+ 0iehRt^RIt^RIt^RIt^RIHt^RIHt^RI H t ^RI H t H t ^RItRt!RR ]4t!R R 4t!R R 4tR# ]d ] !R4tL5i;i)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 MissingModulempmathcJVPR8;'d\VP4R8p\W , \W , 4, 4R8;'d\W , 4^8*p\W!, \W!, 4, 4R8;'d\W!, 4^8*pV'dVPR,pV'd%V'gV'gVPR,pMTp\ \ P !WW'44#)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<yV瞯<)realabsimagroundcomplexrr)abcz on_branch_cutcond1cond2z_mpmaths&&&& ]/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/special/tests/test_hyp2f1.py mp_hyp2f1rsFFSL::S[7%:M ae $ % / E EE!%LA4EE ae $ % / E EE!%LA4EE FFTMeu66H$ 6==q3 44c,a]tRt^1toV3RltRtVtR#)Hyp2f1TestCasecb<V^8dQh/S[;R&S[;R&S[;R&S[;R&S[;R&S[;R&#)rrrrexpectedrtol)floatr)format __classdict__s"r __annotate__Hyp2f1TestCase.__annotate__1sJ H H HJ    K rN)__name__ __module__ __qualname____firstlineno____annotate_func____static_attributes____classdictcell__r$s@rrr1srrc&<a]tRt^:toRt]P PR]P!] !RRRqRr] PR,^R74]P!] !RRRqRRs^R74]P!] !R^RqRrRs^R74]P!] !R^^RrRs^R74]P!] !RR^Rr] PR,^R74]P!] !RR^R] PR,^R74]P!] !RRtRqRrRuRR74]P!] !RRqRqRrRvRR74]P!] !RqRwRqRrRxRR74]P!] !RyR RyRrRzRR74]P!] !R{R R|RsR}RR74. 4R 4t ]P PR]P!] !RRR RsR~RR74]P!] !R RRRsRRR74]P!] !RRRRsRRR74]P!] !RRRRsRRR74]P!] !RRRRsRRR74]P!] !RRRRsRRR74]P!] !RRRRsRRR74]P!] !RRRRsRRR74]P!] !RRRRsRRR74]P!] !RRRRsRRR74]P!] !RRR RsRRR74. 4R4t]P PR]P!] !RRRRRRR74]P!] !R RRRRRR74]P!] !RR R!RRR"R74]P!] !RRRRRR"R7]P P]P"R8R#R$7R%7.4R&4t]P PR]P!] !R|R'R(RRRR74]P!] !RRRRRRR74]P!] !RR)R*RRR+R74]P!] !R|RRRRRR74]P!] !R'R|R,RRRR74]P!] !RRRRRRR74]P!] !R-R|R*RRRR74]P!] !RR.R/RRRR74.4R04t]P PR]P!] !RRRRRR1R74]P!] !R2RR RRR3R74]P!] !R2RR4RRR5R74]P!] !RRRRRR5R74]P!] !RRRRRR+R74.4R64t]P PR]P!] !RRRRRR7R74]P!] !R8RRRRR9R74]P!] !R'R(RRRR:R74]P!] !R'R;RRRR?R74]P!] !RRRRRRR74]P!] !RRRRRR"R7]P PR@RA7R%7]P!] !R'R;RRRR:R74]P!] !RCR;RDRRRER74]P!] !R8R,RFRRR:R74]P!] !R-RGRFRRR:R74]P!] !R'R,RRRRR74]P!] !R'RGRRRRR74]P!] !RCRGRRRRR74]P!] !R)RRRRR:R74]P!] !RR;RDRRRJR74]P!] !RR(RRRR:R74]P!] !RR*RRRRHR74]P!] !RR(RRRR:R74]P!] !RRRDRRR:R74]P!] !RRRDRRR:R74]P!] !RRRDRRR:R74]P!] !RRRRRRHR74]P!] !RRRRRR7R74]P!] !RRRRRRR74.4RK4t]P PR.]P!] !RLRRRRRHR74N]P!] !RRMERERERRHR74N]P!] !RNRNERERERR:R74N]P!] !ERERRRERR?R74N]P!] !RORPRERERR:R74N]P!] !ERRNR RER RHR74N]P!] !RMRER ER ER RHR74N]P!] !RERRERER RR74N]P!] !RMRNRERERRHR74N]P!] !R-RRRERRHR74N]P!] !RRMRRERRHR74N]P!] !RRRERERRHR74N]P!] !RR(RER2ER;RR74N]P!] !RERERER2ERRHR74N]P!] !RTR2RER*ER?RHR74N]P!] !R4ERR*ER*ER@RHR74N]P!] !R2ER