o
    à8Vaüu  ã                   @   sÜ  d dl mZmZmZmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZ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mZmZm Z  d dl!m"Z" d dl#m$Z$ d dl%m&Z&m'Z( d dl)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2 dd„ Z3d	d
„ Z4dd„ Z5dd„ Z6dd„ Z7dd„ Z8e$dd„ ƒZ9dd„ Z:dd„ Z;dd„ Z<dd„ Z=e$dd„ ƒZ>dd „ Z?d!d"„ Z@e$d#d$„ ƒZAe$d%d&„ ƒZBd'd(„ ZCd)d*„ ZDd+d,„ ZEd-d.„ ZFd/d0„ ZGd1d2„ ZHd3d4„ ZId5d6„ ZJd7d8„ ZKd9d:„ ZLd;d<„ ZMd=d>„ ZNd?d@„ ZOdAS )Bé    )ÚmeijergÚIÚSÚ	integrateÚIntegralÚooÚgammaÚcoshÚsincÚhyperexpandÚexpÚsimplifyÚsqrtÚpiÚerfÚerfcÚsinÚcosÚ	exp_polarÚ	polygammaÚhyperÚlogÚexpand_funcÚRational)Ú_rewrite_singleÚ	_rewrite1Úmeijerint_indefiniteÚ
_inflate_gÚ_create_lookup_tableÚmeijerint_definiteÚmeijerint_inversion)Údefault_sort_key)Úslow)Úverify_numericallyÚrandom_complex_number)	ÚxÚyÚaÚbÚcÚdÚsÚtÚzc                  C   s   dd„ } dd„ }| t dt ƒ | t d dt d ƒ | t d tt d   td t d ƒ |t d t  ƒ |t t ƒ dd„ }|tt  ƒtt ƒ t ƒ ttt ƒtt ƒ t ƒtdƒ dttƒ  d	ttd
dƒd	tddƒt	j
tddƒfdfdtd
dƒd	ffdtdt t ƒ t d  ƒfgdfksŽJ ‚d S )Nc                 S   sn   t ttgtg|gtg| ƒtƒ}|d usJ ‚t|d d d tƒs"J ‚|d d d j t¡||ffks5J ‚d S )Nr   é   )	r   r   r'   r(   r*   r%   Ú
isinstanceÚargumentZas_coeff_mul)Úexprr)   ÚmÚe© r4   úF/usr/lib/python3/dist-packages/sympy/integrals/tests/test_meijerint.pyr,      s   *ztest_rewrite_single.<locals>.tc                 S   s*   t ttgtgtgtg| ƒtƒd u sJ ‚d S ©N)r   r   r'   r(   r)   r*   r%   ©r1   r4   r4   r5   Útn   s   *ztest_rewrite_single.<locals>.tné   r.   c                 S   sP   ddl m}m}m} t| |ƒ}|dd„ |d D ƒŽ  ||¡}t|| |ƒs&J ‚d S )Nr   )ÚAddr   r   c                 S   s   g | ]
}|d  |d  ‘qS )r   r.   r4   )Ú.0Úresr4   r4   r5   Ú
<listcomp>!   s    z2test_rewrite_single.<locals>.u.<locals>.<listcomp>)Úsympyr:   r   r   r   Úreplacer#   )r1   r%   r:   r   r   Úrr3   r4   r4   r5   Úu   s   
ÿztest_rewrite_single.<locals>.ur   éÿÿÿÿé   é   )r9   r4   é@   éüÿÿÿT)r%   r&   r   r   r   r   r   r   r   r   ÚHalfr   r   )r,   r8   rA   r4   r4   r5   Útest_rewrite_single   s$   $&*ÿÿþÿrH   c                   C   sz   t td ttgtgtgtgtd ttd   ƒ d tƒdtd ddttgtgtgtgtd td  ƒfgdfks;J ‚d S )NrD   r.   é   r9   r   T)r   r%   r   r'   r(   r)   r*   r&   r4   r4   r4   r5   Útest_rewrite17   s   86ÿrJ   c                  C   s~   dd„ } | dt ƒ | dt ƒ | ddt  ƒ | dt d ƒ | dt tdƒ ƒ | t d t ƒ | dt tdƒ  dt td	ƒ  ƒ d S )
