Q(hddlZddlmZddlmZmZmZddlm Z dgZ dZ dZ dZ d Ze ed d ed d dddddZy)N)stats) _SimpleNormalSignificanceResult _get_pvalue)_axis_nan_policy_factory chatterjeexic|jd}tj|d}tj||\}}tj||d}t j |dd}t j | dd}tjtjtj|dd}|rdd|z|dzdz z z }n+dtj||z |zdz} d||z| z z }|||fS)Naxismax)methodr ) shapenpargsortbroadcast_arraystake_along_axisrrankdatasumabsdiff) xy y_continuousnjrlnum statisticdens V/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/scipy/stats/_correlation.py _xi_statisticr&s  A 12A  q! $DAq 1ab)A qR0A r%b1A &&+,2 6CC16A:.. "&&!a%12..C# % a?ctj|jd}|r+tjdtj|z Stjd|dz}tj |d}tj |d}d|dzz tjd|zd|zz dz|dzzdz}d|dzz tj|||z |zzdzdz}d|dzz tjd|zd|zz dz|zdz} d|dzz tj|||z zdz} |d|zz | dzz| dzz } tj| tj|z S) Nr g?rr rr)rfloat64rsqrtarangesortcumsumr) r r!rriuvanbncndntau2s r%_xi_stdr8*se 1772;Awwu~ ** !QUA A !"A QTBFFAaC!A#IMQT1; ;B QTBFFAQ MA-B7 7B QTBFFAaC!A#IMQ.R8 8B QTBFFAQKr2 2B 2IA Q &D 774=2771: %%r'c|dvr tdt|tjs"|j }d}|dk7r t|||fS)N>FTz`y_continuous` must be boolean.z@`method` must be 'asymptotic' or a `PermutationMethod` instance. asymptotic) ValueError isinstancerPermutationMethodlower)rrmessages r%_chatterjeexi_ivr@DsV=(:;; fe55 6T \ !W% %  r'c2|j|jfS)N)r#pvalue)ress r%_unpackrDTs ==#** $$r'Trr)paired n_samplesresult_to_tuple n_outputs too_smallFr:)r rrct|\}d}|dk(r:t|\}}}t||} t} t || z | |} nct |t jrIt jd |ffd|dd|jddi} | 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]) greaterr:) alternativec$t|dS)Nr)r&)rr rrs r%zchatterjeexi..sq!\1RST1Ur'pairings)datar#rLpermutation_typer r ) r@r&r8rrr<rr=permutation_test_asdictr#rBr) rrr rrrLxir r!stdnormrBrCs ` ` r%rrXsJ,L&AL& K  A|4AqaL)R#XtE FE33 4$$!U#jEKNNDT  ]]CJJF b& ))r')numpyrscipyrscipy.stats._stats_pyrrrscipy.stats._axis_nan_policyr__all__r&r8r@rDrrRr'r%r]sdPPA  8&4  %,TQ*1Q!M u\x*Mx*r'