ó
+»Ã[c           @   s  d  Z  d d l Z d d l Z d d l Z d d l Te d „ Z e d ƒ Z e d ƒ Z e	 d ƒ Z
 e	 d ƒ Z e	 d	 ƒ Z d
 „  Z d „  Z d „  Z d „  Z d „  Z d „  Z d „  Z d „  Z d „  Z d „  Z d „  Z d „  Z d „  Z d „  Z d „  Z d S(   s  
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

iÿÿÿÿN(   t   *c         C   sF   t  } | o! |  j j | j | ƒ } | o? |  j j | j | ƒ } | S(   N(   t   Truet   realt   aet   imag(   t   at   bt   epst   res(    (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   mpc_ae   s    i    i   t   snt   cnt   dnc         C   s   t  d |  ƒ S(   Nt   k(   t   qfrom(   R   (    (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   <lambda>#   s    c           C   s¡  d t  _ t d d d ƒ d k s' t ‚ t d d d ƒ d k sE t ‚ t d d d ƒ d k sc t ‚ t d d d ƒ d k s t ‚ t d d	 d ƒ j t d	 ƒ ƒ s¨ t ‚ t d
 d	 d ƒ j t d	 ƒ ƒ sÏ t ‚ t d d	 d ƒ j d ƒ sð t ‚ t d d	 d ƒ j t d	 ƒ ƒ st ‚ t d d	 d ƒ j t d	 ƒ ƒ s>t ‚ t d d	 d ƒ j d ƒ s_t ‚ t d d	 d ƒ j t	 d	 ƒ ƒ s†t ‚ t d d	 d ƒ j t d	 ƒ ƒ s­t ‚ t d d	 d ƒ j t d	 ƒ ƒ sÔt ‚ t d d	 d ƒ j t
 d	 ƒ ƒ sût ‚ t d d	 d ƒ j t d	 ƒ ƒ s"t ‚ t d d	 d ƒ j t d	 ƒ ƒ sIt ‚ t d d	 d ƒ j t d	 ƒ ƒ spt ‚ t d
 d	 d ƒ j t d	 ƒ ƒ s—t ‚ t d d	 d ƒ j t d	 ƒ ƒ s¾t ‚ t d d	 d ƒ j t d	 ƒ ƒ såt ‚ t d d	 d ƒ j t d	 ƒ ƒ st ‚ t d d	 d ƒ j t d	 ƒ ƒ s3t ‚ t d d	 d ƒ j t d	 ƒ ƒ sZt ‚ t d d	 d ƒ j t d	 ƒ ƒ st ‚ t d d	 d ƒ j d ƒ s¢t ‚ t d d	 d ƒ j t d	 ƒ ƒ sÉt ‚ t d d	 d ƒ j d ƒ sêt ‚ t d d	 d ƒ j t d	 ƒ ƒ st ‚ t d d	 d ƒ j d ƒ s2t ‚ t d
 d	 d ƒ j d ƒ sSt ‚ t d d	 d ƒ j d ƒ stt ‚ t d d	 d ƒ j d ƒ s•t ‚ t d d	 d ƒ j d ƒ s¶t ‚ t d d	 d ƒ j d ƒ s×t ‚ t d d	 d ƒ j d ƒ søt ‚ t d d	 d ƒ j d ƒ st ‚ t d d	 d ƒ j d ƒ s:t ‚ t d d	 d ƒ j d ƒ s[t ‚ t d d	 d ƒ j d  ƒ s|t ‚ t d d	 d ƒ j d! ƒ st ‚ d  S("   Ni   t   ssi    i   t   cct   ddt   nnR
   g      Ð?R   R   t   nst   nct   ndt   sct   sdt   cdt   cst   dct   dsg      à?g@p4ü(‚Ï?gTiÍ$íï?gý>x¤ò‚ï?gô(ÔÌæ?@gZx:Ç	‚ð?g Ï~?ð?gbUaåAÐ?g]`w73ÿÏ?g’Þòkï?g)– Ì@g
oüì†Að?g¡Óff @(   t   mpt   dpst   ellipfunt   AssertionErrorR   t   sint   cost   csct   sect   tant   cott   tanht   secht   cotht   cosht   sinht   csch(    (    (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_ellipfun%   sR    	''!''!''''''''''''''!'!'!!!!!!!!!!!c          C   sƒ  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
 ƒ d t d ƒ f 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 ƒ d t d ƒ f t d ƒ d t d ƒ f t d ƒ d t d ƒ f g
 } xC | D]; } | d } t t | ƒ ƒ }  |  j | d ƒ s7t ‚ q7Wd t  _ d  S(   Nid   i   i   i