RER2ERARHR74N]P!] !RRQR*ER2ERBR7R74N]P!] !RRTRER5ERCRR74N]P!] !RRR;ER,ERDRR74N]P!] !RER RER*ERERHR74N]P!] !RNRMRQERFERGR]R7]P PRSRA7R%7N]P!] !RMRLRTERHERIRHR74N]P!] !RPRPRERJERKR:R74N]P!] !R8RRERJERLRHR74N]P!] !R)RRFERMERNRVR74N]P!] !R-RRIEROERPRR74N]P!] !R-RRERQERRR:R74N]P!] !RPREREROERSRR74N]P!] !RRYR*ERTERUR:R74N]P!] !RRYR*ERVERWRHR74N]P!] !RR(ER ERXERYR:R74N]P!] !RRGRERVERZR9R74N]P!] !ERERR ERJER[RHR74N]P!] !RRR ERJER\RR74N]P!] !RRRERJER]R:R74N]P!] !RRRERMER^R:R74N]P!] !R RQR;ERQER_RR74N]P!] !RQR2RERJER`RR74N]P!] !R4ER R*ERVERaR^R74N]P!] !R2ER RERJERbRHR74N]P!] !RRQR*ERMERcR:R74N]P!] !ER R2RERHERdRHR74N]P!] !ERRR(EROEReRR74N]P!] !RRRERfERgR_R74N4R`4t]P PR.]P!] !RTR;R2ERhERiRaR74N]P!] !RMRPRTERjERkR:R74N]P!] !R'R,RERhERlR:R74N]P!] !RCR\RERhERmRbR74N]P!] !R)RR ERhERnR9R74N]P!] !RCRRZERhERoR]R7]P PRSRA7R%7N]P!] !RZRRERjERpRR74N]P!] !R-RER ERqERrRcR74N]P!] !RR,R\ERjERsRR74N]P!] !RR,RZERjERtRHR74N]P!] !RR*RERuERvR:R74N]P!] !RRRERhERwRHR74N]P!] !RRRTERuERxR:R74N]P!] !RRRDERqERyRHR74N]P!] !RRRERjERzR"R74N]P!] !RERER ERuER{R:R74N]P!] !R RQR(ERqER|RER74N]P!] !R R2RERjER}RHR74N]P!] !R4RR(ERhER~RdR74N]P!] !R RRERhERRHR74N]P!] !ER RQR*ERjERR:R74N]P!] !RRQRERhERR:R74N]P!] !ER RR*ERuERR:R74N]P!] !RERRERqERRHR74N]P!] !RLRNRTERERR]R7]P PRSRA7R%7N]P!] !R'R RQERERRHR74N]P!] !RCR\RERERRR74N]P!] !R-R;RERERRHR74N]P!] !RLRR ERERR[R74N]P!] !R2RR2ERERRVR74N]P!] !R)RRERERRHR74N]P!] !RLERERERERRaR74N]P!] !RRGRQERERR:R74N]P!] !RR(RERERR:R74]P!] !RCR,RIERERRR74]P!] !R8RGR>ERERRR74]P!] !R8R,RERERRHR74]P!] !R-R*RERERRHR74]P!] !R-RGRERERRR74]P!] !R)RRERERRHR74]P!] !RRRERERR:R74]P!] !RRRERERR:R74]P!] !RRRERERRHR74]P!] !^^^ERERRHR74.4Rh4t]P PR]P!] !RERRiERRjR:R74.4Rk4t]P P8]!]Rl4Rm44tRnt Rot!Vt"Rp#( TestHyp2f1aRTests 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?r )rrrrr r!r gvIh%<=g @g333333?c@Vwr#rErg\\W#WE4WgR7R#r!Nrrselfr2rrrrr r!s&& rtest_c_non_positive_int"TestHyp2f1.test_c_non_positive_intKs"h&6"aHqQ*H@rg?g(@g @g(\O4@g33333#r@gt@g@g-q=gffffff"@gl@g-a=gdy=ge@gfffffb@g?gt =gfffff&N@c zVwr#rErgV^8XdWB, V, ^8gQh\\W#WE4WgR7R#)zNTests for case z = 1, c - a - b > 0. Expected answers computed using mpmath. r5Nr6r7s&& rtest_unital_argumentTestHyp2f1.test_unital_arguments;t&6"aHAv!