Nc                 S   s€   t tgtgtgtg|ƒ|  }ttƒ d ttƒ d t ttƒ ttƒ i}t|tƒ}|d us-J ‚t	| 
|¡| t¡ 
|¡tƒs>J ‚d S )Né
   )r   r'   r(   r)   r*   Úrandcplxr   r   r%   r#   ÚsubsÚdiff)ZfacÚargÚgrM   Zintegralr4   r4   r5   r,   =   s   ÿ
&z0test_meijerint_indefinite_numerically.<locals>.tr9   r.   rI   ú3/2rD   rC   z7/3)r%   r   ©r,   r4   r4   r5   Ú%test_meijerint_indefinite_numerically<   s   

&rS   c                  C   sL   t ttddƒ\} }| jr|du sJ ‚t ttttƒ\} }| jr"|du s$J ‚d S )Nr   T)r   r%   Zis_zeror   )Úvr(   r4   r4   r5   Útest_meijerint_definiteM   s   rU   c                     s´   t tƒ d ttƒ d t ttƒ ttƒ ttƒ d i‰ ‡ fdd„} | t gtggtgtggtdƒs0J ‚| t tgtggtgtggtdƒsBJ ‚| t gtggttgtggdtd  dƒsXJ ‚d S )NrK   c                    sD   ddl m} t| ||ƒ}|t||ƒŽ }t| ˆ ¡| ˆ ¡tdddS )Nr   )ÚMulgš™™™™™¹?gš™™™™™¹¿)r(   r*   )r>   rV   r   r   r#   rM   r%   )r'   r(   rO   ÚnrV   Zm1Zm2©rM   r4   r5   r,   X   s   ztest_inflate.<locals>.trD   r.   )r'   rL   r(   r   r)   r*   r&   r%   rR   r4   rX   r5   Útest_inflateT   s   ÿ"$0rY   c                  C   s   ddl m}  | ddd\}}}tt| d  ƒtt| d  ƒ }t|tdtfdd}t| ¡ ƒtdƒtt	ƒ t
tdƒ||  d ƒd t|d  d ||  |d d  ƒ  d	 ks^J ‚ttt| d  ƒtt| d  ƒ t|t ƒ tdtfdd}t|ƒtdƒtt	ƒ t
tdƒd| d|  |  d	 ƒd  t|d  |d  d| d|  | d d
  ƒ d	 ks»J ‚tttt| | | d  ƒtdtfddƒtt	ƒd dt
|| | ƒ  ksäJ ‚tttt| | | d  ƒtdtfddƒtt	ƒd dt
|| | ƒ  ksJ ‚d S )Nr   ©Úsymbolsza b cT©Úpositiver.   ©r   r9   rC   é   )r>   r[   r   r%   r   r   r   Úexpandr   r   r   )r[   r'   r(   r)   r@   r3   r4   r4   r5   Útest_recursived   s2   $
@ÿÿÿ@Hÿÿÿ,ÿ,ÿra   c               	   C   s.  ddl m} m}m} | ddd\}}}ttg g dgg || ƒtg g |d g| d g|d d ƒ |dtfƒjs:J ‚| ddd	}tt| tg g gdgg gtƒ tdtfƒt	|d
 ƒks]J ‚tt| tg g gdgg gtƒ tdtfddt	|d
 ƒks|J ‚t
tt| tg g gdgg gtƒ tdtfddtƒs˜J ‚tttƒtƒttƒks¥J ‚| ddd	\}}ttt| td|ƒd ƒ||d
  |d
  ksÆJ ‚ttd
 d tt ƒ tdtƒdk | ddd	\}}ttt| d|  d  ƒtdtƒ\}	}
t|	ƒttƒ| dt|d|  ƒ  ksJ ‚|
dksJ ‚tt| t ƒt|t ƒ tdtƒ\}	}t|	ƒd
||  ks3J ‚tttƒtt dƒtdƒdfksFJ ‚|tttƒtdtƒd ƒttƒd
 ks\J ‚|ttt ƒtdtƒd ƒd
