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mstats_extras.cpython-35.pyc
�B�W�7 � @ s� d Z d d l m Z m Z m Z d d d d d d d d d d g Z d d l Z d d l m Z m Z m Z d d l j Z d d l m Z d d l m Z d d l m Z m Z m Z m Z e d d d g � d d d d � Z d$ d d d � Z e d d d g � d d d � Z d% d& d d d d � Z d d d g d d d � Z d d d g d d d d � Z d d d d � Z d d! d � Z d d" d � Z d d# d � Z d S)'zB Additional statistics functions with support for masked arrays. � )�division�print_function�absolute_import�compare_medians_ms� hdquantiles�hdmedian�hdquantiles_sd� idealfourths� median_cihs�mjci�mquantiles_cimj�rsh�trimmed_mean_ciN)�float_�int_�ndarray)� MaskedArray� )� mstats_basic)�norm�beta�t�binomg �?g �?g �?Fc C s� d d � } t j | d d d t �} t j | d d d d �} | d k s] | j d k rr | | | | � } n= | j d k r� t d | j � � t j | | | | | � } t j | d d �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. c S s� t j t j | j � j t � � � } | j } t j d t | � f t � } | d k rx t j | _ | rp | S| d St j | d � t | � } t j } x� t | � D]� \ } } | | | d | | d d | � } | d d � | d d � } t j | | � } | | d | f <t j | | | d � | d | f <q� W| d | d | d k f <| d | d | d k f <| r�t j | d | d k f <| d | d k f <| S| d S)zGComputes the HD quantiles for a 1D array. Returns nan for invalid data.� r r N���r )�np�squeeze�sort� compressed�viewr �size�empty�lenr �nan�flat�arange�floatr �cdf� enumerate�dot) �data�prob�var�xsorted�nZhd�v�betacdf�i�p�_w�wZhd_mean� r5 �/mstats_extras.py�_hd_1D: s, ' & (-zhdquantiles.<locals>._hd_1D�copyF�dtype�ndminr Nr zDArray 'data' must be at most two dimensional, but got data.ndim = %d)�ma�arrayr r �ndim� ValueError�apply_along_axis� fix_invalid)r* r+ �axisr, r7 r2 �resultr5 r5 r6 r s c C s( t | d g d | d | �} | j � S)a\ 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. g �?rA r, )r r )r* rA r, rB r5 r5 r6 r f s c C s� d d � } t j | d d d t �} t j | d d d d �} | d k r` | | | � } n: | j d k r� t d | j � � t j | | | | � } t j | d d �j � 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. c s} t j | j � � � t � � � t j t | � t � } � d k rQ t j | _ t j � � t � d � } t j } x� t | � D]� \ } } | | � d | � d d | � } | d d � | d d � � t j � � � f d d � t � � D� d t �} t j | j � d d d d �� t � d � } t � d � t j t j | � j � t � � � | | <q� W| S) z%Computes the std error for 1D arrays.r r Nc s^ g | ]T } t j � � t j t t d | � � t t | d � � � f j t � � � q S)r r )r r) Zr_�list�range�astyper )�.0�k)r. r4 r- r5 r6 � <listcomp>� s z4hdquantiles_sd.<locals>._hdsd_1D.<locals>.<listcomp>r9 r8 Fr: r )r r r r" r! r r# r$ r% r& r r' r( ZfromiterrD r< r, �sqrtZdiagZdiagonal) r* r+ ZhdsdZvvr0 r1 r2 r3 Zmx_Zmx_varr5 )r. r4 r- r6 �_hdsd_1D� s & 3>z hdquantiles_sd.<locals>._hdsd_1Dr8 Fr9 r: r Nr zDArray 'data' must be at most two dimensional, but got data.ndim = %d) r; r< r r r= r> r? r@ Zravel)r* r+ rA rJ r2 rB r5 r5 r6 r y s 皙�����?Tg�������?c C s� t j | d d �} t j | d | d | d | �} | j | � } t j | d | d | d | �} | j | � d } t j d | d | � } t j | | | | | | f � S)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. r8 F�limits� inclusiverA r g @) r; r< �mstatsZtrimrZmeanZ trimmed_stde�countr �ppfr ) r* rL rM �alpharA ZtrimmedZtmeanZtstde�dfZtppfr5 