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ArtStudies/Calculs Numériques/DM2.ipynb

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"DEVOIR MAISON 2\n",
"\n",
"---\n",
"# Splines cubiques\n",
"---"
]
},
{
"cell_type": "code",
"execution_count": 193,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**IMPORTANT** \n",
"> 1. Dans ce DM on demande d'essayer d'éviter l'utilisation de boucles `for` dans *les définitions de fonctions*. Une solution utilisant des commandes vectorielles (commandes de `numpy`) apportera plus de points qu'une solution utilisant des boucles `for`.\n",
"> 2. Tout graphique doit avoir un titre et une légende."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"L'un des problèmes d'approximation d'une fonction par son polynome interpolateur de Lagrange est le phénomène de Runge: le fait que le polynome interpolateur ne tend pas forcément vers la fonction interpolée quand le nombre de points d'interpolation augmente. L'une des solutions possibles à ce problème est la segmentation: on approche la fonction par des fonctions polynomiales *par morceaux*. Dans ce cas, pour améliorer l'approximation on augmente le nombre de morceaux et non le dégré des polynomes. Ceci est l'idée des *splines*."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Définition\n",
"On considère sur un segment $ [ a, b ] $ une division $ a = x_0 < x_1 < \\ldots < x_N = b $ définie par $ N + 1 $ points $ x_0, x_1, x_2, \\ldots, x_N $. Une fonction $ s : [ a, b ] \\to \\mathbb{R} $ est appelée *spline* cubique relative aux noeuds $ x_i $ si \n",
"- $ s $ est une fonction $ C^2 $ sur $ [a, b ] $: $ s \\in C^2( [ a, b ] ) $ et\n",
"- sur chaque intervalle $ [ x_{ i }, x_{i+1} ] $ la fonction $ s $ est un polynome de degré $ 3 $: $ s_i \\in \\mathbb{R}_3[ X ] $, où $ s_i = \\left. s \\right|_{ [ x_{ i }, x_{i+1} ] } $, $ i = 0, 1, \\ldots, N-1 $.\n",
"\n",
"On dit qu'une spline $ s $ est une spline d'interpolation aux points $ ( x_i, y_i ) $, $ i = 0, 1, \\ldots, N $, si en plus\n",
"- $ s( x_i ) = y_i $, $ i = 0, 1, \\ldots, N $. "
]
},
{
"cell_type": "markdown",
"metadata": {
"tags": []
},
"source": [
"## Construction\n",
"\n",
"Dans ce qui suit nous allons utiliser la notation suivante: on dénote $ h_i = x_{ i + 1 } - x_i $, $ i = 0, 1, \\ldots, N-1 $, et on appelle différences divisées $ \\delta y $ les expressions définies par\n",
"\\begin{equation*}\n",
"\\delta y[ x_{ i + 1 }, x_i ] = \\frac{ y_{ i + 1 } - y_i }{ x_{ i+1 } - x_i }, \\quad i = 0, 1, \\ldots, N-1.\n",
"\\end{equation*}\n",
"\n",
"Pour chaque intervalle $ [ x_{ i }, x_{i+1} ] $, $ i = 0, 1, \\ldots, N-1 $, nous allons construire le polynome $ s_i $ ( la restriction de $ s $ sur $ [ x_{ i }, x_{i+1} ] $) comme le polynome de degré 3 vérifiant les conditions\n",
"\\begin{equation*}\n",
"\\begin{aligned}\n",
"& s_i( x_{ i } ) = y_{ i }, & s_i( x_{i+1} ) = y_{i+1}, \\\\\n",
"& s'_i( x_{ i } ) = p_{ i }, & s'_i( x_{i+1} ) = p_{i+1}, \\\\\n",
"\\end{aligned}\n",
"\\tag{1}\n",
"\\end{equation*}\n",
"avec $ p_0, p_1, \\ldots, p_N $ (les pentes) données. On peut montrer que pour tous $ y_{i}, y_{i+1}, p_{i}, p_{i+1} $ il existe unique polynome $ s_i $ de degré 3 vérifiant les 4 conditions (1). Comment choisir les pentes $ p_0, p_1, \\ldots, p_N $? On va choisir les valeurs $ p_1, \\ldots, p_{N-1} $ de telle sorte que la fonction $ s $ soit $ C^2 $ sur $ [ a, b ] $. Plus particulièrement, il est possible de montrer que pour que $ s_{i-1}''( x_{i} ) = s_{i}''( x_i ) $, $ i = 1, 2, \\ldots, N-1 $, il faut que $ p_1, p_2, \\ldots, p_{N-1} $ vérifient le système linéaire suivant:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation*}\n",
