+c53GDBgQJ2V6XhSd98ijciJ2N231B119y0iInVCASEiIpEUECIiEkkBIdLINKR6R6m5o/m9xy0gzGyqmW01s+VVrL/LzHLDabmZFZvZSeG6DWa2LFynWmeROtK8eXO2b9+ukGhk3J3t27fTvHnzWu0Xz2auTwO/BiK7aHT3R4BHAMxsHPBdd98Rs8lod98Wx/KJNDqZmZnk5+dTWFiY6KLIcda8efMKzYtrIm4B4e5zzaxHDTcfD0yLV1lEJJCSkkLPnj0TXQw5QSS8DsLMWgBjgT/FLHZgtpktNLOJR9h/opnlmFmO/ioSEak7CQ8IYBzwXqXbS2e7exZwKXCbmY2qamd3n+Lu2e6e3aFDh3iXVUSk0agPAXE9lW4vufum8OdWYAYwPAHlEhFp1BIaEGbWBjgPeCVmWUszSyt9DVwCRLaEEhGR+IlbJbWZTQPOB9qbWT5wH5AC4O6Tw82uBma7+xcxu3YCZoRd6TYBXnD3v8arnCIiEi2erZjG12Cbpwmaw8YuWw8Mjk+pRESkpupDHYSIiNRDCggREYmkgBARkUgKCBERiaSAEBGRSAoIERGJpIAQEZFICggREYmkgBARkUgKCBERiaSAEBGRSAoIERGJpIAQEZFICggREYmkgBARkUgKCBERiaSAEBGRSAoIERGJpIAQEZFICggREYmkgBARkUgKCBERiaSAEBGRSAoIERGJpIAQEZFICggREYmkgBARkUgKCBERiaSAEBGRSAoIERGJpIAQEZFICggREYkUt4Aws6lmttXMllex/nwz22VmueH0o5h1Y81stZnlmdmkeJVRRESqFs8riKeBsUfY5h13HxJO/wVgZsnAY8ClQH9gvJn1j2M5RUQkQtwCwt3nAjuOYtfhQJ67r3f3g8CLwJV1WjgRETmiRNdBjDSzJWb2upkNCJdlABtjtskPl0Uys4lmlmNmOYWFhfEsq4hIo5LIgFgEdHf3wcCvgJnhcovY1qs6iLtPcfdsd8/u0KFD3ZdSRKSRSlhAuPvn7r4nfP0akGJm7QmuGLrGbJoJbEpAEUVEGrWEBYSZnWxmFr4eHpZlO7AAONXMeppZU+B6YFaiyiki0lg1ideBzWwacD7Q3szygfuAFAB3nwx8GfimmRUB+4Dr3d2BIjO7HXgDSAamuvuKeJVTRESiWfCd3DBkZ2d7Tk5OooshInLCMLOF7p4dtS7RrZhERKSeUkCIiEgkBYSIiERSQIiISCQFhIiIRFJAiIhIJAWEiIhEUkCIiEgkBYSIiERSQIiISCQFhIiIRFJAiIhIJAWEiIhEUkCIiEgkBYSIiERSQIiISCQFhIiIRFJAiIhIJAWEiIhEUkCIiEgkBYSIiERSQIiISCQFhIiIRFJAiIhIJAWEiIhEUkCIiEgkBYSIiERSQIiISCQFhIiIRFJAiIhIJAWEiIhEUkCIiEikuAWEmU01s61mtryK9TeY2dJwet/MBses22Bmy8ws18xy4lVGERGpWjyvIJ4Gxlaz/iPgPHcfBPw3MKXS+tHuPsTds+NUPhERqUaTeB3Y3eeaWY9q1r8fMzsfyIxXWUREpPbqSx3EzcDrMfMOzDazhWY2sbodzWyimeWYWU5hYWFcCyki0pjE7QqipsxsNEFAnBOz+Gx332RmHYG/mdkqd58btb+7TyG8PZWdne1xL7CISCOR0CsIMxsEPAlc6e7bS5e7+6bw51ZgBjA8MSUUEWm8EhYQZtYNmA78m7uviVne0szSSl8DlwCRLaFERCR+4naLycymAecD7c0sH7gPSAFw98nAj4B2wONmBlAUtljqBMwIlzUBXnD3v8arnCIiEi2erZjGH2H9LcAtEcvXA4MP30NERI6n+tKKSURE6hkFhIiIRFJAiIhIJAWEiIhEUkCIiEgkBYSIiERSQIiISCQFhIiIRFJAiIhIJAWEiIhEUkCIiEgkBYSIiERSQIiISCQFhIiIRFJAiIhIJAWEiIhEUkCIiEgkBYSIiERSQIiISCQFhIiIRFJAiIhIJAWEiIhEUkCIiEgkBYSIiERSQIiISCQFhIiIRFJAiIhIJAWEiIhEUkCIiEikJtWtNLOlNThGobtfWEflERGReqLagACSgcuqWW/ArLorjoiI1BdHusX0DXf/uJppA/CtqB3NbKqZbTWz5VWsNzN71MzyzGypmWXFrBtrZqvDdZOO+uxEROSoVRsQ7v4ugJn9R+V1pctKt4nwNDC2msNfCpwaThOB34THTQYeC9f3B8abWf/qyikiInWvppXUN0Ysm1DdDu4+F9hRzSZXAs96YD6QbmadgeFAnruvd/eDwIvhtiIichwdqZJ6PPAVoKeZxdY1pAHbj/G9M4CNMfP54bKo5Wce43uJiEgtHamS+n1gM9Ae+HnM8t1ATVo4Vccilnk1y6MPYjaR4BYV3bp1O8YiiYhIqWoDwt0/Bj4GRsbhvfOBrjHzmcAmoGkVy6sq4xRgCkB2dnaVQSIiIrVTbR2Emb16pAPUZJsqzAK+FrZmGgHscvfNwALgVDPraWZNgetRU1oRkePuSLeYzqlU91CZEbQ0OnyF2TTgfKC9meUD9wEpAO4+GXiN4BmLPGAv8PVwXZGZ3Q68QfAcxlR3X1HTExIRkbpxpIAoAP4JVNWUFeBg1EJ3H1/dgd3dgduqWPcaQYCIiEiCHCkgphDc4vl34CVgmrvnxrtQIiKSeEd6UO6X7j4SOI/gmYbfmdlKM/uRmfU5LiUUEZGEqNGDcmG3Gj9x96EEz0VcDayMa8lERCShahQQZpZiZuPM7HngdWAN8C9xLZmIiCTUkZ6kvhgYD1wOfEDQ7cVEd//iOJRNREQS6EiV1PcCLwDfd/fq+lUSEZEG5khPUo8+XgUREZH6RUOOiohIJAWEiIhEOlIdRIM3c3EBj7yxmk0799ElPZW7xvTlqqEZiS6WiEjCNeqAmLm4gHumL2PfoWIACnbu457pywAUEiLS6DXqW0yPvLG6LBxK7TtUzCNvrE5QiURE6o9GfQWxaec+AB5s8gRb/CRyvTe5Jb3YtDOx5RIRqQ8adUB0SU+lcOfnDE3Ko6/lk2TBeEOfWGeY/gpkZEPmMOg0EJo0TXBpRUSOr0YdEHeN6cs905dx6cGf0Iq9DEz6iDOarGN8l62wfg4sfSnYMLkZdB4EmWdAxjDIzIb07mBRo6OKiDQMjTogSiuig1ZM8EnrbK4bcwOdh2aAO+zKh4IcyA+nnKkw//Fg5xbtg6AovcrokgWp6Qk7FxGRumbBuD0NQ3Z2tufk5MTvDYoPwZYVYWgsDH5uW1O+vn2f8sDIyIZOAyA5JfJQal4rIvWBmS109+zIdQqIY7RvJ2xaVB4Y+Tmwd1uwrkkqdBlSflsqIxvaZDIzd1OF5rUAqSnJPHTNQIWEiBxXCojjyR12fhwERcHC4OfmJVB8IFjfqhNz93Zn/oGeLPbeLC05hS9IBSAjPZX3Jl2QwMKLSGNTXUA06jqIuDCDtj2CaeCXg2VFB2HL8rLA6Jo7h1EpHwBQ4sZaz2BxSW+W7O4Nn3aEjv0gKTlhpyAiArqCSIizH36LPTsLGZK0jiGWx5CkPIYkraOt7Qk2SGkJXYaW12VkZkPrLokttIg0SLqCqGeC5rUH+cehwfyDwVAMqSlJPHpJGy5ukx/ensqBeY9DyaFgp7QuFQOjy1Bo2jKxJyIiDZoCIgEqNq8tb8V0cWkF9aB/DX4WHYBPl5UHRn4OrPxzsM6SoGP/ihXgHfrq1pSI1BndYjrRfLGtvPK7IKwI378rWNc0DTKGll9lZGRDWqfDDqEmtiJSSreYGpKW7aHPmGACKCmBHesqXmW8/yiUFAXr23StcJXx560duGdWnnqwFZEj0hVEQ3RoH2xeWh4YBTmw8xMAikhiVUk3ckt6keu9WVzSm/XemS7pLdXEVqQR0hVEY5OSCt3ODKZSe7ZCwUImP/cigy2PK5Lf56v2dwA+9xYs+aIXvPV++e2plu0TVHgRqS8UEI1Fq47Q91KmtWrGz3buwyihl21iaFIeQ2wdZ6Ssh3f+Fzx8uju9e0xfU9lw8iBIaZ7YcxCR40oB0ciU9mC77xDkeSZ5xZm8mnIhD10xkD4D0oOnvktvS33yT1j+p2DHpBQ4+fSKFeDteqlHW5EGTAHRyFTVxLasgrr7WcFUavenFSvAl0yDBU8E65qnl1eAl3aF3uKk43tCIhI3qqSW2ikphsJVMaGxEApXgpcE6086peJVxsmnQ5NmgJrXitRHqqSWupOUHHRj3mkADLsxWHZgD2xaXH6VseEdWPaHYF1yUzh5EOuanca7eW1JPnQKTkc1rxU5AcQ1IMxsLPBLIBl40t0frrT+LuCGmLL0Azq4+w4z2wDsBoqBoqoSTuqBZq2g57nBVGpXQUwz24V0Wf9HfpZ0AJrBdk9jSUkvckt684/XVnDVaTdBatvElV9EIsXtFpOZJQNrgIuBfGABMN7dP6xi+3HAd939gnB+A5Dt7ttq+p66xVR/9Z40i1MtP2w1FXRQ2Ns2lY0DTrve5bemMrOh0+lVDrYkInUnUbeYhgN57r4+LMSLwJVAZEAA44FpcSyPJFCn9Fas3NmdlcXdeYELAWjFXi5IK+DRc4uCLkPWvQVLXwx2aNIcOg+uOEJfeje1mhI5juIZEBnAxpj5fODMqA3NrAUwFrg9ZrEDs83Mgd+6+5Qq9p0ITATo1q1bHRRb4qG8eW35KHrFKWlccNm1UFoH4Q67NlYcbCnnKZj/WLC+ZYeKgZGRBc3bJOBsRBqHeAZE1J96Vd3PGge85+47Ypad7e6bzKwj8DczW+Xucw87YBAcUyC4xXSshZb4OGLzWgiuDtK7BdPp1wTLKo8Dnr8A1rxeukMwDnhmdnlz244DIFltL0TqQjz/J+UDXWPmM4FNVWx7PZVuL7n7pvDnVjObQXDL6rCAkBPHVUMzat9iKTklGNe7yxA445Zg2b7PoGBR+VXGmr9C7vPBumrGAVcTW5HaiWcldROCSuoLgQKCSuqvuPuKStu1AT4Curr7F+GylkCSu+8OX/8N+C93/2t176lK6kbKHT7bULEb9M1LoPggAPubtefd/T1YVNSrbBzwkpRWPHTNQIWENHoJqaR29yIzux14g6CZ61R3X2Fmt4brJ4ebXg3MLg2HUCdghgUVkk2AF44UDtKImcFJPYOpwjjgyyB/IXPeeJW+voqLUoI/HkrcWOOZrH21L5SMC64yNA64yGH0JLU0eD0n/QUH0tkdjAMedlA4WOOAi+hJamncuqSnUrBzHztJY07JEOaUDAEgo01z3pvYo2JfUxoHXKSMAkIavKgmtqkpydw19jRolxH0Sjv4umDFof3BOOClgZG/4PBxwGO7QW/fR7empMFSQEiDV6MmtqVSmkPXM4Kp1BfbKl5lLJ8BC58O1tVwHHCRE5HqIERqq6QEtudVHNJ1y4rIccDn7u3O/QtS+GhXiZrXSr1UXR2EAkKkLhzaV3GwpfyFsCscB9yTWOXBOOArkvpw4UWXcdE550BSUoILLaKAEEmIcQ/9iU67VzA0aS1DbB2DktaTZvuClc3aBF2FxNZnaBxwSQC1YhJJgOW7mrOMYbxZMgyApJhxwH867GBwlfHOz8sHW9I44FLPKCBE4qS0eW2pEpJY65nsTTsVxl0QLDz4BWzKLa/P+GS+xgGXekMBIRInVTavHdO3fKOmLaHH2cFU6vPNYWAsCK4ycl8oHwc8tW1QAV4WGhoHXOJHASESJ7VqXhurdWdoPQ76jQvmS4ph68oKI/SR9xPKOkc+bBzwgcxcVqjOCeWYqZJa5ER0YHcwDnjs2Bl7PgWgOCmF5cXdWVTci8Ulvcn13hQ26cxD1wxSSMhhVEkt0tA0S4Oeo4IJgh5tPy+A/Bxemj6dXr6a65Pf5utN3gCCccBX/7kP7BpTfmsqNT1x5ZcTggJCpCEwgzaZ0CaTHzyXggNNKKKv5YedE+YxxNfBnAfL92l3asXBljQOuFSigBBpYEpbTxXRhBXegxXFPXiei8hIT+W97wwLB1sKH+bLexOWhGN1aRxwqUQBIdLAVNt6qnkb6DU6mCC4NbXzk/LAKMiBBU/GjAPeMbzCGAaZZ0CXLGjeOgFnJYmggBBpYGrVesoM2nYPptP/JVhWdBC2LK84Ql/sOOAd+la8yujYv8I44DMXF6gFVQOhVkwicmT7PgsDY2F5c9t9O4J1KS2g8xDIHMYHh07h7vlN+ehQOhDcmkpNSdbwrvWY+mISkbrlDp99VDEwPl1aNg74Fk8nt6Q3uSW9Wey92ZbWnzfvuTzBhZYoauYqInXLLHhA76RTYNC1wbKiA1z1w8kMTlpX1kHhmHAc8OL9Bo/3rzhCX4fTNNhSPaeAEJG60aQZhW0G8szO3jxTPAaAtnzO4KR1jEr9mJvStsOHs2DRs8H2TVsFw7iWNrPNyA6eIpd6QwEhInWmcguqz2jNP5OzuepLX4ehGcGtqe3rKg62NO/X5YMttc6oGBhdhmgc8ARSQIhInTliCyozaN87mAZfHyw7tD+ovygdA7wgB1bOCrdPhk79K/Y11b6PBls6TlRJLSL1z57CilcZBYvgwOfBumatg1tTsWNntOqo5rVHSZXUInJiadUB+l4aTBCOA742ZkjXHHj3/8CDW1l7U7vQ7IvujC0+hVzrzfKdPbln+jIAhcQxUECISP2XlBQ8oNehLwy9IVh2cG8wDnhBDvPf/AuDbA2XpswD4JAns9K7sfbVvmBXBVcZJ/XSralaUkCIyImpaQvoPhK6j+TmWafgQAc+Y2hSHkOS1jHE8hhTNAdm/jXYvnmbSoMtZUPLdok8g3pPASEiJ7zSDgoLacvskjOYXXIGAF3bNOWdmzIqDrb0zs/KxwFv26NiYHQeBE2aJe5E6hkFhIic8KrqoPB7Y/tDp4ygJVTW14IVB/bA5tzy+oyP34flLwfrklLg5IEVK8BPOqXR9mirgBCRE16tOihs1gp6nBNMpXYVVLzKWPx7+GBKsC71pIrPZmRkHTYOeENtQaVmriIilRUXQeHKmFZTC6FwFeXjgPcqC4w5X3Tj228X8fmh8quME6mDQnXWJyJyrPZ/HowDHjt2xp4tABzwFFZ497IOChd5b7x1N96758IEF/rIFBAiInXNHXZt5PafPsHgpDyGJOUx0D6iuR0CYJu3pn3fs8rHzuiSVS/HAU/Yg3JmNhb4JZAMPOnuD1dafz7wCvBRuGi6u/9XTfYVEUkoM0jvxuLWo3l15wigdBzwjQxNyuOsZhu4bMd6WPPX8n3a96k42FKnAfV6HPC4BYSZJQOPARcD+cACM5vl7h9W2vQdd//SUe4rIpJQsS2ognHAe7I+qTfZ4wYGHRTu2wmbFpXfllo7G5a8EOzcJDXokDC2ErxNZo1bTcW7cjyeVxDDgTx3Xw9gZi8CVwI1+ZI/ln1FRI6bI7agSk2HXhcEE4TjgH9c3mIqPwc+eCLo1RagVaeKVxkZWdAs7bD3nbm4oELT3oKd++q8e5F4BkQGsDFmPh84M2K7kWa2BNgEfN/dV9RiX8xsIjARoFu3bnVQbBGR2rlqaEbNv5TNggf02vaAgV8OlpWOAx7b19Tqv5TuEAyulDkMMs8IxwHvxyNvrK7w3AfAvkPFPPLG6hMiIKKukSrXiC8Curv7HjO7DJgJnFrDfYOF7lOAKRBUUh91aUVEEqVJ0+BKISOL8O9d2Lsj6MW2NDBW/SV4PgMgpSU/P9CN3Ca9WVzSi9yS3mwheDZj0859dVesOjvS4fKBrjHzmQRXCWXc/fOY16+Z2eNm1r4m+4qINGgtToJTLwomCG5N7VhfdlsqbcFb3GSv0bRJMZ97CwYfmIKTRJf01DorQjwDYgFwqpn1BAqA64GvxG5gZicDW9zdzWw4kARsB3YeaV8RkUbFDNr1CqZB/8razgWMn76IU4rW08l24CSRmpLMXWP61tlbxi0g3L3IzG4H3iBoqjrV3VeY2a3h+snAl4FvmlkRsA+43oMHMyL3jVdZRURONOWV4y1ZsnMfGXFoxaQH5UREGrHqHpTT6BkiIhJJASEiIpEUECIiEkkBISIikRQQIiISSQEhIiKRFBAiIhJJASEiIpEUECIiEkkBISIikRQQIiISSQEhIiKRFBAiIhJJASEiIpEUECIiEkkBISIikRQQIiISSQEhIiKRFBAiIhJJASEiIpEUECIiEkkBISIikRQQIiISSQEhIiKRFBAiIhJJASEiIpEUECIiEkkBISIikRQQIiISSQEhIiKRFBAiIhJJASEiIpHiGhBmNtbMVptZnplNilh/g5ktDaf3zWxwzLoNZrbMzHLNLCee5RQRkcM1ideBzSwZeAy4GMgHFpjZLHf/MGazj4Dz3P0zM7sUmAKcGbN+tLtvi1cZRUSkavG8ghgO5Ln7enc/CLwIXBm7gbu/7+6fhbPzgcw4lkdERGohngGRAWyMmc8Pl1XlZuD1mHkHZpvZQjObWNVOZjbRzHLMLKewsPCYCiwiIuXidosJsIhlHrmh2WiCgDgnZvHZ7r7JzDoCfzOzVe4+97ADuk8huDVFdnZ25PFFRKT24nkFkQ90jZnPBDZV3sjMBgFPAle6+/bS5e6+Kfy5FZhBcMtKRESOk3gGxALgVDPraWZNgeuBWbEbmFk3YDrwb+6+JmZ5SzNLK30NXAIsj2NZRUSkkrjdYnL3IjO7HXgDSAamuvsKM7s1XD8Z+BHQDnjczACK3D0b6ATMCJc1AV5w97/Gq6wiInI4c284t+2zs7M9J0ePTIiI1JSZLQz/MD+MnqQWEZFICggREYmkgBARkUgKCBERiaSAEBGRSAoIERGJpIAQEZFICggREYmkgBARkUgKCBERiaSAEBGRSAoIERGJpIAQEZFICggREYmkgBARkUgKCBERiaSAEBGRSAoIERGJpIAQEZFICggREYmkgBARkUgKCBERiaSAEBGRSAoIERGJpIAQEZFICggREYmkgBARkUgKCBERiaSAEBGRSAoIERGJpIAQEZFIcQ0IMxtrZqvNLM/MJkWsNzN7NFy/1MyyarqviIjEV9wCwsySgceAS4H+wHgz619ps0uBU8NpIvCbWuwrIiJxFM8riOFAnruvd/eDwIvAlZW2uRJ41gPzgXQz61zDfUVEJI7iGRAZwMaY+fxwWU22qcm+IiISR03ieGyLWOY13KYm+wYHMJtIcHsKYI+Zra5xCStqD2w7yn1PVDrnhq+xnS/onGure1Ur4hkQ+UDXmPlMYFMNt2lag30BcPcpwJRjLayZ5bh79rEe50Sic274Gtv5gs65LsXzFtMC4FQz62lmTYHrgVmVtpkFfC1szTQC2OXum2u4r4iIxFHcriDcvcjMbgfeAJKBqe6+wsxuDddPBl4DLgPygL3A16vbN15lFRGRw8XzFhPu/hpBCMQumxzz2oHbarpvnB3zbaoTkM654Wts5ws65zpjwXe0iIhIRepqQ0REIjX6gGioXXqYWVcze9vMVprZCjP7j3D5SWb2NzNbG/5sG7PPPeHnsNrMxiSu9EfPzJLNbLGZvRrON+jzBTCzdDN72cxWhb/vkQ35vM3su+G/6eVmNs3MmjfE8zWzqWa21cyWxyyr9Xma2TAzWxaue9TMoh4jiObujXYiqABfB5xC0LR2CdA/0eWqo3PrDGSFr9OANQTdlvwUmBQunwT8JHzdPzz/ZkDP8HNJTvR5HMV53wm8ALwazjfo8w3P5RnglvB1UyC9oZ43wQOzHwGp4fwfgAkN8XyBUUAWsDxmWa3PE/gAGEnwfNnrwKU1LUNjv4JosF16uPtmd18Uvt4NrCT4z3UlwRcK4c+rwtdXAi+6+wF3/4igZdnw41roY2RmmcDlwJMxixvs+QKYWWuCL5KnANz9oLvvpGGfdxMg1cyaAC0InpFqcOfr7nOBHZUW1+o8w66LWrv7PA/S4tmYfY6osQdEo+jSw8x6AEOBfwKdPHjWhPBnx3CzhvBZ/B/wn0BJzLKGfL4QXP0WAr8Lb609aWYtaaDn7e4FwM+AT4DNBM9OzaaBnm+E2p5nRvi68vIaaewBUeMuPU5UZtYK+BPwHXf/vLpNI5adMJ+FmX0J2OruC2u6S8SyE+Z8YzQhuA3xG3cfCnxBcOuhKif0eYf33K8kuI3SBWhpZl+tbpeIZSfM+dbCMXdbFKWxB0RNugM5YZlZCkE4PO/u08PFW8LLTsKfW8PlJ/pncTZwhZltILhVeIGZ/Z6Ge76l8oF8d/9nOP8yQWA01PO+CPjI3Qvd/RAwHTiLhnu+ldX2PPPD15WX10hjD4gG26VH2FLhKWClu/9vzKpZwI3h6xuBV2KWX29mzcysJ8EYHR8cr/IeK3e/x90z3b0Hwe/xLXf/Kg30fEu5+6fARjPrGy66EPiQhnvenwAjzKxF+G/8QoL6tYZ6vpXV6jzD21C7zWxE+Hl9LWafI0t0TX2iJ4KuPtYQ1Pr/INHlqcPzOofgUnIpkBtOlwHtgL8Da8OfJ8Xs84Pwc1hNLVo61LcJOJ/yVkyN4XyHADnh73om0LYhnzfwALAKWA48R9Byp8GdLzCNoJ7lEMGVwM1Hc55AdvhZrQN+TfiAdE0mPUktIiKRGvstJhERqYICQkREIikgREQkkgJCREQiKSBERCSSAkJERCIpIETqQNjl9rfC1+eb2S4zq3ZExLA79j1mVueDzYvUBQWESN1IB74VM/+Ou19W3Q7uPprgATeReimuY1KLNCIPA73MLJfgydctpSvCPnNeAloT/J/7pru/k4hCitSGriBE6sYkYJ27DwHuqrTuK8Ab4brBBN2eiNR7uoIQib8FwNSwd92Z7p6b4PKI1IiuIETizIORwUYBBcBzZva1BBdJpEYUECJ1YzfB2N+HMbPuBIMZPUHQBXvW8SyYyNHSLSaROuDu283sPTNbDuwjppKaoPvxu8zsELCHoE9+kXpPASFSR9z9KxA8BwF8P2b5M5QPNC9ywtAtJpG6dxA4vSYPygGnEDSLFal3NGCQiIhE0hWEiIhEUkCIiEgkBYSIiERSQIiISCQFhIiIRPr/w8ueSb7nm5gAAAAASUVORK5CYII=\n",
- "text/plain": [
- ""
- ]
- },
- "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": [
- "\n",
- "\n",
- "
\n",
- " \n",
- " \n",
- " | \n",
- " 0 | \n",
- " 1 | \n",
- " 2 | \n",
- "
\n",
- " \n",
- " \n",
- " \n",
- " 0 | \n",
- " 0.102 | \n",
- " 0.319 | \n",
- " 0.565 | \n",
- "
\n",
- " \n",
- " 1 | \n",
- " 0.204 | \n",
- " 0.452 | \n",
- " 0.672 | \n",
- "
\n",
- " \n",
- " 2 | \n",
- " 0.306 | \n",
- " 0.553 | \n",
- " 0.744 | \n",
- "
\n",
- " \n",
- " 3 | \n",
- " 0.408 | \n",
- " 0.639 | \n",
- " 0.799 | \n",
- "
\n",
- " \n",
- " 4 | \n",
- " 0.510 | \n",
- " 0.714 | \n",
- " 0.845 | \n",
- "
\n",
- " \n",
- "
\n",
- "
"
- ],
- "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": [
- ""
- ]
- },
