Ë
    1Ò^j[;  ã                   óê  — d dl Z d dlZd dlmZ d dlZd dlmZmZmZm	Z	m
Z
mZmZmZmZ d dlmZmZmZmZ d dlmZ  G d„ d«      Z G d„ d	«      Z G d
„ d«      Z G d„ d«      Z G d„ d«      Z G d„ d«      Z G d„ de«      Z G d„ de«      Z G d„ de«      Z G d„ de«      Z G d„ d«      Z ejB                  jE                  dddg«      ejB                  jE                  deeeeg«      d „ «       «       Z#y)!é    N)Úassert_allclose)	ÚsinÚcosÚsinhÚcoshÚexpÚinfÚnanÚr_Úpi)Úspherical_jnÚspherical_ynÚspherical_inÚspherical_kn)Úquadc                   ó<   — e Zd Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
y	)
ÚTestSphericalJnc                 ó¸   — t        j                  g d¢«      }t        t        d|«      d|z  d|dz  z  z   t	        |«      z  d|dz  z  t        |«      z  z
  «       y )N©ç¸…ëQ¸¾?ç®Gáz®ó?ç®Gáz®(@çÍÌÌÌÌÜ^@g     J“@é   éÿÿÿÿé   )ÚnpÚarrayr   r   r   r   ©ÚselfÚxs     út/var/www/ramen.bs-engineer-server.com/venv/lib/python3.12/site-packages/scipy/special/tests/test_spherical_bessel.pyÚtest_spherical_jn_exactz'TestSphericalJn.test_spherical_jn_exact   sV   € ô �H‰HÒ8Ó9ˆÜœ Q¨Ó*Ø˜A™  ! Q¡$¡™¬¨A«Ñ.°°1°a±4±¼¸A»±Ñ>õ	@ó    c                 ó´   — t        j                  g d¢«      }d}t        t        |dz
  |«      t        |dz   |«      z   d|z  dz   |z  t        ||«      z  «       y ©N©é   r   r   é   é   ùš™™™™™ñ?      ø?r(   r   ©r   r   r   r   ©r    Únr!   s      r"   Ú$test_spherical_jn_recurrence_complexz4TestSphericalJn.test_spherical_jn_recurrence_complex   óV   € ä�H‰HÒ%Ó&ˆØˆÜœ Q¨¡U¨AÓ.´¸aÀ!¹eÀQÓ1GÑGØ˜1™˜q™ !™¤L°°AÓ$6Ñ6õ	8r$   c                 ó´   — t        j                  g d¢«      }d}t        t        |dz
  |«      t        |dz   |«      z   d|z  dz   |z  t        ||«      z  «       y ©Nr'   r   r(   r   r,   r-   s      r"   Ú!test_spherical_jn_recurrence_realz1TestSphericalJn.test_spherical_jn_recurrence_real   óV   € ä�H‰HÒ%Ó&ˆØˆÜœ Q¨¡U¨AÓ.´¸aÀ!¹eÀAÓ1FÑFØ˜1™˜q™ !™¤L°°AÓ$6Ñ6õ	8r$   c                 óž   — d}t        j                  t         t        g«      }t        t	        ||«      t        j                  ddg«      «       y ©Né   r   )r   r   r	   r   r   r-   s      r"   Útest_spherical_jn_inf_realz*TestSphericalJn.test_spherical_jn_inf_real&   ó9   € àˆÜ�H‰H”s�dœC�[Ó!ˆÜœ Q¨Ó*¬B¯H©H°a¸°VÓ,<Õ=r$   c           
      óR  — d}t        j                  t         dz   t        dz   t        dz  g«      }t        j                  «       5  t        j
