{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Une matrice est un objet constitué de données en deux dimensions, soit des lignes et des colonnes. Chaque élément de la matrice est situé à l'intersection d'une ligne et d'une colonne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "A<- matrix(c(6,8,1,1,4,2), nrow = 2, ncol = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>6</td><td>1</td><td>4</td></tr>\n",
       "\t<tr><td>8</td><td>1</td><td>2</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lll}\n",
       "\t 6 & 1 & 4\\\\\n",
       "\t 8 & 1 & 2\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 6 | 1 | 4 | \n",
       "| 8 | 1 | 2 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 6    1    4   \n",
       "[2,] 8    1    2   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Il arrive souvent qu'on veuille transposer une matrice. Pour ce faire, il suffit de l'inclure à l'intérieur de `t(matrice)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>6</td><td>8</td></tr>\n",
       "\t<tr><td>1</td><td>1</td></tr>\n",
       "\t<tr><td>4</td><td>2</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{ll}\n",
       "\t 6 & 8\\\\\n",
       "\t 1 & 1\\\\\n",
       "\t 4 & 2\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 6 | 8 | \n",
       "| 1 | 1 | \n",
       "| 4 | 2 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2]\n",
       "[1,] 6    8   \n",
       "[2,] 1    1   \n",
       "[3,] 4    2   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Note** Lorsqu'on transpose un vecteur, R transforme ce vecteur en une matrice à une seule dimension:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "vec<-1:5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lllll}\n",
       "\t 1 & 2 & 3 & 4 & 5\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 1 | 2 | 3 | 4 | 5 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3] [,4] [,5]\n",
       "[1,] 1    2    3    4    5   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t(vec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Note** la fonction `dim()` donne les dimensions d'une matrice. Si l’on vérifie la dimension du vecteur."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NULL"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(vec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Bien évidemment il nous retourne une valeur nulle. Mais lorsqu'on transforme ce vecteur en matrice, on obtient;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>5</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 5\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 5\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(t(vec))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Ce qui veut dire que notre matrice est composée d'une seule ligne et cinq colonnes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Extraction d'un élément d'une matrice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Si l'on veut extraire un élément d'une matrice, il suffit d'indiquer ses coordonnées **`[ligne, colonne]`**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "4"
      ],
      "text/latex": [
       "4"
      ],
      "text/markdown": [
       "4"
      ],
      "text/plain": [
       "[1] 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A[1,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>6</td><td>1</td><td>4</td></tr>\n",
       "\t<tr><td>8</td><td>1</td><td>2</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lll}\n",
       "\t 6 & 1 & 4\\\\\n",
       "\t 8 & 1 & 2\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 6 | 1 | 4 | \n",
       "| 8 | 1 | 2 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 6    1    4   \n",
       "[2,] 8    1    2   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Lorsqu'on veut extraire un élément qui n'existe pas dans la matrice, on obtien alors le message d'erreur `subscript out of bounds`. Un message d'erreur que nous verrons souvent!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in A[1, 4]: subscript out of bounds\n",
     "output_type": "error",
     "traceback": [
      "Error in A[1, 4]: subscript out of bounds\nTraceback:\n"
     ]
    }
   ],
   "source": [
    "A[1,4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Si l'on omet de mettre une valeur au numéro de colonne ou de ligne, on obtient la ligne ou la colonne complète"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>6</li>\n",
       "\t<li>8</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 6\n",
       "\\item 8\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 6\n",
       "2. 8\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 6 8"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A[,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Lorsqu'on crée une matrice, nous ne sommes pas obligés d'indiquer le nombre de colonnes ou de lignes en même temps. Un seul argument suffit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "B<-matrix(seq(1,9.5,.5), 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>1.0</td><td>2.5</td><td>4.0</td><td>5.5</td><td>7.0</td><td>8.5</td></tr>\n",