- "execution_count": 25,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": 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QLPJK7nV0x6hRo3jqqadYt24dAG+//TYvv/xyxnP69OnDW2+91fZ627ZtNDQEf/ndddddnb7nCSec0DZU9Mgjj/Dmm2+2XWffffelV69erFmzhmeffbbtnNra2rbvUabjpDSowF75U4BIcv7whljGQFNzEFOmTOHll19m1qxZ3HrrrRx//PGccMIJTJ06FQh6A6tXr+boo4/mscce47rrrgNgzpw5/OhHP+LII4/k8MMP5+c//3l3PzIAAwYM4M4772TChAkMGzaMUaNGtSXA0xk7dizz589vS1LfcMMNXHDBBRx//PH079+/0/e8/vrrefzxxxkxYgSLFy/moIMOAmDMmDHs2rWLYcOG8Y1vfINRo0a1nTNp0iSGDRvGRRddlPG4ZNOnT2fgwIE0NzczbNgwLrnkkhy+M9JVmSZ8xPX/TPKv4ov1vfTSSxx22GFFalHX9O7du20WkcSvHH9GSp0K7JWPTMX61IMQkbxTgb3KoCR1CVLvQcqJFr1VLvUgRKTLtOitsilAiEiXadFbZdMQk4h0mRa9VTb1IESky9LlFJRrqAwKEAWgct/FK/d90UUXMWTIEI444oh2ixEld1EL37TorbIpQKRaeT/cdgTcUB98XXl/ty+ZqMWUeEyZMqX77UwjUe47zveA7ANEPnU1QKxZs4ZVq1bR0tLCrFmzYmhZ5UuXjAaUa6hgykEkW3k/PPRFaA3HVbetD14DDLswr2+1bds2Ro4cycKFCxkyZAgTJkzglFNO4dJLL6V3795cdtll/Pa3v2Xfffdl3rx5DBgwgD/96U9cddVVbNq0iV69evHDH/6QD3/4w0ycOJH99tuP5cuXt5XlbmpqaqsWW1dXx5o1a/jLX/7Cj3/8Y+666y6eeeYZjjnmGO68804gKPd9/fXX884773DIIYfw4x//mN69ezNo0CA++9nP8tBDD9Ha2soDDzxAz549mTFjBjU1NfzkJz/h9ttvZ+vWrUydOpWdO3fSr18/5syZw/7775/282/ZsoUJEyawadMmRo4c2aHc9/r169mxYwdf+tKXmDRpUrty34cffjhz5syJPC7VWWed1fZ85MiRNDc35+8fsYpkqnSsG/hULvUgkv3mpj3BIaG1JdjeDSr33VGhy323trZyzz33MGbMmCz+xSSVFr5VJ/Ugkm1L89dluu1ZUrnvjgpd7vvKK6/khBNO4Pjjj8/YrmqX7o6KWvhWnRQgkvUdGAwrRW2Pgcp9F6bc94033simTZv4wQ9+0Gmbqlkiz5AYSkrOM0w+Y0i7faBkdDXQEFOyU6+D2pS/iGrrgu0xULnv+Mt9z5o1i0WLFjF37lz22ks/7plkyjOoAmt1Ug8iWSIR/ZubgmGlvgOD4NDNBHUiB5EwZswYLr74YmbNmsUf/vAH+vTp01bu+8Ybb2xX7rtv377cd999QFDu+4orrmDq1Km0trYyfvx4jjzyyG61DdqX+04MW02dOpUPfehDac8ZO3YsH//4x/n5z3/O7bff3lbuu6GhgVGjRvHnP/8543tef/31TJgwgREjRnDiiSe2K/c9Y8YMhg0bxpAhQyLLfY8YMYLZs2enPS7Z5ZdfzsEHH9w2ZDZu3Li28unSXmd5Bi18qz4q912CVO67sMrxZyQOKtFdnTKV+1YPQqQKRSWjlWeQVBqULUHqPUictOhNsqUehEiV0aI3yVZV9CAqKc8i+VWNPxta9CbZiq0HYWazgXOA1939iIj9k4GLktpxGDDA3d8ws1eBt4DdwK50CZRs9OzZky1bttCvX7/IefdSvdydLVu20LNnz2I3JTa625t0R2yzmMzsBGA7cHdUgEg5dixwjbufEr5+FWh098zlPVNEzWJqbW2lubk57SIqqW49e/Zk4MCB1NbWFrspeZe68A2CpPO/Ht3Az5Zu6LBd+YbqVJRZTO7+uJkNyvLwCUD0Mt5uqq2t7bTsg0gl6uxub1ElNUSSFT1JbWa9gDFA8k0DHFhsZg78wN1nZjh/EjAJaFtsJSK625t0XykkqccCT7n7G0nbRrv7COBM4KpwuCqSu89090Z3bxwwYEDcbRUpG7rbm3RXKQSI8aQML7n7xvDr68B8YGQR2iVSFqLu9Abobm/SbUUdYjKzvsCJwKeStu0D7OXub4XPTwe6d0MGkQqVqQJrYghJuQbpqjinuc4FTgL6m1kzcD1QC+DuM8LD/gVY7O7/SDp1f2B+OCW1B3Cvu/8qrnaKlLPOKrAq1yDdEecspglZHHMncGfKtleA7pcoFakCWvQmcSqFHISIdJES0RKnok9zFZHsqAKrFJp6ECJlQBVYpRjUgxApA6rAKsWgHoRIGVAyWopBAUKkDCgZLcWgISaREqNktJQK9SBESoiS0VJK1IMQKSFKRkspUQ9CpIQoGS2lRAFCpIQoGS2lRAFCpAhUolvKgXIQIgWmEt1SLhQgRApMJbqlXGiISaTAlIiWcqEAIVJgSkRLudAQk0iMtCpaypl6ECIx0apoKXfqQYjERKuipdypByESEyWjpdwpQIjERMloKXcKECIx0apoKXfKQYjkQdRsJa2KlnKnACHSTZ2VzlBAkHKlISaRbso0W0mknClAiHSTZitJpVKAEOkmzVaSSqUAIZIl3cNBqo2S1CJZ0D0cpBopQIhkQfdwkGqkISaRLCgRLdVIAUIkC0pESzWKLUCY2Wwze93MXkiz/yQz22ZmK8LHdUn7xpjZWjNbZ2ZT4mqjSLaUiJZqFGcO4k7gDuDuDMc84e7nJG8wsxrge8BpQDPwnJktdPcX42qoSDKVzZCysfJ++M1NsK0Z+g6EU6+DYRfm7fKxBQh3f9zMBnXh1JHAOnd/BcDM5gHnAQoQEjuVzZCSFBUIAB76IrSGebBt64PXkLcgUewcxLFm9ryZPWJmh4fbGoD1Scc0h9simdkkM2sys6ZNmzbF2VapAiqbIUWz8n647Qi4oT74uvL+Pdsf+mIQAPA9geCRr+0JDgmtLUEgyZNiTnNdBhzs7tvN7CxgAXAoYBHHerqLuPtMYCZAY2Nj2uNEsqHZSlIUiSAQ1Rv4zU3RgSB1W8K25rw1q2g9CHf/u7tvD58/DNSaWX+CHsOBSYcOBDYWoYlShTRbSWIX1VNIFwQSw0q56Dswb00tWg/CzN4H/M3d3cxGEgSrLcBW4FAzGwxsAMYDnyxWO6VyRSWjJ58xpF0OAjRbSbool7xBpt5A34Hh8FKKuv1gV0pPorZuz/vkQZzTXOcCzwBDzKzZzD5vZpeb2eXhIR8HXjCz54HpwHgP7AKuBhYBLwH3u/vquNop1SmRjN6wtQWnfTL65nFDaaivw4CG+jpuHjdUyWmJlq+8gdWkXjmQCCy1KT3Y2jo4879h7HToeyBgwdex0/M6i8ncK2fYvrGx0ZuamordDCkDo6c9xoaIvEJDfR1PTTmlCC2SspOaN4DgF/fY6WHPIeKv/kxq66KvNezCWKezmtlSd2+M2qdaTFKVlIyWnET9gs5r3uDAPdeMCgLDLsxrzyBbChBSlQ6or4vsQSgZXeWKmTcoUhDIpNjrIESKQqUzpIMKyRvkk3oQUtHSlc1Q6Ywqlm48P9f1Br47Om+QPDSUacioDChJLRUrtWwGBL0EzUqqEtkMF8GeZPCDk8iwJrejzvIGZSJTkloBQiqWZipVsXQzjHrUQcsbHY/vG67NzSVvUMJDQ7nIFCCUg5CKpZlKVSKXlclRwQGCHkCF5A3ySTkIqViaqVRB0uUN0tUwSpc3SKfvwIrJG+STAoRULJXNKEO5lrVO11OwmiCJnKqz8hQlONW0mBQgpCLoJj8VIF1voEdd7gvS0s0wOvO/g+dlnlguFAUIKXu6yU8ZymVlclcWpGWzMlk6pQAhZS/TTX4UHEpQPvMGp14XPVupRFcmlxvNYpKyp9lKJSpdpdNMeYModftFzy5KBIEqnWFUCOpBSNnTbKUiyzWxnO+8gXoKsdFCOSl7WjFdRPlckFYhK5PLjcp9S8XQbKUiyldiedxM5Q3KhAKElA3NViqiQi5Ik5KhACFlQ7OVCiDXSqdakFbRFCCkbGi2Uh4VO7EsZUEBQsqGZivlSVdWLGtBWlVSgJCyodpKXaDEsnSDAoSUHN0FLk+UWJZu0joIKSla09AF6RLLtx0RPSyUa2JZK5Mrmm4YJGUj00wliZDoJWxbD/ieXsLK+ztPLCer8hvjSDQNMUlJ0UylDHLJJyixLHmgACElRTOV0sg1n6DEsuSBhpikpEw+Ywh1te2relbdTKVc7rGcrgJqIrGsISPpBvUgpGhUVylCrj2FdAvVtGJZ8kABQoqi6usq5aukhSqgSowUIKQoqrquUrpeAuRe0kL5BImRchBSFFUzWymXfEJi5lGURP5A+QQpIPUgpCiqYraSZh5JmYutB2Fms83sdTN7Ic3+i8xsZfh42syOTNr3qpmtMrMVZqal0RWo4mYraeaRVKA4exB3AncAd6fZ/2fgRHd/08zOBGYCxyTtP9ndN8fYPimiipqtpJlHUqFiCxDu/riZDcqw/+mkl88CaQZfpdxlKr5XVgFBM4+kypRKDuLzwCNJrx1YbGYO/MDdZ6Y70cwmAZMADjrooFgbKbnrbDpr2dDMI6lCRZ/FZGYnEwSIryVtHu3uI4AzgavM7IR057v7THdvdPfGAQMGxNxayVVZFt/TzCMRoMg9CDMbBswCznT3LYnt7r4x/Pq6mc0HRgKPF6eV0h1lN51VM49E2hStB2FmBwEPAp9295eTtu9jZn0Sz4HTgciZUFL60k1bLYnprJp5JJJRbD0IM5sLnAT0N7Nm4HqgFsDdZwDXAf2A75sZwK7wphX7A/PDbT2Ae939V3G1U+JVsrcJ1cwjkU7FOYtpQif7LwEuidj+CnBkxzOkHJXsdFbNPBLpVKnMYpIyl6kya1Gns6abmqqZRyKdKvosJil/iamsG7a24OyZyrpg+YbiNizT7Tg180ikU+pBSLeVRGXWXG/Heep1mnkk0gkFCOm2ok9l7crU1EQAUE5BJC0FCOm2oldmzTnhHA4vqacgkpFyENJtBa3MGrV2obOEc7LkqakikpEChHTb+cMbuHncUBrq6zCgob6Om8cNzX/+IV3SuW7f6OOVcBbpFnP3YrchbxobG72pSbePiFOm6ayxu+2IMDikqNsPdrV0TDgrGIh0ysyWhouUO1APQrJWsOmsUcNIkH4oqeVN9RREYqAktWStINNZM5XV7jswugeRqIekgCCSV+pBSNYKMp21s7ULSjqLFIx6EJK1vE9njVrclm4YSWsXRApOAUKyltfKrOmGkur2hZY3Oh6vtQsiBacAIVnrcmXWXMpg9KjLXFZbRApG01wlUt6ms6b2FKBjAGjHgju0aRhJpCAyTXNVD0I6SExnTQwlJaazArkHia6UwdAwkkhJ0Cwm6SDTdNacqQyGSNlSgJAOujSdNd3iNt13QaRsaYhJOsh5OmumxW2674JI2VIPQjrIuTprpsVtwy5UT0GkTKkHIR1knM6a6+I2UE9BpEwpQEik84c3dJyx1NXFbSJSlhQgqljOax20uE2kqigHUaU6Ld2dy53bVG5bpCJpJXWVGj3tsciZSg31dTx11ubomUc96tIMJR0I17wQY2tFJC66YZB0kHGtQ7qhJNDiNpEqogBRpdKtaTigvk5DSSICKEldtSafMYQn53+fLzOPA2wzG70/32E8x51xJSzRndtERD2IqnV+zVNMq53FwL02s5fBwL02M612FufXPKU7t4kI0EkPwsxWZnGNTe5+ap7aI4Xym5vosXtHu009du8I8g+JhLNKbotUtc6GmGqAszLsN2Bh/pojcYhc76DVzyLSic4CxGXu/pdMB5jZlWm2zwbOAV539yMi9hvwXYIA9DYw0d2XhfvGhPtqgFnuPq2zDyLRFizfwJPzv899zOOA92xm49v9+c788Zy+z/vo1fJaxxO0+llEQhlzEO7+JICZfSl1X2Jb4pgIdwJjMlz+TODQ8DEJ+N/wujXA98L9HwEmmNlHMrVT0lvxy5ncZDPb