Ë
    âQ(h³:  ã                   óî  — d dl Zd dlmZmZmZ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jF                  jI                  dddg«      ejF                  jI                  deeeeg«      d „ «       «       Z%y)!é    N)Úassert_almost_equalÚassert_allcloseÚassert_array_almost_equalÚsuppress_warnings)	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     úg/var/www/skyplay_api_hub/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/   r0   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$6Ñ6õ	8r'   c                 óž   — d}t        j                  t         t        g«      }t        t	        ||«      t        j                  ddg«      «       y ©Né   r   )r    r!   r   r   r   r0   s      r%   Útest_spherical_jn_inf_realz*TestSphericalJn.test_spherical_jn_inf_real%   ó9   € àˆÜ�H‰H”s�dœC�[Ó!ˆÜœ Q¨Ó*¬B¯H©H°a¸°VÓ,<Õ=r'   c           
      ó4  — d}t        j                  t         dz   t        dz   t        dz  g«      }t        «       5 }|j	                  t
        d«       t        t        ||«      t        j                  ddt        dz  g«      «       d d d «       y # 1 sw Y   y xY w©Nr,   ù                ù      ð?      ð?z%invalid value encountered in multiplyr   )r    r!   r   r   ÚfilterÚRuntimeWarningr   r   ©r#   r1   r$   Úsups       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Ó ð 	N CØ�J‰J”~Ð'NÔOÜœL¨¨AÓ.´·±¸!¸QÄÀTÁ
Ð9KÓ0LÔM÷	N÷ 	Nñ 	Núó   »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_13   s   € ô 	œ Q¨Ó1Ð3JÕKr'   c                 ó0   — t        t        dd«      d«       y )Nr   i'  g°µ|¸	 ?rI   rJ   s    r%   Útest_spherical_jn_large_arg_2z-TestSphericalJn.test_spherical_jn_large_arg_29   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/   r0   s      r%   Útest_spherical_jn_at_zeroz)TestSphericalJn.test_spherical_jn_at_zero?   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&   r2   r6   r;   rE   rK   rM   rT   © 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_exactH   sU   € ô �H‰HÒ8Ó9ˆÜœ Q¨Ó*Ø˜1™˜q  A¡™v™¤s¨1£vÑ-°°!°Q±$±´s¸1³v±Ñ=õ	?r'   c                 ó´   — t        j                  g d¢«      }d}t        t        |dz
  |«      t        |dz   |«      z   d|z  dz   |z  t        ||«      z  «       y r5   ©r    r!   r   r   r0   s      r%   Ú!test_spherical_yn_recurrence_realz1TestSphericalYn.test_spherical_yn_recurrence_realP   r7   r'   c                 ó´   — t        j                  g d¢«      }d}t        t        |dz
  |«      t        |dz   |«      z   d|z  dz   |z  t        ||«      z  «       y r)   r_   r0   s      r%   Ú$test_spherical_yn_recurrence_complexz4TestSphericalYn.test_spherical_yn_recurrence_complexW   r3   r'   c                 óž   — d}t        j                  t         t        g«      }t        t	        ||«      t        j                  ddg«      «       y r9   )r    r!   r   r   r   r0   s      r%   Útest_spherical_yn_inf_realz*TestSphericalYn.test_spherical_yn_inf_real^   r<   r'   c           