ttt|tƒ ƒ ttƒ ƒ ks~J ‚tttd  ƒtt tƒttƒdfks”J ‚ttttƒ ƒtt tƒdks¦J ‚ttdt d d  ƒtt tƒttƒd dfksÂJ ‚tttdt d ƒ ƒtt tƒdksØJ ‚ttt| | d  d ƒtdt |d  ƒ tt tƒdksúJ ‚tttƒd tt tƒtdfksJ ‚ttt ƒttƒ tdtƒtjdfks#J ‚dd„ }tdƒD ]}ttt ƒttƒ t|  tdtfdd||ƒksIJ ‚q+tttt ƒtt| ƒ tdtfddƒtdƒt|td  ƒ d ksqJ ‚| dƒ\}}}ddl m}m} ttg g |d g| d gtd ƒtg g |d g| d gtd ƒ t|d
   tdtƒddd| d   t	d| d
 ƒ t	|d |d  | ƒ t	| d |d  | d
 ƒt	|d |d  | d
 ƒ t	|d |d  | d
 ƒ  |dd|d| ƒ d k d||d |d  | ƒk |d| ƒd
k ƒfksJ ‚ttt| ƒtt| ƒ tdtfddttt| ƒtt| ƒ tdtfƒksDJ ‚tttd  ƒttƒ tdtfddttƒtdtjƒ d  ¡ kshJ ‚ddl m} | ddd}tttt ƒt|  tddƒ||d
 tƒksŽJ ‚| ddd	}tdt | t|t ƒ tddƒttƒ| t	|d
 ƒ td|d tj |d d
 ffddtjftddƒff|d d  ƒ d dfksÙJ ‚| d!dd	\}}ttt| t| td  ƒ tt tfƒƒ|| d tj  d| d
  t	|d tj ƒ d ksJ ‚d S )"Nr   )r[   r`   rO   zs t muT©Úrealr.   rC   r+   r\   r9   r^   Fúa brD   )é   Tzsigma mu)r.   T)r9   Tc                 S   s(   ddt d    t | ¡ t d¡d|   S ©Nr9   r.   rB   )r%   rN   rM   )rW   r4   r4   r5   r<   °   s   (ztest_meijerint.<locals>.resé   za b s)ÚAndÚreéþÿÿÿr_   )Ú
lowergammarW   )ÚintegerÚalphar4   rB   re   za s) r>   r[   r`   rO   r   r   r   Úis_Piecewiser%   r   r/   r   r   r   r   r   r   r   r   r   Úabsr
   r   r   rG   Úrangerh   ri   r   r   rk   r   )r[   r`   rO   r+   r,   Úmur'   r(   ÚsigmaÚir)   Ú_r<   rW   rh   ri   rk   rm   r4   r4   r5   Útest_meijerintv   sÒ   $ÿþþ(
ÿ&ÿ
ÿ 
ÿþÿ$(.(&, 
ÿ,$ 
ÿ,.ÿ
ÿ&,(ÿ(
ÿ" ÿ
ÿÿ:8ÿÿBý
þ&"
ÿ$
ÿ
ÿ &
ÿ ÿÿÿ
ÿ*4ÿru   c                  C   sl  ddl m} m} tt| ttƒ| ttƒ t tdtfdddƒdt	t
td td   ƒ t
tt  tt   ks9J ‚tt| ttƒ| ttƒ t tdtfdddƒddt  ksXJ ‚ttt	tt ƒtd d ttj    tdtfdddd td t tt
ƒ ttjt ƒ  ƒ| ttƒksJ ‚tt| dtƒ tddt| dtƒ ks¤J ‚tt|dtƒ tddt|dtƒ ks¹J ‚t| dtƒtdd| dtƒ ksËJ ‚t| dtƒd t tdd| dtƒd | dtƒd   d ksìJ ‚t| dtƒd td  tddd	t | dtƒd  dt | dtƒd   d| dtƒ | dtƒ  | dtƒd t  ks*J ‚t| dtƒ| dtƒ tdd| dtƒd  d ksFJ ‚ttd | dtƒ | dtƒ tddtd | dtƒd  d ksiJ ‚t| dtƒ| dtƒ t tddt| dtƒd  t| dtƒd   | dtƒ| dtƒ  ks™J ‚t| dtd ƒt tdd| dtd ƒ d ks´J ‚d S )
Nr   ©ÚbesseljÚbesseliTÚnone©r   Úcondsr.   r9   r^   rj   )r>   rw   rx   r   r   r'   r-   r(   r   r   r   r%   r&   r   rG   r   r   rv   r4   r4   r5   Útest_besselà   s^   "ÿ.þ"ÿ
ÿ&ÿþ þý**$ ÿ*ÿÿ
ÿ
ÿ$
ÿ "ÿ
ÿÿr|   c                     s.  ddl m‰ m} m}m}m}m} ‡ fdd„}|dtd d  ƒ|tƒ|tƒ ks*J ‚|ttd d  ƒ|tƒ|tƒ ks>J ‚|t	t ƒt ƒ|td ƒksOJ ‚|d|dtd  ƒ ƒ| dtƒ|tƒ ksfJ ‚t
