o
    `^h~                    @   s  d dl Z d dlZd dlZd dlZd dl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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Zd dlm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) d dl*m)  m+Z, d dl-m.Z.m/Z/m0Z0 d dl-m1Z1m2Z2m3Z3m4Z4m5Z5 d dl-m6Z6 d d	l-m7Z7m8Z8m9Z9 d d
l-m:Z:m;Z;m<Z< d dl=m>Z>m?Z? d dl@mAZAmBZBmCZC d dlDmEZEmFZFmGZG d dlHmIZImJZJmKZK d dlLZLejdkseM d  dkrejNnejOZPG dd dZQG dd dZRG dd dZSG dd dZTG dd dZUG dd dZVG dd dZWG dd  d ZXG d!d" d"ZYG d#d$ d$ZZG d%d& d&Z[G d'd( d(Z\G d)d* d*Z]G d+d, d,Z^G d-d. d.Z_G d/d0 d0Z`G d1d2 d2Zadd3d4ZbG d5d6 d6ZcG d7d8 d8ZdG d9d: d:ZeG d;d< d<ZfG d=d> d>ZgG d?d@ d@ZhG dAdB dBZiG dCdD dDZjG dEdF dFZkG dGdH dHZlG dIdJ dJZmG dKdL dLZnG dMdN dNZoG dOdP dPZpG dQdR dRZqG dSdT dTZrG dUdV dVZsG dWdX dXZtG dYdZ dZZuG d[d\ d\Zvd]d^ Zwd_d` ZxG dadb dbZydcdd Zzdedf Z{dgdh Z|didj Z}dkdl Z~dmdn Zejdodp ZeIdqdr Zdsdt Zdudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zejjdd ZG dd dZG dd dZdS )    N)arrayisnanr_arangefinfopisincostanexplogzerossqrtasarrayinf
nan_to_numrealarctandoublearray_equal)raises)	assert_equalassert_almost_equalassert_array_equalassert_array_almost_equalassert_approx_equalassert_assert_allcloseassert_array_almost_equal_nulpsuppress_warnings)special)ellipeellipkellipkm1)elliprcelliprdelliprfelliprgelliprj)softplus)mathieu_odd_coefmathieu_even_coef	stirling2)lpnlpmnclpmn)np_longnp_ulong)xp_assert_closexp_assert_equalSCIPY_ARRAY_API)_FACTORIALK_LIMITS_64BITS_FACTORIALK_LIMITS_32BITS_is_subdtype)with_special_errorsassert_func_equalFuncDatawin3232bitc                   @   s  e Z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d  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Z d=d> Z!d?d@ Z"dAdB Z#dCdD Z$dEdF Z%dGdH Z&dIdJ Z'dKdL Z(dMdN Z)dOdP Z*dQdR Z+dSdT Z,dUdV Z-dWdX Z.dYdZ Z/e0j1j2d[d\d]d^ Z3d_d` Z4dadb Z5dcdd Z6e0j1j2ded\dfdg Z7dhdi Z8djdk Z9dldm Z:dndo Z;dpdq Z<drds Z=dtdu Z>dvdw Z?dxdy Z@dzd{ ZAd|d} ZBd~d ZCdd ZDdd ZEdd ZFdd ZGdd ZHdd ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQdd ZRdd ZSdd ZTdd ZUdd ZVdd ZWdd ZXdd ZYdd ZZdd Z[dd Z\dd Z]dd Z^dd Z_dd Z`dd Zadd Zbdd Zcdd ZdddÄ Zeddń ZfddǄ ZgddɄ Zhdd˄ Zidd̈́ Zjddτ Zkddф Zlddӄ ZmddՄ Znddׄ Zoddل Zpddۄ Zqdd݄ Zrdd߄ Zsdd Ztdd Zudd Zvdd Zwdd Zxdd Zydd Zzdd Z{dd Z|dd Z}dd Z~dd Zdd Zdd Zdd Zdd Zd d Ze0j1j2dd\dd Ze0j1j2dd\dd Ze0j1j2dd\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$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Zd=d> Zd?d@ ZdAdB ZdCdD ZdEdF ZdGdH ZdIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZdSdT ZdUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr ZdsS (t  
TestCephesc                 C      t d d S Nr   )cephesairyself rD   \/home/air/shanriGPT/back/venv/lib/python3.10/site-packages/scipy/special/tests/test_basic.py	test_airy@      zTestCephes.test_airyc                 C   r>   r?   )r@   airyerB   rD   rD   rE   
test_airyeC   rG   zTestCephes.test_airyec              	   C   s4  t g d}t g d}t t |d d d f |d d d f ddj}t g dg dg dg dg}ttj| |d	d
 t j	
d}t jt ddd|d d f }t dd}t t |d d d f |d d d f ddj}ttjt|d d df |d d df d |ddd d S )N)gL7A`?   g@   )   皙?   gffffff
@rL   )g޸g	TշJ?g	7?geLF)   g*+ @r   gM{@)gףp=
%@gϔ>@g<wg$@)   g,y3@iK  g5@vIh%<=rtol  i       r   f           ?绽|=atolrT   )npr   broadcast_arraysreshapeTr9   r@   binomravelrandomRandomStater   r   rand)rC   nknkrknownrngrD   rD   rE   
test_binomF   s,   (

$(
&
zTestCephes.test_binomc              	   C   s   t jd t jt ddd }t dd}t t |d d d f |d d d f ddj	}t
tjt|d d df |d d df d	 |d
d
d d S )NrU   rZ   ,     r   rY   rL   rO   r[   r\   r]   )r_   re   seedr   logspacer   r   r`   ra   rb   r9   r@   rc   )rC   rh   ri   rj   rD   rD   rE   test_binom_2]   s   (
&
zTestCephes.test_binom_2c              	   C   s   t jdd }t jd t dd}t dd}t t |d d d f |d d d f ddj}||d d df |d d df k }t	t
j||d d df |d d df |ddd	 d S )
Nc                 S   sP   t | } t |}d}d}td|d D ]}|||  | 9 }||9 }qt|| S NrZ   )intrangefloat)rh   ri   numdenirD   rD   rE   	binom_intk   s   
z.TestCephes.test_binom_exact.<locals>.binom_intrU   rZ      r   rL   rO   r]   )r_   	vectorizere   rp   r   r   r`   ra   rb   r9   r@   rc   )rC   rz   rh   ri   rj   rD   rD   rE   test_binom_exactj   s   

