M/Ph:dZddlZddlZddlmZmZGddZdZddZ dd Z dd Z d Z ddZ ddZddZdZdZddZdS) zM Created on Thu Feb 11 09:19:30 2021 Author: Josef Perktold License: BSD-3 N) interpolatestatsceZdZdZddZdS)_GridazCreate Grid values and indices, grid in [0, 1]^d This class creates a regular grid in a d dimensional hyper cube. Intended for internal use, implementation might change without warning. Parameters ---------- k_grid : tuple or array_like number of elements for axes, this defines k_grid - 1 equal sized intervals of [0, 1] for each axis. eps : float If eps is not zero, then x values will be clipped to [eps, 1 - eps], i.e. to the interior of the unit interval or hyper cube. Attributes ---------- k_grid : list of number of grid points x_marginal: list of 1-dimensional marginal values idx_flat: integer array with indices x_flat: flattened grid values, rows are grid points, columns represent variables or axis. ``x_flat`` is currently also 2-dim in the univariate 1-dim grid case. rc ||_d|D}tjtjtjtj||t}||dz }dkr'fd|D}tj |dz }||_ ||_ ||_ dS)NcBg|]}tj||dz z S)nparange).0kis _/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/distributions/tools.py z"_Grid.__init__../s)@@@2bimmrAv.@@@rcBg|]}tj|dz Sr )r clip)r xiepss rrz"_Grid.__init__..6s+III"'"c1s733IIIrr ) k_gridr column_stack unravel_indexr prodastypefloatmaxr x_marginalidx_flatx_flat)selfrrrrrs ` r__init__z_Grid.__init__,s @@@@@ ? 276??!;!;VDD&-- HLLOO+ !88IIIIjIIIJWVS!c'22F$   rNr)__name__ __module__ __qualname____doc__r!rrrrs28rrctj|}|j}t |D]}||}|S)aCumulative probabilities from cell provabilites on a grid Parameters ---------- probs : array_like Rectangular grid of cell probabilities. Returns ------- cdf : ndarray Grid of cumulative probabilities with same shape as probs. axis)r asarraycopyndimrangecumsum)probscdfkis r prob2cdf_gridr4>sU *U   " "C A 1XX!!jjaj   Jrc| tj}tj|}|j}t |D]}tj|||}|S)aCell probabilities from cumulative probabilities on a grid. Parameters ---------- cdf : array_like Grid of cumulative probabilities with same shape as probs. Returns ------- probs : ndarray Rectangular grid of cell probabilities. N)prependr*)r _NoValuer+r,r-r.diff)r1r6probr2r3s r cdf2prob_gridr:Ssb+ :c??   ! !D A 1XX66wtW1555 Krslicingc|j}|dkr|}t|D]}tdddg|z}tdddg|z}tddd||<tddd||<t |}t |}||||zdz }n@|dkr:ddlm}||d |ztj dg|zzd }|Ntj d} t|D]%}| d tj ||z} &|| z}|S) a-Compute average for each cell in grid using endpoints Parameters ---------- values : array_like Values on a grid that will average over corner points of each cell. coords : None or list of array_like Grid coordinates for each axis use to compute volumne of cell. If None, then averaged values are not rescaled. _method : {"slicing", "convolve"} Grid averaging is implemented using numpy "slicing" or using scipy.signal "convolve". Returns ------- Grid with averaged cell values. r;Nr convolver)signalg?valid)mode.N) r-r,r.slicetuplescipyr@r?r onesarrayr8) valuescoords_methodk_dimpdsl1sl2r@dxs r average_gridrRkst$ KE) KKMMu & &AtT**+e3CtT**+e3C4T**CF1dD))CF**C**C3!C&A%AA & J        OOFCJ!u1E1E$E!