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    ZÊ¹jqf  ã                   @   sÔ   d Z ddlZddlZddlZddlT efdd„ZedƒZedƒZe	dƒZ
e	dƒZe	d	ƒZd
d„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zd d!„ Zd"d#„ Zd$d%„ Zd&d'„ ZdS )(a�  
Limited tests of the elliptic functions module.  A full suite of
extensive testing can be found in elliptic_torture_tests.py

Author of the first version: M.T. Taschuk

References:

[1] Abramowitz & Stegun. 'Handbook of Mathematical Functions, 9th Ed.',
    (Dover duplicate of 1972 edition)
[2] Whittaker 'A Course of Modern Analysis, 4th Ed.', 1946,
    Cambridge University Press

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   úY/var/www/html/bwave/python/venv/lib/python3.8/site-packages/mpmath/tests/test_elliptic.pyÚmpc_ae   s    r   é   ÚsnÚcnÚdnc                 C   s
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d	dƒ d¡�s
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   r   Útest_ellipfun%   sR    r/   c                  C   s  dt _ttƒ} | tkst‚dt _tdƒd tdƒftdƒd tdƒftdƒd td	ƒftd
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   z0.006584651553858370274473060é   z0.01394285727531826872146409é   z0.02227743615715350822901627é   z0.03188334731336317755064299é   z0.04321391826377224977441774é   z0.05702025781460967637754953é   z0.07468994353717944761143751é   z0.09927369733882489703607378é	   z0.1401731269542615524091055r   r   )r$   r%   Úcalculate_nomeÚzeror'   ÚmpfÚsqrtr   )ÚqZmath1ÚiÚmr
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ÿ$
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   r
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            rh   c                  C   s¼  dt _tdƒd td  } tdƒd td  }tdƒtdƒt  }td| |ƒ}t||ƒs\t‚td	ƒtd
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   r
   r   Útest_jtheta_complex  sN    
ÿ
ÿ
ÿ
ÿ&.::::"ürm   c            	         sÐ  dt _td td  } td td  ‰tdƒtdƒt  }td| ˆdƒ}t||ƒsVt‚td	ƒtd
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|¡sît‚qîdt _td td ftd td  td ftd td td  ftd td  td td  ffD ]‚\‰} dD ]r‰ tˆ | ˆdƒ}t‡ ‡fdd„| dd�}| 
|¡�søt‚tˆ | ˆdƒ}t‡ ‡fdd„| dd�}| 
|¡�s¾t‚�q¾�q²td ‰t} dgd }td| ˆdƒtd| ˆdƒ |d< dD ]$‰ tˆ | ˆdƒtˆ | ˆƒ |ˆ < �qp|d |d  |d  |d  }| 
d¡�sÆt‚dt _d S )NrV   r8   r4   r9   r6   z$1.5555195883277196036090928995803201z%0.02439761276895463494054149673076275r   z%0.19825296689470982332701283509685662z%0.46038135182282106983251742935250009r3   z%0.36492498415476212680896699407390026z%0.57743812698666990209897034525640369z&-0.38936892528126996010818803742007352z%0.66549886179739128256269617407313625r5   r2   r   é   )r   r3   r4   r5   c                    s   t ˆ | ˆƒS rC   rD   ©Úzz©rG   r?   r
   r   r   m  r   ztest_djtheta.<locals>.<lambda>)rG   c                    s   t ˆ | ˆƒS rC   rD   ro   rq   r
   r   r   p  r   )r3   r4   r5   r   )r$   r%   rK   rZ   r=   rE   r   r'   rJ   rQ   r   Údiffr<   )	rH   r	   rS   r@   r   r   r_   r\   rg   r
   rq   r   Útest_djthetaC  sb    
ÿ
ÿ
ÿ
ÿ$$ ÿ
 " rs   c                  C   s¸   dt _tttƒ} | tkst‚tdƒD ]0}tt ¡ ƒ}t|ƒ}tt|ƒ}| 	d¡s$t‚q$dt _t
d }tdƒ}tt
dƒ}t||ƒ} |  	|¡sŽt‚tdƒ}t||ƒ} |  	|¡s®t‚dt _d	S )
z;
    Test some special cases of the sn(z, q) function.
    r0   r2   r   r1   z0.09983341664682815230681420éœÿÿÿz0.09981686718599080096451168r   N)r$   r%   Újsnr<   r'   rJ   rP   rQ   r=   r   rK   rb   )rS   r@   rT   r?   rg   Úargr	   rA   r
   r
   r   Útest_jsn~  s$    




rw   c                  C   s”   dt _tt ¡ ƒ} t| ƒ}tt|ƒ}| t¡s2t	‚dt _td }t
tdƒ}tdƒ}t||ƒ}| |¡sjt	‚tdƒ}t||ƒ}| |¡sŠt	‚dt _dS )	z;
    Test some special cases of the cn(z, q) function.
    r0   r1   r2   rt   z0.9950041652780257660955620z0.9950058256237368748520459r   N)r$   r%   rP   rQ   r=   Újcnr<   r   rK   r'   rb   )rT   r?   r   rv   rA   r	   rS   r
   r
   r   Útest_jcn«  s    



