Tle Spé - Dosage Beer Lambert (Monte Carlo).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ce programme permet d'estimer la valeur moyenne et l'incertitude-type sur la valeur obtenue lors d'un dosage par étalonnage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dans cet exercice il faudra :\n",
    "###     1. Compléter les listes des concentrations et absorbances\n",
    "###     2. Préciser la valeur de l'absorbance de la solution mystère\n",
    "###     3. Préciser les incertitudes-types sur les concentrations et les absorbances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Chaque partie de code est précédée d'un titre.\n",
    "### Certaines parties de code sont à modifier par vous, cela est indiqué par la mention $\\color {red} {\"A\\: VOUS\\: DE\\: JOUER\\,!\"}$ dans le titre de la partie."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 0 : On importe les bibliothèques nécessaires"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # Bibliothèque permettant le calcul scientifique\n",
    "import matplotlib.pyplot as plt # Bibliothèque permettant de tracer des graphiques\n",
    "from scipy.optimize import curve_fit # Bibliothèque permettant d'optimiser un modèle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 1 : On entre les listes de mesures et les incertitudes associées à ces mesures\n",
    "### $\\color {red} {\"A\\: VOUS\\: DE\\: JOUER\\,!\"}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#déclaration des listes de concentration C et absorbance A et de l'absorbance A_inc de la solution inconnue\n",
    "C = np.array(['modifier']) # Liste contenant les valeurs des concentrations\n",
    "A = np.array(['modifier']) # Liste contenant les valeurs d'absorbances\n",
    "A_inc = 'modifier' # Valeur de l'absorbance de la solution inconnue\n",
    "\n",
    "#déclaration des incertitudes sur les mesures de C et A\n",
    "uC = 0.0002 # Incertitude-type sur les concentrations\n",
    "uA = 0.001 # Incertitudes-types sur les absorbances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 2 : On initialise les variables et la fonction nécessaires aux calculs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Nombre de fois où on fait les calculs (nécessairement supérieur à 1 !)\n",
    "iterations = 1000\n",
    "\n",
    "#Création des listes contenant les valeurs aléatoires calculées pour C, A et C_inc\n",
    "C_alea=[]\n",
    "A_alea=[]\n",
    "LC_inc=[]\n",
    "\n",
    "# Définition de la fonction de modélisation, elle est linéaire ici y = a*x\n",
    "def modele(x, a):\n",
    "    return a * x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 3 : On simule \"iterations\" fois un dosage par étalonnage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#On fait \"iterations\" fois les opérations suivantes\n",
    "for i in range(iterations):    \n",
    "    \n",
    "    #On crée une liste aléatoire de chaque grandeur C et A\n",
    "    for j in range(len(C)):\n",
    "\n",
    "        VC = C[j]+uC*np.random.normal()\n",
    "        C_alea.append(VC)\n",
    "    \n",
    "        VA = A[j]+uA*np.random.normal()\n",
    "        A_alea.append(VA)\n",
    "    \n",
    "    #On fait la régression linéaire de la répartition aléatoire de C et A, A = k*C\n",
    "    k, _ = curve_fit(modele, C_alea, A_alea) # On calcule la meilleure valeur de k pour l'ajustement linéaire\n",
    "    \n",
    "    #On calcule une valeur de C_inc de la concentration inconnue\n",
    "    C_inc = (A_inc+uA*np.random.normal()) / k[0]\n",
    "    \n",
    "    #On stocke la valeur de C_inc dans une liste regroupant l'ensemble des valeurs obtenues\n",
    "    LC_inc.append(C_inc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 4 : On affiche les résultats obtenus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Concentration inconnue (Valeur moyenne) :  0.0529900237058652  g/L\n",
      "u(C_inc):  6.839386166048651e-05  g/L\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#On calcule et on affiche la moyenne des valeurs C_inc calculées et l'incertitude-type\n",
    "MoyCinc = sum(LC_inc)/iterations\n",
    "uCinc = (1/(iterations-1)*sum((np.array(LC_inc)-MoyCinc)**2))**0.5\n",
    "\n",
    "print('Concentration inconnue (Valeur moyenne) : ', MoyCinc, ' g/L')\n",
    "print('u(C_inc): ', uCinc, ' g/L')\n",
    "\n",
    "#On affiche l'histogramme de répartition des valeurs C_inc obtenues\n",
    "plt.hist(LC_inc, range = (MoyCinc-4*uCinc, MoyCinc+4*uCinc), bins = 50, color = 'blue', edgecolor = 'black')\n",
    "plt.axvline(MoyCinc, color=\"orange\", linestyle=\"-.\", label='Valeur moyenne (Concentration inconnue)')\n",
    "plt.title('Pour ' + str(iterations) + ' iterations')\n",
    "plt.xlabel('C (g/L)')\n",
    "plt.ylabel('Nombre de valeurs calculées')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}