+
    0i[;                        ^ RI t ^ RIt^ RIHt ^ RIt^ RIHtHtHtH	t	H
t
HtHtHtHt ^ RIHtHtHtHt ^ RIHt  ! R R4      t ! R R	4      t ! R
 R4      t ! R R4      t ! R R4      t ! R R4      t ! R R]4      t ! R R]4      t ! R R]4      t ! R R]4      t ! R R4      t ]PB                  PE                  RRR.4      ]PB                  PE                  R]]]].4      R  4       4       t#R# )!    N)assert_allclose)	sincossinhcoshexpinfnanr_pi)spherical_jnspherical_ynspherical_inspherical_kn)quadc                   P   a  ] tR t^t o R tR tR tR tR tR t	R t
R tR	tV tR
# )TestSphericalJnc                   \         P                  ! . RO4      p\        \        ^V4      RV,          ^V^,          ,          ,           \	        V4      ,          ^V^,          ,          \        V4      ,          ,
          4       R# )Q?Nr   Gz?Gz(@^@g     J@)nparrayr   r   r   r   selfxs   & g/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/special/tests/test_spherical_bessel.pytest_spherical_jn_exact'TestSphericalJn.test_spherical_jn_exact   sV     HH89Q*A!Q$A.1a4A>	@    c                    \         P                  ! . RO4      pRp\        \        V^,
          V4      \        V^,           V4      ,           ^V,          ^,           V,          \        W4      ,          4       R#    Nr&               ?      ?r   r   r   r   r   nr   s   &  r    $test_spherical_jn_recurrence_complex4TestSphericalJn.test_spherical_jn_recurrence_complex   T    HH%&QUA.a!eQ1GG1q!L$66	8r#   c                    \         P                  ! . RO4      pRp\        \        V^,
          V4      \        V^,           V4      ,           ^V,          ^,           V,          \        W4      ,          4       R# r&   r   Nr'   r-   r.   s   &  r    !test_spherical_jn_recurrence_real1TestSphericalJn.test_spherical_jn_recurrence_real   T    HH%&QUA.a!eA1FF1q!L$66	8r#   c                    ^p\         P                  ! \        ) \        .4      p\        \	        W4      \         P                  ! ^ ^ .4      4       R#    N)r   r   r	   r   r   r.   s   &  r    test_spherical_jn_inf_real*TestSphericalJn.test_spherical_jn_inf_real&   7    HHsdC[!Q*BHHaV,<=r#   c                   ^p\         P                  ! \        ) R,           \        R,           \        R,          .4      p\        P                  ! 4       ;_uu_ 4        \        P
                  ! RR\        4       \        \        W4      \         P                  ! ^ ^ \        R,          .4      4       RRR4       R#   + '       g   i     R# ; ir*                   ignorez%invalid value encountered in multiplyN      ?      ?)	r   r   r	   warningscatch_warningsfilterwarningsRuntimeWarningr   r   r.   s   &  r    test_spherical_jn_inf_complex-TestSphericalJn.test_spherical_jn_inf_complex,       HHsdRir3:67$$&&##A>SL.!QT
9K0LM '&&&   AB99C
	c                2    \        \        ^R4      R4       R# )r(   g%-@Ng<]3r   r   r   s   &r    test_spherical_jn_large_arg_1-TestSphericalJn.test_spherical_jn_large_arg_15   s     	Q13JKr#   c                2    \        \        ^R4      R4       R# )r(   i'  g|	 ?NrL   rM   s   &r    test_spherical_jn_large_arg_2-TestSphericalJn.test_spherical_jn_large_arg_2;   s     	Q.0FGr#   c                    \         P                  ! . RO4      p^ p\        \        W4      \         P                  ! . RO4      4       R# r   Nr   r&   r(      
   d   )r&   r   r   r   r   r   r-   r.   s   &  r    test_spherical_jn_at_zero)TestSphericalJn.test_spherical_jn_at_zeroA   1     HH*+Q*BHH5G,HIr#    N)__name__
