UgLddlZddlZddlmZmZddlmZGddZ dS)N) assert_equalassert_allclose) _iv_ratioceZdZejdgddZejddejdfejddfgdZ ejdej ddej ej ejgejdej e j ej e j ej ej ejgd Zejddej e jejgd Zejd dej e jfdej e jfdej e jd zfd ej e jdfej e jejej e jfgdZejd ddejej e jej e jfgdZejd ej e jej e jfej e jdz ej e jfej e jej e jdz fgdZdS) TestIvRatiozv,x,r))g6Z5Z?g&R͒U?)rg?gZ?)rg?gZr!?)rg?g4e~u?)rg}| @gG)ȿ?)Q@g}P?g1a?)r gj6i?gִN`?)r g:m@g9Ƭ7?)r g5T@g4+?)r gH%@gJ]?)EdL@g9L;w3@g'~V?)r g^s!iFE@g/X?)r gSR@g_8?)r gPT`@g)X?)r g>=s@g\h*?cHtt|||dddS)aThe reference values are computed using mpmath as follows. from mpmath import mp mp.dps = 100 def iv_ratio_mp(v, x): return mp.besseli(v, x) / mp.besseli(v - 1, x) def _sample(n, *, v): '''Return n positive real numbers x such that iv_ratio(v, x) are roughly evenly spaced over (0, 1). The formula is taken from [1]. [1] Banerjee A., Dhillon, I. S., Ghosh, J., Sra, S. (2005). "Clustering on the Unit Hypersphere using von Mises-Fisher Distributions." Journal of Machine Learning Research, 6(46):1345-1382. ''' r = np.arange(1, n+1) / (n+1) return r * (2*v-r*r) / (1-r*r) for v in (1, 2.34, 56.789): xs = _sample(5, v=v) for x in xs: print(f"({v}, {x}, {float(iv_ratio_mp_float(v,x))}),") 缉ؗҼ>>>>>rrcBtt|||dS)zIf exactly one of v or x is inf and the other is within domain, should return 0 or 1 accordingly. Also check that the function never returns -0.0.Nrrrs rtest_infzTestIvRatio.test_inf8s" Xa^^Q'''''rrrcVtt||tjdS)zeIf at least one argument is out of domain, or if v = x = inf, the function should return nan.N)rrnpnanrrrs rtest_nanzTestIvRatio.test_nanDs$ Xa^^RV,,,,,rc~tt|ddtt|dddS)z=If x is +/-0.0, return x to agree with the limiting behavior.ggNr)rrs r test_zero_xzTestIvRatio.test_zero_xMs> Xa%%s+++Xa&&-----rzv,x)@xD{cNtt||d|z|z dS)a9If x is much less than v, the bounds x x --------------------------- <= R <= ----------------------- v-0.5+sqrt(x**2+(v+0.5)**2) v-1+sqrt(x**2+(v+1)**2) collapses to R ~= x/2v. Test against this asymptotic expression. g?Nrrs r test_tiny_xzTestIvRatio.test_tiny_xSs*" Xa^^c!eQY/////r)rg7yAC)r$g\)c=HcBtt||ddS)a9If x is much greater than v, the bounds x x --------------------------- <= R <= ----------------------- v-0.5+sqrt(x**2+(v+0.5)**2) v-1+sqrt(x**2+(v+1)**2) collapses to R ~= 1. Test against this asymptotic expression. g?Nrrs r test_huge_xzTestIvRatio.test_huge_xfs" Xa^^S)))))rc||z }|dtjd|zz }tt|||dddS)aIf both x and v are very large, the bounds x x --------------------------- <= R <= ----------------------- v-0.5+sqrt(x**2+(v+0.5)**2) v-1+sqrt(x**2+(v+1)**2) collapses to R ~= x/(v+sqrt(x**2+v**2). Test against this asymptotic expression, and in particular that no numerical overflow occurs during intermediate calculations. rr rr N)rhypotrr)rrrtexpecteds r test_huge_v_xzTestIvRatio.test_huge_v_xvsK EBHQNN*+Au1EEEEEErN)__name__ __module__ __qualname__pytestmark parametrizerrinfr nextafterrfinfofloatsmallest_normalsmallest_subnormalr maxr"sqrtr'r)r/rrrr se [W'''"??#"?8 [W BFA A'(( ( [S<2<1#5#5w"OPP [SHBHUOO$C#C$,BHUOO$F#F$&F7BFBF#<==--==QP-  [S1hbhuoo&926"BCC..DC.  [U HBHUOO +, HBHUOO ./ HBHUOO .q 01 % a % gbghbhuoo&9::; % 0 0 0 [U %$ % %xrx':;% * *  * [U % hbhuoo12 % q ("(5//"56 % hbhuoo1A56% F F  F F Frr) r3numpyr numpy.testingrrscipy.special._ufuncsrrrr>rrrBs 77777777777777FFFFFFFFFFr