(
$ 
zTestCephes.test_binom_exactc                 C   s.   g d}t |}ttj|dddd  d S )N))rW   rX   gwP~)i  i  gii9~)i  i  gyhY~)i  i  gpvy~)i  i  gzN~)i  i  gGTɳ~)i  i  g@jH~)i  i  gF:aYͦ~)i  i  gɸV)i  i  g
{9)i  i  gyVxY)i    g*I y)i   i   gI)i  i  gW@N)i  i  g5y)r   rZ   rL   -q=rS   )r_   r   r:   r@   rc   check)rC   datasetrD   rD   rE   test_binom_nooverflow_8346   s   
z%TestCephes.test_binom_nooverflow_8346c                 C      t tdddd d S )NrZ         ?      ?)r   r@   bdtrrB   rD   rD   rE   	test_bdtr      zTestCephes.test_bdtrc                 C      t tdddd d S NrZ      r   )r   r@   bdtrirB   rD   rD   rE   
test_bdtri   r   zTestCephes.test_bdtric                 C   r   r   )r   r@   bdtrcrB   rD   rD   rE   
test_bdtrc   r   zTestCephes.test_bdtrcc                 C      t tdddd d S NrZ   r         @)r   r@   bdtrinrB   rD   rD   rE   test_bdtrin   r   zTestCephes.test_bdtrinc                 C      t ddd d S r   )r@   bdtrikrB   rD   rD   rE   test_bdtrik      zTestCephes.test_bdtrikc                 C      t tdd d S Nr           )r   r@   beirB   rD   rD   rE   test_bei      zTestCephes.test_beic                 C   r   r   )r   r@   beiprB   rD   rD   rE   	test_beip   r   zTestCephes.test_beipc                 C   r   Nr   r   )r   r@   berrB   rD   rD   rE   test_ber   r   zTestCephes.test_berc                 C   r   r   )r   r@   berprB   rD   rD   rE   	test_berp   r   zTestCephes.test_berpc                 C      t tdddd d S r   )r   r@   
besselpolyrB   rD   rD   rE   test_besselpoly   r   zTestCephes.test_besselpolyc                 C   r   NrZ   r   )r   r@   btdtriarB   rD   rD   rE   test_btdtria   r   zTestCephes.test_btdtriac                 C   r   r   )r   r@   btdtribrB   rD   rD   rE   test_btdtrib   r   zTestCephes.test_btdtribc                 C   r   NrZ   r   )r   r@   cbrtrB   rD   rD   rE   	test_cbrt   r   zTestCephes.test_cbrtc                 C      t tddd d S NrZ   r   r   )r   r@   chdtrrB   rD   rD   rE   
test_chdtr      zTestCephes.test_chdtrc                 C   r   NrZ   r   r   )r   r@   chdtrcrB   rD   rD   rE   test_chdtrc   r   zTestCephes.test_chdtrcc                 C      t tddd d S NrZ   r   )r   r@   chdtrirB   rD   rD   rE   test_chdtri   r   zTestCephes.test_chdtric                 C   r   )Nr   r   )r   r@   chdtrivrB   rD   rD   rE   test_chdtriv   r   zTestCephes.test_chdtrivc                 C   s8  t tdddd tg dg dg dg dg dg d	g d
g dg dg dg dg dg dg}t|d d df |d d df |d d df }t||d d df dd tttjtjdd ttddtjd tt	ttj
dd tt	tdtj
d tt	tddtj
 d S )Nr   rZ   r   )      9@      4@  gL94)r          @   g7Fh9)gMbP?r         D@ggåc;){Gz?r   r   g	;)r          @k   g8x@x>)g     6@r   r   gg1\>>)r   r   r   g`>)      @r   r   gp!P?)g     u@g     r@      $@g j
?)      Y@      +@r   g]?)g     @r   r   g4ۙ?)g     b@r   r   g?)g      d@r   r   r   rL   r   r   rS   r      )r   r@   chndtrr_   r   r   r   r   r   r   nan)rC   valuescdfrD   rD   rE   test_chndtr   s.   2zTestCephes.test_chndtrc                 C   r   Nr   rZ   r   )r   r@   	chndtridfrB   rD   rD   rE   test_chndtridf   r   zTestCephes.test_chndtridfc                 C   r   r   )r   r@   	chndtrincrB   rD   rD   rE   test_chndtrinc   r   zTestCephes.test_chndtrincc                 C   r   Nr   rZ   r   )r   r@   chndtrixrB   rD   rD   rE   test_chndtrix   r   zTestCephes.test_chndtrixc                 C   r   r   )r   r@   cosdgrB   rD   rD   rE   
test_cosdg   r   zTestCephes.test_cosdgc                 C   r   r   )r   r@   cosm1rB   rD   rD   rE   
test_cosm1   r   zTestCephes.test_cosm1c                 C   r   N-   r   )r   r@   cotdgrB   rD   rD   rE   
test_cotdg   r   zTestCephes.test_cotdgc                 C   s$   t tdd ttdd d S )Nr   r   gGz?gf?)r   r@   dawsnr   rB   rD   rD   rE   
test_dawsn   s   zTestCephes.test_dawsnc                 C   sV  g d}t dt j d t j}tt||ddd t dt j d t j}tt||ddd t dt j d	 t j}tt||ddd t	t d
rmt dt j d t j
}tt||ddd g d}t dt j d t j}tt||ddd t dt j dt j dt j }g d}tt|d|dd d S )N)rZ   r      rL   g-C6
?r   rN   decimal&.>r{   V瞯<float128r      )rL   rJ            皙?)gg?gsOB?gsaL?g
7I^ʿr   )r_   r   r   astypefloat32r   r    diricfloat64hasattrr   r   )rC   n_oddxn_evenoctave_resultrD   rD   rE   
test_diric   s    
 zTestCephes.test_diricc                 C   sH   t d}t g d}tt|d d t jf |j|j|jfk d S )Nr   )rZ   r   rN   )	r_   r   r   r   r    r   newaxisshapesize)rC   r   rh   rD   rD   rE   test_diric_broadcasting  s   
0z"TestCephes.test_diric_broadcastingc                 C   r   r   )r   r@   r!   rB   rD   rD   rE   test_ellipe  r   zTestCephes.test_ellipec                 C   r   r   )r   r@   	ellipeincrB   rD   rD   rE   test_ellipeinc  r   zTestCephes.test_ellipeincc                 C      t dd d S Nr   rZ   )r@   ellipjrB   rD   rD   rE   test_ellipj"     zTestCephes.test_ellipjc                 C   s   t tdtd  d S )Nr   rL   )r   r"   r   rB   rD   rD   rE   test_ellipk%  r   zTestCephes.test_ellipkc                 C   r   r   )r   r@   	ellipkincrB   rD   rD   rE   test_ellipkinc(  r   zTestCephes.test_ellipkincc                 C   r   r   r   r@   erfrB   rD   rD   rE   test_erf+  r   zTestCephes.test_erfc                 C   s$   d}t t|t|  d d S )Ng#8x@r   r  rC   r   rD   rD   rE   test_erf_symmetry.  s    zTestCephes.test_erf_symmetryc                 C   r   r   )r   r@   erfcrB   rD   rD   rE   	test_erfc2  r   zTestCephes.test_erfcc                 C   r   )NrL   r   )r   r@   exp10rB   rD   rD   rE   
test_exp105  r   zTestCephes.test_exp10c                 C   r   )NrL         @)r   r@   exp2rB   rD   rD   rE   	test_exp28  r   zTestCephes.test_exp2c                 C   sP   t tdd t ttjtj t ttj d t ttjtj d S )Nr   r   rO   )r   r@   expm1r_   r   r   rB   rD   rD   rE   
test_expm1;  s   zTestCephes.test_expm1c                 C   s  t j}t|dd t|ttjdttjd t|ttjdttjtj t|ttjdttj tj t|ttjdttj tj  t|ttjdttjtj  t|tdtjttjtj t|tdtjttjtj t|ttjtjttjtj t|ttj tjtdd t|ttj tjtdd t|ttjtjttjtj t|tdtjttjtj t|tdtjttjtj t|ttjdttjtj t|ttjtjttjtj d S )N                r   rZ   rL   rJ   r   rO   )r@   r  r   complexr_   r   r   )rC   r  rD   rD   rE   test_expm1_complexA  s"    "$"  "  "   &zTestCephes.test_expm1_complexz-The real part of expm1(z) bad at these pointsreasonc                 C   sh   t g d}t t | }|d|  }t g d}t|}t|j|jd t|j|jd d S )N)皙?r   333333?r      ro                 ?)y=Cw?yC7gg)gF<Ug?yQ<D*?yg:><sKy>񸣼$	Um>ly;Vl <@r   ro   )	r_   r   r   r	   r@   r  r   imagr   )rC   yr   zexpectedfoundrD   rD   rE   test_expm1_complex_hardT  s   
z"TestCephes.test_expm1_complex_hardc                 C   0   t tdddd ttdddddd	 d S )
NrZ   r   r   ư>r   
   g2?r   rS   )r   r@   fdtrr   rB   rD   rD   rE   	test_fdtri  s   
zTestCephes.test_fdtrc                 C   r$  )
NrZ   r   r   rL   r  g    _BgDIXl?r   rS   )r   r@   fdtrcr   rB   rD   rD   rE   
test_fdtrco  s   
zTestCephes.test_fdtrcc                 C   sD   t tddddgtddgdd d}t td	d|d
dd d S )NrZ   gV-?gx&1?g
}?g<zO'?r%  rS   g׀?r  r   r   )r   r@   fdtrir   )rC   prD   rD   rE   
test_fdtriv  s
   zTestCephes.test_fdtrizReturns nan on i686.c                 C   s   t tdddd d S )NrZ   r   )r   r@   r+  rB   rD   rD   rE   test_fdtri_mysterious_failure~  s   z(TestCephes.test_fdtri_mysterious_failurec                 C      t tdddd d S r   )r   r@   fdtridfdrB   rD   rD   rE   test_fdtridfd  r   zTestCephes.test_fdtridfdc                 C   r   Nr   r   r   )r   r@   fresnelrB   rD   rD   rE   test_fresnel  r   zTestCephes.test_fresnelc                 C   r   Nr         8@)r   r@   gammarB   rD   rD   rE   
test_gamma  r   zTestCephes.test_gammac                 C   r   )Nr   rZ   r   )r   r@   gammainccinvrB   rD   rD   rE   test_gammainccinv  r   zTestCephes.test_gammainccinvc                 C   r>   )Nr&  )r@   gammalnrB   rD   rD   rE   test_gammaln  rG   zTestCephes.test_gammalnc                 C   s^   t t j dddddddt jg	t j}t t jt jdd	d	ddddg	t j}tt|| d S )
N      gffffff       r   rZ   g@r   r   )r_   r   r   r   r   r   r@   gammasgn)rC   vals	referencerD   rD   rE   test_gammasgn  s   zTestCephes.test_gammasgnc                 C   r   r   )r   r@   gdtrrB   rD   rD   rE   	test_gdtr  r   zTestCephes.test_gdtrc                 C   s   t tddtjd d S r   )r   r@   rE  r_   r   rB   rD   rD   rE   test_gdtr_inf     zTestCephes.test_gdtr_infc                 C   r   r   )r   r@   gdtrcrB   rD   rD   rE   
test_gdtrc  r   zTestCephes.test_gdtrcc                 C   r/  r   )r   r@   gdtriarB   rD   rD   rE   test_gdtria  r   zTestCephes.test_gdtriac                 C   s   t ddd d S NrZ   r   )r@   gdtribrB   rD   rD   rE   test_gdtrib  r   zTestCephes.test_gdtribc                 C   s   t ddd d S NrZ   r  )r@   gdtrixrB   rD   rD   rE   test_gdtrix  r   zTestCephes.test_gdtrixc                 C      t dd d S rs   )r@   hankel1rB   rD   rD   rE   test_hankel1  r  zTestCephes.test_hankel1c                 C   rS  rs   )r@   hankel1erB   rD   rD   rE   test_hankel1e  r  zTestCephes.test_hankel1ec                 C   rS  rs   )r@   hankel2rB   rD   rD   rE   test_hankel2  r  zTestCephes.test_hankel2c                 C   rS  rs   )r@   hankel2erB   rD   rD   rE   test_hankel2e  r  zTestCephes.test_hankel2ec                 C   s>   t tdddtd t tdddd tddd d S )NrZ   r   r   rJ   g㈮?)r   r@   hyp1f1r   rB   rD   rD   rE   test_hyp1f1  s   zTestCephes.test_hyp1f1c                 C      t tddddd d S r   )r   r@   hyp2f1rB   rD   rD   rE   test_hyp2f1  rH  zTestCephes.test_hyp2f1c                 C   r   r   )r   r@   i0rB   rD   rD   rE   test_i0  r   zTestCephes.test_i0c                 C   r   r   )r   r@   i0erB   rD   rD   rE   test_i0e  r   zTestCephes.test_i0ec                 C   r   r   )r   r@   i1rB   rD   rD   rE   test_i1  r   zTestCephes.test_i1c                 C   r   r   )r   r@   i1erB   rD   rD   rE   test_i1e  r   zTestCephes.test_i1ec                 C   r>   rs   )r@   it2i0k0rB   rD   rD   rE   test_it2i0k0  rG   zTestCephes.test_it2i0k0c                 C   r>   rs   )r@   it2j0y0rB   rD   rD   rE   test_it2j0y0  rG   zTestCephes.test_it2j0y0c                 C   r>   rs   )r@   
it2struve0rB   rD   rD   rE   test_it2struve0  rG   zTestCephes.test_it2struve0c                 C   r>   rs   )r@   itairyrB   rD   rD   rE   test_itairy  rG   zTestCephes.test_itairyc                 C   r   r2  )r   r@   iti0k0rB   rD   rD   rE   test_iti0k0  r   zTestCephes.test_iti0k0c                 C   r   r2  )r   r@   itj0y0rB   rD   rD   rE   test_itj0y0  r   zTestCephes.test_itj0y0c                 C   r   r   )r   r@   itmodstruve0rB   rD   rD   rE   test_itmodstruve0  r   zTestCephes.test_itmodstruve0c                 C   r   r   )r   r@   	itstruve0rB   rD   rD   rE   test_itstruve0  r   zTestCephes.test_itstruve0c                 C   r   r   )r   r@   ivrB   rD   rD   rE   test_iv  r   zTestCephes.test_ivc                 C   r   r   )r   r@   iverB   rD   rD   rE   test_ive  r   zTestCephes.test_ivec                 C   r   r   )r   r@   j0rB   rD   rD   rE   test_j0  r   zTestCephes.test_j0c                 C   r   r   )r   r@   j1rB   rD   rD   rE   test_j1  r   zTestCephes.test_j1c                 C   r   r   )r   r@   jnrB   rD   rD   rE   test_jn  r   zTestCephes.test_jnc                 C   r   r   )r   r@   jvrB   rD   rD   rE   test_jv  r   zTestCephes.test_jvc                 C   r   r   )r   r@   jverB   rD   rD   rE   test_jve  r   zTestCephes.test_jvec                 C   r>   NrL   )r@   k0rB   rD   rD   rE   test_k0  rG   zTestCephes.test_k0c                 C   r>   r  )r@   k0erB   rD   rD   rE   test_k0e  rG   zTestCephes.test_k0ec                 C   r>   r  )r@   k1rB   rD   rD   rE   test_k1   rG   zTestCephes.test_k1c                 C   r>   r  )r@   k1erB   rD   rD   rE   test_k1e  rG   zTestCephes.test_k1ec                 C   r>   r  )r@   keirB   rD   rD   rE   test_kei  rG   zTestCephes.test_keic                 C   r   r   )r   r@   keiprB   rD   rD   rE   	test_keip	  r   zTestCephes.test_keipc                 C   r>   r  )r@   kerrB   rD   rD   rE   test_ker  rG   zTestCephes.test_kerc                 C   r>   r  )r@   kerprB   rD   rD   rE   	test_kerp  rG   zTestCephes.test_kerpc                 C   r>   r  )r@   kelvinrB   rD   rD   rE   test_kelvin  rG   zTestCephes.test_kelvinc                 C   rS  rs   )r@   knrB   rD   rD   rE   test_kn  r  zTestCephes.test_knc                 C   *   t tdd ttttj d S r   )r   r@   kolmogir   r_   r   r   rB   rD   rD   rE   test_kolmogi     zTestCephes.test_kolmogic                 C   r   r   )r   r@   
kolmogorovrB   rD   rD   rE   test_kolmogorov  r   zTestCephes.test_kolmogorovc                 C   r   )Nr   r@  )r   r@   _kolmogprB   rD   rD   rE   test_kolmogp  r   zTestCephes.test_kolmogpc                 C   r   r   )r   r@   _kolmogcrB   rD   rD   rE   test_kolmogc"  r   zTestCephes.test_kolmogcc                 C   r  r   )r   r@   	_kolmogcir   r_   r   r   rB   rD   rD   rE   test_kolmogci%  r  zTestCephes.test_kolmogcic                 C   rS  rs   )r@   kvrB   rD   rD   rE   test_kv)  r  zTestCephes.test_kvc                 C   rS  rs   )r@   kverB   rD   rD   rE   test_kve,  r  zTestCephes.test_kvec                 C   sL   t j}t|dd t|dtj  t|dtj t|tjtj d S )Nr   r   rO   )r@   log1pr   r_   r   r   )rC   r  rD   rD   rE   
test_log1p/  s
   zTestCephes.test_log1pc                 C   s  t j}t}t|dd t||dd|tj d t }|td t	||dtj|tjtj
d  t||dtj|tjtj t	||tj d|tjtj
 t||tjd|tjd t	||tj tj|tjdtj
 d  t	||tjtj|tjtj
d  t||tjtj|tjtj t||tj tj|tjtj t||tjtj|tjtj t||tjd|tjtj t||tjtj|tjtj W d    d S 1 sw   Y  d S )	Nr  rO   r   z%invalid value encountered in multiplyrZ   rL   r   rJ   )r@   r  r  r   r_   r   r   filterRuntimeWarningr   r   r   )rC   r  csuprD   rD   rE   test_log1p_complex6  s$   $ ",&"$" $"zTestCephes.test_log1p_complexc                 C   r   )Nr   rZ   r   )r   r@   lpmvrB   rD   rD   rE   	test_lpmvI  r   zTestCephes.test_lpmvc                 C   r   r   )r   r@   	mathieu_arB   rD   rD   rE   test_mathieu_aL  r   zTestCephes.test_mathieu_ac                 C   r   r   )r   r@   	mathieu_brB   rD   rD   rE   test_mathieu_bO  r   zTestCephes.test_mathieu_bc                 C   s   t tdddd tjdd }tdd}tjdtddd	f }tt|d d d f |d d d f d
d ||d d d f |d d d f d
ddd d S )NrZ   r   r   r   c                 S   s   |t jd 9 }| dkrddd| td|    S | dkr+t||d td|   S | dkrAtd| |td	| d
 d   S t| | |t| d | d	| d   t| d | d	| d      S )N   r   g;f?rZ   r   rL      r   rJ            ?)r_   r   r	   mqr   rD   rD   rE   	ce_smallqV  s   $Hz.TestCephes.test_mathieu_cem.<locals>.ce_smallqd   r&  rh|?+=rT   r^   )	r   r@   mathieu_cemr_   r|   r   r   rq   r   )rC   r  r  r  rD   rD   rE   test_mathieu_cemR  s   
*"
zTestCephes.test_mathieu_cemc                 C   s   t tdddd tjdd }tdd}tjdtddd	f }tt|d d d f |d d d f d
d ||d d d f |d d d f d
ddd d S )NrZ   r   r   r   c                 S   s   |t jd 9 }| dkrt||d td|   S | dkr-td| |td|  d  S t| | |t| d | d| d   t| d | d| d      S )Nr  rZ   r  r   rL   rJ   r  )r_   r   r   r  rD   rD   rE   	se_smallqo  s    Hz.TestCephes.test_mathieu_sem.<locals>.se_smallqr  r  r  r&  r  r  r  )	r   r@   mathieu_semr_   r|   r   r   rq   r   )rC   r  r  r  rD   rD   rE   test_mathieu_semk  s   
*"
zTestCephes.test_mathieu_semc                 C   r/  NrZ   r   r3  )r   r@   mathieu_modcem1rB   rD   rD   rE   test_mathieu_modcem1  r   zTestCephes.test_mathieu_modcem1c                 C   s   t ddd tddd d d d f }tjtddd d d d d f }tdddd d d d f }t ||| d }t ||dd  t ||dd  }t |||d  d| t |||d   }t||dd	 d S )
NrZ   r   rJ   r  rL   r&  rN   r\   rS   )	r@   mathieu_modcem2r_   r   r   rq   linspacer  r   rC   r  r  r   y1fry2rD   rD   rE   test_mathieu_modcem2  s   "&zTestCephes.test_mathieu_modcem2c                 C   r/  r  )r   r@   mathieu_modsem1rB   rD   rD   rE   test_mathieu_modsem1  r   zTestCephes.test_mathieu_modsem1c                 C   s   t ddd tddd d d d f }tjtddd d d d d f }tdddd d d d f }t ||| d }t ||dd t ||dd  }t |||d d| t |||d   }t||dd	 d S )
NrZ   rJ   r  rL   r&  r   rN   r\   rS   )	r@   mathieu_modsem2r_   r   r   rq   r  r  r   r  rD   rD   rE   test_mathieu_modsem2  s   "$zTestCephes.test_mathieu_modsem2c                 C   s   t tdddtjtjf t tdddtjtjf t tdddtjtjf t tdddtjtjf t tdddtjtjf t tdddtjtjf t tdddtjtjf t t	dddtjtjf d S )N'  r   g?      ?)
r   r@   r  r_   r   r  r  r  r  r  rB   rD   rD   rE   test_mathieu_overflow  s    z TestCephes.test_mathieu_overflowc                 C   sD   t dD ]}tddd}t|d ddd t|d	 d
dd qd S )N<   rL   r  rO   r   g.dS?r\   rS   rZ   gGc?-C6?)ru   r@   r  r   )rC   ri   vrD   rD   rE   test_mathieu_ticket_1847  s
   z#TestCephes.test_mathieu_ticket_1847c                 C   r>   r?   )r@   modfresnelmrB   rD   rD   rE   test_modfresnelm  rG   zTestCephes.test_modfresnelmc                 C   r>   r?   )r@   modfresnelprB   rD   rD   rE   test_modfresnelp  rG   zTestCephes.test_modfresnelpc                 C   r   r   )r   r@   	modstruverB   rD   rD   rE   test_modstruve  r   zTestCephes.test_modstruvec                 C   r   r   )r   r@   nbdtrrB   rD   rD   rE   
test_nbdtr  r   zTestCephes.test_nbdtrc                 C   r   r   )r   r@   nbdtrcrB   rD   rD   rE   test_nbdtrc  r   zTestCephes.test_nbdtrcc                 C   r   r   )r   r@   nbdtrirB   rD   rD   rE   test_nbdtri  r   zTestCephes.test_nbdtric                 C   r   )NrZ   rM   r   )r@   nbdtrikrB   rD   rD   rE   test_nbdtrik  r   zTestCephes.test_nbdtrikc                 C   r/  r   )r   r@   nbdtrinrB   rD   rD   rE   test_nbdtrin  r   zTestCephes.test_nbdtrinc                 C   r_  r   )r   r@   ncfdtrrB   rD   rD   rE   test_ncfdtr  rH  zTestCephes.test_ncfdtrc                 C   sH   t tddddd g d}tddd|}ttddd|| d S )NrZ   r   r   )r   rZ   r  rL   r   r  )r   r@   ncfdtrir  r   )rC   fr,  rD   rD   rE   test_ncfdtri  s   zTestCephes.test_ncfdtrizpncfdtr uses a Boost math implementation but ncfdtridfdinverts the less accurate cdflib implementation of ncfdtr.c                 C   s2   g d}t d|dd}tt d|dd| d S )NrZ   rL   r   rL   r  r{   )r@   r  r   
ncfdtridfd)rC   dfdr,  rD   rD   rE   test_ncfdtridfd     zTestCephes.test_ncfdtridfdzpncfdtr uses a Boost math implementation but ncfdtridfninverts the less accurate cdflib implementation of ncfdtr.c                 C   s6   g d}t |ddd}tt |ddd|dd d S )N)r  rZ   rL   r   g     @rL   r  r{   gh㈵>rS   )r@   r  r   
ncfdtridfn)rC   dfnr,  rD   rD   rE   test_ncfdtridfn  s   zTestCephes.test_ncfdtridfnzoncfdtr uses a Boost math implementation but ncfdtrincinverts the less accurate cdflib implementation of ncfdtr.c                 C   s2   g d}t dd|d}tt dd|d| d S )N)r   r  r   rL   r   r{   )r@   r  r   	ncfdtrinc)rC   ncr,  rD   rD   rE   test_ncfdtrinc  r  zTestCephes.test_ncfdtrincc                 C   s   t tdddd t tdddd tttjdddd	 tttd
tjd ttd
dtjd ttttjdd tttd
tjd tttd
dtj d S )NrZ   r   r   	   i   r   r   r   r   r   r   )	r   r@   nctdtrr   r_   r   r   r   r   rB   rD   rD   rE   test_nctdtr  s   zTestCephes.test_nctdtrc                 C   r   )NrZ   r   r   )r@   	nctdtridfrB   rD   rD   rE   test_nctdtridf  r   zTestCephes.test_nctdtridfc                 C   s   t ddd d S rM  )r@   	nctdtrincrB   rD   rD   rE   test_nctdtrinc
  r   zTestCephes.test_nctdtrincc                 C   r   )Nr  r   r   )r@   nctdtritrB   rD   rD   rE   test_nctdtrit  r   zTestCephes.test_nctdtritc                 C   r/  )Nr   rZ   r   )r   r@   nrdtrimnrB   rD   rD   rE   test_nrdtrimn  r   zTestCephes.test_nrdtrimnc                 C   s   t tddddddd d S )Nr   r   r   r]   )r   r@   nrdtrisdrB   rD   rD   rE   test_nrdtrisd  s   
zTestCephes.test_nrdtrisdc                 C      t dddd d S rM  )r@   obl_ang1rB   rD   rD   rE   test_obl_ang1  r   zTestCephes.test_obl_ang1c                 C   s2   t ddddd}t|d d t|d d d S )NrZ   r   r   r   )r@   obl_ang1_cvr   )rC   resultrD   rD   rE   test_obl_ang1_cv  s   zTestCephes.test_obl_ang1_cvc                 C   r   NrZ   r   r   )r   r@   obl_cvrB   rD   rD   rE   test_obl_cv  r   zTestCephes.test_obl_cvc                 C   r  rM  )r@   obl_rad1rB   rD   rD   rE   test_obl_rad1"  r   zTestCephes.test_obl_rad1c                 C      t ddddd d S rM  )r@   obl_rad1_cvrB   rD   rD   rE   test_obl_rad1_cv%  r   zTestCephes.test_obl_rad1_cvc                 C   r  rM  )r@   obl_rad2rB   rD   rD   rE   test_obl_rad2(  r   zTestCephes.test_obl_rad2c                 C   r  rM  )r@   obl_rad2_cvrB   rD   rD   rE   test_obl_rad2_cv+  r   zTestCephes.test_obl_rad2_cvc                 C   r   )NrZ   r   r  )r   r@   pbdvrB   rD   rD   rE   	test_pbdv.  r   zTestCephes.test_pbdvc                 C   r   rM  )r@   pbvvrB   rD   rD   rE   	test_pbvv1  r  zTestCephes.test_pbvvc                 C   r   rM  )r@   pbwarB   rD   rD   rE   	test_pbwa4  r  zTestCephes.test_pbwac                 C   s>   t dd}t|td t g dd}t|g d d S )Nr   rZ   rO   r   rZ   rL   )rZ   rZ   rZ   )r@   pdtrr   r_   r   r   rC   valrD   rD   rE   	test_pdtr7  s   zTestCephes.test_pdtrc                 C   sB   t dd}t|dtd  t g dd}t|g d d S )Nr   rZ   rO   r*  r   )r   r   r   )r@   pdtrcr   r_   r   r   r,  rD   rD   rE   
test_pdtrc>  s   zTestCephes.test_pdtrcc                 C   sD   t  }|td tdd W d    d S 1 sw   Y  d S )N-floating point number truncated to an integerr   )r   r  r  r@   pdtri)rC   r  rD   rD   rE   
test_pdtriE  s   "zTestCephes.test_pdtric                 C   sR   t dd}tt |d dd t dgdgdggg d}t|td d S )Nr   rZ   r   r  ffffff?)r   #B;r%  )r   r   )r@   pdtrikr   	gammainccr   r_   r   )rC   ri   rD   rD   rE   test_pdtrikJ  s   zTestCephes.test_pdtrikc                 C   r  rM  )r@   pro_ang1rB   rD   rD   rE   test_pro_ang1Q  r   zTestCephes.test_pro_ang1c                 C   s    t tdddddtd d S )NrZ   r   r  )r   r@   pro_ang1_cvr   rB   rD   rD   rE   test_pro_ang1_cvT  s   zTestCephes.test_pro_ang1_cvc                 C   r   r  )r   r@   pro_cvrB   rD   rD   rE   test_pro_cvX  r   zTestCephes.test_pro_cvc                 C   r  rP  )r@   pro_rad1rB   rD   rD   rE   test_pro_rad1[  r   zTestCephes.test_pro_rad1c                 C   r  rM  )r@   pro_rad1_cvrB   rD   rD   rE   test_pro_rad1_cv^  r   zTestCephes.test_pro_rad1_cvc                 C   r  rM  )r@   pro_rad2rB   rD   rD   rE   test_pro_rad2a  r   zTestCephes.test_pro_rad2c                 C   r  rM  )r@   pro_rad2_cvrB   rD   rD   rE   test_pro_rad2_cvd  r   zTestCephes.test_pro_rad2_cvc                 C   r>   rs   )r@   psirB   rD   rD   rE   test_psig  rG   zTestCephes.test_psic                 C   s   t tdddd d S r?   )r   r@   radianrB   rD   rD   rE   test_radianj  r   zTestCephes.test_radianc                 C   r   r   )r   r@   rgammarB   rD   rD   rE   test_rgammam  r   zTestCephes.test_rgammac                 C   sd   t tdd t tdd t tdd t tdd t td	d t td
d d S )N333333@r   333333      g@r  gg            @r?  )r   r@   roundrB   rD   rD   rE   
test_roundp  s   zTestCephes.test_roundc                 C   r>   rs   )r@   shichirB   rD   rD   rE   test_shichix  rG   zTestCephes.test_shichic                 C   sl   t d t tj\}}t|tjd  t|d t tj \}}t|tj d  tt|d d S )NrZ   r   r   z cosine integral(-inf) is not nan)r@   sicir_   r   r   r   r   r   )rC   sr  rD   rD   rE   	test_sici{  s   

zTestCephes.test_sicic                 C   r   NZ   r   )r   r@   sindgrB   rD   rD   rE   
test_sindg  r   zTestCephes.test_sindgc                 C   s.   t tddd tttdtj d S )NrZ   r  ?)r   r@   smirnovr   r_   r   r   rB   rD   rD   rE   test_smirnov  s   zTestCephes.test_smirnovc                 C   sR   t tddd t tddd t tddd tttdtj d S )	NrZ   r  rO   rL         ?      r   g      ȿ)r   r@   	_smirnovpr   r_   r   r   rB   rD   rD   rE   test_smirnovp  s   zTestCephes.test_smirnovpc                 C   s   t tddd tttdtj tjddddd}ttd|dt	d|  tjddddd}ttd	|dt	d	|  d S )
NrZ   r  r   r  Tendpointr   r   rJ   )
r   r@   	_smirnovcr   r_   r   r   r  r   r]  )rC   x10x4rD   rD   rE   test_smirnovc  s   "zTestCephes.test_smirnovcc                 C   P   t tdtddd t tdtddd tttdtj d S NrZ   rM   333333?)r   r@   r]  smirnovir   r_   r   r   rB   rD   rD   rE   test_smirnovi     zTestCephes.test_smirnovic                 C   ri  rj  )r   r@   re  
_smirnovcir   r_   r   r   rB   rD   rD   rE   test_smirnovci  rn  zTestCephes.test_smirnovcic                 C   r   r   )r   r@   spencerB   rD   rD   rE   test_spence  r   zTestCephes.test_spencec                 C   s:   t tddd ttddd ttddd d S )NrZ   r   r   r_  rL   gMoF?)r   r@   stdtrr   rB   rD   rD   rE   
test_stdtr     zTestCephes.test_stdtrc                 C   r   )Nffffff?rZ   )r@   stdtridfrB   rD   rD   rE   test_stdtridf  r  zTestCephes.test_stdtridfc                 C   r   )NrZ   rv  )r@   stdtritrB   rD   rD   rE   test_stdtrit  r  zTestCephes.test_stdtritc                 C   r   r   )r   r@   struverB   rD   rD   rE   test_struve  r   zTestCephes.test_struvec                 C   r   r   )r   r@   tandgrB   rD   rD   rE   
test_tandg  r   zTestCephes.test_tandgc                 C   r   r   )r   r@   tklmbdarB   rD   rD   rE   test_tklmbda  r   zTestCephes.test_tklmbdac                 C   r>   rs   )r@   y0rB   rD   rD   rE   test_y0  rG   zTestCephes.test_y0c                 C   r>   rs   )r@   r  rB   rD   rD   rE   test_y1  rG   zTestCephes.test_y1c                 C   rS  rs   )r@   ynrB   rD   rD   rE   test_yn  r  zTestCephes.test_ync                 C   rS  rs   )r@   yvrB   rD   rD   rE   test_yv  r  zTestCephes.test_yvc                 C   rS  rs   )r@   yverB   rD   rD   rE   test_yve  r  zTestCephes.test_yvec                 C   s  t ddt ddt ddt ddt dd	t dd
t ddt ddt ddt ddt ddt ddt ddt ddt ddt ddg}t ddt dd t d!d"t d#d$t d%d&t d'd(t d)d*t d+d,t d-d.t d/dt d0d1t d2d3t d4d5t d6d7t d8d9t d:d:g}ttj||d;d< d S )=Ng@g+п皙ٿr   rk  r   r   r   g      "g      "@g4׵/Yg8EGr?rO  gffffff@ig>@r   g|Pk?r  rZ   ir  r  i   ig     j@  ļBg0"bgpتO#M?gMF>?g5-g`?g	S+?g6U?gǗʿgjD{?/,Gg` 0Gg!^?gnF5o{gI\Y?g7f8goC9	?gyhgEbr?g{g.
?ga~gT-s?gɤ,P&?g|bgޗY3g!ؑ-@gi$bghgy(V@^gһ>g>gx\h<rR   rS   )r  r9   r@   wofz)rC   r   wrD   rD   rE   	test_wofz  sr   "zTestCephes.test_wofzN)__name__
__module____qualname__rF   rI   rm   rr   r}   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r	  r  r  r  r  r  r  pytestmarkxfailr#  r(  r*  r-  r.  r1  r5  r9  r;  r=  rD  rF  rG  rJ  rL  rO  rR  rU  rW  rY  r[  r^  ra  rc  re  rg  ri  rk  rm  ro  rq  rs  ru  rw  ry  r{  r}  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r	  r  r  r  r  r  r  r  r  r  r!  r#  r%  r'  r)  r.  r0  r3  r8  r:  r<  r>  r@  rB  rD  rF  rH  rJ  rL  rR  rT  rW  r[  r^  rb  rh  rm  rp  rr  rt  rx  rz  r|  r~  r  r  r  r  r  r  r  rD   rD   rD   rE   r=   ?   s   

		r=   c                   @   sT   e Zd Zdd Zdd Zdd Zdd Zej	d	d
d Z
ej	d	dd ZdS )TestAiryc                 C   s^   t d}t|tg dd t d}t|tg dd t d}t|tg dd d S )NGz?)g*?gTk'kPĿge+?gyCyt?r  g=
ףp=?)g'$'?geοgL?g
HVV?g
ףp=
׿)gl@D|?gV~׭ͿgU?g3{ɔ?)r    rA   r   r   r
  rD   rD   rE   rF     s$   





zTestAiry.test_airyc                 C   s   t d}t d}d gd }tdD ]}|| tdtd  ||< qtddD ]}|| tttdtd   ||< q)t||d d S )Nr   rJ   rL   gN贁N{?rP   )	r    rH   rA   ru   r   r   absr   r   )rC   abb1rh   rD   rD   rE   rI     s   