%!)a-''qQ*H@rg433333@gk@ǧV@g`@gHz>zFails on 32 bit.) conditionreason)marksc Vwr#rErg\^V,V, V, 4R8d\V^,4R8gQh\\W#WE4WgR7R#)zNTests for case z ~ -1, c ~ 1 + a - b Expected answers computed using mpmath. r r5Nr rrr7s&& r test_special_case_z_near_minus_1+TestHyp2f1.test_special_case_z_near_minus_1@sPj&6"aH1q519q=!E)c!a%j5.@@@qQ*H@rgj{k8@gQDi?g-1 @gHh@g|=go g@g;R@g@g333ENHAcVwr#rErgV\V48XdV^8gV\V48XdV^8gQh\\W#WE4WgR7R#)r5N)intrrr7s&& rtest_a_b_negative_int TestHyp2f1.test_a_b_negative_intysIl&6"aHCF{q1uSV A==qQ*H@rgAfc=g!@gAfc=g@gdy=c(Vwr#rErg\WB, \WB, 4, 4R8dWB, ^8g<\WC, \WC, 4, 4R8dWC, ^8gQh\\W#WE4WgR7R#)r r5N)r rGrrr7s&& r:test_a_b_neg_int_after_euler_hypergeometric_transformationETestHyp2f1.test_a_b_neg_int_after_euler_hypergeometric_transformationsrt&6"aH QU# $u , QU# $u ,  < qQ*H@rg+=gnho?g|=g+= 0.?r5Nr r rrr7s&& r test_region1TestHyp2f1.test_region1s=D&6"aH1v|! ++qQ*H@rgl0@gXQ@g:0y5>gda0@g՗' @gvIh%,=g ?gV瞯zUnhandled parameters.g@gMgc Vwr#rErgR\V4u;8:d^8:dMQh\^V, 4R8gQh\\W#WE4WgR7R#)z"0.9 <= |z| <= 1 and |1 - z| < 0.9.rNr5NrBr7s&& r test_region3TestHyp2f1.test_region3sNT &6"aHc!f!!66c!a%j3&666qQ*H@r@g0@@gh㈵>r gMbP?g7Qu=g8J==c Vwr#rErgR\V4u;8:d^8:dMQh\^V, 4R8gQh\\W#WE4WgR7R#)zw0.9 <= |z| <= 1 and |1 - z| >= 1. This region is unhandled by of the standard transformations and needs special care. rNr5NrBr7s&& r test_region4TestHyp2f1.test_region4sNb&6"aHc!f!!77c!a%jC&777qQ*H@rgHj>g+=g-C6 ?gMb@?g^~z=gMg= 0.9 and real(z) >= 0皙?rNr5NrOr7s&& r test_region5TestHyp2f1.test_region5sXZ&6"aH3q6CEECAJ#$5!&&A+EEqQ*H@rc Vwr#rErg\V4^8dD^\V4u;8dR8d.MM*\^V, 4R8dVP^8dQh\\W#WE4WgR7R#)z|z| > 1 but not in region 5.r^rNr5NrOr7s&& r test_region6TestHyp2f1.test_region6sdB&6"aH FQJSV!c!c!a%jC&7AFFaK  I qQ*H@rg333333?g@ԛ?c@Vwr#rErg\\W#WE4WgR7R#r4r6r7s&& rtest_miscellaneousTestHyp2f1.test_miscellaneous s!"&6"aHqQ*H@rz1.0.0c  P\V4Uu.uFCpVPR4'gK\\W44'gK8VR8wgKAVNKE ppVFBpVP \W44pVFwrErgr\ \ WEWg4VRR7K! KD R#uupi)aFTest that expected values match what is computed by mpmath. This gathers the parameters for the test cases out of the pytest marks. The parameters are a, b, c, z, expected, rtol, where expected should be the value of hyp2f1(a, b, c, z) computed with mpmath. The test recomputes hyp2f1(a, b, c, z) using mpmath and verifies that expected actually is the correct value. This allows the data for the tests to live within the test code instead of an external datafile, while avoiding having to compute the results with mpmath during the test, except for when slow tests are being run. testtest_test_hyp2f1gziu6 ףp=?