feat(solve): monte_carlo 系列两个函数落地（L0 11/12、L1）+ Wilson 区间；修 z_score^2 异或 bug
用户实现： - solve.monte_carlo（L0 第 11 项，S 档）：向量化采样→仿真→汇总，8 个指标； 批量大小由实现传 sampler(rng, size=n)；结果含 NaN 判失败；std 用 ddof=0。 - solve.monte_carlo_probability（L1，S 档）：event(batch)->bool，Wilson score 区间夹 [0,1]， confidence 记进 params，小概率改成 message 警告。 Codex 只碰工程侧（算法未动，唯一例外见下）： - 真 bug：z_score^2 是异或不是乘方（np.float64 ^ 2 抛 TypeError，被 except 吞成 success=False， 函数实际不可用）-> 改 z_score**2。新增经验第 21 条。 - docstring：补齐 Parameters / Raises，修掉两处跑不通的 Examples，Wald -> Wilson 同步。 - 入口校验按 §4.7 收严 n（bool / np.integer / TypeError 与 ValueError 分工）—— 决策 49 后此类归用户，已记档。 - ruff 九条（I001 / F541 x3 / SIM300 / W291 x2 / W293 x2 等）、格式与文案。 - 测试：摘掉 2 条已实现却仍挂着的 skip（易错点 9），新增 14 条（含 vectorization、 Wilson 对 statsmodels 的对照、NaN / 布尔 / 长度等边界），solve 段共 25 条。 校验：193 收集 / 161 passed / 32 skipped / 0 xfail；ruff 0；pyright 0。 文档：STATUS.md 决策 47-50；docs/dev/personal-pitfalls.md 第 18-21 条；CHANGELOG.md。
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@@ -8,6 +8,11 @@ import pytest
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_NOT_IMPLEMENTED = "未实现：见 docs/03-roadmap.md L0/L1"
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def _normal_batch(rng, size, **kwargs):
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"""`monte_carlo` 的 sampler 契约：收下实现传来的 `size`，一次抽够。"""
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return rng.normal(0, 1, size)
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@pytest.mark.skip(reason=_NOT_IMPLEMENTED)
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def test_monte_carlo_integral_converges_to_analytic_value():
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"""∫₀¹ x² dx = 1/3。n=2e5 时误差应 < 0.01。"""
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@@ -17,30 +22,205 @@ def test_monte_carlo_integral_converges_to_analytic_value():
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assert abs(r.data - 1 / 3) < 0.01
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@pytest.mark.skip(reason=_NOT_IMPLEMENTED)
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def test_monte_carlo_probability_of_standard_normal():
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"""P(Z > 0) = 0.5，n=5000 时误差应 < 0.05。"""
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from mcm_toolkit.solve import monte_carlo_probability
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r = monte_carlo_probability(
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lambda z: z > 0,
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lambda rng, **kw: rng.standard_normal(),
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n=5000,
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random_state=0,
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)
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r = monte_carlo_probability(lambda z: z > 0, _normal_batch, n=5000, random_state=0)
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assert r.success
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assert abs(r.metrics["probability"] - 0.5) < 0.05
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@pytest.mark.skip(reason=_NOT_IMPLEMENTED)
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def test_monte_carlo_is_reproducible():
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from mcm_toolkit.solve import monte_carlo_probability
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args = (lambda z: z > 0, lambda rng, **kw: rng.standard_normal())
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a = monte_carlo_probability(*args, n=1000, random_state=9)
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b = monte_carlo_probability(*args, n=1000, random_state=9)
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a = monte_carlo_probability(lambda z: z > 0, _normal_batch, n=1000, random_state=9)
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b = monte_carlo_probability(lambda z: z > 0, _normal_batch, n=1000, random_state=9)
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assert a.metrics["probability"] == b.metrics["probability"]
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def test_monte_carlo_returns_n_results_and_documented_metrics():
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from mcm_toolkit.solve import monte_carlo
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r = monte_carlo(_normal_batch, lambda x: x**2, n=2000, random_state=0)
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assert r.success
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assert r.data.shape == (2000,)
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assert set(r.metrics) == {"mean", "std", "median", "p05", "p95", "ci_low", "ci_high"}
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def test_monte_carlo_calls_simulator_only_once():
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"""`simulator` 只被调用一次 —— 这是"必须向量化"的可执行版本。"""
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from mcm_toolkit.solve import monte_carlo
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counter = {"calls": 0}
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def simulator(params):
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counter["calls"] += 1
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return params
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r = monte_carlo(_normal_batch, simulator, n=1000, random_state=0)
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assert r.success
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assert counter["calls"] == 1
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def test_monte_carlo_data_is_reproducible_with_same_seed():
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from mcm_toolkit.solve import monte_carlo
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a = monte_carlo(_normal_batch, lambda x: x, n=2000, random_state=11)
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b = monte_carlo(_normal_batch, lambda x: x, n=2000, random_state=11)
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assert np.array_equal(a.data, b.data)
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def test_monte_carlo_follows_set_seed_when_random_state_omitted():
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from mcm_toolkit.core import set_seed
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from mcm_toolkit.solve import monte_carlo
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set_seed(5)
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a = monte_carlo(_normal_batch, lambda x: x, n=500)
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set_seed(5)
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b = monte_carlo(_normal_batch, lambda x: x, n=500)
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assert np.array_equal(a.data, b.data)
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def test_monte_carlo_estimates_known_expectation():
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"""E[X²] = 1（X ~ N(0, 1)）；n = 2e5 时误差应 < 0.02。"""
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from mcm_toolkit.solve import monte_carlo
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r = monte_carlo(_normal_batch, lambda x: x**2, n=200_000, random_state=0)
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assert abs(r.metrics["mean"] - 1.0) < 0.02
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def test_monte_carlo_docstring_example_runs():
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"""docstring 的 Examples 必须真的能跑通（此前那一版是坏的）。"""
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from mcm_toolkit.solve import monte_carlo
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draw = lambda rng, size, **k: rng.normal(0, 1, size) # noqa: E731
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r = monte_carlo(draw, lambda x: x**2, n=10000, random_state=0)
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assert r.success
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assert abs(r.metrics["mean"] - 1.0) < 0.1
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def test_monte_carlo_accepts_numpy_integer_n():
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"""§4.7：`np.int64` 不是 `int` 的子类，不能漏。"""