                  ddt        «       t        t        ||«      t        j                  ddt        dz  g«      «       d d d «       y # 1 sw Y   y xY w©Nr)   ù                ù      ð?      ð?Úignorez%invalid value encountered in multiplyr   )	r   r   r	   ÚwarningsÚcatch_warningsÚfilterwarningsÚRuntimeWarningr   r   r-   s      r"   Útest_spherical_jn_inf_complexz-TestSphericalJn.test_spherical_jn_inf_complex,   ó‹   € àˆÜ�H‰H”s�d˜R‘i¤ r¡¬3°©:Ð6Ó7ˆÜ×$Ñ$Ó&ñ 	NÜ×#Ñ#ØÐAÄ>ôSäœL¨¨AÓ.´·±¸!¸QÄÀTÁ
Ð9KÓ0LÔM÷	N÷ 	Nñ 	Núó   ÁABÂB&c                 ó0   — t        t        dd«      d«       y )Nr   g%�•-ª@g·õ<«]�3¿©r   r   ©r    s    r"   Útest_spherical_jn_large_arg_1z-TestSphericalJn.test_spherical_jn_large_arg_15   s   € ô 	œ Q¨Ó1Ð3JÕKr$   c                 ó0   — t        t        dd«      d«       y )Nr   i'  g°µ|¸	 ?rG   rH   s    r"   Útest_spherical_jn_large_arg_2z-TestSphericalJn.test_spherical_jn_large_arg_2;   s   € ô 	œ Q¨Ó.Ð0FÕGr$   c                 óŒ   — t        j                  g d¢«      }d}t        t        ||«      t        j                  g d¢«      «       y ©N©r   r(   r   é   é
   éd   r   )r(   r   r   r   r   r   r,   r-   s      r"   Útest_spherical_jn_at_zeroz)TestSphericalJn.test_spherical_jn_at_zeroA   ó3   € ô �H‰HÒ*Ó+ˆØˆÜœ Q¨Ó*¬B¯H©HÒ5GÓ,HÕIr$   N)Ú__name__Ú
__module__Ú__qualname__r#   r/   r3   r8   rC   rI   rK   rR   © r$   r"   r   r      s/   „ ò@ò8ò8ò>òNòLòHóJr$   r   c                   ó6   — e Zd Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	y)	ÚTestSphericalYnc                 ó¸   — t        j                  g d¢«      }t        t        d|«      d|z  d|dz  z  z
  t	        |«      z  d|dz  z  t        |«      z  z
  «       y )Nr   r   r(   r   )r   r   r   r   r   r   r   s     r"   Útest_spherical_yn_exactz'TestSphericalYn.test_spherical_yn_exactJ   sU   € ô �H‰HÒ8Ó9ˆÜœ Q¨Ó*Ø˜1™˜q  A¡™v™¤s¨1£vÑ-°°!°Q±$±´s¸1³v±Ñ=õ	?r$   c                 ó´   — t        j                  g d¢«      }d}t        t        |dz
  |«      t        |dz   |«      z   d|z  dz   |z  t        ||«      z  «       y r2   ©r   r   r   r   r-   s      r"   Ú!test_spherical_yn_recurrence_realz1TestSphericalYn.test_spherical_yn_recurrence_realR   r4   r$   c                 ó´   — t        j                  g d¢«      }d}t        t        |dz
  |«      t        |dz   |«      z   d|z  dz   |z  t        ||«      z  «       y r&   r]   r-   s      r"   Ú$test_spherical_yn_recurrence_complexz4TestSphericalYn.test_spherical_yn_recurrence_complexY   r0   r$   c                 óž   — d}t        j                  t         t        g«      }t        t	        ||«      t        j                  ddg«      «       y r6   )r   r   r	   r   r   r-   s      r"   Útest_spherical_yn_inf_realz*TestSphericalYn.test_spherical_yn_inf_real`   r9   r$   c           