(zTestAiry.test_airyec                 C   s   t d}tddgtddgtddgtdd	gf}t||d
 t d}t|d tg dd t|d tg dd t|d tg dd t|d tg dd d S )NrL   glgoe2+
g(0[g X*JgUfݿg˰zU`?g4c1=C?gCuTrJ   r   r   )g&g(.2+
gRg}`g%́r  rZ   )g7;1[ge*JgVwgL g<3r&  )gNݿg3%IQ`?gZyΌ׿gʀ11^?g33tտr   )gqM0=C?g7uTg\G`?gp⍞vg$.m?)r    bi_zerosr   r   )rC   bibiarD   rD   rE   test_bi_zeros  s(   





zTestAiry.test_bi_zerosc                 C   s:   t d}t|tdgtdgtdgtdgfd d S )NrZ   gcqg!xLgMSt$?g ~:p?rJ   )r    ai_zerosr   r   )rC   airD   rD   rE   test_ai_zeros:  s   
zTestAiry.test_ai_zerosr   c                 C   s   t d\}}}}t |\}}}}t |\}}	}}dt|d  }
t|d }t||dd t||dd t||
 dddd t|	| dddd t|d d g d	dd t|d d g d
dd d S )NP  rZ   r  r\   rS   r   r]   rP   )guqgqHkZg4g9Ζ%gB~gL")gLgQO	gMQnGg3:g)}g )r    r  rA   r  r   )rC   r   zpai_zpxaip_zxai_zaip_z_ai_zpaip_zpai_envelopeaip_enveloperD   rD   rE   test_ai_zeros_bigA  "   
zTestAiry.test_ai_zeros_bigc                 C   s   t d\}}}}t |\}}}}t |\}}}}	dt|d  }
t|d }t||dd t||dd t||
 dddd t|	| dddd t|d d g d	dd t|d d g d
dd d S )Nr  rZ   r  r\   rS   r   r]   rP   )gx&gg-2+
gRgg`gu%́g{ )g K;1[g*JgVwg<w gd
3g/{
")r    r  rA   r  r   )rC   r   r  bi_zpxbip_zxr  bi_zbip_zbi_zpbip_zpbi_envelopebip_enveloperD   rD   rE   test_bi_zeros_bigZ  r  zTestAiry.test_bi_zeros_bigN)r  r  r  rF   rI   r  r  r  r  	fail_slowr  r  rD   rD   rD   rE   r    s    
!


r  c                   @      e Zd Zdd ZdS )TestAssocLaguerrec                 C   sL   t dd}t ddd}t||dd t ddd}t||dd d S )Nr  rZ   r   r  )r    genlaguerreassoc_laguerrer   )rC   a1a2rD   rD   rE   test_assoc_laguerreu  s
   z%TestAssocLaguerre.test_assoc_laguerreN)r  r  r  r  rD   rD   rD   rE   r  t      r  c                   @   r  )TestBesselpolyc                 C      d S NrD   rB   rD   rD   rE   r   ~     zTestBesselpoly.test_besselpolyN)r  r  r  r   rD   rD   rD   rE   r  }  r  r  c                   @   s   e Z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d  Zd!d" Zd#d$ Zd%S )&
TestKelvinc                 C      t d}t|dd d S )NrL   gT?r   )r    r   r   )rC   mbeirD   rD   rE   r        
zTestKelvin.test_beic                 C   r  )NrL   gD,X?r   )r    r   r   )rC   mbeiprD   rD   rE   r     r  zTestKelvin.test_beipc                 C   r  )NrL   gPA4?r   )r    r   r   )rC   mberrD   rD   rE   r     r  zTestKelvin.test_berc                 C   r  )NrL   gii߿r   )r    r   r   )rC   mberprD   rD   rE   r     r  zTestKelvin.test_berpc                 C   "   t d}t|tg dd d S )Nr   g&jj@g+"@g(rw+@gU2@g`<6@rJ   )r    	bei_zerosr   r   )rC   r  rD   rD   rE   test_bei_zeros  s   
zTestKelvin.test_bei_zerosc                 C   r  )Nr   )gyWo.@g╲ݏ @gנ{)@gK11@gWc"5@r  )r    
beip_zerosr   r   )rC   biprD   rD   rE   test_beip_zeros     
zTestKelvin.test_beip_zerosc                 C   r  )Nr   g\@g6ُ@gӟHY'@g>"D0@ggaO;4@rJ   )r    	ber_zerosr   r   )rC   r   rD   rD   rE   test_ber_zeros  r  zTestKelvin.test_ber_zerosc                 C   r  )Nr   g '@gs%@gF ^-@gvۅj3@gB7@rJ   )r    
berp_zerosr   r   )rC   brprD   rD   rE   test_berp_zeros  r  zTestKelvin.test_berp_zerosc              	   C   sr   t d}t|t dt dd  t dt dd  t dt dd  t 	dt 
dd  fd d S )NrL   r  r  )r    r  r   r   r   r  r  r   r   r  r  )rC   mkelvrD   rD   rE   r    s   
zTestKelvin.test_kelvinc                 C   r  )NrL   g>ɿr   )r    r  r   )rC   mkeirD   rD   rE   r    r  zTestKelvin.test_keic                 C   r  )NrL   gr@d"?r   )r    r  r   )rC   mkeiprD   rD   rE   r    r  zTestKelvin.test_keipc                 C   r  )NrL   gܙUr   )r    r  r   )rC   mkerrD   rD   rE   r    r  zTestKelvin.test_kerc                 C   r  )NrL   g^.n3Jr   )r    r  r   )rC   mkerprD   rD   rE   r    r  zTestKelvin.test_kerpc                 C   r  )Nr   gE>Q@gB= @gPN)@gm91@g
%5@rJ   )r    	kei_zerosr   r   )rC   r  rD   rD   rE   test_kei_zeros  r  zTestKelvin.test_kei_zerosc                 C   r  )Nr   gWf,@g?"@gFZ*o+@gOpN2@gEa6@rJ   )r    
keip_zerosr   r   )rC   r  rD   rD   rE   test_keip_zeros  r  zTestKelvin.test_keip_zerosc           
      C   s   t d}|\}}}}}}}}	t|tg dd t|tg dd t|tg dd t|tg dd t|tg dd t|tg dd t|tg d	d t|	tg d
d d S )Nr   r  rJ   r  )#?Q5U@q89 %@ol`.@gO0q3@r  r  )gum.@gݏ @gs{)@g䠄11@gN(D!5@gS@g89@@g^C'@g1ZG0@g+ڇ4@r  )r    kelvin_zerosr   r   )
rC   tmpberzbeizkerzkeizberpzbeipzkerpzkeipzrD   rD   rE   test_kelvin_zeros  s4   
zTestKelvin.test_kelvin_zerosc                 C   r  )Nr   )r  r  r  r  gD;q3@rJ   )r    	ker_zerosr   r   )rC   r  rD   rD   rE   test_ker_zeros
  r  zTestKelvin.test_ker_zerosc                 C   r  )Nr   r  rJ   )r    
kerp_zerosr   r   )rC   r  rD   rD   rE   test_kerp_zeros  r  zTestKelvin.test_kerp_zerosN)r  r  r  r   r   r   r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  rD   rD   rD   rE   r    s&    		.r  c                   @   r  )TestBernoullic                 C   r  )Nr   )r   r`  g-!lV?r   g镲r   rJ   )r    	bernoullir   r   )rC   brnrD   rD   rE   test_bernoulli  s   
zTestBernoulli.test_bernoulliN)r  r  r  r  rD   rD   rD   rE   r    r  r  c                   @   s(   e Zd ZdZdd Zdd Zdd ZdS )	TestBetaz
    Test beta and betaln.
    c                 C   s~   t tddd ttddtd ttddddd	d
 tdd}tdtd td }t||dd d S )NrZ   r   33333YN~h?   g6.8@rR   r   r  rL   rJ   rP   rS   )r   r    betar   r8  )rC   betbetgrD   rD   rE   	test_beta+  s   zTestBeta.test_betac                 C   s   t ttdd d S )NrO   rL   )r   r_   isinfr    r  rB   rD   rD   rE   test_beta_inf5  rH  zTestBeta.test_beta_infc                 C   st   t tddd ttddtd ttddddd	d
 tdd}tttdd}t||dd d S )NrZ   r   r   r  r     gIs	@r  r   r  rL   rJ   rR   rS   )r   r    betalnr   r<  r   r  r  )rC   betlnr  rD   rD   rE   test_betaln8  s   zTestBeta.test_betalnN)r  r  r  __doc__r  r	  r  rD   rD   rD   rE   r  &  s
    
r  c                   @   s   e Zd ZdZdd Zejdg ddd Zejdg dd	d
 Z	ejdg ddd Z
ejdejejejejgejdg ddd Zejdejejgdd ZdS )TestBetaIncz?
    Tests for betainc, betaincinv, betaincc, betainccinv.
    c                 C   sj   t g d}ttdd|| ttdd|| ttdd|d|  ttdd|d|  d S )N)r   r  rZ   rZ   )r_   r   r   r    betainc
betaincinvbetainccbetainccinvr
  rD   rD   rE   
test_a1_b1I  s
   zTestBetaInc.test_a1_b1z
a, b, x, p))rL   rJ   g@w?r   )r  g     `e@r\   g*?)r  r  g"Yx;r  )g   `1?g    ئAg\aY4g    ?)rJ   i g-߇)?g;?c                 C   <   t |||}t||dd t |||}t||dd d S )Nr   rS   g-a=)r    r  r   r  rC   r  r  r   r,  p1x1rD   rD   rE   test_betainc_betaincinv`  s   z#TestBetaInc.test_betainc_betaincinv))      @r   r  g     ?)      @g     *@      ?g&?)      ?r  g333333?gFoE?)r        2@r%  gg2$Z?)r  r  gZd;?g6)r  r7  r_  g`<)      0@r_  g?g<dEA>)g?g7Ê@g/3J?Hz>c                 C   r  )N+<rS   gV瞯=)r    r  r   r  r  rD   rD   rE   test_betaincc_betainccinvu  s   z%TestBetaInc.test_betaincc_betainccinvza, b, y, ref))cj,@r#  ghHISOa gڭ Y;)g      ,@g      -@g둤g}c]춫;)rP        .@gUv \U,gS^%:)r   g      ?gMoigKB;)r  g    i@g1$-g\_cp:c                 C   s    t |||}t||dd d S )Nr  rS   )r    r  r   )rC   r  r  r  refr   rD   rD   rE   test_betaincinv_tiny_y  s   z"TestBetaInc.test_betaincinv_tiny_yfuncargs))r   rL   r   )r   rL   r   )r         r   )r  r   r   )r  r   333333ӿ)r  r   皙?c              	   C   s|   t jdd. tjt jdd t j|  W d    n1 sw   Y  W d    d S W d    d S 1 s7w   Y  d S )Nraise)domainr-  match)r    errstater  r   SpecialFunctionErrorr  )rC   r'  r(  rD   rD   rE   test_betainc_domain_errors  s   "z&TestBetaInc.test_betainc_domain_errorsdtypec                 C   sL   t jdg|d}t jdg|d}t|||}t||dt |j d d S )Nr   r3  r   r&  rS   )r_   r   r    r  r   r   eps)rC   r3  r  r   r  rD   rD   rE   test_gh21426  s   zTestBetaInc.test_gh21426N)r  r  r  r  r  r  r  parametrizer  r"  r&  r    r  r  r  r  r2  r_   r   r   r6  rD   rD   rD   rE   r  D  s0    



	r  c                   @   sT   e Zd Zdd Zdd Zdd Zejjdd Z	d	d
 Z
dd Zejjdd ZdS )TestCombinatoricsc                 C   s   t tddgddgddg t tddd ttjddddd ttjddddd	d
 t dd tdD tdttddd ttj	d }ttj||d dd| d}tjdddd|kshJ d S )Nr&  r   rJ         ^@g     @j@Texactx   )r;  
repetition   c                 S   s   g | ]
}t jd |ddqS )ro   Tr:  )r    comb.0ri   rD   rD   rE   
<listcomp>  s    z/TestCombinatorics.test_comb.<locals>.<listcomp>r  ro   r   r^   rZ   l   hU7`S?Q r  2   )
r   r    r?  r   ru   listr_   iinfort   max)rC   iir!  rD   rD   rE   	test_comb  s   zTestCombinatorics.test_combc                 C   sL   d}d}t |}t |}tj||dd}tj||dd}||ks$J d S )NF   rV   Tr:  )r_   int64r    r?  )rC   rh   ri   np_nnp_kres_npres_pyrD   rD   rE   test_comb_with_np_int64  s   

z)TestCombinatorics.test_comb_with_np_int64c                 C   z   t tjddddd t tjddddd t tjddddd t tjddddd ttg dg d	g d
 d S )NrL   r   Tr:  r   rO   FrL   rO   rL   r&  r   r   rO   r   )r   r   r   r9  )r   r    r?  r   rB   rD   rD   rE   test_comb_zeros  
   "z!TestCombinatorics.test_comb_zerosc                 C   sF   d}t j|d tjdddd W d    d S 1 sw   Y  d S )Nz`exact=True`r.  rM  rJ   Tr:  )r  deprecated_callr    r?  )rC   msgrD   rD   rE   test_comb_exact_non_int_dep  s   "z-TestCombinatorics.test_comb_exact_non_int_depc                 C   sJ   t tddgddgddg ttddd ttjddddd d S )	Nr&  r   rJ        @g     @Tr:  i  )r   r    permr   r   rB   rD   rD   rE   	test_perm  s   zTestCombinatorics.test_permc                 C   rQ  )NrL   r   Tr:  r   rO   FrR  rS  )r   r   r   rY  )r   r    rZ  r   rB   rD   rD   rE   test_perm_zeros  rU  z!TestCombinatorics.test_perm_zerosc                 C   s>  t jtdd tjddgddgdd W d    n1 sw   Y  t jd	d tjd
ddd W d    n1 s<w   Y  t jd	d tjdddd W d    n1 sZw   Y  t jd	d tjdddd W d    n1 sxw   Y  t jtd	d tjdd
dd W d    d S 1 sw   Y  d S )Nzscalar integersr.  rZ   rL   rJ   r   Tr:  zNon-integergffffff@rP   gffffffr   g333333      @)r  r   
ValueErrorr    rZ  rV  rB   rD   rD   rE   test_perm_iv  s   "zTestCombinatorics.test_perm_ivN)r  r  r  rI  rP  rT  r  r  thread_unsaferX  r[  r\  r_  rD   rD   rD   rE   r8    s    	
r8  c                   @   sd   e Z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 )TestTrigonometricc                 C      t d}d}t|| d S )N   r   )r    r   r   )rC   cbcbrlrD   rD   rE   r        
zTestTrigonometric.test_cbrtc                 C      t d}d}t||d d S )Ngfffff;@g鎖C@r  )r    r   r   )rC   cb1cbrl1rD   rD   rE   test_cbrtmore     
zTestTrigonometric.test_cbrtmorec                 C   &   t d}ttd }t||d d S )NrY  r   r  r    r   r	   r   r   )rC   cdgcdgrlrD   rD   rE   r        
zTestTrigonometric.test_cosdgc                 C   rl  NrV   r]  r  rm  )rC   cdgmcdgmrlrD   rD   rE   test_cosdgmore  rp  z TestTrigonometric.test_cosdgmorec                 C   sV   t dt dt td f}tdd tdd ttd d f}t||d d S )Nr   r  r&  rZ   r  )r    r   r   r	   r   )rC   cscsrlrD   rD   rE   r     s    &zTestTrigonometric.test_cosm1c                 C   *   t d}ttd d }t||d d S )NrV   r]  rO   r  r    r   r
   r   r   )rC   ctctrlrD   rD   rE   r        
zTestTrigonometric.test_cotdgc                 C   rw  )Nr   r  rO   r  rx  )rC   ct1ctrl1rD   rD   rE   test_cotdgmore  r{  z TestTrigonometric.test_cotdgmorec                 C   s   t tddd t tddd t tddd t tddd t td	dd t td
dd t tddd t tddd t tddd t tddd t tddd t tddd t tddd d S )Nr   r      r   rY  r   i   y   i  i;  i  )r   r    r   rB   rD   rD   rE   test_specialpoints!  s   z$TestTrigonometric.test_specialpointsc                 C   s&   t tdgd ttdd d S )Nr   rZ   r   r   )r   r    sincr   rB   rD   rD   rE   	test_sinc0  s   zTestTrigonometric.test_sincc                 C      t d}t|d d S rX  )r    rZ  r   )rC   snrD   rD   rE   r[  5     
zTestTrigonometric.test_sindgc                 C   H   t d}ttd }t||d t d}ttd }t||d d S )NrV   r]  r  r   r  )r    rZ  r   r   r   )rC   snmsnmrlsnm1snmrl1rD   rD   rE   test_sindgmore9     