       "\t<tr><td>1.5</td><td>3.0</td><td>4.5</td><td>6.0</td><td>7.5</td><td>9.0</td></tr>\n",
       "\t<tr><td>2.0</td><td>3.5</td><td>5.0</td><td>6.5</td><td>8.0</td><td>9.5</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllll}\n",
       "\t 1.0 & 2.5 & 4.0 & 5.5 & 7.0 & 8.5\\\\\n",
       "\t 1.5 & 3.0 & 4.5 & 6.0 & 7.5 & 9.0\\\\\n",
       "\t 2.0 & 3.5 & 5.0 & 6.5 & 8.0 & 9.5\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 1.0 | 2.5 | 4.0 | 5.5 | 7.0 | 8.5 | \n",
       "| 1.5 | 3.0 | 4.5 | 6.0 | 7.5 | 9.0 | \n",
       "| 2.0 | 3.5 | 5.0 | 6.5 | 8.0 | 9.5 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3] [,4] [,5] [,6]\n",
       "[1,] 1.0  2.5  4.0  5.5  7.0  8.5 \n",
       "[2,] 1.5  3.0  4.5  6.0  7.5  9.0 \n",
       "[3,] 2.0  3.5  5.0  6.5  8.0  9.5 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Si l'on veut extraire la deuxième et la quatrième colonne"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>2.5</td><td>5.5</td></tr>\n",
       "\t<tr><td>3.0</td><td>6.0</td></tr>\n",
       "\t<tr><td>3.5</td><td>6.5</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{ll}\n",
       "\t 2.5 & 5.5\\\\\n",
       "\t 3.0 & 6.0\\\\\n",
       "\t 3.5 & 6.5\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 2.5 | 5.5 | \n",
       "| 3.0 | 6.0 | \n",
       "| 3.5 | 6.5 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2]\n",
       "[1,] 2.5  5.5 \n",
       "[2,] 3.0  6.0 \n",
       "[3,] 3.5  6.5 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B[,c(2,4)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "B<-t(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>1.0</td><td>1.5</td><td>2.0</td></tr>\n",
       "\t<tr><td>2.5</td><td>3.0</td><td>3.5</td></tr>\n",
       "\t<tr><td>4.0</td><td>4.5</td><td>5.0</td></tr>\n",
       "\t<tr><td>5.5</td><td>6.0</td><td>6.5</td></tr>\n",
       "\t<tr><td>7.0</td><td>7.5</td><td>8.0</td></tr>\n",
       "\t<tr><td>8.5</td><td>9.0</td><td>9.5</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lll}\n",
       "\t 1.0 & 1.5 & 2.0\\\\\n",
       "\t 2.5 & 3.0 & 3.5\\\\\n",
       "\t 4.0 & 4.5 & 5.0\\\\\n",
       "\t 5.5 & 6.0 & 6.5\\\\\n",
       "\t 7.0 & 7.5 & 8.0\\\\\n",
       "\t 8.5 & 9.0 & 9.5\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 1.0 | 1.5 | 2.0 | \n",
       "| 2.5 | 3.0 | 3.5 | \n",
       "| 4.0 | 4.5 | 5.0 | \n",
       "| 5.5 | 6.0 | 6.5 | \n",
       "| 7.0 | 7.5 | 8.0 | \n",
       "| 8.5 | 9.0 | 9.5 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 1.0  1.5  2.0 \n",
       "[2,] 2.5  3.0  3.5 \n",
       "[3,] 4.0  4.5  5.0 \n",
       "[4,] 5.5  6.0  6.5 \n",
       "[5,] 7.0  7.5  8.0 \n",
       "[6,] 8.5  9.0  9.5 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Si l'on veut extraire la troisième et la cinquième ligne;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>4  </td><td>4.5</td><td>5  </td></tr>\n",
       "\t<tr><td>7  </td><td>7.5</td><td>8  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lll}\n",
       "\t 4   & 4.5 & 5  \\\\\n",
       "\t 7   & 7.5 & 8  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 4   | 4.5 | 5   | \n",
       "| 7   | 7.5 | 8   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 4    4.5  5   \n",
       "[2,] 7    7.5  8   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B[c(3,5),]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## diag"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Cette fonction crée une matrice identité, c'est une matrice carrée avec des 1 sur la diagonale et des 0 partout ailleurs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lllll}\n",
       "\t 1 & 0 & 0 & 0 & 0\\\\\n",
       "\t 0 & 1 & 0 & 0 & 0\\\\\n",
       "\t 0 & 0 & 1 & 0 & 0\\\\\n",
       "\t 0 & 0 & 0 & 1 & 0\\\\\n",
       "\t 0 & 0 & 0 & 0 & 1\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 1 | 0 | 0 | 0 | 0 | \n",
       "| 0 | 1 | 0 | 0 | 0 | \n",
       "| 0 | 0 | 1 | 0 | 0 | \n",
       "| 0 | 0 | 0 | 1 | 0 | \n",
       "| 0 | 0 | 0 | 0 | 1 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3] [,4] [,5]\n",
       "[1,] 1    0    0    0    0   \n",
       "[2,] 0    1    0    0    0   \n",
       "[3,] 0    0    1    0    0   \n",
       "[4,] 0    0    0    1    0   \n",
       "[5,] 0    0    0    0    1   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diag(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Opértaion sur les matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "On peut aussi appliquer des fonctions mathématiques sur des matrices comme nous l'avons fait avec des vecteurs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>36</td><td>1 </td><td>16</td></tr>\n",
       "\t<tr><td>64</td><td>1 </td><td> 4</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lll}\n",
