{ "cells": [ { "cell_type": "markdown", "id": "21200f69", "metadata": {}, "source": [ "# S'entraîner (Régression linéaire)\n", "La partie donnant les concepts pour faire ces exercices est [accessible ici](https://pcsi3physiquestan.github.io/intro_python/notebook/np_polyfit.html).\n", "\n", "## Exemple simple\n", "On veut mesurer une capacité $C$ d'un condensateur. On étudie pour cela le régime libre d'un circuit RC avec une résistance $R$ variable. On mesure le temps caractéristique $\\tau$ pour différente valeur de $R$. On obtient les valeurs suivantes :" ] }, { "cell_type": "code", "execution_count": 1, "id": "8c966231", "metadata": { "tags": [ "remove-input" ] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
 R(Ohm)tau(micro s)
0100.00164.00
1150.00196.00
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3250.00294.00
4300.00354.00
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\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "\n", "R = np.array([100, 150, 200, 250, 300, 350, 400, 450, 500])\n", "tau = np.array([164, 196, 275, 294, 354, 396, 481, 497, 558])\n", "\n", "donnees = pd.DataFrame(\n", " {\n", " \"R(Ohm)\": [\"{:.2f}\".format(val) for val in R],\n", " \"tau(micro s)\": [\"{:.2f}\".format(val) for val in tau],\n", " }\n", ")\n", "\n", "donnees.style" ] }, { "cell_type": "markdown", "id": "9ba2824d", "metadata": {}, "source": [ "Un bilan sur les sources d'incertitude amène aux conclusions suivantes :\n", "* l'incertitude sur le temps caratéristique est de 5%\n", "* l'incertitude sur les résistances sont de 2%\n", "\n", "````{admonition} Détermination de C\n", ":class: tip\n", "1. Représenter $\\tau$ en fonction de R avec les croix d'incertitudes. On utilisera la fonction `errorbar`.\n", "2. Vérifier que le modèle attendu $\\tau = RC$ est visuellement possible.\n", "3. Estimer la capacitance $C$ par régression linéaire puis représenter la droite d'ajustement affine.\n", "4. Une méthode qualitative pour vérifier si le modèle est cohérent avec les incertitudes de mesure est de vérifier si la droite d'ajustement passe bien par les barres d'incertitude. Tester ici la cohérence du modèle.\n", "5. La relation étant linéaire, on peut aussi estimer $C$ comme la moyenne des rapport $\\frac{\\tau}{R}$. Estimer la capacitance de cette manière et vérifier qu'on obtient le même ordre de grandeur.\n", "```{tip}\n", "On rappelle la fonction pour tracer des points de mesures avec des barres d'erreurs :\n", "\n", "`errorbar(x, y, xerr=inc_x, yerr=inc_y, options...)`\n", "\n", "```\n", "````" ] }, { "cell_type": "code", "execution_count": 2, "id": "0ada3f5d", "metadata": { "tags": [ "hide-input", "remove-output" ] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "filenames": { "image/png": "D:\\cedri\\Dropbox\\Enseignement prepas\\approche_numeriques\\intro_python_td\\_build\\jupyter_execute\\notebook\\exo_polyfit_3_0.png" } }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Les points sont plutôt alignés. C'est encourageant pour l'utilisation de la relation tau = RC\n" ] } ], "source": [ "\"\"\"Importation des bibliothèques\"\"\"\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "\"\"\"Saisie des données\"\"\"\n", "R = np.array([100, 150, 200, 250, 300, 350, 400, 450, 500])\n", "tau = np.array([164, 196, 275, 294, 354, 396, 481, 497, 558])\n", "\n", "\"\"\"Incertitude sur les valeurs\"\"\"\n", "uR = R * 0.02\n", "utau = tau * 0.05\n", "\n", "\"\"\"Création du graphique et analyse des points de mesure\"\"\"\n", "f, ax= plt.subplots()\n", "f.suptitle(\"Détermination de C\")\n", "ax.set_xlabel(\"R(Ohm)\")\n", "ax.set_ylabel(\"tau(micro s\")\n", "\n", "ax.errorbar(R, tau, xerr=uR, yerr=utau, marker='+', linestyle='', color='red', label=\"Points de mesure\")\n", "\n", "ax.legend()\n", "plt.show()\n", "print(\"Les points sont plutôt alignés. C'est encourageant pour l'utilisation de la relation tau = RC\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "e262850b", "metadata": { "tags": [ "hide-input", "remove-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "----------------\n", "Droite d'ajustement :\n", "tau = 0.9976666666666667* R + 57.92222222222202\n", "Il faudrait arrondir en réfléchissant aux chiffres significatifs\n", "----------------\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "filenames": { "image/png": "D:\\cedri\\Dropbox\\Enseignement prepas\\approche_numeriques\\intro_python_td\\_build\\jupyter_execute\\notebook\\exo_polyfit_4_1.png" } }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "La droite passe globalement par les croix d'incertitude à part les points 2 et 3 pour lesquels il faudrait approfondir l'analyse.