^MhchdZddlZddlZddlZddlmZddlmZddl m Z ddl m Z m Z  ddlZn#e$re dZYnwxYwdZGd d eZGd d ZGd dZdS)zTests for hyp2f1 for complex values. Author: Albert Steppi, with credit to Adam Kullberg (FormerPhycisist) for the implementation of mp_hyp2f1 below, which modifies mpmath's hyp2f1 to return the same branch as scipy's on the standard branch cut. N) NamedTuple)assert_allclose)hyp2f1) check_version MissingModulempmathc|jdkot|jdk}t||z t||z z dkot||z dk}t||z t||z z dkot||z dk}|r |jdz}|r|s |s |jdz}n|}t t j||||S)a)Return mpmath hyp2f1 calculated on same branch as scipy hyp2f1. For most values of a,b,c mpmath returns the x - 0j branch of hyp2f1 on the branch cut x=(1,inf) whereas scipy's hyp2f1 calculates the x + 0j branch. Thus, to generate the right comparison values on the branch cut, we evaluate mpmath.hyp2f1 at x + 1e-15*j. The exception to this occurs when c-a=-m in which case both mpmath and scipy calculate the x + 0j branch on the branch cut. When this happens mpmath.hyp2f1 will be evaluated at the original z point. ?V瞯eZdZdZejdejedddde j dzd ejeddddd d ejeddddd d ejeddddd d ejedddde j dzd ejedddde j dzd ejedd ddd d ejedddddd ejedddddd ejedddddd ejedddd dd g dZ ejdejedddd dd ejedddd dd ejed d!d"d d#d$ ejed%d&d"d d'd( ejed&d%d"d d)d* ejed+d,d-d d.d ejed,d+d-d d.d( ejed/d0d1d d2d( ejed0d/d1d d2d( ejed3d4d5d d6d7 ejed8d9dd d:d$ g d;Z ejdejeddd5ddd?d ejedddސd<d@d( ejedɐddVdAdBd ejedQddVdCdDd ejedkdMddEdFd ejedQdd|dCdGd ejedddd7dHd ejedkddd7dId( ejedddid7dJd ejedYdRdd:dKd ejedddd>dLd ejeddodZd7dMd( ejedrddVdCdNd$ ejedoddRd7dOd ejedddVd:dPd ejeddodjd5dQd ejeddidMd<dRd ejedidkddSdTdU dVZejdgejedddodWdXdY ejeddddZd[d ejedLd]ddWd\d ejedddRdWd]d^ ejedUdiddWd_d ejeddRddWd`d) ejdJejeddYdRdZdad( ejedadkddbdcdd ejedd]ddZded( ejedQd]ddZdfd ejedQdVddgdhd ejeddddWdid ejeddjddgdjd ejedQdjddbdkd ejeddRddZdldD ejeddddgdmd ejedddMdbdnd ejeddodZdZdod ejedrdkdMdWdpdq ejeddidRdWdrd ejedddVdZdsd ejedkddjdWdtd ejedddVdgdud ejedkddjdbdvd ejeddddwdxd) ejdJejedLdddydzd ejedddZd{d|d( ejedaddd}d~d ejedddddd ejedoddoddd ejedUddddd ejedddސdddY ejedddddd ejedxdMdd}dd ejedddkddd( ejedddkddd ejedQdjdddd ejedkdRdddd* ejedddِddd ejedQdkdd{dd ejedddMddd ejedrddZddd ejedddMddd ejeddddydd ejeddoddyddĬ ejedddZddd ejeddd]ddd ejedkddjddd dZejdejedUdVdddd ejedd]dddd ejedddddd ejedd]d|ddd ejedadVd|ddd ejedaddddd* ejedUddddd ejedddddd ejeddjdddd ejedddddd ejedadZdddd ejeddRdddd ejedYdVdddd ejedddddd ejedYddddd