import math

import numpy as np
import pytest

from gausse.physics.inductance import (
    CoilInductanceModel,
    air_core_inductance_wheeler,
    demagnetizing_factor_prolate,
    effective_permeability,
    winding_geometry,
)


def test_winding_geometry_scales_with_turns_and_layers():
    geo = winding_geometry(tube_od_m=0.02, wire_od_m=0.001, turns_per_layer=50, layers=3)
    assert geo.total_turns == 150
    assert geo.coil_length_m == pytest.approx(0.05)
    assert geo.radial_depth_m == pytest.approx(0.003)
    assert geo.total_wire_length_m > 0
    # больше слоёв -> больше провода при тех же витках на слой
    geo_more_layers = winding_geometry(0.02, 0.001, 50, 5)
    assert geo_more_layers.total_wire_length_m > geo.total_wire_length_m


def test_wheeler_inductance_is_positive_and_grows_with_turns():
    l_small = air_core_inductance_wheeler(mean_radius_m=0.015, length_m=0.05, depth_m=0.003, turns=50)
    l_large = air_core_inductance_wheeler(mean_radius_m=0.015, length_m=0.05, depth_m=0.003, turns=200)
    assert l_small > 0
    assert l_large > l_small


def test_demagnetizing_factor_bounds():
    # почти сфера (aspect_ratio -> 1): классическое значение 1/3
    assert demagnetizing_factor_prolate(1.001) == pytest.approx(1 / 3, abs=0.02)
    # очень вытянутый стержень: коэффициент размагничивания стремится к 0
    assert demagnetizing_factor_prolate(200.0) < 0.01


def test_effective_permeability_limits():
    # без размагничивания (Nd=0) эффективная проницаемость равна мю материала
    assert effective_permeability(mu_r=500.0, demagnetizing_factor=0.0) == pytest.approx(500.0)
    # полное размагничивание (Nd=1) гасит эффект проницаемости до 1
    assert effective_permeability(mu_r=500.0, demagnetizing_factor=1.0) == pytest.approx(1.0)


@pytest.fixture
def model() -> CoilInductanceModel:
    return CoilInductanceModel(
        l_air_h=100e-6,
        coil_length_m=0.05,
        slug_length_m=0.03,
        mu_eff=50.0,
        smoothing_width_m=0.001,
    )


def test_inductance_peaks_when_slug_centered(model):
    l_center = model.l_of_x(np.array(0.0))
    l_far = model.l_of_x(np.array(0.2))
    assert l_center > l_far
    assert l_far == pytest.approx(model.l_air_h, rel=1e-3)


def test_dl_dx_vanishes_at_symmetric_center(model):
    assert model.dl_dx(np.array(0.0)) == pytest.approx(0.0, abs=1e-9)


def test_dl_dx_sign_flips_across_center(model):
    # слева от центра индуктивность растёт (dL/dx > 0), справа убывает (< 0)
    assert model.dl_dx(np.array(-0.01)) > 0
    assert model.dl_dx(np.array(0.01)) < 0


def test_analytic_dl_dx_matches_finite_difference(model):
    xs = np.linspace(-0.06, 0.06, 25)
    h = 1e-7
    analytic = np.array([model.dl_dx(x) for x in xs])
    finite_diff = np.array(
        [(model.l_of_x(x + h) - model.l_of_x(x - h)) / (2 * h) for x in xs]
    )
    assert np.allclose(analytic, finite_diff, rtol=1e-3, atol=1e-9)