B d1@s,dZddlZddlZdgZGdddZdS)zF This module implements functions and classes for spatial statistics. NRipleysKEstimatorc@seZdZdZd!ddZeddZejddZedd Zejd d Zed d Z e jd d Z eddZ e jddZ eddZ e jddZ d"ddZ ddZ ddZd#ddZd$ddZd%dd ZdS)&ra Estimators for Ripley's K function for two-dimensional spatial data. See [1]_, [2]_, [3]_, [4]_, [5]_ for detailed mathematical and practical aspects of those estimators. Parameters ---------- area : float Area of study from which the points where observed. x_max, y_max : float, float, optional Maximum rectangular coordinates of the area of study. Required if ``mode == 'translation'`` or ``mode == ohser``. x_min, y_min : float, float, optional Minimum rectangular coordinates of the area of study. Required if ``mode == 'variable-width'`` or ``mode == ohser``. Examples -------- >>> import numpy as np >>> from matplotlib import pyplot as plt # doctest: +SKIP >>> from astropy.stats import RipleysKEstimator >>> z = np.random.uniform(low=5, high=10, size=(100, 2)) >>> Kest = RipleysKEstimator(area=25, x_max=10, y_max=10, ... x_min=5, y_min=5) >>> r = np.linspace(0, 2.5, 100) >>> plt.plot(r, Kest.poisson(r)) # doctest: +SKIP >>> plt.plot(r, Kest(data=z, radii=r, mode='none')) # doctest: +SKIP >>> plt.plot(r, Kest(data=z, radii=r, mode='translation')) # doctest: +SKIP >>> plt.plot(r, Kest(data=z, radii=r, mode='ohser')) # doctest: +SKIP >>> plt.plot(r, Kest(data=z, radii=r, mode='var-width')) # doctest: +SKIP >>> plt.plot(r, Kest(data=z, radii=r, mode='ripley')) # doctest: +SKIP References ---------- .. [1] Peebles, P.J.E. *The large scale structure of the universe*. .. [2] Spatial descriptive statistics. .. [3] Package spatstat. .. [4] Cressie, N.A.C. (1991). Statistics for Spatial Data, Wiley, New York. .. [5] Stoyan, D., Stoyan, H. (1992). Fractals, Random Shapes and Point Fields, Akademie Verlag GmbH, Chichester. NcCs"||_||_||_||_||_dS)N)areax_maxy_maxx_miny_min)selfrrrrrr b/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/astropy/stats/spatial.py__init__=s zRipleysKEstimator.__init__cCs|jS)N)_area)rr r r rDszRipleysKEstimator.areacCs2t|ttfr|dkr||_ntd|ddS)Nrz.area is expected to be a positive number. Got .) isinstancefloatintr ValueError)rvaluer r r rHscCs|jS)N)_y_max)rr r r rOszRipleysKEstimator.y_maxcCs0|dkst|ttfr||_ntd|dS)Nz6y_max is expected to be a real number or None. Got {}.)rrrrrformat)rrr r r rSscCs|jS)N)_x_max)rr r r r[szRipleysKEstimator.x_maxcCs0|dkst|ttfr||_ntd|dS)Nz6x_max is expected to be a real number or None. Got {}.)rrrrrr)rrr r r r_scCs|jS)N)_y_min)rr r r rgszRipleysKEstimator.y_mincCs2|dkst|ttfr||_ntd|ddS)Nz+y_min is expected to be a real number. Got r )rrrrr)rrr r r rkscCs|jS)N)_x_min)rr r r rrszRipleysKEstimator.x_mincCs2|dkst|ttfr||_ntd|ddS)Nz+x_min is expected to be a real number. Got r )rrrrr)rrr r r rvsnonecCs|j|||dS)N)dataradiimode)evaluate)rrrrr r r __call__}szRipleysKEstimator.