
    (ph+                     t   S r SSKrSSKJrJrJr  SSKJr  SSKrSSK	r	SSK
Jr  SSKJr  SSKJrJrJrJr  SSKJrJrJrJrJrJrJrJrJrJr  SSKJ r J!r!J"r"J#r#J$r$J%r%   SSK&r&\" \&S
5      S 5       r(\" \&S5      S 5       r)\" \&S5      S 5       r*\" \&S5      S 5       r+\" \&S5      S 5       r,\" \&S5      S 5       r-\" \&S5      S 5       r.\" \&S5      S 5       r/\" \&S5      S 5       r0\" \&S5      \Rb                  Rd                  S 5       5       r3\" \&S5      S 5       r4\" \&S5      S 5       r5\" \&S5      S 5       r6Sr7\" \&S5      S  5       r8\" \&S5      S! 5       r9\" \&S5      \Rb                  Rd                  S" 5       5       r:\" \&S5      \Rb                  Rd                  S# 5       5       r;\" \&S5      S$ 5       r<\" \&S5      S% 5       r=\" \&S5      \Rb                  Rd                  S& 5       5       r>\" \&S5      \Rb                  Rd                  S' 5       5       r?\" \&S5      S( 5       r@\" \&S5      S) 5       rA\" \&S5      S* 5       rBS+ rC\Rb                  Rd                  \" \&S5      S, 5       5       rD\Rb                  Rd                  \" \&S5      S- 5       5       rE\Rb                  Rd                  \" \&S5      S. 5       5       rF\Rb                  Rd                  \" \&S5      S/ 5       5       rG\H" S0S0S19rI\Rb                  Rd                  \" \&S25       " S3 S45      5       5       rJg! \' a    \" S	5      r& GNf = f)5z4
Test SciPy functions versus mpmath, if available.

    N)assert_assert_allclosesuppress_warnings)pi)_pep440)MissingModulecheck_versionFuncDataassert_func_equal)
ArgFixedArg
ComplexArgIntArgassert_mpmath_equalnonfunctional_tooslow
trace_argstime_limitedexception_to_nan
inf_to_nan)_sinpi_cospi_lgam1p_lanczos_sum_expg_scaled_log1pmx	_igam_facmpmathz0.10c            
         / n [         R                  " SSS5       H  n[         R                  " SS[         R                  -  S5       HO  nU[         R                  " SU-  5      -  nU R                  U[        [        R                  " U5      5      45        MQ     M     [         R                  " U [         R                  S9n [        [        R                  U SS5      R                  5         g )	Ni   
   r                    ?dtype   )nplogspacelinspacer   expappendcomplexr   eiarraycdoubler
   scexpicheck)datasetrpzs       R/var/www/html/venv/lib/python3.13/site-packages/scipy/special/tests/test_mpmath.pytest_expi_complexr6   #   s    G[[a$Q"%%,A"&&A,ANNAwvyy|456 - % hhwbjj1GRWWgq!$**,    z0.19c                     / n S Hq  n[         R                  " SSS5       HR  n[        R                  " S5         U R	                  X[        [        R                  " X5      5      45        S S S 5        MT     Ms     [         R                  " U 5      n [        [        R                  U SSSS	9R                  5         g ! , (       d  f       M  = f)
N)2   3   r         d   r   r$   r   vIh%<=rtol)r%   r&   r   workdpsr)   floatexpintasarrayr
   r.   expnr0   )r1   nxs      r5   test_expn_large_nrI   3   s     GQ3'A$eFMM!,?&@AB %$ (  jj!GRWWgvqu5;;=	 %$s   1B::
C	c            
      ~   / n / SQnU Hn  nU He  nU H\  nUSU-  -   n[         R                  " S5         [        [         R                  " X%5      5      nS S S 5        U R	                  X%W45        M^     Mg     Mp     [
        R                  " U 5      n [        S U SSSS9R                  5         g ! , (       d  f       N`= f)	N)g     Xg      #            ?g      #@g     X@r!   x   c                 D    [         R                  " U R                  U5      $ Nr.   hyp0f1realvr4   s     r5   <lambda>$test_hyp0f1_gh5764.<locals>.<lambda>U   s    "))AFFA.r7   r>   r   r?   r@   )	r   rB   r*   rQ   r)   r%   r,   r
   r0   )r1   axisrT   rH   yr4   ress          r5   test_hyp0f1_gh5764rZ   D   s     G.DA1H ^^C(!&--"56C )c{+    hhwG. )(s    B.	.
B<c            	         [         R                  " SSS5      n [        R                  " U S5      n[         R                  " U  Vs/ s H  n[
        R                  " US5      PM     sn5      n[        XR                  [        5      SS9  g s  snf )N         rL   -q=r@   )	r%   r'   r.   rQ   r,   r   r   astyperC   )vvafrT   mfs       r5   test_hyp0f1_gh_1609rd   Y   sf     
S#r	"B	2s	B	"5"Q6==C("5	6BB		%(u5 6s   !B
z1.1.0c                  j   / n [         R                  " SS5       H  n[         R                  " SSS5       Hs  nU* nU R                  X2S[	        [
        R                  " X2S5      5      45        U* U-   S-
  nU R                  X2S[	        [
        R                  " X2S5      5      45        Mu     M     S H>  nS H5  nU R                  X2S[	        [
        R                  " X2S5      5      45        M7     M@     [         R                  " U 5      n [        [        R                  U SS	S
SS9R                  5         g )N      r   r$   )      %      rK   r   rL   r$   r   )      rK   r   rL   r$         ?r         @r   r$   r      V瞯<-a=rA   atol)r%   aranger'   r)   rC   r   hyperur,   r
   r.   r0   )r1   rG   bas       r5   test_hyperu_around_0rx   f   s    GYYr1RB'AANNA!U6==q+A%BCDQ
ANNA!U6==q+A%BCD	 (  05ANNA!U6==q+A%BCD 6 0 hhwGRYYAEFLLNr7   1.0.0c                     SS/n U [        [        R                  " / SQSS95      -  n U  VVVVs/ s H2  u  pp4X#:X  d  M  [        U5      U:X  d  M  US:  d  M&  US:w  d  M.  XX44PM4     n nnnn[	        SS	9nU  Vs/ s H%  of[        [        R                  " U0 UD65      4-   PM'     nn[        R                  " U[        R                  S
9n[        [        R                  USSSS9R                  5         g s  snnnnf s  snf )N)r   r{   ffffff?)r   r}   r|   )r   r$   gffffffr;   )repeatr   r~   T)	eliminater"   r   r$   r   ro   绽|=r@   )list	itertoolsproductrounddictrC   r   hyp2f1r%   r,   float64r
   r.   r0   )ptsrw   rv   crH   kwr3   r1   s           r5   test_hyp2f1_strange_pointsr   }   s     	C 4	!!"5a@AAC'*'*q6 	Ah!m 	()A 	23u* 	qs   
	B>ABcE&--1b1244cGBhhwbjj1GRYYAE:@@B
 Cs"   C5
C5
C5
C5
 C5
:,C=z0.13c            	      h   / SQn U  Vs/ s H"  o[        [        R                  " U6 5      4-   PM$     nn[        R                  " U[        R
                  S9n[        R                  " SS9   [        [        R                  USSSS9R                  5         S S S 5        g s  snf ! , (       d  f       g = f)	N)r$   r   ro   r   )UUUUUU?gUUUUUU?g?g      ?)      ?rL   g      ?gX<ݚ?)r   r}   ro   )r   r   r}   ro   )r   rj   rj   ro   r   )gx&?r{   rf   g333333?)r   r   r   +?)r   r   r   r{   )r   ro   rg   Gz?)rl   rK   ro   r   )r   rm   g      
r   )g*4]92@g|O%@gCu?)  ri   r   )r   r         %@r   )r{   r   r$         ?)r{   r   r$   rk   )r      rg   r   )r   r   rg   rk   )rL   g     prl   gm˟?r"   ignoreinvalidr   r;   r   r@   )
rC   r   r   r%   r,   r   errstater
   r.   r0   )r   r3   r1   s      r5   test_hyp2f1_real_some_pointsr      s    C. 9<<1E&--+,..G<hhwbjj1G	X	&GY>DDF 
'	& = 
'	&s   )B+*B##
B10.14c            	      8   / SQn S nU  Vs/ s H5  n[        [        X5      5      [        [        R                  " U6 5      4-   PM7     nn[
        R                  " U[
        R                  S9n[        [        R                  USSSS9R                  5         g s  snf )N))p   )r:   r   )r   gwJ)r   |r   r   )r   r   ri   r   c                 X    [        U [        5      (       a  [        U S   5      U S   -  $ U $ )Nr   r$   )
isinstancetuplerC   rH   s    r5   fev&test_hyp2f1_some_points_2.<locals>.fev   s+    a1;1%%Hr7   r"   r   r;   r   r@   )r   maprC   r   r   r%   r,   r   r
   r.   r0   )r   r   r3   r1   s       r5   test_hyp2f1_some_points_2r      s|    C JMMAuS[!U6==!+<%=$??GMhhwbjj1GRYYAE:@@B Ns   <Bc                     / n S HS  nS HJ  nS HA  nS H8  n [        [        R                  " XX45      5      nU R	                  XX4U45        M:     MC     ML     MU     [
        R                  " U [
        R                  S9n [
        R                  " SS9   [        [        R                  U SS	S
SS9R                  5         S S S 5        g ! [         a     M  f = f! , (       d  f       g = f)N)r   rf   g?rg   r   )g      r{   r$   g@)r   r   rg   gffffff4@)r   g)\(Gzr   g333333?gffffff?rl   r   r"   r   r   r   r;   &.>TrA   ignore_inf_sign)rC   r   r   	Exceptionr)   r%   r,   r   r   r
   r.   r0   )r1   rw   rv   r   r4   rT   s         r5   test_hyp2f1_real_somer      s    G(#A(CA!!&--a";< NNA!?3 D ) $ ) hhwbjj1G	X	&GY!%	'',uw 
'	& % ! !
 
'	&s    C+C
CC
C&z0.12c            
      z   Sn [         R                  " U S4[         R                  5      n[         R                  R	                  S5        [         R                  R                  SU 5      US S 2S4'   [         R                  R                  SU 5      US S 2S4'   [         R                  R                  SU 5      US S 2S4'   S[         R                  R                  U 5      -  S-
  US S 2S4'   US S 2S4==   S	[         R                  R                  SU 5      -  -  ss'   US S 2S4==   S	[         R                  R                  SU 5      -  -  ss'   US S 2S4==   S	[         R                  R                  SU 5      -  -  ss'   U H  n[        R                  S
:  aK  [        US S 5      R                  5       [        US   5      :  a  [        US S 5      R                  5       US'   [        [        R                  " [        US S 5      6 5      US'   M     [        [         R                  USSSS9R#                  5         g )N  rg     rl   r   r$   r   ro   r{   r   r;   r   r   r@   )r%   zerosr   randomseedparetorandrandintr   __version__absmaxrC   r   r   r
   r.   r0   )npointsr1   dss      r5   test_hyp2f1_real_randomr      s    Ghh|RZZ0GIINN4II$$S'2GAqDMII$$S'2GAqDMII$$S'2GAqDMbiinnW--1GAqDMAqDMb299,,Q888MAqDMb299,,Q888MAqDMb299,,Q888M&2bq6{ 3r!u:-BrF)1fmmU2bq6]341  RYYqt<BBDr7   c                     [         R                  R                  [         R                  R                  p S[         R                  l        [        R
                  " [        R                  " SSS5      [        R                  " SSS5      5      u  p#[        R
                  " [        R                  " SSS5      [        R                  " SSS5      5      u  pE[        R                  UR                  5       UR                  5       4   S[        R                  UR                  5       UR                  5       4   -  -   n[        [        R                  S	 US
SS9  [        [        R                  S US
SS9  Xs[         R                  l        [         R                  l        g ! Xs[         R                  l        [         R                  l        f = f)NF   r   r$         ig?r!   c                 @    [        [        R                  " U 5      5      $ rO   )r*   r   erfr   s    r5   rU   "test_erf_complex.<locals>.<lambda>   s    GFJJqM,Br7   Fr?   
vectorizedrA   c                 @    [        [        R                  " U 5      5      $ rO   )r*   r   erfcr   s    r5   rU   r     s    WV[[^-Dr7   )r   mpdpsprecr%   meshgridr'   r&   r_ravelr   r.   r   r   )old_dpsold_precx1y1x2y2pointss          r5   test_erf_complexr      s%    		vyy~~X:		R[[a4bkk#q"6MNR[[b"5r{{3B7OPrxxz"((*,-255RXXZ9O3P0PP"&&"BF%*	8"''#Df%*	8 )0%		vyy~%		vyy~s   D=F ,G	z0.15c                  F   / n S H|  nU R                  SSU4SSU4SSU4SSU4SSU4SSU4SSU4SSU4SSU4SS	U4S
SU4SS	U4SSU4SS	U4S
SU4SSU4SSU4SSU4S
SU4SSU4SSU4SSU4S
SU4SSU4SSU4SSU4/5        M~     S nU  Vs/ s H  o3U" US   US   US   5      4-   PM     nn[        R                  " U[        R                  S9nS n[        R                  " SS9   [        XTSS
SSS9R                  5         S S S 5        g s  snf ! , (       d  f       g = f) N)r   gmư>gL7A`?r$   r$   r{   r}   g333333?g333333gr   r   ro      rg   r   rf   r   ig @g&@g g&c                 j    U[        U5      :X  a  US:X  a  US:X  a  gg[        R                  " XU5      $ Nr$   r   )intr   legenp)numurH   s      r5   mplegenptest_lpmv.<locals>.mplegenp-  s1    R=Q!VQw}}RQ''r7   r   r   r"   c                 V    [         R                  " U R                  [        5      X5      $ rO   )r.   lpmvr`   r   )r   r   rH   s      r5   evftest_lpmv.<locals>.evf9  s    wwryy~r--r7   r   r   rn   r   +=rr   )extendr%   r,   r   r   r
   r0   )r   rH   r   r3   r1   r   s         r5   	test_lpmvr     s   
C,

1IAJAJQKQKaLaLqMAJAJ1IAJAJQKAJQKQKaLQKaLaLqMaLqMqMN5
 	 -<( ;>>#QHQqT1Q41.00#G>hhwbjj1G. 
