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    "# Utilisation de numpy\n",
    "\n",
    "## Calcul Monte-Carlo de la surface d'un disque\n",
    "\n",
    "On rappelle que la fonction np.random.rand permet de créer une distribution uniforme de points entre 0 et 1.\n",
    "\n",
    "1. Créer des tableaux X et Y de variables uniforméments réparties entre -1 et 1\n",
    "2. Evaluer la probabilité que le point de coordonnées (x, y) soit dans le cercle unité ?\n",
    "3. En déduire une estimation ed $\\pi$\n",
    "4. De la même façon, évaluer le volume d'une sphère en dimension 13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b8b9b882",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimation de pi 3.143348\n"
     ]
    }
   ],
   "source": [
    "N = 1000000\n",
    "\n",
    "X = 2*(np.random.rand(N)-.5)\n",
    "Y = 2*(np.random.rand(N)-.5)\n",
    "\n",
    "R = np.sqrt(X**2 + Y**2)\n",
    "print('Estimation de pi', np.mean(R<1)*4)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ace289cc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00011\n"
     ]
    }
   ],
   "source": [
    "dim = 13\n",
    "\n",
    "X = 2*(np.random.rand(dim, N)-.5)\n",
    "\n",
    "R = np.sqrt(np.sum(X**2, axis=0))\n",
    "print(np.mean(R<1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67d2282f",
   "metadata": {},
   "source": [
    "## Calcul de la moyenne \n",
    "\n",
    "Un tableau numpy contient les notes d'une classe. Chaque ligne correspond à un élève et chaque colone à un examen. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2558b2be",
   "metadata": {
    "tags": [
     "keep"
    ]
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "N_eleves = 35\n",
    "N_examens = 3\n",
    "\n",
    "notes = np.random.rand(N_eleves, N_examens)*20"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "084010e3",
   "metadata": {},
   "source": [
    "1. Calculer la moyenne de chaque élève. Calculer la moyenne pour chaque examen. \n",
    "2. Calculer la moyenne de chaque élève, sachant que les coeficients pour les 3 examens sont de 1, 3 et 2. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f46d07cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Moyenne eleves : [ 4.86475764 13.87157763 16.63133782 12.54131626  7.78354896 14.91060888\n",
      " 11.49341153  7.40491898  7.7408721  12.83294063  5.19142779  7.16174387\n",
      " 11.72812901 16.37947513 13.78278386  9.49417344 14.78770611 10.32141726\n",
      "  7.73516296 12.93635595 12.0172946   6.32059816 14.24920113  7.9846933\n",
      "  9.34793038  4.97840815  0.93303272 11.61755392  4.74755408  6.75401493\n",
      "  7.58238456 12.39258674 16.24376983  8.61322578  9.22967243]\n",
      "Moyenne exams : [10.51405794 10.77392961  8.93534844]\n"
     ]
    }
   ],
   "source": [
    "moyenne_eleve = notes.mean(axis=1)\n",
    "moyenne_exams = notes.mean(axis=0)\n",
    "\n",
    "print(f'Moyenne eleves : {moyenne_eleve}')\n",
    "print(f'Moyenne exams : {moyenne_exams}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b07a5f31",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Moyenne eleves : [ 4.8469425  14.99684316 17.5957476  13.28084804  7.38128184 14.16213389\n",
      " 10.37123986  5.34245749  7.19795841 14.43345158  6.1073791   5.54566383\n",
      " 10.46290838 15.54873099 12.71400994  7.05525354 13.60650382 12.16244485\n",
      " 10.58650973 14.71984854 13.36255598  4.45639921 14.35210974  9.04184847\n",
      " 10.33807833  3.32534396  0.65691568 10.95163956  3.27687672  7.73253324\n",
      "  8.73697947 12.65795077 16.75820541  8.44130762 11.91460335]\n"
     ]
    }
   ],
   "source": [
    "moyenne_ponderee = (notes*np.array([1, 3, 2])[np.newaxis, :]).sum(axis=1)/6\n",
    "print(f'Moyenne eleves : {moyenne_ponderee}')\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "f22c756d",
   "metadata": {},
   "outputs": [],
   "source": []
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