{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3d22f9ad-4990-43fb-9b79-cd2c03883b2a",
   "metadata": {},
   "source": [
    "# Simulation de variables aléatoires\n",
    "\n",
    "## Notebook jupyter\n",
    "Le notebook est un document interactif, qui permet de mélanger du texte et des lignes de code (pour nous, c'est du code `python`). Il est possible d'exécuter le code, de le modifier, et d'ajouter (ou de supprimer) des cellules de code ou de commentaire. Vous avez la possibilité d'enregistrer les modifications par le bouton correspondant dans la barre à outils en haut. \n",
    "\n",
    "Pour lire ou éditer un notebook (fichier au format .ipynb) vous pouvez utiliser deux environnements qui s'ouvrent dans un navigateur web: \n",
    "\n",
    "- `jupyter notebook` la version classique qui ouvre un serveur sur l'adresse `http://localhost:8888/`\n",
    "- `jupyter lab` la version plus moderne avec du code javascript pour \"une IDE\" plus dynamique `http://localhost:8888/lab`\n",
    "\n",
    "Dans la cellule de code suivante, vous voyez des instructions en `python`. Pour les exécuter, il faut d'abord cliquer dans la cellule pour la sélectionner, puis faire `Shift+Enter`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6b5cb3c9-d75d-45a2-9b38-6d23db106605",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 17\n",
    "x      # pour afficher la valeur de x on utilise print(x)\n",
    "y = x + 3\n",
    "y      # la dernière instruction est renvoyée, pour éviter l'affichage on peut mettre un ; à la fin: y; "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cc77fce-ae6f-46e1-832d-973f4a208b03",
   "metadata": {
    "tags": []
   },
   "source": [
    "Les variables `x` et `y` sont désormais définies. Dans la suite, vous pouvez les utiliser et travailler avec. Autrement dit, les notebooks sont un moyen pour excécuter du code progressivement. \n",
    "Exécuter la cellule suivante pour calculer le carré de `y`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0636fb2d-ff25-416e-93eb-1508df57d497",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "400"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43b7bcd0-660b-4a5d-9a05-daec70485e81",
   "metadata": {},
   "source": [
    "Au fur et à mesure que vous exécutez des cellules de code, vous voyez apparaître des numéros entre crochets à gauche de la cellule. Ces numéros vous aident à garder une trace de l'ordre dans lequel vous exécutez les cellules. Juste pour voir, revenez à la première cellule de code et modifiez la valeur de `y`. Puis, réexécutez la cellule. Cela change la sortie de la première cellule, mais pas de la deuxième (alors que la valeur de `y` a changé). Les numéros entre crochets vous permettent donc de vous répérer plus facilement.\n",
    "\n",
    "Parfois, quand on vient d'exécuter plein de cellules, on perd un peu le contrôle, et on ne sait plus quelles sont les valeurs actuelles des différentes variables. Dans ce cas, il vaut mieux de reprendre à zéro. Pour cela, sélectionnez **Kernel** en haut de la page et choissisez **Restart**. Vous pouvez observer que tous les numéros entre crochets disparaissent ainsi que toutes les sorties en-dessous des cellules de code. Un **Restart** du **Kernel** revient alors à supprimer tous les objets créés.\n",
    "\n",
    "Vous pouvez modifier un notebook comme bon vous semble. Par exemple pour ajouter une cellule, cliquer sur le symbole **+** dans la barre à outils. Cela crée une nouvelle cellule juste en-dessous de la dernière cellule sélectionnée. Par défaut, il s'agit d'une cellule de code dans laquelle vous pouvez écrire des instructions en `python`. Si la nouvelle cellule doit contenir du texte, il suffit de modifier son type par le menu déroulant en changeant **Code** en **Markdown**. Le **Markdown** permet d'écrire du texte, le formatage est très simple. Si cela vous intéresse, double-cliquez sur les cellules de type **Markdown** dans ce notebook pour voir comment ajouter un titre, mettre du texte **en gras** ou *en italique*, créer une liste etc. N'oubliez pas qu'il faut aussi exécuter les cellules **Markdown** en appuyant sur la flèche vers la droite dans la barre à outils."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0d6df987-a11e-40ec-b640-dd80926fcba1",
   "metadata": {
    "attributes": {
     "classes": [],
     "eval": "FALSE",
     "id": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x <- 17\n",
    "x\n",
    "y <- x + 3\n",
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89f1ed13-aeb9-4f25-872e-fc540d6c1aec",
   "metadata": {},
   "source": [
    "Pour des rappels sur le langage `python` et sur le module `numpy` nous renvoyons sur les pages suivantes:\n",