__module____qualname____firstlineno__r!   r0   r5   r;   rG   rN   rQ   rY   __static_attributes____classdictcell____classdict__s   @r    r   r      s8     @88>NLHJ Jr#   r   c                   J   a  ] tR t^It o R tR tR tR tR tR t	R t
RtV tR	# )
TestSphericalYnc                   \         P                  ! . RO4      p\        \        ^V4      ^V,          ^V^,          ,          ,
          \	        V4      ,          ^V^,          ,          \        V4      ,          ,
          4       R# )r   Nr   )r   r   r   r   r   r   r   s   & r    test_spherical_yn_exact'TestSphericalYn.test_spherical_yn_exactJ   sU     HH89Q*1qAvs1v-!Q$s1v=	?r#   c                    \         P                  ! . RO4      pRp\        \        V^,
          V4      \        V^,           V4      ,           ^V,          ^,           V,          \        W4      ,          4       R# r4   r   r   r   r   r.   s   &  r    !test_spherical_yn_recurrence_real1TestSphericalYn.test_spherical_yn_recurrence_realR   r7   r#   c                    \         P                  ! . RO4      pRp\        \        V^,
          V4      \        V^,           V4      ,           ^V,          ^,           V,          \        W4      ,          4       R# r%   rk   r.   s   &  r    $test_spherical_yn_recurrence_complex4TestSphericalYn.test_spherical_yn_recurrence_complexY   r2   r#   c                    ^p\         P                  ! \        ) \        .4      p\        \	        W4      \         P                  ! ^ ^ .4      4       R# r9   )r   r   r	   r   r   r.   s   &  r    test_spherical_yn_inf_real*TestSphericalYn.test_spherical_yn_inf_real`   r=   r#   c                   ^p\         P                  ! \        ) R,           \        R,           \        R,          .4      p\        P                  ! 4       ;_uu_ 4        \        P
                  ! RR\        4       \        \        W4      \         P                  ! ^ ^ \        R,          .4      4       RRR4       R#   + '       g   i     R# ; ir?   )	r   r   r	   rC   rD   rE   rF   r   r   r.   s   &  r    test_spherical_yn_inf_complex-TestSphericalYn.test_spherical_yn_inf_complexf   rI   rJ   c                    \         P                  ! . RO4      p^ p\        \        W4      \         P                  ! VP
                  \        ) 4      4       R# r   NrU   )r   r   r   r   fullshaper	   r.   s   &  r    test_spherical_yn_at_zero)TestSphericalYn.test_spherical_yn_at_zeroo   s6    HH*+Q*BGGAGGcT,BCr#   c                    \         P                  ! . RO4      pRp\        \        W4      \         P                  ! VP
                  \        4      4       R# r   r@   NrU   )r   r   r   r   ry   rz   r
   r.   s   &  r    !test_spherical_yn_at_zero_complex1TestSphericalYn.test_spherical_yn_at_zero_complexu   s6     HH*+Q*BGGAGGS,ABr#   r\   N)r]   r^   r_   r`   rh   rl   ro   rr   ru   r{   r   ra   rb   rc   s   @r    rf   rf   I   s1     ?88>NDC Cr#   rf   c                   ,   a  ] tR t^t o R tR tRtV tR# )TestSphericalJnYnCrossProductc                2   \         P                  ! . RO4      p\         P                  ! . RO4      p\        V^,           V4      \        W4      ,          \        W4      \        V^,           V4      ,          ,
