MCM-ICM_Toolkit/tests/test_stats.py

"""stats 包测试。

原则（见 docs/02-architecture.md §5）：**测已知解析解，不测实现细节**。

未实现的函数**逐条** `skip`——**不要**用模块级 `pytestmark`：那会把同文件里
已经写好的函数一起跳过，绿灯就是假的（决策 26 / 个人易错点 9）。
"""

from __future__ import annotations

import numpy as np
import pandas as pd
import pytest

_NOT_IMPLEMENTED = "未实现：见 docs/03-roadmap.md L1"


def _pearson_p_from_r(r: float, n: int) -> float:
    """Pearson 相关系数的 p 值**解析式**（测解析解，不测实现细节）：

    ``t = r * sqrt((n - 2) / (1 - r^2))``，``p = 2 * P(T > |t|)``，``T ~ t(n - 2)``。
    """
    from scipy import stats as sps

    t_stat = r * np.sqrt((n - 2) / (1 - r**2))
    return float(2 * sps.t.sf(abs(t_stat), n - 2))


@pytest.mark.skip(reason=_NOT_IMPLEMENTED)
def test_bootstrap_ci_matches_normal_theory_on_large_n(rng):
    """大样本下 bootstrap 百分位区间应逼近正态解析区间（±10% 容差）。"""
    from mcm_toolkit.stats import bootstrap_ci

    x = rng.normal(10, 2, size=5000)
    r = bootstrap_ci(x, statistic=np.mean, confidence=0.95, n_resamples=5000, random_state=0)
    se = x.std(ddof=1) / np.sqrt(x.size)
    assert abs((r.params["high"] - r.params["low"]) - 2 * 1.96 * se) < 0.1 * 2 * 1.96 * se


@pytest.mark.skip(reason=_NOT_IMPLEMENTED)
def test_bootstrap_ci_works_for_arbitrary_statistic(rng):
    """bootstrap 的核心价值：任意统计量都能给区间（这里用中位数）。"""
    from mcm_toolkit.stats import bootstrap_ci

    x = rng.lognormal(0, 1, size=2000)
    r = bootstrap_ci(x, statistic=np.median, random_state=0)
    assert r.params["low"] < r.params["high"]
    assert r.params["low"] < np.median(x) < r.params["high"]


@pytest.mark.skip(reason=_NOT_IMPLEMENTED)
def test_bootstrap_ci_is_reproducible(rng):
    from mcm_toolkit.stats import bootstrap_ci

    x = rng.normal(size=500)
    a = bootstrap_ci(x, statistic=np.mean, random_state=123)
    b = bootstrap_ci(x, statistic=np.mean, random_state=123)
    assert a.params["low"] == b.params["low"]


def test_confidence_interval_matches_scipy(rng):
    from scipy import stats

    from mcm_toolkit.stats import confidence_interval

    x = rng.normal(5, 1, size=50)
    lo, hi = confidence_interval(x, confidence=0.95, method="t")
    ref = stats.t.interval(0.95, len(x) - 1, loc=x.mean(), scale=stats.sem(x))
    assert np.allclose([lo, hi], ref, rtol=1e-6)


def test_confidence_interval_normal_matches_z_formula(rng):
    """normal 走 z 解析式：`mean ± z·s/√n`，s 用**样本**标准差（ddof=1）。"""
    from scipy import stats as sps

    from mcm_toolkit.stats import confidence_interval

    x = rng.normal(8.5, 1, size=200)
    lo, hi = confidence_interval(x, confidence=0.95, method="normal")

    half = float(sps.norm.ppf(0.975)) * x.std(ddof=1) / np.sqrt(len(x))
    assert lo == pytest.approx(x.mean() - half)
    assert hi == pytest.approx(x.mean() + half)


def test_confidence_interval_mean_is_not_clamped_to_unit_range(rng):
    """均值区间不该被夹到 [0, 1]：平均身高 170cm 的下界不可能是 0。"""
    from mcm_toolkit.stats import confidence_interval

    x = rng.normal(170, 8, size=50)
    lo, hi = confidence_interval(x, method="t")

    assert lo > 100.0
    assert lo < hi


def test_confidence_interval_proportion_stays_in_unit_interval():
    """比例的区间必须落在 [0, 1] 里 —— 只有这一种 method 需要夹。"""
    from mcm_toolkit.stats import confidence_interval