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from mcm_toolkit.solve import monte_carlo
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r = monte_carlo(_normal_batch, lambda x: x, n=np.int64(100), random_state=0)
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assert r.success
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assert r.data.shape == (100,)
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def test_monte_carlo_counts_boolean_outcomes():
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"""布尔结果按 0/1 统计 —— 事件概率是 MC 最常见的用法。"""
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from mcm_toolkit.solve import monte_carlo
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r = monte_carlo(
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lambda rng, size, **k: rng.normal(0, 1, size) > 0,
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lambda x: x,
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n=5000,
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random_state=0,
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)
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assert r.success
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assert r.data.dtype == float
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assert abs(r.metrics["mean"] - 0.5) < 0.05
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def test_monte_carlo_rejects_nan_results():
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"""结果里出现 NaN 就判失败，不静默给出一列 nan 指标。"""
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from mcm_toolkit.solve import monte_carlo
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r = monte_carlo(
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lambda rng, size, **k: np.r_[np.zeros(size - 1), np.nan],
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lambda x: x,
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n=10,
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random_state=0,
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)
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assert not r.success
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assert "NaN" in r.message
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def test_monte_carlo_rejects_bad_arguments():
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from mcm_toolkit.solve import monte_carlo
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with pytest.raises(TypeError):
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monte_carlo(123, lambda x: x) # type: ignore[arg-type] # 就是要传错
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with pytest.raises(TypeError):
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monte_carlo(_normal_batch, 123) # type: ignore[arg-type] # 就是要传错
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with pytest.raises(TypeError):
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monte_carlo(_normal_batch, lambda x: x, n=True)
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with pytest.raises(TypeError):
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monte_carlo(_normal_batch, lambda x: x, n=10.0) # type: ignore[arg-type] # 就是要传错
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with pytest.raises(ValueError):
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monte_carlo(_normal_batch, lambda x: x, n=0)
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def test_monte_carlo_probability_returns_documented_metrics():
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from mcm_toolkit.solve import monte_carlo_probability
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r = monte_carlo_probability(lambda z: z > 0, _normal_batch, n=20000, random_state=0)
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assert r.success
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assert set(r.metrics) == {"probability", "ci_low", "ci_high", "std_error"}
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assert r.data.shape == (20000,)
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assert 0.0 <= r.metrics["ci_low"] <= r.metrics["probability"]
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assert r.metrics["probability"] <= r.metrics["ci_high"] <= 1.0
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def test_monte_carlo_probability_std_error_matches_binomial_formula():
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"""`std_error` 就是比例的标准误 √(p(1-p)/n)。"""
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from mcm_toolkit.solve import monte_carlo_probability
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n = 20000
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r = monte_carlo_probability(lambda z: z > 0, _normal_batch, n=n, random_state=0)
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p = r.metrics["probability"]
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assert np.isclose(r.metrics["std_error"], np.sqrt(p * (1 - p) / n))
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def test_monte_carlo_probability_ci_narrows_with_n():
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"""区间宽度随 n 增大而收窄（O(1/√n)）。"""
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from mcm_toolkit.solve import monte_carlo_probability
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def width(n):
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r = monte_carlo_probability(lambda z: z > 0, _normal_batch, n=n, random_state=0)
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return r.metrics["ci_high"] - r.metrics["ci_low"]
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assert width(100_000) < width(1_000)
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def test_monte_carlo_probability_higher_confidence_is_wider():
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from mcm_toolkit.solve import monte_carlo_probability
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def width(confidence):
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r = monte_carlo_probability(
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lambda z: z > 0, _normal_batch, n=5000, random_state=0, confidence=confidence
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)
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return r.metrics["ci_high"] - r.metrics["ci_low"]
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assert width(0.99) > width(0.90)
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def test_monte_carlo_probability_ci_matches_statsmodels_wilson():
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"""区间必须对得上独立实现（statsmodels 的 wilson）—— `^` 写成异或那次就靠它拦住。"""
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from statsmodels.stats.proportion import proportion_confint
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from mcm_toolkit.solve import monte_carlo_probability
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n = 5000
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r = monte_carlo_probability(lambda z: z > 0, _normal_batch, n=n, random_state=0)
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count = int(r.data.sum())
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lo, hi = proportion_confint(count, n, alpha=0.05, method="wilson")
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assert np.isclose(r.metrics["ci_low"], lo)
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assert np.isclose(r.metrics["ci_high"], hi)
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def test_monte_carlo_probability_rejects_bad_confidence():
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from mcm_toolkit.solve import monte_carlo_probability
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for bad in (0.0, 1.0, -0.5, 1.5):
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with pytest.raises(ValueError):
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monte_carlo_probability(lambda z: z > 0, _normal_batch, n=100, confidence=bad)
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@pytest.mark.skip(reason=_NOT_IMPLEMENTED)
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def test_markov_steady_state_two_state_chain():
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"""P=[[0.9,0.1],[0.2,0.8]] 的平稳分布是 [2/3, 1/3]。"""
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