ry   c                  C   sj   dt _tt ¡ ƒ} t| ƒ}tt|ƒ}| t¡s2t	‚dt _tdƒ}td }t||ƒ}| |¡s`t	‚dt _dS )z;
    Test some special cases of the dn(z, q) function.
    r0   r1   z0.9995017055025556219713297r2   r   N)
r$   r%   rP   rQ   r=   Újdnr<   r   rK   r'   )ÚmstringrA   r   r	   rv   rS   r
   r
   r   Útest_jdnÐ  s    

r|   c                  C   sî  dt _d} t| ƒD ]f}tt ¡ ƒ}t|ƒ}tdt ¡  ƒ}t|ƒ}t||ƒd }t||ƒd }t| | }| 	d¡st
‚qt| ƒD ]v}tt ¡ ƒ}	t|ƒ}
|
 ¡ }tdt ¡  ƒ}t|ƒ}|d t||
ƒd  }t||
ƒd }t| | }| 	d¡s‚t
‚q‚t| ƒD ]à}tt ¡ ƒ}	t|	ƒ}
|
 ¡ }tt ¡ ƒ}t|ƒ}|d t||
ƒd  }d|d  }t||
ƒd }|| | }| 	d¡�s‚t
‚t|d ƒ}t||
ƒ}| 	t¡�s¨t
‚t||
ƒ}| 	d¡�sÂt
‚|
}t|tƒ}| 	t¡�st
‚�qdt _dS )	zx
    Tests the some of the jacobi elliptic function identities found
    on Mathworld. Haven't found in Abramowitz.
    r0   r6   r3   r   r2   r   r   N)r$   r%   rJ   rP   rQ   r=   ru   rx   rK   r   r'   r>   rz   Zellipkr<   )ÚNr@   rT   r?   rc   rH   rd   re   rg   r{   rA   r   rf   ÚKr_   rR   r
   r
   r   Útest_sn_cn_dn_identitiesç  sR    


r   c                  C   s¼   dt _tdƒtdƒt  } tdƒd td  }tdƒd td  }t||ƒ}t|| ƒsZt‚td	ƒtd
ƒt  } t||ƒ}t|| ƒs†t‚tdƒtdƒt  } t||ƒ}t|| ƒs²t‚dt _d S )NrV   z!0.2495674401066275492326652143537z"0.12017344422863833381301051702823r   r5   r9   r4   r8   z!0.9762691700944007312693721148331z!0.0307203994181623243583169154824z%0.99639490163039577560547478589753039z%0.01346296520008176393432491077244994r   )	r$   r%   r=   rZ   ru   r   r'   rx   rz   )r	   ÚurA   r_   r
   r
   r   Útest_sn_cn_dn_complex+  s&    
ÿ

ÿ

ÿ
r�   c                  C   sˆ  dt _tdddƒ d¡st‚tdddƒ d¡s2t‚ttt dƒ d	¡sJt‚tdtt ƒ d
¡sbt‚tdtd tƒ d¡s|t‚tdt t dt ƒ d¡sœt‚tdddƒdks°t‚tdddƒ d¡sÆt‚tdddƒ d¡sÜt‚tdddƒ d¡sòt‚tdddƒ d¡�s
t‚tdddƒ d¡�s"t‚tdddƒ d¡�s:t‚d\} }}t| ||ƒ d¡�s\t‚t| ||ƒ d¡�stt‚t|| |ƒ d¡�sŒt‚t||| ƒ d¡�s¤t‚t|| |ƒ d¡�s¼t‚t||| ƒ d¡�sÔt‚dD �]4}|t _tdddƒ d¡�süt‚tdddƒ d¡�st‚ttt dƒ d¡�s.t‚ttd tdƒ tddƒ¡�sPt‚tdddƒ d¡�sht‚ttt dƒ d¡�s‚t‚ttd tdt ƒ tddƒ¡�s¨t‚t	ddƒ t

 ¡�sÀt‚t	ddƒ t
 ¡�sØt‚t	dtƒ tdd ƒ¡�sôt‚t	t tƒ td!d"ƒ¡�st‚t	ddƒ td ¡�s,t‚t	tdƒ td#d$ƒ¡�sHt‚tddddƒ d%¡�sbt‚tdddd&ƒ d'¡�s|t‚tddddt ƒ td(d)ƒ¡�s t‚ttt ddƒ d*¡�s¼t‚tdt dt ddƒ d+¡�sÞt‚ttt ddt ƒ td,d-ƒ¡�st‚tdt dt dd.t ƒ td/d0ƒ¡�s0t‚tdt dt t dt ƒ td1d2ƒ¡�s^t‚tdddƒ t

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