      ó4  — d}t        j                  t         dz   t        dz   t        dz  g«      }t        «       5 }|j	                  t
        d«       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   rA   rB   r   r   rC   s       r%   Útest_spherical_yn_inf_complexz-TestSphericalYn.test_spherical_yn_inf_complexd   rF   rG   c                 ó¨   — t        j                  g d¢«      }d}t        t        ||«      t        j                  |j
                  t         «      «       y ©NrP   r   )r    r!   r   r   ÚfullÚshaper   r0   s      r%   Útest_spherical_yn_at_zeroz)TestSphericalYn.test_spherical_yn_at_zerol   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 ©NrP   r?   )r    r!   r   r   ri   rj   r   r0   s      r%   Ú!test_spherical_yn_at_zero_complexz1TestSphericalYn.test_spherical_yn_at_zero_complexr   s8   € ô �H‰HÒ*Ó+ˆØˆÜœ Q¨Ó*¬B¯G©G°A·G±G¼SÓ,AÕBr'   N)
rV   rW   rX   r]   r`   rb   rd   rf   rk   rn   rY   r'   r%   r[   r[   G   s(   „ ò?ò8ò8ò>òNòDóCr'   r[   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+   rQ   é   ©gš™™™™™¹?r+   rR   r+   r   ©r    r!   r   r   r   ©r#   r1   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 )Nrr   rt   r   r   ru   rv   s        r%   Ú$test_spherical_jn_yn_cross_product_2zBTestSphericalJnYnCrossProduct.test_spherical_jn_yn_cross_product_2‡   sx   € ä�H‰H’YÓˆÜ�H‰H’\Ó"ˆÜ˜Q ™U AÓ&¬°a¸Ó);Ñ;Ü˜Q Ó"¤\°!°a±%¸Ó%;Ñ;ñ<ˆà�1‘�q‘˜!˜Q™$‘ˆÜ˜˜eÕ$r'   N)rV   rW   rX   ry   r{   rY   r'   r%   rp   rp   }   s   „ ò%ó%r'   rp   c                   ó0   — e Zd Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zy)ÚTestSphericalInc                 ó¸   — t        j                  g d¢«      }t        t        d|«      d|z  d|dz  z  z   t	        |«      z  d|dz  z  t        |«      z  z
  «       y ©N)r   r   r   r   r   r+   r   )r    r!   r   r   r	   r
   r"   s     r%   Útest_spherical_in_exactz'TestSphericalIn.test_spherical_in_exact’   sT   € ä�H‰HÒ0Ó1ˆÜœ Q¨Ó*Ø˜1™˜q  A¡™v™¤t¨A£wÑ.°°1°a±4±¼¸Q»±Ñ?õ	Ar'   c                 ó´   — t        j                  g d¢«      }d}t        t        |dz
  |«      t        |dz   |«      z
  d|z  dz   |z  t        ||«      z  «       y r5   ©r    r!   r   r   r0   s      r%   Ú!test_spherical_in_recurrence_realz1TestSphericalIn.test_spherical_in_recurrence_real˜   r7   r'   c                 ó´   — t        j                  g d¢«      }d}t        t        |dz
  |«      t        |dz   |«      z