   s   0.006584651553858370274473060i   s   0.01394285727531826872146409i   s   0.02227743615715350822901627i   s   0.03188334731336317755064299i   s   0.04321391826377224977441774i   s   0.05702025781460967637754953i   s   0.07468994353717944761143751i   s   0.09927369733882489703607378i	   s   0.1401731269542615524091055i    i   (   R   R   t   calculate_nomet   zeroR    t   mpft   sqrtR   (   t   qt   math1t   it   m(    (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_calculate_nomeS   s&    		
c             s/  d t  _ t ‰ ‰ xC t d d ƒ D]2 ‰  t ˆ  ˆ ˆ ƒ }  |  ˆ  d d k s# t ‚ q# WxS t t d ƒ g D]? ‰ x6 t d d ƒ D]% ‰  t j	 t
 ‡  ‡ ‡ f d †  ƒ q‚ Wql Wt d ‰ t d ‰ t d ƒ } t d ˆ ˆ ƒ } | j | ƒ sö t ‚ t d	 ƒ } t d ˆ ˆ ƒ } | j | ƒ s)t ‚ t d
 ƒ } t d ˆ ˆ ƒ } | j | ƒ s\t ‚ t d ƒ } t d ˆ ˆ ƒ } | j | ƒ st ‚ t } t d } x€ t d ƒ D]r } t t j ƒ  ƒ } t | ƒ ‰ t d | ˆ ƒ } | j d ƒ s÷t ‚ t d | ˆ ƒ } | j d ƒ s¬t ‚ q¬Wd t  _ d  S(   Ni   i   i   i   c              s   t  ˆ  ˆ ˆ ƒ S(   N(   t   jtheta(    (   t   nR2   t   z(    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyR   w   s    i
   i   s   0.1069552990104042681962096s   1.101385760258855791140606s   1.178319743354331061795905i   s   0.8219318954665153577314573i   i    i   (   R   R   R/   t   rangeR7   R    t   oneR0   t   pytestt   raisest
   ValueErrorR   t   pit   strt   random(   t   valueR   t   resultt   z1t   z2R4   t   qstring(    (   R8   R2   R9   s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_jthetam   s@    	
'


c             s  d t  _ t  j d 7_ t d ƒ d t d t d ƒ d t ‰  t  j d 8_ t d ƒ t d ƒ t }  t d d ˆ  ƒ } t  j d 7_ t d ƒ d t d t d ƒ d t ‰  t  j d 8_ t j t ‡  f d
 †  ƒ d t  _ d t d } t d ƒ d t d ƒ d  t ‰  t d ƒ t d ƒ t }  d t  _ t d | ˆ  ƒ } | j	 |  ƒ sat
 ‚ d t  _ d d t } d d t ‰  t d | ˆ  ƒ } d t  _ t d | ˆ  ƒ } | j	 | ƒ sÈt
 ‚ d t  _ d t } t t d ƒ } xi t d d ƒ D]X } d t  _ | d t d ƒ d | ‰  t d | ˆ  ƒ } d t  _ t d | ˆ  ƒ } qûW| j	 | ƒ slt
 ‚ d t  _ t d d d d ƒ j	 d ƒ s™t
 ‚ t d d d d ƒ j	 d ƒ s½t
 ‚ d t  _ t d d d d ƒ } | j	 d ƒ sðt
 ‚ t d d d d ƒ } | j	 d ƒ st
 ‚ d  S(!   Ni   i   i
   i   s   32.0031009628901652627099524264s   16.6153027998236087899308935624i   i   i   c              s   t  d d ˆ  ƒ S(   Ni   i   (   R7   (    (   R2   (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyR   °   s    id   I³§²Å–O i   ItQ~ôÄB s$   2.4439389177990737589761828991467471s$   0.5446453005688226915290954851851490iP   i   g      à?i   g      @g      Ð?i	   gîlÞ2<•@i2   g‹3må,òòÆs2   1359.048926806828939547859396600218966947753213803s4   -6148327726309051673317975084654262.4119215720343656i@B i€–˜ I €Æ¤~ I €Æ¤~ (   R   R   R0   R;   t   jR7   R<   R=   R>   R   R    t   expR:   (   R   RC   R9   t   r1t   r2t   q1R8   t   r(    (   R2   s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_jtheta_issue_79ž   sX    	*	*	"					