(  * * Xa[[u 4 4AI!3!33BB F Hrd:0yE>c tj|}d}t|D])}|}t|jD]I t fdt|jD}|||dz}J|}||z}g}t|jD]m t fdt|jD}||d} |tj| nt||krd}n+|sddl m } tj d| |S) anearest matrix with uniform margins Parameters ---------- mat : array_like, 2-D Matrix that will be converted to have uniform margins. Currently, `mat` has to be two dimensional. maxiter : in Maximum number of iterations. tol : float Tolerance for convergence, defined for difference between largest and smallest margin in each dimension. Returns ------- ndarray, nearest matrix with uniform margins. Notes ----- This function is intended for internal use and will be generalized in future. API will change. changed in 0.14 to support k_dim > 2. Fc g|] }|k| Sr'r'r r3axs rrz*nearest_matrix_margins..BBBq!r'''''rT)r*keepdimsc g|] }|k| Sr'r'rWs rrz*nearest_matrix_margins..rYrr)ConvergenceWarningz,Iterations did not converge, maxiter reached)r r+r.r,r-rEsumappendptprstatsmodels.tools.sm_exceptionsr\warningswarn) matmaxitertolpc converged_pc0axsmptpsmargr\rXs @rnearest_matrix_marginsrms6 CBI 7^^ggii.. 3 3BBBBBE"'NNBBBCCC 266sT622 2CC  bffhh.. ' 'BBBBBE"'NNBBBCCC66sU633D LL & & & & u::  I E  *FFFFFF D( * * * Irc|j\}}tj||f}tj|d}tjd|dzdddf||tj|f<|S)zrankdata without ties for 2-d array This is a simplified version for ranking data if there are no ties. Works vectorized across columns. See Also -------- scipy.stats.rankdata rr)r N)shaper rGargsortr )xnobsk_varsrankssidxs r_rankdata_no_tiesrvsq7LD& GT6N # #E :aa D%'Yq$(%;%;AAAtG%DE$ &!! !" LrTctj|}|jd}|dz}t|g|zd}|r t ||jddzz }tj||j\}}|S)a=count of observations in bins (histogram) currently only for bivariate data Parameters ---------- data : array_like Bivariate data with observations in rows and two columns. Binning is in unit rectangle [0, 1]^2. If use_rank is False, then data should be in unit interval. k_bins : int Number of bins along each dimension in the histogram use_ranks : bool If use_rank is True, then data will be converted to ranks without tie handling. Returns ------- bin counts : ndarray Frequencies are the number of observations in a given bin. Bin counts are a 2-dim array with k_bins rows and k_bins columns. Notes ----- This function is intended for internal use and will be generalized in future. API will change. r=r rr)bins)r r+rorrv histogramddr)datak_bins use_ranksrLr2g2freqrrhs rfrequencies_fromdatars8 :d  D JrNE A sU{ " " "B= &&$*Q-!*;< ~d777HE1 Lr Fc|j}|dz}t|g|z}|rt|g|zd|z }||jj|}|d||zz z}t |} |rt| dd} nw| | z } n_t|g|zd}| |jj|} t| d } | | z} | S) aHistogram probabilities as approximation to a copula density. Parameters ---------- copula : instance Instance of a copula class. Only the ``pdf`` method is used. k_bins : int Number of bins along each dimension in the approximating histogram. force_uniform : bool If true, then the pdf grid will be adjusted to have uniform margins using `nearest_matrix_margin`. If false, then no adjustment is done and the margins may not be exactly uniform. use_pdf : bool If false, then the grid cell probabilities will be computed from the copula cdf. If true, then the density, ``pdf``, is used and cell probabilities are approximated by averaging the pdf of the cell corners. This is only useful if the cdf is not available. Returns ------- bin probabilites : ndarray Probability that random variable falls in given bin. This corresponds to a discrete distribution, and is not scaled to bin size to form a piecewise uniform, histogram density. Bin probabilities are a k-dim array with k_bins segments in each dimensionrows. Notes ----- This function is intended for internal use and will be generalized in future. API will change. r g?rxrSrT)rdregư>N)r6) rLrErpdfrreshaperRrmr]r1r:) copular| force_uniformuse_pdfrLr2ksgpdfgagpdf_gridcdfgs rapprox_copula_pdfrsF LE A sU{  B# 1#+3< 0 0 0+vzz!(##+R0 AuH  $    %-b#4HHHHHBFFHH}HH 1#+4 ( ( (+vzz!