Refactor code for improved readability and consistency across multiple Jupyter notebooks

- Added missing commas in various print statements and function calls for better syntax.
- Reformatted code to enhance clarity, including breaking long lines and aligning parameters.
- Updated function signatures to use float type for sigma parameters instead of int for better precision.
- Cleaned up comments and documentation strings for clarity and consistency.
- Ensured consistent formatting in plotting functions and data handling.

L3/Calculs Numériques/DM1.ipynb

@@ -113,9 +113,7 @@
     "\n",
     "\n",
     "def C(t):\n",
-    "    \"\"\"\n",
-    "    Fonction retournant la solution exacte du problème au temps t\n",
-    "    \"\"\"\n",
+    "    \"\"\"Fonction retournant la solution exacte du problème au temps t\"\"\"\n",
     "    return K_star + K / (1 + (K / K0 - 1) * np.exp(-r * (t - t_fl)))\n",
     "\n",
     "\n",
@@ -137,9 +135,7 @@
     "\n",
     "\n",
     "def dN(N, t, C_sol):\n",
-    "    \"\"\"\n",
-    "    Fonction calculant la dérivée de la solution approchée du problème à l'instant t dépendant de N(t) et de C(t)\n",
-    "    \"\"\"\n",
+    "    \"\"\"Fonction calculant la dérivée de la solution approchée du problème à l'instant t dépendant de N(t) et de C(t)\"\"\"\n",
     "    return r_N * N * (1 - N / C_sol(t))\n",
     "\n",
     "\n",
@@ -239,13 +235,19 @@
     "# On crée une figure à trois graphiques\n",
     "fig = plt.figure(figsize=(12, 6))\n",
     "ax = fig.add_subplot(\n",
-    "    1, 2, 2\n",
+    "    1,\n",
+    "    2,\n",
+    "    2,\n",
     ")  # subplot pour le champ de vecteurs et le graphe sardines vs requins\n",
     "axr = fig.add_subplot(\n",
-    "    2, 2, 1\n",
+    "    2,\n",
+    "    2,\n",
+    "    1,\n",
     ")  # subplot pour le graphe du nombre de requins en fonction du temps\n",
     "axs = fig.add_subplot(\n",
-    "    2, 2, 3\n",
+    "    2,\n",
+    "    2,\n",
+    "    3,\n",
     ")  # subplot pour le graphe du nombre de sardines en fonction du temps\n",
     "ax.quiver(sardines, requins, fsardines / n_sndmb, frequins / n_sndmb)\n",
     "\n",
@@ -317,12 +319,10 @@
    "outputs": [],
    "source": [
     "def crank_nicolson(y0, T, N, r):\n",
-    "    \"\"\"\n",
-    "    schéma de Crank-Nicolson pour le modèle de Malthus\n",
+    "    \"\"\"schéma de Crank-Nicolson pour le modèle de Malthus\n",
     "\n",
     "    Parameters\n",
     "    ----------\n",
-    "\n",
     "    y0: float\n",
     "        donnée initiale\n",
     "    T: float\n",
@@ -334,13 +334,12 @@
     "\n",
     "    Returns\n",
     "    -------\n",
-    "\n",
     "    t: ndarray\n",
     "        les instants où la solution approchée est calculée\n",
     "    y: ndarray\n",
     "        les valeurs de la solution approchée par le theta-schema\n",
-    "    \"\"\"\n",
     "\n",
+    "    \"\"\"\n",
     "    dt = T / N\n",
     "    t = np.zeros(N + 1)\n",
     "    y = np.zeros(N + 1)\n",
@@ -357,12 +356,10 @@
     "\n",
     "\n",
     "def euler_explicit(y0, T, N, r):\n",
-    "    \"\"\"\n",
-    "    schéma de d'Euler pour le modèle de Malthus\n",
+    "    \"\"\"schéma de d'Euler pour le modèle de Malthus\n",
     "\n",
     "    Parameters\n",
     "    ----------\n",
-    "\n",
     "    y0: float\n",
     "        donnée initiale\n",
     "    T: float\n",
@@ -374,11 +371,11 @@
     "\n",
     "    Returns\n",
     "    -------\n",
-    "\n",
     "    t: ndarray\n",
     "        les instants où la solution approchée est calculée\n",
     "    y: ndarray\n",
     "        les valeurs de la solution approchée par le theta-schema\n",
+    "\n",
     "    \"\"\"\n",
     "    dt = T / N\n",
     "    t = np.zeros(N + 1)\n",
@@ -396,9 +393,7 @@
     "\n",
     "\n",
     "def solution_exacte(t):\n",
-    "    \"\"\"\n",
-    "    Fonction calculant la solution exacte du modèle de Malthus à l'instant t\n",
-    "    \"\"\"\n",
+    "    \"\"\"Fonction calculant la solution exacte du modèle de Malthus à l'instant t\"\"\"\n",
     "    return y0 * np.exp(r * t)"
    ]
   },
@@ -462,7 +457,10 @@
     "ax = fig.add_subplot(1, 2, 2)\n",
     "for n in liste_N:\n",
     "    t, y = crank_nicolson(\n",
-    "        y0, T, n, r\n",
+    "        y0,\n",
+    "        T,\n",
+    "        n,\n",
+    "        r,\n",
     "    )  # On calcule la fonction Crank-Nicolson pour chaque n\n",
     "    ax.scatter(t, y, label=f\"Solution approchée pour N={n}\")\n",
     "ax.plot(t_exact, solution_exacte(t_exact), label=\"Solution exacte\")\n",