"\\begin{pmatrix}\n",
"2\\left( \\frac{1}{h_0} + \\frac{1}{h_1} \\right) & \\frac{1}{h_1} & & \\ldots & \\\\\n",
"\\frac{1}{h_1} & 2\\left( \\frac{1}{h_1} + \\frac{1}{h_2} \\right) & \\frac{1}{h_2} & & \\\\\n",
" & \\frac{1}{h_2} & 2\\left( \\frac{1}{h_2} + \\frac{1}{h_3} \\right) & & \\\\\n",
" & & \\ldots & & \\frac{1}{h_{ N - 2 }} \\\\\n",
" & & & \\frac{1}{h_{ N - 2 }} & 2\\left( \\frac{1}{h_{N-2}} + \\frac{1}{h_{N-1}} \\right)\n",
"\\end{pmatrix}\n",
"\\begin{pmatrix}\n",
"p_1 \\\\\n",
"p_2 \\\\\n",
"p_3 \\\\\n",
"\\ldots \\\\\n",
"p_{ N - 1 }\n",
"\\end{pmatrix} = \n",
"\\begin{pmatrix}\n",
"\\hat c_1 \\\\\n",
"c_2 \\\\\n",
"c_3 \\\\\n",
"\\ldots \\\\\n",
"\\hat c_{ N - 1 }\n",
"\\end{pmatrix}\n",
"\\tag{2}\n",
"\\end{equation*}\n",
"avec $ c_i $ donné par la formule \n",
"\\begin{equation}\n",
"\\begin{aligned}\n",
"& c_i = 3 \\left( \\frac{ \\delta y [ x_i, x_{ i -1 } ] }{ h_{ i - 1 } } + \\frac{ \\delta y[ x_{ i + 1 }, x_i ] }{ h_i } \\right), \\quad i = 1, 2, \\ldots, N - 1, \\text{ et } \\\\\n",
"& \\hat c_1 = c_1 - \\frac{ p_0 }{h_0 }, \\quad \\hat c_{ N-1 } = c_{ N-1 } - \\frac{ p_N }{ h_{N-1} }.\n",
"\\end{aligned}\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Dans ce DM nous allons étudier les splines dites *scellées*, i.e. nous allons préscire les valeurs de la dérivée de la spline au bord de l'intervalle $ [ a,b ] $.\n",
"En d'autres termes nous allons préscrire les valeurs $ p_0 $, $ p_N $. Notamment si on cherche une spline interpolant une fonction $ f $ aux points $ x_0, x_1, \\ldots, x_N $, i.e. telle que $ s( x_i ) = f( x_i ) $ pour tout $ i $, alors nous allons imposer les conditions aux bords suivantes\n",
"$$\n",
"s'_0( a ) = f'( a ), \\quad s'_{N-1}(b) = f'( b ).\n",
"$$\n",
"Ces conditions nous donnent donc les valeurs des pentes $ p_0 $ et $ p_N $: $ p_0 = f'( a ) $, $ p_N = f'( b ) $. Etant donné les valeurs de $ p_0 $ et $ p_N $ on peur résoudre le système (2) pour trouver les valeurs $ p_1, p_2, \\ldots, p_{N-1} $."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Question 1.** Proposer une fonction `M` qui prend en argument un tableau `x` contenant les valeurs $ x_0, x_1, \\ldots, x_{N} $ et qui retourne la matrice du système (2). On essayera d'eviter l'utilisation de boucle. Pour construire une matrice tridiagonale on pourra utiliser la commande `diag` du module `numpy`. Testez votre fonction sur un vecteur `x` contenant peu de points."
]
},
{
"cell_type": "code",
"execution_count": 194,
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[4. 1. 0.]\n",
" [1. 4. 1.]\n",
" [0. 1. 4.]]\n"
]
}
],
"source": [
"def M(x):\n",
" \"\"\"\n",
" Retourne la matrice du système (2)\n",
" \n",
" Parameters\n",
" ----------\n",
" \n",
" x: ndarray\n",
" vecteurs contenant les valeurs [x0, x1, ..., xN]\n",
" \n",
" Returns\n",
" -------\n",
" \n",
" out: ndarray\n",
" matrice du système (2)\n",
" \"\"\"\n",
" h = x[1:] - x[:-1] # x[i+1] - x[i]\n",
" return np.diag(2*(1/h[:-1] + 1/h[1:])) + np.diag(1/h[1:-1], k=-1) + np.diag(1/h[1:-1], k=1)\n",
" \n",
"# Test\n",
"print(M(np.array([0, 1, 2, 3, 4])))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Question 2.** Proposer une fonction `sprime` qui prend en argument deux tableaux `x` et `y` de meme taille $ N + 1 $ et deux réels `p0` et `pN` et qui retourne un vecteur de taille $ N - 1 $ des valeurs $ p_1, p_2, \\ldots, p_{N-1} $ solution du système (2). On essayera d'eviter l'utilisation de boucle. Pour résoudre un système linéaire on pourra se servir de la commande `solve` du module `numpy.linalg`."