z TestTrigonometric.test_sindgmoreN)r  r  r  r   rj  r   rt  r   r   r~  r  r  r[  r  rD   rD   rD   rE   ra    s    ra  c                   @   $   e Zd Zdd Zdd Zdd ZdS )	TestTandgc                 C   rl  rq  r    r}  r
   r   r   )rC   tntnrlrD   rD   rE   r~  D  rp  zTestTandg.test_tandgc                 C   r  )Nr   r  r  r  r   r  )rC   tnmtnmrltnm1tnmrl1rD   rD   rE   test_tandgmoreI  r  zTestTandg.test_tandgmorec                 C   s   t tddd t tddd t tddd t tddd t td	dd t td
dd t tddd t tddd t tddd t tddd t tddd d S )Nr   r   r  r   r   r  r   r  r  r  iLr  r  r  r  )r   r    r}  rB   rD   rD   rE   r  Q  s   zTestTandg.test_specialpointsN)r  r  r  r~  r  r  rD   rD   rD   rE   r  B  s    r  c                   @   T   e Z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 )	TestEllipc                 C   s   t dtj dS )zRegression test for #912.r   N)r    r  r_   r   rB   rD   rD   rE   test_ellipj_nan`  s   zTestEllip.test_ellipj_nanc                 C   s0   t dd}tdtdddg}t||d d S )Nr   r   r      )r    r  r   r	   r   )rC   elrelrD   rD   rE   r  d     zTestEllip.test_ellipjc                 C   s   t d}t|dd tt dtj tt dtd  tt tjd tt tjtj tt dtj t	t dd	 d S )
Nr   g;{yэ?r  r   r   rL   rO   gN?)
r    r"   r   r   r#   r_   r   r   r   r   )rC   elkrD   rD   rE   r  i  s   
zTestEllip.test_ellipkc                 C   s  t td d}t d}t||d dt d }dt d }t|d }t ||}t|dd tt td d	td  tt td d
tj tt td tj d	 tt td tj	tj	 tt td dtj	 tt ddd	 tt tjdtj tt tj dtj  tt tjtjtj	 tt tjtj tj	 tt tj tj tj	 tt tj tjtj	 tt tj	dtj	 tt tj	tj	tj	 t
t ddddd t
t ddd d S )NrL   r   r{   ro   r  r   gfoKh?r  r   r   r   r   gt?rZ   rM   r  rS   6<R!?r  gfON?)r    r  r   r"   r   r   r   r_   r   r   r   )rC   elkincr  alphaphir  rD   rD   rE   r  t  s0   
zTestEllip.test_ellipkincc                 C   s   d}d}t |d}g }tdD ]}|| t |d}qt||}t|t |dd t|t |}t|t |dd d S )	N    ?Pag?r   r&  rZ   gV^8j?g,j6Ƅ@rL   )	r_   	nextafterru   appendr    r  r   	full_liker   rC   mbadr  r  mvalsjr  f1rD   rD   rE   test_ellipkinc_2     
zTestEllip.test_ellipkinc_2c                 C   sD  t ddd}t ddd}t jdtd ddd}tt|d	t t |d
d tt|d	t t |d
d tt|d	t t |d
d t	tt jd d	t j
 tt| d	t t | d
d tt| d	t t | d
d tt| d	t t | d
d t	tt j d d	t j
 d S )Niir   gFFg<r  rL   Frc  rZ   r  rS   )r_   rq   r  r   r   r    r  arcsinhr
   r   r   )rC   xlogxlinxlin2rD   rD   rE   test_ellipkinc_singular  s.    z!TestEllip.test_ellipkinc_singularc                 C   s   t d}t|dd tt dtd  tt dd tt tj tj tt tjtj tt dtj tt dd d S )	Nr   gl?r  r   rL   r   r  g?eg@)	r    r!   r   r   r   r_   r   r   r   )rC   elerD   rD   rE   r     s   
zTestEllip.test_ellipec                 C   s  t td d}t d}t||d dt d dt d }}t|d }t ||}t|dd tt td d	td  tt td d
d
 tt td tj tj tt td tj	tj	 tt td dtj	 tt ddd	 tt tjdtj tt tj dtj  tt tjtj tj tt tj tj tj  tt tjtjtj	 tt tj tjtj	 tt tj	dtj	 tt tj	tj	tj	 t
t ddd d S )NrL   r   r  4   r  #   g'?r  r   r   r   r   r  r  gL@)r    r   r   r!   r   r   r   r_   r   r   r   )rC   eleincr  r  r  r  rD   rD   rE   r     s,   
zTestEllip.test_ellipeincc                 C   s   d}d}t |d}g }tdD ]}|| t |d}qt||}t|t |dd t|t |}t|t |dd	 d S )
Nr  r  r   r&  rZ   g%?rL   gXo
@rJ   )	r_   r  ru   r  r    r   r   r  r   r  rD   rD   rE   test_ellipeinc_2  r  zTestEllip.test_ellipeinc_2N)r  r  r  r  r  r  r  r  r  r   r   r  rD   rD   rD   rE   r  _  s    r  c                   @   sN   e Zd ZdZdd Zdd Zdd Zdd	 Zd
d Ze	j
jdddd ZdS )TestEllipCarlsonzTest for Carlson elliptic integrals ellipr[cdfgj].
    The special values used in these tests can be found in Sec. 3 of Carlson
    (1994), https://arxiv.org/abs/math/9409227
    c                 C   s   t tddd tdtdksJ ttddsJ tdtdtdks&J tddgddgddgddgdd	gdd
gg}ttjtdddtdd dg}t	|D ]\}}t t| ||  qSd S )NrZ   r   r   r  g      @r   r               r)  r   y
c?
cy=B?CGֿr   y檠f?P9lb?)
r   r$   r   r   r  r   r_   r   r   	enumeraterC   r(  expected_resultsry   arrrD   rD   rE   test_elliprc  s*   zTestEllipCarlson.test_elliprcc                 C   s(  t tdddd t tdddd d tddtdksJ ttddds)J ttddtdds7J ttddtddsEJ ttddttjj	 d sWJ ttddtddsdJ t
g d	g d
g dg dg dg dg}t
g d}t|D ]\}}t t| ||  qd S )NrZ   r   rL   r   g`C+?r   r   rO   )r   r   r   r   r   r  r  r  r   r   r  r  )r               ?r  )y             r  r  )gfe_?gi+"?gP$M?ytgFU?7?@yR<8*y{62?z)r   r%   r   r_   r  r  r   r   r   tinyr   r  r  rD   rD   rE   test_elliprd  s&   $zTestEllipCarlson.test_elliprdc              	   C   s   t tdddd t tdddd tdtddksJ ttddds'J ttddds1J tttdddks=J ttddtt dsKJ tg dg dg d	g d
g dg dg dg}tg d}t|D ]\}}t t| ||  qnd S )NrZ   r   rL   gPO?r   rO   )r   r   r   )r  r  r   )r   r   r   r  r  r   r  r  )r  r        ?      )geQO?ʞu5J?r  yp\y?kg2ΰ?gHwд?y|pF?-6Fj)	r   r&   r   r_   r  r   r  r   r  r  rD   rD   rE   test_elliprf  s&   zTestEllipCarlson.test_elliprfc                 C   s   t tdddd t tdddd t tdddd ttdtds&J ttttdds3J tg dg dg dg dg dg d	g}ttjd
ddddg}t|D ]\}}t t| ||  qXd S )NrZ   r   r   )r   r  r  r  r  r  )r  r  r  )r   g8d`?r  gL+?g}^?y旮0?ʋW?yjN?^?gt?)	r   r'   r_   r  r   r  r   r   r  r  rD   rD   rE   test_elliprg6  s,   zTestEllipCarlson.test_elliprgc                 C   s   t tddddd tddtddksJ ttdddds J ttdddds+J tdddtdks6J tg dg dg dg dg d	g d
g dg dg dg	}tg d}t|D ]\}}t t| ||  q_d S )NrZ   r   r   rO   )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   y            ?)r   r   r  r`  )r   r   r        )	g @?gviM?ym?\Isؿg'4Ob?go0 ?yW7?xfOA?ybv㿘ܶ.gHQ?gjߡB7E)r   r(   r   r   r   r  r  rD   rD   rE   test_elliprjK  s&   		zTestEllipCarlson.test_elliprjzInsufficient accuracy on 32-bitr  c                 C   s8   t tdddddddd t td	d
dddddd d S )Ng   gq>g   `W:g    HBg   @ۘ?gRy|>r!  r5  r  g   ,@g    x=g   @e:g   `ݽ>g(HR)A)r   r(   rB   rD   rD   rE   test_elliprj_hardf  s    
z"TestEllipCarlson.test_elliprj_hardN)r  r  r  r  r  r  r  r  r  r  r  r  r  rD   rD   rD   rE   r    s    r  c                   @   s0   e Zd ZdZdd Zdd Zdd Zdd	 Zd
S )"TestEllipLegendreCarlsonIdentitieszTest identities expressing the Legendre elliptic integrals in terms
    of Carlson's symmetric integrals.  These identities can be found
    in the DLMF https://dlmf.nist.gov/19.25#i .
    c                 C   s^   t ddd| _ttj| _ddtdt | j  dd  | _t 	| jg| j| jf| _
d S )Nr   r   r   r   rO   r   )r_   r   m_n1_1r   r   minmax_neglog2
very_neg_mconcatenate
ms_up_to_1rB   rD   rD   rE   setup_class|  s   

z.TestEllipLegendreCarlsonIdentities.setup_classc                 C   s$   | j }tt|tdd| d dS )z5Test identity:
        K(m) = R_F(0, 1-m, 1)
        r   r   N)r  r   r"   r&   rC   r  rD   rD   rE   test_k  s   z)TestEllipLegendreCarlsonIdentities.test_kc                 C   s>   t tj}|dtdt|   }tt|td|d dS )z\Test identity:
        K(m) = R_F(0, 1-m, 1)
        But with the ellipkm1 function
        r   r   r   N)	r   r   r  r   r_   r  r   r#   r&   )rC   r  m1rD   rD   rE   test_km1  s   
z+TestEllipLegendreCarlsonIdentities.test_km1c                 C   s(   | j }tt|dtdd| d  dS )z9Test identity:
        E(m) = 2*R_G(0, 1-k^2, 1)
        r   r   r   N)r  r   r!   r'   r  rD   rD   rE   test_e  s   "z)TestEllipLegendreCarlsonIdentities.test_eN)r  r  r  r  r  r  r  r  rD   rD   rD   rE   r  v  s    r  c                   @   sv   e Zd Zdd Zdd Zd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 )TestErfc                 C   r  )Nr  g);T?r  )r    r  r   )rC   errD   rD   rE   r	    r  zTestErf.test_erfc                 C   s&   t d}tg d}t||d d S )Nr   )yTcJ5?=W?yo@n@y'ʷ@g	@y"[

@,y]+@yld&@-;'j'>@rJ   )r    	erf_zerosr   r   )rC   erzerzrrD   rD   rE   test_erf_zeros  s   
zTestErf.test_erf_zerosr   c                 C   s   t jd}d}|d|d|dd| d  }|d|d|dd| d  }|d|  }	t jdd	> ||	}
||j}t |
}|
| }
|	| }	t |}|| }|| }t||
|	||d
 t|||||d
 W d    d S 1 sww   Y  d S )NrU   r  g{Gz?rL   r   rZ   r  ignoreallr  )	r_   re   rf   paretorandintr0  r   isfiniter9   )rC   r'  
other_funcrT   r^   rl   rh   r   r  r   r  w_realmaskrD   rD   rE   _check_variant_func  s"   ""


"zTestErf._check_variant_funcc                 C   s   | j tjdd ddd d S )Nc                 S   s   dt |  S rs   r@   r  r   rD   rD   rE   <lambda>  s    z.TestErf.test_erfc_consistent.<locals>.<lambda>r   r  r  )r  r@   r  rB   rD   rD   rE   test_erfc_consistent  s   
zTestErf.test_erfc_consistentc                 C      | j tjdd dd d S )Nc                 S   s   t | |  t|  S r  )r_   r   r@   r  r  rD   rD   rE   r    s    z/TestErf.test_erfcx_consistent.<locals>.<lambda>r   rS   )r  r@   erfcxrB   rD   rD   rE   test_erfcx_consistent  
   
zTestErf.test_erfcx_consistentc                 C   r  )Nc                 S   s   dt d|   S )Nr  r  r  r  rD   rD   rE   r    s    z.TestErf.test_erfi_consistent.<locals>.<lambda>r   rS   )r  r@   erfirB   rD   rD   rE   test_erfi_consistent  r  zTestErf.test_erfi_consistentc                 C   r  )Nc                 S   s&   t td t|  |   t|  S r  )r   r   r_   r   r@   r  r  rD   rD   rE   r    s   & z/TestErf.test_dawsn_consistent.<locals>.<lambda>r   rS   )r  r@   r   rB   rD   rD   rE   test_dawsn_consistent  r  zTestErf.test_dawsn_consistentc                 C   6   t jt j t jg}t jddg}tt||dd d S )NrO   rZ   r   rS   )r_   r   r   r   r    r  rC   rB  r!  rD   rD   rE   test_erf_nan_inf     zTestErf.test_erf_nan_infc                 C   r   )NrL   r   r   rS   )r_   r   r   r   r    r  r  rD   rD   rE   test_erfc_nan_inf  r  zTestErf.test_erfc_nan_infc                 C   s8   t jt j t jg}t jt jdg}tt||dd d S )Nr   r   rS   )r_   r   r   r   r    r  r  rD   rD   rE   test_erfcx_nan_inf  s   zTestErf.test_erfcx_nan_infc                 C   s<   t jt j t jg}t jt j t jg}tt||dd d S )Nr   rS   )r_   r   r   r   r    r  r  rD   rD   rE   test_erfi_nan_inf  s   zTestErf.test_erfi_nan_infc                 C   r   )Nr@  r   r   rS   )r_   r   r   r   r    r   r  rD   rD   rE   test_dawsn_nan_inf  r  zTestErf.test_dawsn_nan_infc                 C   s@   t jt j t jg}t jt jd  ddg}tt||dd d S )Nr  r  r   rS   )r_   r   r   r   r    r  r  rD   rD   rE   test_wofz_nan_inf  s   zTestErf.test_wofz_nan_infN)r   )r  r  r  r	  r  r  r  r  r  r  r  r  r  r  r  r  rD   rD   rD   rE   r    s    
	r  c                   @   r  )	TestEulerc           
      C   s  t d}t d}t d}t|dgdd t|ddgdd t|g ddd t d}g d}td	d
}tddD ]}|d rNt||  |d| < q<t|| |d| < q<tjdd t|| | }t	|}	W d    n1 svw   Y  t
|	dd d S )Nr   rZ   rL   r   rS   )rZ   r   rO   r   )rZ   rZ   r   =   ii  iY  i=) il   Q~ l   10[l   $8gC
 l   2l   v}Ju: )r   dr  r  r  r   r  )r    eulerr   r   ru   rv   r_   r0  r   rG  r   )
rC   eu0eu1eu2eu24	mathworldcorrectri   errerrmaxrD   rD   rE   
test_euler  s$   





zTestEuler.test_eulerN)r  r  r  r  rD   rD   rD   rE   r	    r  r	  c                   @   s<   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd ZdS )TestExpc                 C   rb  )NrL   rJ   )r    r  r   rC   exexrlrD   rD   rE   r    rf  zTestExp.test_exp2c                 C   rg  )Nr  g;f@r  )r    r  r   rC   exmexmrlrD   rD   rE   test_exp2more#  rk  zTestExp.test_exp2morec                 C   rb  )NrL   r  )r    r  r   r  rD   rD   rE   r  (  rf  zTestExp.test_exp10c                 C   rg  )Nr  gYs@r  )r    r  r   r  rD   rD   rE   test_exp10more-  rk  zTestExp.test_exp10morec                 C   N   t dt dt df}tdd tdd tdd f}t||d d S )NrL   r   rJ   rZ   r  r    r  r   r   r  rD   rD   rE   r  2     "zTestExp.test_expm1c                 C   r  )NrL    @皙@rZ   r  r   )rC   ex1exrl1rD   rD   rE   test_expm1more7  r!  zTestExp.test_expm1moreN)	r  r  r  r  r  r  r  r  r&  rD   rD   rD   rE   r    s    r  c                    s    fdd}dd }t | t |u s J dt |  dt | t| tjrJ| j|jks.J || | t|  | D ]\}}t|| d q<d	S t| rht|rht	t | drh|| oe|| d	S  d	S || | d	S )
a  
    Sharper assertion function that is stricter about matching types, not just values

    This is useful/necessary in some cases:
      * dtypes for arrays that have the same _values_ (e.g. element 1.0 vs 1)
      * distinguishing complex from real NaN
      * result types for scalars

    We still want to be able to allow a relative tolerance for the values though.
    The main logic comparison logic is handled by the xp_assert_* functions.
    c                    s(    d u rt | | d S t| | d d S )NrS   )r3   r2   r   r  rS   rD   rE   assert_funcI  s   (z(assert_really_equal.<locals>.assert_funcc                 S   s    t | jrt | jsJ d S r  )r_   r   r   r  r   rD   rD   rE   assert_complex_nanL      z/assert_really_equal.<locals>.assert_complex_nanztypes not equal: z, rS   r  N)
type
isinstancer_   ndarrayr3  ziprd   assert_really_equalr   r7   )r   r  rT   r(  r*  elem_xelem_yrD   rS   rE   r0  =  s   ,
"r0  c                   @   sr  e Zd Zdd Zejdg ddd Zejdg dejd	d
dgdd Zejd	d
dgdd Z	ejdg ddd Z
ejdddgejdg ddd Zejdd
dgejdddgejjdejedejejd  edejejd ej ej d d ed!g
g d"d#ejd$ejejejgd%d& Zejddd'ejd(gd)d* Zejd+ed,d-ejd	d
dgd.d/ Zejd	d
dgejd0d eejejejejejej ej!ej"g
ejd1edd-d2d3 Z#ejd	d
dgejd4ed,d-d5d6 Z$ejd0ejej ej!ej"gejdg dd7d8 Z%ejded9d:d;d<d= Z&ejde'edd>e'ed9d:d; d?d@ Z(dAdB Z)dCdD Z*ejd0ejejeje+gejdddgejd	d
dgejd1edd-ejjdEg d,gd'gejgejejd  gejd,ggg dFd#dGdH Z,ejdddgejd	d
dgejjdd,d'dIejejejd  d gg dJd#dKdL Z-ejded9d:dMdNdO Z.ejde'edd>e'ed9d:dM dPdQ Z/dRdS Z0ejd0ejejeje+gejdddgejd	d
dgejd1edd-ejjdEg d,gd'gejgejejd  gejd,ggg dFd#dTdU Z1ejdddgejd	d
dgejjdd,d'dIejejejd  d gg dJd#dVdW Z2ejdXed,d-ejdedYdZd[d\d] Z3ejdXe'ed,d-d;dZg ejde'edd>e'ed>d^dM d_d` Z4dadb Z5ejd0ejejeje+gejdddgejd	d
dgejd1edd-ejjdEg d,gd'gejgejejd  gejd,ggg dFd#dcdd Z6ejdddgejd	d
dgejdXed,d-ejjdd,d'dIejejejd  d gg dJd#dedf Z7ejdd
dgejdg dejdXdgdhddidd'ejgdjdk Z8ejdd
dgejdg dejjdXd(ed!gd(dlgd#dmdn Z9ejdg dejdXed,dodpdq Z:drds Z;d S )tTestFactorialFunctionsc                 C   st   |r
t j||ddS |dkrt||nd}t||| | t || d  t || d  }|t|d S )NTri   r;  zerorZ   )r    
factorialkr_   modpowerr8  rK  maximum)rC   rh   ri   r;  extendrrB  rD   rD   rE   factorialk_refb  s
   8z%TestFactorialFunctions.factorialk_refzexact,extend))Tr5  )Fr5  )Fr  c                 C   s`   ||d}t tjdi |sJ t tjdi |sJ t tjdddi|s.J d S )Nr;  r:  rZ   ri   r   rZ   )r_   isscalarr    	factorial
factorial2r6  )rC   r;  r:  kwrD   rD   rE   "test_factorialx_scalar_return_typek  s   
"z9TestFactorialFunctions.test_factorialx_scalar_return_typerh   )rO   r  r;  TFc                 C   sX   d|i}t tj|fi |d t tj|fi |d t tj|fddi|d d S )Nr;  r   ri   r   )r   r    r@  rA  r6  )rC   r;  rh   rB  rD   rD   rE   $test_factorialx_negative_extend_zeros  s    z;TestFactorialFunctions.test_factorialx_negative_extend_zeroc                 C   s   d|i}d}g d}t jg d|rtnt jd}ttj|fi |||d ttj|fi |||d ttj|fddi|||d d S )	Nr;  r   )r>  r   rZ   )r   r   rZ   rZ   r4  rS   ri   r   )	r_   r   
native_intr   r0  r    r@  rA  r6  )rC   r;  rB  rT   rh   r!  rD   rD   rE   *test_factorialx_negative_extend_zero_array{  s   $zATestFactorialFunctions.test_factorialx_negative_extend_zero_arraygggffffff
c                 C   s  ddi}dddd}ddd	d}d
ddd}d}t tj|fi ||| |d t tj|fi ||| |d t tj|fddi||| |d t tj|gfi |d || |d t tj|gfi |d || |d t tj|gfddi|d || |d d S )Nr:  r  gRc/a_%g:\Oag@g*BZ'rI  go	08G)?goNb]gMxcQgNy?g=u?g7K [n<rS   ri   r   r   )r   r    r@  rA  r6  )rC   rh   rB  exp_1exp_2exp_krT   rD   rD   rE   'test_factorialx_negative_extend_complex  s(     $&&.z>TestFactorialFunctions.test_factorialx_negative_extend_complexr  r   r  n_outerc                    s4   ddi  fdd}|||  |d| |  d S )Nr:  r  c                    s8  t t| d}td}|rtdntd}ttj| fi  | ttj| d fi  | ttj	| d fddi | d}ttj	| | fd|i | ttj| gfi  d | ttj| d gfi  d | ttj	| d gfddi d | ttj	| | gfd|i d | d S )	Nr  nan+nanjr   rL   r   ri   y      ?       r   )
r7   r,  r_   
complex128r   r0  r    r@  rA  r6  )rh   
complexifycomplex_nanr   r  rB  rD   rE   _check  s   
  "&*zTTestFactorialFunctions.test_factorialx_negative_extend_complex_poles.<locals>._checki rD   )rC   rO  r  rU  rD   rT  rE   -test_factorialx_negative_extend_complex_poles  s   zDTestFactorialFunctions.test_factorialx_negative_extend_complex_polesboxedr:  r5  r  r   r  rP  Nnat)
NaNznp.float64('nan')	NaN+i*NaNznp.complex128('nan+nanj')r   zinf+0iz-infz-inf+0iNoneNaT)ids
factorialxc                 C   s  d|d}|t jkrd|d< |rg dndddtd g}|t jkr#dnddg}tt||sUtjtd	d
 ||r<|gn|fi | W d    d S 1 sNw   Y  d S tt||r|dkrtjtdd
 ||rn|gn|fi | W d    d S 1 sw   Y  d S |dkott|d}|rt	dnt
d}	tt|drt|rt
|dkrdnd}
|dkrt
dn|
}	|r||gfi |d n||fi |}t||	 d S )NFr=  r   ri   ry   r  r  ry   r  r  Unsupported data type.*r.  r  In order to use non-integer.*rP  r   r5  r   r   )r    r6  r,  r@  r7   r  r   r^  r_   rQ  r   r  r0  )rC   r^  rh   r:  rW  rB  permissible_typestypes_need_complex_extrR  r!  neg_inf_resultr  rD   rD   rE   test_factorialx_inf_nan  s(   