          p^V^,          ,          p\	        W44       R# r&   N)r&   rV      )g?r&   rW   r   r   r   r   r   r   r/   r   leftrights   &    r    $test_spherical_jn_yn_cross_product_1BTestSphericalJnYnCrossProduct.test_spherical_jn_yn_cross_product_1   sj    HHYHH\"QUA&a);;Q"\!a%%;;<!Q$$r#   c                N   \         P                  ! . RO4      p\         P                  ! . RO4      p\        V^,           V4      \        W4      ,          \        W4      \        V^,           V4      ,          ,
          p^V,          ^,           V^,          ,          p\	        W44       R# r   r   r   s   &    r    $test_spherical_jn_yn_cross_product_2BTestSphericalJnYnCrossProduct.test_spherical_jn_yn_cross_product_2   sr    HHYHH\"QUA&a);;Q"\!a%%;;<1q!Q$$r#   r\   N)r]   r^   r_   r`   r   r   ra   rb   rc   s   @r    r   r      s     %% %r#   r   c                   D   a  ] tR t^t o R tR tR tR tR tR t	Rt
V tR# )	TestSphericalInc                   \         P                  ! . RO4      p\        \        ^V4      ^V,          ^V^,          ,          ,           \	        V4      ,          ^V^,          ,          \        V4      ,          ,
          4       R# r   N)r   r   r   r   )r   r   r   r   r   r   r   s   & r    test_spherical_in_exact'TestSphericalIn.test_spherical_in_exact   sT    HH01Q*1qAvtAw.1a4Q?	Ar#   c                    \         P                  ! . RO4      pRp\        \        V^,
          V4      \        V^,           V4      ,
          ^V,          ^,           V,          \        W4      ,          4       R# r4   r   r   r   r   r.   s   &  r    !test_spherical_in_recurrence_real1TestSphericalIn.test_spherical_in_recurrence_real   r7   r#   c                    \         P                  ! . RO4      pRp\        \        V^,
          V4      \        V^,           V4      ,
          ^V,          ^,           V,          \        W4      ,          4       R# r%   r   r.   s   &  r    $test_spherical_in_recurrence_complex4TestSphericalIn.test_spherical_in_recurrence_complex   sT    HH%&QUA.a!eA1FF1q!L$66	8r#   c                    ^p\         P                  ! \        ) \        .4      p\        \	        W4      \         P                  ! \        ) \        .4      4       R# rV   N)r   r   r	   r   r   r.   s   &  r    test_spherical_in_inf_real*TestSphericalIn.test_spherical_in_inf_real   s9    HHsdC[!Q*BHHsdC[,ABr#   c                    ^p\         P                  ! \        ) R,           \        R,           \        R,          .4      p\        \	        W4      \         P                  ! \        ) \        \
        .4      4       R# r*   r@   NrB   )r   r   r	   r   r   r
   r.   s   &  r    test_spherical_in_inf_complex-TestSphericalIn.test_spherical_in_inf_complex   sM     HHsdRir3:67Q*BHHsdC5E,FGr#   c                    \         P                  ! . RO4      p^ p\        \        W4      \         P                  ! . RO4      4       R# rT   r   r.   s   &  r    test_spherical_in_at_zero)TestSphericalIn.test_spherical_in_at_zero   r[   r#   r\   N)r]   r^   r_   r`   r   r   r   r   r   r   ra   rb   rc   s   @r    r   r      s-     A88C	HJ Jr#   r   c                   J   a  ] tR t^t o R tR tR tR tR tR t	R t
RtV tR	# )
TestSphericalKnc                
   \         P                  ! . RO4      p\        \        ^V4      \        ^,          \        V) 4      ,          ^V,          ^V^,          ,          ,           ^V^,          ,          ,           ,          4       R# r   )r   r   r   r   r   r   r   s   & r    test_spherical_kn_exact'TestSphericalKn.test_spherical_kn_exact   sU    HH01Q*1S!WacAadFlQq!tV&;<	>r#   c                ^   \         P                  ! . RO4      pRp\        RV^,