X	&wEBHHJ 
'	& ? 
'	&s    D(D
D c                     [         R                  R                  S5        [         R                  [         R                  " SSS5      [         R                  " SSS5      [         R                  " SSS5      [         R
                  " SS	S5      [         R
                  " SS	S5      S
-   SSSSS4
   n U n[         R                  " [         R                  " US S 2S 4   U S S S 24   5      5      R                  SS5      R                  n[        R                  R                  [        R                  R                  pC S[        R                  l        [        [        R                   S USSSS9  [        [        R"                  S USSS9  X4s[        R                  l        [        R                  l        g ! X4s[        R                  l        [        R                  l        f = f)Nr   8r<   r;   r   r   r{   r$   r   rL   gffffffr   g33333Yg3333r     c                 @    [        [        R                  " X5      5      $ rO   )rC   r   betarw   rv   s     r5   rU   test_beta.<locals>.<lambda>W  s    uV[[->'?r7   Fr   T)r   rA   r   c           
      z    [        [        R                  " [        [        R                  " X5      5      5      5      $ rO   )rC   r   logr   r   r   s     r5   rU   r   _  s     vzz#fkk!.?*@ABr7   r   )r%   r   r   r   r&   rt   r,   broadcast_arraysreshapeTr   r   r   r   r   r.   r   betaln)rv   rw   abr   r   s        r5   	test_betar   D  sY   IINN4
bkk$Q'kk#r1%kk"a#iiR#iiR#c)$FH- 	.A 	
A	"%%a$i46;	<	D	DQ	K	M	MB		vyy~~X:		"''?%*$*.	0 	IIB	 )0%		vyy~%		vyy~s   7AF0 0,Gg?c            	      6   [         [        R                  " / SQ5      -   n [        R                  " SS[        R                  -  S5      n[        R
                  " X5      u  pU [        R                  " SU-  5      -  n[        R                  SU-   SU-   4   R                  5       nU Vs/ s H#  oD[        [        R                  " U5      5      4PM%     nn[        R                  " U5      n[        [        R                  USSSS9R                  5         g s  snf )	N)gg{Gzr   g{Gz?g?r   r   rh   r!   r$   vIh%,=r@   )LOGGAMMA_TAYLOR_RADIUSr%   r,   r'   r   r   r(   r   flattenr*   r   loggammar
   r.   r0   r2   thetadzr4   z0r1   s         r5   test_loggamma_taylor_transitionr  n  s    
 	*E!FFAKK1RUU7B'E{{1$HA	
266"U(	B
a"fa"fn%%'A<=>AbGFOOB/01AG>hhwGR[['1ae4::< ?s   **Dc            	      X   [         R                  " S[         R                  " [        5      S5      n [         R                  " SS[         R
                  -  S5      n[         R                  " X5      u  pU [         R                  " SU-  5      -  n[         R                  SU-   SU-   4   R                  5       nU Vs/ s H#  oD[        [        R                  " U5      5      4PM%     nn[         R                  " U5      n[        [        R                  USSSS	9R!                  5         g s  snf )
Nir   r   r   rh   r!   r$   r   r@   )r%   r&   log10r   r'   r   r   r(   r   r  r*   r   r  r,   r
   r.   r0   r  s         r5   test_loggamma_taylorr
    s     	C"892>AKK1RUU7B'E{{1$HA	
266"U(	B
a"fa"fn%%'A<=>AbGFOOB/01AG>hhwGR[['1ae4::< ?s   ;*D'c            
         [         R                  [         R                  " SSS5      * S[         R                  " SSS5      4   n U R                  5       n[         R                  " X5      u  pU SU-  -   n[         R
                  " SSS5      R                  SSS5      nU[         R                  " U4UR                  -  5      -   R                  5       n[        R                  " S5         U Vs/ s H#  oU[        [        R                  " U5      5      4PM%     nnS S S 5        [         R                  " W5      n[        [         R                  USSS	S
9R#                  5         g s  snf ! , (       d  f       NS= f)Nr{   ro   r   r!   iVr$   r=   r_   r@   )r%   r   r&   copyr   rt   r   dstacksizer  r   rB   r*   rgammar,   r
   r.   r0   )dxdyr  r   r4   r  r1   s          r5   test_rgamma_zerosr    s    
BQ''BKKR,CC	DB	B[[ FB	beBIIar"**1a4E	B5+,	,557A		>?@ab 123a@ 
 hhwGRYYAE288: A 
	s   (E&-*E!E&!E&&
E4c            
         [         R                  " [         R                  S5      n [        U 5      /n[         R                  " [         R                  S5      n UR	                  [        U 5      5        [
        R                  " U5      n[
        R                  S[
        R                  " SSS5      * S[
        R                  " SSS5      S4   nUR                  5       n[
        R                  " X#5      u  p#US	U-  -   nU[
        R                  " U4UR                  -  5      -   R                  5       n[         R                  " S
5         U Vs/ s H#  of[        [         R                  " U5      5      4PM%     nnS S S 5        [
        R                  " W5      n[!        ["        R                  USSSS9R%                  5         g s  snf ! , (       d  f       NS= f)Nrl   rK   gQοr{   r   r   gQ?r!   r    r$   r   r@   )r   findrootdigammarC   r)   r%   r,   r   r&   r  r   r  r  r  rB   r*   r
   r.   r0   )rootrootsr  r  r  r4   r  r1   s           r5   test_digamma_rootsr    sM    ??6>>3/D4[ME??6>>40D	LLtHHUOE 
ur{{2sB//BKKR4LdR	SB	B[[ FB	beB	B5+,	,557A		?@Aqr 234qA 
 hhwGRZZ!QU399; B 
	s   G*G 6G G
Gc            
      v   [        [        R                  5      n [        R                  " SSS5      * n[        R
                  [        R                  " SSS5      * S[        R                  " SSS5      4   n[        R                  " X5      u  pUSU-  -   R                  5       n[        R                  " S5         U Vs/ s H  oD[        U " U5      5      4PM     nnS S S 5        [        R                  " W5      n[        [        R                  USS	S
S9R                  5         g s  snf ! , (       d  f       NS= f)N,  r=   r   r   rg   r!   (   r$   r?   r@   )r   r   r  r%   r&   r   r   r  rB   r*   rE   r
   r.   r0   )r  rH   rX   r4   r  r1   s         r5   test_digamma_negrealr    s     v~~.G	S#s	##A
r{{1b!$$aRA)>>?A;;qDA	
RTA		89:",-: 
jj!GRZZ!QU399; ; 
	s   :D*?D%D*%D**
D8c            
      
   [         R                  " SSS5      * n [         R                  " / SQ5      n[         R                  " X5      u  pU SU-  -   R	                  5       n[
        R                  " S5         U Vs/ s H#  o3[        [
        R                  " U5      5      4PM%     nnS S S 5        [         R                  " W5      n[        [        R                  USSS	S
9R                  5         g s  snf ! , (       d  f       NS= f)Nr  r  r=   )gffffffgg@gffffff@r!   r    r   r$   r?   r@   )r%   r&   r,   r   r  r   rB   r*   r  rE   r
   r.   r0   rH   rX   r4   r  r1   s        r5   test_digamma_boundaryr"    s    
 
S#s	##A
'(A;;qDA	
RTA		?@Aqr 234qA 
jj!GRZZ!QU399; B 
	s   6C4;*C/%C4/C44
Dc                  6   Sn [         R                  " SU -  SU -  S5      nUR                  5       n[         R                  " X5      u  pUR	                  5       UR	                  5       p![
        R                  " S5         [        X5       VVs/ s H%  u  p4X4[        [
        R                  " X4SS95      4PM'     nnnS S S 5        [         R                  " W5      n[        [        R                  USSS	S
9R                  5         g s  snnf ! , (       d  f       NT= f)Nrh   rL   r   r9   r=   Trv   regularizedr>   r_   r@   )r%   r'   r  r   r  r   rB   ziprC   gammaincr,   r
   r.   r0   )smallrw   rH   a0x0r1   s         r5   test_gammainc_boundaryr+    s     E
CIqw+A	A;;qDA99;		q		!$Q,!*vr E&//""MNO!* 	 , 
 hhwGR[['6159??A	, 
	s   >D
,D9D
D


Dc            	         S n [         R                  " SS5      n[         R                  " SS[        -  5      nS[         R                  " U[         R                  " SU-  5      5      -   R                  5       n[         R                  " U Vs/ s H  oDU " U5      4PM     sn5      n[        [        R                  USSSS	9R                  5         g s  snf )
Nc                 H    [        [        R                  " SSU -
  5      5      $ Nr   r$   )r*   r   polylogr4   s    r5   spence"test_spence_circle.<locals>.spence  s    v~~aQ/00r7   rL   rl   r   r   r$   r!   r   r@   )r%   r'   r   outerr(   r  rE   r
   r.   r1  r0   )r1  r2   r  r4   r  r1   s         r5   test_spence_circler4    s    1 	CAKK1R4 E	
RXXa5)*	*335AjjQ7Qrvbz*Q78GRYYAE288: 8s   Cc                     [         R                  " [        5      R                  n [         R                  [         R
                  " SSS5      * S[         R
                  " SSS5      4   nUR                  5       n[         R                  " X5      u  pUSU-  -   n[         R                  " SSS5      R                  SSS5      nU[         R                  " U4UR                  -  5      -   R                  5       n[         R                  " U Vs/ s H$  nU[        [        R                   " U5      5      4PM&     sn5      n[#        [$        USSS	U -  S
9R'                  5         g s  snf )Nr   r  ro   r!   r=   r$   r{   r   r@   )r%   finforC   epsr   r&   r  r   rt   r   r  r  r  rE   r*   r   sinpir
   r   r0   r8  r  r  r  r   r4   r  r1   s           r5   test_sinpi_zerosr;    s   
((5/

C	AsA&&2;;sAq+AA	BB	B[[ FB	beBIIdC#++Aq"5E	B5+,	,557Ajj$%'$%b wv||B'789$%' (GVWa3/557's   
+Ec                     [         R                  " [        5      R                  n [         R                  [         R
                  " SSS5      * S[         R
                  " SSS5      4   nUR                  5       n[         R                  " X5      u  pUSU-  -   n[         R                  " SSS5      S-   R                  SSS	5      nU[         R                  " U4UR                  -  5      -   R                  5       n[         R                  " U Vs/ s H$  nU[        [        R                   " U5      5      4PM&     sn5      n[#        [$        USSS
U -  S9R'                  5         g s  snf )Nr   r  ro   r!   r6  r=   r$   rL   r{   r   r@   )r%   r7  rC   r8  r   r&   r  r   rt   r   r  r  r  rE   r*   r   cospir
   r   r0   r:  s           r5   test_cospi_zerosr>  $  s   
((5/

C	AsA&&2;;sAq+AA	BB	B[[ FB	beBYYtS!$s*33Aq"=E	B5+,	,557Ajj$%'$%b wv||B'789$%' (G VWa3/557's   +E"c            
         S n S n[         R                  " SSS5      n[         R                  [         R                  " SSS5      * S[         R                  " SSS5      4   n/ nU HH  n[	        [
        R                  " U5      5      nU H   nXg-   nUR                  XU" X5      45        M"     MJ     [         R                  " U5      n[        XS	S
SS9R                  5         g )Nc                 4    [         R                  " X5      S   $ Nr   r.   ellipjums     r5   dn"test_dn_quarter_period.<locals>.dn9  s    yyq!!r7   c                 >    [        [        R                  " SXS95      $ NrG  rD  )rC   r   ellipfunrD  s     r5   	mpmath_dn)test_dn_quarter_period.<locals>.mpmath_dn<  s    V__TQ455r7   r   r$   rh   r{   r  r   r>   r   r   r@   )r%   r'   r   r&   rC   r   ellipkr)   rE   r
   r0   )	rG  rL  rF  dur1   m0u0du0r3   s	            r5   test_dn_quarter_periodrS  7  s    "6 	Aq"A	BR((!R[[b"-EE	FBG6==$%CANNA9Q#345  
 jj!GR&!%0668r7   c                 t   [         R                  " U5         [         R                  " U 5      n [         R                  " U R                  [         R
                  -
  S[         R
                  -  -  5      n[         R                  " [         R                  " U 5      U5      nS S S 5        U$ ! , (       d  f       W$ = frA  )r   rB   mpcceilimagr   lambertwr(   )r4   r   unwindrY   s       r5   _mpmath_wrightomegarZ  P  sw    		JJqMaffvyy01VYY;?@oofjjmV4 
 J	 
	 Js   BB((
B7c                     [         R                  " SSS5      * n [         R                  " [         R                  [         R                  5      /n[         R                  " [         R                  [         R                  * 5      /n[         R                  " [         R                  * [         R                  5      /n[         R                  " [         R                  * [         R                  * 5      /n[        S5       H  nUR                  [         R                  " US   [         R                  5      5        UR                  [         R                  " US   [         R                  * 5      5        UR                  [         R                  " US   [         R                  5      5        UR                  [         R                  " US   [         R                  * 5      5        M     [         R                  " XX445      n[         R                  " X5      u  pU SU-  -   R                  5       n[         R                  " U Vs/ s H  nU[        [        US5      5      4PM     sn5      n	[        [        R                  U	SSSS	9R!                  5         g s  snf )
Nr   r      r9   r{   r!   r$   :0yE>r@   )r%   r&   	nextafterr   infranger)   hstackr   r  rE   r*   rZ  r
   r.   wrightomegar0   )
rH   picut_abovepicut_belownpicut_abovenpicut_belowirX   r4   r  r1   s
             r5   test_wrightomega_branchrh  X  s    
RB	A<<rvv./K<<w/0KLL"%%01LLL"%%"&&12L2Y2<<B@A2<<B"&&ABBLLb)9266BCBLLb)9BFF7CD	 