       "\t 36 & 1  & 16\\\\\n",
       "\t 64 & 1  &  4\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 36 | 1  | 16 | \n",
       "| 64 | 1  |  4 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 36   1    16  \n",
       "[2,] 64   1     4  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>0.50</td><td>1.25</td><td>2.00</td><td>2.75</td><td>3.50</td><td>4.25</td></tr>\n",
       "\t<tr><td>0.75</td><td>1.50</td><td>2.25</td><td>3.00</td><td>3.75</td><td>4.50</td></tr>\n",
       "\t<tr><td>1.00</td><td>1.75</td><td>2.50</td><td>3.25</td><td>4.00</td><td>4.75</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllll}\n",
       "\t 0.50 & 1.25 & 2.00 & 2.75 & 3.50 & 4.25\\\\\n",
       "\t 0.75 & 1.50 & 2.25 & 3.00 & 3.75 & 4.50\\\\\n",
       "\t 1.00 & 1.75 & 2.50 & 3.25 & 4.00 & 4.75\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 0.50 | 1.25 | 2.00 | 2.75 | 3.50 | 4.25 | \n",
       "| 0.75 | 1.50 | 2.25 | 3.00 | 3.75 | 4.50 | \n",
       "| 1.00 | 1.75 | 2.50 | 3.25 | 4.00 | 4.75 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3] [,4] [,5] [,6]\n",
       "[1,] 0.50 1.25 2.00 2.75 3.50 4.25\n",
       "[2,] 0.75 1.50 2.25 3.00 3.75 4.50\n",
       "[3,] 1.00 1.75 2.50 3.25 4.00 4.75"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "C<-B*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>3.0 </td><td> 7.5</td><td>12.0</td><td>16.5</td><td>21.0</td><td>25.5</td></tr>\n",
       "\t<tr><td>4.5 </td><td> 9.0</td><td>13.5</td><td>18.0</td><td>22.5</td><td>27.0</td></tr>\n",
       "\t<tr><td>6.0 </td><td>10.5</td><td>15.0</td><td>19.5</td><td>24.0</td><td>28.5</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllll}\n",
       "\t 3.0  &  7.5 & 12.0 & 16.5 & 21.0 & 25.5\\\\\n",
       "\t 4.5  &  9.0 & 13.5 & 18.0 & 22.5 & 27.0\\\\\n",
       "\t 6.0  & 10.5 & 15.0 & 19.5 & 24.0 & 28.5\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 3.0  |  7.5 | 12.0 | 16.5 | 21.0 | 25.5 | \n",
       "| 4.5  |  9.0 | 13.5 | 18.0 | 22.5 | 27.0 | \n",
       "| 6.0  | 10.5 | 15.0 | 19.5 | 24.0 | 28.5 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3] [,4] [,5] [,6]\n",
       "[1,] 3.0   7.5 12.0 16.5 21.0 25.5\n",
       "[2,] 4.5   9.0 13.5 18.0 22.5 27.0\n",
       "[3,] 6.0  10.5 15.0 19.5 24.0 28.5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B+C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Créons une matrice `A=5X3`. Cette matrice contient les températures en Fahrenheit des trois villes \"Fairbanks\",\"San Francisco\" et \"Chicago\" (nom de colonnes). Les lignes sont les données du mois de mars 2012 au mois de mars 2016."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>30</td><td>72</td><td>55</td></tr>\n",
       "\t<tr><td>32</td><td>60</td><td>57</td></tr>\n",
       "\t<tr><td>31</td><td>78</td><td>56</td></tr>\n",
       "\t<tr><td>27</td><td>67</td><td>55</td></tr>\n",
       "\t<tr><td>36</td><td>71</td><td>49</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lll}\n",
       "\t 30 & 72 & 55\\\\\n",
       "\t 32 & 60 & 57\\\\\n",
       "\t 31 & 78 & 56\\\\\n",
       "\t 27 & 67 & 55\\\\\n",
       "\t 36 & 71 & 49\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 30 | 72 | 55 | \n",
       "| 32 | 60 | 57 | \n",
       "| 31 | 78 | 56 | \n",
       "| 27 | 67 | 55 | \n",
       "| 36 | 71 | 49 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] 30   72   55  \n",
       "[2,] 32   60   57  \n",
       "[3,] 31   78   56  \n",
       "[4,] 27   67   55  \n",
       "[5,] 36   71   49  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A<-matrix(c(30,32,31,27,36,72,60,78,67,71,55,57,56,55,49),ncol=3)\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Convertissons ces données en Celsius avec la formule suivante;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{equation}\\label{eq:}\n",
    "℃= \\frac{℉-32}{1.8000}\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>-1</td><td>22</td><td>13</td></tr>\n",
       "\t<tr><td> 0</td><td>16</td><td>14</td></tr>\n",
       "\t<tr><td>-1</td><td>26</td><td>13</td></tr>\n",
       "\t<tr><td>-3</td><td>19</td><td>13</td></tr>\n",
       "\t<tr><td> 2</td><td>22</td><td> 9</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lll}\n",
       "\t -1 & 22 & 13\\\\\n",
       "\t  0 & 16 & 14\\\\\n",
       "\t -1 & 26 & 13\\\\\n",
       "\t -3 & 19 & 13\\\\\n",
       "\t  2 & 22 &  9\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| -1 | 22 | 13 | \n",
       "|  0 | 16 | 14 | \n",
       "| -1 | 26 | 13 | \n",
       "| -3 | 19 | 13 | \n",
       "|  2 | 22 |  9 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     [,1] [,2] [,3]\n",
       "[1,] -1   22   13  \n",
       "[2,]  0   16   14  \n",
       "[3,] -1   26   13  \n",
       "[4,] -3   19   13  \n",