|tƒ|dtd  ƒ ttƒd u szJ ‚|t	td ƒƒd u s†J ‚t
t	td  ƒttƒd u s•J ‚d S )Nr   )Úpiecewise_foldrw   r   r   r   Ú	Heavisidec                    s   ˆ t | ttƒƒS r6   )r    r+   r,   ©Úf©r}   r4   r5   Úinv  s   ztest_inversion.<locals>.invr9   r.   )r>   r}   rw   r   r   r   r~   r+   r,   r   r    )rw   r   r   r   r~   r‚   r4   r   r5   Útest_inversion  s    ((".("rƒ   c                  C   sô   ddl m} m} | ddd}tt| ƒtdt|ƒ ttƒ ƒ }t|ttƒ}|j	r+J ‚| ddd}| 
||¡}t|ttƒ}|j	sBJ ‚|jd d | 
||¡ksQJ ‚|jd	 d
 sZJ ‚||ttd ƒ}|jd	 d |ksv|jd	 d |jksxJ ‚d S d S )Nr   )ÚSymbolÚInverseLaplaceTransformr'   Tr\   rj   r(   rb   rB   r9   )r>   r„   r…   r   r   r   r+   r    r,   rn   rM   ÚargsZas_integral)r„   r…   r'   ÚFr€   r(   Úf2ZILTr4   r4   r5   Ú!test_inversion_conditional_output   s   $

2r‰   c                  C   sÈ   ddl m} m} | ddd}| ddd}d	d
t  }| dƒ}tt|t ƒttƒjr+J ‚tt|t ƒttƒd u s9J ‚tt|t ƒttƒd u sGJ ‚tt|t ƒttƒ}|jsVJ ‚t	|j
d d |ƒsbJ ‚d S )Nr   )r„   Ú
DiracDeltar@   Trb   r)   F)Zextended_realr9   r.   r-   )r>   r„   rŠ   r   r    r   r+   r,   rn   r/   r†   )r„   rŠ   r@   r)   r'   r-   r€   r4   r4   r5   Ú%test_inversion_exp_real_nonreal_shift4  s   
r‹   c                  C   sb  ddl m} m} ddlm} ddlm} i }t|ƒ t| 	¡ ƒD ]Ž\}}t|t
dD ]ƒ\}}}	}
i }t|jƒ|g D ]}t|dƒrL|jrL|ddƒ||< q:| d	d
ƒ||< q:t|tƒs]||ƒ}dd„ |D ƒ}tdd„ |D ƒƒsoJ ‚|dd„ |D ƒŽ }|j|d|j|d}}tt|ƒt|ƒƒ}|dk rŸt|| ƒ ¡ dksžJ ‚q*t|| ƒ|  ¡ dks­J ‚q*q d S )Nr   )ÚuniformÚ	randrange)r:   )r-   )ÚkeyÚ
propertiesr9   rK   g      ø?g       @c                 S   s   g | ]\}}t |ƒ‘qS r4   )r   )r;   rt   rP   r4   r4   r5   r=   V  ó    z%test_lookup_table.<locals>.<listcomp>c                 s   s"    | ]}|j p| t¡ V  qd S r6   )rn   Úhasr   )r;   r%   r4   r4   r5   Ú	<genexpr>W  s   €  z$test_lookup_table.<locals>.<genexpr>c                 S   s   g | ]\}}|| ‘qS r4   r4   )r;   r€   r%   r4   r4   r5   r=   Z  r   rX   g»½×Ùß|Û=)ZrandomrŒ   r   r>   r:   Úsympy.integrals.meijerintr-   r   ÚsortedÚitemsr!   ÚlistZfree_symbolsÚhasattrr   r/   ÚallrW   Úminro   )rŒ   r   r:   Zz_dummyÚtablert   ÚlZformulaZtermsZcondZhintrM   ZaiZexpandedr'   r(   r@   r4   r4   r5   Útest_lookup_tableB  s0   
