{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"Fiche Régression linéaire MC.ipynb","provenance":[{"file_id":"1gsFdaERIUab39KxRbLDN6P5c0nnQYo12","timestamp":1655449402593}],"collapsed_sections":[],"authorship_tag":"ABX9TyMesUYxmtCo+TZ9vDymrany"},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["**À l’aide d’un langage de programmation ou d’un tableur, simuler un processus aléatoire de variation des valeurs expérimentales de l’une des grandeurs – simulation Monte-Carlo – pour évaluer l’incertitude type sur les paramètres du modèle.**"],"metadata":{"id":"t3u_TL0CeaoN"}},{"cell_type":"markdown","source":[""],"metadata":{"id":"8vlCn5R5ecYK"}},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":442},"id":"QgxHrmyffgVe","executionInfo":{"status":"ok","timestamp":1655449497495,"user_tz":-120,"elapsed":1297,"user":{"displayName":"Lionnel Malara","userId":"16342666118884215780"}},"outputId":"74dcd5c7-ce9e-4513-f08d-50c6ead293f0"},"source":["import numpy as np\n","import matplotlib.pyplot as plt\n","\n","\n","############### Données expérimentales   ###############\n","\n","# Données mesurées\n","\n","x=np.array([0.01,2.5,5,7.5,10]) \n","y=np.array([2.2,7.7,12.4,17.7,21.1]) \n","\n","\n","# Précisions mesurées (éventuellement nuls)\n","\n","D_x = 0.05*x\n","D_y=1\n","\n","# Possibilité de changer les labels des axes\n","plt.figure(figsize=(8,6))\n","plt.xlabel('x')\n","plt.ylabel('y')\n","\n","\n","\n","############### Régression ###################\n","\n","\n","N=10000\n","\n"," # La valeur mesurée\n","a,b = np.polyfit(x,y,1)\n","\n"," # Estimation de son incertitude-type par simulation Monte-Carlo\n","ta,tb=[],[]\n","\n","for i in range(0,N):\n","    nbpts = len(x) \n","    mx = x + D_x*np.random.uniform(-1,1,nbpts)\n","    my = y + D_y*np.random.uniform(-1,1,nbpts)\n","\n","    p=np.polyfit(mx,my,1)\n","    \n","    ta.append(p[0])\n","    tb.append(p[1])\n","\n","\n","# Incertitude type pente et ordonnée à l'origine\n","u_a = np.std(ta,ddof=1)\n","u_b = np.std(tb,ddof=1)\n","\n","# Equation de la droite de régression\n","yfit = a*x + b\n","xfit=np.linspace(min(x),max(x),2) \n","\n","# Tracé\n","plt.plot(xfit, a*xfit + b, 'r', label='Régression linéaire')\n","plt.errorbar(x,y,xerr=D_x/np.sqrt(3),yerr=D_y/np.sqrt(3),fmt='bo',label='Mesures')\n","plt.legend()\n","plt.show()\n","\n","\n","print (\"Pente (et incertitude-type) :\", a ,\"±\", u_a,\"(incertitude-type)\")\n","print (\"Ordonnée à l'origine (et incertitude-type) :\", b ,\"±\", u_b,\"(incertitude-type)\")\n","print(\"ATTENTION à limiter les chiffres significatifs dans l'écriture de votre résultat !\")"],"execution_count":1,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 576x432 with 1 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}},{"output_type":"stream","name":"stdout","text":["Pente (et incertitude-type) : 1.9134558801847694 ± 0.08863415347817598 (incertitude-type)\n","Ordonnée à l'origine (et incertitude-type) : 2.648893687315794 ± 0.46972809339082855 (incertitude-type)\n","ATTENTION à limiter les chiffres significatifs dans l'écriture de votre résultat !\n"]}]}]}