       "[5,]  2   22    9  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A<-round((A-32)/1.8,0)\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "On peut donner des noms à chacune des colonnes avec la fonction `colnames()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "colnames(A)<-c(\"Fairbanks\",\"San Francisco\",\"Chicago\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "et des nom aux lignes avec la fonction `rownames()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "rownames(A)<-paste(\"3/\",12:16,sep='')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "La fonction `paste` ci-haut permet de concatener des caractères "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'3/___12'</li>\n",
       "\t<li>'3/___13'</li>\n",
       "\t<li>'3/___14'</li>\n",
       "\t<li>'3/___15'</li>\n",
       "\t<li>'3/___16'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item '3/\\_\\_\\_12'\n",
       "\\item '3/\\_\\_\\_13'\n",
       "\\item '3/\\_\\_\\_14'\n",
       "\\item '3/\\_\\_\\_15'\n",
       "\\item '3/\\_\\_\\_16'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. '3/___12'\n",
       "2. '3/___13'\n",
       "3. '3/___14'\n",
       "4. '3/___15'\n",
       "5. '3/___16'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"3/___12\" \"3/___13\" \"3/___14\" \"3/___15\" \"3/___16\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "paste(\"3/\",12:16,sep='___')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Fairbanks</th><th scope=col>San Francisco</th><th scope=col>Chicago</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>3/12</th><td>-1</td><td>22</td><td>13</td></tr>\n",
       "\t<tr><th scope=row>3/13</th><td> 0</td><td>16</td><td>14</td></tr>\n",
       "\t<tr><th scope=row>3/14</th><td>-1</td><td>26</td><td>13</td></tr>\n",
       "\t<tr><th scope=row>3/15</th><td>-3</td><td>19</td><td>13</td></tr>\n",
       "\t<tr><th scope=row>3/16</th><td> 2</td><td>22</td><td> 9</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & Fairbanks & San Francisco & Chicago\\\\\n",
       "\\hline\n",
       "\t3/12 & -1 & 22 & 13\\\\\n",
       "\t3/13 &  0 & 16 & 14\\\\\n",
       "\t3/14 & -1 & 26 & 13\\\\\n",
       "\t3/15 & -3 & 19 & 13\\\\\n",
       "\t3/16 &  2 & 22 &  9\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Fairbanks | San Francisco | Chicago | \n",
       "|---|---|---|---|---|\n",
       "| 3/12 | -1 | 22 | 13 | \n",
       "| 3/13 |  0 | 16 | 14 | \n",
       "| 3/14 | -1 | 26 | 13 | \n",
       "| 3/15 | -3 | 19 | 13 | \n",
       "| 3/16 |  2 | 22 |  9 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     Fairbanks San Francisco Chicago\n",
       "3/12 -1        22            13     \n",
       "3/13  0        16            14     \n",
       "3/14 -1        26            13     \n",
       "3/15 -3        19            13     \n",
       "3/16  2        22             9     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Créons une autre matrice `B`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "B<-matrix(c(88,85,83,81,78,62,61,54,60,65,90,92,91,89,90),ncol=3)\n",
    "colnames(B)<-c(\"Los Angeles\",\"Seattle\",\"Honolulu\")\n",
    "rownames(B)<-paste(\"3/\",12:16,sep='')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Los Angeles</th><th scope=col>Seattle</th><th scope=col>Honolulu</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>3/12</th><td>31</td><td>17</td><td>32</td></tr>\n",
       "\t<tr><th scope=row>3/13</th><td>29</td><td>16</td><td>33</td></tr>\n",
       "\t<tr><th scope=row>3/14</th><td>28</td><td>12</td><td>33</td></tr>\n",
       "\t<tr><th scope=row>3/15</th><td>27</td><td>16</td><td>32</td></tr>\n",
       "\t<tr><th scope=row>3/16</th><td>26</td><td>18</td><td>32</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & Los Angeles & Seattle & Honolulu\\\\\n",
       "\\hline\n",
       "\t3/12 & 31 & 17 & 32\\\\\n",
       "\t3/13 & 29 & 16 & 33\\\\\n",
       "\t3/14 & 28 & 12 & 33\\\\\n",
       "\t3/15 & 27 & 16 & 32\\\\\n",
       "\t3/16 & 26 & 18 & 32\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Los Angeles | Seattle | Honolulu | \n",
       "|---|---|---|---|---|\n",
       "| 3/12 | 31 | 17 | 32 | \n",
       "| 3/13 | 29 | 16 | 33 | \n",
       "| 3/14 | 28 | 12 | 33 | \n",
       "| 3/15 | 27 | 16 | 32 | \n",
       "| 3/16 | 26 | 18 | 32 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     Los Angeles Seattle Honolulu\n",
       "3/12 31          17      32      \n",
       "3/13 29          16      33      \n",
       "3/14 28          12      33      \n",
       "3/15 27          16      32      \n",
       "3/16 26          18      32      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "B<-round((B-32)/1.8,0)\n",
    "B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## cbind"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "La fonction `cbind` permet de concaténer deux matrices ensemble en colonne"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Fairbanks</th><th scope=col>San Francisco</th><th scope=col>Chicago</th><th scope=col>Los Angeles</th><th scope=col>Seattle</th><th scope=col>Honolulu</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>3/12</th><td>-1</td><td>22</td><td>13</td><td>31</td><td>17</td><td>32</td></tr>\n",