 			;\HIA;;qDA	
RTAjj$%'$%b w':2r'BCD$%' (G R^^Wa6<<>'s   8!J
c                     [         R                  " SS5      n [         R                  " SS[         R                  -  5      n[         R                  " X5      u  pU SU-  -   R	                  5       n[         R
                  " U Vs/ s H  nU[        [        US5      5      4PM     sn5      n[        [        R                  USSSS9R                  5         g s  snf )	Nr}   r$   r   r!   r\  r   rp   r@   r%   r'   r   r   r  rE   r*   rZ  r
   r.   rb  r0   r!  s        r5   test_wrightomega_region1rk  o  s     	BA
AqwA;;qDA	
RTAjj$%'$%b w':2r'BCD$%' (G R^^Wa7==?'   !Cc                     [         R                  " SS5      n [         R                  " S[         R                  -  S5      n[         R                  " X5      u  pU SU-  -   R	                  5       n[         R
                  " U Vs/ s H  nU[        [        US5      5      4PM     sn5      n[        [        R                  USSSS9R                  5         g s  snf )	Nr}   r$   r{   r!   r\  r   rp   r@   rj  r!  s        r5   test_wrightomega_region2rn  ~  s     	BA
BruuHb!A;;qDA	
RTAjj$%'$%b w':2r'BCD$%' (G R^^Wa7==?'rl  c                     [         R                  " SSS5      [         R                  " SSS5      p[         R                  " X5      u  pU SU-  -   R                  5       n[         R                  " U Vs/ s H$  nU[        [        R                  " U5      5      4PM&     sn5      n[        [        R                  USSSS9R                  5         g s  snf )Nr{   r$   r\  r!   r   r?   r@   )r%   r'   r   r  rE   r*   r   rX  r
   r.   r0   r!  s        r5   test_lambertw_smallzrp    s     ;;r1b!2;;r1b#9q;;qDA	
RTAjj$%'$%b wvr':;<$%' (G R[['1ae4::<'s   2+Cr<   maxprecmaxtermsz0.17c                   *   \ rS rSrS rS rS rS rS rS r	S r
S	 rS
 rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS r\R>                  RA                  SSS9S 5       r!S  r"\R>                  RA                  SSS9S! 5       r#S" r$S# r%S$ r&S% r'S& r(S' r)S( r*S) r+S* r,S+ r-S, r.S- r/S. r0S/ r1S0 r2S1 r3S2 r4S3 r5S4 r6S5 r7S6 r8S7 r9S8 r:S9 r;S: r<S; r=S< r>S= r?S> r@S? rAS@ rBSA rCSB rDSC rESD rFSE rGSF rHSG rISH rJSI rKSJ rLSK rMSL rNSM rOSN rPSO rQ\R>                  RA                  SSP9SQ 5       rRSR rS\R>                  RA                  SSP9SS 5       rT\UST 5       rVSU rWSV rX\R>                  RA                  SSWS9SX 5       rYSY rZSZ r[S[ r\\R>                  RA                  SSP9S\ 5       r]\US] 5       r^\R>                  RA                  SSP9S^ 5       r_\R>                  R                  S_5      S` 5       raSa rbSb rc\R>                  RA                  SSP9Sc 5       rdSd reSe rfSf rg\USg 5       rhSh ri\R>                  R                  Si5      Sj 5       rjSk rk\USl 5       rlSm rmSn rnSo roSp rp\R>                  RA                  SSqS9Sr 5       rq\USs 5       rrSt rsSu rt\R>                  RA                  SSP9Sv 5       ru\R>                  RA                  SSwS9Sx 5       rvSy rw\R>                  RA                  SSzS9S{ 5       rxS| ryS} rz\R>                  RA                  S~S9S 5       r{S r|S r}S r~S rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS r\R>                  RA                  SSS9S 5       rSrg)TestSystematici  c                     [        S [        R                  [        SS5      /SS9  [        S [        R                  [        SS5      /5        g )	Nc                 4    [         R                  " U 5      S   $ Nr   r.   airyr0  s    r5   rU   ,TestSystematic.test_airyai.<locals>.<lambda>      bggajmr7       ח    חAh㈵>r@   c                 4    [         R                  " U 5      S   $ rx  ry  r0  s    r5   rU   r{    r|  r7        @     @@)r   r   airyair   selfs    r5   test_airyaiTestSystematic.test_airyai  sC    3"MM s^,!%	' 	3"MM s^,	.r7   c                 N    [        S [        R                  [        5       /5        g )Nc                 4    [         R                  " U 5      S   $ rx  ry  r0  s    r5   rU   4TestSystematic.test_airyai_complex.<locals>.<lambda>  r|  r7   )r   r   r  r   r  s    r5   test_airyai_complex"TestSystematic.test_airyai_complex  s    3"MM'\N	,r7   c                 j    [        S S [        SS5      /SS9  [        S S [        S	S
5      /5        g )Nc                 4    [         R                  " U 5      S   $ Nr$   ry  r0  s    r5   rU   2TestSystematic.test_airyai_prime.<locals>.<lambda>  r|  r7   c                 ,    [         R                  " U SS9$ Nr$   )
derivativer   r  r0  s    r5   rU   r        "MM!:r7   r}  r~  r  r@   c                 4    [         R                  " U 5      S   $ r  ry  r0  s    r5   rU   r    r|  r7   c                 ,    [         R                  " U SS9$ r  r  r0  s    r5   rU   r    r  r7   r  r  r   r   r  s    r5   test_airyai_prime TestSystematic.test_airyai_prime  ?    3 6; s^,!%	' 	3 6; s^,	.r7   c                 4    [        S S [        5       /5        g )Nc                 4    [         R                  " U 5      S   $ r  ry  r0  s    r5   rU   :TestSystematic.test_airyai_prime_complex.<locals>.<lambda>  r|  r7   c                 ,    [         R                  " U SS9$ r  r  r0  s    r5   rU   r    r  r7   r   r   r  s    r5   test_airyai_prime_complex(TestSystematic.test_airyai_prime_complex      3 6;'\N	,r7   c                 j    [        S S [        SS5      /SS9  [        S S [        S	S
5      /5        g )Nc                 4    [         R                  " U 5      S   $ rA  ry  r0  s    r5   rU   ,TestSystematic.test_airybi.<locals>.<lambda>  r|  r7   c                 .    [         R                  " U 5      $ rO   r   airybir0  s    r5   rU   r        "MM!,r7   r}  r~  r  r@   c                 4    [         R                  " U 5      S   $ rA  ry  r0  s    r5   rU   r    r|  r7   c                 .    [         R                  " U 5      $ rO   r  r0  s    r5   rU   r    r  r7   r  r  r  r  s    r5   test_airybiTestSystematic.test_airybi  s?    3 6- s^,!%	' 	3 6- s^,	.r7   c                 4    [        S S [        5       /5        g )Nc                 4    [         R                  " U 5      S   $ rA  ry  r0  s    r5   rU   4TestSystematic.test_airybi_complex.<locals>.<lambda>  r|  r7   c                 .    [         R                  " U 5      $ rO   r  r0  s    r5   rU   r    r  r7   r  r  s    r5   test_airybi_complex"TestSystematic.test_airybi_complex  s    3 6-'\N	,r7   c                 j    [        S S [        SS5      /SS9  [        S S [        S	S
5      /5        g )Nc                 4    [         R                  " U 5      S   $ Nro   ry  r0  s    r5   rU   2TestSystematic.test_airybi_prime.<locals>.<lambda>  r|  r7   c                 ,    [         R                  " U SS9$ r  r  r0  s    r5   rU   r    r  r7   r}  r~  r  r@   c                 4    [         R                  " U 5      S   $ r  ry  r0  s    r5   rU   r    r|  r7   c                 ,    [         R                  " U SS9$ r  r  r0  s    r5   rU   r    r  r7   r  r  r  r  s    r5   test_airybi_prime TestSystematic.test_airybi_prime  r  r7   c                 4    [        S S [        5       /5        g )Nc                 4    [         R                  " U 5      S   $ r  ry  r0  s    r5   rU   :TestSystematic.test_airybi_prime_complex.<locals>.<lambda>  r|  r7   c                 ,    [         R                  " U SS9$ r  r  r0  s    r5   rU   r    r  r7   r  r  s    r5   test_airybi_prime_complex(TestSystematic.test_airybi_prime_complex  r  r7   c                 d    [        [        R                  [        S 5      [	        SS5      /5        g )Nc                 :    [         R                  " SU 40 [        D6$ rx  )r   beiHYPERKWr0  s    r5   rU   )TestSystematic.test_bei.<locals>.<lambda>      vzz!Q7R'7Rr7   r  r  )r   r.   r  r   r   r  s    r5   test_beiTestSystematic.test_bei  %    BFF,-RS s^,	.r7   c                 d    [        [        R                  [        S 5      [	        SS5      /5        g )Nc                 :    [         R                  " SU 40 [        D6$ rx  )r   berr  r0  s    r5   rU   )TestSystematic.test_ber.<locals>.<lambda>  r  r7   r  r  )r   r.   r  r   r   r  s    r5   test_berTestSystematic.test_ber  r  r7   c                 8    [        S S [        SS5      /SSS9  g )Nc                 X    [         R                  " [        U 5      5      [        U 5         $ rO   )r.   	bernoullir   rG   s    r5   rU   /TestSystematic.test_bernoulli.<locals>.<lambda>  s    bll3q6&:3q6&Br7   c                 R    [        [        R                  " [        U 5      5      5      $ rO   )rC   r   r  r   r  s    r5   rU   r    s    eF,<,<SV,D&Er7   r   i2  r   rA   rG   )r   r   r  s    r5   test_bernoulliTestSystematic.test_bernoulli  s"    BE#Au-.!%	0r7   c                 t    [        [        R                  [        S 5      [	        SS5      [	        5       /SS9  g )Nc                 8    [         R                  " X40 [        D6$ rO   r   besselir  rS   s     r5   rU   -TestSystematic.test_besseli.<locals>.<lambda>       &..*I*Ir7   }Ô%I}Ô%ITgJDrs   )r   r.   ivr   r   r  s    r5   test_besseliTestSystematic.test_besseli  s.    EEIJ'		
r7   c                 \    [        S [        S 5      [        SS5      [        5       /5        g )Nc                 D    [         R                  " U R                  U5      $ rO   )r.   r  rR   rS   s     r5   rU   5TestSystematic.test_besseli_complex.<locals>.<lambda>      qvvq)r7   c                 8    [         R                  " X40 [        D6$ rO   r  rS   s     r5   rU   r    r  r7   r  r  r   r   r   r   r  s    r5   test_besseli_complex#TestSystematic.test_besseli_complex  '    )IJ.	
r7   c           	          [        [        R                  [        S 5      [	        SS5      [	        SS5      /SS9  [        [        R                  [        S 5      [	        SS5      [	        S	S
5      /SSS9  g )Nc                 8    [         R                  " X40 [        D6$ rO   r   besseljr  rS   s     r5   rU   -TestSystematic.test_besselj.<locals>.<lambda>  r  r7   r  r  r  r  Tr   c                 8    [         R                  " X40 [        D6$ rO   r  rS   s     r5   rU   r    r  r7   r}  r~  r  )r   rA   )r   r.   jvr   r   r  s    r5   test_besseljTestSystematic.test_besselj  sg    EEIJT30 		
 	EEIJT30 	
r7   c                 X    [        S [        S 5      [        5       [        5       /5        g )Nc                 D    [         R                  " U R                  U5      $ rO   )r.   r  rR   rS   s     r5   rU   5TestSystematic.test_besselj_complex.<locals>.<lambda>  r  r7   c                 8    [         R                  " X40 [        D6$ rO   r  rS   s     r5   rU   r     r  r7   r  r  s    r5   test_besselj_complex#TestSystematic.test_besselj_complex  s"    )IJUJL!	
r7   c           	          [        [        R                  [        R                  [        SS5      [        S[        R                  5      /SSS9  g Nr   r<   r   Fr_   nan_okrA   )r   r.   kvr   besselkr   r%   r_  r  s    r5   test_besselkTestSystematic.test_besselk$  s6    EENNs^SBFF^,	
r7   c           	          [        [        R                  [        R                  [        SS5      [        S[        R                  5      /SSS9  g r  )	r   r.   knr   r  r   r   r%   r_  r  s    r5   test_besselk_intTestSystematic.test_besselk_int-  s7    EENND#Arvv/	
r7   c                 \    [        S [        S 5      [        SS5      [        5       /5        g )Nc                 D    [         R                  " U R                  U5      $ rO   )r.   r  rR   rS   s     r5   rU   5TestSystematic.test_besselk_complex.<locals>.<lambda>8  r  r7   c                 8    [         R                  " X40 [        D6$ rO   )r   r  r  rS   s     r5   rU   r  9  r  r7   r  r  r  r  s    r5   test_besselk_complex#TestSystematic.test_besselk_complex6  r  r7   c           	      |    S n[        [        R                  [        U5      [	        SS5      [	        SS5      /SS9  g )Nc                    [        [        R                  " X40 [        D65      n[	        U5      S:  a'  [
        R                  [
        R                  " U5      -  n[	        U5      S:X  a  US:X  a  [
        R                  $ U$ )NقnQ:Br   )	rC   r   besselyr  r   r%   r_  signnanrT   rH   r2   s      r5   	mpbessely.TestSystematic.test_bessely.<locals>.mpbessely>  sZ    fnnQ5W56A1v~FFRWWQZ'1v{qAvvvHr7   r  r  r}  r~    r  )r   r.   yvr   r   r  r  s     r5   test_besselyTestSystematic.test_bessely=  s8    	 	EEY'T30		
r7   c                 Z    S n[        S [        U5      [        5       [        5       /SS9  g )Nc                    [        [        R                  " X40 [        D65      n[	        U5      S:  aF  [
        R                  " SS9   [
        R                  [
        R                  " U5      -  nS S S 5        U$ U$ ! , (       d  f       U$ = f)Nr  r   r   )	r*   r   r  r  r   r%   r   r_  r  r  s      r5   r  6TestSystematic.test_bessely_complex.<locals>.mpbesselyO  sc    q7w78A1v~[[2+A 3H1H 32Hs   (A<<
Bc                 D    [         R                  " U R                  U5      $ rO   )r.   r  rR   rS   s     r5   rU   5TestSystematic.test_bessely_complex.<locals>.<lambda>W  r  r7   i:  r  r  r  s     r5   test_bessely_complex#TestSystematic.test_bessely_complexN  s+    	 	)Y'UJL!		