êÿrœ   c                  C   sú   ddl m} m} | tttd ƒtdd t¡dddttd ƒ ttddƒƒ d ttddƒƒ ks4J ‚tttd ƒtdddt ttd ƒ ttddƒƒ dttddƒƒ  dttddƒƒ |tddƒtd	 ƒ dt	t
ƒ ttddƒƒ   ks{J ‚d S )
Nr   ©Ú	powdenestrk   rD   Tr^   ©Zpolarr.   rI   rg   )r>   rž   rk   r   r   r%   rN   r   r   r   r   r   r4   r4   r5   Útest_branch_bugc  s   ÿ.ÿ2>ÿÿr    c                  C   sd   ddl m}  tttd ƒtddtdt ƒ ksJ ‚t| dtd ƒtdd| ddt ƒ ks0J ‚d S )Nr   ©rw   r9   Tr^   )r>   rw   r   r   r%   r   r¡   r4   r4   r5   Útest_linear_subsm  s   (0r¢   c            &         s.  ddl m‰m‰ ddlm} m}m}m‰ m}m	}m
} | ddd\‰}| ddd\‰}|d	dd‰d
d„ ‰dd„ ‰tˆˆˆˆƒˆt tfdddksKJ ‚tˆˆˆˆˆƒ ˆt tfddˆks`J ‚tˆd ˆˆˆˆƒ ˆt tfddˆd ˆd  ks}J ‚tˆd ˆˆˆˆƒ ˆt tfddˆd dˆ ˆd   ksžJ ‚tˆˆˆˆƒˆˆ||ƒ ˆt tfˆt tfdddks¼J ‚tˆˆˆˆˆƒ ˆˆ||ƒ ˆt tfˆt tfddˆksÜJ ‚tˆˆˆˆˆƒ ˆˆ||ƒ ˆt tfˆt tfdd|ksüJ ‚tˆˆ ˆˆˆˆƒ ˆˆ||ƒ ˆt tfˆt tfddˆ| ks!J ‚tˆˆ d ˆˆˆˆƒ ˆˆ||ƒ ˆt tfˆt tfdddˆ | ksJJ ‚tˆˆ d ˆˆˆˆƒ ˆˆ||ƒ ˆt tfˆt tfdddˆ | kssJ ‚tˆd ˆˆˆˆƒ ˆˆ||ƒ ˆt tfˆt tfdd}| |¡r™J ‚t|ƒˆd ˆd  ks¨J ‚tˆd ˆˆˆˆƒ ˆˆ||ƒ ˆt tfˆt tfdd|d |d  ksÑJ ‚tˆˆˆƒˆdtfdddksãJ ‚tˆˆˆˆƒ ˆdtfdddˆ ksùJ ‚tˆd ˆˆˆƒ ˆdtfdddˆd  ksJ ‚‡ ‡‡‡‡‡‡‡fdd„}	|	dƒdks)J ‚|	ˆˆ ƒˆˆ ks6J ‚|	ˆˆd  ƒˆd ˆ ˆd ˆ  ksMJ ‚ˆd dˆd   }
t|	ˆˆ d d ƒ|	ˆˆ d ƒd  ƒ|
ksrJ ‚t|	ˆˆ d d ƒ|	ˆˆ d ƒd  ƒ|
ksJ ‚t|	ˆˆ d ƒ|	ˆˆ ƒd  ƒ|
ks¤J ‚| ddd\}}ˆ|d  dˆ | |   t|| ƒ t|ƒ t|ƒ }t|ˆdtfdddksØJ ‚tˆ| ˆdtfddd}||d ƒ|d f||d  d|k fksüJ ‚tˆd | ˆdtfddd}|d d|d k ksJ ‚||d |d d  ƒ|| d | |d  |d d  ks9J ‚| ddd\}}ˆ|d  ˆ d |d   t|| ƒ t|ƒt|ƒ  }tt|ˆddfddƒdksoJ ‚ttˆ| ˆddfddƒ|||  ks†J ‚ttˆd | ˆddfddƒ||d  ||  || d  ks©J ‚ttˆˆ | ˆddfddƒt|| ƒt|ˆ ƒ t|ƒ t|| ˆ ƒ ksÔJ ‚|dddd}dd|d   ˆ|d   tˆd  d ƒ t|d ƒ }|t|ˆdtfddƒdks	J ‚ttˆ| ˆdtfddƒtdƒt|d d ƒ t|d ƒ ks,J ‚ttˆd | ˆdtfddƒ|ksAJ ‚d| d  t|d ƒ ˆ|d d   tˆ d ƒ }|t|ˆdtfddƒdksnJ ‚ttˆ| ˆdtfddƒ|ksJ ‚ttˆd | ˆdtfddƒ||d  ksšJ ‚|tˆ| td| ƒ d | ˆdtfddƒdtdƒ t|ƒ ks¿J ‚| ddd\}}}|| ˆ ˆ| ||   dˆ| ||   |d   }tt|ˆdtfddƒdksõJ ‚ˆ| }tt|ˆdtfdddƒ|| tdd|  ƒ t|d d|  ƒ || d t|ƒ  ks)J ‚ttˆ| ˆdtfdddƒ||d  tdd|  ƒ t|d d|  ƒ || d t|ƒ  ks]J ‚| ddd\}}t|ˆ | ||  |ˆ | ||   ƒˆ t|d ƒ t|d ƒ t|| d ƒ }tt|ˆdtfddƒdks¢J ‚ttˆ| ˆdtfdddƒ||d  ksºJ ‚ttˆd | ˆdtfdddƒ|d |d  | |d  |d  ksàJ ‚| ddd\}}t|d t ƒˆtd dƒ  t| ˆ| d  ˆ d |d  ƒ }d!d"„ }|t|ˆdtfƒƒdksJ ‚|tˆ| ˆdtfƒƒ|ks.J ‚|tˆ| d | ˆdtfƒƒ|d | ksGJ ‚|tˆ| d | ˆdtfƒƒd|d#  |d  ksdJ ‚|d$dd}tt|d t