5Rpuspk8suNI5RlEJKNsk9Sfjdg2MdMJ7v44ELGqqs15wN0eeBaoN7P3AyOBde7+irvvBOaFx0oXXLLzJ/Syne229bKdHLO7SVNWRSSjzpLUE4BPAoPNLDnX0AfY0s33bgCS51I2h9uith/TzfeqWgfsFf3PdMBeW5RnEJGMOstBPA28BvQHbk3a/haQzQynTCxim2fYHn0Rs0kEQ1QcdNBB3WxSGYsqwz3sQnbURecadtS9j15FaKaIlI+MASJMUP8FODaG924GDkx6PRDYCOydZnu6Ns4EZkJQiyn/zSwDGe7o1uvMm9j18y+0m9K6q6Ynvc68qRgtFZEykjEHYWa/6OwC2RyTxkLgMxYYBWxz99eA54BDzWywme0NjEdTaTPr5I5uPc67vV2uocd5t2toSUQ61dkQ03EpuYdURjDTqOMOs7nASUB/M2sGrgdqAdx9BvAwwRTXdQTTXD8X7ttlZlcDiwimuc5299XZfqCqpDUNIhKDzgLEBuD3QLqprAA7oza6+4RMF/agzvhVafY9TBBAJBt9M9ROEhHpos4CxEyCIZ5LgfuAue6+Iu5GSQYRyejnDvkCRyz9D+qSprO2+N68cMgX+OciNlVEyltnC+W+6+7HAicSrGn4sZm9ZGbXmdmHCtJC2SORjN62HvC2ZPQvV27ka62X0Pxuf951o/nd/nyt9RK+/OKhxW6xiJSxnO8oZ2bDgdnAMHeviaVVXVTxd5S77YjIoaTmd/tz3M7pHbYb8OdpZxegYSJSrrp9RzkzqzWzsWY2B3gEeBn41zy2UbKRJhmddjFcmpsCiYhko7OV1KcBE4CzgT8QlL2Y5O7/KEDbJFWaZPSOuvdRt7uGltbdbdvqamuYfMaQQrZORCpMZz2IrwPPAIe5+1h3n6PgUCAr7w+GlG6oD76uvD/tjXx6nXkTN48bSkN9HQY01Ndx87ihnD+8oRgtF5EKkXMOopRVTA4idWU0BIFhbJhn0I18RCRPup2DkALLsDJ6we7RjH5nOoN3zGH0O9NZsHt0cdooIhWvs3UQUgxpktG+rZlrH1zVlmvYsLWFax9cBaDhJBHJO/UgSlGaFdB/o3+7RDRAS+tublm0thCtEpEqowBRTFGJaEibjL555wWRl9m4tSVyu4hId2iIqVgylOhuSzqnJKObHu4PEcFA6x1EJA4KEMXSSYnuqAqsk3dvaJeDAK13EJH4KEAUS2cluiMkEtG3LFrLxq0tHFBfx+QzhihBLSKxUIAoli6W6D5/eIMCgogUhJLUxZImEc2p1xWnPSIiKRQgimXYhcHK6KRbgTJ2ulZFi0jJ0BBTIUTc5CddIjphwfINyjWISFEpQMQtm+msKRYs36AV0yJSdBpiilum6axp3LJorVZMi0jRKUDErQvTWdOtjNaKaREpJAWIuKWbtpphOmu6ldFaMS0ihaQAEbcuTGedfMYQ6mrb3+5bK6ZFpNCUpI5bmrpKmaazasW0iJQC3VEun9JNZxURKVGZ7iinHkS+dGE6q4hIKVMOIl+6MJ1VRKSUqQeRL12YzqrV0iJSytSDyJccp7MmVktv2NqCs2e19ILlG+Jro4hIDhQg8iXH6axaLS0ipU4BIl9yrM6q1dIiUuqUg8inDNVZUx1QX8cG3V9aREpYrD0IMxtjZmvNbJ2ZTYnYP9nMVoSPF8xst5ntF+571cxWhfuKuLghHlotLSKlLrYehJnVAN8DTgOagefMbKG7v5g4xt1vAW4Jjx8LXOPubyRd5mR33xxXG7skT4vhtFpaREpdnENMI4F17v4KgJnNA84DXkxz/ARgbozt6b48L4bT/aVFpJTFOcTUAKxPet0cbuvAzHoBY4CfJW12YLGZLTWzSenexMwmmVmTmTVt2rQpD83OQIvhRKSKxBkgLGJbusJPY4GnUoaXRrv7COBM4CozOyHqRHef6e6N7t44YMCA7rW4M11YDCciUq7iDBDNwIFJrwcCG9McO56U4SV33xh+fR2YTzBkVVxduLeDiEi5ijNAPAccamaDzWxvgiCwMPUgM+sLnAj8PGnbPmbWJ/EcOB14Ica2ZqcL93aAYNX06GmPMXjKLxk97TGtlhaRshBbktrdd5nZ1cAioAaY7e6rzezycP+M8NB/ARa7+z+STt8fmG9miTbe6+6/iqutWevCvR0SJTUSq6YTJTUAJahFpKTpfhAxGz3tscgFcQ31dTw15ZQitEhEZI9M94NQqY2YqaSGiJQrBYiYpSudoZIaIlLqFCBippIaIlKuVKwvZiqpISLlSgEinTzVXAKV1BCR8qQAESXPNZdERMqRchBRVHNJREQBIpJqLomIKEBEUs0lEREFiEhdrLkkIlJJlKSO0oWaSxDUXdJ0VhGpFAoQ6Qy7MKcZSyrKJyKVRkNMeXLLorVtwSGhpXU3tyxaW6QWiYh0jwJEnqgon4hUGgWIPFFRPhGpNAoQeaKifCJSaZSkzhMV5RORSqMAkUcqyicilURDTCIiEkkBQkREIilAiIhIJAUIERGJpACx8n647Qi4oT74uvL+YrdIRKQkVPcsJt05TkQkreoOEJnuHJcmQKhiq4hUi+oOEDneOU4VW0WkmlR3DiLHO8epYquIVJPqDhA53jlOFVtFpJpUd4AYdiGMnQ59DwQs+Dp2etr8gyq2ikg1qe4cBOR057jJZwxpl4MAVWwVkcqlAJEDVWwVkWqiAJEjVWwVkWoRaw7CzMaY2VozW2dmUyL2n2Rm28xsRfi4LttzRUQkXrH1IMysBvgecBrQDDxnZgvd/cWUQ59w93O6eK6IiMQkzh7ESGCdu7/i7juBecB5BThXRETyIM4A0QCsT3rdHG5LdayZPW9mj5jZ4Tmei5lNMrMmM2vatGlTPtotIiLEGyAsYpunvF4GHOzuRwK3AwtyODfY6D7T3RvdvXHAgAFdbauIiKSIM0A0AwcmvR4IbEw+wN3/7u7bw+cPA7Vm1j+bc0VEJF5xBojngEPNbLCZ7Q2MBxYmH2Bm7zMzC5+PDNuzJZtzRUQkXrHNYnL3XWZ2NbAIqAFmu/tqM7s83D8D+DhwhZntAlqA8e7uQOS5cbVVREQ6suD3cWVobGz0pqamvFxL930QkWpgZkvdvTFqn1ZSR9B9H0REqr2aaxq674OIiAJEJN33QUREASKS7vsgIqIAEWnyGUOoq61pt033fRCRaqMkdQTd90FERAEiLd33QUSqnYaYREQkkgKEiIhEUoAQEZFIChAiIhJJAUJERCIpQIiISCQFCBERiaQAISIikRQgREQkkgKEiIhEUoAQEZFIChAiIhJJAUJERCIpQIiISKSqL/e9YPkG3fdBRCRCVQeIBcs3cO2Dq2hp3Q3Ahq0tXPvgKgAFCRGpelU9xHTLorVtwSGhpXU3tyxaW6QWiYiUjqoOEBu3tuS0XUSkmlR1gDigvi6n7SIi1aSqA8TkM4ZQV1vTbltdbQ2TzxhSpBaJiJSOqk5SJxLRmsUkItJRVQcICIKEAoKISEdVPcQkIiLpKUCIiEgkBQgREYkUa4AwszFmttbM1pnZlIj9F5nZyvDxtJkdmbTvVTNbZWYrzKwpznaKiEhHsSWpzawG+B5wGtAMPGdmC939xaTD/gyc6O5vmtmZwEzgmKT9J7v75rjaKCIi6cXZgxgJrHP3V9x9JzAPOC/5AHd/2t3fDF8+CwyMsT0iIpKDOANEA7A+6XVzuC2dzwOPJL12YLGZLTWzSelOMrNJZtZkZk2bNm3qVoNFRGSPONdBWMQ2jzzQ7GSCAHFc0ubR7r7RzP4J+LWZrXH3xztc0H0mwdAUjY2NkdcXEZHcxdmDaAYOTHo9ENiYepCZDQNmAee5+5bEdnffGH59HZhPMGQlIiIFEmeAeA441MwGm9newHhgYfIBZnYQ8CDwaXd/OWn7PmbWJ/EcOB14Ica2iohIitiGmNx9l5ldDSwCaoDZ7r7azC4P988ArgP6Ad83M4Bd7t4I7A/MD7f1AO5191/F1VYREenI3Ctn2L6xsdGbmrRkQkQkW2a2NPzDvAOtpBYRkUgKECIiEkkBQkREIilAiIhIJAUIERGJpAAhIiKRFCBERCSSAoSIiERSgBARkUgKECIiEkkBQkREIilAiIhIJAUIERGJpAAhIiKRFCBERCSSAoSIiERSgBARkUgKECIiEkkBQkREIilAiIhIJAUIERGJpAAhIiKRFCBERCSSAoSIiERSgBARkUgKECIiEkkBQkREIilAiIhIJAUIERGJpAAhIiKRFCBERCRSrAHCzMaY2VozW2dmUyL2m5lND/evNLMR2Z4rIiLxii1AmFkN8D3gTOAjwAQz+0jKYWcCh4aPScD/5nCuiIjEKM4exEhgnbu/4u47gXnAeSnHnAfc7YFngXoze3+W54qISIziDBANwPqk183htmyOyeZcERGJUY8Yr20R2zzLY7I5N7iA2SSC4SmA7Wa2NkOb+gObM+yvZNX62fW5q4s+d+4OTrcjzgDRDByY9HogsDHLY/bO4lwA3H0mMDObBplZk7s3ZnNspanWz67PXV30ufMrziGm54BDzWywme0NjAcWphyzEPhMOJtpFLDN3V/L8lwREYlRbD0Id99lZlcDi4AaYLa7rzazy8P9M4CHgbOAdcDbwOcynRtXW0VEpKM4h5hw94cJgkDythlJzx24Kttz8yCroagKVa2fXZ+7uuhz55EFv6NFRETaU6kNERGJVDUBolpLd5jZbDN73cxeKHZbCsXMDjSz35rZS2a22sy+VOw2FYKZ9TSzP5jZ8+HnvrHYbSokM6sxs+Vm9otit6WQzOxVM1tlZivMrCmv166GIaawdMfLwGkEU2ufAya4+4tFbVgBmNkJwHaCFetHFLs9hRCuxn+/uy8zsz7AUuD8Sv/3NjMD9nH37WZWCzwJfCmsUlDxzOwrQCPwXnc/p9jtKRQzexVodPe8r/+olh5E1ZbucPfHgTeK3Y5CcvfX3H1Z+Pwt4CWqYCV+WLJme/iyNnxU/l+AgJkNBM4GZhW7LZWkWgKESndUKTMbBAwHfl/kphREOMyyAngd+LW7V8XnBr4D/DvwbpHbUQwOLDazpWFlibyplgCRdekOqRxm1hv4GfBld/97sdtTCO6+292PIqg+MNLMKn5Y0czOAV5396XFbkuRjHb3EQTVr68Kh5XzoloCRDZlP6SChGPwPwPmuPuDxW5Pobn7VmAJMKa4LSmI0cC54Vj8POAUM/tJcZtUOO6+Mfz6OjCfYEg9L6olQKh0RxUJk7U/Al5y928Xuz2FYmYDzKw+fF4HfAxYU9RGFYC7X+vuA919EMH/7cfc/VNFblZBmNk+4UQMzGwf4HQgbzMWqyJAuPsuIFG64yXg/mop3WFmc4FngCFm1mxmny92mwpgNPBpgr8kV4SPs4rdqAJ4P/BbM1tJ8EfRr929qqZ8VqH9gSfN7HngD8Av3f1X+bp4VUxzFRGR3FVFD0JERHKnACEiIpEUIEREJJIChIiIRFKAEBGRSAoQIiISSQFCJA/MrN7Mrgyfn2Rm28ws4x0Rw5Lk280s7zebF8kHBQiR/KgHrkx6/YS7Z1yc5+4nA3mt3y+ST7Hek1qkikwDDgkrqbYCf0vsCO9PcR/wXoL/c1e4+xPFaKRILtSDEMmPKcCfwkqqk1P2fRJYFO47ElhR0JaJdJF6ECLxew6YHVaYXeDuK4rcHpGsqAchErPwrn4nABuAe8zsM0VukkhWFCBE8uMtoE/UDjM7mOCGNj8kKEM+opANE+kqDTGJ5IG7bzGzp8zsBaCFpCQ1cBIw2cxage2AehBSFhQgRPLE3T8JwToI4N+Stt8F3FWcVol0nYaYRPJvJ3BENgvlgA8QTIsVKTm6YZCIiERSD0JERCIpQIiISCQFCBERiaQAISIikRQgREQk0v8HkTbpfomCloYAAAAASUVORK5CYII=\n",
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