σ šίΘ[c@`ssddlmZmZmZmZddlZddlmZddgZ idgd6Z d„Z d d „Z dS( i(tabsolute_importtdivisiontprint_functiontunicode_literalsNi(trangeujackknife_resamplingujackknife_statsu scipy.specialcC`sr|jd}|dkr(tdƒ‚ntj||dgƒ}x*t|ƒD]}tj||ƒ|| .. [2] Efron, Bradley. "The Jackknife, the Bootstrap, and other Resampling Plans". Technical Report No. 63, Division of Biostatistics, Stanford University, December, 1980. .. [3] Jackknife resampling iu+data must contain at least one measurement.i(tshapet ValueErrortnptemptyRtdelete(tdatatnt resamplesti((s6lib/python2.7/site-packages/astropy/stats/jackknife.pytjackknife_resampling s"  gffffffξ?cC`s:ddlm}|jd}|dkr8tdƒ‚nt|ƒ}||ƒ}tj|d|ƒ}tj|ddƒ}|d||} tj|dtj||||ddƒƒ} || } d|koίdknsσtdƒ‚ntjdƒ||ƒ} | | tj | | fƒ} | | | | fS(u• Performs jackknife estimation on the basis of jackknife resamples. This function requires `SciPy `_ to be installed. Parameters ---------- data : numpy.ndarray Original sample (1-D array). statistic : function Any function (or vector of functions) on the basis of the measured data, e.g, sample mean, sample variance, etc. The jackknife estimate of this statistic will be returned. conf_lvl : float, optional Confidence level for the confidence interval of the Jackknife estimate. Must be a real-valued number in (0,1). Default value is 0.95. Returns ------- estimate : numpy.float64 or numpy.ndarray The i-th element is the bias-corrected "jackknifed" estimate. bias : numpy.float64 or numpy.ndarray The i-th element is the jackknife bias. std_err : numpy.float64 or numpy.ndarray The i-th element is the jackknife standard error. conf_interval : numpy.ndarray If ``statistic`` is single-valued, the first and second elements are the lower and upper bounds, respectively. If ``statistic`` is vector-valued, each column corresponds to the confidence interval for each component of ``statistic``. The first and second rows contain the lower and upper bounds, respectively. Examples -------- 1. Obtain Jackknife resamples: >>> import numpy as np >>> from astropy.stats import jackknife_resampling >>> from astropy.stats import jackknife_stats >>> data = np.array([1,2,3,4,5,6,7,8,9,0]) >>> resamples = jackknife_resampling(data) >>> resamples array([[ 2., 3., 4., 5., 6., 7., 8., 9., 0.], [ 1., 3., 4., 5., 6., 7., 8., 9., 0.], [ 1., 2., 4., 5., 6., 7., 8., 9., 0.], [ 1., 2., 3., 5., 6., 7., 8., 9., 0.], [ 1., 2., 3., 4., 6., 7., 8., 9., 0.], [ 1., 2., 3., 4., 5., 7., 8., 9., 0.], [ 1., 2., 3., 4., 5., 6., 8., 9., 0.], [ 1., 2., 3., 4., 5., 6., 7., 9., 0.], [ 1., 2., 3., 4., 5., 6., 7., 8., 0.], [ 1., 2., 3., 4., 5., 6., 7., 8., 9.]]) >>> resamples.shape (10, 9) 2. Obtain Jackknife estimate for the mean, its bias, its standard error, and its 95% confidence interval: >>> test_statistic = np.mean >>> estimate, bias, stderr, conf_interval = jackknife_stats( ... data, test_statistic, 0.95) >>> estimate 4.5 >>> bias 0.0 >>> stderr 0.95742710775633832 >>> conf_interval array([ 2.62347735, 6.37652265]) 3. Example for two estimates >>> test_statistic = lambda x: (np.mean(x), np.var(x)) >>> estimate, bias, stderr, conf_interval = jackknife_stats( ... data, test_statistic, 0.95) >>> estimate array([ 4.5 , 9.16666667]) >>> bias array([ 0. , -0.91666667]) >>> stderr array([ 0.95742711, 2.69124476]) >>> conf_interval array([[ 2.62347735, 3.89192387], [ 6.37652265, 14.44140947]]) IMPORTANT: Note that confidence intervals are given as columns i(terfinvu+data must contain at least one measurement.itaxisu#confidence level must be in (0, 1).g@( t scipy.specialRRRRRtapply_along_axistmeantsqrttarray(R t statistictconf_lvlRR R t stat_datat jack_stattmean_jack_stattbiaststd_errtestimatetz_scoret conf_interval((s6lib/python2.7/site-packages/astropy/stats/jackknife.pytjackknife_stats;s"[     ( t __future__RRRRtnumpyRtextern.six.movesRt__all__t__doctest_requires__RR (((s6lib/python2.7/site-packages/astropy/stats/jackknife.pyts "   .