      óR  — d}t        j                  t         dz   t        dz   t        dz  g«      }t        j                  «       5  t        j
                  ddt        «       t        t        ||«      t        j                  ddt        dz  g«      «       d d d «       y # 1 sw Y   y xY wr;   )	r   r   r	   r?   r@   rA   rB   r   r   r-   s      r"   Útest_spherical_yn_inf_complexz-TestSphericalYn.test_spherical_yn_inf_complexf   rD   rE   c                 ó¨   — t        j                  g d¢«      }d}t        t        ||«      t        j                  |j
                  t         «      «       y ©NrN   r   )r   r   r   r   ÚfullÚshaper	   r-   s      r"   Útest_spherical_yn_at_zeroz)TestSphericalYn.test_spherical_yn_at_zeroo   s8   € ä�H‰HÒ*Ó+ˆØˆÜœ Q¨Ó*¬B¯G©G°A·G±G¼c¸TÓ,BÕCr$   c                 ó¦   — t        j                  g d¢«      }d}t        t        ||«      t        j                  |j
                  t        «      «       y ©NrN   r<   )r   r   r   r   rg   rh   r
   r-   s      r"   Ú!test_spherical_yn_at_zero_complexz1TestSphericalYn.test_spherical_yn_at_zero_complexu   s8   € ô �H‰HÒ*Ó+ˆØˆÜœ Q¨Ó*¬B¯G©G°A·G±G¼SÓ,AÕBr$   N)
rT   rU   rV   r[   r^   r`   rb   rd   ri   rl   rW   r$   r"   rY   rY   I   s(   „ ò?ò8ò8ò>òNòDóCr$   rY   c                   ó   — e Zd Zd„ Zd„ Zy)ÚTestSphericalJnYnCrossProductc                 óú   — t        j                  g d¢«      }t        j                  g d¢«      }t        |dz   |«      t        ||«      z  t        ||«      t        |dz   |«      z  z
  }d|dz  z  }t	        ||«       y )N©r(   rO   é   ©gš™™™™™¹?r(   rP   r(   r   ©r   r   r   r   r   ©r    r.   r!   ÚleftÚrights        r"   Ú$test_spherical_jn_yn_cross_product_1zBTestSphericalJnYnCrossProduct.test_spherical_jn_yn_cross_product_1�   sp   € ä�H‰H’YÓˆÜ�H‰H’\Ó"ˆÜ˜Q ™U AÓ&¬°a¸Ó);Ñ;Ü˜Q Ó"¤\°!°a±%¸Ó%;Ñ;ñ<ˆà�!�Q‘$‘ˆÜ˜˜eÕ$r$   c                 ó  — t        j                  g d¢«      }t        j                  g d¢«      }t        |dz   |«      t        ||«      z  t        ||«      t        |dz   |«      z  z
  }d|z  dz   |dz  z  }t	        ||«       y )Nrp   rr   r   r   rs   rt   s        r"   Ú$test_spherical_jn_yn_cross_product_2zBTestSphericalJnYnCrossProduct.test_spherical_jn_yn_cross_product_2Š   sx   € ä�H‰H’YÓˆÜ�H‰H’\Ó"ˆÜ˜Q ™U AÓ&¬°a¸Ó);Ñ;Ü˜Q Ó"¤\°!°a±%¸Ó%;Ñ;ñ<ˆà�1‘�q‘˜!˜Q™$‘ˆÜ˜˜eÕ$r$   N)rT   rU   rV   rw   ry   rW   r$   r"   rn   rn   €   s   „ ò%ó%r$   rn   c                   ó0   — e Zd Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zy)ÚTestSphericalInc                 ó¸   — t        j                  g d¢«      }t        t        d|«      d|z  d|dz  z  z   t	        |«      z  d|dz  z  t        |«      z  z
