U
    9%eqf                     @   s   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ZedZe	dZ
e	dZe	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&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

    N)*c                 C   s0   d}|o| j |j |}|o*| j|j|}|S )NT)realaeimag)abepsres r
   Y/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/mpmath/tests/test_elliptic.pympc_ae   s    r      sncndnc                 C   s
   t | dS )Nk)qfromr   r
   r
   r   <lambda>#       r   c                   C   s  dt _tddddksttddddks.ttddddksBttddddksVttdd	dtd	spttd
d	dtd	sttdd	ddsttdd	dtd	sttdd	dtd	sttdd	ddsttdd	dt	d	sttdd	dtd	s"ttdd	dtd	s>ttdd	dt
d	sZttdd	dtd	svttdd	dtd	sttdd	dtd	sttd
d	dtd	sttdd	dtd	sttdd	dtd	sttdd	dtd	sttdd	dtd	s:ttdd	dtd	sVttdd	dtd	srttdd	ddsttdd	dtd	sttdd	ddsttdd	dtd	sttdd	ddsttd
d	dds
ttdd	dds"ttdd	dds:ttdd	ddsRttdd	ddsjttdd	ddsttdd	ddsttdd	ddsttdd	ddsttdd	dd sttdd	dd!std S )"N   ssr   r   ccddnnr         ?r   r   nsncndscsdcdcsZdcZds      ?g@p4(?gTi$?g>x?g(?@gZx:	?g~??gbUaA?g]`w73?gk?g) @g
oA?gff @)mpdpsellipfunAssertionErrorr   sincosZcscsectanZcottanhZsechZcothcoshsinhZcschr
   r
   r
   r   test_ellipfun%   sR    r/   c                  C   s  dt _tt} | tkstdt _tdd tdftdd tdftdd td	ftd
d tdftdd tdftdd tdftdd tdftdd tdftdd tdftdd tdfg
}|D ]*}|d }tt|} | |d stqdt _d S )Nd      r   
   z0.006584651553858370274473060   z0.01394285727531826872146409   z0.02227743615715350822901627   z0.03188334731336317755064299   z0.04321391826377224977441774   z0.05702025781460967637754953   z0.07468994353717944761143751   z0.09927369733882489703607378	   z0.1401731269542615524091055r   r   )r$   r%   calculate_nomezeror'   mpfsqrtr   )qZmath1imr
   r
   r   test_calculate_nomeS   s(    rB   c                     s  dt _t tddD ]$ t } |  d d kstqttdfD ],tddD ] t	t
 fdd qXqJtd td td	}td}||sttd
}td}||sttd}td}||sttd}td}||stt}td }tdD ]R}tt }t|td|}|dsZttd|}|ds&tq&dt _d S )Nr1   r   r6   r3   c                      s   t  S Njthetar
   nr?   zr
   r   r   w   r   ztest_jtheta.<locals>.<lambda>r2      z0.1069552990104042681962096z1.101385760258855791140606z1.178319743354331061795905r4   z0.8219318954665153577314573r5   r   r   )r$   r%   r<   rangerE   r'   oner=   pytestraises
ValueErrorr   pistrrandom)valuer	   resultZz1Zz2r@   qstringr
   rF   r   test_jthetam   s@    rU   c                     sb  dt _t  jd7  _tdd td  tdd t   t  jd8  _tdtdt  } tdd	 }t  jd7  _tdd td
  tdd t   t  jd8  _tt fdd dt _d	t d }tdd tdd t   tdtdt  } dt _td	| }|	| st
dt _ddt  }ddt   td	| }dt _td	| }|	|sjt
dt _dt }ttd }td	dD ]B}dt _|d	td	d|     td	| }dt _td	| }q|	|st
dt _tdddd	dst
tdddd	dst
dt _tdddd}|	ds@t
tdddd}|	ds^t
d S ) N   r7   r2   i@B r9   z32.0031009628901652627099524264z16.6153027998236087899308935624r4   r   i c                      s   t dd S )Nr4   r   rD   r
   r?   r
   r   r      r   z&test_jtheta_issue_79.<locals>.<lambda>r0   l   'e[>
 l     I5 l   tQh z$2.4439389177990737589761828991467471z$0.5446453005688226915290954851851490P   r5   r#   r   r3   g      @r   r:   gl2<@2   g3m,z21359.048926806828939547859396600218966947753213803z4-6148327726309051673317975084654262.4119215720343656)r$   r%   r=   rK   jrE   rL   rM   rN   r   r'   exprJ   )r	   rS   rH   r1r2q1rG   rr
   rW   r   test_jtheta_issue_79   s\    $
$
r`   c            
      C   s  dt _ttd} tdD ]}tt }t|}tdt  }t|}td||d tdt	|d  }td||d tdt	|d  }td||d tdt	|d  }|| | }	|	
d| sttd	t  }t|}td||d tdt	|d  }td||d tdt	|d  }td||d tdt	|d  }|| | }	|	
d| s\ttd||d tdt	|d  }td||d tdt	|d  }td||d tdt	|d  }|| | }	|	
d| sttd||d tdt	|d  }td||d tdt	|d  }td||d tdt	|d  }|| | }	|	
d| sXttdt	|d }tdt	|d }tdt	|d }|| | }	|	
d| stqd
t _dS )z
    Tests the some of the jacobi identidies found in Abramowitz,
    Sec. 16.28, Pg. 576. The identities are tested to 1 part in 10^98.
    n   rV   r2   r   r3   r5   r4   r   r0   r   N)r$   r%   ldexpr   rJ   rP   rQ   r=   rE   r<   r   r'   )
Zeps1r@   rT   r?   zstringrH   term1term2term3equalityr
   r
   r   test_jtheta_identities   sF    
            rh   c                  C   s  dt _tdd td  } tdd td  }tdtdt  }td| |}t||s\ttd	td
t  }td| |}t||sttdtdt  }td| |}t||sttdtdt  }td| |}t||stdt _tdd td  } tdd td  }t  jd7  _ddtdd|tdd|tdd|g}dtd| |td| |td| |td| |g}|d |d  d |d |d  d  |d |d  d  |d |d  d |d |d  d  |d |d  d  |d |d  d |d |d  d  |d |d  d  |d |d  d |d |d  d  |d |d  d  |d d |d d  |d d  g}t  jd8  _|D ]}t|tdstqdt _d S )NrV   r   r5   r9   r4   r8   z%0.31618034835986160705729105731678285z%0.07542013825835103435142515194358975z$1.6530986428239765928634711417951828z$0.2015344864707197230526742145361455r3   z$1.6520564411784228184326012700348340z$0.1998129119671271328684690067401823z%0.37619082382228348252047624089973824z%0.15623022130983652972686227200681074r0   r2   r   r   )	r$   r%   r=   rZ   rE   r   r'   dosmpc)rH   r?   r	   r_   r   txr
   r
   r   test_jtheta_complex  sN    