    "\n",
    "- [rappels python](https://perso.lpsm.paris/~vlemaire/4ma074/tp/outils/bases_python.html): parcourir rapidement cette page pour se rafraichir la mémoire sur python\n",
    "- [numpy array](https://perso.lpsm.paris/~vlemaire/4ma074/tp/outils/numpy.html): structure de donnée que l'on utilisera tout au long de ce cours: **à connaitre rapidement!** \n",
    "\n",
    "Dans la cellule suivante, on charge les modules que l'on utilisera pendant ces séances de TP. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ffd70230-5922-4067-a67f-f9747f4b2f71",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns # pour des jolis plot\n",
    "sns.set_theme() "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "203a42cd-983a-44c9-9338-3cd70c49c3f7",
   "metadata": {},
   "source": [
    "## Nombres pseudo-aléatoires\n",
    "\n",
    "Depuis la version 1.17 de `numpy` en juillet 2019, le module `random` a évolué. Vous trouverez encore beaucoup de code sur internet ou dans des livres qui n'utilisent pas la nouvelle syntaxe de ce module, mais dans ce cours nous utiliserons cette nouvelle syntaxe. La différence majeure (en dehors des algorithmes utilisés en interne) est l'utilisation d'un **objet** que nous appelerons `rng` de type `Generator` qui correspond au générateur de nombres pseudo-aléatoires. Pour simuler une loi classique on fera appel à **une méthode**. \n",
    "\n",
    "Par défaut, l'algorithme utilisé est le `PCG64` à la différence du Mersenne-Twister qui était le standard auparavant. \n",
    "\n",
    "Exécuter les commandes suivantes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "29e5839c-7d26-41f5-b365-08c93425a9d9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Le type de l'objet rng est:  Generator(PCG64)\n",
      "Les méthodes utilisables avec l'objet rng sont:\n",
      " ['__class__', '__delattr__', '__dir__', '__doc__', '__eq__', '__format__', '__ge__', '__getattribute__', '__getstate__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__setstate__', '__sizeof__', '__str__', '__subclasshook__', '_bit_generator', '_poisson_lam_max', 'beta', 'binomial', 'bit_generator', 'bytes', 'chisquare', 'choice', 'dirichlet', 'exponential', 'f', 'gamma', 'geometric', 'gumbel', 'hypergeometric', 'integers', 'laplace', 'logistic', 'lognormal', 'logseries', 'multinomial', 'multivariate_hypergeometric', 'multivariate_normal', 'negative_binomial', 'noncentral_chisquare', 'noncentral_f', 'normal', 'pareto', 'permutation', 'permuted', 'poisson', 'power', 'random', 'rayleigh', 'shuffle', 'spawn', 'standard_cauchy', 'standard_exponential', 'standard_gamma', 'standard_normal', 'standard_t', 'triangular', 'uniform', 'vonmises', 'wald', 'weibull', 'zipf']\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy.random import default_rng\n",
    "\n",
    "rng = default_rng()\n",
    "print(\"Le type de l'objet rng est: \", rng)\n",
    "print(\"Les méthodes utilisables avec l'objet rng sont:\\n\", dir(rng))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "088f068a-b3d8-435a-b8f2-b7f93dc01e0d",
   "metadata": {},
   "source": [
    "L'objet `rng` est défini une fois pour toute et tout l'aléatoire de notre code se fera par des appels à des méthodes de cet objet. C'est un peu comme si on fixait un espace de probabilité $(\\Omega, \\mathcal{A}, \\mathbf{P})$ (notre espace de simulation) et que l'on construisait toutes les variables aléatoires sur cet espace.\n",
    "\n",
    "Vérifions tout d'abord que les nombres pseudo-aléatoires produits $(X_1, \\dots, X_n)$ sont uniforméments répartis et qu'il y a indépendance entre 2 tirages $X_k$ et $X_{k+1}$ pour $k=1,\\dots,n-1$. On fait cette vérification uniquement visuellement en traçant l'histogramme de l'échantillon $(X_1, \\dots, X_n)$ et le nuage de points des paires adjacentes $(X_k, X_{k+1})_{k=1,\\dots,n-1}$ (ce nuage doit remplir uniformément le carré unité $[0,1]\\times[0,1]$).\n",
    "\n",
    "Voici le graphique obtenu avec un échantillon de taille $n = 100\\,000$.\n",
    "\n",
    "![](img/pseudo_alea.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daeadd7f-1b75-4b38-b6ad-f561c7cc88db",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: `rng.random`\n",
    "Lire la documentation de la fonction `rng.random`. Construire un échantillon `sample` de taille `100000`. Reproduire le graphe de l'histogramme de `sample` et des paires adjacentes ci-dessus (le nombre de `bins` pour l'histogramme est 20 et la taille d'un point est `s=0.5` de transparence `alpha=0.2`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "65fa00f3-0e1b-4824-8569-afe4153a2774",
   "metadata": {
    "tags": [