__call__cCst|}tj||dddftjd}d}xPt|dD]@}||d}t||||dd||||<||7}q:W|S)N)shapedtyper)lennpzerosdoublerangeabs)rrnptsdiffkisizer r r _pairwise_diffss  ( z!RipleysKEstimator._pairwise_diffscCstj||S)a Evaluates the Ripley K function for the homogeneous Poisson process, also known as Complete State of Randomness (CSR). Parameters ---------- radii : 1D array Set of distances in which Ripley's K function will be evaluated. Returns ------- output : 1D array Ripley's K function evaluated at ``radii``. )r#pi)rrr r r poissonszRipleysKEstimator.poissoncCst|j|||dtjS)zs Evaluates the L function at ``radii``. For parameter description see ``evaluate`` method. )r)r#sqrtrr.)rrrrr r r LfunctionszRipleysKEstimator.LfunctioncCs|j|||d|S)zs Evaluates the H function at ``radii``. For parameter description see ``evaluate`` method. )r)r1)rrrrr r r HfunctionszRipleysKEstimator.Hfunctionc$ Cs8t|}|jddks tdt|}tt|}|dkr||}t|dddf|dddf}x(tt|D]}|||k ||<qzW|j d|||d}n|dkr~||}t|dddf|dddf}|j |j |dddf|j |j|dddf} x6tt|D]&}|||k} d| |  ||<q2W|j d||dd|}n|d kr||}t|dddf|dddf}|j } t|j |j|j |j |j |j |j |j} |t| | } t| | d| dk}t| | | d| t| ddk| | k}tjd| dd| | | | }dtd| | dkd| d| |}dt| ||| | | | k| t| ddkd|d|| | d| | | }| tj|| dk| dk|| dk| | k|| | k| t| ddk}x6tt|D]&}|||k} d||  ||<qhW|j d||dd|}n|d krtt|j |dddf|j |dddft|dddf|j |dddf|j}xtt|D]}xt|D]~}xvt|D]j}||krLt||||}t|| }|||kr||krLnn||d||<qLWq>W|||k }|dks0|||||<q0W|j ||}n2|d kr$tj||ddtjd }tj||ddtjd }xt|dD]}t|j ||d||d|j }t|j ||d||d|j}|d|d|dd}|dd|d|d}|t|d||||<|t|d||||<qRW||}t|dddf|dddf}|t||k} dtt|||tt|||tj}!d dt||| t||| tj}"| |!| |"}#x.tt|D]}|||k|# ||<qW|j d|||d}ntd|d|S)a Evaluates the Ripley K estimator for a given set of values ``radii``. Parameters ---------- data : 2D array Set of observed points in as a n by 2 array which will be used to estimate Ripley's K function. radii : 1D array Set of distances in which Ripley's K estimator will be evaluated. Usually, it's common to consider max(radii) < (area/2)**0.5. mode : str Keyword which indicates the method for edge effects correction. Available methods are 'none', 'translation', 'ohser', 'var-width', and 'ripley'. * 'none' this method does not take into account any edge effects whatsoever. * 'translation' computes the intersection of rectangular areas centered at the given points provided the upper bounds of the dimensions of the rectangular area of study. It assumes that all the points lie in a bounded rectangular region satisfying x_min < x_i < x_max; y_min < y_i < y_max. A detailed description of this method can be found on ref [4]. * 'ohser' this method uses the isotropized set covariance function of the window of study as a weight to correct for edge-effects. A detailed description of this method can be found on ref [4]. * 'var-width' this method considers the distance of each observed point to the nearest boundary of the study window as a factor to account for edge-effects. See [3] for a brief description of this method. * 'ripley' this method is known as Ripley's edge-corrected estimator. The weight for edge-correction is a function of the proportions of circumferences centered at each data point which crosses another data point of interest. See [3] for a detailed description of this method. Returns ------- ripley : 1D array Ripley's K function estimator evaluated at ``radii``. rrzGdata must be an n by 2 array, where n is the number of observed points.rNrg@ translationZohserz var-widthripley)r r!g?g?zmode z is not implemented.)r#Zasarrayr rr"r$r-hypotr&sumrrrrrmaxmathr0r.Zarcsinminimumr'r%minZonesZarccos)$rrrrr(r4r)Z distancesrZ intersec_areaZdist_indicatorabxuvc1c2c3Zcov_funcZlt_distr+jdistZ lt_dist_sumZhor_distZver_distr*Z min_hor_distZ min_ver_diststartendZdist_indZw1Zw2weightr r r rs2  $  $ "  $4&.dL " 22 $    $ $ 4zRipleysKEstimator.evaluate)NNNN)r)r)r)r)__name__ __module__ __qualname____doc__r propertyrsetterrrrrrr-r/r1r2rr r r r rs$-          )rLnumpyr#r8__all__rr r r r s