{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f0853696",
   "metadata": {},
   "source": [
    "# Numpy, le manipulateur de matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e754d97",
   "metadata": {},
   "source": [
    "Dans cet exercice, nous allons nous intéresser à la bibliothèque Numpy. Pour pouvoir l'utiliser, il est nécessaire au préalable qu'elle soit installée :\n",
    "\n",
    "**pip install numpy**\n",
    "\n",
    "(uniquement sur votre propre machine en local)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a669dd5f",
   "metadata": {},
   "source": [
    "Puis de l'importer via l'instruction suivante :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "32823167",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef6c9f7f",
   "metadata": {},
   "source": [
    "## Premiers vecteurs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e47f31dd",
   "metadata": {},
   "source": [
    "> **Exécutez les instructions suivantes**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "79a3dcbb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "x = np.array( [1,2,3] )\n",
    "y = np.sin(x)\n",
    "\n",
    "print(f'type de x : {type(x)} - shape de x : {x.shape}')\n",
    "print(f'type de y : {type(y)} - shape de y : {y.shape}')\n",
    "\n",
    "print( y )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "941a393f",
   "metadata": {},
   "source": [
    "Que contiennent les variables x et y ?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b08c114b",
   "metadata": {},
   "source": [
    "Réponse :"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd74d8f9",
   "metadata": {},
   "source": [
    "## Premières matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3163cb3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "mb = np.array( [[1,2,3] , [4,5,6]] )\n",
    "mc = np.array( [[1,2,3] , [4,5,6]] ) \n",
    "mm = mb + mc\n",
    "print(f'type de mm : {type(mm)} - shape de mm : {mm.shape}')\n",
    "print( mm )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6ffb721",
   "metadata": {},
   "source": [
    "## Matrices particulières"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3d8dcdb",
   "metadata": {},
   "source": [
    "> **Exécutez les instructions suivantes**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b7f564a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "vz = np.zeros( 10 )\n",
    "print( f'shape de vz : {vz.shape}' )\n",
    "print( f'valeurs de vz : {vz}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c04f796f",
   "metadata": {},
   "source": [
    "A quoi sert la fonction zeros ?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bce7796",
   "metadata": {},
   "source": [
    "Réponse :"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95ca754b",
   "metadata": {},
   "source": [
    "> Exécutez les instructions suivantes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "58ab02a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "mo = np.ones( (10,3) )\n",
    "print( f'shape de mo : {mo.shape}' )\n",
    "print( f'valeurs de mo : {mo}' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83b932c7",
   "metadata": {},
   "source": [
    "> **Exécutez les instructions suivantes** et déterminez le rôle des fonctions linspace, logspace et arange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e014c40a",
   "metadata": {},
   "outputs": [],
   "source": [
    "vlin = np.linspace( -1, 3, 21 )\n",
    "vlog = np.logspace( 1, 5, 11 )\n",
    "vara = np.arange( 5, step=0.5 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d3dcc398",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TO DO"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b47e126a",
   "metadata": {},
   "source": [
    "## Calculs sur des matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "294692f1",
   "metadata": {},
   "source": [
    "> **Exécutez les instructions suivantes** et déterminez le rôle de la fonction *sum* et du paramètre *axis*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4217125d",
   "metadata": {},
   "outputs": [],
   "source": [
    "mb = np.array( [[1,2,3] , [4,5,6]] )\n",
    "\n",
    "total = np.sum(mb) \n",
    "total_c = np.sum(mb, axis=0)\n",
    "total_r = np.sum(mb, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e635b604",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TO DO"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8e320bc",
   "metadata": {},
   "source": [
    "> **Exécutez les instructions suivantes** et déterminez le rôle de la fonction *mean* et du paramètre *axis*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "49df7f78",
   "metadata": {},
   "outputs": [],
   "source": [
    "moy = np.mean(mb) \n",
    "moy_c = np.mean(mb, axis=0)\n",
    "moy_r = np.mean(mb, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2239131b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TO DO"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0806a138",
   "metadata": {},
   "source": [
    "## Matrices partielles"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4111b34",
   "metadata": {},
   "source": [
    "> **Exécutez les instructions suivantes** et déterminez les actions des deux dernières instructions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b872e948",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "vect = np.arange( 100 ) \n",
    "vect_p = vect[ 10 : 30 ]\n",
    "vect_s = vect[ 50 : ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4ee5d2a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TO DO"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b234911d",
   "metadata": {},
   "source": [
    "> **Exécutez les instructions suivantes** et déterminez l'action de la dernière instruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1fb40bf0",
   "metadata": {},
   "outputs": [],
   "source": [
    "mb = np.array( [[1,2,3] , [4,5,6]] )\n",
    "mc = md[ : , 1:3 ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a2a7d58d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TO DO"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4527a02b",
   "metadata": {},
   "source": [
    "## Tests sur les matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b59bf0c",
   "metadata": {},
   "source": [
    "> **Exécutez les instructions suivantes** et déterminez le contenu des deux vecteurs c et tf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0edb3fee",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = vect[(vect > 2) & (vect < 11)]\n",
    "tf = (vect > 2) & (vect < 11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fb4b5e17",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TO DO"
   ]
  }
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