""*z.TestFactorialFunctions.test_factorialx_inf_nanr+  stringc                 C   s   t jtdd tjd|d W d    n1 sw   Y  t jtdd tjd|d W d    n1 s7w   Y  t jtdd tjddd|d W d    d S 1 sXw   Y  d S )Nzargument `extend` must be.*r.  rZ   )r:  r   Tri   r;  r:  )r  r   r^  r    r@  rA  r6  )rC   r:  rD   rD   rE   test_factorialx_raises_extend  s   "z4TestFactorialFunctions.test_factorialx_raises_extendlevelsrZ   r   c                    s   d fdd	  fdd}t  ddgd}d	tdgd
tjdddgdtjddddgd}|tj||d|d  |tj||d|d  |tj|d|d|d  d S )NrZ   c                    s   |dkr| S  | | g|d S )z
            Double x and nest it k times

            For example:
            >>> _nest_me([3, 4], 2)
            [[[3, 4], [3, 4]], [[3, 4], [3, 4]]]
            r   rZ   rD   r   ri   _nest_merD   rE   rl    s   zDTestFactorialFunctions.test_factorialx_array_shape.<locals>._nest_mec                    s4   t j |dtd}t| t j|t j d S )Nri   r4  )r_   r   objectr   r   r   )resnucleusr   rl  ri  rD   rE   rU  	  s   zBTestFactorialFunctions.test_factorialx_array_shape.<locals>._checkr   r   rm  r<  r{   Tr:  r&  r   r  rL   r>  )r_   r   mathr@  r    rA  r6  )rC   ri  r;  rU  rh   exp_nucleusrD   rq  rE   test_factorialx_array_shape  s   z2TestFactorialFunctions.test_factorialx_array_shaper3  dimc                 C   s   t jd||d}dddd}ttj||dt j|d |d	 ttj||dt j|d
 |d	 ttj|d|dt j|d |d	 d S )Nr   )r3  ndminr<  r{   r&  r  r:  rZ   rv  rL   r   )r_   r   r   r    r@  rA  r6  )rC   ru  r3  r;  rh   r   rD   rD   rE   test_factorialx_array_dimension	  s   z6TestFactorialFunctions.test_factorialx_array_dimensionlevelc                    s   d fdd	  dg|d d}dddd	}|rt nt}|tj||d
tj|d |d |tj||d
tj|d |d |tj|d|d
tj|d |d d S )NrZ   c                    s   |dkr| S  | g|d S r   rD   rj  rk  rD   rE   rl  $	  s   zCTestFactorialFunctions.test_factorialx_array_like.<locals>._nest_mer   rm  r<  r{   r&  r  r:  rw  rL   r   r>  )r   r   r    r@  r_   r   rA  r6  )rC   ry  r;  rh   rs  r(  rD   rk  rE   test_factorialx_array_like!	  s   z1TestFactorialFunctions.test_factorialx_array_likec                    sh   ||d|r	t nt  fdd}||d ||d |tjd|d |tjddg|d d S )Nr=  c                    s   t | tjr| tjnt| } tj| fi tj|fi   tj| fi tj|fi   tj| fdditj|fddi d S )Nri   r   )	r-  r_   r.  r   rK  r    r@  rA  r6  )rh   n_refr(  rB  rD   rE   rU  ;	  s   "&&z;TestFactorialFunctions.test_factorialx_uint.<locals>._checkr   rZ   r4  )r   r   r_   r   )rC   r;  r:  r3  rU  rD   r|  rE   test_factorialx_uint4	  s   
z+TestFactorialFunctions.test_factorialx_uintrV   r  r&  c                 C   h   t jdkrdnd}tttj|ddtj|dd|d ttj|gddttj|gdd|d d S )Nr;   t0=r   Tr:  FrS   )sysplatformr   rv   r    r@  r   rC   rh   rT   rD   rD   rE   test_factorial_accuracyG	     
z.TestFactorialFunctions.test_factorial_accuracy   c                 C   s   t |}t|tj|dd t|tj|gddd  tjdkr#dnd}t|}t|tj|dd|d t|tj|gddd |d dd	d
}t|tj|fi ||d t|tj|gfi |d |d d S )NTr:  r   r;   +6=r   FrS   r  r=  )rr  r@  r   r    r  r  rv   r   rC   rh   r  rT   rB  rD   rD   rE   test_factorial_int_referenceS	  s   

&z3TestFactorialFunctions.test_factorial_int_referencec                 C   sf   dd }|dd |dd |dd |d	d
 |dd |dd |dd |dd |dd d S )Nc                 S   s   t jdkrdnd}tt| ||d tt| gd ||d tjtdd tj| dd	 W d    n1 s9w   Y  tjtdd tj| gdd	 W d    d S 1 sYw   Y  d S )
Nr;   r  r   rS   r   `exact=True` only supports.*r.  Tr:  )r  r  r   r    r@  r  r   r^  )rh   r!  rT   rD   rD   rE   rU  g	  s   "zETestFactorialFunctions.test_factorial_float_reference.<locals>._checkr   gr?g(\?gc?g333333@g4s@g333333&@gމOAfffff@@g	²Gg     K@gC$JOglS@g }WgX@gX>%`g\CSe@gG=rD   rC   rU  rD   rD   rE   test_factorial_float_referencef	  s   







z5TestFactorialFunctions.test_factorial_float_referencec                 C   sH   dd }|ddd |ddd |dd	d |d
dd |ddd d S )Nc                 S   s^   t jdkrdnd}ddd}ttj| fi |||d ttj| gfi |d ||d d S )	Nr;   rJ  V瞯<Fr  r=  rS   r   )r  r  r   r    r@  rh   r!  rT   rB  rD   rD   rE   rU  ~	  s   
&zGTestFactorialFunctions.test_factorial_complex_reference.<locals>._checkr`  gkﴑ[?r!                ykﴑ[?               @       @yB}ۿ?gH.gK	!@y      -C6?yI{xQrD   r  rD   rD   rE    test_factorial_complex_reference}	  s   z7TestFactorialFunctions.test_factorial_complex_referencecontent)z[]z[1]z[1.1]z[NaN]z[NaN+i*NaN]z[NaN, 1]c                    s  |t u rtrtd |tju rtdd |D rtd |tjkr1tdd |D r1td ||d |dks@t|dkrB|n|d }tj	|||d	}d }|d
krw|rwtj
tdd tj|fi   W d    n1 sqw   Y  nt|jg dstj
tdd tj|fi   W d    n1 sw   Y  n]t|jdr|d
krtj
tdd tj|fi   W d    n1 sw   Y  n2|rt|jdstj
tdd tj|fi   W d    n1 sw   Y  n	tj|fi  }|d urH fdd| D }t|dkr|d n|}|jr7|d
ko(t|jd}	|	r/tjn|r4tntj}tj	|||d	}
t||
dd d S d S )Nz+object arrays unsupported in array API modec                 s   &    | ]}t |p|t|kV  qd S r  r_   r   rt   rA  r   rD   rD   rE   	<genexpr>	     $ zKTestFactorialFunctions.test_factorial_array_corner_cases.<locals>.<genexpr>impossible combinationc                 s       | ]
}t t|d V  qdS r  Nr7   r,  r  rD   rD   rE   r  	      r=  r   rZ   rv  r3  r  Incompatible options:.*r.  r_  r`  r  ra  ry   r  c                       g | ]}t j|fi  qS rD   )r    r@  r  rT  rD   rE   rB  	      zLTestFactorialFunctions.test_factorial_array_corner_cases.<locals>.<listcomp>r   rS   )rn  r4   r  skipr_   rK  anyr   lenr   r   r^  r    r@  r7   r3  rd   r   rQ  rG  r0  rC   r  ru  r;  r:  r3  rh   r  r%  cxr!  rD   rT  rE   !test_factorial_array_corner_cases	  sP   



 
z8TestFactorialFunctions.test_factorial_array_corner_casesr  )1z1.1z2+2jrY  rZ  r[  c                 C   s  ||d}|dkr.|r.t jtdd tj|fi | W d    d S 1 s'w   Y  d S tt|dddtd gs^t jtdd tj|fi | W d    d S 1 sWw   Y  d S tt|dr|dkrt jtd	d tj|fi | W d    d S 1 sw   Y  d S |d u st|r|dkott|d}|rt	d
nt
d}ttj|fi || d S |rtt|drt jtdd tj|fi | W d    d S 1 sw   Y  d S ttj|fi |t|d  d S )Nr=  r  r  r.  ry   r  r  r`  ra  rP  r   r  rZ   )r  r   r^  r    r@  r7   r,  r_   r   rQ  r   r0  r   r8  rC   rh   r;  r:  rB  rR  r!  rD   rD   rE   "test_factorial_scalar_corner_cases	  s,   
""""&z9TestFactorialFunctions.test_factorial_scalar_corner_casesr  c                 C   r~  )Nr;   +=r   Tr:  FrS   )r  r  r   rv   r    rA  r   r  rD   rD   rE   test_factorial2_accuracy	  r  z/TestFactorialFunctions.test_factorial2_accuracyc                 C   s   t tjtt|ddd}t|tj|dd t|tj|gddd  t	j
dkr,dnd}t|}t|tj|d	d|d
 t|tj|gd	dd |d
 d	dd}|d dkryt|tj|fi ||d
 t|tj|gfi |d |d
 d S d S )Nr   r  rZ   Tr:  r;   r  r   FrS   r  r=  rL   )	functoolsreduceoperatormulrE  ru   r   r    rA  r  r  rv   r   r  rD   rD   rE   test_factorial2_int_reference	  s   
&z4TestFactorialFunctions.test_factorial2_int_referencec                 C   s   dd }|ddd |dt dtdtj  d |dt dtdtj  d |dd	d |d
dd |ddd |ddd |ddd d S )Nc                 S   sP   d}ddd}t tj| fi |||d t tj| gfi |d ||d d S )Nr!  Fr  r=  rS   r   )r   r    rA  r  rD   rD   rE   rU  
  s   
&zHTestFactorialFunctions.test_factorial2_complex_reference.<locals>._checkr   r  rJ   rL   ro   r`  g^D]?JO?r  y^D]?JO?        y      @      @y&0!:?gSt$gtQ*@y       -C6?yqj?x*)r    rA  rr  r   r   r  rD   rD   rE   !test_factorial2_complex_reference
  s   ""z8TestFactorialFunctions.test_factorial2_complex_referencec                    s(  |t jkrtdd |D rtd |t jkr&tdd |D r&td ||d |dks5t|dkr7|n|d }t j|||d}d }|d	krl|rltjt	d
d t
j|fi   W d    n1 sfw   Y  n_t|jg dstjt	dd t
j|fi   W d    n1 sw   Y  n6t|jddgr|d	krtjt	dd t
j|fi   W d    n1 sw   Y  n	t
j|fi  }|d ur fdd| D }t|dkr|d n|}|jr|d	kot|jd}	|	rt jn|rtnt j}t j|||d}
t||
dd d S d S )Nc                 s   r  r  r  r  rD   rD   rE   r  $
  r  zLTestFactorialFunctions.test_factorial2_array_corner_cases.<locals>.<genexpr>r  c                 s   r  r  r  r  rD   rD   rE   r  &
  r  r=  r   rZ   r  r  r  r.  r_  r`  r  r  ra  c                    r  rD   )r    rA  r  rT  rD   rE   rB  =
  r  zMTestFactorialFunctions.test_factorial2_array_corner_cases.<locals>.<listcomp>r  rS   )r_   rK  r  r  r  r   r  r   r   r^  r    rA  r7   r3  rd   r   rQ  rG  r0  r  rD   rT  rE   "test_factorial2_array_corner_cases
  sB   


 
z9TestFactorialFunctions.test_factorial2_array_corner_casesc                 C   s  ||d}|dkr.|r.t jtdd tj|fi | W d    d S 1 s'w   Y  d S tt|dddtd gs^t jtdd tj|fi | W d    d S 1 sWw   Y  d S tt|ddgr|dkrt jtd	d tj|fi | W d    d S 1 sw   Y  d S |d u st|r|dkott|d}|rt	d
nt
d}ttj|fi || d S | j|fddi|}ttj|fi ||dd d S )Nr=  r  r  r.  ry   r  r  r`  ra  rP  r   ri   rL   r   rS   )r  r   r^  r    rA  r7   r,  r_   r   rQ  r   r0  r<  r  rD   rD   rE   #test_factorial2_scalar_corner_casesH
  s&   
""" z:TestFactorialFunctions.test_factorial2_scalar_corner_casesri   r
  ro   ic                 C   sp   t jdkrdnd}tttj||ddtj||dd|d ttj|g|ddttj|g|dd|d d S )Nr;   r  r  Tr4  FrS   )r  r  r   rv   r    r6  r   )rC   rh   ri   rT   rD   rD   rE   test_factorialk_accuracy`
  s   
z/TestFactorialFunctions.test_factorialk_accuracyr  c                 C   s  t tjtt|d| d}t|tj||dd t|tj|g|ddd  t	j
dkr/dnd}t|}t|tj||dd|d	 t|tj|g|ddd |d	 |dd
d}|| dkrd}t|tj|fi ||d	 t|tj|gfi |d |d	 d S d S )Nr   rZ   Tr:  r;   gt =r  FrS   r  rg  r  )r  r  r  r  rE  ru   r   r    r6  r  r  rv   r   )rC   rh   ri   r  rT   rB  rD   rD   rE   test_factorialk_int_referenceo
  s    &z4TestFactorialFunctions.test_factorialk_int_referencec                 C   s   dd }|ddt j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ddd |dddd |dddd |d dd!d |d"dd#d d S )$Nc                 S   sR   d}|ddd}t tj| fi |||d t tj| gfi |d ||d d S )Nr  Fr  rg  rS   r   )r   r    r6  )rh   ri   r   rT   rB  rD   rD   rE   rU  
  s   &zHTestFactorialFunctions.test_factorialk_complex_reference.<locals>._checkrJ   r   Tr4  )rh   ri   r   r   gD!)@g      @gNq53@r  gG`@r  g     @y             @y            @y      @      @yRsU#[@y      @      y?M,a?y@/n?'?r`  gyL_ǚZ?r  yyL_ǚZ?        g333333@gffffffyNV?*V7?g333333y)kh]bg):giߑT@y      -C6?y(5E?WTr    r6  r  rD   rD   rE   !test_factorialk_complex_reference
  s    z8TestFactorialFunctions.test_factorialk_complex_referencec                    s*  |t jkrtdd |D rtd |t jkr&tdd |D r&td d||d |dks6t|dkr8|n|d }t j|||d	}d }|d
krm|rmtjt	dd t
j|fi   W d    n1 sgw   Y  n_t|jg dstjt	dd t
j|fi   W d    n1 sw   Y  n6t|jddgr|d
krtjt	dd t
j|fi   W d    n1 sw   Y  n	t
j|fi  }|d ur fdd| D }t|dkr|d n|}|jr|d
kot|jd}	|	rt jn|rtnt j}t j|||d	}
t||
dd d S d S )Nc                 s   r  r  r  r  rD   rD   rE   r  
  r  zLTestFactorialFunctions.test_factorialk_array_corner_cases.<locals>.<genexpr>r  c                 s   r  r  r  r  rD   rD   rE   r  
  r  r   rg  r   rZ   r  r  r  r.  r_  r`  r  r  ra  c                    r  rD   r  r  rT  rD   rE   rB  
  r  zMTestFactorialFunctions.test_factorialk_array_corner_cases.<locals>.<listcomp>r  rS   )r_   rK  r  r  r  r   r  r   r   r^  r    r6  r7   r3  rd   r   rQ  rG  r0  r  rD   rT  rE   "test_factorialk_array_corner_cases
  sB   

 
z9TestFactorialFunctions.test_factorialk_array_corner_casesc                 C   s  |||d}|dkr/|r/t jtdd tj|fi | W d    d S 1 s(w   Y  d S tt|dddtd gs_t jtdd tj|fi | W d    d S 1 sXw   Y  d S tt|ddgr|dkrt jtd	d tj|fi | W d    d S 1 sw   Y  d S |d u st|r|dkott|d}|rt	d
nt
d}ttj|fi || d S | j|fi |}ttj|fi ||dd d S )Nrg  r  r  r.  ry   r  r  r`  ra  rP  r   r   rS   )r  r   r^  r    r6  r7   r,  r_   r   rQ  r   r0  r<  )rC   rh   ri   r;  r:  rB  rR  r!  rD   rD   rE   #test_factorialk_scalar_corner_cases
  s&   """ z:TestFactorialFunctions.test_factorialk_scalar_corner_casesrO   r   r   c                 C   s   |rdgnd}|||d}|dkrCd}t t|dr |dk r d}tjt|d tj|fi | W d    d S 1 s<w   Y  d S |dkrjtjtd	d tj|fi | W d    d S 1 scw   Y  d S tj|fi | d S )
NrZ   rg  r5  ra  ry   zFor `extend='zero'`.*r.  r   zParameter k cannot be zero!)r7   r,  r  r   r^  r    r6  )rC   ri   r;  r:  rW  rh   rB  rW  rD   rD   rE    test_factorialk_raises_k_complex
  s   ""z7TestFactorialFunctions.test_factorialk_raises_k_complexr\  c                 C   s`   |rdgnd}|||d}t jtdd tj|fi | W d    d S 1 s)w   Y  d S )NrZ   rg  r`  r.  )r  r   r^  r    r6  )rC   ri   r;  r:  rW  rh   rB  rD   rD   rE   test_factorialk_raises_k_other  s
   "z5TestFactorialFunctions.test_factorialk_raises_k_otherr  c                 C   sD  |||d}|r|t  v rtt| g}ttj|fi |jt	 ttj|d fi |jtj
 tj|d fi |ttjjksGJ tt | g}ttj|fi |jtj
 ttj|d fi |jt tj|d fi |ttj
jksJ d S tt |dg}|rtntj}ttj|fi |j| d S )Nrg  rZ   )r5   keysr_   r   r6   r   r    r6  r3  r0   rK  rF  int32rG  rn  getr   )rC   ri   r;  r:  rB  rh   r3  rD   rD   rE   test_factorialk_dtype  s    (,z,TestFactorialFunctions.test_factorialk_dtypec                 C   s   t t jdddt jg}t t jdddt jg}ttj|dd| tjtdd tj|d	d W d    d S 1 s<w   Y  d S )
NrZ   rL   r   rP   Fr:  r  r.  T)	r_   r   r   r   r    r@  r  r   r^  rC   r   r!  rD   rD   rE   test_factorial_mixed_nan_inputs)  s   "z6TestFactorialFunctions.test_factorial_mixed_nan_inputs)<r  r  r  r<  r  r  r7  rC  rE  rH  rN  rV  r_   r   r   rQ  r   
datetime64r    r@  rA  r6  re  rh  ru   rt  rt   int8int16r  rK  uint8uint16uint32uint64rx  rz  r}  r  rE  r  r  r  rn  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rD   rD   rD   rE   r3  a  s*   	



"&!