r7   c           	      d    S n[        S [        U5      [        SS5      [        SS5      /5        g )Nc                     [        [        R                  " X5      5      n[        U5      S:X  a  US:X  a  [        R
                  $ U$ rx  )rC   r   r  r   r%   r  r  s      r5   r  2TestSystematic.test_bessely_int.<locals>.mpbessely^  s4    fnnQ*+A1v{qAvvvHr7   c                 B    [         R                  " [        U 5      U5      $ rO   )r.   ynr   rS   s     r5   rU   1TestSystematic.test_bessely_int.<locals>.<lambda>e  s    s1vq)r7   r~     r}  r~  r   r   r   r   r  s     r5   test_bessely_intTestSystematic.test_bessely_int]  s1    	 	)Y'E4 #dC.1	
r7   c           	         ^^ / mSU4S jjm[        [        R                  U4S j[        5       [        5       /SSS9  [        [        R                  T[        R
                  " T5      SSSS9  g )	Nc                 2  > U S:  d  US:  a  [         R                  $ U S:  d  US:  aY  [        [        X-   5      5      S-  S:X  a<  U(       a5  TR	                  [        U 5      [        U5      45        [         R                  $ [
        R                  " X5      $ )Ng   mr   r$   )r%   r  r   rC   r)   r   r   )rw   rv   nonzero
bad_pointss      r5   r   &TestSystematic.test_beta.<locals>.betam  sw    5yAI vvAQSqu%6%:q$@ %%uQxq&:;66M;;q$$r7   c                    > T" XSS9$ NT)r4   )rw   rv   r   s     r5   rU   *TestSystematic.test_beta.<locals>.<lambda>~  s    aD1r7   r   Tr   r   dy=)r   r   rs   F)r   r.   r   r   r%   r,   )r  r5  r   s    @@r5   r   TestSystematic.test_betaj  s[    
	% 	GG1UCEN 	
 	GGHHZ  	
r7   c                     [        [        R                  [        5       " [	        S 5      5      [        5       [        5       [        5       /5        g )Nc                 0    [         R                  " XSUSS9$ )Nr   Tr%  r   betaincrw   rv   rH   s      r5   rU   -TestSystematic.test_betainc.<locals>.<lambda>      FNN1A4$Pr7   )r   r.   rC  r   r   r   r  s    r5   test_betaincTestSystematic.test_betainc  s8    JJN P
 UCE35!	
r7   c                     [        [        R                  [        5       " [	        S 5      5      [        5       [        5       [        5       /SS9  g )Nc                 0    [         R                  " XUSSS9$ )Nr$   TrA  rB  rD  s      r5   rU   .TestSystematic.test_betaincc.<locals>.<lambda>  rF  r7   r   r   )r   r.   betainccr   r   r   r  s    r5   test_betainccTestSystematic.test_betaincc  s;    KKN P
 UCE35!		
r7   c                    ^^ / mSU4S jjm[        [        R                  U4S j[        5       [        5       /SS9  [        [        R                  T[        R
                  " T5      SSS9  g )Nc           	        > [        U5      S[        U 5      S-   -  :  a  [        R                  $ X:  ax  [        [        X-
  5      [        R                  " [        X-
  5      5      -
  5      S:  a<  U(       a5  TR                  [        U 5      [        U5      45        [        R                  $ [        R                  " X5      $ )Nr~  r$   rp   )r   r%   r  rC   r   r)   r   binomial)rG   kr4  r5  s      r5   rR  +TestSystematic.test_binom.<locals>.binomial  s    1vSVaZ(( vvuU13Z"((5:*>>?%G %%uQxq&:;66M??1((r7   c                    > T" XSS9$ r8  r9  )rG   rS  rR  s     r5   rU   +TestSystematic.test_binom.<locals>.<lambda>  s    !5r7   r   rL  r   r   rs   r=  )r   r.   binomr   r%   r,   )r  r5  rR  s    @@r5   
test_binomTestSystematic.test_binom  sU    
	) 	HH5UCEN		
 	HHHHZ 	
r7   c                 V    [        S [        S 5      [        5       [        5       /SS9  g )Nc                 B    [         R                  " [        U 5      U5      $ rO   )r.   eval_chebytr   rG   rH   s     r5   rU   0TestSystematic.test_chebyt_int.<locals>.<lambda>      A2r7   c                 8    [         R                  " X40 [        D6$ rO   )r   chebytr  r^  s     r5   rU   r_        &--*H*Hr7   r9   rL  r/  r  s    r5   test_chebyt_intTestSystematic.test_chebyt_int  %    2HIXsu		
r7   Fz'some cases in hyp2f1 not fully accurate)runreasonc                 b    [        [        R                  S [        SS5      [        5       /SS9  g )Nc                 f    [        5       " [        [        R                  5      5      " X40 [        D6$ rO   )r   r   r   rb  r  r^  s     r5   rU   ,TestSystematic.test_chebyt.<locals>.<lambda>  '     /r7   e   '  r  )r   r.   r]  r   r  s    r5   test_chebytTestSystematic.test_chebyt  s+    NN s^SU#	
r7   c                 V    [        S [        S 5      [        5       [        5       /SS9  g )Nc                 B    [         R                  " [        U 5      U5      $ rO   )r.   eval_chebyur   r^  s     r5   rU   0TestSystematic.test_chebyu_int.<locals>.<lambda>  r`  r7   c                 8    [         R                  " X40 [        D6$ rO   )r   chebyur  r^  s     r5   rU   ru    rc  r7   r9   rL  r/  r  s    r5   test_chebyu_intTestSystematic.test_chebyu_int  rf  r7   c                 d    [        [        R                  S [        SS5      [        5       /5        g )Nc                 f    [        5       " [        [        R                  5      5      " X40 [        D6$ rO   )r   r   r   rw  r  r^  s     r5   rU   ,TestSystematic.test_chebyu.<locals>.<lambda>  rl  r7   rm  rn  )r   r.   rt  r   r  s    r5   test_chebyuTestSystematic.test_chebyu  s(    NN s^SU#	
r7   c                     S n[        U[        R                  [        5       /5        [        U[        R                  [	        / SQ5      /5        g )Nc                 4    [         R                  " U 5      S   $ r  r.   shichir   s    r5   chi$TestSystematic.test_chi.<locals>.chi      99Q<?"r7   gU@X   g   V@)r   r   r  r   r   r  r  s     r5   test_chiTestSystematic.test_chi  4    	#CceW5Ch7Q.R-STr7   c                     S n[        U[        R                  [        [	        [
        R                  * S5      [	        [
        R                  S5      5      /SS9  g )Nc                 4    [         R                  " U 5      S   $ r  r  r0  s    r5   r  ,TestSystematic.test_chi_complex.<locals>.chi  r  r7   r}  r~  r_   r@   )r   r   r  r   r*   r%   r_  r  s     r5   test_chi_complexTestSystematic.test_chi_complex  C    	# 	JJ.0DEF		
r7   c                 V    S n[        U[        R                  [        SS5      /5        g )Nc                 4    [         R                  " U 5      S   $ r  r.   sicir   s    r5   ci"TestSystematic.test_ci.<locals>.ci      771:a= r7   r}  r~  )r   r   r  r   r  r  s     r5   test_ciTestSystematic.test_ci  s"    	! 	B		CcN+;<r7   c                     S n[        U[        R                  [        [	        S[
        R                  * 5      [	        S[
        R                  5      5      /SS9  g )Nc                 4    [         R                  " U 5      S   $ r  r  r0  s    r5   r  *TestSystematic.test_ci_complex.<locals>.ci  r  r7   r}  r~  r]  r@   )r   r   r  r   r*   r%   r_  r  s     r5   test_ci_complexTestSystematic.test_ci_complex  sC    	! 	IIrvvg.RVV0DEF		
r7   c                     [         R                  " [        5      R                  n[	        [
        [        R                  [        5       /SSU-  S9  g NFr   r  )	r%   r7  rC   r8  r   r   r   r=  r   r  r8  s     r5   
test_cospiTestSystematic.test_cospi  s2    hhuo!!FFLL35'%aPSeTr7   c                 T    [        [        [        R                  [	        5       /SSS9  g )NFr?   r  )r   r   r   r=  r   r  s    r5   test_cospi_complex!TestSystematic.test_cospi_complex  !    LL\N	
r7   c                 z    [        [        R                  [        [        R                  5      [        5       /SSS9  g )Nr_   r9   rA   r   )r   r.   r  r   r   r   r  s    r5   test_digammaTestSystematic.test_digamma  s*    JJV^^,UG	
r7   c           	          S n[        [        R                  [        [        R                  5      [        5       /SSUS9  g )Nc                     [         R                  " U R                  S:  [         R                  " U R                  5      S:  -  SS5      $ )Nr   gQ?FT)r%   whererR   r   rW  r0  s    r5   param_filter9TestSystematic.test_digamma_complex.<locals>.param_filter&  s3    88QVVaZBFF166NT,ABE4PPr7   r?   r  rA   r   r  )r   r.   r  r   r   r   )r  r  s     r5   test_digamma_complex#TestSystematic.test_digamma_complex#  s5    	Q 	JJV^^,\N%	
r7   c                 f    [        [        R                  [        R                  [        5       /SS9  g )Nr   r@   )r   r.   exp1r   e1r   r  s    r5   test_e1TestSystematic.test_e12  s"    GGIIUG		
r7   c                    [        [        R                  [        R                  [        [        [        R                  * S5      [        [        R                  S5      5      /SS9  [        [        R                  [        R                  [        R                  " SSS5      S S 2S 4   [        R                  S[        R                  " S	S
S5      [        R                  " S	S
S5      * 4   S-  -   R                  5       SS9  [        [        R                  [        R                  [        R                  " SSS5      S-   SS9  g )Nr}  r~  r<  r@   r9      r   r   r   =   r   r!   iro  y                )r   r.   r  r   r  r   r*   r%   r_  r'   r   r&   r   r  s    r5   test_e1_complexTestSystematic.test_e1_complex:  s    GGII.0DEF		
 	GGII[[b#&q$w/uuQB2.RB1G0GGHKLMRUW	
 	GGII[[c5)B.		
