"""
ROC curve illustration for ROLL-AOC.

Shows how ROLL-AOC converts the single-threshold ROLL into AUC optimization:
- ROC curve traced by sweeping threshold τ
- 10 evenly-spaced FPR sample points (as ROLL evaluates in miniature)
- Green shaded region = AUC (area under curve, what we maximize)
- Red shaded region  = AOC = 1 − AUC (area over curve, the loss we minimize)
- Vertical segments  = per-threshold loss 1 − TPR(αᵢ), one per sampled FPR

Run from the thesis root:
    nix develop --command python3 content/method/figures/roll_aoc_roc.py
"""

import numpy as np
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
from scipy.stats import norm

OUT_DIR = "content/method/figures"

# --- Parameters (same distributions as roll_principle.py) ------------------
mu0, sig0 = 0.0, 1.00
mu1, sig1 = 1.5, 1.00

# --- ROC curve -------------------------------------------------------------
# Sweep τ from high to low → FPR rises from 0 to 1
tau_grid = np.linspace(norm.ppf(0.9999, mu0, sig0),
                       norm.ppf(0.0001, mu0, sig0), 3000)
fpr_curve = 1.0 - norm.cdf(tau_grid, mu0, sig0)
tpr_curve = 1.0 - norm.cdf(tau_grid, mu1, sig1)

# Pin endpoints so the fill covers the full unit square correctly
fpr_full = np.concatenate([[0.0], fpr_curve, [1.0]])
tpr_full = np.concatenate([[0.0], tpr_curve, [1.0]])

auc = float(np.trapezoid(tpr_full, fpr_full))

# --- 10 sample FPR points: αᵢ = i/11 for i = 1…10 ------------------------
n_samples = 10
alpha_s = np.array([(i / (n_samples + 1)) for i in range(1, n_samples + 1)])
tpr_s   = np.interp(alpha_s, fpr_full, tpr_full)

# --- Palette (matches roll_principle.py) -----------------------------------
C_POS   = "#CC6633"   # ROC curve (positive-class colour)
C_GREEN = "#44AA77"   # AUC fill
C_RED   = "#BB3333"   # AOC fill / vertical segments
C_DOT   = "#333333"   # sample dots

# ── Figure ─────────────────────────────────────────────────────────────────
fig, ax = plt.subplots(figsize=(4.8, 4.4))

# Random-classifier diagonal
ax.plot([0, 1], [0, 1], color="#AAAAAA", linestyle="--",
        linewidth=0.9, zorder=1, label="Random classifier")

# AUC — green fill under ROC curve
ax.fill_between(fpr_full, 0, tpr_full,
                color=C_GREEN, alpha=0.25, zorder=2,
                label=rf"AUC $\approx$ {auc:.2f}  (maximize)")

# AOC — red fill above ROC curve
ax.fill_between(fpr_full, tpr_full, 1.0,
                color=C_RED, alpha=0.22, zorder=2,
                label=r"AOC $= 1-\mathrm{AUC}$  (minimize)")

# ROC curve itself
ax.plot(fpr_full, tpr_full, color=C_POS, linewidth=2.0, zorder=3,
        label="ROC curve")

# Per-threshold loss segments: vertical from TPR(αᵢ) up to 1
for a_i, t_i in zip(alpha_s, tpr_s):
    ax.plot([a_i, a_i], [t_i, 1.0],
            color=C_RED, linewidth=1.0, alpha=0.55, zorder=4)

# Sample dots on the ROC curve
ax.scatter(alpha_s, tpr_s,
           color=C_DOT, s=35, zorder=5,
           label=r"Sampled $\alpha_i$ (ROLL evaluations)")

# --- Axes / labels ---------------------------------------------------------
ax.set_xlabel(r"FPR $(\alpha)$", fontsize=9)
ax.set_ylabel(r"TPR", fontsize=9)
ax.set_xlim(0.0, 1.0)
ax.set_ylim(0.0, 1.0)
ax.set_aspect("equal")
ax.tick_params(labelsize=8)
ax.spines[["top", "right"]].set_visible(False)
ax.legend(fontsize=7.5, loc="lower right", framealpha=0.88)

fig.tight_layout()
fig.savefig(f"{OUT_DIR}/roll_aoc_roc.pdf", bbox_inches="tight")
fig.savefig(f"{OUT_DIR}/roll_aoc_roc.png", bbox_inches="tight", dpi=180)
print(f"Saved to {OUT_DIR}/roll_aoc_roc.{{pdf,png}}")
print(f"AUC = {auc:.4f}  AOC = {1-auc:.4f}")