M/PhE6dZddlZd dZdZdZd dZd dZdS) zLow discrepancy sequence tools.Nc tj|}|j\}}|7|d}|d}||z ||z z }t |dz }tjtjdd|zzd|dzzz d}d}t|D]i} |dd| f} |ddt | dddfdz zzdt | dz zzdt | dddf| z zz z}j|} d|zd|z |zz d |dzz | zz} | S) aDiscrepancy. Compute the centered discrepancy on a given sample. It is a measure of the uniformity of the points in the parameter space. The lower the value is, the better the coverage of the parameter space is. Parameters ---------- sample : array_like (n_samples, k_vars) The sample to compute the discrepancy from. bounds : tuple or array_like ([min, k_vars], [max, k_vars]) Desired range of transformed data. The transformation apply the bounds on the sample and not the theoretical space, unit cube. Thus min and max values of the sample will coincide with the bounds. Returns ------- discrepancy : float Centered discrepancy. References ---------- [1] Fang et al. "Design and modeling for computer experiments", Computer Science and Data Analysis Series Science and Data Analysis Series, 2006. Nraxis?gUUUUUU?g@?) npasarrayshapeminmaxabssumprodrange) sampleboundsn_sampledimmin_max_abs_disc1prod_arris0disc2c2s [/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tools/sequences.py discrepancyr!s6Z  FLMHczzqz!!zzqz!!4-D4K0 v|  D F271sTz>C$!)O;!DDD E EEH 3ZZ22 AAAqD\Q3r!!!T'{S0111247#b3h--4GH3r!!!T'{R/0001 2 LLNNE 3 x%!7 7 Q % ' (B Ictj|dz|dzdkzt}tdt |dzdzdzD]C}||r9d|zdzdz}d|||zdzdd|z<d|||d|dzzz d zzdzdd|z<Dtjdddtj|d ddzdzdzfS) a(Prime numbers from 2 to *n*. Parameters ---------- n : int Sup bound with ``n >= 6``. Returns ------- primes : list(int) Primes in ``2 <= p < n``. References ---------- [1] `StackOverflow `_. r)dtyperrFNr)r onesboolrintr_nonzero)nsieverks r primes_from_2_tor0:s" GAFa!eqj) 6 6 6E 1c!s(mmq(1, - -AA 8 AA A A',E!a%1*#a!e# $;@E!q1A;*+q07!a%7 8 5ARZ..q1!""559Q>? @@r"cgdd|}t||kr4d} t|d|}t||krn|dz }1|S)zList of the n-first prime numbers. Parameters ---------- n : int Number of prime numbers wanted. Returns ------- primes : list(int) List of primes. )rr$ %)+/5;=CGIOSYaegkmqiii iiiii%i3i7i9i=iKiQi[i]iaigioiui{iiiiiiiiiiiiiiiiiiiiiii i ii#i-i3i9i;iAiKiQiWiYi_ieiiikiwiiiiiiiiiiiiiiiiiiiiiiiii)i+i5i7i;i=iGiUiYi[i_imiqisiwiiiiiiiiiiiiiiN zNot enought primesi)lenr0)r-primes big_numbers r n_primesrjTs| 1 1 124! 5F 6{{Q  %j11"1"5F6{{a $ J   Mr"rcg}t|||zD]J}d\}}|}|dkr&t||\}}||z}|||z z }|dk&||K|S)aVan der Corput sequence. Pseudo-random number generator based on a b-adic expansion. Parameters ---------- n_sample : int Number of element of the sequence. base : int Base of the sequence. start_index : int Index to start the sequence from. Returns ------- sequence : list (n_samples,) Sequence of Van der Corput. )gr r)rdivmodappend) rbase start_indexsequencer n_th_numberdenomquotient remainders r van_der_corputruzs&H ; h 6 7 7%%# Ull"(4"8"8 Hi TME 9u, ,Kll  $$$$ Or"ct|}fd|D}tj|jdd}|7|d}|d}|||z z|z}|S)aHalton sequence. Pseudo-random number generator that generalize the Van der Corput sequence for multiple dimensions. Halton sequence use base-two Van der Corput sequence for the first dimension, base-three for its second and base-n for its n-dimension. Parameters ---------- dim : int Dimension of the parameter space. n_sample : int Number of samples to generate in the parametr space. bounds : tuple or array_like ([min, k_vars], [max, k_vars]) Desired range of transformed data. The transformation apply the bounds on the sample and not the theoretical space, unit cube. Thus min and max values of the sample will coincide with the bounds. start_index : int Index to start the sequence from. Returns ------- sequence : array_like (n_samples, k_vars) Sequence of Halton. References ---------- [1] Halton, "On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals", Numerische Mathematik, 1960. Examples -------- Generate samples from a low discrepancy sequence of Halton. >>> from statsmodels.tools import sequences >>> sample = sequences.halton(dim=2, n_sample=5) Compute the quality of the sample using the discrepancy criterion. >>> uniformity = sequences.discrepancy(sample) If some wants to continue an existing design, extra points can be obtained. >>> sample_continued = sequences.halton(dim=2, n_sample=5, start_index=5) c8g|]}tdz|S)r)ru).0bdimrros r zhalton..s) O O O$nX\4== O O Or"rNrr)rjr arrayTr r)rrrrornrrrs ` ` r haltonr}s\ C==DP O O O O$ O O OF Xf    #Fzzqz!!zzqz!!4$;'$. Mr")N)rr)Nr)__doc__numpyr r!r0rjrur}r"r rs%%2222jAAA4###L@::::::r"