    y = [0.0, 1.0, 1.0, 1.0, 0.0, 1.0]
    lo, hi = confidence_interval(y, method="proportion")

    assert 0.0 <= lo < hi <= 1.0


def test_confidence_interval_accepts_documented_containers():
    """docstring 的 Examples 传 list、L0 用例传 ndarray，两边都得收。"""
    from mcm_toolkit.stats import confidence_interval

    data = [1.0, 2.0, 3.0, 4.0, 5.0]
    expected = confidence_interval(data)

    assert confidence_interval(pd.Series(data)) == pytest.approx(expected)
    assert confidence_interval(np.asarray(data)) == pytest.approx(expected)
    assert confidence_interval(pd.DataFrame({"x": data})) == pytest.approx(expected)


def test_confidence_interval_rejects_bad_input(rng):
    from mcm_toolkit.stats import confidence_interval

    x = rng.normal(size=20)
    with pytest.raises(TypeError):
        confidence_interval("abc")
    with pytest.raises(ValueError):
        confidence_interval(x, method="bogus")
    with pytest.raises(ValueError):
        confidence_interval(x, confidence=1.5)
    with pytest.raises(ValueError):
        confidence_interval(x, confidence=0.0)
    with pytest.raises(ValueError):
        confidence_interval(pd.DataFrame({"city": ["X", "Y"]}))
    with pytest.raises(ValueError):
        confidence_interval([1.0])


# ------------------------------------------------------ stats: t_test


def test_t_test_one_sample_matches_analytic_formula(rng):
    """单样本：`t = (mean - value) / (s/√n)`，`df = n - 1`，`p = 2·P(T > |t|)`。"""
    from scipy import stats as sps

    from mcm_toolkit.stats import t_test

    x = rng.normal(5, 1, size=30)
    r = t_test(x, value=5.0)

    t_stat = (x.mean() - 5.0) / (x.std(ddof=1) / np.sqrt(len(x)))
    assert r["statistic"] == pytest.approx(t_stat)
    assert r["pvalue"] == pytest.approx(float(2 * sps.t.sf(abs(t_stat), len(x) - 1)))
    assert r["df"] == pytest.approx(29.0)
    assert r["significant"] == (r["pvalue"] < 0.05)
    assert isinstance(r["conclusion"], str) and r["conclusion"]


def test_t_test_two_sample_welch_df_matches_formula(rng):
    """默认 Welch：`df` 用 Welch–Satterthwaite 公式解析对照。"""
    from mcm_toolkit.stats import t_test

    a = rng.normal(0, 1, size=25)
    b = rng.normal(1, 4, size=35)
    r = t_test(a, b)

    v1, v2 = a.var(ddof=1), b.var(ddof=1)
    n1, n2 = len(a), len(b)
    expected_df = (v1 / n1 + v2 / n2) ** 2 / ((v1 / n1) ** 2 / (n1 - 1) + (v2 / n2) ** 2 / (n2 - 1))
    assert r["df"] == pytest.approx(expected_df)
    assert r["pvalue"] < 0.05


def test_t_test_equal_var_uses_pooled_df(rng):
    from mcm_toolkit.stats import t_test

    a = rng.normal(0, 1, size=25)
    b = rng.normal(1, 1, size=35)

    assert t_test(a, b, equal_var=True)["df"] == pytest.approx(58.0)


def test_t_test_paired_reports_key_set_and_df(rng):
    from mcm_toolkit.stats import t_test

    a = rng.normal(size=20)
    r = t_test(a, a + rng.normal(0, 0.1, 20), paired=True)

    assert set(r) == {"statistic", "pvalue", "df", "significant", "conclusion"}
    assert r["df"] == pytest.approx(19.0)


def test_t_test_rejects_bad_input(rng):
    from mcm_toolkit.stats import t_test

    a = rng.normal(size=20)
    with pytest.raises(ValueError):
        t_test(a, alpha=1.5)
    with pytest.raises(ValueError):
        t_test([1.0])
    with pytest.raises(ValueError):
        t_test(a, rng.normal(size=19), paired=True)
    with pytest.raises(ValueError):
        t_test(pd.DataFrame({"city": ["X", "Y"]}))
    with pytest.raises(TypeError):
        t_test("abc")