ƒt| d ˆ|  ƒ ˆ| td%ƒ  ˆ|tfƒdksJ ‚| ddd\}}|| ˆ|d   ||d   dˆ| ||   d  }tt|ˆdtfƒƒdksÃJ ‚ttˆ| ˆdtfdd&ƒt| | |t| ƒ ksàJ ‚ttˆˆ | ˆdtfdd&ƒt|ˆ  ˆ | |tˆ | ƒ ksJ ‚|ddd}|d'dd} || ˆ| |d   tˆ| |  ƒ }tt|ˆdtfƒƒdks5J ‚ttˆ|  | ˆdtfƒƒ||  td| |  ƒ ksRJ ‚dd(lm}! | d)dd\}"}#ˆ|#d  tˆd |"d   d |#d  ƒ |!dˆ|" |#d  ƒ }$t|$ˆdtfdddks‘J ‚|d*dd+}|d,dd}ttˆ| ƒ | ƒd | }%t|%ˆt tfdddks¼J ‚tˆ|% ˆt tfdd|ksÎJ ‚tˆd |% ˆt tfddd|d  |d  ksêJ ‚|ddd}|ˆ ttˆƒˆ|d   tˆ ƒ t|ƒ ˆdtfƒƒƒtd|ƒksJ ‚d S )-Nr   )r%   r&   )r[   r„   ÚAbsÚ
expand_mulÚ	gammasimpÚpowsimpr   zmu1 mu2T)Znonzerozsigma1 sigma2r\   Úlambdac                 S   s6   dt dt |d  ƒ t| | d  d |d  ƒ S ©Nr9   r.   )r   r   r   )r%   rq   rr   r4   r4   r5   Únormal|  s   6z test_probability.<locals>.normalc                 S   s   |t | |  ƒ S r6   )r   )r%   Úrater4   r4   r5   Úexponential  s   z%test_probability.<locals>.exponentialr^   r9   r.   rD   rB   c                    s€   t | ˆˆˆƒ ˆˆˆˆƒ ˆdtfˆt tfdd}t | ˆˆˆƒ ˆˆˆˆƒ ˆt tfˆdtfdd}ˆ |ƒˆ |ƒks>J ‚|S )Nr   Tr^   )r   r   )r1   Zres1Zres2©r¤   r«   Zmu1r©   rª   Zsigma1r%   r&   r4   r5   ÚE¥  s   ÿÿztest_probability.<locals>.Ez
alpha betaZseparaterz   rd   Úk)rl   r]   za b pry   zd1 d2rC   zlamda muéýÿÿÿc                 S   s   t |  t¡ƒS r6   )r   Úrewriter   r7   r4   r4   r5   Ú<lambda>ý  s    z"test_probability.<locals>.<lambda>rI   r)   rQ   )r{   rW   )rx   znu sigmarq   rb   r(   )Ú	sympy.abcr%   r&   r>   r[   r„   r£   r¤   r¥   r¦   r   r   r   r‘   r   r   r   r   r   r   r   rx   ro   r   r   )&r[   r„   r£   r¥   r¦   r   Zmu2Zsigma2rs   r­   Zansrm   ZbetaZbetadistÚjr'   r(   r®   ZchiZ
chisquaredÚpZdagumrO   Zd1Zd2r€   Zlamdarq   ZdistZmysimpr)   ZdistnrW   rx   Znurr   ZriceZlaplacer4   r¬   r5   Útest_probabilitys  sˆ  $& ÿ$ÿ$ÿÿÿÿÿÿÿ ÿ
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
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þ ÿ ÿ
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ÿ.66.(ÿÿ.$ÿ
ÿ:"
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ÿD $
ÿ*ÿÿrµ   c                  C   s  ddl m} m}m}m}m}m}m}m}m	}m
}	m}
m} t|ttt t ƒtt  tdtfddd | ¡jddƒƒ| ttƒksBJ ‚ttt t ƒt tdtfddd | ¡ ¡ | dtƒks`J ‚ttt t ƒtd  tdtfddd | ¡ ¡ | dtƒ |¡ | ¡ks†J ‚ttt t ƒtd	  tdtfddd | ¡ ¡ | d	tƒ |¡ | ¡ ¡ ks®J ‚|d