     "aremplir"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Paires adjacentes des échantillons')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "sample = rng.random(size=100000)  # génère un nombre aléatoire uniforme entre 0 et 1\n",
    "fig, ax = plt.subplots(ncols=2, nrows=1, figsize=(8, 4))\n",
    "ax[0].hist(sample, bins=20, density=True, alpha=0.6, color='b')\n",
    "ax[0].set_title(\"Histogramme des échantillons\")\n",
    "\n",
    "ax[1].scatter(sample[:-1], sample[1:], alpha=0.6, color='b', s=0.1)\n",
    "ax[1].set_title(\"Paires adjacentes des échantillons\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74efe4f3",
   "metadata": {},
   "source": [
    "## La loi exponentielle\n",
    "\n",
    "On considère la loi exponentielle de paramètre $\\lambda = 2$. On rappelle la densité $f_\\lambda$ et l'inverse de la fonction de répartition (la fonction quantile) $F_\\lambda^{-1}$\n",
    "\n",
    "$$\n",
    "f_\\lambda(x) = \\lambda e^{-\\lambda x} \\mathbf{1}_{x > 0} \\quad \\text{et} \\quad \\forall u \\in [0, 1[, \\; F_\\lambda^{-1}(u) = \\frac{-\\log(1-u)}{\\lambda}.\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41a0c5bf-664f-40f9-b4d3-00ebb13185bf",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: 2 façons de simuler\n",
    "\n",
    "On veut comparer 2 échantillons de taille $n = 10\\,000$ de la loi $\\mathcal{E}(\\lambda)$, $\\lambda = 2$:\n",
    "\n",
    "- le premier `sample_numpy` obtenu par un appel de `rng.exponential`\n",
    "- le second `sample_quantile` obtenu par transformation par $F_\\lambda^{-1}$ d'un échantillon $(U_1, \\dots, U_n)$ _i.i.d._ avec $U_i \\sim \\mathcal{U}([0, 1[)$.\n",
    "\n",
    "Vérifier que la moyenne de chacun de ces échantillons est proche de $\\frac{1}{\\lambda}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "85822341-6d6f-42ab-b572-746f118d2adc",
   "metadata": {
    "tags": [
     "aremplir"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.48994123302523057 0.23981454920912565\n",
      "0.502839099975329 0.2584579583529911\n"
     ]
    }
   ],
   "source": [
    "lambd = 2.0\n",
    "n = 10000\n",
    "sample_exp = rng.exponential(scale=1/lambd, size=n)\n",
    "sample_uniform = rng.random(size=n)\n",
    "sample_exp_quantile = -np.log(1 - sample_uniform) / lambd\n",
    "\n",
    "print(np.mean(sample_exp), np.var(sample_exp))\n",
    "print(np.mean(sample_exp_quantile), np.var(sample_exp_quantile))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e586765d-300c-4972-bfe9-79eedd75fb63",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: représentation graphique\n",
    "\n",
    "On compare graphiquement les histogrammes de ces échantillons `sample_numpy` et `sample_quantile` avec la densité de la loi exponentielle (de paramètre $\\lambda=2$). Ecrire le code pour obtenir le graphique suivante:\n",
    "\n",
    "![](img/expo.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "5e89e544-d1f5-451a-bbc4-ae6f2c269f85",
   "metadata": {
    "tags": [
     "aremplir"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'échantillons exponentiels (quantile)')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(ncols=2, nrows=1, figsize=(8, 4))\n",
    "ax[0].hist(sample_exp, bins=50, density=True, alpha=0.6, color='b')\n",
    "ax[0].plot(np.linspace(0, 4, 50), lambd * np.exp(-lambd * np.linspace(0, 4, 50)), 'r')\n",
    "ax[0].set_title(\"échantillons exponentiels (directe)\")\n",
    "ax[1].hist(sample_exp_quantile, bins=50, density=True, alpha=0.6, color='b')\n",
    "ax[1].plot(np.linspace(0, 4, 50), lambd * np.exp(-lambd * np.linspace(0, 4, 50)), 'r')\n",
    "ax[1].set_title(\"échantillons exponentiels (quantile)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "821dc76d-5b0d-4146-8d36-e50b2e090f0e",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: utilisation de `scipy.stats`\n",
    "\n",
    "Reprendre les 2 questions précédentes en utilisant un objet `E` de classe `stats.expon`. Lire la documentation de cette classe et utiliser les méthodes `rvs` (avec l'argument `random_state=rng`), `ppf` et `pdf`. Le but est d'écrire un code qui pourrait s'executer avec n'importe quelle loi à densité (une classe qui contient un méthode `pdf` et non `pmf`). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "2cc9836e-9f08-4044-bec8-bd15d51df564",
   "metadata": {
    "tags": [
     "aremplir"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x187b5924910>]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "E = stats.expon(scale=1/lambd)  # distribution exponentielle avec paramètre lambda\n",
    "U = stats.uniform(loc=0, scale=1)  # distribution uniforme entre 0 et 1\n",