\n" ] } ], "source": [ "\"\"\"Ajustement linéaire\"\"\"\n", "p = np.polyfit(R, tau, 1)\n", "\n", "tau_adj = p[0] * R + p[1]\n", "\n", "print(\"----------------\")\n", "print(\"Droite d'ajustement :\")\n", "print(\"tau = \" + str(p[0]) + \"* R + \" + str(p[1]))\n", "print(\"Il faudrait arrondir en réfléchissant aux chiffres significatifs\")\n", "print(\"----------------\")\n", "\n", "\n", "\"\"\"Création du graphique et analyse des points de mesure\"\"\"\n", "f, ax= plt.subplots()\n", "f.suptitle(\"Détermination de C\")\n", "ax.set_xlabel(\"R(Ohm)\")\n", "ax.set_ylabel(\"tau(micro s\")\n", "\n", "ax.plot(R, tau_adj, linestyle=':', color='blue', label=\"Ajustement\")\n", "ax.errorbar(R, tau, xerr=uR, yerr=utau, marker='+', linestyle='', color='red', label=\"Points de mesure\")\n", "\n", "ax.legend()\n", "plt.show()\n", "\n", "print(\"La droite passe globalement par les croix d'incertitude à part les points 2 et 3 pour lesquels il faudrait approfondir l'analyse.\")" ] }, { "cell_type": "code", "execution_count": 4, "id": "e3b6f061", "metadata": { "tags": [ "hide-input", "remove-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "----------------\n", "Estimation de C :\n", "C = 9.976666666666666e-07 F\n", "Il faudrait arrondir en réfléchissant aux chiffres significatifs.\n", "----------------\n" ] } ], "source": [ "\"\"\"Détermination de C par régression linéaire\"\"\"\n", "C = p[0] * 1e-6 # Passage en secondes pour tau.\n", "print(\"----------------\")\n", "print(\"Estimation de C :\")\n", "print(\"C = \" + str(C) + \" F\")\n", "print(\"Il faudrait arrondir en réfléchissant aux chiffres significatifs.\")\n", "print(\"----------------\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "11699c41", "metadata": { "tags": [ "hide-input", "remove-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "----------------\n", "Estimation de C par moyenne des rapports :\n", "C = 1.2480044091710756e-06 F\n", "Il faudrait arrondir en réfléchissant aux chiffres significatifs.\n", "----------------\n" ] } ], "source": [ "\"\"\"Détermination de C par moyenne des rapports\"\"\"\n", "C_s = tau / R * 1e-6 # Calcul des C pour chaque valeur de R\n", "C2 = np.mean(C_s) # Calcul de la moyenne\n", "print(\"----------------\")\n", "print(\"Estimation de C par moyenne des rapports :\")\n", "print(\"C = \" + str(C2) + \" F\")\n", "print(\"Il faudrait arrondir en réfléchissant aux chiffres significatifs.\")\n", "print(\"----------------\")" ] }, { "cell_type": "markdown", "id": "732d6223", "metadata": {}, "source": [ "```{dropdown} Commentaire sur les valeurs trouvées.\n", "Vous devriez trouver le même ordre de grandeur mais pas la même valeur (plus de 20% d'écart tout de même). Cela peut s'expliquer par :\n", "* les incertitudes qui, si on les estime sont relativement grandes\n", "* un biais dans les mesures : l'ordonnée à l'origine devrait être nulle or la régression linéaire donne une valeur relativement importante (jusqu'à 30% des valeurs mesurées). Le modèle est donc plutôt affine et non linéaire. La méthode des rapports $\\tau/R$ n'est donc peut-être pas adaptée. C'est l'avantage de la régression linéaire qui permet de tenir compte d'un possible biais dans les mesures.\n", "```\n", "\n", "\n", "## Utiliser un modèle ajusté\n", "\n", "On veut mesurer la concentration de l'additif alimentaire E131 (bleu patenté) dans des bonbons gélifiées. On réalise pour cela un dosage par absorbance, c'est-à-dire qu'on va mesurer l'absorbance $A_{640nm}$ à la longueur d'onde $640nm$ de plusieurs solutions contenant du bleu de patenté à des concentrations connues $C_i$. En mesurant ensuite l'absorbance d'une solution contenant un bonbon gélifié bleu dissous, on déterminera sa concentration.