diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst index 0396d1704b579..b4f8b4379b99d 100644 --- a/doc/source/whatsnew/v3.0.0.rst +++ b/doc/source/whatsnew/v3.0.0.rst @@ -1254,6 +1254,7 @@ Groupby/resample/rolling - Bug in :meth:`DataFrameGroupby.transform` and :meth:`SeriesGroupby.transform` with a reducer and ``observed=False`` that coerces dtype to float when there are unobserved categories. (:issue:`55326`) - Bug in :meth:`Rolling.apply` for ``method="table"`` where column order was not being respected due to the columns getting sorted by default. (:issue:`59666`) - Bug in :meth:`Rolling.apply` where the applied function could be called on fewer than ``min_period`` periods if ``method="table"``. (:issue:`58868`) +- Bug in :meth:`Rolling.skew` incorrectly computing skewness for windows following outliers due to numerical instability. The calculation now properly handles catastrophic cancellation by recomputing affected windows (:issue:`47461`) - Bug in :meth:`Series.resample` could raise when the date range ended shortly before a non-existent time. (:issue:`58380`) - Bug in :meth:`Series.resample` raising error when resampling non-nanosecond resolutions out of bounds for nanosecond precision (:issue:`57427`) diff --git a/pandas/_libs/window/aggregations.pyx b/pandas/_libs/window/aggregations.pyx index 0c8ea28b60ce8..dccd93e8dafd9 100644 --- a/pandas/_libs/window/aggregations.pyx +++ b/pandas/_libs/window/aggregations.pyx @@ -1,6 +1,7 @@ # cython: boundscheck=False, wraparound=False, cdivision=True from libc.math cimport ( + fabs, round, signbit, sqrt, @@ -60,6 +61,12 @@ cdef: float64_t MAXfloat64 = np.inf float64_t NaN = np.nan + float64_t EpsF64 = np.finfo(np.float64).eps + + # Consider an operation ill-conditioned if + # it will only have up to 3 significant digits in base 10 remaining. + # https://en.wikipedia.org/wiki/Condition_number + float64_t InvCondTol = EpsF64 * 1e3 cdef bint is_monotonic_increasing_start_end_bounds( ndarray[int64_t, ndim=1] start, ndarray[int64_t, ndim=1] end @@ -482,18 +489,15 @@ def roll_var(const float64_t[:] values, ndarray[int64_t] start, cdef float64_t calc_skew(int64_t minp, int64_t nobs, - float64_t x, float64_t xx, float64_t xxx, + float64_t mean, float64_t m2, float64_t m3, int64_t num_consecutive_same_value ) noexcept nogil: cdef: float64_t result, dnobs - float64_t A, B, C, R + float64_t moments_ratio, correction if nobs >= minp: dnobs = nobs - A = x / dnobs - B = xx / dnobs - A * A - C = xxx / dnobs - A * A * A - 3 * A * B if nobs < 3: result = NaN @@ -501,21 +505,21 @@ cdef float64_t calc_skew(int64_t minp, int64_t nobs, # uniform case, force result to be 0 elif num_consecutive_same_value >= nobs: result = 0.0 - # #18044: with uniform distribution, floating issue will - # cause B != 0. and cause the result is a very + # #18044: with degenerate distribution, floating issue will + # cause m2 != 0. and cause the result is a very # large number. # # in core/nanops.py nanskew/nankurt call the function # _zero_out_fperr(m2) to fix floating error. # if the variance is less than 1e-14, it could be # treat as zero, here we follow the original - # skew/kurt behaviour to check B <= 1e-14 - elif B <= 1e-14: + # skew/kurt behaviour to check m2 <= n * 1e-14 + elif m2 <= dnobs * 1e-14: result = NaN else: - R = sqrt(B) - result = ((sqrt(dnobs * (dnobs - 1.)) * C) / - ((dnobs - 2) * R * R * R)) + moments_ratio = m3 / (m2 * sqrt(m2)) + correction = dnobs * sqrt((dnobs - 1)) / (dnobs - 2) + result = moments_ratio * correction else: result = NaN @@ -523,34 +527,36 @@ cdef float64_t calc_skew(int64_t minp, int64_t nobs, cdef void add_skew(float64_t val, int64_t *nobs, - float64_t *x, float64_t *xx, - float64_t *xxx, - float64_t *compensation_x, - float64_t *compensation_xx, - float64_t *compensation_xxx, + float64_t *mean, float64_t *m2, + float64_t *m3, + bint *numerically_unstable, int64_t *num_consecutive_same_value, float64_t *prev_value, ) noexcept nogil: """ add a value from the skew calc """ cdef: - float64_t y, t + float64_t n, delta, delta_n, term1, m3_update, new_m3 + + # Formulas adapted from + # https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Higher-order_statistics # Not NaN if val == val: - nobs[0] = nobs[0] + 1 - - y = val - compensation_x[0] - t = x[0] + y - compensation_x[0] = t - x[0] - y - x[0] = t - y = val * val - compensation_xx[0] - t = xx[0] + y - compensation_xx[0] = t - xx[0] - y - xx[0] = t - y = val * val * val - compensation_xxx[0] - t = xxx[0] + y - compensation_xxx[0] = t - xxx[0] - y - xxx[0] = t + nobs[0] += 1 + n = (nobs[0]) + delta = val - mean[0] + delta_n = delta / n + term1 = delta * delta_n * (n - 1.0) + + m3_update = delta_n * (term1 * (n - 2.0) - 3.0 * m2[0]) + new_m3 = m3[0] + m3_update + if (fabs(m3_update) + fabs(m3[0])) * InvCondTol > fabs(new_m3): + # possible catastrophic cancellation + numerically_unstable[0] = True + + m3[0] = new_m3 + m2[0] += term1 + mean[0] += delta_n # GH#42064, record num of same values to remove floating point artifacts if val == prev_value[0]: @@ -562,69 +568,63 @@ cdef void add_skew(float64_t val, int64_t *nobs, cdef void remove_skew(float64_t val, int64_t *nobs, - float64_t *x, float64_t *xx, - float64_t *xxx, - float64_t *compensation_x, - float64_t *compensation_xx, - float64_t *compensation_xxx) noexcept nogil: + float64_t *mean, float64_t *m2, + float64_t *m3, + bint *numerically_unstable) noexcept nogil: """ remove a value from the skew calc """ cdef: - float64_t y, t + float64_t n, delta, delta_n, term1, m3_update, new_m3 + + # This is the online update for the central moments + # when we remove an observation. + # + # δ = x - m_{n+1} + # m_{n} = m_{n+1} - (δ / n) + # m²_n = Σ_{i=1}^{n+1}(x_i - m_{n})² - (x - m_{n})² # uses new mean + # = m²_{n+1} - (δ²/n)*(n+1) + # m³_n = Σ_{i=1}^{n+1}(x_i - m_{n})³ - (x - m_{n})³ # uses new mean + # = m³_{n+1} - (δ³/n²)*(n+1)*(n+2) + 3 * m²_{n+1}*(δ/n) # Not NaN if val == val: - nobs[0] = nobs[0] - 1 + nobs[0] -= 1 + n = (nobs[0]) + delta = val - mean[0] + delta_n = delta / n + term1 = delta_n * delta * (n + 1.0) - y = - val - compensation_x[0] - t = x[0] + y - compensation_x[0] = t - x[0] - y - x[0] = t - y = - val * val - compensation_xx[0] - t = xx[0] + y - compensation_xx[0] = t - xx[0] - y - xx[0] = t - y = - val * val * val - compensation_xxx[0] - t = xxx[0] + y - compensation_xxx[0] = t - xxx[0] - y - xxx[0] = t + m3_update = delta_n * (term1 * (n + 2.0) - 3.0 * m2[0]) + new_m3 = m3[0] - m3_update + + if (fabs(m3_update) + fabs(m3[0])) * InvCondTol > fabs(new_m3): + # possible catastrophic cancellation + numerically_unstable[0] = True + + m3[0] = new_m3 + m2[0] -= term1 + mean[0] -= delta_n -def roll_skew(ndarray[float64_t] values, ndarray[int64_t] start, +def roll_skew(const float64_t[:] values, ndarray[int64_t] start, ndarray[int64_t] end, int64_t minp) -> np.ndarray: cdef: Py_ssize_t i, j - float64_t val, min_val, mean_val, sum_val = 0 - float64_t compensation_xxx_add, compensation_xxx_remove - float64_t compensation_xx_add, compensation_xx_remove - float64_t compensation_x_add, compensation_x_remove - float64_t x, xx, xxx + float64_t val + float64_t mean, m2, m3 float64_t prev_value - int64_t nobs = 0, N = len(start), V = len(values), nobs_mean = 0 + int64_t nobs = 0, N = len(start) int64_t s, e, num_consecutive_same_value - ndarray[float64_t] output, values_copy + ndarray[float64_t] output bint is_monotonic_increasing_bounds + bint requires_recompute, numerically_unstable = False minp = max(minp, 3) is_monotonic_increasing_bounds = is_monotonic_increasing_start_end_bounds( start, end ) output = np.empty(N, dtype=np.float64) - min_val = np.nanmin(values) - values_copy = np.copy(values) with nogil: - for i in range(0, V): - val = values_copy[i] - if val == val: - nobs_mean += 1 - sum_val += val - mean_val = sum_val / nobs_mean - # Other cases would lead to imprecision for smallest values - if min_val - mean_val > -1e5: - mean_val = round(mean_val) - for i in range(0, V): - values_copy[i] = values_copy[i] - mean_val - for i in range(0, N): s = start[i] @@ -632,46 +632,48 @@ def roll_skew(ndarray[float64_t] values, ndarray[int64_t] start, # Over the