       "\t<tr><th scope=row>3/13</th><td> 0</td><td>16</td><td>14</td><td>29</td><td>16</td><td>33</td></tr>\n",
       "\t<tr><th scope=row>3/14</th><td>-1</td><td>26</td><td>13</td><td>28</td><td>12</td><td>33</td></tr>\n",
       "\t<tr><th scope=row>3/15</th><td>-3</td><td>19</td><td>13</td><td>27</td><td>16</td><td>32</td></tr>\n",
       "\t<tr><th scope=row>3/16</th><td> 2</td><td>22</td><td> 9</td><td>26</td><td>18</td><td>32</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllll}\n",
       "  & Fairbanks & San Francisco & Chicago & Los Angeles & Seattle & Honolulu\\\\\n",
       "\\hline\n",
       "\t3/12 & -1 & 22 & 13 & 31 & 17 & 32\\\\\n",
       "\t3/13 &  0 & 16 & 14 & 29 & 16 & 33\\\\\n",
       "\t3/14 & -1 & 26 & 13 & 28 & 12 & 33\\\\\n",
       "\t3/15 & -3 & 19 & 13 & 27 & 16 & 32\\\\\n",
       "\t3/16 &  2 & 22 &  9 & 26 & 18 & 32\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Fairbanks | San Francisco | Chicago | Los Angeles | Seattle | Honolulu | \n",
       "|---|---|---|---|---|\n",
       "| 3/12 | -1 | 22 | 13 | 31 | 17 | 32 | \n",
       "| 3/13 |  0 | 16 | 14 | 29 | 16 | 33 | \n",
       "| 3/14 | -1 | 26 | 13 | 28 | 12 | 33 | \n",
       "| 3/15 | -3 | 19 | 13 | 27 | 16 | 32 | \n",
       "| 3/16 |  2 | 22 |  9 | 26 | 18 | 32 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     Fairbanks San Francisco Chicago Los Angeles Seattle Honolulu\n",
       "3/12 -1        22            13      31          17      32      \n",
       "3/13  0        16            14      29          16      33      \n",
       "3/14 -1        26            13      28          12      33      \n",
       "3/15 -3        19            13      27          16      32      \n",
       "3/16  2        22             9      26          18      32      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cbind(A,B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## rbind"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "La fonction `rbind` permet de concaténer deux matrices ensemble une par-dessus l'autre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Fairbanks</th><th scope=col>San Francisco</th><th scope=col>Chicago</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>3/12</th><td>-1</td><td>22</td><td>13</td></tr>\n",
       "\t<tr><th scope=row>3/13</th><td> 0</td><td>16</td><td>14</td></tr>\n",
       "\t<tr><th scope=row>3/14</th><td>-1</td><td>26</td><td>13</td></tr>\n",
       "\t<tr><th scope=row>3/15</th><td>-3</td><td>19</td><td>13</td></tr>\n",
       "\t<tr><th scope=row>3/16</th><td> 2</td><td>22</td><td> 9</td></tr>\n",
       "\t<tr><th scope=row>3/12</th><td>31</td><td>17</td><td>32</td></tr>\n",
       "\t<tr><th scope=row>3/13</th><td>29</td><td>16</td><td>33</td></tr>\n",
       "\t<tr><th scope=row>3/14</th><td>28</td><td>12</td><td>33</td></tr>\n",
       "\t<tr><th scope=row>3/15</th><td>27</td><td>16</td><td>32</td></tr>\n",
       "\t<tr><th scope=row>3/16</th><td>26</td><td>18</td><td>32</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & Fairbanks & San Francisco & Chicago\\\\\n",
       "\\hline\n",
       "\t3/12 & -1 & 22 & 13\\\\\n",
       "\t3/13 &  0 & 16 & 14\\\\\n",
       "\t3/14 & -1 & 26 & 13\\\\\n",
       "\t3/15 & -3 & 19 & 13\\\\\n",
       "\t3/16 &  2 & 22 &  9\\\\\n",
       "\t3/12 & 31 & 17 & 32\\\\\n",
       "\t3/13 & 29 & 16 & 33\\\\\n",
       "\t3/14 & 28 & 12 & 33\\\\\n",
       "\t3/15 & 27 & 16 & 32\\\\\n",
       "\t3/16 & 26 & 18 & 32\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Fairbanks | San Francisco | Chicago | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 3/12 | -1 | 22 | 13 | \n",
       "| 3/13 |  0 | 16 | 14 | \n",
       "| 3/14 | -1 | 26 | 13 | \n",
       "| 3/15 | -3 | 19 | 13 | \n",
       "| 3/16 |  2 | 22 |  9 | \n",
       "| 3/12 | 31 | 17 | 32 | \n",
       "| 3/13 | 29 | 16 | 33 | \n",
       "| 3/14 | 28 | 12 | 33 | \n",
       "| 3/15 | 27 | 16 | 32 | \n",
       "| 3/16 | 26 | 18 | 32 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     Fairbanks San Francisco Chicago\n",
       "3/12 -1        22            13     \n",
       "3/13  0        16            14     \n",
       "3/14 -1        26            13     \n",
       "3/15 -3        19            13     \n",
       "3/16  2        22             9     \n",
       "3/12 31        17            32     \n",
       "3/13 29        16            33     \n",
       "3/14 28        12            33     \n",
       "3/15 27        16            32     \n",