  «       y ©N)r   r   r   r   r   r(   r   )r   r   r   r   r   r   r   s     r"   Útest_spherical_in_exactz'TestSphericalIn.test_spherical_in_exact•   sT   € ä�H‰HÒ0Ó1ˆÜœ Q¨Ó*Ø˜1™˜q  A¡™v™¤t¨A£wÑ.°°1°a±4±¼¸Q»±Ñ?õ	Ar$   c                 ó´   — t        j                  g d¢«      }d}t        t        |dz
  |«      t        |dz   |«      z
  d|z  dz   |z  t        ||«      z  «       y r2   ©r   r   r   r   r-   s      r"   Ú!test_spherical_in_recurrence_realz1TestSphericalIn.test_spherical_in_recurrence_real›   r4   r$   c                 ó´   — t        j                  g d¢«      }d}t        t        |dz
  |«      t        |dz   |«      z
  d|z  dz   |z  t        ||«      z  «       y r&   r€   r-   s      r"   Ú$test_spherical_in_recurrence_complexz4TestSphericalIn.test_spherical_in_recurrence_complex¢   sV   € ä�H‰HÒ%Ó&ˆØˆÜœ Q¨¡U¨AÓ.´¸aÀ!¹eÀAÓ1FÑFØ˜1™˜q™ !™¤L°°AÓ$6Ñ6õ	8r$   c                 ó°   — d}t        j                  t         t        g«      }t        t	        ||«      t        j                  t         t        g«      «       y )NrO   )r   r   r	   r   r   r-   s      r"   Útest_spherical_in_inf_realz*TestSphericalIn.test_spherical_in_inf_real©   s;   € àˆÜ�H‰H”s�dœC�[Ó!ˆÜœ Q¨Ó*¬B¯H©H´s°d¼C°[Ó,AÕBr$   c                 óÖ   — d}t        j                  t         dz   t        dz   t        dz  g«      }t        t	        ||«      t        j                  t         t        t
        g«      «       y )Nr)   r<   r=   )r   r   r	   r   r   r
   r-   s      r"   Útest_spherical_in_inf_complexz-TestSphericalIn.test_spherical_in_inf_complex¯   sO   € ð ˆÜ�H‰H”s�d˜R‘i¤ r¡¬3°©:Ð6Ó7ˆÜœ Q¨Ó*¬B¯H©H´s°d¼CÄÐ5EÓ,FÕGr$   c                 óŒ   — t        j                  g d¢«      }d}t        t        ||«      t        j                  g d¢«      «       y rM   r€   r-   s      r"   Útest_spherical_in_at_zeroz)TestSphericalIn.test_spherical_in_at_zeroº   rS   r$   N)	rT   rU   rV   r~   r�   rƒ   r…   r‡   r‰   rW   r$   r"   r{   r{   ”   s$   „ òAò8ò8òCò	HóJr$   r{   c                   ó6   — e Zd Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	y)	ÚTestSphericalKnc                 ó¶   — t        j                  g d¢«      }t        t        d|«      t        dz  t        | «      z  d|z  d|dz  z  z   d|dz  z  z   z  «       y r}   )r   r   r   r   r   r   r   s     r"   Útest_spherical_kn_exactz'TestSphericalKn.test_spherical_kn_exactÃ   sU   € ä�H‰HÒ0Ó1ˆÜœ Q¨Ó*Ü˜1™œS ! ›W™ a¨¡c¨A¨a°©d©F¡l°Q°q¸!±t±VÑ&;Ñ<õ	>r$   c                 óä   — t        j                  g d¢«      }d}t        d|dz
  z  t        |dz
  |«      z  d|dz   z  t        |dz   |«      z  z