  d|z  dz   |z  t        ||«      z  «       y r)   r‚   r0   s      r%   Ú$test_spherical_in_recurrence_complexz4TestSphericalIn.test_spherical_in_recurrence_complexŸ   sV   € ä�H‰HÒ%Ó&ˆØˆÜœ Q¨¡U¨AÓ.´¸aÀ!¹eÀAÓ1FÑFØ˜1™˜q™ !™¤L°°AÓ$6Ñ6õ	8r'   c                 ó°   — d}t        j                  t         t        g«      }t        t	        ||«      t        j                  t         t        g«      «       y )NrQ   )r    r!   r   r   r   r0   s      r%   Útest_spherical_in_inf_realz*TestSphericalIn.test_spherical_in_inf_real¦   s;   € àˆÜ�H‰H”s�dœC�[Ó!ˆÜœ Q¨Ó*¬B¯H©H´s°d¼C°[Ó,AÕBr'   c                 óÖ   — d}t        j                  t         dz   t        dz   t        dz  g«      }t        t	        ||«      t        j                  t         t        t
        g«      «       y )Nr,   r?   r@   )r    r!   r   r   r   r   r0   s      r%   Útest_spherical_in_inf_complexz-TestSphericalIn.test_spherical_in_inf_complex¬   sO   € ð ˆÜ�H‰H”s�d˜R‘i¤ r¡¬3°©:Ð6Ó7ˆÜœ Q¨Ó*¬B¯H©H´s°d¼CÄÐ5EÓ,FÕGr'   c                 óŒ   — t        j                  g d¢«      }d}t        t        ||«      t        j                  g d¢«      «       y rO   r‚   r0   s      r%   Útest_spherical_in_at_zeroz)TestSphericalIn.test_spherical_in_at_zero·   rU   r'   N)	rV   rW   rX   r€   rƒ   r…   r‡   r‰   r‹   rY   r'   r%   r}   r}   ‘   s$   „ 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_exactÀ   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   r0   s      r%   Ú!test_spherical_kn_recurrence_realz1TestSphericalKn.test_spherical_kn_recurrence_realÆ   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‘   r0   s      r%   Ú$test_spherical_kn_recurrence_complexz4TestSphericalKn.test_spherical_kn_recurrence_complexÏ   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 )NrQ   r   )r    r!   r   r   r   r0   s      r%   Útest_spherical_kn_inf_realz*TestSphericalKn.test_spherical_kn_inf_realØ   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   r0   s      r%   Útest_spherical_kn_inf_complexz-TestSphericalKn.test_spherical_kn_inf_complexÞ   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 rh   )r    r!   r   r   ri   rj   r   r0   s      r%   Útest_spherical_kn_at_zeroz)TestSphericalKn.test_spherical_kn_at_zeroç   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 rm   )r    r!   r   r   ri   rj   r   r0   s      r%   Ú!test_spherical_kn_at_zero_complexz1TestSphericalKn.test_spherical_kn_at_zero_complexí   s6   € ä�H‰HÒ*Ó+ˆØˆÜœ Q¨Ó*¬B¯G©G°A·G±G¼SÓ,AÕBr'   N)
rV   rW   rX   r�   r’   r”   r–   r˜   rš   rœ   rY   r'   r%   r�   r�   ¿   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zr1   r#   s    €€r%   ú<lambda>zBSphericalDerivativesTestCase.fundamental_theorem.<locals>.<lambda>ö   s   ø€ ¨T¯W©W°Q¸«]€ r'   )Úatol)r   r   Úf)r#   r1   ÚaÚbÚintegralÚ	tolerances   ``    r%   Úfundamental_theoremz0SphericalDerivativesTestCase.fundamental_theoremõ   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«   rJ   s    r%   Útest_fundamental_theorem_0z7SphericalDerivativesTestCase.test_fundamental_theorem_0û   s   € à× Ñ   C¨Õ.r'   c                 ó*   — | j                  ddd«       y )Nr,   ç      à?g333333ó?r®   rJ   s    r%   Útest_fundamental_theorem_7z7SphericalDerivativesTestCase.test_fundamental_theorem_7ÿ   s   € à× Ñ   C¨Õ-r'   N)	rV   rW   rX   r«   ÚpytestÚmarkÚslowr¯   r²   rY   r'   r%   rž   rž   ô   sC   „ ò(ð ‡[�[×Ññ/ó ð/ð ‡[�[×Ññ.ó ñ.r'   rž   c                   ó   — e Zd Zd„ Zd„ Zd„ Zy)ÚTestSphericalJnDerivativesc                 ó   — t        ||«      S r¡   ©r   ©r#   r1   r£   s      r%   r¦   zTestSphericalJnDerivatives.f  ó   € Ü˜A˜qÓ!Ð!r'   c                 ó   — t        ||d¬«      S ©NT©Ú
