#!/usr/bin/env python3
"""model_lut.py — КАНОНИЧЕСКАЯ модель B.12 (2026-08-18).

Диагностический мост (model_fir.py) ЗАМЕНИЛ эмпирический tilt реальной цепочкой
FUN_180529fe0: C(f) = g·LUT(xv) + w·warp(f)^a  (АДДИТИВНЫЙ аккумулятор 0x5407c8).

МОДЕЛЬ (rmse=0.236 dB на 36 точках — dual_b1q 22 + t1kq fc-скан 7 + t1k fc-скан 7,
3 уровня входа: -7.14 / -18.06 / 0 dBFS):

  red(f) = -20*log10(1 - C(f))
  C(f)   = g * LUT(log10(L0 / res(f)))  +  w * warp(f)^a
  res(f) = |2·B/A|(f; fc, Q, gain)      case8/m2c (freq-path, близнец 0x180535880)
  warp(f)= 0.87·K·x/(K+x), K=exp(2.0723), x=f/2000   (0x5406a8, FUN_180530850)
  LUT    = PCHIP-узлы B.11 (заморожены), таблица ниже
  g=1.221  w=0.358  a=3.143   (фит, bounds [0.9..1.5],[0.2..1.2],[2..6])
  L0     = линейный уровень входа (dual 10^(-7.142/20), t1kq 10^(-18.063/20), t1k 1.0)

СВОЙСТВА (открытие B.12, bridge):
  - C500-константа dual = res_band(500; fc=500)=0.117 Q-НЕЗАВИСИМ (твин в центре полосы)
    -> крас500 const по Q БЕЗ tilt; C500 = g·LUT(0.574)·warp^a(500≈0) = 0.692.
  - Глубина dual2000 = АДДИТИВНЫЙ терм w·warp(f)^3.14: на 2000 Гц +0.149, на 1000 <=0.02
    (иначе t1k/t1kq рушатся) — это шаг 5 декомпа `0x5407c8 += веса·res + mask`, НЕ
    мультипликация warp·LUT (та проваливается >10 dB).
  - xv(2000)=log10(L0/res): 0.308(Q=0.1)..-0.656(Q=10) -> C2000-Q-зависимость совпадает.
  - Остаток 0.7 dB (Q=0.1) = тонкая форма LUT-колена 0.574; warp^3.14~pi => подозрение
    на кратный каскад (freq-axis 0x540698 / ∏0x540688 / двойной FFT-проход 0x535a70).
  - Структура level-path подтверждена: per-bin уровень (0x540678 IIR) -> кривая +0x188
    (FUN_180563440) -> аддитивный аккумулятор 0x5407c8 -> warp -> FFT-conv.
"""
import numpy as np
from scipy.interpolate import PchipInterpolator

FS = 44100.0
GAIN_FIT = 4.132

QS = [0.1, 0.2, 0.3, 0.5, 0.7, 1.0, 1.5, 2.0, 3.0, 5.0, 10.0]
DUAL = np.array([(10.220, 15.224), (10.219, 13.963), (10.219, 12.947),
                 (10.219, 11.725), (10.218, 11.119), (10.216, 10.689),
                 (10.210, 10.412), (10.203, 10.305), (10.182, 10.225),
                 (10.113, 10.183), (9.822, 10.165)])
FCS = [800.0, 900.0, 950.0, 1000.0, 1050.0, 1100.0, 1200.0]
T1KQ = np.array([7.868, 8.536, 8.726, 8.788, 8.729, 8.575, 8.115])
T1K = np.array([14.548, 15.332, 15.553, 15.626, 15.557, 15.378, 14.840])

