o
    4Bi                    @   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-m6Z6m7Z7m8Z8 d d	l9m:Z: d d
l;m<Z<m=Z= d dl>m?Z?m@Z@ d dlAmBZBmCZCmDZD d dlEZEG dd dZFG dd dZGG dd dZHG dd dZIG dd dZJG dd dZKG dd dZLG dd dZMG dd dZNG dd  d ZOG d!d" d"ZPG 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/d0 d0ZWG d1d2 d2ZXG d3d4 d4ZYG d5d6 d6ZZG d7d8 d8Z[G d9d: d:Z\G d;d< d<Z]G d=d> d>Z^G d?d@ d@Z_G dAdB dBZ`G dCdD dDZaG dEdF dFZbG dGdH dHZcG dIdJ dJZdG dKdL dLZeG dMdN dNZfG dOdP dPZgG dQdR dRZhG dSdT dTZiG dUdV dVZjG dWdX dXZkdYdZ Zld[d\ ZmG d]d^ d^Znd_d` Zodadb Zpdcdd Zqdedf Zrdgdh Zsdidj ZteBdkdl Zudmdn Zvdodp Zwdqdr Zxdsdt Zydudv Zzdwdx Z{dydz Z|d{d| Z}d}d~ Z~G dd dZd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)mathieu_odd_coefmathieu_even_coef	stirling2)_NoValue)np_longnp_ulong)_FACTORIALK_LIMITS_64BITS_FACTORIALK_LIMITS_32BITS)with_special_errorsassert_func_equalFuncDatac                   @   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^ Z1e2j3j4d_d`dadb Z5dcdd Z6dedf Z7dgdh Z8e2j3j4did`djdk 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 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$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds ZdtS (u  
TestCephesc                 C      t d d S Nr   )cephesairyself r;   ^/var/www/html/Trade-python/venv/lib/python3.10/site-packages/scipy/special/tests/test_basic.py	test_airy7      zTestCephes.test_airyc                 C   r5   r6   )r7   airyer9   r;   r;   r<   
test_airye:   r>   zTestCephes.test_airyec              	   C   s6  t g d}t g d}t t |d d d f |d d d f ddj}t g dg dg dg dg}ttj| |d	d
 t j	
d t jt dddt j	d d f }t dd}t t |d d d f |d d d f ddj}ttjt|d d df |d d df d |ddd d S )N)gL7A`?   g@   )   皙?   gffffff
@rC   )g޸g	TշJ?g	7?geLF)   g*+ @r   gM{@)gףp=
%@gϔ>@g<wg$@)   g,y3@iK  g5@vIh%<=rtol  i       r   f           ?绽|=atolrK   )npr   broadcast_arraysreshapeTr2   r7   binomravelrandomseedr   r   rand)r:   nknkrknownr;   r;   r<   
test_binom=   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 )NrL   rQ   ,     r   rP   rC   rF   rR   rS   rT   )rV   r\   r]   r   logspacer   r   rW   rX   rY   r2   r7   rZ   )r:   r_   r`   ra   r;   r;   r<   test_binom_2T   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 NrQ   )intrangefloat)r_   r`   numdenir;   r;   r<   	binom_intb   s   
z.TestCephes.test_binom_exact.<locals>.binom_intrL   rQ      r   rC   rF   rT   )rV   	vectorizer\   r]   r   r   rW   rX   rY   r2   r7   rZ   )r:   ro   r_   r`   ra   r;   r;   r<   test_binom_exacta   s   

(
$ 
zTestCephes.test_binom_exactc                 C   s.   g d}t |}ttj|dddd  d S )N))rN   rO   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   rQ   rC   -q=rJ   )rV   r   r3   r7   rZ   check)r:   datasetr;   r;   r<   test_binom_nooverflow_8346x   s   
z%TestCephes.test_binom_nooverflow_8346c                 C      t tdddd d S )NrQ         ?      ?)r   r7   bdtrr9   r;   r;   r<   	test_bdtr      zTestCephes.test_bdtrc                 C      t tdddd d S NrQ      ry   )r   r7   bdtrir9   r;   r;   r<   
test_bdtri   r}   zTestCephes.test_bdtric                 C   r~   r   )r   r7   bdtrcr9   r;   r;   r<   