(##+R0 t444 HLLNN" Orbinomc|jd}tj|}tj|t }|dz }|dkrtj5tj dttj |||d}dddn #1swxYwY||zd}n|dkr-tj|dddfdd g} | |}n|d krtj5tj dttj|d|d z||z d z|d zz }dddn #1swxYwY||zd}nt'd |S) aEvaluate 1-dimensional bernstein polynomial given grid of values. experimental, comparing methods Parameters ---------- x : array_like Values at which to evaluate the Bernstein polynomial. fvals : ndarray Grid values of coefficients for Bernstein polynomial basis in the weighted sum. method: "binom", "beta" or "bpoly" Method to construct Bernstein polynomial basis, used for comparison of parameterizations. - "binom" uses pmf of Binomial distribution - "beta" uses pdf of Beta distribution - "bpoly" uses one interval in scipy.interpolate.BPoly Returns ------- Bernstein polynomial at evaluation points, weighted sum of Bernstein polynomial basis. r=g?rignorerCNbpolygr betazmethod not recogized)ror r+r rrlowerracatch_warnings simplefilterRuntimeWarningrrpmfr]rBPolyrr ValueError) rqfvalsmethodk_termsxxr2n poly_base bp_valuesbpbs r_eval_bernstein_1drMsC2k"oG AB '!!%((A" A ||~~   $ & & = =  !(N ; ; ; 1bm<AC  CC!AF>>GGc |j}|j}|dkrtdtj|}|jddkrtd|j\}}|ddz |ddz }}tj|dt} tj|dt} tj | ddddf||ddddftj | ddddf||ddddfz} || z d d} | S)aEvaluate 2-dimensional bernstein polynomial given grid of values experimental Parameters ---------- x : array_like Values at which to evaluate the Bernstein polynomial. fvals : ndarray Grid values of coefficients for Bernstein polynomial basis in the weighted sum. Returns ------- Bernstein polynomial at evaluation points, weighted sum of Bernstein polynomial basis. r>z `fval` needs to be 2-dimensionalr z*x needs to be bivariate and have 2 columnsrNr=) ror-rr atleast_2dTr rrrrrr]) rqrrrLrx1x2n1n2k1k2rrs r_eval_bernstein_2drs[$kG JE zz;<<< q  B x{aEFFF TFB QZ!^WQZ!^B 71:   % %e , ,B 71:   % %e , ,BD!!!TM!2B111dD=8IJJD$M!2B111dD=8IJJKI"''++//33I rcb|j}|j}tj|}tj|jd}t |D]}tj||t}t |dzD] }|d} ||dz } |dd|f} |dtj || | z}tj |}|j d|z} t |D]}| d} | S)aEvaluate d-dimensional bernstein polynomial given grid of valuesv experimental Parameters ---------- x : array_like Values at which to evaluate the Bernstein polynomial. fvals : ndarray Grid values of coefficients for Bernstein polynomial basis in the weighted sum. Returns ------- Bernstein polynomial at evaluation points, weighted sum of Bernstein polynomial basis. rr rCN)N.)ror-r rzerosr.r rrrr_logpmfexprr]) rqrrrLrrr3rrhnirrs r_eval_bernstein_ddrs%$kG JE q  B $$I 5\\KK Ywqz " " ) )% 0 0qs  AIBB QZ!^ 1Xi(5;+>+>r2r+J+JJ y!!I "Y.I 5\\%%MM!$$ rseqc tj|jd}|rt|z |dkr0fdt |D}tj|}n|drttjdddf}|}|ddddf fdt |D}tjjd}|||<ntd|fS) a Multivariate empiricial distribution function, empirical copula Notes ----- Method "seq" is faster than method "brute", but supports mainly bivariate case. Speed advantage of "seq" is increasing in number of observations and decreasing in number of variables. (see Segers ...) Warning: This does not handle ties. The ecdf is based on univariate ranks without ties. The assignment of ranks to ties depends on the sorting algorithm and the initial ordering of the data. When the original data is used instead of ranks, then method "brute" computes the correct ecdf counts even in the case of ties. rbrutecrg|]3}|kd4Sr allr])r r3rqs rrz_ecdf_mv..s9>>>1!9//!$$))++>>>rrNr cg|]>}d||kddz?S)Nr r)r r3rs rrz_ecdf_mv..sHNNN"RaR&BqE/..q115577!;NNNrzmethod not available) r r+rorvr. startswithrpemptyr) r{rr}rcount sort_idx0x_s0 count_smallerrqrs @@r_ecdf_mvrs( 4A  A% a 1 $ >>>>U1XX>>> 5!!   5 ! !1JqAw'' | !!!QRR%[NNNNU1XXNNN $$(i/000 !8Orr")Nr;)rSrT)T)rTF)r)rT)r&ranumpyr rFrrrr4r:rRrmrvrrrrrrr'rrrs@$$$$$$$$,,,,,,,,^*0- - - - `4444n$''''T::::~0000f$$$N)))X%%%%%%r