first window, observations can only be added # never removed - if i == 0 or not is_monotonic_increasing_bounds or s >= end[i - 1]: - - prev_value = values[s] - num_consecutive_same_value = 0 - - compensation_xxx_add = compensation_xxx_remove = 0 - compensation_xx_add = compensation_xx_remove = 0 - compensation_x_add = compensation_x_remove = 0 - x = xx = xxx = 0 - nobs = 0 - for j in range(s, e): - val = values_copy[j] - add_skew(val, &nobs, &x, &xx, &xxx, &compensation_x_add, - &compensation_xx_add, &compensation_xxx_add, - &num_consecutive_same_value, &prev_value) - - else: + requires_recompute = ( + i == 0 + or not is_monotonic_increasing_bounds + or s >= end[i - 1] + ) + if not requires_recompute: # After the first window, observations can both be added # and removed # calculate deletes for j in range(start[i - 1], s): - val = values_copy[j] - remove_skew(val, &nobs, &x, &xx, &xxx, &compensation_x_remove, - &compensation_xx_remove, &compensation_xxx_remove) + val = values[j] + remove_skew(val, &nobs, &mean, &m2, &m3, &numerically_unstable) # calculate adds for j in range(end[i - 1], e): - val = values_copy[j] - add_skew(val, &nobs, &x, &xx, &xxx, &compensation_x_add, - &compensation_xx_add, &compensation_xxx_add, + val = values[j] + add_skew(val, &nobs, &mean, &m2, &m3, &numerically_unstable, &num_consecutive_same_value, &prev_value) - output[i] = calc_skew(minp, nobs, x, xx, xxx, num_consecutive_same_value) + if requires_recompute or numerically_unstable: + + prev_value = values[s] + num_consecutive_same_value = 0 + + mean = m2 = m3 = 0.0 + nobs = 0 + + for j in range(s, e): + val = values[j] + add_skew(val, &nobs, &mean, &m2, &m3, &numerically_unstable, + &num_consecutive_same_value, &prev_value) + + numerically_unstable = False + + output[i] = calc_skew(minp, nobs, mean, m2, m3, num_consecutive_same_value) if not is_monotonic_increasing_bounds: nobs = 0 - x = 0.0 - xx = 0.0 - xxx = 0.0 + mean = 0.0 + m2 = 0.0 + m3 = 0.0 return output diff --git a/pandas/tests/window/test_rolling.py b/pandas/tests/window/test_rolling.py index 3003b142edd3b..5b00aeed79db6 100644 --- a/pandas/tests/window/test_rolling.py +++ b/pandas/tests/window/test_rolling.py @@ -1175,7 +1175,9 @@ def test_rolling_decreasing_indices(method): increasing = getattr(df.rolling(window=5), method)() decreasing = getattr(df_reverse.rolling(window=5), method)() - assert np.abs(decreasing.values[::-1][:-4] - increasing.values[4:]).max() < 1e-12 + tm.assert_almost_equal( + decreasing.values[::-1][:-4], increasing.values[4:], atol=1e-12 + ) @pytest.mark.parametrize( @@ -1441,17 +1443,30 @@ def test_rolling_skew_kurt_numerical_stability(method): @pytest.mark.parametrize( - ("method", "values"), + ("method", "data", "values"), [ - ("skew", [2.0, 0.854563, 0.0, 1.999984]), - ("kurt", [4.0, -1.289256, -1.2, 3.999946]), + ( + "skew", + [3000000, 1, 1, 2, 3, 4, 999], + [np.nan] * 3 + [2.0, 0.854563, 0.0, 1.999984], + ), + ( + "skew", + [1e6, -1e6, 1, 2, 3, 4, 5, 6], + [np.nan] * 3 + [-5.51135192e-06, -2.0, 0.0, 0.0, 0.0], + ), + ( + "kurt", + [3000000, 1, 1, 2, 3, 4, 999], + [np.nan] * 3 + [4.0, -1.289256, -1.2, 3.999946], + ), ], ) -def test_rolling_skew_kurt_large_value_range(method, values): - # GH: 37557 - s = Series([3000000, 1, 1, 2, 3, 4, 999]) +def test_rolling_skew_kurt_large_value_range(method, data, values): + # GH: 37557, 47461 + s = Series(data) result = getattr(s.rolling(4), method)() - expected = Series([np.nan] * 3 + values) + expected = Series(values) tm.assert_series_equal(result, expected) @@ -1837,9 +1852,11 @@ def test_rolling_skew_kurt_floating_artifacts(): sr = Series([1 / 3, 4, 0, 0, 0, 0, 0]) r = sr.rolling(4) result = r.skew() - assert (result[-2:] == 0).all() + expected = Series([np.nan, np.nan, np.nan, 1.9619045191072484, 2.0, 0.0, 0.0]) + tm.assert_series_equal(result, expected) result = r.kurt() - assert (result[-2:] == -3).all() + expected = Series([np.nan, np.nan, np.nan, 3.8636048803878786, 4.0, -3.0, -3.0]) + tm.assert_series_equal(result, expected) def test_numeric_only_frame(arithmetic_win_operators, numeric_only):