test_bdtrc   r}   zTestCephes.test_bdtrcc                 C      t tdddd d S NrQ   r         @)r   r7   bdtrinr9   r;   r;   r<   test_bdtrin   r}   zTestCephes.test_bdtrinc                 C      t ddd d S r   )r7   bdtrikr9   r;   r;   r<   test_bdtrik      zTestCephes.test_bdtrikc                 C      t tdd d S Nr           )r   r7   beir9   r;   r;   r<   test_bei      zTestCephes.test_beic                 C   r   r   )r   r7   beipr9   r;   r;   r<   	test_beip   r   zTestCephes.test_beipc                 C   r   Nr   rz   )r   r7   berr9   r;   r;   r<   test_ber   r   zTestCephes.test_berc                 C   r   r   )r   r7   berpr9   r;   r;   r<   	test_berp   r   zTestCephes.test_berpc                 C      t tdddd d S r   )r   r7   
besselpolyr9   r;   r;   r<   test_besselpoly   r}   zTestCephes.test_besselpolyc                 C   H   t jdd tddd}W d    n1 sw   Y  t|d d S Nzdeprecated in SciPy 1.12.0matchrQ   rz   )pytestdeprecated_callr    btdtrr   r:   yr;   r;   r<   
test_btdtr      zTestCephes.test_btdtrc                 C   r   r   )r   r   r    btdtrir   r   r;   r;   r<   test_btdtri   r   zTestCephes.test_btdtric                 C   r   NrQ   r   )r   r7   btdtriar9   r;   r;   r<   test_btdtria   r}   zTestCephes.test_btdtriac                 C   r   r   )r   r7   btdtribr9   r;   r;   r<   test_btdtrib   r}   zTestCephes.test_btdtribc                 C   r   NrQ   rz   )r   r7   cbrtr9   r;   r;   r<   	test_cbrt   r   zTestCephes.test_cbrtc                 C      t tddd d S NrQ   r   r   )r   r7   chdtrr9   r;   r;   r<   
test_chdtr      zTestCephes.test_chdtrc                 C   r   NrQ   r   rz   )r   r7   chdtrcr9   r;   r;   r<   test_chdtrc   r   zTestCephes.test_chdtrcc                 C      t tddd d S NrQ   r   )r   r7   chdtrir9   r;   r;   r<   test_chdtri   r   zTestCephes.test_chdtric                 C   r   )Nr   r   )r   r7   chdtrivr9   r;   r;   r<   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   rQ   r   )      9@      4@  gL94)r          @   g7Fh9)MbP?r         D@ggåc;){Gz?r   r   g	;)r          @k   g8x@x>)g     6@r   r   gg1\>>)r   r   r   g`>)      @r   rz   gp!P?)g     u@g     r@      $@g j
?)      Y@      +@r   g]?)g     @r   r   g4ۙ?)g     b@r   r   g?)g      d@r   r   rz   rC   r   rt   rJ   r      )r   r7   chndtrrV   r   r   r   r   r   r   nan)r:   valuescdfr;   r;   r<   test_chndtr   s.   2zTestCephes.test_chndtrc                 C   rx   Nr   rQ   r   )r   r7   	chndtridfr9   r;   r;   r<   test_chndtridf   r}   zTestCephes.test_chndtridfc                 C   r   r   )r   r7   	chndtrincr9   r;   r;   r<   test_chndtrinc   r}   zTestCephes.test_chndtrincc                 C   r   Nr   rQ   r   )r   r7   chndtrixr9   r;   r;   r<   test_chndtrix   r}   zTestCephes.test_chndtrixc                 C   r   r   )r   r7   cosdgr9   r;   r;   r<   
test_cosdg   r   zTestCephes.test_cosdgc                 C   r   r   )r   r7   cosm1r9   r;   r;   r<   
test_cosm1   r   zTestCephes.test_cosm1c                 C   r   N-   rz   )r   r7   cotdgr9   r;   r;   r<   
test_cotdg   r   zTestCephes.test_cotdgc                 C   s$   t tdd ttdd d S )Nr   r   gGz?gf?)r   r7   dawsnr   r9   r;   r;   r<   