    "sample = E.rvs(size=n)  # échantillons aléatoires\n",
    "sample_quantile = E.ppf(U.rvs(size=n))  # échantillons par la méthode du quantile\n",
    "\n",
    "fig, ax = plt.subplots(ncols=2, nrows=1, figsize=(8, 4))\n",
    "ax[0].hist(sample, bins = 50, density=True, alpha = 0.6, color='b')\n",
    "ax[0].plot(np.linspace(0, 4, 50), E.pdf(np.linspace(0, 4, 50)), 'r')\n",
    "\n",
    "ax[1].hist(sample_quantile, bins = 50, density=True, alpha = 0.6, color='b')\n",
    "ax[1].plot(np.linspace(0, 4, 50), E.pdf(np.linspace(0, 4, 50)), 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c48b03e3-6de1-4bf0-8238-d5f11bb57a88",
   "metadata": {},
   "source": [
    "## Illustration de la méthode du rejet"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c709d792-02bc-427d-8be6-a05f700cf5df",
   "metadata": {},
   "source": [
    "On propose d'illustrer la méthode du rejet dans le cas d'une loi bêta de paramètres $\\alpha > 1$ et $\\beta > 1$. On rappelle la forme de la densité de la loi\n",
    "\n",
    "$$\n",
    "  f_{\\alpha, \\beta}(x) = \\frac{1}{B(\\alpha, \\beta)} \n",
    "  x^{\\alpha-1} (1-x)^{\\beta-1} \\mathbf{1}_{[0,1]}(x)\n",
    "$$\n",
    "\n",
    "où $B(\\alpha, \\beta)$ est la constante de normalisation de la loi. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14bc87a5-0b6b-4cc2-bce3-529bed7dde02",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: illustration du rejet\n",
    "\n",
    "Le but est de créer le graphique suivant représentant la méthode du rejet pour une loi bêta de paramètres $\\alpha = 1.5$ et $\\beta = 3$ et une loi auxiliaire qui est la loi uniforme sur $[0,1]$, c'est à dire $g(x) = \\mathbf{1}_{[0,1]}(x)$. La ligne rouge represente $c g(x)$ avec $c = 2$, la courbe bleue correspond à la densité $f_{\\alpha, \\beta}$, les points bleus sont les réalisations acceptées (parmi 5000 réalisations) et les points orangés sont les réalisations rejetées.\n",
    "\n",
    "![](img/rejet.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "f427a3a8-4a48-40cf-b646-c33e9257a0ed",
   "metadata": {
    "tags": [
     "aremplir"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_45896\\706370816.py:27: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n",
      "  ax[1].legend()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x187b8ecb610>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = 1.5\n",
    "beta = 3.0\n",
    "n = 5000\n",
    "c = 2\n",
    "sample_uniform = rng.random(size=n)\n",
    "unif_test = rng.random(size=n)\n",
    "c_sample = c * sample_uniform\n",
    "E = stats.beta(a=alpha, b=beta)\n",
    "\n",
    "fig, ax = plt.subplots(ncols=2, nrows=1, figsize=(20, 4))\n",
    "ax[0].plot(np.linspace(0, 1, 100), np.full((100), c), 'r', label='cg(x)')\n",
    "ax[0].plot(np.linspace(0, 1, 100), np.full((100), 1), 'g', label='g(x)')\n",
    "ax[0].plot(np.linspace(0, 1, 100), E.pdf(np.linspace(0, 1, 100)), 'b', label='f_alpha,beta(x)')\n",
    "\n",
    "accepted = c_sample < E.pdf(unif_test)\n",
    "rejected = c_sample >= E.pdf(unif_test)\n",
    "\n",
    "ax[0].scatter(unif_test[accepted], c_sample[accepted], s=0.1, alpha=0.6, color='green', label='échantillons acceptés')\n",
    "ax[0].scatter(unif_test[rejected], c_sample[rejected], s=0.1, alpha=0.6, color='orange', label='échantillons rejetés')\n",
    "\n",
    "ax[0].set_title(\"Rejet pour la loi Beta\")\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].hist(unif_test[accepted], bins=50, density=True, alpha=0.6, color='b')\n",
    "ax[1].plot(np.linspace(0, 1, 100), E.pdf(np.linspace(0, 1, 100)), 'r')\n",
    "ax[1].set_title(\"Histogramme des échantillons acceptés\")\n",
    "ax[1].legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ad3c29e-0b2f-4946-ae5c-4a5b46773dca",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: optimisation de la constante $c$ \n",
    "\n",
    "La constante optimale $c$ que l'on peut utiliser dans cet exemple (en considérant $g(x) = \\mathbf{1}_{[0,1]}(x)$) est $c^* = \\max_{x \\in [0,1]} f_{\\alpha, \\beta}(x)=f_{\\alpha,\\beta}(x^*)$. On peut calculer explicitement ce maximum qui correspond au mode de la distribution bêta\n",
    "\n",
    "$$\n",
    "    x^* = \\operatorname{argmax}_{x \\in [0,1]} f_{\\alpha, \\beta}(x) = \\frac{\\alpha-1}{\\alpha + \\beta - 2} \\quad \\text{pour $\\alpha > 1, \\beta > 1$}.\n",
    "$$\n",
    "\n",
    "Dans un cas plus général on ne connaît pas forcément ce maximum mais on peut l'approcher et trouver une approximation par un algorithme type dichotomie ou descente de gradient (méthode de Newton). \n",
    "\n",