ejeddMdddd ejedxdMdddd ejeddddddu ejedQdZdddd ejedxdRdddd ejedxddddd ejedYdZdddd ejedYdRdddd ejedYdRdddd ejedddddd gd„Zejdejed5dÐdĐdŐdd gdDŽZejjeedȦdɄZdʄZdS( TestHyp2f1aTests for hyp2f1 for complex values. Expected values for test cases were computed using mpmath. See `scipy.special._precompute.hyp2f1_data`. The verbose style of specifying test cases is used for readability and to make it easier to mark individual cases as expected to fail. Expected failures are used to highlight cases where improvements are needed. See `scipy.special._precompute.hyp2f1_data.make_hyp2f1_test_cases` for a function to generate the boilerplate for the test cases. Assertions have been added to each test to ensure that the test cases match the situations that are intended. A final test `test_test_hyp2f1` checks that the expected values in the test cases actually match what is computed by mpmath. This test is marked slow even though it isn't particularly slow so that it won't run by default on continuous integration builds. hyp2f1_test_caseg?g?iy??r r)rrrrrr y?yV?t[59?r y. |?lo8?iyx R?gvIh%<=g @y> ףp=?|Gz?g333333?yQ?c\|\}}}}}}tt||||||dSNr rrselfr)rrrrrr s rtest_c_non_positive_intz"TestHyp2f1.test_c_non_positive_intKs@h&6"1aHdq!Q**H4@@@@@@rg?y d?g(@g @g(\O4@y*kAg33333#r@gt@g@yk| @Xg-q=gffffff"@gl@y:5>dAg-a=yk@5>dAgdy=gLYgfffffyg33333eyF%佰Gge@g)igfffffb@youMď$gfffffYgL4g?y (Dgt =g33333Sigfffff&N@yRU3Tc|\}}}}}}|dkr ||z |z dksJtt||||||dS)z^Tests for case z = 1, c - a - b > 0. Expected answers computed using mpmath. rr0Nr1r2s rtest_unital_argumentzTestHyp2f1.test_unital_arguments]t&6"1aHdAvv!a%!)a----q!Q**H4@@@@@@ryy+i,?g433333@y7G&SԾgk@ǧV@g`@y-$F7gHz>g333333TyL"CAlzFails on 32 bit.) conditionreason)marksc|\}}}}}}td|z|z |z dkrt|dzdksJtt||||||dS)z^Tests for case z ~ -1, c ~ 1 + a - b Expected answers computed using mpmath. r6r r0Nrrrr2s r test_special_case_z_near_minus_1z+TestHyp2f1.test_special_case_z_near_minus_1@syj&6"1aHd1q519q=!!E))c!a%jj5.@.@.@.@q!Q**H4@@@@@@rgj{k8@gQDi?y 5P?0y,B.j?kggRigKgty/y@0yyv?1AAeg-1 @gHh@y)14#<6i1Gg|=gB!uZgsStyl(?`Cy 5Կy aƮ('qgo g@yL2|R?ѓB*?yP^Cy ? ?y4=2UX6K[:g;R@y]AאPE0Cig@g333ENHAy@@y4$?s)0>c|\}}}}}}|t|kr|dks|t|kr|dksJtt||||||dS)Nrr0)intrrr2s rtest_a_b_negative_intz TestHyp2f1.test_a_b_negative_intysql&6"1aHdCFF{{q1uuSVV Aq!Q**H4@@@@@@rggbɰg/yl(?l(yJ?^&?gAfc=g!@y$i8Q@#;$gAfc=g@yl(?0yU tv?gdy=y4P^C?l(y{h`?@,/gާ7 yx 5? ?yj?