          ,          \        V^,
          V4      ,          RV^,           ,          \        V^,           V4      ,          ,
          RV,          ^V,          ^,           ,          V,          \        W4      ,          4       R# )r&   r   Nr'   r   r   r   r   r   r.   s   &  r    !test_spherical_kn_recurrence_real1TestSphericalKn.test_spherical_kn_recurrence_real   s{    HH%&1q5M,q1ua00B!a%=aRSeTUAV3VV!GQqS1WaQ 22	
r#   c                ^   \         P                  ! . RO4      pRp\        RV^,
          ,          \        V^,
          V4      ,          RV^,           ,          \        V^,           V4      ,          ,
          RV,          ^V,          ^,           ,          V,          \        W4      ,          4       R# )r&   Nr'   r,   r   r   r.   s   &  r    $test_spherical_kn_recurrence_complex4TestSphericalKn.test_spherical_kn_recurrence_complex   s{    HH%&1q5M,q1ua00B!a%=aRSeTUAV3VV!GQqS1WaQ 22	
r#   c                    ^p\         P                  ! \        ) \        .4      p\        \	        W4      \         P                  ! \        ) ^ .4      4       R# r   )r   r   r	   r   r   r.   s   &  r    test_spherical_kn_inf_real*TestSphericalKn.test_spherical_kn_inf_real   s9    HHsdC[!Q*BHHsdAY,?@r#   c                    ^p\         P                  ! \        ) R,           \        R,           \        R,          .4      p\        \	        W4      \         P                  ! \        ) ^ \
        .4      4       R# r   )r   r   r	   r   r   r
   r.   s   &  r    test_spherical_kn_inf_complex-TestSphericalKn.test_spherical_kn_inf_complex   sL    
 HHsdRir3:67Q*BHHsdAs^,DEr#   c                    \         P                  ! . RO4      p^ p\        \        W4      \         P                  ! VP
                  \        4      4       R# rx   )r   r   r   r   ry   rz   r	   r.   s   &  r    test_spherical_kn_at_zero)TestSphericalKn.test_spherical_kn_at_zero   s4    HH*+Q*BGGAGGS,ABr#   c                    \         P                  ! . RO4      pRp\        \        W4      \         P                  ! VP
                  \        4      4       R# r~   )r   r   r   r   ry   rz   r
   r.   s   &  r    !test_spherical_kn_at_zero_complex1TestSphericalKn.test_spherical_kn_at_zero_complex   s4    HH*+Q*BGGAGGS,ABr#   r\   N)r]   r^   r_   r`   r   r   r   r   r   r   r   ra   rb   rc   s   @r    r   r      s2     >

AFCC Cr#   r   c                      a  ] tR t^t o R t]P                  P                  R 4       t]P                  P                  R 4       t	Rt
V tR# )SphericalDerivativesTestCasec                   a a \        VV 3R  lW#4      w  rE\        VS P                  SV4      S P                  SV4      ,
          VR7       R# )c                 (   < SP                  SV 4      # N)df)zr/   r   s   &r    <lambda>BSphericalDerivativesTestCase.fundamental_theorem.<locals>.<lambda>   s    TWWQ]r#   )atolN)r   r   f)r   r/   abintegral	tolerances   ff&&  r    fundamental_theorem0SphericalDerivativesTestCase.fundamental_theorem   s<    "#:AAq!tvva|3&	(r#   c                ,    V P                  ^ RR4       R# )r   g      @      .@Nr   rM   s   &r    test_fundamental_theorem_07SphericalDerivativesTestCase.test_fundamental_theorem_0   s      C.r#   c                ,    V P                  ^RR4       R# )r*         ?g333333?Nr   rM   s   &r    test_fundamental_theorem_77SphericalDerivativesTestCase.test_fundamental_theorem_7  s      C-r#   r\   N)r]   r^   r_   r`   r   pytestmarkslowr   r   ra   rb   rc   s   @r    r   r      sF     ( [[/ / [[. .r#   r   c                   2   a  ] tR tRt o R tR tR tRtV tR# )TestSphericalJnDerivativesi  c                    \        W4      # r   r   r   r/   r   s   &&&r    r   TestSphericalJnDerivatives.f      A!!r#   c                    \        WR R7      # T