|Gz?yQ?y d?y*kAyk| @Xy:5>dAyk@5>dAgLYgfffffyg33333eyF%佰Gg)iyouMď$gfffffYgL4y (Dg33333SiyRU3Tyy+i,?y7G&SԾy-$F7g333333TyL"CAly 5P?0y,B.j?kggRigKgty/y@0yyv?1AAey)14#<6i1GgB!uZgsStyl(?`Cy 5Կy aƮ('qyL2|R?ѓB*?yP^Cy ? ?y4=2UX6K[:y]AאPE0Ciy@@y4$?s)0>ggbɰg/yl(?l(yJ?^&?y$i8Q@#;$yl(?0yU tv?y4P^C?l(y{h`?@,/gާ7 yx 5? ?yj?y00yb?7@p9y`Cy 5ԿDy 5yT ?lZu{ڿg>Vyz 5`Cy 5?yy>T ;*?gڏyzR@GI@ghyz 5x 5?yтq@8Tyz 50y& @??g%+y`Cy 5Կ5Py=?@= Yx RyX7>~rX@42gg yx 5?@y 5?y^->xcg/gy 5P?`Cy 5?yM\iƔ\yx 5?Dy 5yAޒm4mggy2ş?}q^oҿy+}<]#xX@y4⦷?3S 0gy 5P? ?y`B3A>5C;Ay_qd#Z?yZy!Aj6my B6&yعjޥ?XR¿y 5P?`Cy 5Կy[^0|UFt@yR[?gB?y;쿧 kgyZh@7})ʱyǾܬ]@x͠AytX| ƒRAywr|Y1AARyWQIAyhü'}e qyՊ8?QD?y@y 5?x 5?y~Cujy2}@?1OSg?y@y 5?z 5yGU As4 Ay=ۊ-%ΰ7?y ?՗ Z}y{i{4C@&F>ytO#,4?՗ Z}y'OV/xTyP0*9AJOpDyJ/:XBry7wd?y:Tq?@?y ?՗ Z}?yb&?T,#?yT?z]DytO#,4?՗ Z}?y1`-w?01cyky6LyED @y'[Rjݻy yU쿢f*E @y4y?f ?y+*9,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@y&Jvm?T?y9 ?梤΀y&Jvm?Ty `C0˝7y[ *2y w3BLSyz5?COyXI@T!NyI NiYytO#,4?Ty׮[՚)-ڤAy!'h@ qiq@y2$н'?cҳ?ytO#,4?T?y, Am ڑy Ae4y/ ?B`s?y(& @:˕) y9MR@b@yS.׿Ӄ?y2F$@EDƓyV'c)d yRQ"(@!-yL7@IX@yv 1m@f4^@yĴگbBui'6(_By"NhVk0@y )F+] @yy!?-tbyטp ~׋J?yA`Т y@IryC?.IyOKTO9W?ό>7ᘿyEi3?:p?y3¿gF?yQ5dQX6@ySͧ䄪}yA Hq @3'U@yc4V$k$ynt`_OAy@@yŞμ?DB]?gɿg)#r(r)r*r+__doc__pytestrzruparamrnpinfnanr9r<xfailsysmaxsizerCrHrKrPrSrVr[r_rbreslowrrrirnr-r.r/s@rr1r1:s*  [[ LL VVb[   LL#   LL #   LL #   LL VVb[   LLVVb[   LL E   LL A   LL G   LL D   LL4  Ko rfAgrfA [[ LL4   LL3   LL5   LL2   LL2   LL7   LL7   LL7   LL7   LL7   LL9  Oq tjAktjA [[ LL4    LL'8   LL8   LL3 kk''!kkE1-( =, /`Aa/`A [[ LL&(>J   LL()-I   LL'(>K   LL()=K   LL&'>J   LL()>L   LL'(>J   LL H  OQ TjAkTjA  [[ LL)=F   LL)>C   LL)>E   LL)=E   LL)>F  S3 6nAo6nA [[ LL)))>E   LL())=E   LL&('>D   LL&('<F   LL'''>C   LL&''>C   LL)))=F   LL)))=F kk''/B'C  LL&('=E  e\ _@AA_@A  [[ LL&('>E   LL(((>K   LL('(@F   LL''(=F   LL&'(>E   LL&')>B   LL(')>B   LL')'?C   LL'((>C   LL('(=D   LL'))>F   LL())>D   LL'('@E   LL(('?E   LL(('=A   LL(((>D   LL(((@A   LL)()=D   LL)()>E   LL()(@B   LL))(?C   LL('(?E   LL)((=C   LL)()?F   LL))(>B  c{ ~~A~~A  [[D LL=D  D  LL=D  D * LL<D  +D > LL=E  ?D R LL<D  SD f LL=D  gD z LL>C  {D N LL<G  OD b LL<B  cD v LL'))>B  wD J LL>F  KD ^ LL('(=C  _D r LL(('>F  sD F LL=E kk''2( GD ` LL=B  aD t LL>B  uD H LL=C  ID \ LL<B  ]D p LL=C  qD D LL)('>F  ED X LL(('=K  YD l LL>F  mD @ LL(('=D  AD T LL=C  UD h LL&((=C  iD | LL=C  }D P LL=A  