Plot an idealized stability curve for illustrative purposes.

Author: njhenry

scripts/exploratory/idealized_stability_curve.py

@@ -0,0 +1,114 @@
+"""
+Idealized percent-still-unchanged curve for fixed (delta, lambda) = (0.05, 0.5).
+
+Mimics the axis and theme styling of scripts/osm_data/data_viz.py but plots
+only the analytic trend implied by the ZIE turnover model, with no observed
+data and no uncertainty band:
+
+    P(still unchanged at t) = (1 - delta) * exp(-lambda * t)
+
+with t in years.
+"""
+
+from pathlib import Path
+
+import numpy as np
+import pandas as pd
+
+import matplotlib
+matplotlib.use("Agg")  # noqa: E402
+import plotnine as gg  # noqa: E402
+
+# ----------------------------------------------------------------------------------------
+# Fixed parameters
+# ----------------------------------------------------------------------------------------
+
+DELTA = 0.05
+LAMBDA = 0.25  # per year
+YEAR_RANGE = 10
+N_POINTS = 1001
+
+OUT_PATH = Path("~/data/openpois/exploratory/idealized_stability_curve.png").expanduser()
+
+# ----------------------------------------------------------------------------------------
+# Plot construction
+# ----------------------------------------------------------------------------------------
+
+
+def idealized_curve(
+    delta: float,
+    lam: float,
+    year_range: float,
+    n_points: int = 1001,
+) -> pd.DataFrame:
+    """Return a DataFrame with columns (year, y) for the analytic trend."""
+    year = np.linspace(0, year_range, n_points)
+    y = (1.0 - delta) * np.exp(-lam * year)
+    return pd.DataFrame({'year': year, 'y': y})
+
+
+def idealized_plot_create(
+    df: pd.DataFrame,
+    title: str | None = None,
+    subtitle: str | None = None,
+    x_label: str = '',
+    y_label: str = '',
+    year_range: float = 10,
+) -> gg.ggplot:
+    """Single-trend stability plot, styled to match change_plot_create."""
+    fig = (
+        gg.ggplot(
+            data = df,
+            mapping = gg.aes(x = 'year', y = 'y'),
+        ) +
+        gg.geom_line(color = 'darkred', size = 1) +
+        gg.labs(
+            title = title,
+            subtitle = subtitle,
+            x = x_label,
+            y = y_label,
+        ) +
+        gg.scale_y_continuous(
+            limits = (0, 1.01),
+            breaks = np.arange(0, 1.01, 0.25),
+            labels = [f"{x * 100:.0f}%" for x in np.arange(0, 1.01, 0.25)],
+        ) +
+        gg.scale_x_continuous(
+            limits = (0, year_range + 0.01),
+            breaks = np.arange(year_range + 1),
+            labels = [f"{x:.0f}" for x in np.arange(year_range + 1)],
+        ) +
+        gg.theme_bw()
+    )
+    return fig
+
+
+# ----------------------------------------------------------------------------------------
+# Main workflow
+# ----------------------------------------------------------------------------------------
+
+if __name__ == "__main__":
+    df = idealized_curve(
+        delta = DELTA,
+        lam = LAMBDA,
+        year_range = YEAR_RANGE,
+        n_points = N_POINTS,
+    )
+    fig = idealized_plot_create(
+        df = df,
+        title = "Idealized stability curve",
+        subtitle = f"δ = {DELTA}, λ = {LAMBDA} / year",
+        x_label = "Years since tag",
+        y_label = "Proportion remaining unchanged",
+        year_range = YEAR_RANGE,
+    )
+    OUT_PATH.parent.mkdir(parents = True, exist_ok = True)
+    fig.save(
+        filename = OUT_PATH,
+        width = 10,
+        height = 6,
+        units = 'in',
+        dpi = 300,
+        verbose = False,
+    )
+    print(f"Saved: {OUT_PATH}")