]
},
{
"cell_type": "code",
"execution_count": 195,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def sprime(x, y, p0, pN):\n",
" \"\"\"\n",
" Retourne la solution du système (2)\n",
" \n",
" Parameters\n",
" ----------\n",
" \n",
" x: ndarray\n",
" vecteurs contenant les valeurs [x0, x1, ..., xN]\n",
" y: ndarray\n",
" vecteurs contenant les valeurs [y0, y1, ..., yN]\n",
" p0: int\n",
" première valeur du vecteur p\n",
" pN: int\n",
" N-ième valeur du vecteur p\n",
" \n",
" Returns\n",
" -------\n",
" \n",
" out: ndarray\n",
" solution du système (2)\n",
" \"\"\"\n",
" h = x[1:] - x[:-1]\n",
" delta_y = (y[1:] - y[:-1]) / h\n",
" c = 3 * (delta_y[1:]/h[1:] + delta_y[:-1]/h[:-1])\n",
" c[0] -= p0/h[0]\n",
" c[-1] -= pN/h[-1]\n",
" return np.linalg.solve(M(x), c)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Nous nous proposons de construire une interpolation par spline cubique de la fonction $f$ suivante:\n",
"$$\n",
"f( x ) = \\frac{ 1 }{ 1 + x^2 }. \n",
"$$\n",
"On va considérer cette fonction sur l'intervalle $ [ -5, 5 ] $."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Question 3.** \n",
"> 1. Définir la fonction `f` et sa dérivée `fprime`\n",
"> 2. Tracer dans une fenetre graphique le graphe de la dérivée de $ f $ sur $ [-5,5] $. Pour tester la fonction `sprime` definir un vecteur `x` de $ N+1 $ points équirepartis entre $ a = -5 $ et $ b =5 $ (on peut prendre $ N = 20 $, par exemple) et construire le vecteur de pentes `p`. Tracer les pentes `p` en fonction de `x` à l'aide de la commande `ax.scatter` *dans la meme fenetre graphique*. Vérifier que les valeurs $p_0, p_1, \\ldots, p_N$ fournissent une bonne approximation de la dérivée de $ f $. On peut essayer d'obtenir une figure qui ressemble à celle-ci:\n",
"<div>\n",
"<img src=\"sprime.png\" width=\"500\"/>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 196,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Les pentes de la spline cubique')"
]
},
"execution_count": 196,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 600x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def f(x):\n",
" \"\"\"\n",
" Retourne la fonction f évaluée aux points x\n",
" \n",
" Parameters\n",
" ----------\n",
" \n",
" x: ndarray\n",
" vecteurs contenant les valeurs [x0, x1, ..., xN]\n",
" \n",
" Returns\n",
" -------\n",
" \n",
" out: ndarray\n",
" Valeur de la fonction f aux points x\n",
" \"\"\"\n",
" return 1 / (1 + x**2)\n",
"\n",
"def fprime(x):\n",
" \"\"\"\n",
" Retourne la fonction dérivée de f évaluée aux points x\n",
" \n",
" Parameters\n",
" ----------\n",
" \n",
" x: ndarray\n",
" vecteurs contenant les valeurs [x0, x1, ..., xN]\n",
" \n",
" Returns\n",
" -------\n",
" \n",
" out: ndarray\n",
" Valeur de la fonction dérivée de f aux points x\n",
" \"\"\"\n",
" return -2*x/((1+x**2)**2)\n",
"\n",
"# Paramètres \n",
"xx = np.linspace(-5, 5, 200)\n",
"x = np.linspace(-5, 5, 21)\n",
"pi = sprime(x, f(x), fprime(-5), fprime(5))\n",
"\n",
"# Graphique\n",
"fig, ax = plt.subplots(figsize=(6, 6))\n",
"ax.plot(xx, fprime(xx), label=f'$f\\'$', color='red')\n",
"ax.scatter(x[1:-1], pi, label=f'$p_i$')\n",
"ax.legend()\n",
"ax.set_xlabel(f'$x$')\n",
"ax.set_ylabel(f'$f(x)$')\n",
"ax.set_title('Les pentes de la spline cubique')"
]
},
{
"cell_type": "markdown",
"metadata": {
"jp-MarkdownHeadingCollapsed": true,
"tags": []
},
"source": [
"#### Après avoir determiné les pentes $ p_0, p_1, \\ldots, p_N $ nous allons trouver les expressions explicites pour les polynomes cubiques $ s_i $. Nous supposons que les polynomes cubiques $ s_i $ sont donnés par la formule\n",