r7   c                    [        [        R                  S [        [        R
                  " [        R                  " [        R                  5      R                  5      * [        R
                  " [        R                  " [        R                  5      R                  5      S9/5        [        [        R                  S [        R                  " SSSSS[        R                  /5      S	S
9  [        [        R                  " [        R                  " [        R                  5      5      5        [        [        R                  " [        R                  * 5      S:H  5        g )Nc                 l    U S:w  a  [         R                  " U 5      U -  $ [         R                  " S5      $ Nr   z1.0r   expm1mpfr   s    r5   rU   ,TestSystematic.test_exprel.<locals>.<lambda>U  (    16fll1oa'Hvzz%7HHr7   r   c                 l    U S:w  a  [         R                  " U 5      U -  $ [         R                  " S5      $ r  r  r   s    r5   rU   r  [  r  r7   r_   gW:r   g   mBgyCxDr<  r@   )r   r.   exprelr   r%   r   r7  r   r   r,   r_  r   isinfr  s    r5   test_exprelTestSystematic.test_exprelR  s    IIHBFF288BJJ/334466"((2::.2235 6	
 	IIHHHeUAtT266:;		
 	266*+,		266'"a'(r7   c                     [        [        R                  [        R                  [	        [        [        R                  * S5      [        [        R                  S5      5      /5        g )N    c    cA)r   r.   r  r   r   r*   r%   r_  r  s    r5   test_expm1_complex!TestSystematic.test_expm1_complexb  s=    HHLL.0DEF	
r7   c                 L    [        [        R                  S [        5       /SS9  g )Nc                 4    [         R                  " U S-   5      $ r  r   r   r   s    r5   rU   3TestSystematic.test_log1p_complex.<locals>.<lambda>m  s    fjj1or7   <   rL  )r   r.   log1pr   r  s    r5   test_log1p_complex!TestSystematic.test_log1p_complexj  s    HH%\N		
r7   c                 :    [        [        S [        5       /SSS9  g )Nc                 :    [         R                  " U S-   5      U -
  $ r  r  r   s    r5   rU   -TestSystematic.test_log1pmx.<locals>.<lambda>u  s    fjjQ'!+r7   r  r   )r   rA   )r   r   r   r  s    r5   test_log1pmxTestSystematic.test_log1pmxr  s    +UG	
r7   c                 f    [        [        R                  [        R                  [        5       /SS9  g )Nr<  r@   )r   r.   r/   r   r+   r   r  s    r5   test_eiTestSystematic.test_ei{  s    BGGVYYeDr7   c                     [        [        R                  [        R                  [        [        [        R                  * S5      [        [        R                  S5      5      /SS9  g )Nr}  r~  r   r@   )	r   r.   r/   r   r+   r   r*   r%   r_  r  s    r5   test_ei_complexTestSystematic.test_ei_complex~  s@    GGII.0DEF		
r7   c                 f    [        [        R                  [        R                  [	        SS9/5        g )Nr   rv   )r   r.   elliper   r   r  s    r5   test_ellipeTestSystematic.test_ellipe  s    BIIv}}sSzlCr7   c           	      |    [        [        R                  [        R                  [        SS5      [        SS9/5        g )Nr  r  r   r  r   r.   	ellipeincr   r  r   r  s    r5   test_ellipeincTestSystematic.test_ellipeinc  s&    BLL&--#dC.#PS*9UVr7   c                 z    [        [        R                  [        R                  [        5       [        5       /5        g rO   r  r  s    r5   test_ellipeinc_largephi&TestSystematic.test_ellipeinc_largephi      BLL&--#%Hr7   c                 ~    [        [        R                  [        R                  [        SS5      [        5       /5        g Nr  r  r   r.   	ellipkincr   ellipfr   r  s    r5   test_ellipfTestSystematic.test_ellipf  s#    BLL&--#dC.#%9PQr7   c                 z    [        [        R                  [        R                  [        5       [        5       /5        g rO   r  r  s    r5   test_ellipf_largephi#TestSystematic.test_ellipf_largephi  r  r7   c                     [        [        R                  [        R                  [	        SS9/5        [        [        R
                  S [	        SS9/SS9  g )Nr   r  c                 4    [         R                  " SU -
  5      $ r  )r   rN  )rF  s    r5   rU   ,TestSystematic.test_ellipk.<locals>.<lambda>  s    fmmAE*r7   g        )rw   r   rL  )r   r.   rN  r   r   ellipkm1r  s    r5   test_ellipkTestSystematic.test_ellipk  s:    BIIv}}sSzlCKK*3ZL		
r7   c           	      d    S n[        [        R                  U[        SS5      [        SS9/SS9  g )Nc                 0    [         R                  " SX5      $ rx  r   ellippiphirF  s     r5   r  0TestSystematic.test_ellipkinc.<locals>.ellipkinc      >>!S,,r7   r  r  r   r  Tr  r   r.   r  r   r  r  s     r5   test_ellipkincTestSystematic.test_ellipkinc  s.    	-LLs^S3Z( 		
r7   c           	      `    S n[        [        R                  U[        5       [        SS9/SS9  g )Nc                 0    [         R                  " SX5      $ rx  r  r  s     r5   r  9TestSystematic.test_ellipkinc_largephi.<locals>.ellipkinc  r  r7   r   r  Tr  r  r  s     r5   test_ellipkinc_largephi&TestSystematic.test_ellipkinc_largephi  s*    	-LLUC#J 		
r7   c           
      L    S n[        S U[        SS5      [        SSS9/SS	9  g )
Nc                 :    U S:X  a  g[         R                  " SXS9$ )Nr   snrD  r   rK  rD  s     r5   r  +TestSystematic.test_ellipfun_sn.<locals>.sn  s    Avtq66r7   c                 4    [         R                  " X5      S   $ rx  rB  rD  s     r5   rU   1TestSystematic.test_ellipfun_sn.<locals>.<lambda>      1+r7       .    .Ar   r$   r   r]  r@   r  )r  r  s     r5   test_ellipfun_snTestSystematic.test_ellipfun_sn  s.    	7 	+s^S1]+		
r7   c           
      H    [        S S [        SS5      [        SSS9/SS	9  g )
Nc                 4    [         R                  " X5      S   $ r  rB  rD  s     r5   rU   1TestSystematic.test_ellipfun_cn.<locals>.<lambda>  r  r7   c                 ,    [         R                  " SXS9$ )NcnrD  r  rD  s     r5   rU   r#        8r7   r  r  r   r$   r   r]  r@   r  r  s    r5   test_ellipfun_cnTestSystematic.test_ellipfun_cn  '    +8s^S1]+		
r7   c           
      H    [        S S [        SS5      [        SSS9/SS	9  g )
Nc                 4    [         R                  " X5      S   $ rA  rB  rD  s     r5   rU   1TestSystematic.test_ellipfun_dn.<locals>.<lambda>  r  r7   c                 ,    [         R                  " SXS9$ rJ  r  rD  s     r5   rU   r,    r&  r7   r  r  r   r$   r   r]  r@   r  r  s    r5   test_ellipfun_dnTestSystematic.test_ellipfun_dn  r)  r7   c                 N    [        [        R                  S [        5       /5        g )Nc                 .    [         R                  " U 5      $ rO   r   r   r0  s    r5   rU   )TestSystematic.test_erf.<locals>.<lambda>      fjjmr7   )r   r.   r   r   r  s    r5   test_erfTestSystematic.test_erf  s    BFF$;ceWEr7   c                 L    [        [        R                  S [        5       /SS9  g )Nc                 .    [         R                  " U 5      $ rO   r2  r0  s    r5   rU   1TestSystematic.test_erf_complex.<locals>.<lambda>  r4  r7   r<   r  )r   r.   r   r   r  s    r5   r   TestSystematic.test_erf_complex  s    BFF$;jl^sSr7   c                 ^    [        [        R                  [        S 5      [	        5       /SS9  g )Nc                 .    [         R                  " U 5      $ rO   r   r   r0  s    r5   rU   *TestSystematic.test_erfc.<locals>.<lambda>      v{{1~r7   r?   r@   )r   r.   r   r   r   r  s    r5   	test_erfcTestSystematic.test_erfc  s$    GG56UG		
r7   c                 ^    [        [        R                  [        S 5      [	        5       /SS9  g )Nc                 .    [         R                  " U 5      $ rO   r=  r0  s    r5   rU   2TestSystematic.test_erfc_complex.<locals>.<lambda>  r?  r7   r<   r  )r   r.   r   r   r   r  s    r5   test_erfc_complex TestSystematic.test_erfc_complex  s$    GG56\N		
r7   c                 f    [        [        R                  [        R                  [	        5       /SS9  g Nr<   r  )r   r.   erfir   r   r  s    r5   	test_erfiTestSystematic.test_erfi  s    BGGV[[35'SAr7   c                 f    [        [        R                  [        R                  [	        5       /SS9  g rH  )r   r.   rI  r   r   r  s    r5   test_erfi_complex TestSystematic.test_erfi_complex  s    BGGV[[:<.CHr7   c                 ^    [        [        R                  [        S 5      [	        5       /SS9  g )Nc                 .    [         R                  " U 5      $ rO   )r   ncdfr0  s    r5   rU   *TestSystematic.test_ndtr.<locals>.<lambda>  r?  r7   r<   r  )r   r.   ndtrr   r   r  s    r5   	test_ndtrTestSystematic.test_ndtr  s$    GG56UG		
r7   c                 t    [        [        R                  S [        [	        SS5      [	        SS5      S9/SS9  g )Nc                 d    [         R                  " U * [        R                  " S5      -  5      S-  $ Ng       @)r   r   r%   sqrtr0  s    r5   rU   2TestSystematic.test_ndtr_complex.<locals>.<lambda>  s     fkk1"RWWR[.1"4r7   ro  r   r   r  )r   r.   rS  r   r*   r  s    r5   test_ndtr_complex TestSystematic.test_ndtr_complex  s2    GG4'&&1WUE5JKL		
r7   c           	      b    [        [        R                  [        S 5      [	        5       /SSSS9  g )Nc                 V    [         R                  " [         R                  " U 5      5      $ rO   )r   r   rQ  r0  s    r5   rU   .TestSystematic.test_log_ndtr.<locals>.<lambda>  s    vzz&++a.'Ar7   iX  r  r?   rG   r   rA   )r   r.   log_ndtrr   r   r  s    r5   test_log_ndtrTestSystematic.test_log_ndtr  s'    KKABUGs%	
r7   c                     [        [        R                  [        S 5      [	        [        SS5      [        SS5      S9/SSS	9  g )
Nc                     [         R                  " [         R                  " U * [        R                  " S5      -  5      S-  5      $ rX  )r   r   r   r%   rY  r0  s    r5   rU   6TestSystematic.test_log_ndtr_complex.<locals>.<lambda>  s)    vzz&++qbn2Mb2P'Qr7   r[  r6  ro  r=   r   r<   r  rG   r   )r   r.   rb  r   r   r*   r  s    r5   test_log_ndtr_complex$TestSystematic.test_log_ndtr_complex
  s:    KKQR'&$/75#3FGHs		
r7   c                 P    [        S [        R                  [        SS5      /SS9  g )Nc                 4    [         R                  " U 5      S   $ )Nr{   )r.   eulerr  s    r5   rU   .TestSystematic.test_eulernum.<locals>.<lambda>  s    bhhqk"or7   r$   ro  r  )r   r   eulernumr   r  s    r5   test_eulernumTestSystematic.test_eulernum  s$    %OOAu		
r7   c           	          [        [        R                  [        R                  [        SS5      [        S[        R                  5      /SSS9  g )Nr   r<   r?      r  )	r   r.   rF   r   rD   r   r   r%   r_  r  s    r5   test_expintTestSystematic.test_expint  s6    GGMMAs^SBFF^,	
r7   c                 R    S n[        U[        R                  [        5       /5        g )Nc                 4    [         R                  " U 5      S   $ rx  r.   fresnelr   s    r5   fresnels.TestSystematic.test_fresnels.<locals>.fresnels$      ::a=##r7   )r   r   rz  r   )r  rz  s     r5   test_fresnelsTestSystematic.test_fresnels#      	$Hfoow?r7   c                 R    S n[        U[        R                  [        5       /5        g )Nc                 4    [         R                  " U 5      S   $ r  rx  r   s    r5   fresnelc.TestSystematic.test_fresnelc.<locals>.fresnelc)  r|  r7   )r   r   r  r   )r  r  s     r5   test_fresnelcTestSystematic.test_fresnelc(  r  r7   c                 z    [        [        R                  [        [        R                  5      [        5       /5        g rO   )r   r.   gammar   r   r   r  s    r5   
test_gammaTestSystematic.test_gamma-  s     BHH&6v||&DsugNr7   c                 x    [        [        R                  [        [        R                  5      [        5       /SS9  g Nrq   r@   )r   r.   r  r   r   r   r  s    r5   test_gamma_complex!TestSystematic.test_gamma_complex0  s'    HHV\\*\N		
r7   c           
      f    [        [        R                  S [        SSSS9[        SS5      /SSS9  g )Nc                 ,    [         R                  " XSS9$ )NTr$  r   r'  )r4   rv   s     r5   rU   .TestSystematic.test_gammainc.<locals>.<lambda><      TBr7   r        @Finclusive_ar<  r  )r   r.   r'  r   r  s    r5   test_gammaincTestSystematic.test_gammainc8  s1    KKBCU+SC[9	
r7   c           
      f    [        [        R                  S [        SSSS9[        SS5      /SSS9  g )Nc                 ,    [         R                  " XSS9$ )NT)rw   r%  r  )r4   rw   s     r5   rU   /TestSystematic.test_gammaincc.<locals>.<lambda>F  r  r7   r   r  Fr  r<  r  )r   r.   	gammainccr   r  s    r5   test_gammainccTestSystematic.test_gammainccB  s1    LLBCU+SC[9	
r7   c                 d    S n[        [        R                  [        U5      [	        5       /5        g )Nc                 B    [         R                  " U 5      R                  $ rO   r   r  rR   r0  s    r5   f&TestSystematic.test_gammaln.<locals>.fN  s    ??1%***r7   )r   r.   gammalnr   r   )r  r  s     r5   test_gammalnTestSystematic.test_gammalnL  s#    	+ 	BJJ(8(;ceWEr7   )rg  c                     [        [        R                  [        [        R
                  5      [        SS5      [        5       [        5       /5        g r  )r   r.   eval_gegenbauerr   r   
