Start coding of solutions

- Implement OLS and Ridge as well as python structure
- Start with gradient descent
- Create plots for the above mentioned
- Create a basic structure for the python source
- Install pre commit hooks to check and format the code

src/plotting.py

@@ -0,0 +1,133 @@
+import matplotlib.pyplot as plt
+from matplotlib.colors import SymLogNorm
+import numpy as np
+
+FIG_WIDTH = 6
+
+
+def get_rc_params():
+    colors = ["FF220C", "70D6FF", "8AAA79", "666370", "1C1F33"]
+    rcParams = plt.rcParams
+    # Use LaTeX for rendering
+    # Setup fonts
+    rcParams["text.usetex"] = True
+    rcParams["font.family"] = "serif"
+    rcParams["font.size"] = 12
+    rcParams["axes.labelsize"] = 12
+    rcParams["axes.titlesize"] = 12
+    rcParams["legend.fontsize"] = 10
+    rcParams["xtick.labelsize"] = 10
+    rcParams["ytick.labelsize"] = 10
+    # Figure size and resolution
+    rcParams["figure.figsize"] = (FIG_WIDTH, 4)
+    rcParams["figure.dpi"] = 300
+    # Use colors from the palette
+    rcParams["axes.prop_cycle"] = plt.cycler(color=[f"#{color}" for color in colors])
+    # Grid
+    rcParams["axes.grid"] = True
+    rcParams["grid.alpha"] = 0.5
+    rcParams["grid.linestyle"] = "--"
+    # Point ticks to the inside of the axes
+    rcParams["xtick.direction"] = "in"
+    rcParams["ytick.direction"] = "in"
+    rcParams["xtick.top"] = True
+    rcParams["ytick.right"] = True
+    return rcParams
+
+
+def set_rc_params():
+    plt.rcParams.update(get_rc_params())
+
+
+set_rc_params()
+
+
+def get_figsize(rel_height: float = 2 / 3) -> tuple[float, float]:
+    """Returns a figure size tuple based on the global FIG_WIDTH and a relative height.
+    Args:
+        rel_height: The relative height of the figure compared to FIG_WIDTH.
+    Returns:
+        A tuple (width, height) for the figure size.
+    """
+    return (FIG_WIDTH, FIG_WIDTH * rel_height)
+
+
+def mse_r2_plot(
+    polynomial_degrees: np.ndarray,
+    train_mse_list: list[float],
+    mse_list: list[float],
+    train_r2_list: list[float],
+    r2_list: list[float],
+    labels: dict[str, str] | None = None,
+) -> tuple[plt.Figure, tuple[plt.Axes, plt.Axes]]:
+    std_labels = {
+        "set1": "Train Set",
+        "set2": "Test Set",
+        "xlabel": "Polynomial Degree",
+        "ylabel1": "Mean Squared Error",
+        "ylabel2": "$R^2$ Score",
+    }
+
+    if labels is None:
+        labels = std_labels
+    else:
+        for key in std_labels:
+            if key not in labels:
+                labels[key] = std_labels[key]
+
+    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=get_figsize(0.5))
+    ax1.plot(polynomial_degrees, train_mse_list, marker="o", label=labels["set1"])
+    ax1.plot(polynomial_degrees, mse_list, marker="o", label=labels["set2"])
+    ax1.legend()
+    ax1.set_xlabel(labels["xlabel"])
+    ax1.set_ylabel(labels["ylabel1"])
+
+    ax2.plot(polynomial_degrees, train_r2_list, marker="o", label=labels["set1"])
+    ax2.plot(polynomial_degrees, r2_list, marker="o", label=labels["set2"])
+    ax2.legend()
+    ax2.set_xlabel(labels["xlabel"])
+    ax2.set_ylabel(labels["ylabel2"])
+
+    fig.tight_layout()
+    return fig, (ax1, ax2)
+
+
+def parameter_plot(
+    polynomial_degrees: np.ndarray,
+    beta_OLS_list: list[np.ndarray],
+    labels: dict[str, str] | None = None,
+) -> tuple[plt.Figure, plt.Axes]:
+    std_labels = {
+        "xlabel": "Polynomial Degree of Fit",
+        "ylabel": "Coefficient Index $i$",
+        "cbar": "Coefficient Value",
+    }
+
+    if labels is None:
+        labels = std_labels
+    else:
+        for key in std_labels:
+            if key not in labels:
+                labels[key] = std_labels[key]
+
+    fig, ax = plt.subplots(figsize=get_figsize(0.5))
+    beta_OLS = np.zeros((beta_OLS_list[-1].shape[0], len(polynomial_degrees)))
+    beta_OLS[:] = np.nan
+    for i in range(len(beta_OLS_list)):
+        for j in range(len(beta_OLS_list[i])):
+            beta_OLS[j, i] = beta_OLS_list[i][j]
+    cmap = plt.get_cmap("coolwarm")
+    norm = SymLogNorm(
+        linthresh=1e-3, vmin=np.nanmin(beta_OLS), vmax=np.nanmax(beta_OLS)
+    )
+    im = ax.imshow(beta_OLS, aspect="auto", cmap=cmap, origin="lower", norm=norm)
+    cbar = fig.colorbar(im, ax=ax)
+    cbar.set_label(labels["cbar"])
+    ax.set_xlabel(labels["xlabel"])
+    ax.set_ylabel(labels["ylabel"])
+    ax.set_xticks(np.arange(0, len(polynomial_degrees), step=3))
+    ax.set_xticklabels(polynomial_degrees[::3])
+    ax.set_yticks(np.arange(0, beta_OLS.shape[0], 5))
+    ax.set_yticklabels(np.arange(1, beta_OLS.shape[0] + 1, step=5))
+    fig.tight_layout()
+    return fig, ax