test_dawsn   s   zTestCephes.test_dawsnc                 C   sV  g d}t dt j d t j}tt||ddd t dt j d t j}tt||ddd t dt j d	 t j}tt||ddd t	t d
rmt dt j d t j
}tt||ddd g d}t dt j d t j}tt||ddd t dt j dt j dt j }g d}tt|d|dd d S )N)rQ   r      rC   g-C6
?rz   rE   decimal&.>rp   V瞯<float128rt      )rC   rA            皙?)gg?gsOB?gsaL?g
7I^ʿr   )rV   r   r   astypefloat32r   r    diricfloat64hasattrr   r   )r:   n_oddxn_evenoctave_resultr;   r;   r<   
test_diric   s    
 zTestCephes.test_diricc                 C   sH   t d}t g d}tt|d d t jf |j|j|jfk d S )Nr   )rQ   r   rE   )	rV   r   r   r   r    r   newaxisshapesize)r:   r   r_   r;   r;   r<   test_diric_broadcasting  s   
0z"TestCephes.test_diric_broadcastingc                 C   r   r   )r   r7   r!   r9   r;   r;   r<   test_ellipe  r   zTestCephes.test_ellipec                 C   r   r   )r   r7   	ellipeincr9   r;   r;   r<   test_ellipeinc   r   zTestCephes.test_ellipeincc                 C      t dd d S Nr   rQ   )r7   ellipjr9   r;   r;   r<   test_ellipj#     zTestCephes.test_ellipjc                 C   s   t tdtd  d S )Nr   rC   )r   r"   r   r9   r;   r;   r<   test_ellipk&  r   zTestCephes.test_ellipkc                 C   r   r   )r   r7   	ellipkincr9   r;   r;   r<   test_ellipkinc)  r   zTestCephes.test_ellipkincc                 C   r   r   r   r7   erfr9   r;   r;   r<   test_erf,  r   zTestCephes.test_erfc                 C   s$   d}t t|t|  d d S )Ng#8x@r   r
  r:   r   r;   r;   r<   test_erf_symmetry/  s    zTestCephes.test_erf_symmetryc                 C   r   r   )r   r7   erfcr9   r;   r;   r<   	test_erfc3  r   zTestCephes.test_erfcc                 C   r   )NrC   r   )r   r7   exp10r9   r;   r;   r<   
test_exp106  r   zTestCephes.test_exp10c                 C   r   )NrC         @)r   r7   exp2r9   r;   r;   r<   	test_exp29  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   rF   )r   r7   expm1rV   r   r   r9   r;   r;   r<   
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   rQ   rC   rA   r   rF   )r7   r  r   complexrV   r   r   )r:   r  r;   r;   r<   test_expm1_complexB  s"    "$"  "  "   &zTestCephes.test_expm1_complexz-The real part of expm1(z) bad at these pointsreasonc                 C   sh   t g d}t t | }|d|  }t g d}t|}t|j|jd t|j|jd d S )N)皙?r   333333?r      re                 ?)y=Cw?yC7gg)gF<Ug?yQ<D*?yg:><sKy>񸣼$	Um>ly;Vl <@r   re   )	rV   r   r   r	   r7   r  r   imagr   )r:   r   r   zexpectedfoundr;   r;   r<   test_expm1_complex_hardU  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 )
NrQ   r   r   ư>r   
   g2?rt   rJ   )r   r7   fdtrr   r9   r;   r;   r<   	test_fdtrj  s   
zTestCephes.test_fdtrc                 C   r&  )
NrQ   r   rz   rC   r  g    _BgDIXl?rt   rJ   )r   r7   fdtrcr   r9   r;   r;   r<   
test_fdtrcp  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 )NrQ   gV-?gx&1?g
}?g<zO'?r'  rJ   g׀?r  r   rt   )r   r7   fdtrir   )r:   pr;   r;   r<   
test_fdtriw  s