dd}t|tƒ t t|tfdd ¡ ||ƒksËJ ‚t|tƒ t t|tfdd ¡ ||ƒtd  ksæJ ‚t|tƒt tdtfdd|tƒksúJ ‚t|	tƒt tdtfdd|tƒksJ ‚ttt ƒt tdd ¡  | ¡tt | dtƒ ks,J ‚ttt ƒtd  tdd | ¡ ¡ | dtƒtt ƒt  tt  ksRJ ‚|ddd}t||ƒ| |dd ¡  |¡d ||ƒksqJ ‚t|
|ƒ| |dd ¡  |¡d ||ƒksŠJ ‚t| dtƒtdd | ¡ ¡ t| dtƒ tt ƒ ks¨J ‚t| dtƒtdd | ¡ ¡ td  | dtƒ d ttt ƒ d  tt ƒd  ksÖJ ‚t|t| ttƒtdd | ¡jddƒƒ| td tƒ ksöJ ‚t|tƒtddt|tƒ |tƒ ksJ ‚t||ƒ|dd ¡ |||ƒ ||ƒ ks$J ‚t|tƒtddt|tƒ |
tƒ ks:J ‚t||ƒ|dd ¡ |||ƒ |	|ƒ ksRJ ‚t|tƒtt ƒ tdtfddtd ksjJ ‚t| dtƒ|tƒ tdtfddtdƒd ks„J ‚dS )z% Test various exponential integrals. r   )ÚexpintÚ
unpolarifyr„   ÚCiÚSiÚShiÚChir   r   Úsinhr	   ÚEir9   Try   rz   )Úfuncr.   rD   r,   r\   r^   rA   rŸ   rC   N)r>   r¶   r·   r„   r¸   r¹   rº   r»   r   r   r¼   r	   r½   r   r   r   r-   r%   r&   r   r°   r`   r   r   Zas_independentr   )r¶   r·   r„   r¸   r¹   rº   r»   r   r   r¼   r	   r½   r,   rA   r4   r4   r5   Útest_expint8  s„   8"ÿ
þþÿ
þ ÿ
þ ÿ
þ. ÿ(* 
ÿ$
ÿ"
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6
þÿ
ÿ
þ,0,008r¿   c                  C   sv  ddl m} m}m}m}m}m}m}m}m	}m
}	m}
m}m}m}m} | |tƒttƒ|tƒ td  t ddfks:J ‚| |tƒttƒ|tƒt dtdkfksOJ ‚| |tƒttƒttd ƒtddtd   ƒ dt  dtdkfksrJ ‚| |ttƒttƒdd … d||td ƒtj tjk|td ƒd tjkƒfks›J ‚||dtƒt ttdd|dd	ttd td  ƒ dkfd|d
td  td  d ƒ dfƒtdkfksÑJ ‚t|tƒ|dtƒ tdtfddtd|dƒ ƒksìJ ‚t|tƒ|dtƒ tdtfddttj|dƒd  ƒksJ ‚tdt |dtd  ƒ tdd||	dt ƒ ttd ƒdkft|
dt ƒ dfƒks9J ‚d S )Nr   ©Úlaplace_transformr¹   rº   r»   ÚatanÚ	PiecewiseÚacothÚE1rw   ÚacoshÚasinrh   ri   Úfourier_transformr   r.   Tr9   rj   F)ZnocondsrC   rF   r^   )r>   rÁ   r¹   rº   r»   rÂ   rÃ   rÄ   rÅ   rw   rÆ   rÇ   rh   ri   rÈ   r   r%   r+   r   r   r'   r   rG   ZZeroro   r   r   r   rÀ   r4   r4   r5   Ú
test_messyn  s2   D0*0ÿ2ÿ "ÿÿÿ ÿ 
ÿ 2ÿrÉ   c                   C   sJ   t tt td  ƒtt tfddt ttƒ ttt d ƒ ks#J ‚d S )Nr.   Tr^   rC   )r   r   r   r%   r   r   r   r4   r4   r4   r5   Útest_issue_6122Ž  s   "ÿrÊ   c                  C   s>   dt  ttt   tddƒ  } t| t dd}| t¡rJ ‚d S )Nr9   rD   Tr^   )r%   r'   r(   r   r   r‘   r   )r1   Zantir4   r4   r5   Útest_issue_6252“  s   rË   c                   C   sD   t ttt ƒdtd   tt tfƒ ¡  t¡ttdƒ ks J ‚d S rf   )r   r   r   r%   r   r   r°   r   r4   r4   r4   r5   Útest_issue_6348›  s   .