&.::::"rm   c            	         s  dt _td td  } td td  tdtdt  }td| d}t||sVttd	td
t  }td| d}t||sttdtdt  }td| d}t||sttdtdt  }td| d}t||sttdD ]`}tt		  tt		   d tddd}tddtdd tdd }|
|stqd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 | d}t fdd| dd}|
|stt | d}t fdd| dd}|
|stqqtd t} dgd }td| dtd| d |d< dD ]$ t | dt |  | < qp|d |d  |d  |d  }|
dstdt _d S )NrV   r8   r4   r9   r6   z$1.5555195883277196036090928995803201z%0.02439761276895463494054149673076275r   z%0.19825296689470982332701283509685662z%0.46038135182282106983251742935250009r3   z%0.36492498415476212680896699407390026z%0.57743812698666990209897034525640369z&-0.38936892528126996010818803742007352z%0.66549886179739128256269617407313625r5   r2   r      )r   r3   r4   r5   c                    s   t  | S rC   rD   zzrG   r?   r
   r   r   m  r   ztest_djtheta.<locals>.<lambda>)rG   c                    s   t  | S rC   rD   ro   rq   r
   r   r   p  r   )r3   r4   r5   r   )r$   r%   rK   rZ   r=   rE   r   r'   rJ   rQ   r   diffr<   )	rH   r	   rS   r@   r   r   r_   r\   rg   r
   rq   r   test_djthetaC  sb    



$$ 
 " rs   c                  C   s   dt _ttt} | tksttdD ]0}tt }t|}tt|}|	ds$tq$dt _t
d }td}tt
d}t||} | 	|sttd}t||} | 	|stdt _d	S )
z;
    Test some special cases of the sn(z, q) function.
    r0   r2   r   r1   z0.09983341664682815230681420z0.09981686718599080096451168r   N)r$   r%   jsnr<   r'   rJ   rP   rQ   r=   r   rK   rb   )rS   r@   rT   r?   rg   argr	   rA   r
   r
   r   test_jsn~  s$    