*+$

*&$*&$r3  c                   @   sb   e Zd Zejddddddddd	d
ejddfej ddfgdd Zdd Z	dd Z
dd ZdS )TestFresnelzz, s, c)r   gN?ց[?)y      ?        r  r  )y       ?yn<ӿj<Cy)BR;߿ux7Q?)y      yھ|}-2?y/?!ۿ)r]  GM?pBR?)y      @        r  r  )y              @y       GMܿy        pBR?)y              gGMܿgpBR߿)y             y        GM?y       pBR߿r   r`  c                 C   s&   t t|}t|t ||gd d S )Nr  )r   r    r4  r   )rC   r   rV  r  frsrD   rD   rE   test_fresnel_values2  s    zTestFresnel.test_fresnel_valuesc                 C   sn   t d\}}t|tg dd t|tg dd t |d }t |d }t|dd t|dd d S )Nr   )y @X9v?y^I@48E?y=
ףp@+?y@eX?yO@Ǻ?r   )y.1?ǘ?yʡE6@:#J{/?yq-
@y&1?yh o@߾3?yW2q@qh?r   rZ   r  )r    fresnel_zerosr   r   r4  )rC   szoczovals1vals2rD   rD   rE   test_fresnel_zerosW  s   

zTestFresnel.test_fresnel_zerosc                 C   s(   t d\}}t d}t||d d S )NrP   r  )r    r  fresnelc_zerosr   )rC   r  r  frcrD   rD   rE   test_fresnelc_zerosj     
zTestFresnel.test_fresnelc_zerosc                 C   s(   t d\}}t d}t||d d S )Nr   r  )r    r  fresnels_zerosr   )rC   r  r  r  rD   rD   rE   test_fresnels_zeroso  r  zTestFresnel.test_fresnels_zerosN)r  r  r  r  r  r7  r_   r   r  r  r  r  rD   rD   rD   rE   r  1  s$    

r  c                   @   s   e Zd Zdd Zdd Zdd Zedd Zed	d
 Zdd Z	dd Z
ejdej ejgejejgfddgej ejgfeddedejfedddedejfdgejgfgdd ZdS )	TestGammac                 C   r  r6  )r    r8  r   )rC   gamrD   rD   rE   r9  v  r  zTestGamma.test_gammac                 C   s(   t d}tt d}t||d d S )Nr   r  )r    r<  r   r8  r   )rC   gamlnlngamrD   rD   rE   r=  z     
zTestGamma.test_gammalnc                 C   s(   t dd}t dd}t||d d S )Nr   r  )r    r:  gammaincinvr   )rC   gccinvgcinvrD   rD   rE   r;       zTestGamma.test_gammainccinvc                 C   sv   t dd}t d|}t|dd t dd}t dd}td|dd t|ddd t dd}td	|dd d S )
NrM   rZ   r&  g?g`	\;r   rD  gmb<g      &@)r    r  gammaincr   rC   r  r   rD   rD   rE   test_gammaincinv  s   zTestGamma.test_gammaincinvc                 C   sR   dt dddt dddg}|D ]}td|}td|}t||dd qd S )	Nr  r   gCs?rZ   g^F    ?rM   r   rS   )r_   r  r    r  r  r   )rC   ptsxpr  r   rD   rD   rE   test_975  s   zTestGamma.test_975c                 C   s(   t d}dt d }t||d d S )Nr  rZ   )r    rK  r8  r   )rC   rgamrlgamrD   rD   rE   rL    r  zTestGamma.test_rgammac                 C   r   )NrO   r   )r   r    rK  rB   rD   rD   rE   test_infinity  r   zTestGamma.test_infinityz
x,expectedr@  r   ir       i c   r  gP²Zdbc                 C   s   t t|| d S r  )r   r    r8  r  rD   rD   rE   
test_poles  s   zTestGamma.test_polesN)r  r  r  r9  r=  r;  r8   r  r  rL  r  r  r  r7  r_   r   r   ru   fullr  rD   rD   rD   rE   r  u  s(    

r  c                   @   r  )
TestHankelc                 C   "   t tddtdd d d S NrD  rL   r   r  )r   r    rT  rB   rD   rD   rE   
test_negv1     "zTestHankel.test_negv1c                 C   8   t dd}t ddt ddd  }t||d d S NrZ   r  r  r  )r    rT  r  r  r   )rC   hank1hankrlrD   rD   rE   rU       zTestHankel.test_hankel1c                 C   r  r  )r   r    rV  rB   rD   rD   rE   test_negv1e  r  zTestHankel.test_negv1ec                 C   0   t dd}t ddtd }t||d d S )NrZ   r  y       r  )r    rV  rT  r   r   )rC   hank1ehankrlerD   rD   rE   rW    r  zTestHankel.test_hankel1ec                 C   r  r  )r   r    rX  rB   rD   rD   rE   
test_negv2  r  zTestHankel.test_negv2c                 C   8   t dd}t ddt ddd  }t||d d S r  )r    rX  r  r  r   )rC   hank2hankrl2rD   rD   rE   rY    r  zTestHankel.test_hankel2c                 C   r  r  )r   r    rZ  rB   rD   rD   rE   
test_neg2e  r  zTestHankel.test_neg2ec                 C   s(   t dd}t dd}t||d d S )NrZ   r  r  )r    rZ  r   )rC   hank2ehankrl2erD   rD   rE   test_hankl2e  r  zTestHankel.test_hankl2ec                 C   s0   t dd}t|jsJ t|jsJ d S r?   )r    rX  r_   r   r   isposinfr  rC   ro  rD   rD   rE   test_hankel2_gh4517  s   zTestHankel.test_hankel2_gh4517N)r  r  r  r  rU  r  rW  r  rY  r  r  r  rD   rD   rD   rE   r    s    r  c                   @   s\   e Z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 )	TestHyperc                 C   r  r  )r    h1vpjvpyvpr   )rC   h1h1realrD   rD   rE   	test_h1vp  r  zTestHyper.test_h1vpc                 C   r  r  )r    h2vpr  r  r   )rC   h2h2realrD   rD   rE   	test_h2vp  r  zTestHyper.test_h2vpc                 C   s  t tddddd t tddddd td	g d
}tg d}t ||dd td	tg d
d }t ||tdd g d}g d}t||}g d}t ||dd tt|gd |}t |t|gd dd tt	tjt|gd ddg d S )Nr  r   Qvo?r   rS   r   r   r   r   )g      rO   r   rZ   r  )g̷?g3|t-Ք?r   go?g{h?r  r   r  r  )r   rZ   r   )r   gc?r  rL   r   rZ   )
r   r    hyp0f1r_   r   r   r  vstackassert_raisesr^  )rC   r   r!  r  x2rD   rD   rE   test_hyp0f1  s"   zTestHyper.test_hyp0f1c                 C   s   t dd}t|d d S )N皙?y      ?      ?y;EG?uM?)r    r  r   r
  rD   rD   rE   test_hyp0f1_gh5764  s   zTestHyper.test_hyp0f1_gh5764c                 C   s  t ddd}t|dd tg g dg dg dg dg d	g d
g dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg d g d!g d"g d#g d$g d%g d&g d'g d(g d)g d*g d+g d,g d-g d.g d/g d0g d1g d2g d3g d4g d5g d6g d7g d8g d9g d:g d;g d<g d=g d>g d?g d@g dAg dBg dCg dDg dEg dFg dGg dHg dIg dJg dKg dLg dMg dNg dOg dPg dQg dRg dSg dTg dUg dVg dWg dXg dYg dZg d[g d\g d]g d^g d_g d`g dag dbg dcg ddg deg dfg dgg dh}|D ]\}}}}t |||}tt|| | dik  qd S )jNr  r  g?rN   )g{*= g˱a)g5=gvX@)g)AI@gDAhg$Pj)g~٭@)g,qUp,g@=&?gX 3@gZ@)g\@g88*@g\ֳ!=@g   ƞA)gAZ;gOFA'gxŝO<g_Dc D)g^g@g V*E7g4)3@g7-XtD)gΧU(@g2Tj8g$@g  LhB)ge;@gJgogr@g `屫B)g5'.@gqZ=g7߈Y.g8w)gB,@g"^#@grT[	R3@g  B)gYgN],*@g*!j,g1@)g#r @gq{874*gWs%o.@gMdD)g8|.2@g*!,g?I(#@gJ
r .)gu8g#=)@g*'1g)ψvA)g%0N:@gUx1@gx@gr),c@)g:M8@gGb+=@g3ҜV/@gX9ҙim@)g"dxz@gqKgv7##@g  >B)g kx-gD8L+8@g܈2g72LU@)gtd@Q4h6@g%@}gr3b @gu߯ѡ)g򋷺?g"p$`E2@gY|T3g\D?)gV-(+@g$[3@g;/@gEQwв@)g[fgLL4gQV@g0#.@)g;@g/?jvgx.<N&@g^I)g+9gX[?gbZSH%@g5/)@)g}RgŢ	@g},*@g6@g1w-@)gRA(g_@g5A} :=g   FA)gQz5@gq.#gTq&gc ?)gφ%#gZV@
g%@0@g   Syd)gB۽ܟ%@g*>8gV@'g	ʦ)g/H:gn@S g)bǙ9@g  9)gT쁹3!gD gkLFr%@g3333`4A)g:k
g\=)'gi,k9gbx?)giXwg-CwU5@g'jin9gX5@)gb@gTy4#/@g]pH=gIw?)g63@g2XxM:@g~?^0gW1?)g37g R{@gicx.4?gmm?)gv܏%7@g9Ma%=g}ygGr##@)gG8-xы.@gǂ@ghb(@g  A)gw1@gq2@gO],@g0ɷ-X@)g2@g́y#<@gͣx?g]?)g];˄f$@g1}0g_9g8ڃ@)g:!ω1g)q(@gg2gv%)A)gYN:+gn	Ȱ-?g>gZd|I.A)gr/K@g\}L9@g*gΙ?)gQq5V@g?)@g'@0@glۭ`@)gVn:gRQ0gT&g QC)gR4 8gi+gK @g{G)gtiq+g(O?3g	1=@g  8cB)g|>oϘg\!<@g"?4V?g%c\q?)g gpfP!gAO:@g,\)g=R8@g%;gz3@g~0G)g.CVl@ge< .@g9@gkq1A)g=~$gpR7@g 77g,ǆ@)g^g{)gRA2@g  dL)gf=4,R@gyO-g#ޕ~8@g)g|ݩ%P4g:<9@gKzs4g$(~O4@)g2y3@g1$6g&TpxA6gG!JA)gf^XH
^;@g7r:@g`,/@gi{dA)gihx@g!B8(@g7j*@gh@)glmF<gpO4@g`2"@g-)gnV3!2@g.mq1g!Z{.@grOE)gs`m@gzAUguC=V#@g  \)gPL-(@g,9$"9g6u7@geRF)gw8gv=5@gjRW+g(\-@)gyg~=@g4MVgwz:@)g^0g+7%g-@j81g5ׂ,j)gj4gz0g-</;gݽ]
D)gN43@g}W6@gLUS!9gɍF>)g Q4@g=}gȮ5@g]nhgF)gV9g9gf9,#gF|}fv?)g=^ee;@gy}2g'T> g#o@)g+5g;gN8Cg8@g   bkA)gSx+26@g@gI0gSMC)gT*0@g`<6gWy5@gǟRj)gӰk
g/:?gJLHR"@gxu-)gKu@g6gt8_x7@gd;=')g+:;@gBͤ10@g";gK$?)gp @g dg	=@g=6` F)gTbR.g9:g3@gUfgRbKZ@)g!g%P73;g]?gr	y?)g)Yv2gȹq@g/3g   A)g?j/|g7:@g#~oݽ?g8pE?)gPj/gS"X)gYgt0N?)ggo&	xT7@g-hT@#@g.;%r?)g'_@gɖ@7g:Kڞ$@g [B)gk5ں9gѼ:gk%tp;@g  .<^)gf:OI&gO/g#01|2gf`Y)gqv~@guFd9@gz+S7gF1/$?)gx3g~[6:g;s9@gKw*1@)gP@gv;K,gҬd&<@g!s)gֈ`|.gOwx=@g+MK<gUU@)gکI@g©jG1g4g؃66@g(4ν4E)gS>?gD-lgSL,c<gԉE4?)gd?A g3$)glx^?gs>|T?)g(%@g:ĉ$@g~^gv2gJHF&?)g}r":@g3\z;@go)@g+hA)g@')"gVv/@guQU-gfy2yt@)gM6y%$g/;R#@g):@gw%",6Կ)g%x'g$6g5gu$9?)glkC9g<tF8gp?g ?r  )r    r]  r   r   r   r  )rC   hyp1ref_datar  r  r  r!  r  rD   rD   rE   r^    s  	
 !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdgzTestHyper.test_hyp1f1c                 C   s,   t ddd}t ddd}t||d d S )Nr   r  g7B.g|:B.r  r    r]  r   )rC   r   hyp2rD   rD   rE   test_hyp1f1_gh2957  s   zTestHyper.test_hyp1f1_gh2957c                 C   s   t ddd}t|dd d S )Nr   r  ig<`?r  r"  )rC   hyprD   rD   rE   test_hyp1f1_gh2282  s   zTestHyper.test_hyp1f1_gh2282c           	      C   s  dddddt d gdddddtd	 gddd
d	dt d gg ddddtd	d
 tdgddddtdtd td td gdd
d
ddtt td
 td td gdd
dddtt td td td gdddddtd td td td gg dg d g d!g d"g d#d$d%g}t|D ]\}\}}}}}t	||||}t
||dd&| d' qd S )(Nr   rZ   r  |Gz?r  g?g|Gzr   r   rL   r  r  )r   rP  r  r'  gYi2?rD  r   g433333?rJ   r  r   rO   r  r   g      ?r         @g      gUUUUUUտg  @gUUUUUU?g)r  r`  r         $gEciH!@)r  r   rZ   r4  gzG?)rL   rD  rZ   r4  gy&1|)r\  r   rZ   r4  g"nN%@?)rL   rF  rZ   r4  g!J)r&  |      %@r  gzS;)r&  r*  g      %r  g[B.VP<test #%derr_msg)r   r   r   r	   r    r8  r   r   r  r`  r   )	rC   r   ry   r  r  r  r   r  cvrD   rD   rE   ra    sZ   zTestHyper.test_hyp2f1c                 C   s   t ddd}t|dd g dg d}}t|t|}}d}t |||}ttt|  t |||t d| | t |  |d|  t d| | d	| | t |t d	|     }t||d
 d S )NrZ   r  r  g D?rN   )r  rk  333333?g)r  g	@r  g	r   rL   r  )	r    hyperur   r   r   r   r]  r8  r   )rC   val1r  r  r   hypuhprlrD   rD   rE   test_hyperu  s   $zTestHyper.test_hyperuc                 C   s   t tddddd d S )NrZ   r  g3333334@g(¨?r  )r   r    r1  rB   rD   rD   rE   test_hyperu_gh2287  s   zTestHyper.test_hyperu_gh2287N)r  r  r  r  r  r  r  r^  r$  r&  ra  r5  r6  rD   rD   rD   rE   r    s    t$r  c                   @   s  e Z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d  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Z d=d> Z!d?d@ Z"dAdB Z#dCdD Z$dEdF Z%dGdH Z&dIdJ Z'dKdL Z(dMdN Z)dOdP Z*dQdR Z+dSdT Z,dUdV Z-dWdX Z.dYdZ Z/d[d\ Z0d]d^ Z1d_d` Z2dadb Z3ddfdgZ4e5j6j7e89 dhkdidjdkdl Z:e5j6j7e89 dhkdidjdmdn Z;dodp Z<dqdr Z=e5j6j>dsdt Z?dudv Z@dwdx ZAdydz ZBd{d| ZCd}d~ ZDdd ZEdd ZFdddZGdd ZHdd ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQdd ZRdd ZSdd ZTdd ZUdeS )
TestBesselc                 C   &   t td}t|t ddgd d S )Nr   gbɃ?gΝJ ֿr  )r   r    rt  r   )rC   it0rD   rD   rE   ru       
zTestBessel.test_itj0y0c                 C   r8  )Nr   gbqTtt?g/]ooۿr  )r   r    rl  r   )rC   it2rD   rD   rE   rm    r:  zTestBessel.test_it2j0y0c                 C      t tddtdd d S Nr   rL   rD  )r   r    rz  rB   rD   rD   rE   test_negv_iv     zTestBessel.test_negv_ivc                 C   &   t d}t dd}t||d d S Nr  r   r  )r    r~  r  r   rC   ozozrrD   rD   rE   r    rp  zTestBessel.test_j0c                 C   r@  Nr  rZ   r  )r    r  r  r   rC   o1o1rrD   rD   rE   r    rp  zTestBessel.test_j1c                 C      t dd}t|dd d S )NrZ   r   ;x?r  )r    r  r   )rC   jnnrrD   rD   rE   r       zTestBessel.test_jnc                 C   r  r  )r   r    r  rB   rD   rD   rE   test_negv_jv  r  zTestBessel.test_negv_jvc                 C   s^   g dg dg dg dg dg}t |D ]\}\}}}t||}t||dd| d qd S )	N)r   r  g
Ye?)UUUUUU?:0yE>g˿+>)rN  r\   g)%->)g@r\   g5c)!9)rN  r  g%,Ϳr  r,  r-  )r  r    r  r   )rC   r   ry   r  r   r  ycrD   rD   rE   r    s   zTestBessel.test_jvc                 C   r  r  )r   r    r  rB   rD   rD   rE   test_negv_jve  r  zTestBessel.test_negv_jvec                 C   sT   t dd}t|dd t dd}d}t d|tt|j  }t||d d S )NrZ   r   rJ  r  ?      ?)r    r  r   r  r   r  r  )rC   jvexpjvexp1r   jvexprrD   rD   rE   r    s   zTestBessel.test_jvec                 C   s   t dd}t dd}t|tg dd t|tg dd t dd}t|tg dd	d
 t dd}t|tg dd	d
 d S )Nr   r   rZ   )go@.=@gzj,[@glN!@g5/ D'@gh>-@rJ   gW@g0@gQX$@g*@g8*5{x0@rY   )gEk[@g~Cju]@gYrʝ^@g, `@gf	`@rR   rS   -  )gts@g&ǭr3t@gWt@g,$Y&u@gu@)r    jn_zerosr   r   r   )rC   jn0jn1jn102jn301rD   rD   rE   test_jn_zeros  s    
zTestBessel.test_jn_zerosc                 C   s   t dd}t|d ddd t|d ddd t|d	 d
dd t dd}t|d ddd t|d ddd t|d	 ddd t dd}t|tg ddd d S )Nr   rn   i  g;@rR   rS   i  g8v@i+  gׂMm@r&  gxi@g	,@gи{>@i  r   )gUDX@g!@g*HS@gz5 @g@2;@rO  )r    rX  r   r   )rC   rY  jn10jn3010rD   rD   rE   test_jn_zeros_slow  s   
zTestBessel.test_jn_zeros_slowc           
         s   t j  fdd}tddD ]:}t |\}}}}t|||D ](\}}}	|	dkr3t ||ddd q|	dkrBt|||ddd qtd| qd S )	Nc                    s     | d | | d | d S )NrZ   rL   rD   )rh   r   r  rD   rE   jnp,  r+  z(TestBessel.test_jnjnp_zeros.<locals>.jnprZ   rV   r   r%  rC  zInvalid t return for nt=%d)r    r  ru   jnjnp_zerosr/  r   AssertionError)
rC   rb  ntr   rh   r  tzznnttrD   ra  rE   test_jnjnp_zeros)  s   zTestBessel.test_jnjnp_zerosc                 C   sF   t dd}t|tg dd t dd}tt d|ddd d S )	NrZ   r   g(yu?gOXeS@ga!@gxi'@g'Nw(-@rJ     r   r   rC  )r    	jnp_zerosr   r   r   r  )rC   rb  rD   rD   rE   test_jnp_zeros8  s   zTestBessel.test_jnp_zerosc                 C   sD   t dd}t|tg dtg dtg dtg dfd d S )NrZ   r   rV  rk  )"@g+@g-9(1!@gȘ'@g>tA}-@)g0v@gjt@gH.?$@g}"O*@gGŧp0@)r    
jnyn_zerosr   r   )rC   jnzrD   rD   rE   test_jnyn_zerosB  s   


