Refactor error messages and function signatures across multiple notebooks for clarity and consistency

- Updated error messages in Gauss method and numerical methods to use variables for better readability.
- Added return type hints to function signatures in various notebooks to improve code documentation.
- Corrected minor grammatical issues in docstrings for better clarity.
- Adjusted print statements and list concatenations for improved output formatting.
- Enhanced plotting functions to ensure consistent figure handling.

M1/Numerical Methods/TP2_DANJOU_Arthur.ipynb

@@ -46,12 +46,12 @@
    "outputs": [],
    "source": [
     "def S(t, S0, mu, sigma, W):\n",
-    "    \"\"\"Solution exacte de l'EDS de Black-Scholes\"\"\"\n",
+    "    \"\"\"Solution exacte de l'EDS de Black-Scholes.\"\"\"\n",
     "    return S0 * np.exp((mu - 0.5 * sigma**2) * t + sigma * W)\n",
     "\n",
     "\n",
     "def euler_maruyama(mu, sigma, T, N, X0=0.0):\n",
-    "    \"\"\"Simulation d'une EDS de Black-Scholes par la méthode d'Euler-Maruyama\n",
+    "    \"\"\"Simulation d'une EDS de Black-Scholes par la méthode d'Euler-Maruyama.\n",
     "\n",
     "    Paramètres :\n",
     "        mu (float) : drift\n",
@@ -80,8 +80,8 @@
     "    return t, X\n",
     "\n",
     "\n",
-    "def plot_brownien(t, X, B=None):\n",
-    "    \"\"\"Plot la simulation d'Euler-Maruyama\n",
+    "def plot_brownien(t, X, B=None) -> None:\n",
+    "    \"\"\"Plot la simulation d'Euler-Maruyama.\n",
     "\n",
     "    Paramètres :\n",
     "        t (array-like) : tableau des temps\n",
@@ -164,8 +164,8 @@
     "np.random.seed(333)\n",
     "\n",
     "\n",
-    "def plot_convergence(S0, mu, sigma, T):\n",
-    "    \"\"\"Plot la convergence du schéma d'Euler-Maruyama\n",
+    "def plot_convergence(S0, mu, sigma, T) -> None:\n",
+    "    \"\"\"Plot la convergence du schéma d'Euler-Maruyama.\n",
     "\n",
     "    Paramètres :\n",
     "        S0 (int) : valeur initiale\n",
@@ -271,7 +271,7 @@
     "\n",
     "def is_barrier_breached(X, B):\n",
     "    \"\"\"Renvoie True si la barrière est franchie, False sinon\n",
-    "    La barrière est franchie si X >= B\n",
+    "    La barrière est franchie si X >= B.\n",
     "\n",
     "    Paramètres:\n",
     "        X (array-like): Trajectoire des valeurs\n",
@@ -297,8 +297,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "def plot_browniens(trajectories, B):\n",
-    "    \"\"\"Trace les trajectoires de Brownien et la barrière\n",
+    "def plot_browniens(trajectories, B) -> None:\n",
+    "    \"\"\"Trace les trajectoires de Brownien et la barrière.\n",
     "\n",
     "    Paramètres:\n",
     "        trajectories (list of tuples): Liste des trajectoires avec le temps et les valeurs\n",
@@ -451,7 +451,7 @@
     "np.random.seed(333)\n",
     "\n",
     "\n",
-    "def plot_payoff_errors():\n",
+    "def plot_payoff_errors() -> None:\n",
     "    \"\"\"Trace l'erreur de convergence du payoff actualisé en fonction de N.\"\"\"\n",
     "    errors = []\n",
     "\n",