ÿrÌ   c                  C   sh   ddl m} m} tttttd  d ƒtƒƒ| tƒksJ ‚tttttd  d ƒtƒƒ|tƒks2J ‚d S )Nr   ©ÚfresnelsÚfresnelcr.   )	r>   rÎ   rÏ   r   r   r   r   r%   r   rÍ   r4   r4   r5   Útest_fresnel   s   *.rÐ   c                   C   s   t ttt  tƒd u sJ ‚d S r6   )r   r%   r4   r4   r4   r5   Útest_issue_6860§  s   rÑ   c                  C   sr   t ttdt d ƒ tƒ ¡ } | tdt d ƒdtd  t d  d ks'J ‚|  ttjtj¡tddƒks7J ‚d S )Nr.   rD   rI   )	r   r%   r   ZtogetherZ_eval_intervalr   ZNegativeOneZOner   r   r4   r4   r5   Útest_issue_7337«  s   0$rÒ   c                   C   sh   t ttƒtt t ƒ tƒt d ttƒ t d tt ƒ  tt t ƒ d td d  ks2J ‚d S r¨   )r   r	   r%   r   r,   r4   r4   r4   r5   Útest_issue_8368±  s   0ÿÿ
ÿrÓ   c                  C   st   ddl m} m} tdttt d | d  ƒd  td|ftd|fƒdtd|d | d   ƒ |  d|   ks8J ‚d S )Nr   ©ÚhÚwr9   r.   rD   )r²   rÕ   rÖ   r   r   r&   r%   rÔ   r4   r4   r5   Útest_issue_10211¶  s   2&ÿr×   c                  C   sr   ddl m}  | ddd\}}tdttd |d  ƒd  t| |fƒd| |d t|d |d  ƒ  ks7J ‚d S )	Nr   rZ   zy LTr\   r9   r.   rD   )r>   r[   r   r   r%   )r[   r&   ÚLr4   r4   r5   Útest_issue_11806¼  s
   ("ÿrÙ   c                  C   s®   ddl m}  ddlm}m} t|d |d |d  d  |dd}d|d	  |d
  tdtd
dƒftddƒf|d tdt	 t
 ƒ |d  ƒ }|  ||  ¡ d	d¡sUJ ‚d S )Nr   )ÚRR)ÚRr@   r.   g      à?Tr^   gUUUUUUÕ?g      ð?rD   g      à¿rI   gê-™—q=)r>   rÚ   r²   rÛ   r@   r   r   r   r   r   r   ZalmosteqrW   )rÚ   rÛ   r@   r€   rP   r4   r4   r5   Útest_issue_10681Â  s   &*ÿrÜ   c                  C   sB   ddl m}  | dddd}tdtd  tt|fƒd| ksJ ‚d S )	Nr   ©r„   r'   T)rc   r]   r9   r.   rB   )r>   r„   r   r%   r   )r„   r'   r4   r4   r5   Útest_issue_13536Ê  s   (rÞ   c                  C   sj   ddl m}  | dƒ}| dƒ}tt|| ƒ||  |dd |d¡ tt|d ƒ|d  |dd¡s3J ‚d S )Nr   rÝ   r%   rW   Tr^   r.   )r>   r„   r   r   rM   Zequals)r„   r%   rW   r4   r4   r5   Útest_issue_6462Ð  s   &ÿrß   N)Pr>   r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r“   r   r   r   r   r   r   r    Zsympy.utilitiesr!   Zsympy.testing.pytestr"   Zsympy.testing.randtestr#   r$   rL   r²   r%   r&   r'   r(   r)   r*   r+   r,   r-   rH   rJ   rS   rU   rY   ra   ru   r|   rƒ   r‰   r‹   rœ   r    r¢   rµ   r¿   rÉ   rÊ   rË   rÌ   rÐ   rÑ   rÒ   rÓ   r×   rÙ   rÜ   rÞ   rß   r4   r4   r4   r5   Ú<module>   sP   h $,)
i0
 

 E
5 