   zTestCephes.test_fdtrizReturns nan on i686.c                 C   s   t tdddd d S )NrQ   ry   )r   r7   r-  r9   r;   r;   r<   test_fdtri_mysterious_failure  s   z(TestCephes.test_fdtri_mysterious_failurec                 C      t tdddd d S r   )r   r7   fdtridfdr9   r;   r;   r<   test_fdtridfd  r}   zTestCephes.test_fdtridfdc                 C   r   Nr   r   r   )r   r7   fresnelr9   r;   r;   r<   test_fresnel  r   zTestCephes.test_fresnelc                 C   r   Nr         8@)r   r7   gammar9   r;   r;   r<   
test_gamma  r   zTestCephes.test_gammac                 C   r   )Nr   rQ   r   )r   r7   gammainccinvr9   r;   r;   r<   test_gammainccinv  r   zTestCephes.test_gammainccinvc                 C   r5   )Nr(  )r7   gammalnr9   r;   r;   r<   test_gammaln  r>   zTestCephes.test_gammalnc                 C   s2   t g dt j}tt|t t| d S )N)      gffffffrQ   g@)rV   r   r   r   r7   gammasgnsignrgamma)r:   valsr;   r;   r<   test_gammasgn  s    zTestCephes.test_gammasgnc                 C   rx   r   )r   r7   gdtrr9   r;   r;   r<   	test_gdtr  r}   zTestCephes.test_gdtrc                 C   s   t tddtjd d S r   )r   r7   rG  rV   r   r9   r;   r;   r<   test_gdtr_inf     zTestCephes.test_gdtr_infc                 C   rx   r   )r   r7   gdtrcr9   r;   r;   r<   
test_gdtrc  r}   zTestCephes.test_gdtrcc                 C   r1  r   )r   r7   gdtriar9   r;   r;   r<   test_gdtria  r}   zTestCephes.test_gdtriac                 C   s   t ddd d S NrQ   r   )r7   gdtribr9   r;   r;   r<   test_gdtrib  r   zTestCephes.test_gdtribc                 C   s   t ddd d S NrQ   r  )r7   gdtrixr9   r;   r;   r<   test_gdtrix  r   zTestCephes.test_gdtrixc                 C      t dd d S rh   )r7   hankel1r9   r;   r;   r<   test_hankel1  r  zTestCephes.test_hankel1c                 C   rU  rh   )r7   hankel1er9   r;   r;   r<   test_hankel1e  r  zTestCephes.test_hankel1ec                 C   rU  rh   )r7   hankel2r9   r;   r;   r<   test_hankel2  r  zTestCephes.test_hankel2c                 C   rU  rh   )r7   hankel2er9   r;   r;   r<   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 )NrQ   rz   r   rA   g㈮?)r   r7   hyp1f1r   r9   r;   r;   r<   test_hyp1f1  s   zTestCephes.test_hyp1f1c                 C      t tddddd d S r   )r   r7   hyp2f1r9   r;   r;   r<   test_hyp2f1  rJ  zTestCephes.test_hyp2f1c                 C   r   r   )r   r7   i0r9   r;   r;   r<   test_i0  r   zTestCephes.test_i0c                 C   r   r   )r   r7   i0er9   r;   r;   r<   test_i0e  r   zTestCephes.test_i0ec                 C   r   r   )r   r7   i1r9   r;   r;   r<   test_i1  r   zTestCephes.test_i1c                 C   r   r   )r   r7   i1er9   r;   r;   r<   test_i1e  r   zTestCephes.test_i1ec                 C   r5   rh   )r7   it2i0k0r9   r;   r;   r<   test_it2i0k0  r>   zTestCephes.test_it2i0k0c                 C   r5   rh   )r7   it2j0y0r9   r;   r;   r<   test_it2j0y0  r>   zTestCephes.test_it2j0y0c                 C   r5   rh   )r7   