\n", "\n", "> __Fabrication des solutions étalons :__\n", "> \n", "> On utilise une solution mère de concentration $C_0 = (2.04 \\pm 0.01) \\times 10^{-5} mol.L^{-1}$. On prélève un volume $V_1$ (inférieur ou égal à 10mL) qu'on complète par un volume $V_2$ d'eau distillée tel que $V_T= V_1 + V_2 = 10mL$. La concentration $C_i$ dans un tube où $V_1 = V_{1i}$ est alors :\n", ">\n", "> $$C_i = C_0 \\frac{V_{1i}}{V_T}$$\n", ">\n", "> Le mode opératoire utilisé et l'analyse des sources d'incertitudes amène à une expression de l'incertitude sur $C_i$ :\n", ">\n", "> $$u(C_i) = \\frac{C_0 u_i}{V_T} \\sqrt{1 + {\\left (\\frac{C_i}{C_0}\\right )}^2}$$\n", "> avec $u_i = 0.1 mL$ (l'incertitude sur la concentration a une influence négligeable).\n", "\n", "> __Loi de Beer-Lambert :__\n", ">\n", "> La loi de Beer-Lambert prévoit une relation linéaire entre la concentration d'une solution colorée et l'absorbance de cette solution : \n", ">\n", "> $$A_{640nm, i} = \\alpha_{E131, 640nm} C_i$$\n", ">\n", "> Les mesures d'absorbances seront considérées comme d'incertitude négligeable.\n", "\n", "On donne les données mesurées :" ] }, { "cell_type": "code", "execution_count": 6, "id": "3fab7155", "metadata": { "tags": [ "remove-input" ] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
 Vi(mL)A(SI)
01.000.13
12.500.43
25.000.83
37.501.27
410.001.76
\n" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Vi = np.array([1, 2.50, 5.00, 7.50, 10.00])\n", "Ai = np.array([0.128, 0.428, 0.833, 1.267, 1.765])\n", "\n", "donnees = pd.DataFrame(\n", " {\n", " \"Vi(mL)\": [\"{:.2f}\".format(val) for val in Vi],\n", " \"A(SI)\": [\"{:.2f}\".format(val) for val in Ai],\n", " }\n", ")\n", "\n", "donnees.style" ] }, { "cell_type": "markdown", "id": "5feea4cc", "metadata": {}, "source": [ "````{admonition} Dosage par absorbance\n", "1. Créer deux vecteur numpy contenant les volumes $V_{1i}$ et les absorbances $A_i$ puis obtenir deux vecteurs numpy contenant les concentration $C_i$ et les incertitudes $u(C_i)$.\n", "2. Représenter graphiquement $C_i$ en fonction de $A_i$ et vérifier que le modèle linéaire proposé par la loi de Beer-Lambert n'est pas aberrant. _On utilisera la fonction `errorbar` pour représenter les barres d'incertitudes associées aux concentrations_.\n", "3. Réaliser une régression linéaire sans tenir compte des incertitudes sur les concentrations et tracer la droite d'ajustement affine sur le même graphique que précédemment. (_Supprimer le `plt.show()` précédent_).\n", "4. Une méthode qualitative pour vérifier si le modèle est cohérent avec les incertitudes de mesure est de vérifier si la droite d'ajustement passe bien par les barres d'incertitude. Tester ici la cohérence du modèle.\n", "5. On dilue un bonbon dans de l'eau diluée de sorte que le volume de liquide (avec le bonbon) soit $V_f = 50.00 mL$. On mesure alors l'absorbance de la solution ainsi réalisée, on obtient $A_{649nm, f} = 0.665 SI$. Utiliser Python comme calculatrice et les données du modèle ajusté pour déterminer la quantité maximale de bonbons bleus qu'on peut manger par jour sans dépasser la DJA (Dose journalière admissible) de l'additif E131 qui est de 2.5mg par kg de masse corporelle. On donne la masse molaire du bleu patenté $M = 582,66 g.mol^{-1}$.\n", "\n", "```{note}\n", "Le nombre de bonbon trouvé ne tient pas compte de la quantité de sucre ingurgitée...