zTestBessel.test_jnyn_zerosc                 C   s8   t dd}t ddt dd d }t||d d S )NrL   rZ   r   r&  )r    r  r  r   )rC   jvprimjv0rD   rD   rE   test_jvpY  r  zTestBessel.test_jvpc                 C   r@  rA  )r    r  r  r   )rC   ozkozkrrD   rD   rE   r  ^  rp  zTestBessel.test_k0c                 C   r@  rA  )r    r  r  r   )rC   ozkeozkerrD   rD   rE   r  c  rp  zTestBessel.test_k0ec                 C   r@  rE  )r    r  r  r   )rC   o1ko1krrD   rD   rE   r  h  rp  zTestBessel.test_k1c                 C   r@  rE  )r    r  r  r   )rC   o1keo1kerrD   rD   rE   r  m  rp  zTestBessel.test_k1ec           
      C   s  dt j  d }dt j  d }td||}td||}td||}td||}t|jdgd t|jt|| d || gd d || d || d  d|| d  |d  d|d  |d  g}|d |d d|d   |d |d  |d  g}t|jt|d	 d || d || d  || d
  d
|| d  || d  |d  d|| d  |d  |d  d|d  |d  |d  g}|d |d d|d   |d d|d   d|d   |d |d  |d  |d  g}	t|jt|	d d d S )Nr   rZ   r   rL   r   r  r   rJ   r   rP   r  r  g      H@)r_   re   r    jacobir   r  r   )
rC   r  r  P0P1P2P3cpp2cp3crD   rD   rE   test_jacobir  s    &B2D8XzTestBessel.test_jacobic                 C   rI  )Nr   r   _2?r  )r    r  r   )rC   kn1rD   rD   rE   r    rL  zTestBessel.test_knc                 C   r<  Nr   r#  rO  r   r    r  rB   rD   rD   rE   test_negv_kv  r?  zTestBessel.test_negv_kvc                 C   rI  )Nr   r   r  r&  r    r  r   )rC   kv0rD   rD   rE   test_kv0  rL  zTestBessel.test_kv0c                 C   rI  )NrZ   r   gKދ@r&  r  )rC   kv1rD   rD   rE   test_kv1  rL  zTestBessel.test_kv1c                 C   rI  )NrL   r   g)lHH@r&  r  )rC   kv2rD   rD   rE   test_kv2  rL  zTestBessel.test_kv2c                 C   r   )Nr  rZ   g.Ք"H)r   r    r  rB   rD   rD   rE   test_kn_largeorder  r   zTestBessel.test_kn_largeorderc                 C   s   t tddd d S )Nr   g =`XCr  rB   rD   rD   rE   test_kv_largearg  r   zTestBessel.test_kv_largeargc                 C   r<  r  )r   r    r  rB   rD   rD   rE   test_negv_kve  r?  zTestBessel.test_negv_kvec                 C   s`   t dd}t ddtd }t||d d}t d|}t d|t| }t||d d S )Nr   r   r  rR  )r    r  r  r   r   )rC   kve1r  r   kve2r  rD   rD   rE   r    s   zTestBessel.test_kvec                 C   s*   d}t td| tjd|ddd d S )Nr#  rZ   r   rh   r&  )r   r    r  kvp)rC   r   rD   rD   rE   test_kvp_v0n1  s   &zTestBessel.test_kvp_v0n1c                 C   sN   d}d}t |d | || t ||  }t j||dd}t||d d S )Nr   r#  rZ   r  r&  r    r  r  r   rC   r  r   xcr   rD   rD   rE   test_kvp_n1  s
   &zTestBessel.test_kvp_n1c                 C   sd   d}d}|d |d  | |d  t || t |d ||  }t j||dd}t||d d S )Nr   r#  rL   rZ   r  r&  r  r  rD   rD   rE   test_kvp_n2  s
   <zTestBessel.test_kvp_n2c                 C   r@  rA  )r    r  r  r   rB  rD   rD   rE   r    rp  zTestBessel.test_y0c                 C   r@  rE  )r    r  r  r   rF  rD   rD   rE   r    rp  zTestBessel.test_y1c                 C   sp   t d\}}t jddd\}}t||f }t||f }ttt d|dd ttt d|| dd d S )NrL   rZ   r  r   r  )r    y0_zerosr   r   r  r  )rC   yoypozozpor  allvalrD   rD   rE   test_y0_zeros  s    zTestBessel.test_y0_zerosc                 C   s*   t d}t|tdgtdgfd d S )NrZ   ro  gѮBO?r   )r    y1_zerosr   r   )rC   r  rD   rD   rE   test_y1_zeros  s   
 zTestBessel.test_y1_zerosc                 C   s.   t jddd}t|tdgtdgfd d S )NrZ   r  yL
F%u?!rh?y;OnгY?r   )r    	y1p_zerosr   r   )rC   y1prD   rD   rE   test_y1p_zeros  s   zTestBessel.test_y1p_zerosc                 C   sB   t dd}t|tddgd t dd}t|g ddd	 d S )
NrJ   rL   g3@g(A&"@r   rl  )g]E.+"|@gH(|@gff|}@g&b`~@gHO_~@r   rS   )r    yn_zerosr   r   r   )rC   anrD   rD   rE   test_yn_zeros  s   

zTestBessel.test_yn_zerosc                 C   sh   t dd}t|tddgd t dd}tt d|ddd	 t d
d}tt d
|ddd	 d S )Nr   rL   gQhվ@gzN@rP   +   r   r   rC  rl  r   )r    	ynp_zerosr   r   r   r  rC   aorD   rD   rE   test_ynp_zeros  s   zTestBessel.test_ynp_zerosc                 C   s&   t dd}tt d|ddd d S )Nrl  r   r   r  rC  )r    r  r   r  r  rD   rD   rE   test_ynp_zeros_large_order  s   z%TestBessel.test_ynp_zeros_large_orderc                 C   rI  NrZ   r   5,1
r  )r    r  r   )rC   yn2nrD   rD   rE   r    rL  zTestBessel.test_ync                 C   s    t dd}|tj ksJ d S )NrX   rZ   )r@   r  r_   r   )rC   observedrD   rD   rE   test_yn_gh_20405  s   zTestBessel.test_yn_gh_20405c                 C   r  r  )r   r    r  rB   rD   rD   rE   test_negv_yv  r  zTestBessel.test_negv_yvc                 C   rI  r  )r    r  r   )rC   yv2rD   rD   rE   r    rL  zTestBessel.test_yvc                 C   r  r  )r   r    r  rB   rD   rD   rE   test_negv_yve   r  zTestBessel.test_negv_yvec                 C   sH   t dd}t|dd t ddtd }t dd}t||d d S )NrZ   r   r  r  rR  rO   )r    r  r   r  r   )rC   yve2yve2ryve22rD   rD   rE   r    s
   zTestBessel.test_yvec                 C   s8   t ddt dd d }t dd}t||d d S )NrZ   r   r   r   rL   r&  )r    r  r  r   )rC   yvpryvp1rD   rD   rE   test_yvp
     zTestBessel.test_yvpc                 c   sF    g d}g d}t ||E dH  t dtdd dgE dH  dS )z>Yield points at which to compare Cephes implementation to AMOS)ir         4r)  r   r`  r   r   {G(@r9  rW  )ir  rO   r   r        i@g     y@g     Ă@g@  i'  Nr   ir  rP  )	itertoolsproductr   )rC   r  r   rD   rD   rE   _cephes_vs_amos_points  s
   "z!TestBessel._cephes_vs_amos_pointsdy=r   Nc                 C   s   |   D ]a\}}|d ur|||rq||||||d |t||}}	}
t|r9tt|	dk||f qt|rIt|	jdk||f qt||	||f||d |t|kret|
|	||f||d qd S )Nr  u <7~r   )r.  rT   r^   )	r  rt   r_   r  r   r  r   r  r   )rC   r  f2rT   r^   r  r  r   c1c2c3rD   rD   rE   check_cephes_vs_amos  s   *

zTestBessel.check_cephes_vs_amosppc64lezfails on ppc64ler  c                 C      | j tjtjddd d S )Nr\   u5% r  )r  r    r  r  rB   rD   rD   rE   test_jv_cephes_vs_amos*     z!TestBessel.test_jv_cephes_vs_amosc                 C   r  )Nr  r  r  r  r    r  r  rB   rD   rD   rE   test_yv_cephes_vs_amos/  r  z!TestBessel.test_yv_cephes_vs_amosc                 C   s$   dd }| j tjtjdd|d d S )Nc                 S   s   t | dkS )NrD  )r  )r  r   rD   rD   rE   skipper5  s   zDTestBessel.test_yv_cephes_vs_amos_only_small_orders.<locals>.skipperr  r  )rT   r^   r  r  )rC   r  rD   rD   rE   (test_yv_cephes_vs_amos_only_small_orders4  s   
z3TestBessel.test_yv_cephes_vs_amos_only_small_ordersc                 C   sH   t jdd | jtjtjddd W d    d S 1 sw   Y  d S )Nr  r  g:0y5>r  r  )r_   r0  r  r    rz  rB   rD   rD   rE   test_iv_cephes_vs_amos:  s   "z!TestBessel.test_iv_cephes_vs_amosc           	   
   C   sz  d}t jd t jd|dt jjd|d  }t jd|dt jjd|d  }t jjd|dd	k}|| t j||< t jd
dG t	||}t	||d }t j
|t|dk< t j
|t|dk< d	|t|dk < d	|t|dk < t|| d }d	|t |< W d    n1 sw   Y  t |}t|| dk || || t	|| || t	|| || d f d S )Ni@B rZ   r   rO   rL   r   r   r  r   r  r  r  r  gYngH׊>)r_   re   rp   r  r  r   rK  r0  r    rz  r   r  r   argmaxr   )	rC   Nr  r   imskr  r  dcri   rD   rD   rE    test_iv_cephes_vs_amos_mass_test>  s*   ""

6z+TestBessel.test_iv_cephes_vs_amos_mass_testc                 C   s0   | j tjtjddd | j tjtjddd d S )Nr   r  r  )r  r    r  r  rB   rD   rD   rE   test_kv_cephes_vs_amos^     z!TestBessel.test_kv_cephes_vs_amosc                 C   s:   t tddd t tddd t tddd d S )	Nr   rJ   gP?rW  r  g~Omʒ?gY8E@@gKSn)r   r    r  rB   rD   rD   rE   test_ticket_623b  ru  zTestBessel.test_ticket_623c                 C   s  t tddd t tddd t tddd t tddd t tddd t tddd	 t tddd
 t tddd t tddd t tddd t tddd t tddd t tddd t tddd t tddd t tddd t tddd t tddd	 t tddd
 t tddd t tddd t tddd t tddd t tddd t tddd t tddd t tddd t tddd t tddtddtd  t tddtddtd  t t	ddtddtd  t t
ddtddtd  t tddtdddtdd   t tddtdddtdd   dS )zNegative-order BesselsrO   rZ   gl)ܿr  gPj?gk?g%E*2ig敋?gw--`?gÉB?gW?r`  g޴?gz|?a?gpx%?y      ?        y      ?      ?yYD?`{1wy6x?B]#Ӯ?y ?b>?y.}9d?8kؿy      ?333333?r*  y333333?      ?r  N)r   r    r  r  rz  r  r  r   r  r|  r  rT  rX  rB   rD   rD   rE   test_ticket_853g  sP   """"

zTestBessel.test_ticket_853c                 C   sB  t ttdd t ttdd t ttdd t ttdd t ttdd t ttdd t ttdd t ttdd t tt	dd t tt	dd t tt
dd t tt
dd t ttddd  td t ttddd   td dS )zReal-valued Bessel domainsr   rO   rZ   r   rL   rJ   N)r   r   r    r  rz  r  r  r  r|  r  r  rH   r  r  rB   rD   rD   rE   test_ticket_854  s   &,zTestBessel.test_ticket_854c                 C   s0   t tddtjk t tddtjk d S )Nr  r   )r   r    r  r_   r   r  rB   rD   rD   rE   test_gh_7909  r  zTestBessel.test_gh_7909c                 C   s(   t tddd t tddd dS )zReal-valued Bessel I overflowrZ   i  g~rW   i`  g ?los~Nr   r    rz  rB   rD   rD   rE   test_ticket_503  s   zTestBessel.test_ticket_503c                 C   r   )Nr`  rZ   r  r  rB   rD   rD   rE   test_iv_hyperg_poles  r   zTestBessel.test_iv_hyperg_poles   c                 C   s   t d|t}|d|  td|  t|d  t|| d  }t|t|< t|}t	|
 ttj | t	|d d  }| |fS )Nr   rL   r   rZ   rO   r&  )r   r   r   r   r    r<  r   r   r   r  rG  r   r5  sumrC   r  r   rh   ri   r;  r  rD   rD   rE   	iv_series  s   8*zTestBessel.iv_seriesc                 C   4   dD ]}|  d|\}}tt||||d qd S )Nr   r   r  r   r^   r.  )r  r   r    rb  rC   r   valuer  rD   rD   rE   test_i0_series     zTestBessel.test_i0_seriesc                 C   r  )Nr  rZ   r  )r  r   r    rf  r  rD   rD   rE   test_i1_series  r  zTestBessel.test_i1_seriesc                 C   sD   dD ]}dD ]}|  ||\}}tt||||||fd qqd S )N)r  r)  r   r   r   r  r9  )r   r   r  y             @r  )r  r   r    rz  rC   r  r   r  r  rD   rD   rE   test_iv_series  s   zTestBessel.test_iv_seriesc              	   C   sv   ddgddgddgddgddgd	d
gddgddgg}t |D ]\}\}}t|t|  }t||dd| d qd S )Nr   r   r\   r  g0oO?r   g!?grb?r  gpH?r   gC~?r   ggo?r  r,  r-  )r  r    rb  r   r   rC   r   ry   r   r  r/  rD   rD   rE   rc    s   	zTestBessel.test_i0c                 C   r@  rA  )r    rd  r|  r   )rC   oizeoizerrD   rD   rE   re    rp  zTestBessel.test_i0ec                 C   sp   ddgddgddgddgdd	gd
dgddgg}t |D ]\}\}}t|t|  }t||dd| d qd S )Nr   r\   gj|=r  gȕ![1?r   g;͘?r   gRΜ?r   g|?r   g}f?r  r,  r-  )r  r    rf  r   r   r  rD   rD   rE   rg    s   zTestBessel.test_i1c                 C   r@  rE  )r    rh  r|  r   )rC   oi1eoi1errD   rD   rE   ri    rp  zTestBessel.test_i1ec                 C   s&   t td}t|t ddgd d S )Nr   gїJB?@g*u?)r   r    rr  r   )rC   iti0rD   rD   rE   rs    r:  zTestBessel.test_iti0k0c                 C   s"   t d}t|tddgd d S )Nr  gݳɄ|T?gVƥ
@rP   )r    rj  r   r   )rC   it2krD   rD   rE   rk    s   

zTestBessel.test_it2i0k0c                 C   s$   t ddtd }t|dd d S )Nr   r  皙gv M?r&  )r    rz  r   r   )rC   iv1rD   rD   rE   r{    s   zTestBessel.test_ivc                 C   r<  r=  )r   r    r|  rB   rD   rD   rE   test_negv_ive  r?  zTestBessel.test_negv_ivec                 C   r  )Nr   r  r  r&  )r    r|  rz  r   r   )rC   ive1r  rD   rD   rE   r}  
  r  zTestBessel.test_ivec                 C   s    t tddtddd d S )NrZ   rL   r   r&  )r   r    rz  ivprB   rD   rD   rE   	test_ivp0  r+  zTestBessel.test_ivp0c                 C   s8   t ddt dd d }t dd}t||d d S )Nr   rL   rZ   r&  )r    rz  r  r   r  rD   rD   rE   test_ivp  r  zTestBessel.test_ivp)r  r   N)r  )Vr  r  r  ru  rm  r>  r  r  r  rM  r  rQ  r  r]  r`  rj  rn  rr  ru  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  r  r  r  r  r  r  machiner  r  r  r  slowr  r  r  r  r  r  r  r  r  r  r  r  rc  re  rg  ri  rs  rk  r{  r  r}  r  r	  rD   rD   rD   rE   r7    s    
	



2
r7  c                   @      e Zd Zdd Zdd ZdS )TestLaguerrec                 C   s   t d}t d}t d}t d}t d}t d}t|jdgd t|jddgd t|jtg d	d
 d t|jtg dd d t|jtg dd d t|jtg dd d d S )Nr   rZ   rL   r   rJ   r   r  rO   )rZ   r>  rL   r   )rO   r  irP   r]  )rZ   iH   ir   r7  )rO   r   i8iX  ir<  r9  )r    laguerrer   r  r   )rC   lag0lag1lag2lag3lag4lag5rD   rD   rE   test_laguerre  s   





zTestLaguerre.test_laguerrec              	   C   s   dt j  d }td|}td|}td|}td|}t|jdg t|jd|d g t|jtdd|d  |d	 |d
  gd
  t|jtdd|d  d|d  |d  |d |d  |d  gd  d S )Nr   r\  r   rZ   rL   r   rO   r  r   r   rD  r]  )r_   re   r    r  r   r  r   r   )rC   ri   r  r  r  r  rD   rD   rE   test_genlaguerre'  s   $>zTestLaguerre.test_genlaguerreN)r  r  r  r  r  rD   rD   rD   rE   r    s    r  c                   @   r  )
TestLambdac              	   C   sx   t dd}tt dddt dd d gtt dddt dd d dt dd d  gf}t||d d S )NrZ   r  r   rL   r  r   r  )r    lmbdar   r  r  r  r   )rC   lamlamrrD   rD   rE   
test_lmbda:  s
   "6zTestLambda.test_lmbdaN)r  r  r  r  rD   rD   rD   rE   r  9  r  r  c                   @   r  )	TestLog1pc                 C   sB   t dt dt df}tdtdtdf}t||d d S )Nr&  r  r  r  r  r    r  r   r   )rC   l1pl1prlrD   rD   rE   r  D     zTestLog1p.test_log1pc                 C   sB   t dt dt df}tdtdtdf}t||d d S )NrZ   r+  r0  rL   r"  r#  r  r  )rC   l1pml1pmrlrD   rD   rE   test_log1pmoreI  r!  zTestLog1p.test_log1pmoreN)r  r  r  r  r$  rD   rD   rD   rE   r  C  s    r  c                   @   r  )TestMathieuc                 C   r  r  rD   rB   rD   rD   rE   r  Q  r  zTestMathieu.test_mathieu_ac                 C   r   )NrL   r   )r    r+   rB   rD   rD   rE   test_mathieu_even_coefT  r  z"TestMathieu.test_mathieu_even_coefc                 C   r  r  rD   rB   rD   rD   rE   test_mathieu_odd_coefX  s   z!TestMathieu.test_mathieu_odd_coefN)r  r  r  r  r&  r'  rD   rD   rD   rE   r%  O  s    r%  c                   @   r  )TestFresnelIntegralc                 C   r  r  rD   rB   rD   rD   rE   r  _  r  z$TestFresnelIntegral.test_modfresnelpc                 C   r  r  rD   rB   rD   rD   rE   r  b  r  z$TestFresnelIntegral.test_modfresnelmN)r  r  r  r  r  rD   rD   rD   rE   r(  ]  s    r(  c                   @   r  )TestOblCvSeqc                 C   &   t ddd}t|tg dd d S )Nr   r   rZ   )g~T~Oֿgt_J?gm{@g@j'&@r   )r    
obl_cv_seqr   r   )rC   oblrD   rD   rE   test_obl_cv_seqg     zTestOblCvSeq.test_obl_cv_seqN)r  r  r  r-  rD   rD   rD   rE   r)  f  r  r)  c                   @   sD   e Z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 )TestParabolicCylinderc                 C   s0   t dd}t|tddgtddgfd d S )NrZ   r  gQ?gx$(~?gx$(~g(\?rJ   )r    pbdn_seqr   r   )rC   pbrD   rD   rE   test_pbdn_seqp  s   z#TestParabolicCylinder.test_pbdn_seqc                 C   s4   t dd dt ddd  t ddd   d S )NrZ   r   r  r   )r    r$  rB   rD   rD   rE   r%  w  s   (zTestParabolicCylinder.test_pbdvc                 C   s<   t dd}t dd}t|t|d t|d fd d S )NrZ   r  r   rJ   )r    r0  pbdv_seqr   r   )rC   pbnpbvrD   rD   rE   test_pbdv_seq{  s   $z#TestParabolicCylinder.test_pbdv_seqc                 C   s   t ddd}d|d  t t j tdd|   }tt|dd |ddd	 ttd
dd ddd ttddd ddd d S )Nr  r&  r   rL   r   r   r   r  r  gGz$@gq=
ףp4@gHQ9r   rS   g(\#gQ@gkS a>)r_   r  r   r   r    rK  r   r$  )rC   etar   rD   rD   rE   test_pbdv_points  s
   *z&TestParabolicCylinder.test_pbdv_pointsc                 C      t dddd d d f }t dddd d d f }t||}ddt|  }t||| d t||| d  | d	 }t|d
 |ddd d S Nr>  rJ   r  r  r&  r   r   r   r   rZ   r%  r  )r_   r  r    r$  r  r   rC   r   r7  r,  r5  dprD   rD   rE   test_pbdv_gradient     0z(TestParabolicCylinder.test_pbdv_gradientc                 C   r9  r:  )r_   r  r    r&  r  r   r;  rD   rD   rE   test_pbvv_gradient  r>  z(TestParabolicCylinder.test_pbvv_gradientc                 C   s<   t dd\}}t|tg d t|tg d d S )NrL   r   )g:4@g1{н?g7,%n?)gX@g=<'?gʠ?)r    pbvv_seqr   r_   r   )rC   res1res2rD   rD   rE   test_pbvv_seq  s   z#TestParabolicCylinder.test_pbvv_seqN)
r  r  r  r2  r%  r6  r8  r=  r?  rC  rD   rD   rD   rE   r/  o  s    
		r/  c                   @   r  )TestPolygammac                 C   s   t dd}t dd}t|dd t|dd g d}tt d|t | g d	}g d
}g d}tt ||| t|gd }tt |t|gd | tt t|gd || d S )NrL   rZ   r   gX];r&  gOV,@@)rL   r   g  8Br   r*  r  )g2}jg.M?g}2;ο)r    	polygammar   rG  r_   r  )rC   poly2poly3r   rh   r!  rD   rD   rE   test_polygamma  s"   zTestPolygamma.test_polygammaN)r  r  r  rH  rD   rD   rD   rE   rD    s    rD  c                   @   r  )TestProCvSeqc                 C   r*  )Nr   r   rZ   )g"~j?g6?Ң@g)u8F"@g2g)@r   )r    
pro_cv_seqr   r   )rC   prolrD   rD   rE   test_pro_cv_seq  r.  zTestProCvSeq.test_pro_cv_seqN)r  r  r  rL  rD   rD   rD   rE   rI    r  rI  c                   @   r  )TestPsic                 C   r  )NrZ   goxr  )r    rG  r   )rC   psrD   rD   rE   rH    r  zTestPsi.test_psiN)r  r  r  rH  rD   rD   rD   rE   rM    r  rM  c                   @   r  )
TestRadianc                 C   s"   t ddd}t|td d d S )NrY  r   r   r   r    rI  r   r   )rC   radrD   rD   rE   rJ    s   zTestRadian.test_radianc                 C   s&   t ddd}t|td d d d S )NrY  rZ   r  rL   gC?r   rP  )rC   rad1rD   rD   rE   test_radianmore  s   zTestRadian.test_radianmoreN)r  r  r  rJ  rS  rD   rD   rD   rE   rO    s    rO  c                   @   r  )TestRiccatic                 C   |   d\}}t ||f}t|D ]"}t||}tj||dd}|| |d|f< || | |d|f< qt|t||d d S N)rL   r   T)
derivativer   rZ   r  )r_   emptyru   r    spherical_jnr   
riccati_jn)rC   r  r   Srh   r  jprD   rD   rE   test_riccati_jn     zTestRiccati.test_riccati_jnc                 C   rU  rV  )r_   rX  ru   r    spherical_ynr   
riccati_yn)rC   r  r   Crh   r  yprD   rD   rE   test_riccati_yn  r^  zTestRiccati.test_riccati_ynN)r  r  r  r]  rc  rD   rD   rD   rE   rT    s    
rT  c                   @   r  )TestSoftplusc                 C   s   dd l }|jd}d}|jdd|d}|jdd|d}|jdd|d}|jd	d
|d}|||||g}g dg dg dg dg}	t|}
t|
|	dd d S )Nr   l   (sr   iir     r  g
ףp=@@r  )g%~B7gpNf7g8B8)gJR{?g6]=gXes>)g n@?@gWH;@glH.=@)g9lchPR@gS@gzsevB@r  rS   )numpyre   default_rnguniformstackr)   r   )rC   r_   rl   rh   r  r  a3a4r  r%  ro  rD   rD   rE   test_softplus  s   zTestSoftplus.test_softplusc                 C   sT   t dd }t d}| }|dk}t|||d t|| ||< t|| d S )Nr   rL   r   )outwhere)r_   r   onescopyr)   r   )rC   r   rm  r%  rn  rD   rD   rE   test_softplus_with_kwargs  s   
z&TestSoftplus.test_softplus_with_kwargsN)r  r  r  rl  rq  rD   rD   rD   rE   rd    s    rd  c                   @   r  )	TestRoundc              	   C   s@   t tttdtdtdtdf}d}t|| d S )Ng333333$@g$@r+  g333333%@)r&  r&  r&  r  )rE  maprt   r    rQ  r   )rC   rndrndrlrD   rD   rE   rR    s   
zTestRound.test_roundN)r  r  r  rR  rD   rD   rD   rE   rr    r  rr  c                  C   s  t j} tj}tj}tj}tj}tj}t }|j	t
d t| ddddd||  t| ddd|d d|d	d
|   ||d d
   t| ddd|d d|d	d
|    t| dd||d d|dd
|   |dd
| d   ||d
 d
   t| dd|d |d d|dd
|   |dd
| d d   ||d d
  d||d d
  d   t| dd|d |d d|dd
|   |dd| d d   ||d d   W d    d S 1 sw   Y  d S )Ncategoryr   r   r  rL   r   rJ   r  r$  r   r{   r  r  r   r  r   g      @rZ   r   r]  g      ?g     A@)r    sph_harmr_   r   r   r   r   r	   r   r  DeprecationWarningr   )shr   r   r   r   r	   r  rD   rD   rE   test_sph_harm)  sV   
"r{  c                  C   s   t t j} t _}|jtd ttddddj|  ttdgdddj|  ttddgddj|  ttdddgdj|  ttddddgj|  ttdgdgdgdgj|  W d    d S 1 skw   Y  d S )Nrv  r   )	r_   r3  rQ  r   r  ry  r   r    rx  )dtr  rD   rD   rE   "test_sph_harm_ufunc_loop_selectionH  s   ""r}  c                   @   s.   e Zd ZdddZdd Zdd Zdd	 Zd
S )
TestStruver  c                 C   sp   t d|}d| d| d| | d   t|d  t|| d  }t| ttj | }| |fS )z?Compute Struve function & error estimate from its power series.r   rO   r   rL   rZ   r  )	r   r    r8  r  rG  r   r   r5  r  r  rD   rD   rE   _seriesV  s   
@zTestStruve._seriesc                 C   sH   dD ]}dD ]}|  ||\}}tt|||d|d||ff qqdS )z-Check Struve function versus its power series)
ir  (\rN  rO   r   rZ   rM  r     )rZ   r&  r   r  rV   r   r  N)r  r   r    r{  r  rD   rD   rE   test_vs_series]  s   "zTestStruve.test_vs_seriesc                 C   s   t tddddd t tddddd t td	d
ddd t tddddd ttddtdd  ttddtdd  ttddtdd
  ttddtdd
  tttdd tttdd d S )Nr  r  g;cv=?r   rS   gQ g< j?rO  rO  r  g?r   g       igzz?r  i)   r  r  r  gffffffrO   g333333$)r   r    r{  r   r   r   rB   rD   rD   rE   test_some_valuesd  s   zTestStruve.test_some_valuesc                 C   sR   t tddtdd t tddtdd t tddtdd dS )zRegression test for #679r   g3@g*   4@r)  g333333N)r   r    r{  rB   rD   rD   rE   test_regression_679q  s   