			$$	c    
      C   s–  d t  _ t t d ƒ }  xnt d ƒ D]`} t t j ƒ  ƒ } t | ƒ } t d t j ƒ  ƒ } t | ƒ } t d | | ƒ d t d t	 | ƒ d } t d | | ƒ d t d t	 | ƒ d } t d | | ƒ d t d t	 | ƒ d } | | | }	 |	 j
 d |  ƒ st ‚ t d	 t j ƒ  ƒ } t | ƒ } t d | | ƒ d t d t	 | ƒ d } t d | | ƒ d t d t	 | ƒ d } t d | | ƒ d t d t	 | ƒ d } | | | }	 |	 j
 d |  ƒ sÕt ‚ t d | | ƒ d t d t	 | ƒ d } t d | | ƒ d t d t	 | ƒ d } t d | | ƒ d t d t	 | ƒ d } | | | }	 |	 j
 d |  ƒ syt ‚ t d | | ƒ d t d t	 | ƒ d } t d | | ƒ d t d t	 | ƒ d } t d | | ƒ d t d t	 | ƒ d } | | | }	 |	 j
 d |  ƒ st ‚ t d t	 | ƒ d } t d t	 | ƒ d } t d t	 | ƒ d } | | | }	 |	 j
 d |  ƒ s% t ‚ q% Wd
 t  _ d S(   s   
    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.
    in   i   i
   i   i   i   i   i    id   i   N(   R   R   t   ldexpR   R:   R@   RA   R0   R7   R/   R   R    (
   t   eps1R4   RF   R2   t   zstringR9   t   term1t   term2t   term3t   equality(    (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_jtheta_identitiesÙ   sF    	************c          C   s`  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 sz t ‚ t d	 ƒ t d
 ƒ t } t d |  | ƒ } t | | ƒ s» t ‚ t d ƒ t d ƒ t } t d |  | ƒ } t | | ƒ sü t ‚ t d ƒ t d ƒ t } t d |  | ƒ } t | | ƒ s=t ‚ d t  _ t d ƒ d t d }  t d ƒ d t d } t  j d 7_ d d t d d | ƒ t d d | ƒ t d d | ƒ g } d t d |  | ƒ t d |  | ƒ t d |  | ƒ t d |  | ƒ 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_ x) | D]! } t | t d ƒ ƒ s.t ‚ q.Wd t  _ d  S(   Ni   i   i   i   i   i   s%   0.31618034835986160705729105731678285s%   0.07542013825835103435142515194358975s$   1.6530986428239765928634711417951828s$   0.2015344864707197230526742145361455i   s$   1.6520564411784228184326012700348340s$   0.1998129119671271328684690067401823s%   0.37619082382228348252047624089973824s%   0.15623022130983652972686227200681074id   i
   i    i   (	   R   R   R0   RH   R7   R	   R    t   dost   mpc(   R9   R2   R   RM   R   t   tt   x(    (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_jtheta_complex  sD    						9E;;;;)c    	         sÙ  d t  _ t d t d }  t d t d ‰ t d ƒ t d ƒ t } t d |  ˆ d ƒ } t | | ƒ sq t ‚ t d	 ƒ t d
 ƒ t } t d |  ˆ d ƒ } t | | ƒ sµ t ‚ t d ƒ t d ƒ t } t d |  ˆ d ƒ } t | | ƒ sù t ‚ t d ƒ t d ƒ t } t d |  ˆ d ƒ } t | | ƒ s=t ‚ x’ t d ƒ D]„ } t t	 j	 ƒ  t t	 j	 ƒ  d ‰ t d d ˆ d ƒ } t d d ˆ ƒ t d d ˆ ƒ t d d ˆ ƒ } | j