gegenbauerr   r  s    r5   test_gegenbauerTestSystematic.test_gegenbauerS  s5    V../s^SUCE*	
r7   c                    S nS n[        U[        U5      [        SS5      [        SS5      [        5       /SSSS	S
9  [        U[        U5      [        SS5      [        5       [	        [
        R                  " SSS5      5      /SSS9  g )Nc                    [        U5      S:  a  [        R                  $ U S:X  a  SnO&U S:X  a	  SU-  U-  nO[        R                  " XU5      n[        U5      S:X  a  US:  a  [        U5      [        [        U5      5      :X  ag  [        R                  " X[        R                  " S5      -   U5      n[        U5      [        R                  " S5      :  a  [        R                  " S5      n[        U5      S	:  a  [        R                  $ U$ )
Nr  r   r   r$   r   r{   z1e-50z0.0\4@Iw)	r   r%   r  r   r  rC   r   r  r_  rG   rw   rH   r2   s       r5   r  6TestSystematic.test_gegenbauer_int.<locals>.gegenbauer]  s     1v~vv AvaaCE%%aA. Qx1}RE!HE!H,E%%aVZZ-@)@!Dq6FJJw//

5)A 1v~vvHr7   c                     [         R                  " [        U 5      X5      n[        U5      S:  a  [        R
                  $ U$ )Nr  )r.   r  r   r   r%   r_  r  s       r5   sc_gegenbauer9TestSystematic.test_gegenbauer_int.<locals>.sc_gegenbauerx  s1    ""3q610A1v~vvHr7   r   r=   g    eg    eAi@  Tr   )rG   r   r   rA   r  r    r;  )r   r   r   r   r   r%   r&   )r  r  r  s      r5   test_gegenbauer_int"TestSystematic.test_gegenbauer_int[  s    	6	 	Z(As^Ss^SU3d		
 	Z(As^SUHR[[b"-E$FGT		
r7   c                     [        S [        [        R                  5      [	        SS5      [        5       [        5       /5        g )Nc                 X    [         R                  " [        U 5      UR                  U5      $ rO   )r.   r  r   rR   rG   rw   rH   s      r5   rU   8TestSystematic.test_gegenbauer_complex.<locals>.<lambda>  s    B..s1vqvvqAr7   r   r=   )r   r   r   r  r   r   r   r  s    r5   test_gegenbauer_complex&TestSystematic.test_gegenbauer_complex  s/    AV../As^SUJL1	
r7   c                     [        S [        [        R                  5      [	        SS5      [	        5       [        5       /5        g )Nc                 Z    [         R                  " U R                  UR                  U5      $ rO   )r.   r  rR   r  s      r5   rU   @TestSystematic.test_gegenbauer_complex_general.<locals>.<lambda>  s    B..qvvqvvqAr7   r  r  )r   r   r   r  r   r   r  s    r5   test_gegenbauer_complex_general.TestSystematic.test_gegenbauer_complex_general  s/    AV../s^SUJL1	
r7   c                 v    [        [        R                  [        S 5      [	        SS5      [	        5       /5        g )Nc                 8    [         R                  " X40 [        D6$ rO   )r   hankel1r  rT   rH   s     r5   rU   -TestSystematic.test_hankel1.<locals>.<lambda>  r  r7   @x@xD)r   r.   r  r   r   r  s    r5   test_hankel1TestSystematic.test_hankel1  +    JJIJsu%	
r7   c                 v    [        [        R                  [        S 5      [	        SS5      [	        5       /5        g )Nc                 8    [         R                  " X40 [        D6$ rO   )r   hankel2r  r  s     r5   rU   -TestSystematic.test_hankel2.<locals>.<lambda>  r  r7   r  r  )r   r.   r  r   r   r  s    r5   test_hankel2TestSystematic.test_hankel2  r  r7   z%issues at intermediately large ordersc                 v    [        S [        [        R                  5      [	        SS5      [        5       /5        g )Nc                 B    [         R                  " [        U 5      U5      $ rO   )r.   eval_hermiter   r^  s     r5   rU   -TestSystematic.test_hermite.<locals>.<lambda>      Q3r7   r   ro  )r   r   r   hermiter   r   r  s    r5   test_hermiteTestSystematic.test_hermite  s*    3V^^,Ausu%	
r7   c           	         ^ [        SSS9m[        [        R                  U4S j[	        SS5      [	        SS5      /S	S
9  g )Nr   i  rq  c                 2   > [         R                  " X40 TD6$ rO   )r   rQ   )rw   rH   KWs     r5   rU   ,TestSystematic.test_hyp0f1.<locals>.<lambda>  s    q2r2r7   r  r  r   g     j@r  r  )r   r   r.   rQ   r   )r  r  s    @r5   test_hyp0f1TestSystematic.test_hyp0f1  s8    #-II2s^SC[)		
r7   c                     [        S [        S 5      [        SS5      [        [	        SS5      [	        SS5      5      /5        g )Nc                 D    [         R                  " U R                  U5      $ rO   rP   )rw   r4   s     r5   rU   4TestSystematic.test_hyp0f1_complex.<locals>.<lambda>  s    1661-r7   c                 8    [         R                  " X40 [        D6$ rO   )r   rQ   r  rw   rH   s     r5   rU   r    rc  r7   r   r   irM   )r   r   r   r   r*   r  s    r5   test_hyp0f1_complex"TestSystematic.test_hyp0f1_complex  s9    -HIb\:gdD&973;LMN	
r7   c                     S n[        [        R                  U[        SS5      [        SSSS9[        SS5      /SSS9  g )	Nc                 r     [         R                  " XU5      $ ! [         a    [        R                  s $ f = frO   )r   hyp1f1ZeroDivisionErrorr%   r_  rD  s      r5   mpmath_hyp1f11TestSystematic.test_hyp1f1.<locals>.mpmath_hyp1f1  s0    }}Q1--$ vvs    66r  r9   r$   Fr  r   )rG   r  )r   r.   r  r   )r  r  s     r5   test_hyp1f1TestSystematic.test_hyp1f1  s@    	 	IIb\3q"%8#c2,G	
r7   c           	          [        [        S 5      [        S 5      [        SS5      [        SS5      [	        5       /SS9  g )Nc                 Z    [         R                  " U R                  UR                  U5      $ rO   )r.   r  rR   rD  s      r5   rU   4TestSystematic.test_hyp1f1_complex.<locals>.<lambda>  s    ryy'Cr7   c                 :    [         R                  " XU40 [        D6$ rO   )r   r  r  rD  s      r5   rU   r        V]]1-Ng-Nr7   r  r  i  r  )r   r   r   r   r   r  s    r5   test_hyp1f1_complex"TestSystematic.test_hyp1f1_complex  s7    CDNOs^Ss^Z\:		
r7   c           
          [        S [        S 5      [        SS5      [        SS5      [        SS5      [        5       /SS9  g )Nc                 p    [         R                  " U R                  UR                  UR                  U5      $ rO   )r.   r   rR   rw   rv   r   rH   s       r5   rU   4TestSystematic.test_hyp2f1_complex.<locals>.<lambda>  s    ryyCr7   c                 :    [         R                  " XX#40 [        D6$ rO   )r   r   r  r  s       r5   rU   r        aA0TG0Tr7   g      Yg      Y@r   r  r  r  s    r5   test_hyp2f1_complex"TestSystematic.test_hyp2f1_complex  s;     	CTUs^Ss^Ss^Z\J		
r7   c                     [        [        R                  [        S 5      [	        5       [	        5       [	        5       /5        g )Nc                 :    [         R                  " XU40 [        D6$ rO   )r   ru   r  rD  s      r5   rU   ,TestSystematic.test_hyperu.<locals>.<lambda>  r  r7   )r   r.   ru   r   r   r  s    r5   test_hyperuTestSystematic.test_hyperu  s*    IINOUCE35!	
r7   z:mpmath issue gh-342: unsupported operand mpz, long for powc           
      V    S n[        [        U[        SSSS9[        SS5      /SSS9  g )	Nc                     [         R                  " X5      [         R                  " U* 5      -  [         R                  " U 5      -  $ rO   )r   powerr(   r  r  s     r5   mp_igam_fac1TestSystematic.test_igam_fac.<locals>.mp_igam_fac  s-    <<%fjj!n4V\\!_DDr7   r   g  ļBFr  r      r  )r   r   r   )r  r  s     r5   test_igam_facTestSystematic.test_igam_fac  s5    	E 	De,c!Tl;	
r7   c                     [        [        R                  [        R                  [	        SS5      /5        [        [        R                  [        R                  [	        SS5      /SS9  g Nr  r  r}  r~  r  r@   )r   r.   j0r   r   r  s    r5   test_j0TestSystematic.test_j0  s@     	BEE699s4~.>?BEE699s4~.>TJr7   c                     [        [        R                  [        R                  [	        SS5      /5        [        [        R                  [        R                  [	        SS5      /SS9  g r  )r   r.   j1r   r   r  s    r5   test_j1TestSystematic.test_j1  s>    BEE699s4~.>?BEE699s4~.>TJr7   c           	         [        [        R                  [        S 5      [	        5       [	        5       [	        5       [	        5       /5        [        S [        S 5      [        5       [	        5       [	        5       [	        5       /5        g )Nc                 :    [         R                  " XX#40 [        D6$ rO   r   jacobir  r  s       r5   rU   ,TestSystematic.test_jacobi.<locals>.<lambda>  r  r7   c                 D    [         R                  " [        U 5      XU5      $ rO   r.   eval_jacobir   )rG   rv   r   rH   s       r5   rU   r        r~~c!faA>r7   c                 :    [         R                  " XX#40 [        D6$ rO   r  r  s       r5   rU   r    r  r7   )r   r.   r  r   r   r   r  s    r5   test_jacobiTestSystematic.test_jacobi  sX    NNTUUCE35#%(	

 	>TUXsuceSU+	
r7   c           	      x   ^ S m[        S U4S j[        5       [        5       [        5       [        5       /SSS9  g )Nc                 >    U S:X  a  g[         R                  " XX#5      $ )Nr   r   )r   r  rG   rw   rv   rH   s       r5   r  .TestSystematic.test_jacobi_int.<locals>.jacobi#  s    Av==q,,r7   c                 D    [         R                  " [        U 5      XU5      $ rO   r  r!  s       r5   rU   0TestSystematic.test_jacobi_int.<locals>.<lambda>)  r  r7   c                 2   > [        T5      " XX#40 [        D6$ rO   )r   r  )rG   rw   rv   rH   r  s       r5   rU   r$  *  s    /7aNgNr7    N  r9   rh  r   r   r   )r  r  s    @r5   test_jacobi_intTestSystematic.test_jacobi_int!  s2    	-
 	>NXsuceSU+	
r7   c                 T    S n[        [        R                  U[        SS5      /SS9  g )Nc                 l    U S:X  a
  [         * S-  $ [        [        R                  5      " SU 40 [        D6$ )Nr   r;   )r   r   r   keir  r   s    r5   r,  $TestSystematic.test_kei.<locals>.kei1  s/    Avs1u#FJJ/1@@@r7   ꌠ9Y>)ꌠ9Y>)Fr.  r  )r   r.   r,  r   )r  r,  s     r5   test_keiTestSystematic.test_kei0  s&    	A
 	BFFC#eT*:);tDr7   c                 b    [        [        R                  [        S 5      [	        SS5      /SS9  g )Nc                 :    [         R                  " SU 40 [        D6$ rx  )r   kerr  r   s    r5   rU   )TestSystematic.test_ker.<locals>.<lambda>;  s    vzz!Q'B''Br7   r.  r/  r.  r  )r   r.   r4  r   r   r  s    r5   test_kerTestSystematic.test_ker8  s*    FFBC		
r7   c                 r    [        [        [        R                  5      S [	        5       [	        5       /5        g )Nc                 J    [        [        R                  5      " X40 [        D6$ rO   r   r   laguerrer  r^  s     r5   rU   .TestSystematic.test_laguerre.<locals>.<lambda>D      )&//:1K7Kr7   )r   r   r.   eval_laguerrer   r  s    r5   test_laguerreTestSystematic.test_laguerre@  s&    r''(KUCEN	
r7   c                 D    [        S S [        5       [        5       /SS9  g )Nc                 B    [         R                  " [        U 5      U5      $ rO   )r.   r>  r   r^  s     r5   rU   2TestSystematic.test_laguerre_int.<locals>.<lambda>J      ))#a&!4r7   c                 J    [        [        R                  5      " X40 [        D6$ rO   r:  r^  s     r5   rU   rC  K  r=  r7   r&  r  r'  r  s    r5   test_laguerre_int TestSystematic.test_laguerre_intH  s    4KXsu		
r7   zsee gh-3551 for bad pointsc           	          [        S S [        [        R                  * [        R                  5      [	        SS5      /SSS9  g )Nc                 V    [         R                  " U [        UR                  5      5      $ rO   )r.   rX  r   rR   rH   rS  s     r5   rU   3TestSystematic.test_lambertw_real.<locals>.<lambda>S  s    QAFF4r7   c                 V    [         R                  " U [        UR                  5      5      $ rO   )r   rX  r   rR   rJ  s     r5   rU   rK  T  s    CK8r7   r   r   r?   FrA   r  )r   r   r%   r_  r   r  s    r5   test_lambertw_real!TestSystematic.test_lambertw_realP  s4    48(&B-8u		
r7   c           
         ^^ Sn[         R                  " S5      mSmUU4S jn[        U[        R                  [        SUSS9/SS	9  g )
NgGase@r$   g  E@c                   > [         R                  " SS9   U T-   S-
  T-  U S-
  -  nU[         R                  :w  a  U[        U 5      -  nO&U T-   S-
  T-  SU S-
  -  -  nU[        U 5      -  nX!-  nS S S 5        U$ ! , (       d  f       W$ = f)Nr   )overrL   )r%   r   r_  r   )rH   facrY   egs      r5   r  :TestSystematic.test_lanczos_sum_expg_scaled.<locals>.gamma^  s    (+AQ!c'2"&&=6q99CECK?c1s7m<C6q99CJC , J ,+ Js   AA;;
B
r   Fr  r?   r@   )r%   r(   r   r   r  r   )r  maxgammar  rT  rU  s      @@r5   test_lanczos_sum_expg_scaled+TestSystematic.test_lanczos_sum_expg_scaledY  sE    &FF1I)		 	LLH%01		
r7   c                 z    [        [        R                  [        R                  [        5       [        5       /5        g rO   )r   r.   eval_legendrer   legendrer   r  s    r5   test_legendreTestSystematic.test_legendrep  s     B,,foosu~Nr7   c                     [        S S [        5       [        5       /SS9  [        S S [        5       [        [        R
                  " SSS	5      5      /5        g )