rw   c                  C   s   dt _tt } t| }tt|}|ts2t	dt _td }t
td}td}t||}||sjt	td}t||}||st	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$   r%   rP   rQ   r=   jcnr<   r   rK   r'   rb   )rT   r?   r   rv   rA   r	   rS   r
   r
   r   test_jcn  s    



ry   c                  C   sj   dt _tt } t| }tt|}|ts2t	dt _td}td }t||}||s`t	dt _dS )z;
    Test some special cases of the dn(z, q) function.
    r0   r1   z0.9995017055025556219713297r2   r   N)
r$   r%   rP   rQ   r=   jdnr<   r   rK   r'   )mstringrA   r   r	   rv   rS   r
   r
   r   test_jdn  s    

r|   c                  C   s  dt _d} t| D ]f}tt }t|}tdt  }t|}t||d }t||d }t| | }|	dst
qt| D ]v}tt }	t|}
|
 }tdt  }t|}|d t||
d  }t||
d }t| | }|	dst
qt| D ]}tt }	t|	}
|
 }tt }t|}|d t||
d  }d|d  }t||
d }|| | }|	dst
t|d }t||
}|	tst
t||
}|	dst
|
}t|t}|	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$   r%   rJ   rP   rQ   r=   ru   rx   rK   r   r'   r>   rz   Zellipkr<   )Nr@   rT   r?   rc   rH   rd   re   rg   r{   rA   r   rf   Kr_   rR   r
   r
   r   test_sn_cn_dn_identities  sR    


r   c                  C   s   dt _tdtdt  } tdd td  }tdd td  }t||}t|| sZttd	td
t  } t||}t|| sttdtdt  } t||}t|| stdt _d S )NrV   z!0.2495674401066275492326652143537z"0.12017344422863833381301051702823r   r5   r9   r4   r8   z!0.9762691700944007312693721148331z!0.0307203994181623243583169154824z%0.99639490163039577560547478589753039z%0.01346296520008176393432491077244994r   )	r$   r%   r=   rZ   ru   r   r'   rx   rz   )r	   urA   r_   r
   r
   r   test_sn_cn_dn_complex+  s&    





r   c                  C   s  dt _tddddsttdddds2tttt dd	sJttdtt d
sbttdtd tds|ttdt t dt dsttddddksttddddsttddddsttddddsttdddds
ttdddds"ttdddds:td\} }}t| ||ds\tt| ||dsttt|| |dstt||| dstt|| |dstt||| dstdD ]4}|t _tddddsttddddstttt dds.tttd tdtddsPttddddshtttt ddstttd tdt tddstt	ddt

 stt	ddt
 stt	dttdd stt	t ttd!d"stt	ddtd s,tt	tdtd#d$sHttddddd%sbttdddd&d's|ttddddt td(d)stttt ddd*sttdt dt ddd+stttt ddt td,d-sttdt dt dd.t td/d0s0ttdt dt t dt td1d2s^ttdddt