derivativer   r   s   &&&r    r   TestSphericalJnDerivatives.df      AT22r#   c                    \         P                  ! . RO4      p\        \        V^ RR7      \         P                  ! . RO4      4       R# )r   Tr   Nr   r&   r(   r)   r*      r   gUUUUUU?r   r   r   r   r-   r   r/   s   & r    test_spherical_jn_d_zero3TestSphericalJnDerivatives.test_spherical_jn_d_zero  s1    HH()Qd;!56	8r#   r\   N)	r]   r^   r_   r`   r   r   r   ra   rb   rc   s   @r    r   r     s     "38 8r#   r   c                   ,   a  ] tR tRt o R tR tRtV tR# )TestSphericalYnDerivativesi  c                    \        W4      # r   r   r   s   &&&r    r   TestSphericalYnDerivatives.f  r   r#   c                    \        WR R7      # r   r   r   s   &&&r    r   TestSphericalYnDerivatives.df  r   r#   r\   Nr]   r^   r_   r`   r   r   ra   rb   rc   s   @r    r   r          "3 3r#   r   c                   2   a  ] tR tRt o R tR tR tRtV tR# )TestSphericalInDerivativesi  c                    \        W4      # r   r   r   s   &&&r    r   TestSphericalInDerivatives.f  r   r#   c                    \        WR R7      # r   r   r   s   &&&r    r   TestSphericalInDerivatives.df   r   r#   c                    \         P                  ! . RO4      p\        V^ RR7       \        \        V^ RR7      \         P                  ! . RO4      4       R# )r   Fr   TNr   r   )r   r   r   r   r   s   & r    test_spherical_in_d_zero3TestSphericalInDerivatives.test_spherical_in_d_zero#  s=    HH()Qe,Qd;!56	8r#   r\   N)	r]   r^   r_   r`   r   r   r  ra   rb   rc   s   @r    r   r     s     "38 8r#   r   c                   ,   a  ] tR tRt o R tR tRtV tR# )TestSphericalKnDerivativesi*  c                    \        W4      # r   r   r   s   &&&r    r   TestSphericalKnDerivatives.f+  r   r#   c                    \        WR R7      # r   r  r   s   &&&r    r   TestSphericalKnDerivatives.df.  r   r#   r\   Nr   rc   s   @r    r  r  *  r   r#   r  c                   >   a  ] tR tRt o R tR tR tR tR tRt	V t
R# )	TestSphericalOldi2  c                   \         P                  ! R
4      pRp\        ^ V4      V^ ,          ^ &   \        ^V4      V^ ,          ^&   \        ^ VRR7      V^,          ^ &   \        ^VRR7      V^,          ^&   V^ ,          ^,          pV^ ,          ^ ,          RV^ ,          ^,          ,          ,
          p\        V^ ,          \         P                  ! RR.4      RRR7       \        V^,          W4.R^ R7       R	# )r(   皙?Tr   gA\?gc"?Afcz=g        r   rtolN)r(   r(         $@)r   emptyr   r   r   )r   i1nr   inp0inp1s   &    r    test_sph_inTestSphericalOld.test_sph_in6  s    hhuo A&Aq	 A&Aq	 A$7Aq	 A$7Aq	Aq	Aq	Gc!fQi//A*?*A*C !D$3	0 	A7Cr#   c                ,   R p\         P                  ! R4      p\        ^ V4      V^ &   \        ^ VRR7      V^&   \         P                  ! \         P                  ! V4      V,          \         P
                  ! V4      V,          \         P                  ! V4      V^,          ,          ,