\n", "```\n", "\n", "\n", "````" ] }, { "cell_type": "code", "execution_count": 7, "id": "17124ac2", "metadata": { "tags": [ "hide-input", "remove-output" ] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "filenames": { "image/png": "D:\\cedri\\Dropbox\\Enseignement prepas\\approche_numeriques\\intro_python_td\\_build\\jupyter_execute\\notebook\\exo_polyfit_10_0.png" } }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "Vi = np.array([1, 2.50, 5.00, 7.50, 10.00])\n", "Ai = np.array([0.128, 0.428, 0.833, 1.267, 1.765])\n", "\n", "Vt = 10 # V_T en mL\n", "C0 = 2.04 # On n'introduit pas la puissance 10^-5\n", "u1 = 0.05 # Incertitude sur les volumes en mL\n", "\n", "\"\"\"Calcul des Ci et uCi. On utilise la vectorialisation des vecteurs numpy\"\"\"\n", "Ci = C0 * Vi / Vt # Calcul des Ci, on n'introduit pas la puissance 10^-5\n", "uCi = C0 * u1 / Vt * np.sqrt(1 + (Ci / C0) ** 2) # Calcul des uCi\n", "\n", "\n", "\"\"\"Tracé des points de mesures\"\"\"\n", "f, ax = plt.subplots()\n", "f.suptitle(\"Dosage par absorbance\")\n", "ax.set_xlabel(\"Absorbance à 640nm (SI)\")\n", "ax.set_ylabel(\"Concentration (10^-5 mol/L)\")\n", "\n", "ax.errorbar(Ai, Ci, yerr=uCi, label=\"Points de mesure\", linestyle='', color='red')\n", "\n", "ax.legend()\n", "\n", "plt.show() # A commenter si on veut afficher le graphique suivant." ] }, { "cell_type": "code", "execution_count": 8, "id": "22daecd1", "metadata": { "tags": [ "hide-input", "remove-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Le tracé précédent rend l'hypothèse linéaire possible.\n", "On réalise donc l'ajustement.\n", "-------------------\n", "Le modèle ajusté a pour équation :\n", "1.1398552474047507 * A + 0.05293999024471913\n", "Il faudra bien sûr réfléchir au nombre de chiffres significatifs à garder\n", "-------------------\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "execution_count": 8, "metadata": { "filenames": { "image/png": "D:\\cedri\\Dropbox\\Enseignement prepas\\approche_numeriques\\intro_python_td\\_build\\jupyter_execute\\notebook\\exo_polyfit_11_1.png" } }, "output_type": "execute_result" } ], "source": [ "print(\"Le tracé précédent rend l'hypothèse linéaire possible.\")\n", "print(\"On réalise donc l'ajustement.\")\n", "\n", "p = np.polyfit(Ai, Ci, 1) # Réalisation de l'ajustement affine\n", "\n", "print(\"-------------------\")\n", "print(\"Le modèle ajusté a pour équation :\")\n", "print(str(p[0]) + \" * A + \" + str(p[1]))\n", "print(\"Il faudra bien sûr réfléchir au nombre de chiffres significatifs à garder\")\n", "print(\"-------------------\")\n", "\n", "Ci_adj = p[0] * Ai + p[1] # On calcule les valeurs ajustées des concentrations.\n", "\n", "ax.plot(Ai, Ci_adj, label=\"Modèle ajusté\", linestyle=':', color='blue')\n", "\n", "ax.legend() # Il faut réafficher la légende car on l'a modifiée\n", "\n", "\n", "f # Inutile sauf avec un notebook Jupyter\n", "# plt.show() A décommenter si on n'utiliser pas Jupyter" ] }, { "cell_type": "code", "execution_count": 9, "id": "2a0a5961", "metadata": { "tags": [ "hide-input", "hide-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "---------------\n", "Le nombre maximal de bonbons qu'on peut manger est :\n", "741.0\n", "---------------\n" ] } ], "source": [ "\"\"\"Le modèle étant plutôt cohérent avec les points de mesures, on va l'utiliser pour évaluer Cf\"\"\"\n", "Af = 0.665\n", "Cf = p[0] * Af + p[1] # Concentration en bleu patenté dans la solution diluée\n", "\n", "Vf = 50e-3 # Volume de la solution diluée (en L)\n", "M = 582.66e-3 # Masse molaire du bleu patenté (en kg)\n", "\"\"\"Pour calculer la masse, on oublier la puissance 10^-5 dans la concentration\"\"\"\n", "mf = Cf * 1e-5 * Vf * M # Calcul de la masse de bleu patenté dans un bonbon (en kg)\n", "\n", "\n", "Mh = 70 # On choisit un humain de 70kg\n", "m_DJA = 2.5e-6 # DJA donnée par l'énoncé\n", "m_max = Mh * m_DJA # Masse maximale de bleu patenté qu'on peut ingérer\n", "N_max = np.ceil(m_max / mf) # Arrondi à l'entier supérieur\n", "\n", "print(\"---------------\")\n", "print(\"Le nombre maximal de bonbons qu'on peut manger est :\")\n", "print(N_max)\n", "print(\"---------------\")" ] } ], "metadata": { "jupytext": { "encoding": "# -*- coding: utf-8 -*-", "formats": "ipynb,md:myst", "split_at_heading": true, "text_representation": { "extension": ".md", "format_name": "myst", "format_version": 0.13, "jupytext_version": "1.10.3" } }, "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": "3.9.15" }, "source_map": [ 15, 23, 41, 62, 90, 120, 131, 141, 175, 190, 207, 238, 263 ] }, "nbformat": 4, "nbformat_minor": 5 }