  d|z  d|z  dz   z  |z  t        ||«      z  «       y )Nr'   r   r   r(   r   ©r   r   r   r   r-   s      r"   Ú!test_spherical_kn_recurrence_realz1TestSphericalKn.test_spherical_kn_recurrence_realÉ   s}   € ä�H‰HÒ%Ó&ˆØˆÜØ�1�q‘5‰Mœ, q¨1¡u¨aÓ0Ñ0°B¸!¸a¹%±=ÄÈaÐRSÉeÐTUÓAVÑ3VÑVØ�!‰G�Q�q‘S˜1‘WÑ˜aÑ¤¨Q°Ó 2Ñ2õ	
r$   c                 óä   — t        j                  g d¢«      }d}t        d|dz
  z  t        |dz
  |«      z  d|dz   z  t        |dz   |«      z  z
  d|z  d|z  dz   z  |z  t        ||«      z  «       y )Nr'   r+   r   r(   r   r�   r-   s      r"   Ú$test_spherical_kn_recurrence_complexz4TestSphericalKn.test_spherical_kn_recurrence_complexÒ   s}   € ä�H‰HÒ%Ó&ˆØˆÜØ�1�q‘5‰Mœ, q¨1¡u¨aÓ0Ñ0°B¸!¸a¹%±=ÄÈaÐRSÉeÐTUÓAVÑ3VÑVØ�!‰G�Q�q‘S˜1‘WÑ˜aÑ¤¨Q°Ó 2Ñ2õ	
r$   c                 ó¨   — d}t        j                  t         t        g«      }t        t	        ||«      t        j                  t         dg«      «       y )NrO   r   )r   r   r	   r   r   r-   s      r"   Útest_spherical_kn_inf_realz*TestSphericalKn.test_spherical_kn_inf_realÛ   s;   € àˆÜ�H‰H”s�dœC�[Ó!ˆÜœ Q¨Ó*¬B¯H©H´s°d¸A°YÓ,?Õ@r$   c                 óÎ   — d}t        j                  t         dz   t        dz   t        dz  g«      }t        t	        ||«      t        j                  t         dt
        g«      «       y )Nr)   r<   r=   r   )r   r   r	   r   r   r
   r-   s      r"   Útest_spherical_kn_inf_complexz-TestSphericalKn.test_spherical_kn_inf_complexá   sN   € ð
 ˆÜ�H‰H”s�d˜R‘i¤ r¡¬3°©:Ð6Ó7ˆÜœ Q¨Ó*¬B¯H©H´s°d¸A¼s°^Ó,DÕEr$   c                 ó¦   — t        j                  g d¢«      }d}t        t        ||«      t        j                  |j
                  t        «      «       y rf   )r   r   r   r   rg   rh   r	   r-   s      r"   Útest_spherical_kn_at_zeroz)TestSphericalKn.test_spherical_kn_at_zeroê   s6   € ä�H‰HÒ*Ó+ˆØˆÜœ Q¨Ó*¬B¯G©G°A·G±G¼SÓ,AÕBr$   c                 ó¦   — t        j                  g d¢«      }d}t        t        ||«      t        j                  |j
                  t        «      «       y rk   )r   r   r   r   rg   rh   r
   r-   s      r"   Ú!test_spherical_kn_at_zero_complexz1TestSphericalKn.test_spherical_kn_at_zero_complexð   s6   € ä�H‰HÒ*Ó+ˆØˆÜœ Q¨Ó*¬B¯G©G°A·G±G¼SÓ,AÕBr$   N)
rT   rU   rV   r�   r�   r’   r”   r–   r˜   rš   rW   r$   r"   r‹   r‹   Â   s)   „ ò>ò
ò
òAòFòCóCr$   r‹   c                   ó‚   — e Zd Zd„ Zej
                  j                  d„ «       Zej
                  j                  d„ «       Zy)ÚSphericalDerivativesTestCasec                 ó’   ‡ ‡— t        ˆˆ fd„||«      \  }}t        |‰ j                  ‰|«      ‰ j                  ‰|«      z
