Serie 5 Aufgabe 11 hyperbolishe Funktionen plotten. Skript plottet sinh und cosh in einem Plot und tanh und coth in einem zweiten.

reelle_funktionen/serie_5_11.py

@@ -0,0 +1,101 @@
+# %%
+# Import required libraries
+import numpy as np  # Numerical operations and array handling
+import matplotlib.pyplot as plt  # Plotting library
+
+# Global plotting parameters
+fig = 0
+lw = 3
+x_0 = -8.0
+x_E = 8.0
+N = 257
+
+# Named color palette mapping descriptive names to hex codes
+colors = {
+    "deep blue": "#1f77b4",
+    "orange": "#ff7f0e",
+    "green": "#2ca02c",
+    "red": "#d62728",
+}
+
+# Each entry describes one figure: a list of curves to overlay,
+# plus the y-axis limits for readability
+figures = [
+    {
+        "curves": [
+            {
+                "f": lambda x: np.sinh(x),
+                "label": r"$f(x) = \sinh(x)$",
+                "color": colors["deep blue"],
+            },
+            {
+                "f": lambda x: np.cosh(x),
+                "label": r"$f(x) = \cosh(x)$",
+                "color": colors["orange"],
+            },
+        ],
+        "y_lim": (-3, 6),
+    },
+    {
+        "curves": [
+            {
+                "f": lambda x: np.tanh(x),
+                "label": r"$f(x) = \tanh(x)$",
+                "color": colors["red"],
+            },
+            {
+                "f": lambda x: 1 / np.tanh(x),
+                "label": r"$f(x) = \coth(x)$",
+                "color": colors["green"],
+            },
+        ],
+        "y_lim": (-4, 4),
+    },
+]
+
+# Generate the shared x-axis data once
+x_data = np.linspace(x_0, x_E, N)
+
+# Loop over each figure definition
+for figure in figures:
+    # Create a new figure
+    fh = plt.figure(fig)
+    fig += 1
+
+    # Retrieve the y-limits for this figure
+    y_lim = figure["y_lim"]
+
+    # Plot each curve in the current figure
+    for curve in figure["curves"]:
+        # Evaluate the function over the shared x-range
+        y_data = curve["f"](x_data)
+
+        # Mask values outside the visible y-range with NaN.
+        # This both hides non-finite values (inf/nan from division by
+        # zero) and breaks the line at vertical asymptotes, so matplotlib
+        # never connects a point from one branch to the next.
+        y_data = np.where((y_data > y_lim[0]) & (y_data < y_lim[1]), y_data, np.nan)
+
+        plt.plot(
+            x_data,
+            y_data,
+            linewidth=lw,
+            color=curve["color"],
+            label=curve["label"],
+        )
+
+    # Set axis labels
+    plt.xlabel(r"$x$")
+    plt.ylabel(r"$y$")
+
+    # Display a grid for readability
+    plt.grid(visible=True)
+
+    # Set y-limits to keep all curves visible
+    plt.ylim(y_lim)
+
+    # Add a legend showing the function expression in LaTeX
+    plt.legend()
+
+# Display all figures
+plt.show()