"\n",
"$$\n",
"s_i( x ) = a_i + b_i ( x - x_i ) + c_i ( x - x_i )^2 + d_i( x - x_i )^3, \\quad i = 0, 1, \\ldots, N-1.\n",
"\\tag{3}\n",
"$$\n",
"\n",
"**Question 4.** Montrer que si $ s_i $ vérifie (1), alors les coéficients $ a_i, b_i, c_i, d_i $ sont donnés par les formules suivantes pour $ i = 0, 1, \\ldots, N-1 $ :\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"& a_i = y_i, \\\\\n",
"& b_i = p_i, \\\\\n",
"& c_i = \\frac{ 3 }{ h_i } \\delta y[ x_{ i + 1 }, x_i ] - \\frac{ p_{ i + 1 } + 2 p_i }{ h_i } \\\\\n",
"& d_i = \\frac{ 1 }{ h_{i}^2 }( p_{i+1} + p_{ i } ) - \\frac{ 2 }{ h_{i}^2 } \\delta y[ x_{i+1}, x_{i} ].\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Question 5.** Programmer une fonction `splines` qui prend en argument un `ndarray` `x` et un `ndarray` `y` de meme taille $ N + 1 $ et deux réels `p0` et `pN` et qui retourne un tableau `S` de taille $ ( N, 4 ) $ tel que la $i$-ème ligne de $ S $ contient les valeurs $ a_i, b_i, c_i, d_i $. (On essayera d'éviter l'utilisation de boucle.)"
]
},
{
"cell_type": "code",
"execution_count": 197,
"metadata": {},
"outputs": [],
"source": [
"def splines(x, y, p0, pN):\n",
" \"\"\"\n",
" Retourne la matrice S de taille (4, N)\n",
" \n",
" Parameters\n",
" ----------\n",
" \n",
" x: ndarray\n",
" vecteurs contenant les valeurs [x0, x1, ..., xN]\n",
" y: ndarray\n",
" vecteurs contenant les valeurs [x0, x1, ..., xN]\n",
" p0: int\n",
" première valeur du vecteur p\n",
" pN: int\n",
" N-ième valeur du vecteur p\n",
" \n",
" Returns\n",
" -------\n",
" \n",
" out: ndarray\n",
" Matrice S de taille (4, N) tel que la i-ième ligne contient les valeurs a_i, b_i, c_i et d_i\n",
" \"\"\"\n",
" h = x[1:] - x[:-1]\n",
" delta_y = (y[1:] - y[:-1]) / h\n",
" \n",
" a = y\n",
" b = np.concatenate((np.array([p0]), sprime(x, y, p0, pN), np.array([pN])))\n",
" c = 3/h * delta_y - (b[1:] + 2*b[:-1]) / h\n",
" d = 1/h**2 * (b[1:] + b[:-1]) - 2/h**2 * delta_y\n",
" return np.transpose([a[:-1], b[:-1], c, d])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Question 6.** Dans cette question nous allons tester la fonction `splines`\n",
"> 1. Créer un vecteur `x` de $ N + 1 $ points equirepartis entre $a = -5 $ et $ b = 5 $ et un vecteur `y` de $ N + 1 $ points aléatoires entre $ 0 $ et $ 1 $ (on pourra prendre $ N = 5 $, par exemple). \n",
"> 2. Construire la spline cubique scellée $ s $ d'interpolation aux points $ (x_i, y_i) $, $ i = 0, 1, \\ldots, N$ à l'aide de la fonction `splines`. On pourra prendre $ p_0 = p_N = 0 $ comme valeurs de pente aux bords.\n",
"> 3. Tracer le graphe de $ s $ sur $ [ a, b ] $. Ajouter le nuage de points $ (x_i, y_i) $, $ i = 0, 1, \\ldots, N $. Vérifier que le graphe de $ s $ passe par les points $ ( x_i, y_i ) $.\n",
"\n",
"Pour tracer le graphe de la spline construite à l'aide de la fonction `splines` pour des points *équirepartis* `x` on pourra utiliser la fonction `spline_eval` définie ci-dessous. Elle prend en argument un vecteur `x` des noeuds de la spline (de taille $N+1$) *équirepartis*, un vecteur `xx` des points où on veut evaluer les valeurs de la spline et un tableau `S` de taille $ (N, 4) $ tel que la $i$-ème ligne de $ S $ contient les coefficients $ a_i, b_i, c_i, d_i $ de la resctriction de la spline à l'intervalle $ [ x[ i ], x[ i + 1 ] ] $ comme définis dans la formule (3). Elle retourne le tableau des valeurs de la spline aux points de `xx`."