= 0.?rr0Nrr rrr2s r test_region1zTestHyp2f1.test_region1s]D&6"1aHd1vv||! q!Q**H4@@@@@@ry`Cy 5Կ@y 5?y$i^?`o ?gl0@gXQ@y5P`Cy 5Կy>g:0y5>gda0@y00yb?7@p9g՗' @y`Cy 5ԿDy 5yT ?lZu{ڿg>Vyz 5`Cy 5?yy>T ;*?gڏyzR@GI@ghyz 5x 5?yтq@8Tyz 50y& @??gvIh%,=g%+g ?y`Cy 5Կ5Py=?@= Yx RyX7>~rX@42c|\}}}}}}t|dkr |jdksJtt||||||dS)z|z| < 1 and real(z) < 0.r6rr0NrEr2s r test_region2zTestHyp2f1.test_region2zs]B&6"1aHd1vvzzafqjjjjq!Q**H4@@@@@@rg@0@gg yx 5?@y 5?y^->xcg/g @gy 5P?`Cy 5?yM\iƔ\g@yx 5?Dy 5yAޒm4mggy2ş?}q^oҿg?g@y+}<]#xX@y4⦷?3S 0gy 5P? ?y`B3A>5C;Ay_qd#Z?yZy!Aj6my B6&yعjޥ?XR¿y 5P?`Cy 5Կy[^0|UFt@yR[?gB?g0@y;쿧 kg:0yE>zUnhandled parameters.gyZh@7})ʱg@yǾܬ]@x͠AytX| ƒRAywr|Y1AARyWQIAyhü'}e qyՊ8?QD?y@y 5?x 5?y~Cujy2}@?1OSg?y@y 5?z 5yGUy~ y> As4 Ay=ۊ-%ΰ7?c|\}}}}}}dt|cxkrdkrnntd|z dksJtt||||||dS)z"0.9 <= |z| <= 1 and |1 - z| < 0.9.rDr6r0Nr<r2s r test_region3zTestHyp2f1.test_region3sT &6"1aHdc!ff!!!!!!!!!c!a%jj3&6&6&6&6q!Q**H4@@@@@@ry ?՗ Z}y{i{4C@&F>@ytO#,4?՗ Z}y'OV/xTyP0*9AJOpDg0@yJ/:XBr@y7wd?gh㈵>y:Tq?@?y ?՗ Z}?yb&?T,#?r yT?z]DytO#,4?՗ Z}?y1`-w?01cyky6LyED @y'[Rjݻy yU쿢f*E @y4y?f ?y+*9,gMbP?yeL@>9@yϞQ} _@y}X4;@A,GIyqR!)?-?yNT+N@>—By?~.9M@yXR>@bNj}Ϧ:yYˊ?ZEyi@CPH më@yy!?lFX?y [? Uf?y](?T?y>e @yy!?jFXy(D!&nyVy\ @!ݨy@6Qk?lFX?yʈNƐӒ@+.AP@y@6Qk?jFXyϝ#9Ġ_ @y](?Ty_k@?p~yXA/?T?y|WEAgܢOAy&+￉31@yl ^@Nt~yEDC@yw3>#i.y*Ay݃}K?""?y2ODGA+Ay ,J8l?|p5˿y@0-nq@y"Yښ4sWKR@y0BCEhBNySd?F?yXA/?TyP lQ;N@g8J==c|\}}}}}}dt|cxkrdkrnntd|z dksJtt||||||dS)z0.9 <= |z| <= 1 and |1 - z| >= 1. This region is unhandled by of the standard transformations and needs special care. rDr6r0Nr<r2s r test_region4zTestHyp2f1.test_region4sb&6"1aHdc!ff!!!!!!!!!c!a%jjC&7&7&7&7q!Q**H4@@@@@@ry&Jvm?T?y9 ?梤΀gHj>y&Jvm?Ty `C0˝7y[ *2y w3BLSg+=yz5?COyXI@T!NyI NiYytO#,4?Ty׮[՚)-ڤAg-C6 ?y!'h@ qiq@y2$н'?cҳ?ytO#,4?T?y, Am ڑy Ae4y/ ?B`s?y(& @:˕) y9MR@b@yS.׿Ӄ?y2F$@EDƓyV'c)d yRQ"(@!-gMb@?yL7@IX@yv 1m@f4^@yĴگbBui'6(_By"NhVk0@y )F+] @yy!?-tbyטp ~׋J?yA`Т y= 0.9 and real(z) >= 0r6皙?rDrr0NrEr2s r test_region5zTestHyp2f1.test_region5sZ&6"1aHd3q66CCAJJ#$5$5!&A++++q!Q**H4@@@@@@ry5Px 5?y j]+B l?yDy 5Dy 5y.թ'."thyz 55Pyٞ? _bMοy5Pz 5yˡ?5rZ]?yhF?@҅PyR,\i@0gA@yDy 5@y 5?yY6c$#y|N"@y?v:[y0 DEw?&Y9߿ylboE,S*5yXٕ*B@vKdo@yxs6A {;yz 5 5P?yt _iNL@IryC?.IyOKTO9W?ό>7ᘿyEi3?:p?y3¿gF?yQ5dQX6@ySͧ䄪}yA Hq @3'U@yc4V$k$ynt`_OAr6y@@yŞμ?DB]?c|\}}}}}}t|dkr>dt|cxkrdkr&nn#td|z dkr |jdkrJtt||||||dS)z|z| > 1 but not in region 5.r6rPrDrr0NrEr2s r test_region6zTestHyp2f1.test_region6sB&6"1aHd FFQJJSVV!!!!c!!!!!c!a%jjC&7&7AFaKKKKq!Q**H4@@@@@@rgɿg333333?gg@ԛ?c\|\}}}}}}tt||||||dSr/r1r2s rtest_miscellaneouszTestHyp2f1.test_miscellaneous s?"