def test_correlation_matrix_diagonal_is_one(rng):
    from mcm_toolkit.stats import correlation_matrix

    x = pd.DataFrame(rng.normal(size=(200, 4)), columns=["a", "b", "c", "d"])
    c = correlation_matrix(x)

    assert np.allclose(np.diag(np.asarray(c)), 1.0)


def test_correlation_matrix_is_numeric_and_symmetric(rng):
    """方案 A：返回**数值**矩阵（不是带星标的字符串表），能直接参与后续计算。"""
    from mcm_toolkit.stats import correlation_matrix

    x = pd.DataFrame(rng.normal(size=(200, 3)), columns=["a", "b", "c"])
    c = correlation_matrix(x)

    assert all(np.issubdtype(dtype, np.floating) for dtype in c.dtypes)
    assert np.allclose(np.asarray(c), np.asarray(x.corr(method="pearson", min_periods=1)))
    assert np.allclose(np.asarray(c), np.asarray(c.T))


def test_correlation_matrix_runs_on_multicolumn_frame(rng):
    """回归：`if numeric_cols == 0` 拿 Index 跟 0 比，多列数值表当场 ValueError 崩掉。"""
    from mcm_toolkit.stats import correlation_matrix

    x = pd.DataFrame(rng.normal(size=(50, 3)), columns=["a", "b", "c"])
    out = correlation_matrix(x)

    assert out.shape == (3, 3)
    assert list(out.columns) == ["a", "b", "c"]
    assert list(out.index) == ["a", "b", "c"]


def test_correlation_matrix_skips_non_numeric_columns(rng):
    from mcm_toolkit.stats import correlation_matrix

    x = pd.DataFrame({"a": rng.normal(size=30), "b": rng.normal(size=30), "city": ["X"] * 30})
    assert list(correlation_matrix(x).columns) == ["a", "b"]


def test_correlation_matrix_rejects_bad_input():
    from mcm_toolkit.stats import correlation_matrix

    with pytest.raises(TypeError):
        correlation_matrix([[1.0, 2.0]])
    with pytest.raises(ValueError):
        correlation_matrix(pd.DataFrame({"city": ["X", "Y"]}))
    with pytest.raises(ValueError):
        correlation_matrix(pd.DataFrame({"a": [1.0, 2.0]}), method="bogus")  # type: ignore[arg-type]


def test_correlation_pvalues_matches_analytic_formula(rng):
    from mcm_toolkit.stats import correlation_matrix, correlation_pvalues

    x = pd.DataFrame(rng.normal(size=(80, 3)), columns=["a", "b", "c"])
    corr = correlation_matrix(x)
    p = correlation_pvalues(x)

    for i in ["a", "b", "c"]:
        for j in ["a", "b", "c"]:
            if i == j:
                continue
            assert p.loc[i, j] == pytest.approx(_pearson_p_from_r(corr.loc[i, j], 80))


def test_correlation_pvalues_diagonal_is_nan(rng):
    """对角线写 0 会被下游读成"极显著"；"自己和自己相关"没有 p 值，必须是 NaN。"""
    from mcm_toolkit.stats import correlation_pvalues

    p = correlation_pvalues(pd.DataFrame(rng.normal(size=(50, 2)), columns=["a", "b"]))

    assert np.isnan(p.loc["a", "a"])
    assert np.isnan(p.loc["b", "b"])


def test_correlation_pvalues_uses_the_same_observations_as_r(rng):
    """含缺失时 p 要和 r 用**同一批**观测：成对删缺失，而不是整行删、也不是干脆不删。"""
    from mcm_toolkit.stats import correlation_pvalues

    a = rng.normal(size=40)
    b = rng.normal(size=40)
    a[[3, 7, 11]] = np.nan
    x = pd.DataFrame({"a": a, "b": b})

    pair = x.dropna()
    r = float(np.corrcoef(pair["a"], pair["b"])[0, 1])

    assert correlation_pvalues(x).loc["a", "b"] == pytest.approx(_pearson_p_from_r(r, len(pair)))


def test_correlation_pvalues_respects_min_periods(rng):
    from mcm_toolkit.stats import correlation_pvalues

    a = rng.normal(size=10)
    a[:5] = np.nan
    x = pd.DataFrame({"a": a, "b": rng.normal(size=10)})

