"""Genome-wide CN/LOH/mosaic hidden Markov model — spec CYTO-004/005/012/018, plan §10.2. Pure functions, no I/O.

[LIT: Wang et al. 2007 Genome Res 17:1665 (PennCNV: LRR/BAF emissions weighted by population B-allele frequency,
distance-dependent transitions); Loh et al. 2018 Nature 559:350 (MoChA: mosaic BAF split); DOC: cnvPartition
technical note (reference LRR state means CN0 −5, CN1 −0.45, CN2 0, CN3 0.3, CN4 0.75)] [OURS: state grid, mixture
weights, switch model]

* Diploid regions: CN0, CN1, CN2, CN2-LOH, CN3, CN3-LOH, CN4 and mosaic loss / gain / CN-LOH at cell fractions
  0.2, 0.4, 0.6, 0.8. Haploid regions (male X outside PAR, male Y): CN0, CN1, CN2 and mosaic gain/loss relative to
  the region's median LRR.
* LRR ~ (1−ε)·N(µ_state, σ) + ε·U(−5, 3); σ = 1.4826·MAD of the sample's autosomal LRR (floor 0.08), scaled per
  probe by the reference's LRR spread (CYTO-042); CN0 σ = 2.
  Mosaic means interpolate linearly between the constitutional means by the cell fraction.
* BAF ~ (1−ε)·Σ_g w_g N(b_g, σ_b) + ε·U(0, 1); genotype weights from the probe's PFB p (binomial in the copy
  number; LOH: {0: 1−p, 1: p}); mosaic heterozygotes split into the two bands 0.5 ± d(f).
* Transitions: switch probability 1 − exp(−d / D) for inter-probe distance d, D = 5·10⁸ bp; a switch lands on state
  j with probability π_j (the same target distribution from every state).
* Viterbi path for segmentation; forward–backward posteriors for QUAL.
"""

from __future__ import annotations

import math
from dataclasses import dataclass, field

import numpy as np
import numpy.typing as npt

F64 = npt.NDArray[np.float64]
FRACTIONS = (0.2, 0.4, 0.6, 0.8)
LRR_MEAN = {0: -5.0, 1: -0.45, 2: 0.0, 3: 0.3, 4: 0.75}
EPS = 0.01
MOSAIC_PRIOR = 0.004  # total switch-target mass of the 12 diploid mosaic states
SWITCH_D = 5e8


@dataclass(frozen=True)
class State:
    name: str
    cn: int  # copy number (baseline-relative for haploid regions: 0, 1, 2)
    loh: bool
    mosaic: str  # "" | "loss" | "gain" | "cnloh"
    fraction: float  # cell fraction of mosaic states, 1.0 otherwise
    call: str  # "" (baseline) | DEL | DUP | LOH | GAINLOH | MDEL | MDUP | MLOH
    lrr_mu: float
    baf: tuple[tuple[str, float], ...]  # (genotype-weight key, BAF mean)
    prior: float


def _d_split(kind: str, f: float) -> float:
    if kind == "loss":
        return f / (2 * (2 - f))
    if kind == "gain":
        return f / (2 * (2 + f))
    return f / 2


def diploid_states(mosaic_prior: float = MOSAIC_PRIOR) -> list[State]:
    s = [
        State("CN0", 0, False, "", 1.0, "DEL", LRR_MEAN[0], (), 0.01),
        State("CN1", 1, False, "", 1.0, "DEL", LRR_MEAN[1], (("h0", 0.0), ("h1", 1.0)), 0.06),
        State("CN2", 2, False, "", 1.0, "", 0.0, (("aa", 0.0), ("ab", 0.5), ("bb", 1.0)), 0.60),
        State("CN2LOH", 2, True, "", 1.0, "LOH", 0.0, (("h0", 0.0), ("h1", 1.0)), 0.06),
        State("CN3", 3, False, "", 1.0, "DUP", LRR_MEAN[3],
              (("t0", 0.0), ("t1", 1 / 3), ("t2", 2 / 3), ("t3", 1.0)), 0.06),
        State("CN3LOH", 3, True, "", 1.0, "GAINLOH", LRR_MEAN[3], (("h0", 0.0), ("h1", 1.0)), 0.02),
        State("CN4", 4, False, "", 1.0, "DUP", LRR_MEAN[4],
              (("q0", 0.0), ("q1", 0.25), ("q2", 0.5), ("q3", 0.75), ("q4", 1.0)), 0.03),
    ]  # fmt: skip
    for kind, call, mu_end in (("loss", "MDEL", LRR_MEAN[1]), ("gain", "MDUP", LRR_MEAN[3]), ("cnloh", "MLOH", 0.0)):
        for f in FRACTIONS:
            d = _d_split(kind, f)
            cn = {"loss": 1, "gain": 3, "cnloh": 2}[kind]
            bands = (("aa", 0.0), ("ab-", 0.5 - d), ("ab+", 0.5 + d), ("bb", 1.0))
            s.append(State(f"M{kind}{f:.1f}", cn, kind == "cnloh", kind, f, call, mu_end * f, bands, mosaic_prior / 12))
    return s


def haploid_states(mosaic_prior: float = MOSAIC_PRIOR) -> list[State]:
    s = [
        State("H0", 0, False, "", 1.0, "DEL", LRR_MEAN[0], (), 0.02),
        State("H1", 1, False, "", 1.0, "", 0.0, (("h0", 0.0), ("h1", 1.0)), 0.80),
        State("H2", 2, False, "", 1.0, "DUP", 0.45, (("h0", 0.0), ("h1", 1.0)), 0.06),
    ]
    for f in FRACTIONS:
        s.append(State(f"Hgain{f:.1f}", 2, False, "gain", f, "MDUP", 0.45 * f, (("h0", 0.0), ("h1", 1.0)),
                       mosaic_prior / 8))  # fmt: skip
        s.append(State(f"Hloss{f:.1f}", 0, False, "loss", f, "MDEL", -1.0 * f, (("h0", 0.0), ("h1", 1.0)),
                       mosaic_prior / 8))  # fmt: skip
    return s