    "Utiliser la fonction `scipy.optimize.minimize_scalar` (après avoir lu la documentation) avec les options `bounds=(0, 1)` et `method=\"bounded\"` pour trouver la valeur $c^*$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "9bef9537-5d4a-444b-b145-c1571cc43263",
   "metadata": {
    "tags": [
     "aremplir"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       " message: Solution found.\n",
       " success: True\n",
       "  status: 0\n",
       "     fun: -1.878297101062972\n",
       "       x: 0.19999841528793666\n",
       "     nit: 11\n",
       "    nfev: 11"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.optimize as optimize\n",
    "\n",
    "optimize.minimize_scalar(lambda x: -stats.beta(a=alpha, b=beta).pdf(x), bounds=(0, 1), method='bounded')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c132c2ad",
   "metadata": {},
   "source": [
    "## Loi binomiale: définition probabiliste _vs_ inverse de la fonction de répartition\n",
    "\n",
    "On veut comparer deux algorithmes pour la simulation d'une loi binomiale $X \\sim B(n, p)$, $n \\ge 2$, $p \\in ]0,1[$.\n",
    "\n",
    "- Le premier algorithme utilise la définition de la loi binomiale comme somme de $n$ variables aléatoires $(B_1, \\dots, B_n)$ indépendantes de Bernoulli de paramètre $p \\in ]0,1[$, $\\mathbf{P}[B_1 = 1] = p = 1 - \\mathbf{P}[B_1 = 0]$, \n",
    "\n",
    "$$\n",
    "  X = \\sum_{k=1}^n B_k. \n",
    "$$ \n",
    "\n",
    "- Le deuxième algorithme utilise l'inverse de la fonction de répartition de la loi binomiale. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb82c513-e77d-4526-8b44-ebeaa2095461",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: algorithme 1.\n",
    "\n",
    "Compléter la fonction `binomial_from_def` qui implémente naïvement le premier algorithme et renvoie un échantillon de taille `size`. Attention cette première approche (la plus naturelle quand on débute) sera améliorée dans la suite. Ce n'est pas la façon optimale d'écrire le code en `numpy`.\n",
    "```\n",
    "def binomial_from_def(size: int, n: int=2, p: float=0.5):\n",
    "    \"\"\" \n",
    "    Draw samples from a binomial distribution B(n, p).\n",
    "    Algorithm: first implementation of sum of independent Bernoulli trials.\n",
    "    \"\"\"\n",
    "    def one_realization():\n",
    "        # code à écrire\n",
    "    # code à écrire\n",
    "    return sample\n",
    "```\n",
    "\n",
    "Vérifier que le code est correct en traçant l'histogramme d'un échantillon de taille $10\\,000$. Vous devez obtenir ce graphique:\n",
    "\n",
    "![](img/binom_def.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "421400d2-e23d-4dd7-b33d-14b99ef4dab9",
   "metadata": {
    "tags": [
     "aremplir"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.9868 5.05482576\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x187c0db3890>"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def binomial_from_def(size: int, n: int=2, p: float=0.5):\n",
    "    \"\"\" \n",
    "    Draw samples from a binomial distribution B(n, p).\n",
    "    Algorithm: first implementation of sum of independent Bernoulli trials.\n",
    "    \"\"\"\n",
    "    def one_realization():\n",
    "        return np.array([int(rng.random() < p) for _ in range(n)]).sum()\n",
    "    \n",
    "    return np.array([one_realization() for _ in range(size)]).astype('int64')\n",
    "\n",
    "n, p = 20, 0.5\n",
    "size = 10000\n",
    "sample = binomial_from_def(size=size, n=n, p=p)\n",
    "empirical_prop = np.bincount(sample, minlength=n+1) / 10000\n",
    "print(np.mean(sample), np.var(sample))\n",
    "\n",
    "support = np.arange(n+1)\n",
    "fig, ax = plt.subplots(layout=\"tight\")\n",
    "ax.bar(support, empirical_prop, label='Empirical proportion')\n",
    "ax.vlines(support, 0, stats.binom.pmf(support, n, p), color='C1', lw=2, alpha=1)\n",
    "ax.scatter(support, stats.binom.pmf(support, n, p), color='C1', lw=2, alpha=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aee9a93c-a97a-421e-8cca-8edbb6106ba6",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: algorithme 2. \n",
    "\n",
    "Ecrire une fonction `binomial_quantile` similaire à celle de la question précédente: qui prend les mêmes arguments et qui renvoie un échantillon de taille `size`. Vérifier graphiquement que l'échantillon produit vérifie la bonne distribution.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d3a2f3aa-a62b-4424-abb1-937de9c9278c",
   "metadata": {
    "tags": [
     "aremplir"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0303 5.048581909999999\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "def binomial_quantile(size: int, n: int=2, p: float=0.5):\n",
    "    \"\"\" \n",