derivativer¹   rº   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   Tr¾   ©r   gUUUUUUÕ?r   r   r   r   r/   ©r#   r1   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)rV   rW   rX   r¦   r¢   rÆ   rY   r'   r%   r·   r·     s   „ ò"ò3ó8r'   r·   c                   ó   — e Zd Zd„ Zd„ Zy)ÚTestSphericalYnDerivativesc                 ó   — t        ||«      S r¡   ©r   rº   s      r%   r¦   zTestSphericalYnDerivatives.f  r»   r'   c                 ó   — t        ||d¬«      S r½   rÊ   rº   s      r%   r¢   zTestSphericalYnDerivatives.df  rÀ   r'   N©rV   rW   rX   r¦   r¢   rY   r'   r%   rÈ   rÈ     ó   „ ò"ó3r'   rÈ   c                   ó   — e Zd Zd„ Zd„ Zd„ Zy)ÚTestSphericalInDerivativesc                 ó   — t        ||«      S r¡   ©r   rº   s      r%   r¦   zTestSphericalInDerivatives.f  r»   r'   c                 ó   — t        ||d¬«      S r½   rÑ   rº   s      r%   r¢   zTestSphericalInDerivatives.df  rÀ   r'   c                 ó¨   — t        j                  g d¢«      }t        |dd¬«       t        t        |dd¬«      t        j                  g d¢«      «       y )NrÂ   r   Fr¾   TrÄ   )r    r!   r   r   rÅ   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)rV   rW   rX   r¦   r¢   rÔ   rY   r'   r%   rÏ   rÏ     s   „ ò"ò3ó8r'   rÏ   c                   ó   — e Zd Zd„ Zd„ Zy)ÚTestSphericalKnDerivativesc                 ó   — t        ||«      S r¡   ©r   rº   s      r%   r¦   zTestSphericalKnDerivatives.f(  r»   r'   c                 ó   — t        ||d¬«      S r½   rØ   rº   s      r%   r¢   zTestSphericalKnDerivatives.df+  rÀ   r'   NrÌ   rY   r'   r%   rÖ   rÖ   '  rÍ   r'   rÖ   c                   ó*   — e Zd Zd„ Zd„ Zd„ Zd„ Zd„ Zy)ÚTestSphericalOldc                 óp  — 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
«       t        |d   ||gd
«       y )N)r   r   çš™™™™™É?r   r+   Tr¾   ç      $@g±µA€\ð?gÐÉc‘"±?r-   )r    Úemptyr   r   r!   )r#   Úi1nr$   Úinp0Úinp1s        r%   Útest_sph_inzTestSphericalOld.test_sph_in3  sÒ   € ä�h‰h�u‹oˆØˆä   AÓ&ˆˆA‰ˆq‰	Ü   AÓ&ˆˆA‰ˆq‰	Ü   A°$Ô7ˆˆA‰ˆq‰	Ü   A°$Ô7ˆˆA‰ˆq‰	à�A‘�q‘	ˆØ�A‘�q‘	˜G c¨!¡f¨Q¡iÑ/Ñ/ˆÜ! # a¡&¬¯©Ð3HØ0Gð3Ió *JØJLô	Nä! # a¡&¨$¨t¨°RÕ8r'   c                 óˆ  — 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        |   |«       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        |   |«       y )
Ng      ð?)r   r   Tr¾   r+   r   r±   g      à¿)r    rß   r   r!   r	   r