       "3/16 26        18            32     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rbind(A,B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## matrcice en vecteur"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "On peut aussi transformer une matrice en un vecteur;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Reprenons la matrice que nous avons créée avec la fonction `rbind`. On lui donne le nom \"mat_comb\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "mat_comb<-cbind(A,B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "On la transforme en vecteur avec `c(nomMatrice)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>-1</li>\n",
       "\t<li>0</li>\n",
       "\t<li>-1</li>\n",
       "\t<li>-3</li>\n",
       "\t<li>2</li>\n",
       "\t<li>22</li>\n",
       "\t<li>16</li>\n",
       "\t<li>26</li>\n",
       "\t<li>19</li>\n",
       "\t<li>22</li>\n",
       "\t<li>13</li>\n",
       "\t<li>14</li>\n",
       "\t<li>13</li>\n",
       "\t<li>13</li>\n",
       "\t<li>9</li>\n",
       "\t<li>31</li>\n",
       "\t<li>29</li>\n",
       "\t<li>28</li>\n",
       "\t<li>27</li>\n",
       "\t<li>26</li>\n",
       "\t<li>17</li>\n",
       "\t<li>16</li>\n",
       "\t<li>12</li>\n",
       "\t<li>16</li>\n",
       "\t<li>18</li>\n",
       "\t<li>32</li>\n",
       "\t<li>33</li>\n",
       "\t<li>33</li>\n",
       "\t<li>32</li>\n",
       "\t<li>32</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item -1\n",
       "\\item 0\n",
       "\\item -1\n",
       "\\item -3\n",
       "\\item 2\n",
       "\\item 22\n",
       "\\item 16\n",
       "\\item 26\n",
       "\\item 19\n",
       "\\item 22\n",
       "\\item 13\n",
       "\\item 14\n",
       "\\item 13\n",
       "\\item 13\n",
       "\\item 9\n",
       "\\item 31\n",
       "\\item 29\n",
       "\\item 28\n",
       "\\item 27\n",
       "\\item 26\n",
       "\\item 17\n",
       "\\item 16\n",
       "\\item 12\n",
       "\\item 16\n",
       "\\item 18\n",
       "\\item 32\n",
       "\\item 33\n",
       "\\item 33\n",
       "\\item 32\n",
       "\\item 32\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. -1\n",
       "2. 0\n",
       "3. -1\n",
       "4. -3\n",
       "5. 2\n",
       "6. 22\n",
       "7. 16\n",
       "8. 26\n",
       "9. 19\n",
       "10. 22\n",
       "11. 13\n",
       "12. 14\n",
       "13. 13\n",
       "14. 13\n",
       "15. 9\n",
       "16. 31\n",
       "17. 29\n",
       "18. 28\n",
       "19. 27\n",
       "20. 26\n",
       "21. 17\n",
       "22. 16\n",
       "23. 12\n",
       "24. 16\n",
       "25. 18\n",
       "26. 32\n",
       "27. 33\n",
       "28. 33\n",
       "29. 32\n",
       "30. 32\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] -1  0 -1 -3  2 22 16 26 19 22 13 14 13 13  9 31 29 28 27 26 17 16 12 16 18\n",
       "[26] 32 33 33 32 32"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c(mat_comb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Quelques fonctions statistiques sur les matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Fairbanks</th><th scope=col>San Francisco</th><th scope=col>Chicago</th><th scope=col>Los Angeles</th><th scope=col>Seattle</th><th scope=col>Honolulu</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>3/12</th><td>-1</td><td>22</td><td>13</td><td>31</td><td>17</td><td>32</td></tr>\n",
       "\t<tr><th scope=row>3/13</th><td> 0</td><td>16</td><td>14</td><td>29</td><td>16</td><td>33</td></tr>\n",
       "\t<tr><th scope=row>3/14</th><td>-1</td><td>26</td><td>13</td><td>28</td><td>12</td><td>33</td></tr>\n",
       "\t<tr><th scope=row>3/15</th><td>-3</td><td>19</td><td>13</td><td>27</td><td>16</td><td>32</td></tr>\n",
       "\t<tr><th scope=row>3/16</th><td> 2</td><td>22</td><td> 9</td><td>26</td><td>18</td><td>32</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllll}\n",
       "  & Fairbanks & San Francisco & Chicago & Los Angeles & Seattle & Honolulu\\\\\n",
       "\\hline\n",
       "\t3/12 & -1 & 22 & 13 & 31 & 17 & 32\\\\\n",
       "\t3/13 &  0 & 16 & 14 & 29 & 16 & 33\\\\\n",
       "\t3/14 & -1 & 26 & 13 & 28 & 12 & 33\\\\\n",
       "\t3/15 & -3 & 19 & 13 & 27 & 16 & 32\\\\\n",
       "\t3/16 &  2 & 22 &  9 & 26 & 18 & 32\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Fairbanks | San Francisco | Chicago | Los Angeles | Seattle | Honolulu | \n",
       "|---|---|---|---|---|\n",
       "| 3/12 | -1 | 22 | 13 | 31 | 17 | 32 | \n",
       "| 3/13 |  0 | 16 | 14 | 29 | 16 | 33 | \n",
       "| 3/14 | -1 | 26 | 13 | 28 | 12 | 33 | \n",
       "| 3/15 | -3 | 19 | 13 | 27 | 16 | 32 | \n",
       "| 3/16 |  2 | 22 |  9 | 26 | 18 | 32 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     Fairbanks San Francisco Chicago Los Angeles Seattle Honolulu\n",
       "3/12 -1        22            13      31          17      32      \n",
       "3/13  0        16            14      29          16      33      \n",
       "3/14 -1        26            13      28          12      33      \n",
       "3/15 -3        19            13      27          16      32      \n",