L0_DUAL = 10 ** (-7.142 / 20)
L0_T1KQ = 10 ** (-18.063 / 20)
L0_T1K = 1.0

# bridge-фит (model_fir.py): C = g*LUT(xv) + w*warp^a
G_FIT, W_FIT, A_FIT = 1.221, 0.358, 3.143

# узлы LUT (x=log10(L0/res), y=норм. маска) — из B.11, заморожены
LUT_KNOTS_X = np.array([-0.750, -0.500, -0.250, 0.000, 0.250, 0.500, 0.574, 0.610, 0.750, 1.000])
LUT_KNOTS_Y = np.array([0.4402, 0.4552, 0.4813, 0.5072, 0.5329, 0.5332, 0.5645, 0.6471, 0.6562, 0.6670])
_LUT = PchipInterpolator(LUT_KNOTS_X, LUT_KNOTS_Y)


def lut(x):
    v = _LUT(np.asarray(x))
    return np.clip(v, LUT_KNOTS_Y[0], LUT_KNOTS_Y[-1])


def warp(f):
    x = np.asarray(f) / 2000.0
    return 0.87 * 7.942 * x / (7.942 + x)


def res_at(ft, fc, Q, gain):
    w0 = fc * 2 * np.pi / FS
    c, s = np.cos(w0), np.sin(w0)
    p = (s * 0.5) / Q
    a, a2 = p * gain, p / gain
    A = [a + 1, -2 * c, 1 - a]
    B = [a2 + 1, -2 * c, 1 - a2]
    w = 2 * np.pi * ft / FS
    z = np.exp(-1j * w)
    return np.abs(2.0 * (B[0] + B[1] * z + B[2] * z * z) /
                  (A[0] + A[1] * z + A[2] * z * z))


def red(f_tone, fc, Q, gain, L0, g=G_FIT, w=W_FIT, a=A_FIT):
    r = res_at(f_tone, fc, Q, gain)
    C = g * lut(np.log10(L0 / r)) + w * warp(f_tone) ** a
    return -20 * np.log10(max(1 - C, 1e-9))


def run():
    preds, meas = [], []
    print('--- dual_b1q (tones 500+2000, band fc=500, -7.142 dBFS) ---')
    for i, q in enumerate(QS):
        for f, m in ((500.0, DUAL[i, 0]), (2000.0, DUAL[i, 1])):
            p = red(f, 500.0, q, GAIN_FIT, L0_DUAL)
            preds.append(p); meas.append(m)
        print(f'q={q:5.1f} 500 {DUAL[i,0]:7.3f}/{preds[2*i]:7.3f} '
              f'2000 {DUAL[i,1]:7.3f}/{preds[2*i+1]:7.3f}')
    print('--- t1kq fc-скан (-18.06 dBFS, q=0.9999978) ---')
    for i, fc in enumerate(FCS):
        p = red(1000, fc, 0.9999978, GAIN_FIT, L0_T1KQ)
        preds.append(p); meas.append(T1KQ[i])
        print(f'fc={fc:5.0f} {T1KQ[i]:6.3f}/{p:6.3f} ({p - T1KQ[i]:+.3f})')
    print('--- t1k fc-скан (0 dBFS, q=0.9999978) ---')
    for i, fc in enumerate(FCS):
        p = red(1000, fc, 0.9999978, GAIN_FIT, L0_T1K)
        preds.append(p); meas.append(T1K[i])
        print(f'fc={fc:5.0f} {T1K[i]:6.3f}/{p:6.3f} ({p - T1K[i]:+.3f})')
    preds = np.array(preds); meas = np.array(meas)
    rmse = np.sqrt(np.mean((preds - meas) ** 2))
    print(f'\nTOTAL rmse={rmse:.4f} dB  (n={len(meas)})  [B.11 эмпирик: 0.072; warp-одиночный: >10]')
    print(f'dual-only rmse={np.sqrt(np.mean((preds[:22]-meas[:22])**2)):.4f}')
    print(f't1kq rmse={np.sqrt(np.mean((preds[22:29]-meas[22:29])**2)):.4f}')
    print(f't1k rmse={np.sqrt(np.mean((preds[29:]-meas[29:])**2)):.4f}')


if __name__ == '__main__':
    run()