"""solve 包测试。"""

from __future__ import annotations

import numpy as np
import pytest

pytestmark = pytest.mark.skip(reason="未实现：见 docs/03-roadmap.md L0/L1")


def test_monte_carlo_integral_converges_to_analytic_value():
    """∫₀¹ x² dx = 1/3。n=2e5 时误差应 < 0.01。"""
    from mcm_toolkit.solve import monte_carlo_integral

    r = monte_carlo_integral(lambda X: X[:, 0] ** 2, bounds=[(0, 1)], n=200_000, random_state=0)
    assert abs(r.data - 1 / 3) < 0.01


def test_monte_carlo_probability_of_standard_normal():
    """P(Z > 0) = 0.5，n=5000 时误差应 < 0.05。"""
    from mcm_toolkit.solve import monte_carlo_probability

    r = monte_carlo_probability(
        lambda z: z > 0,
        lambda rng, **kw: rng.standard_normal(),
        n=5000,
        random_state=0,
    )
    assert abs(r.metrics["probability"] - 0.5) < 0.05


def test_monte_carlo_is_reproducible():
    from mcm_toolkit.solve import monte_carlo_probability

    args = (lambda z: z > 0, lambda rng, **kw: rng.standard_normal())
    a = monte_carlo_probability(*args, n=1000, random_state=9)
    b = monte_carlo_probability(*args, n=1000, random_state=9)
    assert a.metrics["probability"] == b.metrics["probability"]


def test_markov_steady_state_two_state_chain():
    """P=[[0.9,0.1],[0.2,0.8]] 的平稳分布是 [2/3, 1/3]。"""
    from mcm_toolkit.solve import markov_steady_state

    r = markov_steady_state(np.array([[0.9, 0.1], [0.2, 0.8]]))
    assert np.allclose(r.data, [2 / 3, 1 / 3], atol=1e-6)


def test_knapsack_dp_known_optimum():
    from mcm_toolkit.solve import knapsack_dp

    r = knapsack_dp(weights=[1, 3, 4, 5], values=[1, 4, 5, 7], capacity=7)
    assert np.isclose(r.metrics["total_value"], 9.0)
    assert np.isclose(r.metrics["total_weight"], 7.0)


def test_linear_program_basic():
    from mcm_toolkit.solve import linear_program

    r = linear_program(c=[1, 2], A_ub=[[1, 1]], b_ub=[4], bounds=[(0, None)] * 2)
    assert r.success
    assert np.isclose(r.metrics["objective"], 4.0)


def test_mm1_metrics_closed_form():
    from mcm_toolkit.solve import mm1_metrics

    r = mm1_metrics(arrival_rate=2, service_rate=3)
    assert np.isclose(r.metrics["rho"], 2 / 3, rtol=1e-6)
    assert np.isclose(r.metrics["L"], 2.0, rtol=1e-6)


def test_mm1_rejects_unstable_system():
    """λ >= μ 时系统不稳定，应 success=False 而不是返回 inf。"""
    from mcm_toolkit.solve import mm1_metrics

    assert mm1_metrics(arrival_rate=3, service_rate=3).success is False


def test_simulated_annealing_finds_quadratic_minimum():
    from mcm_toolkit.solve import simulated_annealing

    f = lambda v: (v[0] - 3.0) ** 2 + (v[1] + 1.0) ** 2  # noqa: E731
    r = simulated_annealing(f, x0=[0.0, 0.0], n_iter=5000, random_state=0)
    assert np.allclose(r.params["x"], [3.0, -1.0], atol=0.1)