       "3/16  2        22             9      26          18      32      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mat_comb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Lorsqu'on applique la fonction `min`, on obtient alors la valeur minimale de toutes les valeurs contenues dans la matrice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "-3"
      ],
      "text/latex": [
       "-3"
      ],
      "text/markdown": [
       "-3"
      ],
      "text/plain": [
       "[1] -3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "min(mat_comb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "33"
      ],
      "text/latex": [
       "33"
      ],
      "text/markdown": [
       "33"
      ],
      "text/plain": [
       "[1] 33"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "max(mat_comb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>-3</li>\n",
       "\t<li>33</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item -3\n",
       "\\item 33\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. -3\n",
       "2. 33\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] -3 33"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "range(mat_comb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "11.1923619275487"
      ],
      "text/latex": [
       "11.1923619275487"
      ],
      "text/markdown": [
       "11.1923619275487"
      ],
      "text/plain": [
       "[1] 11.19236"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sd(mat_comb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Les statistiques que nous venons d'obtenir, sont applquées à toutes les valeurs de la matrice. Et si nous voulions des statistiques par ligne ou par colonne"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>3/12</dt>\n",
       "\t\t<dd>19</dd>\n",
       "\t<dt>3/13</dt>\n",
       "\t\t<dd>18</dd>\n",
       "\t<dt>3/14</dt>\n",
       "\t\t<dd>18.5</dd>\n",
       "\t<dt>3/15</dt>\n",
       "\t\t<dd>17.3333333333333</dd>\n",
       "\t<dt>3/16</dt>\n",
       "\t\t<dd>18.1666666666667</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[3/12] 19\n",
       "\\item[3/13] 18\n",
       "\\item[3/14] 18.5\n",
       "\\item[3/15] 17.3333333333333\n",
       "\\item[3/16] 18.1666666666667\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "3/12\n",
       ":   193/13\n",
       ":   183/14\n",
       ":   18.53/15\n",
       ":   17.33333333333333/16\n",
       ":   18.1666666666667\n",
       "\n"
      ],
      "text/plain": [
       "    3/12     3/13     3/14     3/15     3/16 \n",
       "19.00000 18.00000 18.50000 17.33333 18.16667 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rowMeans(mat_comb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>Fairbanks</dt>\n",
       "\t\t<dd>-0.6</dd>\n",
       "\t<dt>San Francisco</dt>\n",
       "\t\t<dd>21</dd>\n",
       "\t<dt>Chicago</dt>\n",
       "\t\t<dd>12.4</dd>\n",
       "\t<dt>Los Angeles</dt>\n",
       "\t\t<dd>28.2</dd>\n",
       "\t<dt>Seattle</dt>\n",
       "\t\t<dd>15.8</dd>\n",
       "\t<dt>Honolulu</dt>\n",
       "\t\t<dd>32.4</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[Fairbanks] -0.6\n",
       "\\item[San Francisco] 21\n",
       "\\item[Chicago] 12.4\n",
       "\\item[Los Angeles] 28.2\n",
       "\\item[Seattle] 15.8\n",
       "\\item[Honolulu] 32.4\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "Fairbanks\n",
       ":   -0.6San Francisco\n",
       ":   21Chicago\n",
       ":   12.4Los Angeles\n",
       ":   28.2Seattle\n",
       ":   15.8Honolulu\n",
       ":   32.4\n",
       "\n"
      ],
      "text/plain": [
       "    Fairbanks San Francisco       Chicago   Los Angeles       Seattle \n",
       "         -0.6          21.0          12.4          28.2          15.8 \n",
       "     Honolulu \n",
       "         32.4 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colMeans(mat_comb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Corrélation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Fairbanks</th><th scope=col>San Francisco</th><th scope=col>Chicago</th><th scope=col>Los Angeles</th><th scope=col>Seattle</th><th scope=col>Honolulu</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Fairbanks</th><td> 1.00000000</td><td> 0.07356124</td><td>-0.6918586 </td><td>-0.24325462</td><td> 0.38624364</td><td> 0.05025189</td></tr>\n",
       "\t<tr><th scope=row>San Francisco</th><td> 0.07356124</td><td> 1.00000000</td><td>-0.3084798 </td><td>-0.06947125</td><td>-0.49810768</td><td> 0.00000000</td></tr>\n",
       "\t<tr><th scope=row>Chicago</th><td>-0.69185856</td><td>-0.30847978</td><td> 1.0000000 </td><td> 0.64005690</td><td>-0.48366537</td><td> 0.51512220</td></tr>\n",
       "\t<tr><th scope=row>Los Angeles</th><td>-0.24325462</td><td>-0.06947125</td><td> 0.6400569 </td><td> 1.00000000</td><td>-0.04559608</td><td> 0.14237370</td></tr>\n",
       "\t<tr><th scope=row>Seattle</th><td> 0.38624364</td><td>-0.49810768</td><td>-0.4836654 </td><td>-0.04559608</td><td> 1.00000000</td><td>-0.72057669</td></tr>\n",