Nc                 B    [         R                  " [        U 5      U5      $ rO   r.   r[  r   r^  s     r5   rU   2TestSystematic.test_legendre_int.<locals>.<lambda>v  rD  r7   c                 J    [        [        R                  5      " X40 [        D6$ rO   r   r   r\  r  r^  s     r5   rU   rb  w  r=  r7   r&  r  c                 B    [         R                  " [        U 5      U5      $ rO   ra  r^  s     r5   rU   rb  ~  rD  r7   c                 J    [        [        R                  5      " X40 [        D6$ rO   rd  r^  s     r5   rU   rb    r=  r7   r  r  rh   )r   r   r   r   r%   r&   r  s    r5   test_legendre_int TestSystematic.test_legendre_intt  sK    4KXsu		
 	4KXxCR 89:	
r7   c           
          S nS nS n[        X[        SS5      [        SS5      [        5       /5        [        UU[        SS5      [        SS5      [        SS5      /SS	9  g )
Nc                 p    [        5        nUR                  [        S9  [        R                  " XU5      S   S   nS S S 5        [        W5      S:  a1  [        R                  [        R                  " UR                  5      -  nU$ ! , (       d  f       NP= f! [
         a    [        R                  s $ f = f)Ncategoryr   r{   r{   )#v)r   filterDeprecationWarningr.   lpmn
ValueErrorr%   r  r   r_  r  rR   )rG   rF  r4   suprT   s        r5   lpnm(TestSystematic.test_legenp.<locals>.lpnm  s    &(CJJ(:J;a(+E2A )
 1v~FFRWWQVV_,H )(  vvs-   
B 1BB 
BB B B54B5c                     [         R                  " XU5      n[        U5      S:  a1  [        R                  [        R
                  " UR                  5      -  nU$ )Nrn  )r.   r   r   r%   r_  r  rR   )rG   rF  r4   rT   s       r5   lpnm_2*TestSystematic.test_legenp.<locals>.lpnm_2  s<    a A1v~FFRWWQVV_,Hr7   c                    US:X  d  US:X  aM  [        U 5      U :X  a>  US:X  a7  U S:  a  U * S-
  n [        R                  " [        R                  " U5      U 5      $ g[	        U5      S:  a  [
        R                  $ [	        U5      S::  a  SOSn[        [        R                  5      " XX#S9n[	        U5      S:  a1  [        R                  [        R                  " UR                  5      -  nU$ )	Nr$   r{   r   rp   r   ro   typern  )r   r   r  r  r   r%   r  r   r   r_  rR   )rG   rF  r4   typrT   s        r5   r   *TestSystematic.test_legenp.<locals>.legenp  s    Q!r's1v{ 61uBF!<<A::1v~vv1v{!C /aBA1v~JJQVV!44Hr7   r6  r=   r{   r$   r   r  r'  )r  rt  rw  r   s       r5   test_legenpTestSystematic.test_legenp  sd    
			0 	D6$+<fT3>OQTQV*WXD#D#B
;		
r7   c           	         S nS n[         R                  " / SQ5      n[         R                  " / SQ5      nUS S 2S 4   SUS S S 24   -  -   R                  5       n[        UU[	        / SQ5      [	        / SQ5      [	        U5      /SSS	9  g )
Nc                     [        5        nUR                  [        S9  [        R                  " UR
                  U R
                  USS9S   S   sS S S 5        $ ! , (       d  f       g = f! [         a    [        R                  s $ f = f)Nrk  r   rz  r   rm  	r   ro  rp  r.   clpmnrR   rr  r%   r  rG   rF  r4   rs  s       r5   clpnm3TestSystematic.test_legenp_complex_2.<locals>.clpnm  g    &(CJJ(:J;88AFFAFFAA>qA%H )((  vv/   
A+ AA	A+ 
A($A+ (A+ +BBc                     [        U5      S:  a  [        R                  $ [        [        R
                  5      " [        U R                  5      [        UR                  5      USS9$ Nrp   r   rz  r   r%   r  r   r   r   r   rR   rG   rF  r4   s      r5   r   4TestSystematic.test_legenp_complex_2.<locals>.legenp  A    1v~vv#FMM23qvv;AFFQUVWWr7   	r}   r   rK   r   r  rL   r   rh   g     @@r  rK   rL   g?r!   r}   r{   r   r$   r   r   r   r   r  r%   r,   r   r   r   r  r  r   rH   rX   r4   s         r5   test_legenp_complex_2$TestSystematic.test_legenp_complex_2      		X HHCDHH+,qvYAd1fI%,,.+,+,a[ 	
r7   c           	         S nS n[         R                  " / SQ5      n[         R                  " / SQ5      nUS S 2S 4   SUS S S 24   -  -   R                  5       n[        UU[	        / SQ5      [	        / SQ5      [	        U5      /SSS	9  g )
Nc                     [        5        nUR                  [        S9  [        R                  " UR
                  U R
                  USS9S   S   sS S S 5        $ ! , (       d  f       g = f! [         a    [        R                  s $ f = f)Nrk  ro   rz  r   rm  r  r  s       r5   r  3TestSystematic.test_legenp_complex_3.<locals>.clpnm  r  r  c                     [        U5      S:  a  [        R                  $ [        [        R
                  5      " [        U R                  5      [        UR                  5      USS9$ )Nrp   ro   rz  r  r  s      r5   r   4TestSystematic.test_legenp_complex_3.<locals>.legenp  r  r7   r  r  r!   r  r   r   r  r  r  s         r5   test_legenp_complex_3$TestSystematic.test_legenp_complex_3  r  r7   z*apparently picks wrong function at |z| > 1c           	      h    S nS n[        UU[        SS5      [        SS5      [        5       /5        g )Nc                 <    [         R                  " XU5      S   S   $ Nr   rm  )r.   lqmnr  s      r5   lqnm(TestSystematic.test_legenq.<locals>.lqnm  s    771#A&u--r7   c                 ~    [        U5      S:  a  [        R                  $ [        [        R
                  5      " XUSS9$ r  )r   r%   r  r   r   legenqr  s      r5   r  *TestSystematic.test_legenq.<locals>.legenq  s.    1v~vv#FMM21CCr7   r   r=   r'  r  r  r  s      r5   test_legenqTestSystematic.test_legenq  s5    	.	D 	As^VAs^SU3	
r7   c           	      f    S nS n[        UU[        SS5      [        SS5      [        5       /SS9  g )Nc                     [         R                  " [        UR                  5      [        U R                  5      U5      S   S   $ r  )r.   r  r   rR   r  s      r5   r  0TestSystematic.test_legenq_complex.<locals>.lqnm  s/    773qvv;AFFQ7:5AAr7   c                     [        U5      S:  a  [        R                  $ [        [        R
                  5      " [        U R                  5      [        UR                  5      USS9$ r  )r   r%   r  r   r   r  r   rR   r  s      r5   r  2TestSystematic.test_legenq_complex.<locals>.legenq
  r  r7   r   r=   r  )r   r   r   r  s      r5   test_legenq_complex"TestSystematic.test_legenq_complex  s9    	B	X 	As^VAs^Z\:		
r7   c           	      F    S nS n[        [        U[        5       /SSUS9  g )Nc                 l    [         R                  " [         R                  " U 5      U :H  U S:*  -  SS5      $ )Nr   FT)r%   r  floorr   s    r5   r  0TestSystematic.test_lgam1p.<locals>.param_filter  s+    88RXXa[A-!q&95$GGr7   c                 H    [         R                  " SU -   5      R                  $ r  r  r0  s    r5   	mp_lgam1p-TestSystematic.test_lgam1p.<locals>.mp_lgam1p  s    ??1q5)...r7   r?   r=   r  )r   r   r   )r  r  r  s      r5   test_lgam1pTestSystematic.test_lgam1p  s-    	H	/ 	UG%	
r7   c           	      T    S n[        [        R                  U[        5       /SSSS9  g )Nc                      [         R                  " U 5      nU$ ! [         a,    [        [        R
                  [        R
                  5      n U$ f = frO   )r   r  rr  r*   r%   r  )r4   rY   s     r5   mpmath_loggamma5TestSystematic.test_loggamma.<locals>.mpmath_loggamma*  sF    .ooa( J  .bffbff-J.s    2AAFr   )r  distinguish_nan_and_infrA   )r   r.   r  r   )r  r  s     r5   test_loggammaTestSystematic.test_loggamma)  s+    	 	KK\N$)	
r7   c                 \    S n[        U[        S 5      [        5       [        5       /5        g )Nc                 4    [         R                  " X5      S   $ rx  )r.   pbdvr  s     r5   pcfd&TestSystematic.test_pcfd.<locals>.pcfd<      771=##r7   c                 8    [         R                  " X40 [        D6$ rO   )r   r  r  r  s     r5   rU   *TestSystematic.test_pcfd.<locals>.<lambda>@  s    &++a*Fg*Fr7   )r   r   r   )r  r  s     r5   	test_pcfdTestSystematic.test_pcfd:  s&    	$FGUCEN	
r7   zHit's not the same as the mpmath function --- maybe different definition?c                 H    S n[        US [        5       [        5       /SS9  g )Nc                 4    [         R                  " X5      S   $ rx  )r.   pbvvr  s     r5   pcfv&TestSystematic.test_pcfv.<locals>.pcfvG  r  r7   c                 f    [        5       " [        [        R                  5      5      " X40 [        D6$ rO   )r   r   r   r  r  r  s     r5   rU   *TestSystematic.test_pcfv.<locals>.<lambda>K  s    (8(EFqWwWr7   r.  r  r  )r  r  s     r5   	test_pcfvTestSystematic.test_pcfvD  s#    	$WUCEN		
r7   c           	          S nS nS n[        U[        R                  [        SS5      [        SS5      /SSS9  [        UU[        SS5      [        SS5      /S	SS9  g )
Nc                 4    [         R                  " X5      S   $ rx  r.   pbwar  s     r5   pcfw&TestSystematic.test_pcfw.<locals>.pcfwQ  r  r7   c                 4    [         R                  " X5      S   $ r  r  r  s     r5   dpcfw'TestSystematic.test_pcfw.<locals>.dpcfwT  r  r7   c                 P    [         R                  " [         R                  X4S5      $ )Nr>   )r   diffr  r  s     r5   mpmath_dpcfw.TestSystematic.test_pcfw.<locals>.mpmath_dpcfwW  s    ;;v{{QFF;;r7   rf   rg   g:0yU>r=   r  g&.!>)r   r   r  r   )r  r  r  r  s       r5   	test_pcfwTestSystematic.test_pcfwP  si    	$	$	<
 	KKQZR$	
 	QZR$	
r7   zCissues at large arguments (atol OK, rtol not) and <eps-close to z=0c                     [        [        R                  [        5       " [	        [
        R                  5      5      [        SS5      [        5       /5        g )Nr   r.  )r   r.   	polygammar   r   r   r   r   r  s    r5   test_polygammaTestSystematic.test_polygammal  s9     	LLN+F,<,<=>At_ce$	
r7   c           	          [        [        R                  [        R                  [	        S[
        R                  5      /SSSS9  g )Nir  FT)rG   r  r   )r   r.   r  r   r   r%   r_  r  s    r5   test_rgammaTestSystematic.test_rgammav  s2    IIMM  	
r7   c                 x    [        [        R                  [        [        R                  5      [        5       /SS9  g r  )r   r.   r  r   r   r   r  s    r5   test_rgamma_complex"TestSystematic.test_rgamma_complex  s'    IIV]]+\N		
r7   zNsee gh-3551 for bad points on 32 bit systems and gh-8095 for another bad point)rh  c                     [         R                  " [        R                  5      [         R                  " S5      :  a  [        R
                  nOS n[        [        R                  U[        5       [        5       /SS9  g )Nry   c                     [        X-   5      [        X-   5      :X  a7  [        X-   5      S::  a&  [        R                  " U 5      n [        X-   5      U -
  n[        R                  " X5      $ rx  )rC   r   r   r  rf)rw   rF  s     r5   mppoch&TestSystematic.test_rf.<locals>.mppoch  sO     <3qu:-%,!2C

1AAE
QAyy&r7   r   rL  )
r   parser   r   Versionr  r   r.   pochr   )r  r  s     r5   test_rfTestSystematic.test_rf  sN     ==++,0HHYYF' 	BGGVceSU^Er7   c                     [         R                  " [        5      R                  n[	        [
        [        R                  [        5       /SSU-  S9  g r  )	r%   r7  rC   r8  r   r   r   r9  r   r  s     r5   
test_sinpiTestSystematic.test_sinpi  s8    hhuo!!LLUG3	
r7   c                 T    [        [        [        R                  [	        5       /SSS9  g )NFg+=r  )r   r   r   r9  r   r  s    r5   test_sinpi_complex!TestSystematic.test_sinpi_complex  r  r7   c                     S n[        U[        R                  [        5       /5        [        U[        R                  [	        / SQ5      /5        g )Nc                 4    [         R                  " U 5      S   $ rx  r  r   s    r5   shi$TestSystematic.test_shi.<locals>.shi  r  r7   r  )r   r   r  r   r   r  r  s     r5   test_shiTestSystematic.test_shi  r  r7   c                     S n[        U[        R                  [        [	        [
        R                  * S5      [	        [
        R                  S5      5      /SS9  g )Nc                 4    [         R                  " U 5      S   $ rx  r  r0  s    r5   r  ,TestSystematic.test_shi_complex.<locals>.shi  r  r7   r}  r~  r_   r@   )r   r   r  r   r*   r%   r_  r  s     r5   test_shi_complexTestSystematic.test_shi_complex  r  r7   c                 R    S n[        U[        R                  [        5       /5        g )Nc                 4    [         R                  " U 5      S   $ rx  r  r   s    r5   si"TestSystematic.test_si.<locals>.si  r  r7   )r   r   r  r   r  r  s     r5   test_siTestSystematic.test_si  s    	!B		CE73r7   c                     S n[        U[        R                  [        [	        S[
        R                  * 5      [	        S[
        R                  5      5      /SS9  g )Nc                 4    [         R                  " U 5      S   $ rx  r  r0  s    r5   r  *TestSystematic.test_si_complex.<locals>.si  r  r7   r}  r~  r_   r@   )r   r   r  r   r*   r%   r_  r  s     r5   test_si_complexTestSystematic.test_si_complex  sC    	! 	IIrvvg.RVV0DEF		
r7   c                     S n[        [        R                  [        U5      [	        S[
        R                  5      /SS9  g )Nc                 6    [         R                  " SSU -
  5      $ r.  r   r/  r   s    r5   dilog)TestSystematic.test_spence.<locals>.dilog      >>!QU++r7   r   r   r@   )r   r.   r1  r   r   r%   r_  r  r  s     r5   test_spenceTestSystematic.test_spence  s3    	, 	IIU#BFF^		
r7   c                 b    S n[        [        R                  [        U5      [	        5       /SS9  g )Nc                 6    [         R                  " SSU -