r5 r6 r � s *!!c C s� d d � } t j | d d �} | j d k rC t d | j � � t j | d d d d �} | d k rw | | | � St j | | | | � 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 S s# t j | j � � } | j } t j | � | d j t � } t j } t j t | � t � } t j d | d d t �| } | d | } x� t | � D]� \ } } | | | d | | � | | | d | | � } t j | | � } t j | | d � } t j | | d � | | <q� W| S)Ng �?r r9 g �?r )r r r r r< rE r r r' r! r" r r% r( r) rI ) r* r2 r. r+ r0 Zmj�x�yr1 �m�WZC1ZC2r5 r5 r6 �_mjci_1D� s 2 zmjci.<locals>._mjci_1Dr8 Fr zDArray 'data' must be at most two dimensional, but got data.ndim = %dr: r N)r; r< r= r> r r? )r* r+ rA rW r2 r5 r5 r6 r � s c C s} t | d | � } t j d | d � } t j | | d d d d d | �} t | | d | �} | | | | | | f S)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. r g @Zalphapr ZbetaprA )�minr rP rN Z mquantilesr )r* r+ rQ rA �zZxqZsmjr5 r5 r6 r s $c C s� d d � } t j | d d �} | d k rE | | j � | � } n: | j d k rg t d | j � � t j | | | | � } | 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 S s� t j | j � � } t | � } t | d | � } t t j | d | d � � } t j | | | d � t j | d | d � } | d | k r� | d 8} t j | | | d � t j | d | d � } t j | | d | d � t j | | d � } | d | | | } | | | t | | d | | � } | | | d | | | d | | | | d d | | | | f } | S)Nr g @g �?r ) r r r r" rX �intr Z_ppfr' r& ) r* rQ r. rG ZgkZgkk�I�lambdZlimsr5 r5 r6 �_cihs_1DA s 0 00( -z median_cihs.<locals>._cihs_1Dr8 FNr zDArray 'data' must be at most two dimensional, but got data.ndim = %d)r; Zrrayr r= r> r? )r* rQ rA r] rB r5 r5 r6 r * s c C s� t j | d | �t j | d | �} } t j | d | �t j | d | �} } t j | | � t j | d | d � } d t j | � 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. group_2 : array_like Second dataset. 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`. rA r r ) r; ZmedianrN Z stde_medianr �absrI r r' )Zgroup_1Zgroup_2rA Zmed_1Zmed_2Zstd_1Zstd_2rV r5 r5 r6 r ] s +,c C sW d d � } t j | d | �j t � } | d k r@ | | � St j | | | � Sd S)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`. c S s� | j � } t | � } | d k r4 t j t j g St | d d d � \ } } t | � } d | | | d | | | } | | } d | | | | | | d } | | g S)N� g @� g (@r g�������?)r r" r r# �divmodrZ )r* rS r. �j�hZqlorG Zqupr5 r5 r6 �_idf� s " "zidealfourths.<locals>._idfrA N)r; r r r r? )r* rA rd r5 r5 r6 r ~ s c C s" t j | d d �} | d k r* | } n t j | d d d d �} | j d k r` t d � � | j � } t | d d �} d | d | d | d } | d d � d f | d d d � f | k j d � } | d d � d f | d d d � f | k j d � } | | d | | S)a\ Evaluates Rosenblatt's shifted histogram estimators for each point on the dataset 'data'. Parameters ---------- data : sequence Input data. Masked values are ignored. points : sequence or None, optional Sequence of points where to evaluate Rosenblatt shifted histogram. If None, use the data. r8 FNr: r z#The input array should be 1D only !rA g333333�?r g �?r` g @r g�������?)r; r< r r= �AttributeErrorrO r �sum)r* Zpointsr. �rrc ZnhiZnlor5 r5 r6 r � s 99r )rK rK )TT)!�__doc__Z __future__r r r �__all__Znumpyr r r r Znumpy.mar; r � r rN Zscipy.stats.distributionsr r r r rC r r r r r r r r r r r5 r5 r5 r6 �<module> s0 "$G!82- 3!(
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