       "\t<tr><th scope=row>Honolulu</th><td> 0.05025189</td><td> 0.00000000</td><td> 0.5151222 </td><td> 0.14237370</td><td>-0.72057669</td><td> 1.00000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllll}\n",
       "  & Fairbanks & San Francisco & Chicago & Los Angeles & Seattle & Honolulu\\\\\n",
       "\\hline\n",
       "\tFairbanks &  1.00000000 &  0.07356124 & -0.6918586  & -0.24325462 &  0.38624364 &  0.05025189\\\\\n",
       "\tSan Francisco &  0.07356124 &  1.00000000 & -0.3084798  & -0.06947125 & -0.49810768 &  0.00000000\\\\\n",
       "\tChicago & -0.69185856 & -0.30847978 &  1.0000000  &  0.64005690 & -0.48366537 &  0.51512220\\\\\n",
       "\tLos Angeles & -0.24325462 & -0.06947125 &  0.6400569  &  1.00000000 & -0.04559608 &  0.14237370\\\\\n",
       "\tSeattle &  0.38624364 & -0.49810768 & -0.4836654  & -0.04559608 &  1.00000000 & -0.72057669\\\\\n",
       "\tHonolulu &  0.05025189 &  0.00000000 &  0.5151222  &  0.14237370 & -0.72057669 &  1.00000000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Fairbanks | San Francisco | Chicago | Los Angeles | Seattle | Honolulu | \n",
       "|---|---|---|---|---|---|\n",
       "| Fairbanks |  1.00000000 |  0.07356124 | -0.6918586  | -0.24325462 |  0.38624364 |  0.05025189 | \n",
       "| San Francisco |  0.07356124 |  1.00000000 | -0.3084798  | -0.06947125 | -0.49810768 |  0.00000000 | \n",
       "| Chicago | -0.69185856 | -0.30847978 |  1.0000000  |  0.64005690 | -0.48366537 |  0.51512220 | \n",
       "| Los Angeles | -0.24325462 | -0.06947125 |  0.6400569  |  1.00000000 | -0.04559608 |  0.14237370 | \n",
       "| Seattle |  0.38624364 | -0.49810768 | -0.4836654  | -0.04559608 |  1.00000000 | -0.72057669 | \n",
       "| Honolulu |  0.05025189 |  0.00000000 |  0.5151222  |  0.14237370 | -0.72057669 |  1.00000000 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "              Fairbanks   San Francisco Chicago    Los Angeles Seattle    \n",
       "Fairbanks      1.00000000  0.07356124   -0.6918586 -0.24325462  0.38624364\n",
       "San Francisco  0.07356124  1.00000000   -0.3084798 -0.06947125 -0.49810768\n",
       "Chicago       -0.69185856 -0.30847978    1.0000000  0.64005690 -0.48366537\n",
       "Los Angeles   -0.24325462 -0.06947125    0.6400569  1.00000000 -0.04559608\n",
       "Seattle        0.38624364 -0.49810768   -0.4836654 -0.04559608  1.00000000\n",
       "Honolulu       0.05025189  0.00000000    0.5151222  0.14237370 -0.72057669\n",
       "              Honolulu   \n",
       "Fairbanks      0.05025189\n",
       "San Francisco  0.00000000\n",
       "Chicago        0.51512220\n",
       "Los Angeles    0.14237370\n",
       "Seattle       -0.72057669\n",
       "Honolulu       1.00000000"
      ]
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   "source": [
    "cor(mat_comb)"
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   "source": [
    "## summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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    {
     "data": {
      "text/plain": [
       "   Fairbanks    San Francisco    Chicago      Los Angeles      Seattle    \n",
       " Min.   :-3.0   Min.   :16    Min.   : 9.0   Min.   :26.0   Min.   :12.0  \n",
       " 1st Qu.:-1.0   1st Qu.:19    1st Qu.:13.0   1st Qu.:27.0   1st Qu.:16.0  \n",
       " Median :-1.0   Median :22    Median :13.0   Median :28.0   Median :16.0  \n",
       " Mean   :-0.6   Mean   :21    Mean   :12.4   Mean   :28.2   Mean   :15.8  \n",
       " 3rd Qu.: 0.0   3rd Qu.:22    3rd Qu.:13.0   3rd Qu.:29.0   3rd Qu.:17.0  \n",
       " Max.   : 2.0   Max.   :26    Max.   :14.0   Max.   :31.0   Max.   :18.0  \n",
       "    Honolulu   \n",
       " Min.   :32.0  \n",
       " 1st Qu.:32.0  \n",
       " Median :32.0  \n",
       " Mean   :32.4  \n",
       " 3rd Qu.:33.0  \n",
       " Max.   :33.0  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(mat_comb)"
   ]
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   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    " Si on veut par ligne, rappelons-nous que nous avons appris à transposer les matrices!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      3/12            3/13            3/14            3/15      \n",
       " Min.   :-1.00   Min.   : 0.00   Min.   :-1.00   Min.   :-3.00  \n",
       " 1st Qu.:14.00   1st Qu.:14.50   1st Qu.:12.25   1st Qu.:13.75  \n",
       " Median :19.50   Median :16.00   Median :19.50   Median :17.50  \n",
       " Mean   :19.00   Mean   :18.00   Mean   :18.50   Mean   :17.33  \n",
       " 3rd Qu.:28.75   3rd Qu.:25.75   3rd Qu.:27.50   3rd Qu.:25.00  \n",
       " Max.   :32.00   Max.   :33.00   Max.   :33.00   Max.   :32.00  \n",
       "      3/16      \n",
       " Min.   : 2.00  \n",
       " 1st Qu.:11.25  \n",
       " Median :20.00  \n",
       " Mean   :18.17  \n",
       " 3rd Qu.:25.00  \n",
       " Max.   :32.00  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(t(mat_comb))"
   ]
  }
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