    assert np.isnan(correlation_pvalues(x, min_periods=6).loc["a", "b"])
    assert np.isfinite(correlation_pvalues(x, min_periods=5).loc["a", "b"])


def test_correlation_table_diagonal_has_no_stars():
    """对角线是"自己和自己"，不该有显著性星标；完全负相关则必然是 ***。"""
    from mcm_toolkit.stats import correlation_table

    x = pd.DataFrame({"a": np.arange(30.0), "b": np.arange(30.0) * -2.0})
    table = correlation_table(x)

    assert table.loc["a", "a"] == "1.000"
    assert table.loc["a", "b"] == "-1.000***"


def test_correlation_table_matches_the_numeric_outputs(rng):
    from mcm_toolkit.stats import correlation_matrix, correlation_pvalues, correlation_table

    x = pd.DataFrame(rng.normal(size=(60, 3)), columns=["a", "b", "c"])
    corr = correlation_matrix(x)
    p = correlation_pvalues(x)
    table = correlation_table(x)

    assert list(table.columns) == list(corr.columns)
    assert table.loc["a", "a"] == "1.000"
    assert np.isnan(p.loc["a", "a"])

    pv = p.loc["a", "b"]
    stars = "***" if pv < 0.001 else "**" if pv < 0.01 else "*" if pv < 0.05 else ""
    value = corr.loc["a", "b"]
    assert table.loc["a", "b"] == f"{value:.3f}" + stars


# ------------------------------------------------------ stats: describe


def test_describe_reports_expected_keys(rng):
    from mcm_toolkit.stats import describe

    table = describe(rng.normal(size=(100, 3)))
    for key in ["mean", "std", "min", "max", "median"]:
        assert key in table.index


def test_describe_rows_are_metrics_and_columns_are_variables():
    """方向约定：行 = 指标，列 = 变量。多转置一次就反了。"""
    from mcm_toolkit.stats import describe

    df = pd.DataFrame({"a": [1.0, 2.0, 3.0], "b": [10.0, 20.0, 30.0]})
    table = describe(df)

    assert list(table.columns) == ["a", "b"]
    assert table.loc["mean", "a"] == pytest.approx(2.0)
    assert table.loc["max", "b"] == pytest.approx(30.0)
    assert table.loc["median", "b"] == pytest.approx(20.0)


def test_describe_missing_and_shape_rows_are_not_nan():
    """曾经的静默 bug：转置后 `.loc[指标名] = <按变量索引的 Series>` 对不上列，
    整行会被填成 NaN —— 不报错，但数据全丢。"""
    from mcm_toolkit.stats import describe

    df = pd.DataFrame({"a": [1.0, np.nan, 3.0, 4.0], "b": [1.0, 2.0, 3.0, 4.0]})
    table = describe(df)

    assert table.loc["missing", "a"] == pytest.approx(1.0)
    assert table.loc["missing", "b"] == pytest.approx(0.0)
    assert table.loc["missing_ratio", "a"] == pytest.approx(0.25)
    assert table.loc["missing_ratio", "b"] == pytest.approx(0.0)
    assert table.loc["skewness", "b"] == pytest.approx(0.0, abs=1e-12)
    extra = table.loc[["missing", "missing_ratio", "skewness", "kurtosis"]]
    assert not bool(extra.isna().all(axis=None))


def test_describe_skips_non_numeric_columns():
    from mcm_toolkit.stats import describe

    df = pd.DataFrame({"a": [1.0, 2.0], "city": ["X", "Y"]})
    table = describe(df)

    assert list(table.columns) == ["a"]


def test_describe_accepts_ndarray_list_and_series(rng):
    """兄弟函数都收 ndarray / list，describe 没理由只收 DataFrame。"""
    from mcm_toolkit.stats import describe

    assert "mean" in describe(rng.normal(size=(50, 2))).index
    assert "mean" in describe([[1.0, 2.0], [3.0, 4.0]]).index
    assert "mean" in describe(pd.Series([1.0, 2.0, 3.0])).index


def test_describe_weighted_rows_match_manual_formula():
    from mcm_toolkit.stats import describe

    df = pd.DataFrame({"a": [1.0, 2.0, 3.0]})
    w = np.array([1.0, 1.0, 2.0])
    table = describe(df, weights=w)

    expect_mean = np.average(df["a"], weights=w)
    expect_std = np.sqrt(np.average((df["a"] - expect_mean) ** 2, weights=w))
    assert table.loc["weighted_mean", "a"] == pytest.approx(expect_mean)
    assert table.loc["weighted_std", "a"] == pytest.approx(expect_std)


