o  h@sddlZddlmZddlmZmZmZddlm Z dgZ ddZ dd Z d d Z d d Ze eddedddddddddZdS)N)stats) _SimpleNormalSignificanceResult _get_pvalue)_axis_nan_policy_factory chatterjeexic Cs|jd}tj|dd}t||\}}tj||dd}tj|ddd}tj| ddd}tjttj |dddd}|rKdd||dd}ndtj|||dd} d||| }|||fS)Naxismax)methodr ) shapenpargsortbroadcast_arraystake_along_axisrrankdatasumabsdiff) xy y_continuousnjrlnum statisticdenr#L/var/www/vscode/kcb/lib/python3.10/site-packages/scipy/stats/_correlation.py _xi_statistics  r%c Cs0t|jd}|rtdt|Std|d}tj|dd}tj|dd}d|dtjd|d|d|ddd}d|dtj||||ddd}d|dtjd|d|d|dd} d|dtj|||dd} |d|| d| d} t| t|S) Nrg?r r rr)rfloat64rsqrtarangesortcumsumr) rrrriuvanbncndntau2r#r#r$_xi_std*s2*."r5cCs@|dvrtdt|tjs|}d}|dkrt|||fS)N>FTz`y_continuous` must be boolean.z@`method` must be 'asymptotic' or a `PermutationMethod` instance. asymptotic) ValueError isinstancerPermutationMethodlower)rr messager#r#r$_chatterjeexi_ivDs r<cCs |j|jfS)N)r!pvalue)resr#r#r$_unpackTs r?Trr )paired n_samplesresult_to_tuple n_outputs too_smallFr6)r rr c st|\}d}|dkr)t|\}}}t||} t} t|| | |d} n&t|tjrOtjd |ffdd|dd| dd i} | j | j }} t || S) aCompute the xi correlation and perform a test of independence The xi correlation coefficient is a measure of association between two variables; the value tends to be close to zero when the variables are independent and close to 1 when there is a strong association. Unlike other correlation coefficients, the xi correlation is effective even when the association is not monotonic. Parameters ---------- x, y : array-like The samples: corresponding observations of the independent and dependent variable. The (N-d) arrays must be broadcastable. axis : int, default: 0 Axis along which to perform the test. method : 'asymptotic' or `PermutationMethod` instance, optional Selects the method used to calculate the *p*-value. Default is 'asymptotic'. The following options are available. * ``'asymptotic'``: compares the standardized test statistic against the normal distribution. * `PermutationMethod` instance. In this case, the p-value is computed using `permutation_test` with the provided configuration options and other appropriate settings. y_continuous : bool, default: False Whether `y` is assumed to be drawn from a continuous distribution. If `y` is drawn from a continuous distribution, results are valid whether this is assumed or not, but enabling this assumption will result in faster computation and typically produce similar results. Returns ------- res : SignificanceResult An object containing attributes: statistic : float The xi correlation statistic. pvalue : float The associated *p*-value: the probability of a statistic at least as high as the observed value under the null hypothesis of independence. See Also -------- scipy.stats.pearsonr, scipy.stats.spearmanr, scipy.stats.kendalltau Notes ----- There is currently no special handling of ties in `x`; they are broken arbitrarily by the implementation. [1]_ notes that the statistic is not symmetric in `x` and `y` *by design*: "...we may want to understand if :math:`Y` is a function :math:`X`, and not just if one of the variables is a function of the other." See [1]_ Remark 1. References ---------- .. [1] Chatterjee, Sourav. "A new coefficient of correlation." Journal of the American Statistical Association 116.536 (2021): 2009-2022. :doi:`10.1080/01621459.2020.1758115`. Examples -------- Generate perfectly correlated data, and observe that the xi correlation is nearly 1.0. >>> import numpy as np >>> from scipy import stats >>> rng = np.random.default_rng(348932549825235) >>> x = rng.uniform(0, 10, size=100) >>> y = np.sin(x) >>> res = stats.chatterjeexi(x, y) >>> res.statistic np.float64(0.9012901290129013) The probability of observing such a high value of the statistic under the null hypothesis of independence is very low. >>> res.pvalue np.float64(2.2206974648177804e-46) As noise is introduced, the correlation coefficient decreases. >>> noise = rng.normal(scale=[[0.1], [0.5], [1]], size=(3, 100)) >>> res = stats.chatterjeexi(x, y + noise, axis=-1) >>> res.statistic array([0.79507951, 0.41824182, 0.16651665]) Because the distribution of `y` is continuous, it is valid to pass ``y_continuous=True``. The statistic is identical, and the p-value (not shown) is only slightly different. >>> stats.chatterjeexi(x, y + noise, y_continuous=True, axis=-1).statistic array([0.79507951, 0.41824182, 0.16651665]) greaterr6) alternativecst|dS)Nr)r%)rr rrr#r$szchatterjeexi..pairings)datar!rFpermutation_typer rNr#) r<r%r5rrr8rr9permutation_test_asdictr!r=r) rrr rr rFxirrstdnormr=r>r#rGr$rXs$e   )numpyrscipyrscipy.stats._stats_pyrrrscipy.stats._axis_nan_policyr__all__r%r5r<r?rr#r#r#r$s