B &]\m: @s$dZddlmZmZmZddddddd d d d g Zdd lZddlmZm Z m Z dd l m Z ddl m Z ddlmZddlmZmZmZmZedddgd dfddZd%ddZedddgd fddZd&dd Zdddgd fdd Zdddgdd fd d Zd'd!dZd(d"dZd)d#dZd*d$d Z d S)+zB Additional statistics functions with support for masked arrays. )divisionprint_functionabsolute_importcompare_medians_ms hdquantileshdmedianhdquantiles_sd idealfourths median_cihsmjcimquantiles_cimjrshtrimmed_mean_ciN)float_int_ndarray) MaskedArray) mstats_basic)normbetatbinomg?g?g?FcCsdd}tj|dtd}tj|ddd}|dks:|jdkrH||||}n*|jdkr`td |jt|||||}tj|dd S) a Computes quantile estimates with the Harrell-Davis method. The quantile estimates are calculated as a weighted linear combination of order statistics. Parameters ---------- data : array_like Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. var : bool, optional Whether to return the variance of the estimate. Returns ------- hdquantiles : MaskedArray A (p,) array of quantiles (if `var` is False), or a (2,p) array of quantiles and variances (if `var` is True), where ``p`` is the number of quantiles. See Also -------- hdquantiles_sd c SsNtt|t}|j}tdt|ft }|dkrTtj |_ |rL|S|dSt |dt |}tj}xt|D]t\}} |||d| |dd| } | dd| dd} t| |} | |d|f<t| || d|d|f<qzW|d|d|dkf<|d|d|dkf<|rFtj |d|dkf<|d|dkf<|S|dS)zGComputes the HD quantiles for a 1D array. Returns nan for invalid data.rrN)npsqueezesort compressedviewrsizeemptylenrnanflatarangefloatrcdf enumeratedot) dataprobvarxsortednZhdvbetacdfip_wwZhd_meanr58lib/python3.7/site-packages/scipy/stats/mstats_extras.py_hd_1D>s,    "zhdquantiles.._hd_1DF)copydtyper)r8ndminNrzDArray 'data' must be at most two dimensional, but got data.ndim = %d)r8)maarrayrrndim ValueErrorapply_along_axis fix_invalid)r*r+axisr,r7r2resultr5r5r6rs  rcCst|dg||d}|S)a9 Returns the Harrell-Davis estimate of the median along the given axis. Parameters ---------- data : ndarray Data array. axis : int, optional Axis along which to compute the quantiles. If None, use a flattened array. var : bool, optional Whether to return the variance of the estimate. Returns ------- hdmedian : MaskedArray The median values. If ``var=True``, the variance is returned inside the masked array. E.g. for a 1-D array the shape change from (1,) to (2,). g?)rAr,)rr)r*rAr,rBr5r5r6rjscCsvdd}tj|dtd}tj|ddd}|dkr<|||}n(|jdkrTtd |jt||||}tj|dd S) a The standard error of the Harrell-Davis quantile estimates by jackknife. Parameters ---------- data : array_like Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- hdquantiles_sd : MaskedArray Standard error of the Harrell-Davis quantile estimates. See Also -------- hdquantiles c st|ttt|t}dkr6tj|_tt d}t j }xt |D]\}}||d|dd|}|dd|ddtj fddtDtd}tj|ddd t d} t dtt| t ||<q\W|S) z%Computes the std error for 1D arrays.rrNrc sDg|]<}ttjttd|tt|dftqS)rr)rr)Zr_listrangeastyper).0k)r.r4r-r5r6 sz4hdquantiles_sd.._hdsd_1D..)r9F)r8r:)rrrr"r!rr#r$r%r&rr'r(ZfromiterrDr<r,sqrtZdiagZdiagonal) r*r+ZhdsdZvvr0r1r2r3Zmx_Zmx_varr5)r.r4r-r6_hdsd_1Ds $0z hdquantiles_sd.._hdsd_1DF)r8r9r)r8r:NrzDArray 'data' must be at most two dimensional, but got data.ndim = %d)r8) r;r<rrr=r>r?r@Zravel)r*r+rArJr2rBr5r5r6rs   g?g?TT皙?c Cs|tj|dd}tj||||d}||}tj||||d}||d}td|d|} t || ||| |fS)a Selected confidence interval of the trimmed mean along the given axis. Parameters ---------- data : array_like Input data. limits : {None, tuple}, optional None or a two item tuple. Tuple of the percentages to cut on each side of the array, with respect to the number of unmasked data, as floats between 0. and 1. If ``n`` is the number of unmasked data before trimming, then (``n * limits[0]``)th smallest data and (``n * limits[1]``)th largest data are masked. The total number of unmasked data after trimming is ``n * (1. - sum(limits))``. The value of one limit can be set to None to indicate an open interval. Defaults to (0.2, 0.2). inclusive : (2,) tuple of boolean, optional If relative==False, tuple indicating whether values exactly equal to the absolute limits are allowed. If relative==True, tuple indicating whether the number of data being masked on each side should be rounded (True) or truncated (False). Defaults to (True, True). alpha : float, optional Confidence level of the intervals. Defaults to 0.05. axis : int, optional Axis along which to cut. If None, uses a flattened version of `data`. Defaults to None. Returns ------- trimmed_mean_ci : (2,) ndarray The lower and upper confidence intervals of the trimmed data. F)r8)limits