 sxttdddd3sttdtt d4stttd tdtd5d6sttt td ttd7d8sttdtd9dd:stqdt _td;d<d=d>jd?d@dAs4ttdBdCddDjdEd@dAsRttdFdGdHdIjdJd@dAspttdFdKdHdIjdLdMdAsttdFdNdHdIjdOd@dAsttdFdPdHdIjdQd@dAsttdFdRdHdIdSsttdFdTdHdIdUsttdVdWdXdYsttdZd[d\s,ttd]d^d_sBttd`dadbsXttd[dZdcsnttd[d`ddstd S )eNr   r   r3   r   g2e_?r4   r5   gi+"?gP$M?yfFU?6?@y,R<8*y#62?z   g{ I|`?)r   y              ?y            ?yafG?Etw\?)r6   r   rV   <   r0   zo1.3110287771460599052324197949455597068413774757158115814084108519003952935352071251151477664807145467230678763r#   zn1.854074677301371918433850347195260046217598823521766905585928045056021776838119978357271861650371897277771871zp0.79612586584233913293056938229563057846592264089185680214929401744498956943287031832657642790719940442165621412zp-1.2138566698364959864300942567386038975419875860741507618279563735753073152507112254567291141460317931258599889zp0.58408284167715170669284916892566789240351359699303216166309375305508295130412919665541330837704050454472379308zo1.0441445654064360931078658361850779139591660747973017593275012615517220315993723776182276555339288363064476126zp0.93912050218619371196624617169781141161485651998254431830645241993282941057500174238125105410055253623847335313zq-0.53296252018635269264859303449447908970360344322834582313172115220559316331271520508208025270300138589669326136r   g      @zo1.1107207345395915617539702475151734246536554223439225557713489017391086982748684776438317336911913093408525532zp-1.1107207345395915617539702475151734246536554223439225557713489017391086982748684776438317336911913093408525532zo1.2260849569072198222319655083097718755633725139745941606203839524036426936825652935738621522906572884239069297zq-0.34471136988767679699935618332997956653521218571295874986708834375026550946053920574015526038040124556716711353zp0.77778596920447389875196055840799837589537035343923012237628610795937014001905822029050288316217145443865649819zo0.1983248499342877364755170948292130095921681309577950696116251029742793455964385947473103628983664877025779304zp0.77688623778582332014190282640545501102298064276022952731669118325952563819813258230708177398475643634103990878r6   zp0.14297579667156753833233879421985774801466647854232626336218889885463800128817976132826443904216546421431528308zp0.13613945827770535203521374457913768360237593025944342652613569368333226052158214183059386307242563164036672709zq-0.38207561624427164249600936454845112611060375760094156571007648297226090050927156176977091273224510621553615189zo1.6490011662710884518243257224860232300246792717163891216346170272567376981346412066066050103935109581019055806zp0.94148358841220238083044612133767270187474673547917988681610772381758628963408843935027667916713866133196845063zo1.8260115229009316249372594065790946657011067182850435297162034335356430755397401849070610280860044610878657501zo1.2290661908643471500163617732957042849283739403009556715926326841959667290840290081010472716420690899886276961zq-0.61127970812028172123588152373622636829986597243716610650831553882054127570542477508023027578037045504958619422zp-1.0684038390006807880182112972232562745485871763154040245065581157751693730095703406209466903752930797510491155zo1.8249027393703805304622013339009022294368078659619988943515764258335975852685224202567854526307030593012768954zp-1.2218475784827035854568450371590419833166777535029296025352291308244564398645467465067845461070602841312456831zo1.7255030280692277601061148835701141842692457170470456590515892070736643637303053506944907685301315299153040991zp0.42360654239698954330324956174109581824072295516347109253028968632986700241706737986160014699730561497106114281zp0.44660591677018372656731970402124510811555212083508861036067729944477855594654762496407405328607219895053798354zp0.70768352357515390073102719507612395221369717586839400605901402910893345301718731499237159587077682267374159282zp0.36023392184473309033675652092928695596803358846377334894215349632203382573844427952830064383286995172598964266zp0.40348623401722113740956336997761033878615232917480045914551915169013722542827052849476969199578321834819903921z0.0796zo1.0284758090288040009838871385180217366569777284430590125081211090574701293154645750017813190805144572673802094y            y      $      y      $      y            $@y+͸q?3(?g:0yE>)Zabs_epsgn?y'1@mgQy9]տ9DBٿgQkw?yS%MbX9?gX9v?g>W[yf0č[Ꭳ5yS%MbX9yݶ#?,eĿgh㈵>yS%vq-?yv0ƾ=T󵱿yS% y?yg%Xd毿yS%vq-y9px?`?yS% yycr??^JY?y @Gz?yffffff@\(\?y      @{Gz?y8Y+}ڿ<@y       @      y       @      ?yRع?Y\ny       @      y      ?      ?y;=?>%yg       @y      ?      ?y=R?IOyRع?Y\n?yi2)G@L !'- @)r$   r%   Zelliprdr   r'   rZ   ZelliprgZelliprfrj   ZelliprcrO   Zln2Zelliprjr=   Zellippi)rl   yrH   rG   r
   r
   r   test_elliptic_integralsD  s     

"  r   c                   C   s   t ttdstd S )N)rA   )isnanr   nanr'   r
   r
   r
   r   test_issue_238  s    r   )__doc__ZmpmathrQ   rL   r   r   r=   r<   rK   r&   ru   rx   rz   r;   r/   rB   rU   r`   rh   rm   rs   rw   ry   r|   r   r   r   r   r
   r
   r
   r   <module>   s2   .1;=-;-%DY