    "    Draw samples from a binomial distribution B(n, p).\n",
    "    Algorithm: first implementation of sum of independent Bernoulli trials.\n",
    "    \"\"\"\n",
    "    binom = stats.binom(n=n, p=p)\n",
    "    return binom.ppf(rng.random(size=size)).astype('int64') # attention au type renvoyé par la fonction quantile \n",
    "\n",
    "size = 10000\n",
    "n, p = 20, 0.5\n",
    "sample_quantile = binomial_quantile(size=size, n=n, p=p)\n",
    "\n",
    "empirical_prop = np.bincount(sample_quantile, minlength=n+1) / 10000\n",
    "print(np.mean(sample_quantile), np.var(sample_quantile))\n",
    "\n",
    "support = np.arange(0, n+1)\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(layout=\"tight\")\n",
    "ax.bar(support, empirical_prop, label='Empirical proportion')\n",
    "ax.scatter(support, stats.binom(n=n, p=p).pmf(support), label='Probability mass function')\n",
    "ax.vlines(support, 0, stats.binom(n=n, p=p).pmf(support), color='C1', lw=2, alpha=1)\n",
    "ax.set_title('Samples from a binomial distribution obtained by quantile function.')\n",
    "ax.set_xticks(np.linspace(0,20,21))\n",
    "ax.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e86c7583-1b18-4e4e-bd63-10b0d338b0e3",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: temps de calcul\n",
    "\n",
    "Pour mesurer le temps de calcul, on utilisera le module `timeit` de python. Dans l'environnement `jupyter` il est encore plus facile d'utiliser ce module grâce à une _magic_ commande appelée `%timeit`. Pour en savoir plus sur ces _magic_ commandes vous pouvez [consulter cette page de documentation](https://ipython.readthedocs.io/en/stable/interactive/magics.html).\n",
    "\n",
    "Pour mesurer le temps de calcul complet d'une cellule notebook on utilise `%%timeit`. Le résultat est une moyenne de plusieurs exécutions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "7ea73959-5e7f-42bb-ab53-402ca77b7a23",
   "metadata": {
    "tags": [
     "aremplir"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "178 μs ± 2.85 μs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "size = 10000\n",
    "liste = [i for i in range(size)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc5be755-f42f-4a5b-8006-547e11bd7f20",
   "metadata": {},
   "source": [
    "Pour mesurer le temps d'une seule instruction on utiliser `%timeit` en début de ligne. L'option `-o` permet de sauvegarder le résultat: les mesures des temps d'exécutions et les statistiques associées."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "daf24ad0-9500-4bf0-96a1-96d83b62a4d1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "183 μs ± 4.92 μs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "size = 10000\n",
    "%timeit liste = [i for i in range(size)] # pas de sauvegarde du résultat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "7235e5a0-e0ec-4532-a115-00e5b1a7687e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "187 μs ± 5.47 μs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n",
      "['__class__', '__delattr__', '__dict__', '__dir__', '__doc__', '__eq__', '__firstlineno__', '__format__', '__ge__', '__getattribute__', '__getstate__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__module__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__sizeof__', '__static_attributes__', '__str__', '__subclasshook__', '__weakref__', '_precision', '_repr_pretty_', 'all_runs', 'average', 'best', 'compile_time', 'loops', 'repeat', 'stdev', 'timings', 'worst']\n",
      "Mean time:  0.00018714547142985143\n"
     ]
    }
   ],
   "source": [
    "timings = %timeit -o liste = [i for i in range(size)]\n",
    "print(dir(timings))\n",
    "print(\"Mean time: \", timings.average)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2454a0fe-4871-4087-8c78-0d764c9edd83",
   "metadata": {},
   "source": [
    "Comparer les temps d'exécutions des 2 fonctions `binomial_from_def` et `binomial_quantile` pour différentes valeurs de `size` (par exemple `10000` et `100000`) et de `n` (par exemple `20`, `50` et `200`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "5cfe44fe-e003-4e8a-8d05-e5c99eff7c3c",
   "metadata": {
    "tags": [
     "aremplir"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.74 ms ± 122 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "['__class__', '__delattr__', '__dict__', '__dir__', '__doc__', '__eq__', '__firstlineno__', '__format__', '__ge__', '__getattribute__', '__getstate__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__module__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__sizeof__', '__static_attributes__', '__str__', '__subclasshook__', '__weakref__', '_precision', '_repr_pretty_', 'all_runs', 'average', 'best', 'compile_time', 'loops', 'repeat', 'stdev', 'timings', 'worst']\n",