  5      $ r.  r  r0  s    r5   r  1TestSystematic.test_spence_complex.<locals>.dilog  r  r7   r   r@   )r   r.   r1  r   r   r  s     r5   test_spence_complex"TestSystematic.test_spence_complex  s(    	,IIU#\N		
r7   c                     S n[        U[        R                  [        SS5      [        SS5      [	        S[
        S9[	        SS[
        -  S9/SSSS	9  g )
Nc                     X:  a  [         R                  $ [        5        nUR                  [        S9  [
        R                  " XX25      sS S S 5        $ ! , (       d  f       g = f)Nrk  )r%   r  r   ro  rp  r.   sph_harm)lrF  r  r	  rs  s        r5   	spherharm0TestSystematic.test_spherharm.<locals>.spherharm  sA    uvv"$

$6
7{{14 %$$s   *A
A"r   r=   r   r   r]  ip  r\   )rs   rG   r   )r   r   r'  r   r   r   )r  r'  s     r5   test_spherharmTestSystematic.test_spherharm  sO    	5 	As^VAs^S1^S1"=MN	
r7   c           	          [        [        R                  [        [        R
                  5      [        SS5      [        SS5      /SS9  g )N     r  r   &.>r@   )r   r.   struver   r   struvehr   r  s    r5   test_struvehTestSystematic.test_struveh  s4    IIV^^,s^SC[)		
r7   c           	      ~    S n[        [        R                  [        U5      [	        SS5      [	        SS5      /SSS9  g )Nc                 N   U S:  ap  X* :  aj  [        U 5      S:  a[  [        R                  R                  n S[        R                  l        [        R                  " X5      U[        R                  l        $ [        R                  " X5      $ ! U[        R                  l        f = f)Nr   r.  r   )r   r   r   r   struvel)rT   r4   r   s      r5   
mp_struvel/TestSystematic.test_struvel.<locals>.mp_struvel  sk    1uRCFTM ))--,$'FIIM!>>!/$+FIIM>>!'' %,FIIMs   *B B$r,  r  r   r-  Tr   )r   r.   	modstruver   r   )r  r5  s     r5   test_struvelTestSystematic.test_struvel  s:    		( 	LLZ(s^SC[) 	
r7   c           	      X    S n[        [        R                  U[        SS5      /SSSS9  g )Nc                     [         R                  " [         R                  " U 5      [         R                  " S5      5      $ )Nz-0.5)r   rX  r(   r  r   s    r5   mpmath_wrightomega_realETestSystematic.test_wrightomega_real.<locals>.mpmath_wrightomega_real  s$    ??6::a=&**V2DEEr7   r~   gPKDg+<r   F)rA   rs   r  )r   r.   rb  r   )r  r<  s     r5   test_wrightomega_real$TestSystematic.test_wrightomega_real  s2    	F 	NN#	
r7   c                 N    [        [        R                  S [        5       /SSS9  g )Nc                     [        U S5      $ )Nr\  )rZ  r0  s    r5   rU   1TestSystematic.test_wrightomega.<locals>.<lambda>%  s    )!R0r7   r   FrM  )r   r.   rb  r   r  s    r5   test_wrightomegaTestSystematic.test_wrightomega"  s!    NN0\N	
r7   c           
          [        [        R                  [        [        R                  5      [        SSSS9[        SSS9/5        g )Nr$       _BF)rw   rv   r  r   rw   r  )r   r.   zetar   r   r   r  s    r5   test_hurwitz_zeta TestSystematic.test_hurwitz_zeta+  s5    GGV[[)1%0#u2MN	
r7   c                 R    [        [        R                  S [        SS5      /SSS9  g )Nc                 Z    U S:w  a  [         R                  " U 5      $ [         R                  $ r  r   rH  r_  r   s    r5   rU   2TestSystematic.test_riemann_zeta.<locals>.<lambda>5  s    Qfkk!n>FJJ>r7   r6  r=   Frq   r  )r   r.   rH  r   r  s    r5   test_riemann_zeta TestSystematic.test_riemann_zeta2  s&    GG>s^	
r7   c           	      T    [        [        R                  S [        SS5      /SSSS9  g )Nc                 `    U S:w  a  [         R                  " U 5      S-
  $ [         R                  $ r  rM  r   s    r5   rU   +TestSystematic.test_zetac.<locals>.<lambda>>  s#    AFfkk!nq(B

Br7   r6  r=   F-   rq   )r  r   rA   )r   r.   zetacr   r  s    r5   
test_zetacTestSystematic.test_zetac;  s)    HHBs^	
r7   c           	      x    S n[        [        R                  [        U5      [	        SSS9[	        5       /SSSS9  g )	Nc                    [         R                  R                  U 5      n [         R                  R                  U5      nUS:X  a  [         R                  R                  U 5      $ [         R                  R	                  X5      U-  $ rx  r   r   r  r   powm1)rH   lmbdas     r5   	mp_boxcox-TestSystematic.test_boxcox.<locals>.mp_boxcoxG  sX    		a AIIMM%(Ezyy}}Q''yyq0588r7   r   FrG  r<   r  r?   ra  )r   r.   boxcoxr   r   )r  r]  s     r5   test_boxcoxTestSystematic.test_boxcoxE  s:    	9 	IIY'1%(#%0	
r7   c           	      x    S n[        [        R                  [        U5      [	        SSS9[	        5       /SSSS9  g )	Nc                 T   [         R                  R                  U 5      n [         R                  R                  U5      n[         R                  R                  S5      nUS:X  a!  [         R                  R                  X -   5      $ [         R                  R	                  X -   U5      U-  $ r   rZ  )rH   r\  ones      r5   mp_boxcox1p1TestSystematic.test_boxcox1p.<locals>.mp_boxcox1pZ  sp    		a AIIMM%(E))--"Czyy}}SW--yysw6>>r7   r{   FrG  r<   r  r?   ra  )r   r.   boxcox1pr   r   )r  re  s     r5   test_boxcox1pTestSystematic.test_boxcox1pX  s:    	? 	KK[)25)351	
r7   c           	      j    S n[        S [        U5      [        SS5      [        SS5      /SS S 4S	9  g )
Nc                 "   [         R                  " U5      n[         R                  " U [         R                  " S5      S-  -   U5      [         R                  " SU-  [         R
                  -  5      -  nUR                  S:X  a  UR                  $ U$ Nr$   r   r   r   	mpmathifyr  r  rY  r   rW  rR   rG   r4   argouts       r5   mp_spherical_jn9TestSystematic.test_spherical_jn.<locals>.mp_spherical_jnm  i    ""1%C>>!fjjmAo"5s;;;quVYY/0Cxx1}xx
r7   c                 B    [         R                  " [        U 5      U5      $ rO   )r.   spherical_jnr   rG   r4   s     r5   rU   2TestSystematic.test_spherical_jn.<locals>.<lambda>w  r  r7   r   r<   r}  r~  r  c                 4    [         R                  " U 5      S:  $ )Ng#B;)r%   r   r0  s    r5   rU   rx  |  s    "&&)e*;r7   )r   r  r/  r  rr  s     r5   test_spherical_jn TestSystematic.test_spherical_jnl  s<    	 	3_-As^Ss^, ;<	
r7   c                 `    S n[        S [        U5      [        SS5      [        5       /5        g )Nc                 "   [         R                  " U5      n[         R                  " U [         R                  " S5      S-  -   U5      [         R                  " SU-  [         R
                  -  5      -  nUR                  S:X  a  UR                  $ U$ rl  rm  ro  s       r5   rr  ATestSystematic.test_spherical_jn_complex.<locals>.mp_spherical_jn  rt  r7   c                 V    [         R                  " [        U R                  5      U5      $ rO   )r.   rv  r   rR   rw  s     r5   rU   :TestSystematic.test_spherical_jn_complex.<locals>.<lambda>      QVVa8r7   r   r<   r   r   r   r   rz  s     r5   test_spherical_jn_complex(TestSystematic.test_spherical_jn_complex  ,    	 	8_-As^Z\*	
r7   c           	      b    S n[        S [        U5      [        SS5      [        SS5      /SS9  g )	Nc                 "   [         R                  " U5      n[         R                  " U [         R                  " S5      S-  -   U5      [         R                  " SU-  [         R
                  -  5      -  nUR                  S:X  a  UR                  $ U$ rl  r   rn  r  r  rY  r   rW  rR   ro  s       r5   mp_spherical_yn9TestSystematic.test_spherical_yn.<locals>.mp_spherical_yn  rt  r7   c                 B    [         R                  " [        U 5      U5      $ rO   )r.   spherical_ynr   rw  s     r5   rU   2TestSystematic.test_spherical_yn.<locals>.<lambda>  r  r7   r   r<   g    _rF  r=   rL  r/  r  r  s     r5   test_spherical_yn TestSystematic.test_spherical_yn  s4    	 	3_-As^S-.		
r7   c                 `    S n[        S [        U5      [        SS5      [        5       /5        g )Nc                 "   [         R                  " U5      n[         R                  " U [         R                  " S5      S-  -   U5      [         R                  " SU-  [         R
                  -  5      -  nUR                  S:X  a  UR                  $ U$ rl  r  ro  s       r5   r  ATestSystematic.test_spherical_yn_complex.<locals>.mp_spherical_yn  rt  r7   c                 V    [         R                  " [        U R                  5      U5      $ rO   )r.   r  r   rR   rw  s     r5   rU   :TestSystematic.test_spherical_yn_complex.<locals>.<lambda>  r  r7   r   r<   r  r  s     r5   test_spherical_yn_complex(TestSystematic.test_spherical_yn_complex  r  r7   c                 `    S n[        S [        U5      [        SS5      [        5       /SSS9  g )Nc                 "   [         R                  " U5      n[         R                  " U [         R                  " S5      S-  -   U5      [         R                  " SU-  [         R
                  -  5      -  nUR                  S:X  a  UR                  $ U$ rl  r   rn  r  r  rY  r   rW  rR   ro  s       r5   mp_spherical_in9TestSystematic.test_spherical_in.<locals>.mp_spherical_in  rt  r7   c                 B    [         R                  " [        U 5      U5      $ rO   )r.   spherical_inr   rw  s     r5   rU   2TestSystematic.test_spherical_in.<locals>.<lambda>  r  r7   r   r<   g訰6rW  r/  r  r  s     r5   test_spherical_in TestSystematic.test_spherical_in  s2    	 	3_-As^SU#	
r7   c                 `    S n[        S [        U5      [        SS5      [        5       /5        g )Nc                 "   [         R                  " U5      n[         R                  " U [         R                  " S5      S-  -   U5      [         R                  " SU-  [         R
                  -  5      -  nUR                  S:X  a  UR                  $ U$ rl  r  ro  s       r5   r  ATestSystematic.test_spherical_in_complex.<locals>.mp_spherical_in  rt  r7   c                 V    [         R                  " [        U R                  5      U5      $ rO   )r.   r  r   rR   rw  s     r5   rU   :TestSystematic.test_spherical_in_complex.<locals>.<lambda>  r  r7   r   r<   r  r  s     r5   test_spherical_in_complex(TestSystematic.test_spherical_in_complex  r  r7   c                 ^    S n[        S [        U5      [        SS5      [        5       /SS9  g )Nc                 J   [         R                  " U5      n[         R                  " U [         R                  " S5      S-  -   U5      [         R                  " SU-  [         R
                  -  5      -  n[         R                  " U5      R                  S:X  a  UR                  $ U$ rl  r   rn  r  r  rY  r   rW  rR   ro  s       r5   mp_spherical_kn9TestSystematic.test_spherical_kn.<locals>.mp_spherical_kn  sw    ""1%C>>!fjjmAo"5s;;;quVYY/0C"''1,xx
r7   c                 B    [         R                  " [        U 5      U5      $ rO   )r.   spherical_knr   rw  s     r5   rU   2TestSystematic.test_spherical_kn.<locals>.<lambda>  r  r7   r   r\   r=   rL  r/  r  r  s     r5   test_spherical_kn TestSystematic.test_spherical_kn  s/    	 	3_-As^SU#		
r7   z.Accuracy issues near z = -1 inherited from kv.c                 ^    S n[        S [        U5      [        SS5      [        5       /SS9  g )Nc                 "   [         R                  " U5      n[         R                  " U [         R                  " S5      S-  -   U5      [         R                  " SU-  [         R
                  -  5      -  nUR                  S:X  a  UR                  $ U$ rl  r  ro  s       r5   r  ATestSystematic.test_spherical_kn_complex.<locals>.mp_spherical_kn  rt  r7   c                 V    [         R                  " [        U R                  5      U5      $ rO   )r.   r  r   rR   rw  s     r5   rU   :TestSystematic.test_spherical_kn_complex.<locals>.<lambda>  r  r7   r   r<   rL  r  r  s     r5   test_spherical_kn_complex(TestSystematic.test_spherical_kn_complex  s/    	 	8_-As^Z\*		
r7   r9  N)__name__
__module____qualname____firstlineno__r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r&  r0  r   rG  rN  rY  rd  pytestmarkxfailrp  rx  r}  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r'  r.  r5  r   r@  rE  rJ  rM  rT  r\  rc  ri  rp  rt  r}  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r   xfail_on_32bitr  r  r  r  r(  r0  r6  r?  rF  rN  rX  r]  rg  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r!  r)  r0  r8  r>  rC  rI  rO  rV  r`  rh  r{  r  r  r  r  r  r  r  __static_attributes__r9  r7   r5   ru  ru    sn   .,
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r7   ru  )K__doc__numpyr%   numpy.testingr   r   r   r   r  r   
scipy._libr   scipy.specialspecialr.   scipy.special._testutilsr   r	   r
   r   scipy.special._mptestutilsr   r   r   r   r   r   r   r   r   r   scipy.special._ufuncsr   r   r   r   r   r   r   ImportErrorr6   rI   rZ   rd   rx   r   r   r   r   r  slowr   r   r   r   r   r  r
  r  r  r  r"  r+  r4  r;  r>  rS  rZ  rh  rk  rn  rp  r   r  ru  r9  r7   r5   <module>r     se    E E         % vv- - vv	> 	>  vv! !( vv6 6 vwO  O, vwC  C" vvG G> vvC C* vv/ /$ vvE  E8 vv: :* vv0K 0Kn vv: :L   vv= =  vv= =& vv;  ;. vv<  <* vv< <& vv< <( vvB  B& vv;  ;& vv
8 
8 vv8 8$ vv9 90 vv?  ?* vv
@  
@ vv
@  
@" vv=  =. sS
) vvE
 E
  E
i  %8$F%s    L% %L76L7