 | ƒ sJt ‚ qJWd t  _ x+t d t d f t d t d t d f t d t d t d f t d t d t d t d f g D]¿ \ ‰ }  x° d d d d g D]œ ‰  t ˆ  |  ˆ d ƒ } t ‡  ‡ f d †  |  d d ƒ} | j
 | ƒ s¶t ‚ t ˆ  |  ˆ d ƒ } t ‡  ‡ f d †  |  d d ƒ} | j
 | ƒ set ‚ qeWqFWt d ‰ t }  d g d } t d |  ˆ d ƒ t d |  ˆ d ƒ | d <x@ d d d g D]/ ‰  t ˆ  |  ˆ d ƒ t ˆ  |  ˆ ƒ | ˆ  <qbW| d | d | d | d } | j
 d ƒ sÌt ‚ d t  _ d  S(   Ni   i   i   i   i   s$   1.5555195883277196036090928995803201s%   0.02439761276895463494054149673076275i   s%   0.19825296689470982332701283509685662s%   0.46038135182282106983251742935250009i   s%   0.36492498415476212680896699407390026s%   0.57743812698666990209897034525640369s&   -0.38936892528126996010818803742007352s%   0.66549886179739128256269617407313625i   i
   i    i   c            s   t  ˆ  |  ˆ ƒ S(   N(   R7   (   t   zz(   R8   R2   (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyR   m  s    R8   c            s   t  ˆ  |  ˆ ƒ S(   N(   R7   (   R\   (   R8   R2   (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyR   p  s    i   (   R   R   R;   RH   R0   R7   R	   R    R:   RA   R   t   diffR/   (	   R9   R   RC   R4   R   R   RM   RJ   RU   (    (   R8   R2   s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_djthetaC  sV    					"2	-J!!
,-"c          C   s  d t  _ t t t ƒ }  |  t k s* t ‚ xV t d ƒ D]H } t t j ƒ  ƒ } t | ƒ } t t | ƒ } | j	 d ƒ s7 t ‚ q7 Wd t  _ t
 d } t d ƒ } t t
 d ƒ } t | | ƒ }  |  j	 | ƒ sÕ t ‚ t d ƒ } t | | ƒ }  |  j	 | ƒ st ‚ d t  _ d	 S(
   s;   
    Test some special cases of the sn(z, q) function.
    id   i
   i    i   s   0.09983341664682815230681420iœÿÿÿs   0.09981686718599080096451168i   N(   R   R   t   jsnR/   R    R:   R@   RA   R0   R   R;   RO   (   RC   R4   RF   R2   RU   t   argR   R5   (    (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_jsn~  s$    		
c          C   sÚ   d t  _ t t j ƒ  ƒ }  t |  ƒ } t t | ƒ } | j t ƒ sK t	 ‚ d t  _ t d } t
 t d ƒ } t d ƒ } t | | ƒ } | j | ƒ s t	 ‚ t d ƒ } t | | ƒ } | j | ƒ sÍ t	 ‚ d t  _ d S(	   s;   
    Test some special cases of the cn(z, q) function.
    id   i   i
   iœÿÿÿs   0.9950041652780257660955620s   0.9950058256237368748520459i   N(   R   R   R@   RA   R0   t   jcnR/   R   R;   R    RO   (   RF   R2   R   R`   R5   R   RC   (    (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_jcn«  s    		
c          C   s›   d t  _ t t j ƒ  ƒ }  t |  ƒ } t t | ƒ } | j t ƒ sK t	 ‚ d t  _ t d ƒ } t d } t | | ƒ } | j | ƒ sŽ t	 ‚ d t  _ d S(   s;   
    Test some special cases of the dn(z, q) function.
