tKgDddlZddlZddlmZmZddlmZGddZ y)N) assert_equalassert_allclose) _iv_ratioc2eZdZejj dgddZejj ddejdfejddfgdZ ejj dejddej ejejgejj deje j eje j ej ejejgd Zejj ddeje j"ejgd Zejj d deje jfdeje jfdeje jd zfd eje j"dfeje j"ej&eje j"fgdZejj d ddej&eje j"eje j"fgdZejj d eje j"eje j"feje j"dz eje j"feje j"eje j"dz fgdZy) 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*?c6tt|||ddy)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))}),") 缉ؗҼrrc0tt|||y)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'rrrcLtt||tjy)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^RVV,rc\tt|ddtt|ddy)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{c<tt||d|z|z y)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=Hc0tt||dy)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)rcx||z }|dtjd|zz }tt|||ddy)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_xvs: EBHHQN*+Au1ErN)__name__ __module__ __qualname__pytestmark parametrizerrinfr nextafterrfinfofloatsmallest_normalsmallest_subnormalr maxr"sqrtr'r)r/rrrr s- [[W'"?#"?8 [[W BFFA A'( ( [[S<2<<1#5w"OP [[SHBHHUO$C$C#C$,BHHUO$F$F#F$&FF7BFFBFF#<=-=Q-  [[S1hbhhuo&9&9266"BC.D.  [[U HBHHUO + +, HBHHUO . ./ HBHHUO . .q 01 %  a %  gbgghbhhuo&9&9:; % 0 0 [[U %$$ %xrxx':':;% *  * [[U %  hbhhuo112 %  q ("((5/"5"56 %  hbhhuo11A56% F  Frr) r3numpyr numpy.testingrrscipy.special._ufuncsrrrr>rrrBs!77FFr