  |¬«       y )Nc                 ó(   •— ‰j                  ‰| «      S ©N)Údf)Úzr.   r    s    €€r"   ú<lambda>zBSphericalDerivativesTestCase.fundamental_theorem.<locals>.<lambda>ù   s   ø€ ¨T¯W©W°Q¸«]€ r$   )Úatol)r   r   Úf)r    r.   ÚaÚbÚintegralÚ	tolerances   ``    r"   Úfundamental_theoremz0SphericalDerivativesTestCase.fundamental_theoremø   s@   ù€ Ü"Ô#:¸A¸qÓAÑˆ�)Ü˜ØŸ™˜q !› t§v¡v¨a°£|Ñ3Ø&ö	(r$   c                 ó*   — | j                  ddd«       y )Nr   g      @ç      .@©r©   rH   s    r"   Útest_fundamental_theorem_0z7SphericalDerivativesTestCase.test_fundamental_theorem_0þ   s   € à× Ñ   C¨Õ.r$   c                 ó*   — | j                  ddd«       y )Nr)   ç      à?g333333ó?r¬   rH   s    r"   Útest_fundamental_theorem_7z7SphericalDerivativesTestCase.test_fundamental_theorem_7  s   € à× Ñ   C¨Õ-r$   N)	rT   rU   rV   r©   ÚpytestÚmarkÚslowr­   r°   rW   r$   r"   rœ   rœ   ÷   sC   „ ò(ð ‡[�[×Ññ/ó ð/ð ‡[�[×Ññ.ó ñ.r$   rœ   c                   ó   — e Zd Zd„ Zd„ Zd„ Zy)ÚTestSphericalJnDerivativesc                 ó   — t        ||«      S rŸ   ©r   ©r    r.   r¡   s      r"   r¤   zTestSphericalJnDerivatives.f  ó   € Ü˜A˜qÓ!Ð!r$   c                 ó   — t        ||d¬«      S ©NT©Ú
derivativer·   r¸   s      r"   r    zTestSphericalJnDerivatives.df  ó   € Ü˜A˜q¨TÔ2Ð2r$   c                 óŒ   — t        j                  g d¢«      }t        t        |dd¬«      t        j                  g d¢«      «       y )N©r   r(   r   r   r)   é   r   Tr¼   ©r   gUUUUUUÕ?r   r   r   r   r,   ©r    r.   s     r"   Útest_spherical_jn_d_zeroz3TestSphericalJnDerivatives.test_spherical_jn_d_zero  s1   € Ü�H‰HÒ(Ó)ˆÜœ Q¨°dÔ;ÜŸ™Ò!5Ó6õ	8r$   N)rT   rU   rV   r¤   r    rÄ   rW   r$   r"   rµ   rµ     s   „ ò"ò3ó8r$   rµ   c                   ó   — e Zd Zd„ Zd„ Zy)ÚTestSphericalYnDerivativesc                 ó   — t        ||«      S rŸ   ©r   r¸   s      r"   r¤   zTestSphericalYnDerivatives.f  r¹   r$   c                 ó   — t        ||d¬«      S r»   rÈ   r¸   s      r"   r    zTestSphericalYnDerivatives.df  r¾   r$   N©rT   rU   rV   r¤   r    rW   r$   r"   rÆ   rÆ     ó   „ ò"ó3r$   rÆ   c                   ó   — e Zd Zd„ Zd„ Zd„ Zy)ÚTestSphericalInDerivativesc                 ó   — t        ||«      S rŸ   ©r   r¸   s      r"   r¤   zTestSphericalInDerivatives.f  r¹   r$   c                 ó   — t        ||d¬«      S r»   rÏ   r¸   s      r"   r    zTestSphericalInDerivatives.df   r¾   r$   c                 ó¨   — t        j                  g d¢«      }t        |dd¬«       t        t        |dd¬«      t        j                  g d¢«      «       y )NrÀ   r   Fr¼   TrÂ   )r   r   r   r   rÃ   s     r"   