&6"1aHdq!Q**H4@@@@@@rz1.0.0c fdtD}|D]S}t|}|D]+\}}}}}} tt |||||d,TdS)aTest that expected values match what is computed by mpmath. This gathers the parameters for the test cases out of the pytest marks. The parameters are a, b, c, z, expected, rtol, where expected should be the value of hyp2f1(a, b, c, z) computed with mpmath. The test recomputes hyp2f1(a, b, c, z) using mpmath and verifies that expected actually is the correct value. This allows the data for the tests to live within the test code instead of an external datafile, while avoiding having to compute the results with mpmath during the test, except for when slow tests are being run. cg|]<}|dr%tt|r|dk:|=S)testtest_test_hyp2f1) startswithcallablegetattr).0 test_methodr3s r z/TestHyp2f1.test_test_hyp2f1.. se   '%%f--  WT;// 0 0  - - -  . - -rgziu6. sL   #yM)) ! *) KN))))r) pytestmark)r3r_s rrbzTestHyp2f1._get_test_parameters s&  '2'=    rN) r!r"r#__doc__pytestrlrhparamrnpinfnanr4r7xfailsysmaxsizer=r@rBrFrHrJrNrQrTrVslowrrrZrbr&rrr(r(:s:  [ FL Vb[    FL#    FL #    FL #    FL Vb[    FLVb[    FL E    FL A    FL G    FL D    FL4   Ko rrfAAgrrfA [ FL4    FL3    FL5    FL2    FL2    FL7    FL7    FL7    FL7    FL7    FL9   Oq ttjAAkttjA [ FL4       FL'8    FL8    FL3 k''!kE1-(   =, //`AAa//`A [ FL&(>J    FL()-I    FL'(>K    FL()=K    FL&'>J    FL()>L    FL'(>J    FL H   OQ TTjAAkTTjA  [ FL)=F    FL)>C    FL)>E    FL)=E    FL)>F   S3 66nAAo66nA [ FL)))>E    FL())=E    FL&('>D    FL&('<F    FL'''>C    FL&''>C    FL)))=F    FL)))=F k''/B'CC    FL&('=E   e\ __@AAA__@A  [ FL&('>E    FL(((>K    FL('(@F    FL''(=F    FL&'(>E    FL&')>B    FL(')>B    FL')'?C    FL'((>C    FL('(=D    FL'))>F    FL())>D    FL'('@E    FL(('?E    FL(('=A    FL(((>D    FL(((@A    FL)()=D    FL)()>E    FL()(@B    FL))(?C    FL('(?E    FL)((=C    FL)()?F    FL))(>B   c{ ~~~AA~~~A  [D FL=D   D  FL=D   D * FL<D   +D > FL=E   ?D R FL<D   SD f FL=D   gD z FL>C   {D N FL<G   OD b FL<B   cD v FL'))>B   wD J FL>F   KD ^ FL('(=C   _D r FL(('>F   sD F FL=E k''2(   GD ` FL=B   aD t FL>B   uD H FL=C   ID \ FL<B   ]D p FL=C   qD D FL)('>F   ED X FL(('=K   YD l FL>F   mD @ FL(('=D   AD T FL=C   UD h FL&((=C   iD | FL=C   }D P FL=A   QD d FL''(=D   eD x FL(''=D   yD L FL(((=D   M D ` FL()(=A   a D t FL<E   u D GGP AAQ GGP A  [g FL=C   g  FL((=E   g * FL((=C   +g > FL'(=D   ?g R FL&)=J   Sg f FL&)(=D   gg z FL((=D   {g N FL))=D   Og b FL(=B   cg v FL)((=D   wg J FL))=C   Kg ^ FL)('=C   _g r FL))(=D   sg F FL))'=D   Gg Z FL=E k''2(   [g t FL)''=C   ug H FL'=C   Ig \ FL'=D   ]g p FL(=E   qg D FL)=C   Eg X FL(=E   Yg l FL)=C   mg @ FL(=E   Ag T FL)=D   Ug h FL>D k''2(   ig B FL=C   Cg V FL>C   Wg j FL()>D   kg ~ FL')(>D   g R FL')(>D   S g f FL'>E   g g z FL>C   { g N FL)(>B   O g b FL((=A   c g v FL(=C   w g J FL(')=C   K g ^ FL>C   _ g r FL'>C   s g F FL>E   G g Z FL()(>E   [ g n FL(>E   o g B FL)>C   C g V FL(=E   W g j FL)>D   k g ~ FL(>C    g R FL)=D   Sg f FL(>D   gg z FL(=D   {g jjVAAWjjVA [g FL(=G   g  FL=C   g * FL&')=D   +g > FL()=B   ?g R FL'=D   Sg f FL()=C k''2(   gg @ FL()=D   Ag T FL'=D   Ug h FL)'=C   ig | FL('=G   }g P FL(()=B   Qg d FL)'=C   eg x FL)=C   yg L FL()(=C   Mg ` FL))'=B   ag t FL=E   ug H FL(=D   Ig \ FL)=B   ]g p FL(=D   qg D FL)=C   Eg X FL(=C   Yg l FL)=C   mg @ FL(=D   Ag T FL)=D   Ug h FL=I k''2(   ig B FL&=E   Cg V FL()=B   Wg j FL'()=B   kg ~ FL=>   g R FL(=C   S g f FL'''=D   g g z FL=C   { g N FL'=D   O g b FL)('=E   c g v FL=D   w g J FL=E   K g ^ FL()(=B   _ g r FL)=D   s g F FL=E   G g Z FL(=C   [ g n FL(=C   o g B FL)=C   C g V FL(=C   W g j FL(=E   k g ~ FL(=F    g R FL)<B   Sg f FL'=C   gg z FL)=B   {g jjVAAWjjVA  [ FL'('>J    FL('(<M    FL(''>F    FL(')>D    FL'()>C    FL'''>C    FL'('=D    FL('(>D    FL()(>D    FL('(>E    FL'))>C    FL()(>C    FL(((>D    FL)'(>C    FL('(>C    FL)()>C    FL)()=E    FL)('=C    FL()(>G    FL))(>D    FL)('>E    FL()'>C    FL())>C    FL())>B    FLE   c{ ~~~AA~~~A [ FL/     AA! A []67##PP$#P2     rr(c heZdZejddddej ejgejddddej ejgejdgd ejd d gd Zd Z dS)TestHyp2f1ExtremeInputsrr rK@rrL@r)r{r|g@g@r@?ctjtjtj||gr&tjt ||||sJdSdS)N)rranyisinfasarrayisnanr)r3rrrrs r test_inf_a_bz$TestHyp2f1ExtremeInputs.test_inf_a_b sb 6"(2:q!f--.. / / 18F1aA..// 0 0 0 1 1 0 0rctjtddddsJtjtddddsJtjtddddsJtjtddddsJtjttjdddsJtjtdtjddsJdS)Nir r{r}iigrL)rrrrrs)r3s rtest_large_a_bz&TestHyp2f1ExtremeInputs.test_large_a_b sxuc3 ;;<<===xvsC<<==>>>xsE3 ;;<<===xsFC<<==>>>xrvsC5566777xsBFC556677777rN) r!r"r#rprlrhrrrsrrr&rrrzrz s [S3S26'26"BCC [S3S26'26"BCC [S"6"6"677 [S:,//110/87DCDC1 8 8 8 8 8rrz)rorvrpnumpyrrtypingr numpy.testingr scipy.specialrscipy.special._testutilsrrr ImportErrorrrr(rzr&rrrsX )))))) AAAAAAAA%MMMM%%% ]8 $ $FFF%5552Zw& w& w& w& w& w& w& w& rM8888888888s/AA