feat(plotnine): implement bode-basic (#5159)

## Implementation: `bode-basic` - plotnine

Implements the **plotnine** version of `bode-basic`.

**File:** `plots/bode-basic/implementations/plotnine.py`

**Parent Issue:** #4411

---
:robot: *[impl-generate
workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/23388395508)*

---------

Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

Author: github-actions[bot]

plots/bode-basic/implementations/plotnine.py

@@ -0,0 +1,199 @@
+""" pyplots.ai
+bode-basic: Bode Plot for Frequency Response
+Library: plotnine 0.15.3 | Python 3.14.3
+Quality: 81/100 | Created: 2026-03-21
+"""
+
+import numpy as np
+import pandas as pd
+from plotnine import (
+    aes,
+    element_line,
+    element_rect,
+    element_text,
+    facet_wrap,
+    geom_hline,
+    geom_line,
+    geom_point,
+    geom_segment,
+    geom_text,
+    geom_vline,
+    ggplot,
+    labs,
+    scale_x_log10,
+    scale_y_continuous,
+    theme,
+    theme_minimal,
+)
+
+
+# Data - Third-order open-loop transfer function:
+# G(s) = 5 / [(s+1)(0.5s+1)(0.2s+1)]
+# Poles at s = -1, -2, -5 — stable system with clear gain and phase margins
+frequency_hz = np.logspace(-1.5, 1.5, 600)
+omega = 2 * np.pi * frequency_hz
+jw = 1j * omega
+G = 5.0 / ((jw + 1) * (0.5 * jw + 1) * (0.2 * jw + 1))
+
+magnitude_db = 20 * np.log10(np.abs(G))
+phase_deg = np.degrees(np.unwrap(np.angle(G)))
+
+# Gain crossover: where magnitude crosses 0 dB
+gc_idx = np.argmin(np.abs(magnitude_db))
+gc_freq = frequency_hz[gc_idx]
+phase_at_gc = phase_deg[gc_idx]
+phase_margin = 180 + phase_at_gc
+
+# Phase crossover: where phase crosses -180 degrees
+pc_idx = np.argmin(np.abs(phase_deg + 180))
+pc_freq = frequency_hz[pc_idx]
+mag_at_pc = magnitude_db[pc_idx]
+gain_margin = -mag_at_pc
+
+# Limit magnitude display to relevant range (above -50 dB) to avoid
+# compressing the interesting region around 0 dB
+freq_mag = frequency_hz[magnitude_db >= -50]
+mag_display = magnitude_db[magnitude_db >= -50]
+
+# Panel categories
+panels = ["Magnitude (dB)", "Phase (degrees)"]
+panel_cat = pd.CategoricalDtype(categories=panels, ordered=True)
+
+# Long-format data for faceted plot
+df = pd.concat(
+    [
+        pd.DataFrame({"freq": freq_mag, "value": mag_display, "panel": "Magnitude (dB)"}),
+        pd.DataFrame({"freq": frequency_hz, "value": phase_deg, "panel": "Phase (degrees)"}),
+    ],
+    ignore_index=True,
+)
+df["panel"] = df["panel"].astype(panel_cat)
+
+# Reference lines: 0 dB and -180°
+ref_lines = pd.DataFrame({"panel": pd.Categorical(panels, dtype=panel_cat), "yintercept": [0.0, -180.0]})
+
+# Margin segments and crossover markers
+gm_seg = pd.DataFrame(
+    {"x": [pc_freq], "ymin": [mag_at_pc], "ymax": [0.0], "panel": pd.Categorical(["Magnitude (dB)"], dtype=panel_cat)}
+)
+pm_seg = pd.DataFrame(
+    {
+        "x": [gc_freq],
+        "ymin": [-180.0],
+        "ymax": [phase_at_gc],
+        "panel": pd.Categorical(["Phase (degrees)"], dtype=panel_cat),
+    }
+)
+
+markers = pd.DataFrame(
+    {
+        "freq": [gc_freq, gc_freq, pc_freq, pc_freq],
+        "value": [0.0, phase_at_gc, mag_at_pc, -180.0],
+        "panel": pd.Categorical(
+            ["Magnitude (dB)", "Phase (degrees)", "Magnitude (dB)", "Phase (degrees)"], dtype=panel_cat
+        ),
+        "mtype": ["gc", "gc", "pc", "pc"],
+    }
+)
+
+# Annotation labels positioned to the right of margin segments
+gm_label = pd.DataFrame(
+    {
+        "freq": [pc_freq * 2.0],
+        "value": [mag_at_pc / 2],
+        "label": [f"GM = {gain_margin:.1f} dB"],