Útest_spherical_in_d_zeroz3TestSphericalInDerivatives.test_spherical_in_d_zero#  s=   € Ü�H‰HÒ(Ó)ˆÜ�Q˜ eÕ,Üœ Q¨°dÔ;ÜŸ™Ò!5Ó6õ	8r$   N)rT   rU   rV   r¤   r    rÒ   rW   r$   r"   rÍ   rÍ     s   „ ò"ò3ó8r$   rÍ   c                   ó   — e Zd Zd„ Zd„ Zy)ÚTestSphericalKnDerivativesc                 ó   — t        ||«      S rŸ   ©r   r¸   s      r"   r¤   zTestSphericalKnDerivatives.f+  r¹   r$   c                 ó   — t        ||d¬«      S r»   rÖ   r¸   s      r"   r    zTestSphericalKnDerivatives.df.  r¾   r$   NrÊ   rW   r$   r"   rÔ   rÔ   *  rË   r$   rÔ   c                   ó*   — e Zd Zd„ Zd„ Zd„ Zd„ Zd„ Zy)ÚTestSphericalOldc                 óx  — t        j                  d«      }d}t        d|«      |d   d<   t        d|«      |d   d<   t        d|d¬«      |d   d<   t        d|d¬«      |d   d<   |d   d   }|d   d   d|d   d   z  z
  }t        |d   t        j                  dd	g«      d
d¬«       t        |d   ||gd
d¬«       y )N)r   r   çš™™™™™É?r   r(   Tr¼   ç      $@g±µA€\ð?gÐÉc‘"±?çßÄAfcz=g        ©r£   Úrtol)r   Úemptyr   r   r   )r    Úi1nr!   Úinp0Úinp1s        r"   Útest_sph_inzTestSphericalOld.test_sph_in6  s×   € ä�h‰h�u‹oˆØˆä   AÓ&ˆˆA‰ˆq‰	Ü   AÓ&ˆˆA‰ˆq‰	Ü   A°$Ô7ˆˆA‰ˆq‰	Ü   A°$Ô7ˆˆA‰ˆq‰	à�A‘�q‘	ˆØ�A‘�q‘	˜G c¨!¡f¨Q¡iÑ/Ñ/ˆÜ˜˜A™¤§¡Ð*?Ø*Að*Có !Dà$¨3õ	0ô 	˜˜A™  t °7ÀÖCr$   c                 ó”  — d}t        j                  d«      }t        d|«      |d<   t        d|d¬«      |d<   t        j                  t        j                  |«      |z  t        j
                  |«      |z  t        j                  |«      |dz  z  z
  g«      }t        t        |   |dd¬	«       t        j                  d«      }t        d|«      |d<   t        d|d¬«      |d<   t        j                  d
t        z  t        | «      z  |z  dt        z  t        | «      z  d|z  d|dz  z  z   z  g«      }t        t        |   |dd¬	«       y )Ng      ð?)r   r   Tr¼   r(   r   gvƒôõ!„>rÞ   r¯   g      à¿)r   rà   r   r   r   r   r   r   r   r   r   )r    r!   Úsph_i0Úsph_i0_expectedÚsph_k0Úsph_k0_expecteds         r"   Útest_sph_in_kn_order0z&TestSphericalOld.test_sph_in_kn_order0G  s   € ØˆÜ—‘˜$“ˆÜ   AÓ&ˆˆq‰	Ü   A°$Ô7ˆˆq‰	ÜŸ(™(¤B§G¡G¨A£J¨q¡LÜ$&§G¡G¨A£J¨q¡L´·±¸³¸A¸q¹D±Ñ$@ð$Bó Cˆäœ˜6™
 O¸&ÀqÕIä—‘˜$“ˆÜ   AÓ&ˆˆq‰	Ü   A°$Ô7ˆˆq‰	ÜŸ(™( C¬¡F¬3°¨r«7¡N°1Ñ$4Ø$(¬¡G¬C°°«G¡O°Q°q±S¸¸1¸a¹4¹±ZÑ$@ð$Bó Cˆäœ˜6™
 O¸&ÀqÖIr$   c                 óÊ  — t        j                  d«      }d}t        d|«      |d   d<   t        d|«      |d   d<   t        d|«      |d   d<   t        d|d¬«      |d   d<   t        d|d¬«      |d   d<   t        d|d¬«      |d   d<   |d   d    }|d   d   d|d   d   z  z
  }|d   d   d	|d   d   z  z
  }t        |d   g d