@pytest.mark.parametrize(
    ("weights", "exc"),
    [
        (np.ones(2), ValueError),
        (np.zeros(3), ValueError),
        (np.array([1.0, -1.0, 1.0]), ValueError),
        (np.array([1.0, np.nan, 1.0]), ValueError),
        ("abc", TypeError),
    ],
)
def test_describe_rejects_bad_weights(weights, exc):
    from mcm_toolkit.stats import describe

    with pytest.raises(exc):
        describe(pd.DataFrame({"a": [1.0, 2.0, 3.0]}), weights=weights)


def test_describe_rejects_unsupported_type_and_all_text_frame():
    from mcm_toolkit.stats import describe

    with pytest.raises(TypeError):
        describe({"a": [1.0]})
    with pytest.raises(ValueError):
        describe(pd.DataFrame({"city": ["X", "Y"]}))


# ------------------------------------------------------ stats: zscore


def test_zscore_matches_manual_formula():
    from mcm_toolkit.stats import zscore

    x = np.array([1.0, 2.0, 3.0, 4.0])
    assert np.allclose(np.asarray(zscore(x)), (x - x.mean()) / x.std())


def test_zscore_is_per_column_and_keeps_frame(rng):
    from mcm_toolkit.stats import zscore

    df = pd.DataFrame({"a": rng.normal(size=200), "b": rng.normal(5, 3, size=200)})
    out = zscore(df)

    assert isinstance(out, pd.DataFrame)
    assert list(out.columns) == ["a", "b"]
    assert np.allclose(np.asarray(out).mean(axis=0), 0.0, atol=1e-12)
    assert np.allclose(np.asarray(out).std(axis=0), 1.0, atol=1e-12)


def test_zscore_constant_column_stays_zero():
    from mcm_toolkit.stats import zscore

    assert np.allclose(np.asarray(zscore([2.0, 2.0, 2.0])), 0.0)


def test_zscore_rejects_bad_type_and_all_text_frame():
    from mcm_toolkit.stats import zscore

    with pytest.raises(TypeError):
        zscore("abc")
    with pytest.raises(ValueError):
        zscore(pd.DataFrame({"city": ["X"]}))


# ------------------------------------------- stats: coefficient_of_variation


def test_coefficient_of_variation_matches_manual_formula():
    from mcm_toolkit.stats import coefficient_of_variation

    x = np.array([1.0, 2.0, 3.0, 4.0])
    assert coefficient_of_variation(x) == pytest.approx(x.std() / x.mean())


def test_coefficient_of_variation_accepts_single_column_frame():
    from mcm_toolkit.stats import coefficient_of_variation

    df = pd.DataFrame({"a": [1.0, 2.0, 3.0]})
    single = coefficient_of_variation([1.0, 2.0, 3.0])
    assert coefficient_of_variation(df) == pytest.approx(single)


def test_coefficient_of_variation_uses_absolute_mean():
    """均值为负时 CV 仍是**正数**：符号不该被读成"波动更小"。"""
    from mcm_toolkit.stats import coefficient_of_variation

    x = np.array([-1.0, -2.0, -3.0, -4.0])
    assert coefficient_of_variation(x) == pytest.approx(x.std() / abs(x.mean()))
    assert coefficient_of_variation(x) > 0


def test_coefficient_of_variation_zero_mean_is_value_error():
    """均值为 0 是**取值**问题不是类型问题：必须是 ValueError 而不是 TypeError。"""
    from mcm_toolkit.stats import coefficient_of_variation

    with pytest.raises(ValueError):
        coefficient_of_variation([-1.0, 1.0])


def test_coefficient_of_variation_rejects_empty_2d_and_bad_type():
    from mcm_toolkit.stats import coefficient_of_variation

    with pytest.raises(ValueError):
        coefficient_of_variation([])
    with pytest.raises(ValueError):
        coefficient_of_variation([[1.0, 2.0], [3.0, 4.0]])
    with pytest.raises(ValueError):
        coefficient_of_variation(pd.DataFrame({"a": [1.0], "b": [2.0]}))
    with pytest.raises(TypeError):
        coefficient_of_variation(5.0)