]
},
{
"cell_type": "code",
"execution_count": 198,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def spline_eval( x, xx, S ):\n",
" \"\"\"\n",
" Evalue une spline définie par des noeuds équirepartis\n",
" \n",
" Parameters\n",
" ----------\n",
" \n",
" x: ndarray\n",
" noeuds définissant la spline\n",
" \n",
" xx: ndarray\n",
" abscisses des points d'évaluation\n",
" \n",
" S: ndarray\n",
" de taille (x.size-1, 4)\n",
" tableau dont la i-ème ligne contient les coéficients du polynome cubique qui est la restriction\n",
" de la spline à l'intervalle [x_i, x_{i+1}]\n",
" \n",
" Returns\n",
" -------\n",
" \n",
" ndarray\n",
" ordonnées des points d'évaluation\n",
" \"\"\"\n",
" ind = ( np.floor( ( xx - x[ 0 ] ) / ( x[ 1 ] - x[ 0 ] ) ) ).astype( int )\n",
" ind = np.where( ind == x.size-1, ind - 1 , ind )\n",
" yy = S[ ind, 0 ] + S[ ind, 1 ] * ( xx - x[ ind ] ) + \\\n",
" S[ ind, 2 ] * ( xx - x[ ind ] )**2 + S[ ind, 3 ] * ( xx - x[ ind ] )**3\n",
" return yy"
]
},
{
"cell_type": "code",
"execution_count": 210,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Evaluation de la spline cubique')"
]
},
"execution_count": 210,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 600x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Paramètres \n",
"x = np.linspace(-5, 5, 6)\n",
"y = np.random.rand(5+1)\n",
"xx = np.linspace(-5, 5, 200)\n",
"s = splines(x, y, 0, 0)\n",
"s_eval = spline_eval(x, xx, s)\n",
"\n",
"# Graphique\n",
"fig, ax = plt.subplots(figsize=(6, 6))\n",
"ax.plot(xx, s_eval, label='spline cubique interpolateur', color='red')\n",
"ax.scatter(x, y, label=f'$(x_i, y_i)$')\n",
"ax.legend()\n",
"ax.set_xlabel(f'$x$')\n",
"ax.set_ylabel(f'$f(x)$')\n",
"ax.set_title('Evaluation de la spline cubique')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Question 7.** Pour chacune des valeurs de $ N = 4, 9, 19 $ créer un vecteur `x` de $ N + 1 $ points équirepartis entre $ a $ et $ b $. Tracer dans la meme fenetre graphique la fonction $ f $ et ses splines cubiques interpolateurs aux noeuds définis par le vecteur `x` pour des différentes valeurs de $ N $. Commenter les résultats obtenus. Comparer avec les résultats de la Question 3 du TP05."
]
},
{
"cell_type": "code",
"execution_count": 205,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Evaluation de la spline cubique')"
]
},
"execution_count": 205,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1500x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Paramètres \n",
"a, b = -5, 5\n",
"N_list = [4, 9, 19]\n",
"\n",
"# Graphique\n",
"fig, ax = plt.subplots(figsize=(15, 6))\n",
"\n",
"for N in N_list:\n",
" x = np.linspace(a, b, N+1)\n",
" xx = np.linspace(a, b, 200)\n",
" s = splines(x, f(x), 0, 0)\n",
" s_eval = spline_eval(x, xx, s)\n",
" ax.plot(xx, s_eval, label=f'Spline cubique interpolateur pour N={N}')\n",
" ax.scatter(x, f(x), label=f'f(x) pour N={N}')\n",
" \n",
"ax.legend()\n",
"ax.set_xlabel(f'$x$')\n",
"ax.set_ylabel(f'$f(x)$')\n",
"ax.set_title('Evaluation de la spline cubique')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.10.8"
}
},
"nbformat": 4,
"nbformat_minor": 4
}