¢dd¬«       t        |d   |||gdd¬«       y )N©r   r   rÛ   r   r(   r   Tr¼   rÜ   r«   )gkGì~Éï?g¥Åk‡�ÿ°?g’)ËÜqÈe?rÝ   rÞ   )r   rà   r   r   )r    Ús1r!   Ús10Ús11Ús12s         r"   Útest_sph_jnzTestSphericalOld.test_sph_jnW  s  € Ü�X‰X�e‹_ˆØˆä  1Ó%ˆˆ1‰ˆa‰Ü  1Ó%ˆˆ1‰ˆa‰Ü  1Ó%ˆˆ1‰ˆa‰Ü  1°Ô6ˆˆ1‰ˆa‰Ü  1°Ô6ˆˆ1‰ˆa‰Ü  1°Ô6ˆˆ1‰ˆa‰à�!‰u�Q‰xˆiˆØ�‰e�A‰h�w˜r !™u Q™xÑ'Ñ'ˆØ�‰e�A‰h�w˜r !™u Q™xÑ'Ñ'ˆÜ˜˜1™ò  :ð %¨1õ	.ô 	˜˜1™  S¨#˜°WÀ1ÖEr$   c                 óÎ  — t        j                  d«      }d}t        d|«      |d   d<   t        d|«      |d   d<   t        d|«      |d   d<   t        d|d¬«      |d   d<   t        d|d¬«      |d   d<   t        d|d¬«      |d   d<   |d   d    }|d   d    d|d   d   z  z
  }|d   d    d	|d   d   z  z
  }t        |d   g d
¢dd¬«       t        |d   |||gdd¬«       y )Nrì   rÛ   r   r(   r   Tr¼   rÜ   r«   )gDT»—Ÿ¸@g3Ì±wJC@gè-ßuAI‚@rÝ   rÞ   gßA:ÜÅ>)r   rà   r   r   )r    Úknr!   Úkn0Úkn1Úkn2s         r"   Útest_sph_knzTestSphericalOld.test_sph_knk  s  € Ü�X‰X�e‹_ˆØˆä  1Ó%ˆˆ1‰ˆa‰Ü  1Ó%ˆˆ1‰ˆa‰Ü  1Ó%ˆˆ1‰ˆa‰Ü  1°Ô6ˆˆ1‰ˆa‰Ü  1°Ô6ˆˆ1‰ˆa‰Ü  1°Ô6ˆˆ1‰ˆa‰à�!‰u�Q‰xˆiˆØ�!‰u�Q‰xˆi˜  1¡ a¡Ñ(Ñ(ˆØ�!‰u�Q‰xˆi˜  1¡ a¡Ñ(Ñ(ˆÜ˜˜1™ò  7ð %¨1õ	.ô 	˜˜1™  S¨#˜°VÀ!ÖDr$   c                 óè   — t        dd«      }t        dd«      }t        |ddd¬«       t        |ddd¬«       t        dd«      dt        dd«      z  z
  dz  }t        d	dd
¬«      }t        ||dd¬«       y )Nr   rÛ   r   g[_$´e˜wÀgiUMuï>rÞ   g&$Þð™Àr   r(   Tr¼   ga2U0*©#?)r   r   )r    Úsy1Úsy2ÚsphpyÚsy3s        r"   Útest_sph_ynzTestSphericalOld.test_sph_yn  st   € Ü˜1˜cÓ"ˆÜ˜1˜cÓ"ˆä˜˜Z¨f¸1Õ=Ü˜˜Z¨f¸1Õ=Ü˜a Ó%¨¬,°q¸#Ó*>Ñ(>Ñ>ÀÑAˆÜ˜1˜c¨dÔ3ˆä˜˜U¨°aÖ8r$   N)rT   rU   rV   rä   rê   rñ   r÷   rý   rW   r$   r"   rÙ   rÙ   2  s   „ òDò"Jò Fò(Eó(	9r$   rÙ   r½   FTÚfunc                 óð   — t         j                  j                  d«      }d}|j                  dd|¬«      }|j	                  |¬«      } |||| ¬«      } |||dz   | ¬«      }t        ||j                  «       y )Nl   ¢dnU×Y� é   r   rP   )Úsizer¼   r<   )r   ÚrandomÚdefault_rngÚintegersÚstandard_normalr   Úreal)r½   rþ   Úrngr  r.   r¡   ÚresÚrefs           r"   Útest_negative_real_gh14582r
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-€CÜ�C˜Ÿ™Õ"r$   )$r?   Únumpyr   Únumpy.testingr   r±   r   r   r   r   r   r	   r
   r   r   Úscipy.specialr   r   r   r   Úscipy.integrater   r   rY   rn   r{   r‹   rœ   rµ   rÆ   rÍ   rÔ   rÙ   r²   Úparametrizer
  rW   r$   r"   ú<module>r     sþ   ðó ã Ý )Û ß =× =Õ =ç PÓ PÝ  ÷7Jñ 7J÷t4Cñ 4C÷n%ñ %÷(+Jñ +J÷\2Cñ 2C÷j.ñ .ô 
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8ô3Ð!=ô 3ô8Ð!=ô 8ô3Ð!=ô 3÷V9ñ V9ðr ‡�×Ñ˜¨¨t }Ó5Ø‡�×Ñ˜ ¨|Ø!-¨|ð!=ó >ñ	#ó>ó 6ñ	#r$   