      "Mean time:  0.0047370211429162215\n",
      "5.73 ms ± 96.9 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "['__class__', '__delattr__', '__dict__', '__dir__', '__doc__', '__eq__', '__firstlineno__', '__format__', '__ge__', '__getattribute__', '__getstate__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__module__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__sizeof__', '__static_attributes__', '__str__', '__subclasshook__', '__weakref__', '_precision', '_repr_pretty_', 'all_runs', 'average', 'best', 'compile_time', 'loops', 'repeat', 'stdev', 'timings', 'worst']\n",
      "Mean time:  0.005734530571415755\n",
      "17.1 ms ± 486 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "['__class__', '__delattr__', '__dict__', '__dir__', '__doc__', '__eq__', '__firstlineno__', '__format__', '__ge__', '__getattribute__', '__getstate__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__module__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__sizeof__', '__static_attributes__', '__str__', '__subclasshook__', '__weakref__', '_precision', '_repr_pretty_', 'all_runs', 'average', 'best', 'compile_time', 'loops', 'repeat', 'stdev', 'timings', 'worst']\n",
      "Mean time:  0.017055238000217028\n"
     ]
    }
   ],
   "source": [
    "n = 20\n",
    "timings = %timeit -o sample = binomial_quantile(size=size, n=n, p=0.5)\n",
    "print(dir(timings))\n",
    "print(\"Mean time: \", timings.average)\n",
    "n = 50\n",
    "timings = %timeit -o sample = binomial_quantile(size=size, n=n, p=0.5)\n",
    "print(dir(timings))\n",
    "print(\"Mean time: \", timings.average)\n",
    "n = 200\n",
    "timings = %timeit -o sample = binomial_quantile(size=size, n=n, p=0.5)\n",
    "print(dir(timings))\n",
    "print(\"Mean time: \", timings.average)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "6b9dab6e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "97.7 ms ± 832 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "['__class__', '__delattr__', '__dict__', '__dir__', '__doc__', '__eq__', '__firstlineno__', '__format__', '__ge__', '__getattribute__', '__getstate__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__module__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__sizeof__', '__static_attributes__', '__str__', '__subclasshook__', '__weakref__', '_precision', '_repr_pretty_', 'all_runs', 'average', 'best', 'compile_time', 'loops', 'repeat', 'stdev', 'timings', 'worst']\n",
      "Mean time:  0.09774594142966506\n",
      "213 ms ± 10.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "['__class__', '__delattr__', '__dict__', '__dir__', '__doc__', '__eq__', '__firstlineno__', '__format__', '__ge__', '__getattribute__', '__getstate__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__module__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__sizeof__', '__static_attributes__', '__str__', '__subclasshook__', '__weakref__', '_precision', '_repr_pretty_', 'all_runs', 'average', 'best', 'compile_time', 'loops', 'repeat', 'stdev', 'timings', 'worst']\n",
      "Mean time:  0.2134507571047704\n",
      "795 ms ± 18.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "['__class__', '__delattr__', '__dict__', '__dir__', '__doc__', '__eq__', '__firstlineno__', '__format__', '__ge__', '__getattribute__', '__getstate__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__module__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__sizeof__', '__static_attributes__', '__str__', '__subclasshook__', '__weakref__', '_precision', '_repr_pretty_', 'all_runs', 'average', 'best', 'compile_time', 'loops', 'repeat', 'stdev', 'timings', 'worst']\n",
      "Mean time:  0.795102828598049\n"
     ]
    }
   ],
   "source": [
    "n = 20\n",
    "timings = %timeit -o sample = binomial_from_def(size=size, n=n, p=0.5)\n",
    "print(dir(timings))\n",
    "print(\"Mean time: \", timings.average)\n",
    "n = 50\n",
    "timings = %timeit -o sample = binomial_from_def(size=size, n=n, p=0.5)\n",
    "print(dir(timings))\n",
    "print(\"Mean time: \", timings.average)\n",
    "n = 200\n",
    "timings = %timeit -o sample = binomial_from_def(size=size, n=n, p=0.5)\n",
    "print(dir(timings))\n",
    "print(\"Mean time: \", timings.average)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5da5597e-a686-43e8-95a1-b52e6fbdde9d",
   "metadata": {
    "tags": [
     "question"
    ]
   },
   "source": [
    "### Question: code plus efficace \n",
    "\n",