def _geno_weights(key: str, p: F64) -> F64:
    q = 1 - p
    table = {
        "aa": q * q, "ab": 2 * p * q, "bb": p * p, "ab-": p * q, "ab+": p * q,
        "h0": q, "h1": p,
        "t0": q**3, "t1": 3 * p * q * q, "t2": 3 * p * p * q, "t3": p**3,
        "q0": q**4, "q1": 4 * p * q**3, "q2": 6 * p * p * q * q, "q3": 4 * p**3 * q, "q4": p**4,
    }  # fmt: skip
    return table[key]


def _norm(x: F64, mu: float, sd: float | F64) -> F64:
    return np.exp(-0.5 * ((x - mu) / sd) ** 2) / (sd * math.sqrt(2 * math.pi))


@dataclass
class Params:
    lrr_sd: float | F64  # scalar or per probe (CYTO-042)
    baf_sd: float
    lrr_offset: float = 0.0  # added to every state mean (haploid regions: the region's median LRR)
    switch_d: float = SWITCH_D
    eps: float = EPS
    extra: dict[str, float] = field(default_factory=dict)


def emissions(states: list[State], lrr: F64, baf: F64, pfb: F64, par: Params, het_sd: F64 | None = None) -> F64:
    """Per-probe, per-state emission likelihood (n × S); missing LRR/BAF contribute 1. ``het_sd``: per-probe spread
    of heterozygous BAF in the reference; heterozygous components use max(σ_b, het_sd)."""
    n = len(lrr)
    out = np.ones((n, len(states)), dtype=np.float64)
    lok = np.isfinite(lrr)
    bok = np.isfinite(baf)
    x = np.where(lok, lrr, 0.0)
    b = np.clip(np.where(bok, baf, 0.5), 0.0, 1.0)
    p = np.clip(np.where(np.isfinite(pfb), pfb, 0.5), 0.01, 0.99)
    sd_het: float | F64 = (
        np.maximum(par.baf_sd, np.nan_to_num(het_sd, nan=par.baf_sd)) if het_sd is not None else par.baf_sd
    )
    for j, st in enumerate(states):
        sd = 2.0 if st.cn == 0 and not st.mosaic else par.lrr_sd
        le = (1 - par.eps) * _norm(x, st.lrr_mu + par.lrr_offset, sd) + par.eps / 8.0
        if st.baf:
            be = np.zeros(n)
            for key, mean in st.baf:
                bsd = par.baf_sd if mean in (0.0, 1.0) or het_sd is None else sd_het
                be += _geno_weights(key, p) * _norm(b, mean, bsd)
            be = (1 - par.eps) * be + par.eps
        else:
            be = np.ones(n)
        out[:, j] = np.where(lok, le, 1.0) * np.where(bok, be, 1.0)
    return out


def switch_probs(pos: npt.NDArray[np.int64], switch_d: float = SWITCH_D) -> F64:
    """Switch probability before each probe (the first probe gets 1: it draws from the prior)."""
    d = np.diff(np.asarray(pos, dtype=np.float64), prepend=np.nan)
    p = 1.0 - np.exp(-np.maximum(d, 0.0) / switch_d)
    p[0] = 1.0
    return np.clip(np.nan_to_num(p, nan=1.0), 1e-12, 1.0)


def forward_backward(e: F64, sw: F64, prior: F64) -> F64:
    """Posterior state probabilities (n × S) under the switch model."""
    n, s = e.shape
    alpha = np.empty((n, s))
    c = np.empty(n)
    a = prior * e[0]
    c[0] = a.sum() or 1e-300
    alpha[0] = a / c[0]
    for t in range(1, n):
        a = ((1 - sw[t]) * alpha[t - 1] + sw[t] * prior) * e[t]
        c[t] = a.sum() or 1e-300
        alpha[t] = a / c[t]
    beta = np.ones(s)
    post = np.empty((n, s))
    post[n - 1] = alpha[n - 1]
    for t in range(n - 1, 0, -1):
        eb = e[t] * beta
        beta = ((1 - sw[t]) * eb + sw[t] * float(prior @ eb)) / c[t]
        g = alpha[t - 1] * beta
        post[t - 1] = g / (g.sum() or 1e-300)
    return post


def viterbi(e: F64, sw: F64, prior: F64) -> npt.NDArray[np.int32]:
    """Most likely state path under the switch model (log space)."""
    n, s = e.shape
    le = np.log(np.maximum(e, 1e-300))
    lp = np.log(np.maximum(prior, 1e-300))
    back = np.empty((n, s), dtype=np.int32)
    ld = lp + le[0]
    idx = np.arange(s, dtype=np.int32)
    for t in range(1, n):
        stay = np.log(np.maximum(1 - sw[t] + sw[t] * prior, 1e-300)) + ld
        best = int(np.argmax(ld))
        jump = math.log(max(sw[t], 1e-300)) + lp + ld[best]
        take_jump = jump > stay
        back[t] = np.where(take_jump, best, idx)
        ld = np.where(take_jump, jump, stay) + le[t]
    path = np.empty(n, dtype=np.int32)
    path[-1] = int(np.argmax(ld))
    for t in range(n - 1, 0, -1):
        path[t - 1] = back[t, path[t]]
    return path