          .4      p\        \        V,          VR^ R7       \         P                  ! R4      p\        ^ V4      V^ &   \        ^ VRR7      V^&   \         P                  ! R\        ,          \        V) 4      ,          V,          R\        ,          \        V) 4      ,          ^V,          ^V^,          ,          ,           ,          .4      p\        \        V,          VR^ R7       R# )	g      ?Tr   gv!>r  r   N)r(   g      )r   r  r   r   r   r   r   r   r   r   r   )r   r   sph_i0sph_i0_expectedsph_k0sph_k0_expecteds   &     r    test_sph_in_kn_order0&TestSphericalOld.test_sph_in_kn_order0G  s    $ A&q	 A$7q	((BGGAJqL$&GGAJqLAqD$@$B C6
O&qI$ A&q	 A$7q	((CF3r7N1$4$(GCGOQqS1a4Z$@$B C6
O&qIr#   c                |   \         P                  ! R4      pRp\        ^ V4      V^ ,          ^ &   \        ^V4      V^ ,          ^&   \        ^V4      V^ ,          ^&   \        ^ VRR7      V^,          ^ &   \        ^VRR7      V^,          ^&   \        ^VRR7      V^,          ^&   V^ ,          ^,          ) pV^ ,          ^ ,          RV^ ,          ^,          ,          ,
          pV^ ,          ^,          R	V^ ,          ^,          ,          ,
          p\        V^ ,          . R
OR^ R7       \        V^,          W4V.R^ R7       R# )r(   r  Tr   r  r  Nr(   r)   r  r   )gkG~?gk?g)qe?)r   r  r   r   )r   s1r   s10s11s12s   &     r    test_sph_jnTestSphericalOld.test_sph_jnW  s   XXe_1%1a1%1a1%1a161a161a161a!uQxieAhwr!uQx''eAhwr!uQx''1  : %1	. 	1#W1Er#   c                   \         P                  ! R4      pRp\        ^ V4      V^ ,          ^ &   \        ^V4      V^ ,          ^&   \        ^V4      V^ ,          ^&   \        ^ VRR7      V^,          ^ &   \        ^VRR7      V^,          ^&   \        ^VRR7      V^,          ^&   V^ ,          ^,          ) pV^ ,          ^ ,          ) R	V^ ,          ^,          ,          ,
          pV^ ,          ^,          ) R
V^ ,          ^,          ,          ,
          p\        V^ ,          . ROR^ R7       \        V^,          W4V.R^ R7       R# )r(   r  Tr   r  r  gA:>Nr   r  r   )gDT@g3̱wJC@g-uAI@)r   r  r   r   )r   knr   kn0kn1kn2s   &     r    test_sph_knTestSphericalOld.test_sph_knk  s   XXe_1%1a1%1a1%1a161a161a161a!uQxi!uQxi1a((!uQxi1a((1  7 %1	. 	1#V!Dr#   c                    \        ^R4      p\        ^ R4      p\        VRR^ R7       \        VR	R^ R7       \        ^ R4      ^\        ^R4      ,          ,
          ^,          p\        ^RRR7      p\        WCR^ R7       R# )
r(   r  giUMu>r  Tr   ga2U0*#?Ng[_$ewg&$)r   r   )r   sy1sy2sphpysy3s   &    r    test_sph_ynTestSphericalOld.test_sph_yn  sr    1c"1c"Zf1=Zf1=a%,q#*>(>>A1cd3a8r#   r\   N)r]   r^   r_   r`   r  r  r%  r,  r3  ra   rb   rc   s   @r    r  r  2  s'     D"J F(E(	9 	9r#   r  r   FTfunc                     \         P                  P                  R 4      p^pVP                  ^ ^
VR7      pVP	                  VR7      pV! WEV R7      pV! WER,           V R7      p\        WgP                  4       R# )l   dnUY )sizer   r@   N)r   randomdefault_rngintegersstandard_normalr   real)r   r5  rngr7  r/   r   resrefs   &&      r    test_negative_real_gh14582r@    sm     ))

 3
4CDQ&A&A
az
*C
a2*
-CC"r#   )$rC   numpyr   numpy.testingr   r   r   r   r   r   r   r	   r
   r   r   scipy.specialr   r   r   r   scipy.integrater   r   rf   r   r   r   r   r   r   r   r  r  r   parametrizer@  r\   r#   r    <module>rF     s      )  = = = P P  7J 7Jt4C 4Cn% %(+J +J\2C 2Cj. . 
8!= 
83!= 38!= 83!= 3V9 V9r t}5|!-|!= >	#> 6	#r#   