   r   r   r   r   r   )r#   r$   Úsph_i0Úsph_i0_expectedÚsph_k0Úsph_k0_expecteds         r%   Útest_sph_in_kn_order0z&TestSphericalOld.test_sph_in_kn_order0C  s  € ØˆÜ—‘˜$“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!¤" V¡*¨oÔ>ä—‘˜$“ˆÜ   AÓ&ˆˆq‰	Ü   A°$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!¤" V¡*¨oÕ>r'   c                 óÂ  — 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«       t        |d   |||gd«       y )N©r   r   rÝ   r   r+   r   Tr¾   rÞ   r­   )gkGì~Éï?g¥Åk‡�ÿ°?g’)ËÜqÈe?r-   )r    rß   r   r   )r#   Ús1r$   Ús10Ús11Ús12s         r%   Útest_sph_jnzTestSphericalOld.test_sph_jnS  s  € Ü�X‰X�e‹_ˆØˆä  1Ó%ˆˆ1‰ˆa‰Ü  1Ó%ˆˆ1‰ˆa‰Ü  1Ó%ˆˆ1‰ˆa‰Ü  1°Ô6ˆˆ1‰ˆa‰Ü  1°Ô6ˆˆ1‰ˆa‰Ü  1°Ô6ˆˆ1‰ˆa‰à�!‰u�Q‰xˆiˆØ�‰e�A‰h�w˜r !™u Q™xÑ'Ñ'ˆØ�‰e�A‰h�w˜r !™u Q™xÑ'Ñ'ˆÜ! " Q¡%ò )@à@Bô	Dô 	" " Q¡%¨¨S°¨°bÕ9r'   c                 óÆ  — t        j                  d«      }d}t        d|«      |d   d<   t        d|«      |d   d<   t        d|«      |d   d<   t        d|d¬«      |d   d<   t        d|d¬«      |d   d<   t        d|d¬«      |d   d<   |d   d    }|d   d    d|d   d   z  z
  }|d   d    d	|d   d   z  z
  }t        |d   g d
¢d«       t        |d   |||gd«       y )Nrë   rÝ   r   r+   r   Tr¾   rÞ   r­   )gDT»—Ÿ¸@g3Ì±wJC@gè-ßuAI‚@r-   é	   )r    rß   r   r   )r#   Úknr$   Úkn0Úkn1Úkn2s         r%   Útest_sph_knzTestSphericalOld.test_sph_knf  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! " Q¡%ò )@à@Bô	Dô 	" " Q¡%¨¨S°¨°aÕ8r'   c                 óÜ   — t        dd«      }t        dd«      }t        |dd«       t        |dd«       t        dd«      dt        dd«      z  z
  dz  }t        ddd	¬
«      }t        ||d«       y )Nr   rÝ   r   g[_$´e˜wÀrQ   g&$Þð™Àr   r+   Tr¾   é   )r   r   )r#   Úsy1Úsy2ÚsphpyÚsy3s        r%   Útest_sph_ynzTestSphericalOld.test_sph_yny  sn   € Ü˜1˜cÓ"ˆÜ˜1˜cÓ"ˆÜ˜C 
¨1Ô-Ü˜C 
¨1Ô-Ü˜a Ó%¨¬,°q¸#Ó*>Ñ(>Ñ>ÀÑAˆÜ˜1˜c¨dÔ3ˆä˜C  aÕ(r'   N)rV   rW   rX   rã   ré   rð   r÷   rþ   rY   r'   r%   rÛ   rÛ   /  s   „ ò9ò ?ò :ò&9ó&)r'   rÛ   r¿   FTÚfunc                 ó  — t         j                  j                  d«      }d}|j                  dd|¬«      }|j	                  |¬«      } |||| ¬«      } |||dz   | ¬«      }t         j
                  j                  ||j                  «       y )Nl   ¢dnU×Y� é   r   rR   )Úsizer¾   r?   )r    ÚrandomÚdefault_rngÚintegersÚstandard_normalÚtestingr   Úreal)r¿   rÿ   Úrngr  r1   r£   ÚresÚrefs           r%   Útest_negative_real_gh14582r  „  s}   € ô �)‰)×
Ñ
Ð 3Ó
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-€CÜ‡J�J×Ñ˜s C§H¡HÕ-r'   )&Únumpyr    Únumpy.testingr   r   r   r   r³   r   r   r	   r
   r   r   r   r   r   Úscipy.specialr   r   r   r   Úscipy.integrater   r   r[   rp   r}   r�   rž   r·   rÈ   rÏ   rÖ   rÛ   r´   Úparametrizer  rY   r'   r%   ú<module>r     s  ðó ÷Ió Iã ß =× =Õ =ç PÓ PÝ  ÷6Jñ 6J÷r3Cñ 3C÷l%ñ %÷(+Jñ +J÷\2Cñ 2C÷j.ñ .ô 
8Ð!=ô 
8ô3Ð!=ô 3ô8Ð!=ô 8ô3Ð!=ô 3÷R)ñ R)ðj ‡�×Ñ˜¨¨t }Ó5Ø‡�×Ñ˜ ¨|Ø!-¨|ð!=ó >ñ	.ó>ó 6ñ	.r'   