zTestStruve.test_regression_679N)r  )r  r  r  r  r  r  r  rD   rD   rD   rE   r~  U  s
    
r~  c                   C   r   )Nrk  r   gdX	
?)r   r    r   rD   rD   rD   rE   test_chi2_smalldf{  r   r  c                   C   s   t tdtjd d S )Nrv  r   )r   r    r   r_   r   rD   rD   rD   rE   test_ch2_inf  r   r  c                   C   r   )Nrk  r   yj_?)r   r    r   rD   rD   rD   rE   test_chi2c_smalldf  r   r  c                   C   r   )Nrk  r  r   )r   r    r   rD   rD   rD   rE   test_chi2_inv_smalldf  r   r  c                  C   s  d} t dtdtd d| d d}d}d}t tdgd	ggg d
d||g|d	|gg| d d}t tdd|| d t tdd|| d t tdd| | d t tddd| d t tddd| d t tddd| d t tddd| d t tddd| d t tddd| d t tddd| d td}t t|j|jd | d t td!|j |jd"| d t t|jd	|j d#| d ttd$d$d$ ttd%d$d$ ttdd&tj	 ttd$tj
tj	 tttj
d$tj	 ttd$tj
 tj	 tttj
 d$tj	 tttj
tj
 tj	 tttj
 tj
tj	 ttdtj	tj	 tttj	dtj	 ttdtj
tj
 tttj
dtj
 ttdtj
 tj
  tttj
 dtj
  d S )'NrR   rZ   rL   gDSYC?rS   gQ_?g?@g>;,
i}@r   )rZ   r   r   g=O?rO   r  r   rP   gXs*@r  g   V4oAgO1eAgꌠ9Y>)FgEg^ 9^;gd-?gP.5_gsTNNeg6dgu?j/ g]XC}KdgѧRg"!x{{ r   g][#!Rr_  gٍS1gN_ r   r  r&  )r   r    agmr_   r   r   r  rG  r   r   r   )rT   agm13agm15agm35agm12firD   rD   rE   test_agm_simple  sr   
r  c                  C   s.  t  } | td ttddtdd ttdddtddd ttdddtddd ttdddtddd tt	ddt	dd tt
ddt
dd ttddtdd ttddtdd ttddtdd W d    d S 1 sw   Y  d S )Nr1  rZ   r  g?rL   gffffff@)r   r  r  r   r    expnr  r  r  r2  r  r  r]  rl  )r  rD   rD   rE   test_legacy  s   "r  c                  C   s   dd l } |  S r?   )	threadingLock)r  rD   rD   rE   errstate_lock  s   r  c              	   C   sx   | 0 t jdd tt jt jdd W d    n1 sw   Y  W d    d S W d    d S 1 s5w   Y  d S )Nr,  r  rZ   y        .B}T)r    r0  r  r1  rz  )r  rD   rD   rE   test_error_raising  s   "r  c                  C   s   dd } t jddt jfdt jfdgtd}t j|ddgf }t | |d d df |d d d	f }ttj	||d
d
d t | |d d df |d d d	f }ttj	||d
d
d d S )Nc                 S   b   t jdd! | dkrt |s| W  d    S | t | W  d    S 1 s*w   Y  d S Nr  )invalidr   )r_   r0  r   r   r'  rD   rD   rE   xfunc     $ztest_xlogy.<locals>.xfuncr   r   r   r   r   r4  )r   r  )rZ   r  rZ   rR   r  )
r_   r   r   r   rv   r   r|   r9   r    xlogy)r  z1z2w1w2rD   rD   rE   
test_xlogy  s   "((r  c                  C   sl   dd } t jddt jfdt jfddgtd}t | |d d df |d d df }ttj||d	d	d
 d S )Nc                 S   r  r  )r_   r0  r   r  r'  rD   rD   rE   r    r  ztest_xlog1py.<locals>.xfuncr  r   r  )rZ   gKH9r4  rZ   rR   r  )	r_   r   r   r   rv   r|   r9   r    xlog1py)r  r  r  rD   rD   rE   test_xlog1py  s   (r  c                  C   s   dd } dddt jf}ddg}g }t||D ]\}}|||  qt j|td}t j| t jgd	|}t	t
j||d
d
d d S )Nc                 S   s   | dk rt j S t| |  S r?   )r_   r   r    r  r)  rD   rD   rE   r    s   ztest_entr.<locals>.xfuncr   r   r   rO   rZ   r4  otypesrR   r  )r_   r   r  r  r  r   rv   r|   r   r9   r    entr)r  r   signsr  sgnr  r   r  rD   rD   rE   	test_entr  s   r  c            
      C      dd } d}ddg}g }t ||||D ]\}}}}||| || f qtj|td}tj| tjgd|d d df |d d df }	tt	j
|	|d	d	d
 d S )Nc                 S   sd   | dk s|dk s|dkr| dkrt jS t | st |r t jS | dkr&|S t| | | |  | S r?   )r_   r   r	  r    r  r'  rD   rD   rE   r    s    ztest_kl_div.<locals>.xfuncr   r   r   rO   rZ   r4  r  r   rR   r  )r  r  r  r_   r   rv   r|   r   r9   r    kl_div
r  r   r  r  sgnavasgnbvbr   r  rD   rD   rE   test_kl_div  s   0r  c            
      C   r  )Nc                 S   s:   | dkr|dkrt | | | S | dkr|dkrdS tjS r?   )r    r  r_   r   r'  rD   rD   rE   r  +  s
   ztest_rel_entr.<locals>.xfuncr  rO   rZ   r4  r  r   rR   r  )r  r  r  r_   r   rv   r|   r   r9   r    rel_entrr  rD   rD   rE   test_rel_entr*  s   0r  c                  C   sR   t g d} g d}| d d df }| d d df }tt|||ddd d S )N))gpB?gĬB?)gtK&?gCtK&?)g>уO'?gvуO'?)ggQW"g    G=r   rZ   rR   r  )r_   r   r   r    r  inputsr!  r   r  rD   rD   rE    test_rel_entr_gh_20710_near_zero<  s
   r  c                  C   s^   t jdd tg d} g d}| d d df }| d d df }tt |||ddd d S )	Nr  r  ))rJ   X )r  gZbti)r  g  4&kC)gMG.@g)Z?g wa)r   rZ   rR   r  )r    seterrr_   r   r   r  r  rD   rD   rE   test_rel_entr_gh_20710_overflowO  s   
r  c                  C   s   t tddtj ttdddtd  ttddd dd } tjd	d}tj	| tj
gd
|d d df |d d df }ttj||ddd d S )NrO   r  rL   r   r  r   c                 S   s@   | dk rt jS t || k rdt | S | t |d|    S )Nr   r   )r_   r   r  squaredeltar;  rD   rD   rE   r  j  s
   ztest_huber.<locals>.xfuncr&  r  r   rZ   rR   r  )r   r    huberr_   r   r   r  re   randnr|   r   r9   r  r   r  rD   rD   rE   
test_hubere  s   0r  c                  C   sx   dd } t t jdd ddgddgg }t j| t jgd|d d df |d d df }ttj	||d	d	d
 d S )Nc                 S   s<   | dk rt jS | r|sdS | d t d||  d  d  S )Nr   rL   rZ   )r_   r   r   r  rD   rD   rE   r  x  s
   "z test_pseudo_huber.<locals>.xfuncr&  rL   r   r   r  rZ   rR   r  )
r_   r   re   r  tolistr|   r   r9   r    pseudo_huberr  rD   rD   rE   test_pseudo_huberw  s   (0r  c                  C   s*   d} d}t | |}d}t||dd d S )Nr   gC]r2<gs.-De8rR   rS   )r    r  r   )r  r;  r  r!  rD   rD   rE   test_pseudo_huber_small_r  s
   r  c                   C   sv   t jtdd tdd W d    n1 sw   Y  t jtdd tdd W d    d S 1 s4w   Y  d S )NzToo many predicted coefficientsr.  rW   )r  warnsr  r*   r+   rD   rD   rD   rE   test_runtime_warning  s   "r  c                   @   s  e Zd Zdgddgg dg dg dg dg dg dg d	g d
g dgZejddei fdeddifgdd Z	ejddei fdeddifgdd Z
ejddei fdeddifgdd Zejddei fdeddifgdd Zejddei fdeddifgdd Zdd Zdd Zejd d!d"d#d$ejgejd%g d&ejd'ddgd(d) Zejd'ddgd*d+ Zejddei fdeddifgd,d- Zejddei fdeddifgd.d/ Zd0d1 Zd2S )3TestStirling2rZ   r   )r   rZ   rZ   )r   rZ   r   rZ   )r   rZ   rN   rP   rZ   )r   rZ   r{   r   r&  rZ   )r   rZ      rY  A   r{   rZ   )r   rZ   ?   rW  i^     r  rZ   )	r   rZ      i  i    i
     rZ   )
r   rZ      i  iZ  i'  iV
  i  $   rZ   )r   rZ   r~   r$  i9  i  i+Y    i  r   rZ   zis_exact, comp, kwargsTFrT   r   c                 C   sR   t dt| jD ]}tt |d }| j| }||t|g||dfi | qd S )NrZ   r:  )ru   r  tablerE  r,   )rC   is_exactcompkwargsrh   k_valuesrowrD   rD   rE   test_table_cases  s
   
 zTestStirling2.test_table_casesc                 C   s   |t dd|d| jd d fi | |t dd|d| jd d fi | |t dd|ddfi | |t dgdg|ddgfi | d S )Nr   r:  rJ   rL   r   r   r   )r,   r  rC   r  r  r  rD   rD   rE   test_valid_single_integer  s   &&&z'TestStirling2.test_valid_single_integerc                 C   sX   |t dd|ddfi | |t dd|ddfi | |t dd|ddfi | d S )NrO   r:  r   rL   r,   r  rD   rD   rE   test_negative_integer  s    z#TestStirling2.test_negative_integerc                 C   s   | j d d | j d d g}|ttddgtddg|d| |tddgtddg|d| |ttddgddg|d| d S )Nr&  r   rJ   r:  )r  r,   r   )rC   r  r  r  ansrD   rD   rE   test_array_inputs  s&   


zTestStirling2.test_array_inputsrR   c                 C   s8   g d}g d}g d}|t |||d|fi | d S )N)r   rZ   r   r   r  r  r  )rO   r   r   r   r  r&  r&  )r  r   rL   r   r   rN   r   r:  r  rC   r  r  r  r  rh   ri   rD   rD   rE   test_mixed_values  s    zTestStirling2.test_mixed_valuesc                    s:   dt d }tt |ddd  fdd|D  dS )	z{Test parity follows well known identity.

        en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind#Parity
        r  e   Tr:  rL   c                    s,   g | ]}t  |d   d  | d  qS )rL   rZ   )rr  r?  r@  r  rD   rE   rB    s   , z5TestStirling2.test_correct_parity.<locals>.<listcomp>N)r_   r   r   r,   )rC   KrD   r  rE   test_correct_parity  s
   z!TestStirling2.test_correct_parityc                 C   sl   t ddg}ddg}ddg}tt||dd|sJ t d	d
g}ddg}ddg}tt||dd|s4J d S )Nl   V^;. l   k4-Tr   rV   rK   rJ   Tr:  l	   D,"SBXp!N l   wY)H_1e_*   r     )r   r   r,   )rC   r  rh   ri   rD   rD   rE   test_big_numbers  s   zTestStirling2.test_big_numbersr  r(  r   y      @      ?12r  )rP  r   2Nr  c                 C   s>   t t t|||d W d    d S 1 sw   Y  d S )Nr:  )r  r   	TypeErrorr,   )rC   r  r  r  rD   rD   rE   test_unsupported_input_types  s   "z*TestStirling2.test_unsupported_input_typesc                 C   sz   t | jd dd  }t g dtd}t g dtd}tt tt|||d| W d    d S 1 s6w   Y  d S )NrJ   rZ   rJ   rJ   rJ   rJ   r4  rZ   rL   r   rJ   r:  )r   r  rn  r  r   r  r   r,   )rC   r  r  rh   ri   rD   rD   rE   !test_numpy_array_int_object_dtype	  s   "z/TestStirling2.test_numpy_array_int_object_dtypec                 C   sV   t | jd dd  }t g dtd}t g dtd}|t||dd|fi | d S )NrJ   rZ   r  r4  r  Fr:  )r   r  r1   r,   r  rD   rD   rE   #test_numpy_array_unsigned_int_dtype  s    z1TestStirling2.test_numpy_array_unsigned_int_dtypec                 C   s   t g dg dg}t g dg dg}t g d}|t|||d|fi | t dgdgdgdgdgg}t g d}t d	d
 tdD }|t||dd|fi | d S )N)rZ   r{   r   r&  )rZ   rN   rP   rZ   )r   r   r   r   r  r  r:  rJ   )r   rZ   rL   r   rJ   r   c                 S   s   g | ]}g d qS ))r   rZ   rN   rP   rZ   r   rD   )rA  r  rD   rD   rE   rB  ,  s    zDTestStirling2.test_broadcasting_arrays_correctly.<locals>.<listcomp>r   F)r   r,   ru   r  rD   rD   rE   "test_broadcasting_arrays_correctly  s    z0TestStirling2.test_broadcasting_arrays_correctlyc                 C   sp   t tddd}|D ]+}t td|d }t|g|dd}|t|g|dd }tt|| dk s5J q
d S )	N3   r  r   rZ   Tr:  Fgh㈵>)rE  ru   r,   r_   rG  r  )rC   r   rh   	k_entriesdenomrw   rD   rD   rE   test_temme_rel_max_error/  s   z&TestStirling2.test_temme_rel_max_errorN)r  r  r  r  r  r  r7  r   r   r  r  r  r  r  r  r  r_   r   r  r  r  r  r  rD   rD   rD   rE   r    sr    





	

r  c                   @   s6   e Zd Zdd Zejdeegdd Z	dd Z
dS )	TestLegendreDeprecationc                 C   s@   d}t j|d tdd}W d    d S 1 sw   Y  d S )Nz$`scipy.special.lpn` is deprecated...r.  rZ   r   )r  rV  r-   rC   rW  r  rD   rD   rE   test_warn_lpn<  s   "z%TestLegendreDeprecation.test_warn_lpnxlpmnc                 C   sL   d|j  d}tj|d |ddd}W d    d S 1 sw   Y  d S )Nz`scipy.special.z` is deprecated...r.  rZ   r   )r  r  rV  )rC   r  messager  rD   rD   rE   test_warn_xlpmnA  s   "z'TestLegendreDeprecation.test_warn_xlpmnc                 C   sF   d}t j|d tdddd}W d    d S 1 sw   Y  d S )Nz)`scipy.special.sph_harm` is deprecated...r.  rZ   r   )r  rV  r    rx  r  rD   rD   rE   test_warn_sph_harmG  s   "z*TestLegendreDeprecation.test_warn_sph_harmN)r  r  r  r  r  r  r7  r.   r/   r  r  rD   rD   rD   rE   r  :  s
    
r  r  )r  r  r  r  r  rf  r_   r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r  r   r  numpy.testingr   r   r   r   r   r   r   r   r   scipyr    scipy.special._ufuncs_ufuncsr@   scipy.specialr!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   scipy._lib._utilr0   r1   scipy._lib._array_apir2   r3   r4   scipy.special._basicr5   r6   r7   scipy.special._testutilsr8   r9   r:   rr  architecturer  rK  rG  r=   r  r  r  r  r  r  r  r8  ra  r  r  r  r  r  r	  r  r0  r3  r  r  r  r  r7  r  r  r  r%  r(  r)  r/  rD  rI  rM  rO  rT  rd  rr  r{  r}  r~  r  r  r  r  r  r  fixturer  r  r  r  r  r  r  r  r  r  r  r  r  r`  r  r  r  rD   rD   rD   rE   <module>   s   X,
       @|	 rGE  ,b
 $     UDC) `    \!
		7	
)&=


	 