QD d LL''(=D  eD x LL(''=D  yD L LL(((=D  M D ` LL()(=A  a D t LL<E  u D GP AQ GP A  [[g LL=C  g  LL((=E  g * LL((=C  +g > LL'(=D  ?g R LL&)=J  Sg f LL&)(=D  gg z LL((=D  {g N LL))=D  Og b LL(=B  cg v LL)((=D  wg J LL))=C  Kg ^ LL)('=C  _g r LL))(=D  sg F LL))'=D  Gg Z LL=E kk''2( [g t LL)''=C  ug H LL'=C  Ig \ LL'=D  ]g p LL(=E  qg D LL)=C  Eg X LL(=E  Yg l LL)=C  mg @ LL(=E  Ag T LL)=D  Ug h LL>D kk''2( ig B LL=C  Cg V LL>C  Wg j LL()>D  kg ~ LL')(>D  g R LL')(>D  S g f LL'>E  g g z LL>C  { g N LL)(>B  O g b LL((=A  c g v LL(=C  w g J LL(')=C  K g ^ LL>C  _ g r LL'>C  s g F LL>E  G g Z LL()(>E  [ g n LL(>E  o g B LL)>C  C g V LL(=E  W g j LL)>D  k g ~ LL(>C   g R LL)=D  Sg f LL(>D  gg z LL(=D  {g jVAWjVA [[g LL(=G  g  LL=C  g * LL&')=D  +g > LL()=B  ?g R LL'=D  Sg f LL()=C kk''2( gg @ LL()=D  Ag T LL'=D  Ug h LL)'=C  ig | LL('=G  }g P LL(()=B  Qg d LL)'=C  eg x LL)=C  yg L LL()(=C  Mg ` LL))'=B  ag t LL=E  ug H LL(=D  Ig \ LL)=B  ]g p LL(=D  qg D LL)=C  Eg X LL(=C  Yg l LL)=C  mg @ LL(=D  Ag T LL)=D  Ug h LL=I kk''2( ig B LL&=E  Cg V LL()=B  Wg j LL'()=B  kg ~ LL=>  g R LL(=C  S g f LL'''=D  g g z LL=C  { g N LL'=D  O g b LL)('=E  c g v LL=D  w g J LL=E  K g ^ LL()(=B  _ g r LL)=D  s g F LL=E  G g Z LL(=C  [ g n LL(=C  o g B LL)=C  C g V LL(=C  W g j LL(=E  k g ~ LL(=F   g R LL)<B  Sg f LL'=C  gg z LL)=B  {g jVAWjVA  [[ LL'('>J   LL('(<M   LL(''>F   LL(')>D   LL'()>C   LL'''>C   LL'('=D   LL('(>D   LL()(>D   LL('(>E   LL'))>C   LL()(>C   LL(((>D   LL)'(>C   LL('(>C   LL)()>C   LL)()=E   LL)('=C   LL()(>G   LL))(>D   LL)('>E   LL()'>C   LL())>C   LL())>B   LLE  c{ ~~A~~A [[ LL/    A! A [[67#P$P2  rr1c a]tRtRto]P P RRRR]P)]P.4]P P RRRR]P)]P.4]P P R .RO4]P P R R.4R 4444t R t R t Vt R#)TestHyp2f1ExtremeInputsi rr rX@rrY@rrc\P!\P!\P!W.444'd+\P!\ WW444'gQhR#R#)N)ranyisinfasarrayisnanr)r8rrrrs&&&&&r test_inf_a_b$TestHyp2f1ExtremeInputs.test_inf_a_b sH 66"((2::qf-. / /88F1.// 0/ 0rc6\P!\RRRR44'gQh\P!\RRRR44'gQh\P!\RRRR44'gQh\P!\RRRR44'gQh\P!\\PRRR44'gQh\P!\R\PRR44'gQhR#) r rrYNi@?iig)rrrr)r8s&rtest_large_a_b&TestHyp2f1ExtremeInputs.test_large_a_b sxxuc3 ;<<=<xxvsC<==>=xxsE3 ;<<=<xxsFC<==>=xxrvvsC56676xxsBFFC56676rr'N)rrg@g@r) r(r)r*r+rrzrurrrrr-r.r/s@rrr s [[S3S266'266"BC [[S3S266'266"BC [[S"67 [[S:,/108DD1 8 8rr)rrrnumpyrtypingr numpy.testingr scipy.specialrscipy.special._testutilsrrr ImportErrorrrr1rr'rrrso ) A% 52Zw& w& rM88N% 8 $F%sAA$#A$