"""
algebra/rotor.py — Rotor construction operators for Cl(4,1).

Rotors are operators. They live here, in algebra/, not in vocab/.
A rotor between two word-versors is a contextual, field-level concern:
it describes a transformation being applied, not a property of the vocabulary.
"""

import numpy as np

from .cl41 import N_COMPONENTS, geometric_product, reverse
from .versor import unitize_versor, versor_condition

_TRANSITION_CONDITION_TOL = 1e-4
_NEAR_ZERO_TOL = 1e-12
_SAME_POINT_TOL = 1e-6
_STRICT_RESIDUE_TOL = 1e-2


def _identity(dtype: np.dtype) -> np.ndarray:
    rotor = np.zeros(N_COMPONENTS, dtype=dtype)
    rotor[0] = 1.0
    return rotor


def _result_dtype(*arrays: np.ndarray) -> np.dtype:
    dtype = np.result_type(*arrays)
    return dtype if dtype in (np.dtype(np.float32), np.dtype(np.float64)) else np.dtype(np.float32)


def _strict_unitize_versor(v: np.ndarray, dtype: np.dtype) -> np.ndarray:
    """Unitize only already-closed versor candidates.

    ``unitize_versor`` intentionally supports dense construction seeds for
    ingest/compiler boundaries. Transition construction is not such a boundary:
    if the product candidate is not already a closed versor, fabricating a
    deterministic fallback rotor would sever the transition from its source and
    target. This helper therefore fails closed instead of using construction
    seed fallback semantics.
    """
    arr = np.asarray(v, dtype=np.float64)
    input_norm = float(np.linalg.norm(arr))
    if input_norm < _NEAR_ZERO_TOL:
        raise ValueError("word_transition_rotor: near_zero candidate")

    product = geometric_product(arr, reverse(arr)).astype(np.float64)
    scalar_sq = float(product[0])
    residue = product.copy()
    residue[0] = 0.0
    residue_norm = float(np.linalg.norm(residue))
    if residue_norm >= _STRICT_RESIDUE_TOL:
        raise ValueError(
            "word_transition_rotor: non_closed candidate; "
            f"residue_norm={residue_norm:.6e}"
        )
    if scalar_sq <= 0.0:
        raise ValueError(
            "word_transition_rotor: non_positive candidate; "
            f"scalar_sq={scalar_sq:.6e}"
        )
    return (arr * (1.0 / np.sqrt(scalar_sq))).astype(dtype)


def make_rotor_from_angle(angle: float, bivector_idx: int = 6) -> np.ndarray:
    """Construct a scalar+bivector unit rotor from an angle."""
    if not 0 <= int(bivector_idx) < N_COMPONENTS:
        raise ValueError(f"bivector_idx out of range: {bivector_idx!r}")
    rotor = np.zeros(N_COMPONENTS, dtype=np.float64)
    half_angle = float(angle) / 2.0
    rotor[0] = np.cos(half_angle)
    rotor[int(bivector_idx)] = np.sin(half_angle)
    return unitize_versor(rotor)


def word_transition_rotor(A: np.ndarray, B: np.ndarray) -> np.ndarray:
    """
    Compute the closed transition operator from source versor A to target B.

        R = B * reverse(A)

    Vocabulary coordinates are expected to already be grade-normalized versors.
    The transition between two such states is their closed product. This path
    must never synthesize an unrelated fallback rotor from target components;
    invalid inputs fail loudly so generation can preserve its field invariant.
    """
    dtype = _result_dtype(A, B)
    source = np.asarray(A, dtype=dtype)
    target = np.asarray(B, dtype=dtype)
    if source.shape != (N_COMPONENTS,) or target.shape != (N_COMPONENTS,):
        raise ValueError(
            "word_transition_rotor expects two 32-component multivectors; "
            f"got {source.shape} and {target.shape}."
        )
    if float(np.linalg.norm(source)) < _NEAR_ZERO_TOL or float(np.linalg.norm(target)) < _NEAR_ZERO_TOL:
        raise ValueError("word_transition_rotor: near_zero input")
    if float(np.linalg.norm(target - source)) < _SAME_POINT_TOL:
        return _identity(dtype)

    candidate = geometric_product(target, reverse(source)).astype(dtype)
    rotor = _strict_unitize_versor(candidate, dtype)
    condition = versor_condition(rotor)
    if condition > _TRANSITION_CONDITION_TOL:
        raise ValueError(
            "word_transition_rotor: transition rotor is not a unit versor; "
            f"condition={condition:.3e}"
        )
    return rotor.astype(dtype, copy=False)