feat(matplotlib): implement elbow-curve (#2345)

## Implementation: `elbow-curve` - matplotlib

Implements the **matplotlib** version of `elbow-curve`.

**File:** `plots/elbow-curve/implementations/matplotlib.py`

---
:robot: *[impl-generate
workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/20528202012)*

---------

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/elbow-curve/implementations/matplotlib.py

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+""" pyplots.ai
+elbow-curve: Elbow Curve for K-Means Clustering
+Library: matplotlib 3.10.8 | Python 3.13.11
+Quality: 92/100 | Created: 2025-12-26
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+# Simulate realistic inertia values for K-means elbow curve
+# Based on typical clustering behavior: sharp decline followed by gradual decrease
+np.random.seed(42)
+k_values = np.arange(1, 11)
+
+# Generate realistic inertia decay pattern
+# Inertia typically follows exponential decay with the "elbow" around k=4
+base_inertia = 5000
+inertias = []
+for k in k_values:
+    # Exponential decay with elbow effect at k=4
+    if k <= 4:
+        inertia = base_inertia * np.exp(-0.35 * (k - 1))
+    else:
+        inertia = base_inertia * np.exp(-0.35 * 3) * np.exp(-0.15 * (k - 4))
+    # Add small random noise for realism
+    inertia += np.random.uniform(-50, 50)
+    inertias.append(max(inertia, 100))
+
+inertias = np.array(inertias)
+
+# Identify the elbow point (k=4 is the optimal cluster count)
+elbow_k = 4
+elbow_inertia = inertias[elbow_k - 1]
+
+# Create plot (4800x2700 px at 300 dpi = 16x9 inches)
+fig, ax = plt.subplots(figsize=(16, 9))
+
+# Plot the elbow curve
+ax.plot(
+    k_values,
+    inertias,
+    color="#306998",
+    linewidth=3,
+    marker="o",
+    markersize=12,
+    markerfacecolor="#FFD43B",
+    markeredgecolor="#306998",
+    markeredgewidth=2,
+    label="Inertia",
+)
+
+# Highlight the elbow point
+ax.scatter([elbow_k], [elbow_inertia], s=400, color="#FFD43B", edgecolors="#306998", linewidths=3, zorder=5)
+ax.annotate(
+    f"Elbow Point\n(k={elbow_k})",
+    xy=(elbow_k, elbow_inertia),
+    xytext=(elbow_k + 1.8, elbow_inertia + 600),
+    fontsize=18,
+    fontweight="bold",
+    color="#306998",
+    arrowprops={"arrowstyle": "->", "color": "#306998", "lw": 2.5},
+)
+
+# Labels and styling
+ax.set_xlabel("Number of Clusters (k)", fontsize=20)
+ax.set_ylabel("Inertia (Within-Cluster Sum of Squares)", fontsize=20)
+ax.set_title("elbow-curve · matplotlib · pyplots.ai", fontsize=24)
+ax.tick_params(axis="both", labelsize=16)
+ax.set_xticks(k_values)
+ax.grid(True, alpha=0.3, linestyle="--")
+
+# Add subtle shading to show diminishing returns region
+ax.axvspan(elbow_k, max(k_values), alpha=0.1, color="#306998", label="Diminishing Returns")
+
+plt.tight_layout()
+plt.savefig("plot.png", dpi=300, bbox_inches="tight")

plots/elbow-curve/metadata/matplotlib.yaml

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+library: matplotlib
+specification_id: elbow-curve
+created: '2025-12-26T19:36:06Z'
+updated: '2025-12-26T19:41:50Z'
+generated_by: claude-opus-4-5-20251101
+workflow_run: 20528202012
+issue: 0
+python_version: 3.13.11
+library_version: 3.10.8
+preview_url: https://storage.googleapis.com/pyplots-images/plots/elbow-curve/matplotlib/plot.png
+preview_thumb: https://storage.googleapis.com/pyplots-images/plots/elbow-curve/matplotlib/plot_thumb.png
+preview_html: null
+quality_score: 92
+review:
+  strengths:
+  - Excellent elbow curve visualization with clear elbow point identification at k=4
+  - Professional annotation with arrow pointing to the optimal cluster count
+  - Thoughtful diminishing returns shaded region adds educational value
+  - 'Color scheme (Python blue #306998 and yellow #FFD43B) is visually appealing and
+    brand-consistent'
+  - Realistic inertia decay pattern that demonstrates the typical K-means behavior
+  - Clean, readable code following KISS principles
+  weaknesses:
+  - Legend is defined but not displayed (ax.legend() call is missing), though the
+    label parameter and axvspan label are set
+  - Y-axis label could include units or clarify unitless nature of inertia