inclusiverArg@) r;r<mstatsZtrimrZmeanZ trimmed_stdecountrppfr) r*rNrOalpharAZtrimmedZtmeanZtstdeZdfZtppfr5r5r6rs* cCsddd}tj|dd}|jdkr.td|jtj|ddd}|d krP|||St||||Sd S) a Returns the Maritz-Jarrett estimators of the standard error of selected experimental quantiles of the data. Parameters ---------- data : ndarray Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. c Sst|}|j}t||dt}tj}t t |t }tj d|dt d|}|d|}xnt |D]b\}} ||| d|| ||| d|| } t| |} t| |d} t| | d||<qpW|S)Ng?r)r9g?r)rrrr r<rErrr'r!r"rr%r(r)rI) r*r2r.r+r0Zmjxyr1mWZC1ZC2r5r5r6_mjci_1Ds ( zmjci.._mjci_1DF)r8rzDArray 'data' must be at most two dimensional, but got data.ndim = %dr)r8r:N)r;r<r=r>rr?)r*r+rArXr2r5r5r6r s   cCsZt|d|}td|d}tj||dd|d}t|||d}||||||fS)a Computes the alpha confidence interval for the selected quantiles of the data, with Maritz-Jarrett estimators. Parameters ---------- data : ndarray Data array. prob : sequence, optional Sequence of quantiles to compute. alpha : float, optional Confidence level of the intervals. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- ci_lower : ndarray The lower boundaries of the confidence interval. Of the same length as `prob`. ci_upper : ndarray The upper boundaries of the confidence interval. Of the same length as `prob`. rg@r)ZalphapZbetaprA)rA)minrrRrPZ mquantilesr )r*r+rSrAzZxqZsmjr5r5r6r !s cCsVdd}tj|dd}|dkr*|||}n(|jdkrBtd|jt||||}|S)aA Computes the alpha-level confidence interval for the median of the data. Uses the Hettmasperger-Sheather method. Parameters ---------- data : array_like Input data. Masked values are discarded. The input should be 1D only, or `axis` should be set to None. alpha : float, optional Confidence level of the intervals. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- median_cihs Alpha level confidence interval. c Ss>t|}t|}t|d|}tt|d|d}t|||dt|d|d}|d|kr|d8}t|||dt|d|d}t||d|dt||d}|d|||}|||t ||d||}|||d|||d||||dd||||f}|S)Nrg@g?r) rrrr"rYintrZ_ppfr'r&) r*rSr.rGZgkZgkkIZlambdZlimsr5r5r6_cihs_1DZs$ $$$*zmedian_cihs.._cihs_1DF)r8NrzDArray 'data' must be at most two dimensional, but got data.ndim = %d)r;r<r=r>r?)r*rSrAr]rBr5r5r6r Cs   cCsntj||dtj||d}}tj||dtj||d}}t||t|d|d}dt|S)a+ Compares the medians from two independent groups along the given axis. The comparison is performed using the McKean-Schrader estimate of the standard error of the medians. Parameters ---------- group_1 : array_like First dataset. Has to be of size >=7. group_2 : array_like Second dataset. Has to be of size >=7. axis : int, optional Axis along which the medians are estimated. If None, the arrays are flattened. If `axis` is not None, then `group_1` and `group_2` should have the same shape. Returns ------- compare_medians_ms : {float, ndarray} If `axis` is None, then returns a float, otherwise returns a 1-D ndarray of floats with a length equal to the length of `group_1` along `axis`. )rArr) r;ZmedianrPZ stde_medianrabsrIrr')Zgroup_1Zgroup_2rAZmed_1Zmed_2Zstd_1Zstd_2rWr5r5r6rvs  $cCs>dd}tj||dt}|dkr,||St|||SdS)aC Returns an estimate of the lower and upper quartiles. Uses the ideal fourths algorithm. Parameters ---------- data : array_like Input array. axis : int, optional Axis along which the quartiles are estimated. If None, the arrays are flattened. Returns ------- idealfourths : {list of floats, masked array} Returns the two internal values that divide `data` into four parts using the ideal fourths algorithm either along the flattened array (if `axis` is None) or along `axis` of `data`. cSs|}t|}|dkr$tjtjgSt|ddd\}}t|}d|||d|||}||}d||||||d}||gS)Ng@g?r)rr"rr#divmodr[)r*rTr.jhZqlorGZqupr5r5r6_idfs   zidealfourths.._idf)rAN)r;rrrr?)r*rArcr5r5r6r s  cCstj|dd}|dkr|}ntj|ddd}|jdkr>td|}t|dd}d|d |d |d }|dddf|dddf|kd }|dddf|dddf|kd }||d ||S) a Evaluates Rosenblatt's shifted histogram estimators for each data point. Rosenblatt's estimator is a centered finite-difference approximation to the derivative of the empirical cumulative distribution function. Parameters ---------- data : sequence Input data, should be 1-D. Masked values are ignored. points : sequence or None, optional Sequence of points where to evaluate Rosenblatt shifted histogram. If None, use the data. F)r8Nr)r8r:z#The input array should be 1D only !)rAg333333?rrg?g@)r;r<rr=AttributeErrorrQr sum)r*Zpointsr.rrbZnhiZnlor5r5r6r s  **)rF)rKrLrMN)rMN)N)N)N)!__doc__Z __future__rrr__all__ZnumpyrrrrZnumpy.mar;rrrPZscipy.stats.distributionsrrrrrCrrrrr r r rr r r5r5r5r6s0   K = 2-" 3 ! (