    id   i   s   0.9995017055025556219713297i
   i   N(
   R   R   R@   RA   R0   t   jdnR/   R   R;   R    (   t   mstringR5   R   R   R`   RC   (    (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_jdnÐ  s    		
c          C   s°  d t  _ d }  x t |  ƒ D] } t t j ƒ  ƒ } t | ƒ } t d t j ƒ  ƒ } t | ƒ } t | | ƒ d } t | | ƒ d } t | | } | j	 d ƒ s t
 ‚ q Wx± t |  ƒ D]£ } t t j ƒ  ƒ }	 t | ƒ }
 |
 j ƒ  } t d t j ƒ  ƒ } t | ƒ } | d t | |
 ƒ d } t | |
 ƒ d } t | | } | j	 d ƒ s¼ t
 ‚ q¼ Wx=t |  ƒ D]/} t t j ƒ  ƒ }	 t |	 ƒ }
 |
 j ƒ  } t t j ƒ  ƒ } t | ƒ } | d t | |
 ƒ d } d | d } t | |
 ƒ d } | | | } | j	 d ƒ st
 ‚ t | d ƒ } t | |
 ƒ } | j	 t ƒ sQt
 ‚ t | |
 ƒ } | j	 d ƒ sut
 ‚ |
 } t | t ƒ } | j	 t ƒ spt
 ‚ qpWd t  _ d S(	   sx   
    Tests the some of the jacobi elliptic function identities found
    on Mathworld. Haven't found in Abramowitz.
    id   i   i   i    i
   i   i   N(   R   R   R:   R@   RA   R0   R_   Rb   R;   R   R    R1   Rd   t   ellipkR/   (   t   NR4   RF   R2   RQ   R9   RR   RS   RU   Re   R5   R   RT   t   KRM   RB   (    (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_sn_cn_dn_identitiesç  sR    	c          C   s   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 sw t ‚ t d	 ƒ t d
 ƒ t }  t | | ƒ } t | |  ƒ sµ t ‚ t d ƒ t d ƒ t }  t | | ƒ } t | |  ƒ só t ‚ d t  _ d  S(   Ni   s!   0.2495674401066275492326652143537s"   0.12017344422863833381301051702823i   i   i   i   i   s!   0.9762691700944007312693721148331s!   0.0307203994181623243583169154824s%   0.99639490163039577560547478589753039s%   0.01346296520008176393432491077244994i   (	   R   R   R0   RH   R_   R	   R    Rb   Rd   (   R   t   uR5   RM   (    (    s9   lib/python2.7/site-packages/mpmath/tests/test_elliptic.pyt   test_sn_cn_dn_complex+  s     				c          C   s  d t  _ t d d d ƒ j d ƒ s* t ‚ t d d d ƒ j d ƒ sK t ‚ t t t d ƒ j d	 ƒ sm t ‚ t d t t ƒ j dA ƒ s t ‚ t d t d t ƒ j dB ƒ s´ t ‚ t d t t d t ƒ j dC ƒ sÞ t ‚ t d d d ƒ d k sü t ‚ t d d d ƒ j d ƒ st ‚ t d d d ƒ j d ƒ s>t ‚ t d d d ƒ j d ƒ s_t ‚ t d d d ƒ j d ƒ s€t ‚ t d d d ƒ j d ƒ s¡t ‚ t d d d ƒ j d ƒ sÂt ‚ d d dD }  } } t |  | | ƒ j dE ƒ s÷t ‚ t |  | | ƒ j dF ƒ st ‚ t | |  | ƒ j dG ƒ s9t ‚ t | | |  ƒ j dH ƒ sZt ‚ t | |  | ƒ j dI ƒ s{t ‚ t | | |  ƒ j dJ ƒ sœt ‚ x[d d d d d g D]D} | t  _ t d d d ƒ j d ƒ sât ‚ t d d d ƒ j d ƒ st ‚ t t t d ƒ j d ƒ s%t ‚ t t d t d ƒ j t d d ƒ ƒ sSt ‚ t d d d ƒ j d  ƒ stt ‚ t t t d ƒ j d! ƒ s–t ‚ t t d t d t ƒ j t d" d# ƒ ƒ sÈt ‚ t	 d d$ ƒ j t
 
ƒ sçt ‚ t	 d% d ƒ j t 
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