+        "panel": pd.Categorical(["Magnitude (dB)"], dtype=panel_cat),
+    }
+)
+pm_label = pd.DataFrame(
+    {
+        "freq": [gc_freq * 2.0],
+        "value": [(phase_at_gc - 180) / 2],
+        "label": [f"PM = {phase_margin:.0f}°"],
+        "panel": pd.Categorical(["Phase (degrees)"], dtype=panel_cat),
+    }
+)
+
+# Colors
+PYTHON_BLUE = "#306998"
+GM_COLOR = "#D35400"
+PM_COLOR = "#7D3C98"
+DARK_TEXT = "#1A237E"
+MID_TEXT = "#37474F"
+LIGHT_TEXT = "#546E7A"
+
+# Subtle vertical guides at crossover frequencies
+guides = pd.DataFrame(
+    {
+        "xintercept": [gc_freq, gc_freq, pc_freq, pc_freq],
+        "panel": pd.Categorical(
+            ["Magnitude (dB)", "Phase (degrees)", "Magnitude (dB)", "Phase (degrees)"], dtype=panel_cat
+        ),
+    }
+)
+
+# Plot — landscape format for optimal log-frequency axis display
+plot = (
+    ggplot(df, aes(x="freq", y="value"))
+    + geom_line(size=2.5, color=PYTHON_BLUE, alpha=0.92)
+    # Reference lines
+    + geom_hline(ref_lines, aes(yintercept="yintercept"), linetype="dashed", color="#90A4AE", size=0.8)
+    # Crossover guide lines
+    + geom_vline(guides, aes(xintercept="xintercept"), linetype="dotted", color="#B0BEC5", size=0.5)
+    # Gain margin segment
+    + geom_segment(gm_seg, aes(x="x", xend="x", y="ymin", yend="ymax"), color=GM_COLOR, size=5.0, alpha=0.9)
+    # Phase margin segment
+    + geom_segment(pm_seg, aes(x="x", xend="x", y="ymin", yend="ymax"), color=PM_COLOR, size=5.0, alpha=0.9)
+    # Gain crossover markers (purple circles)
+    + geom_point(
+        markers[markers["mtype"] == "gc"],
+        aes(x="freq", y="value"),
+        color=PM_COLOR,
+        fill=PM_COLOR,
+        size=7,
+        shape="o",
+        stroke=2.5,
+    )
+    # Phase crossover markers (orange squares)
+    + geom_point(
+        markers[markers["mtype"] == "pc"],
+        aes(x="freq", y="value"),
+        color=GM_COLOR,
+        fill=GM_COLOR,
+        size=7,
+        shape="s",
+        stroke=2.5,
+    )
+    # Annotations
+    + geom_text(
+        gm_label, aes(x="freq", y="value", label="label"), color=GM_COLOR, size=18, fontweight="bold", ha="left"
+    )
+    + geom_text(
+        pm_label, aes(x="freq", y="value", label="label"), color=PM_COLOR, size=18, fontweight="bold", ha="left"
+    )
+    + facet_wrap("~panel", ncol=1, scales="free_y")
+    + scale_x_log10(
+        breaks=[0.1, 1, 10], labels=["0.1", "1", "10"], minor_breaks=[0.03, 0.05, 0.2, 0.3, 0.5, 2, 3, 5, 20, 30]
+    )
+    + scale_y_continuous(labels=lambda lst: [f"{v:.0f}" for v in lst])
+    + labs(x="Frequency (Hz)", y="", title="bode-basic · plotnine · pyplots.ai")
+    + theme_minimal()
+    + theme(
+        figure_size=(16, 9),
+        text=element_text(size=14, color=MID_TEXT),
+        axis_title=element_text(size=20, color=MID_TEXT),
+        axis_text=element_text(size=16, color=LIGHT_TEXT),
+        axis_ticks=element_line(color="#CFD8DC", size=0.4),
+        plot_title=element_text(size=24, weight="bold", ha="center", color=DARK_TEXT),
+        strip_text=element_text(size=20, weight="bold", color=DARK_TEXT),
+        strip_background=element_rect(fill="#E8EAF6", color="none"),
+        panel_grid_major=element_line(color="#E0E0E0", size=0.25),
+        panel_grid_minor=element_line(color="#F5F5F5", size=0.12),
+        panel_spacing_y=0.35,
+        plot_background=element_rect(fill="#FAFAFA", color="#FAFAFA"),
+        panel_background=element_rect(fill="white", color="none"),
+    )
+)
+
+# Save
+plot.save("plot.png", dpi=300, verbose=False)