    "Le code de la fonction `binomial_from_def` n'est pas du tout optimal. En effet, en `numpy` (et dans la plupart des langages interprétés) lorsque c'est possible il faut simuler tout l'échantillon d'un coup sans boucle `for`. Dans l'algorithme 1., pour simuler un échantillon de taille `size` on a besoin de `size x n` variables de Bernoullis: on les simule donc d'un seul coup puis on somme uniquement sur l'axe 1 (c'est à dire l'axe de taille `n`). Cette réduction par axe donne un `np.array` de dimension 1 de taille `size`. \n",
    "\n",
    "Cette approche vectorielle est importante et sera utilisée dans la suite lorsque c'est possible.\n",
    "\n",
    "Ecrire la fonction `binomial_from_def_vec` qui implémente l'algorithme 1. de façon efficace et comparer les temps de calculs avec les fonctions précédentes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "21bd93c8-4932-4d12-953f-322b63ad4f6e",
   "metadata": {
    "tags": [
     "aremplir"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.9842 4.923150359999999\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x187bdc8ed50>"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def binomial_from_def_vect(size: int, n: int=2, p: float=0.5):\n",
    "    \"\"\" \n",
    "    Draw samples from a binomial distribution B(n, p).\n",
    "    Algorithm: first implementation of sum of independent Bernoulli trials.\n",
    "    \"\"\"\n",
    "    return (rng.random((size , n)) < p).sum(axis=1)\n",
    "\n",
    "n, p = 20, 0.5\n",
    "size = 10000\n",
    "sample = binomial_from_def_vect(size=size, n=n, p=p)\n",
    "empirical_prop = np.bincount(sample, minlength=n+1) / 10000\n",
    "print(np.mean(sample), np.var(sample))\n",
    "\n",
    "support = np.arange(n+1)\n",
    "fig, ax = plt.subplots(layout=\"tight\")\n",
    "ax.bar(support, empirical_prop, label='Empirical proportion')\n",
    "ax.vlines(support, 0, stats.binom.pmf(support, n, p), color='C1', lw=2, alpha=1)\n",
    "ax.scatter(support, stats.binom.pmf(support, n, p), color='C1', lw=2, alpha=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "03d10827",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "867 μs ± 14.8 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n",
      "['__class__', '__delattr__', '__dict__', '__dir__', '__doc__', '__eq__', '__firstlineno__', '__format__', '__ge__', '__getattribute__', '__getstate__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__module__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__sizeof__', '__static_attributes__', '__str__', '__subclasshook__', '__weakref__', '_precision', '_repr_pretty_', 'all_runs', 'average', 'best', 'compile_time', 'loops', 'repeat', 'stdev', 'timings', 'worst']\n",
      "Mean time:  0.0008668273857162734\n",
      "2.11 ms ± 60.6 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "['__class__', '__delattr__', '__dict__', '__dir__', '__doc__', '__eq__', '__firstlineno__', '__format__', '__ge__', '__getattribute__', '__getstate__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__module__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__sizeof__', '__static_attributes__', '__str__', '__subclasshook__', '__weakref__', '_precision', '_repr_pretty_', 'all_runs', 'average', 'best', 'compile_time', 'loops', 'repeat', 'stdev', 'timings', 'worst']\n",
      "Mean time:  0.002113985142703833\n",
      "8.41 ms ± 199 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "['__class__', '__delattr__', '__dict__', '__dir__', '__doc__', '__eq__', '__firstlineno__', '__format__', '__ge__', '__getattribute__', '__getstate__', '__gt__', '__hash__', '__init__', '__init_subclass__', '__le__', '__lt__', '__module__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__sizeof__', '__static_attributes__', '__str__', '__subclasshook__', '__weakref__', '_precision', '_repr_pretty_', 'all_runs', 'average', 'best', 'compile_time', 'loops', 'repeat', 'stdev', 'timings', 'worst']\n",
      "Mean time:  0.008408617000261855\n"
     ]
    }
   ],
   "source": [
    "n = 20\n",
    "timings = %timeit -o sample = binomial_from_def_vect(size=size, n=n, p=0.5)\n",
    "print(dir(timings))\n",
    "print(\"Mean time: \", timings.average)\n",
    "n = 50\n",
    "timings = %timeit -o sample = binomial_from_def_vect(size=size, n=n, p=0.5)\n",
    "print(dir(timings))\n",
    "print(\"Mean time: \", timings.average)\n",
    "n = 200\n",
    "timings = %timeit -o sample = binomial_from_def_vect(size=size, n=n, p=0.5)\n",
    "print(dir(timings))\n",
    "print(\"Mean time: \", timings.average)"
   ]
  }
 ],
 "metadata": {
  "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": "3.13.5"
  },
  "toc-autonumbering": true,
  "toc-showcode": false,
  "toc-showtags": true
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
