"""
Illustrates the gradient locality property of KDE-ROLL.

Upper panel: score distributions for both classes with operating threshold.
Lower panel: gradient magnitude per sample, showing bell-shaped decay from threshold.

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

import numpy as np
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt

# --- Add these configuration rules right here ---
plt.rcParams.update({
    "text.usetex": False,            # Rely on Matplotlib's math parser instead of the system compiler
    "mathtext.fontset": "cm",         # Emulate standard LaTeX Computer Modern styles flawlessly
    "pdf.fonttype": 42                # Ensure fonts are embedded as TrueType vector curves instead of Type 3 paths
})

OUT_DIR = "content/method/figures"

np.random.seed(7)

# --- Data ------------------------------------------------------------------
n = 120
alpha = 0.25  # target FPR

neg_scores = np.sort(np.random.normal(-0.6, 0.75, n))
pos_scores = np.sort(np.random.normal(1.1, 0.80, n))

# Threshold: alpha-quantile of the negative-class scores
tau = np.percentile(neg_scores, 100 * (1 - alpha))

# --- Bandwidth (Silverman's rule per class) --------------------------------
h_neg = 1.06 * neg_scores.std() * n ** (-1 / 5)
h_pos = 1.06 * pos_scores.std() * n ** (-1 / 5)


def sigma_prime(x, h):
    """Logistic kernel PDF: derivative of the sigmoid-smoothed CDF."""
    e = np.exp(-np.abs(x) / h)
    return e / (h * (1 + e) ** 2)


# --- KDE-ROLL gradients (eq:kde-grad-combined) ----------------------------
# y=1:  (1/n) * sigma_prime(score - tau)
grad_pos = (1.0 / n) * sigma_prime(pos_scores - tau, h_pos)

# y=0:  -(scale) * sigma_prime(tau - score_i) / sum_j[sigma_prime(tau - score_j)]
#   where scale = (1/n) * sum_j[sigma_prime(pos_j - tau)]
neg_kernel = sigma_prime(tau - neg_scores, h_neg)
scale = (1.0 / n) * np.sum(sigma_prime(pos_scores - tau, h_pos))
grad_neg_signed = -scale * neg_kernel / neg_kernel.sum()
grad_neg_abs = np.abs(grad_neg_signed)

# --- Smooth reference bell curves -----------------------------------------
x_ref = np.linspace(neg_scores.min() - 0.3, pos_scores.max() + 0.3, 400)
bell_pos = sigma_prime(x_ref - tau, h_pos)
bell_pos *= (grad_pos.max() / bell_pos.max())
bell_neg = sigma_prime(tau - x_ref, h_neg)
bell_neg *= (grad_neg_abs.max() / bell_neg.max())

# --- Plot -----------------------------------------------------------------
C_NEG = "#4477AA"
C_POS = "#CC6633"
C_TAU = "#333333"

fig, (ax1, ax2) = plt.subplots(
    2, 1, figsize=(5.5, 4.2), sharex=True,
    gridspec_kw={"height_ratios": [1.3, 1.0]}
)
fig.subplots_adjust(hspace=0.06)

# — Top: score distributions —
ax1.hist(neg_scores, bins=20, density=True, alpha=0.45, color=C_NEG,
         label=r"Negative class ($y=0$)")
ax1.hist(pos_scores, bins=20, density=True, alpha=0.45, color=C_POS,
         label=r"Positive class ($y=1$)")
ax1.axvline(tau, color=C_TAU, linestyle="--", linewidth=1.4,
            label=rf"Threshold $\tau$  (FPR $=\alpha={alpha}$)")
ax1.set_ylabel("Density", fontsize=9)
ax1.set_yticks([])
ax1.legend(fontsize=7.5, loc="upper right", framealpha=0.85)

# — Bottom: gradient magnitudes —
ax2.scatter(neg_scores, grad_neg_abs, color=C_NEG, s=12, zorder=3,
            alpha=0.75, label=r"$|\partial\mathcal{L}/\partial f_\theta(\mathbf{x})|$, $y=0$")
ax2.scatter(pos_scores, grad_pos, color=C_POS, s=12, zorder=3,
            alpha=0.75, label=r"$\partial\mathcal{L}/\partial f_\theta(\mathbf{x})$, $y=1$")
ax2.plot(x_ref, bell_neg, color=C_NEG, linewidth=1.2, alpha=0.5)
ax2.plot(x_ref, bell_pos, color=C_POS, linewidth=1.2, alpha=0.5)
ax2.axvline(tau, color=C_TAU, linestyle="--", linewidth=1.4)
ax2.set_ylabel("Gradient magnitude", fontsize=9)
ax2.set_xlabel(r"Score $f_\theta(\mathbf{x})$", fontsize=9)
ax2.set_yticks([])
ax2.legend(fontsize=7.5, loc="upper right", framealpha=0.85)

for ax in (ax1, ax2):
    ax.tick_params(labelsize=8)
    ax.spines[["top", "right"]].set_visible(False)

fig.savefig(f"{OUT_DIR}/threshold_weighting.pdf", bbox_inches="tight")
fig.savefig(f"{OUT_DIR}/threshold_weighting.png", bbox_inches="tight", dpi=180)
print(f"Saved to {OUT_DIR}/threshold_weighting.{{pdf,png}}")
print(f"Sum neg: {np.sum(grad_neg_signed)}, pos: {np.sum(grad_pos)}")