it2struve0r9   r;   r;   r<   test_it2struve0  r>   zTestCephes.test_it2struve0c                 C   r5   rh   )r7   itairyr9   r;   r;   r<   test_itairy  r>   zTestCephes.test_itairyc                 C   r   r4  )r   r7   iti0k0r9   r;   r;   r<   test_iti0k0  r   zTestCephes.test_iti0k0c                 C   r   r4  )r   r7   itj0y0r9   r;   r;   r<   test_itj0y0  r   zTestCephes.test_itj0y0c                 C   r   r   )r   r7   itmodstruve0r9   r;   r;   r<   test_itmodstruve0  r   zTestCephes.test_itmodstruve0c                 C   r   r   )r   r7   	itstruve0r9   r;   r;   r<   test_itstruve0  r   zTestCephes.test_itstruve0c                 C   r   r   )r   r7   ivr9   r;   r;   r<   test_iv  r   zTestCephes.test_ivc                 C   r   r   )r   r7   iver9   r;   r;   r<   test_ive  r   zTestCephes.test_ivec                 C   r   r   )r   r7   j0r9   r;   r;   r<   test_j0  r   zTestCephes.test_j0c                 C   r   r   )r   r7   j1r9   r;   r;   r<   test_j1  r   zTestCephes.test_j1c                 C   r   r   )r   r7   jnr9   r;   r;   r<   test_jn  r   zTestCephes.test_jnc                 C   r   r   )r   r7   jvr9   r;   r;   r<   test_jv  r   zTestCephes.test_jvc                 C   r   r   )r   r7   jver9   r;   r;   r<   test_jve  r   zTestCephes.test_jvec                 C   r5   NrC   )r7   k0r9   r;   r;   r<   test_k0  r>   zTestCephes.test_k0c                 C   r5   r  )r7   k0er9   r;   r;   r<   test_k0e  r>   zTestCephes.test_k0ec                 C   r5   r  )r7   k1r9   r;   r;   r<   test_k1  r>   zTestCephes.test_k1c                 C   r5   r  )r7   k1er9   r;   r;   r<   test_k1e  r>   zTestCephes.test_k1ec                 C   r5   r  )r7   keir9   r;   r;   r<   test_kei  r>   zTestCephes.test_keic                 C   r   r   )r   r7   keipr9   r;   r;   r<   	test_keip  r   zTestCephes.test_keipc                 C   r5   r  )r7   kerr9   r;   r;   r<   test_ker  r>   zTestCephes.test_kerc                 C   r5   r  )r7   kerpr9   r;   r;   r<   	test_kerp  r>   zTestCephes.test_kerpc                 C   r5   r  )r7   kelvinr9   r;   r;   r<   test_kelvin  r>   zTestCephes.test_kelvinc                 C   rU  rh   )r7   knr9   r;   r;   r<   test_kn  r  zTestCephes.test_knc                 C   *   t tdd ttttj d S r   )r   r7   kolmogir   rV   r   r   r9   r;   r;   r<   test_kolmogi     zTestCephes.test_kolmogic                 C   r   r   )r   r7   
kolmogorovr9   r;   r;   r<   test_kolmogorov  r   zTestCephes.test_kolmogorovc                 C   r   )Nr          )r   r7   _kolmogpr9   r;   r;   r<   test_kolmogp  r   zTestCephes.test_kolmogpc                 C   r   r   )r   r7   _kolmogcr9   r;   r;   r<   test_kolmogc  r   zTestCephes.test_kolmogcc                 C   r  r   )r   r7   	_kolmogcir   rV   r   r   r9   r;   r;   r<   test_kolmogci!  r  zTestCephes.test_kolmogcic                 C   rU  rh   )r7   kvr9   r;   r;   r<   test_kv%  r  zTestCephes.test_kvc                 C   rU  rh   )r7   kver9   r;   r;   r<   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   rF   )r7   log1pr   rV   r   r   )r:   r  r;   r;   r<   
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  rF   r   z%invalid value encountered in multiplyrQ   rC   r   rA   )r7   r  r  r   rV   r   r   filterRuntimeWarningr   r   r   )r:   r  csupr;   r;   r<   test_log1p_complex2  s$   $ ",&"$" $"zTestCephes.test_log1p_complexc                 C   rx   )Nr   rQ   rz   )r   r7   lpmvr9   r;   r;   r<   	test_lpmvE  r}   zTestCephes.test_lpmvc                 C   r   r   )r   r7   	mathieu_ar9   r;   r;   r<   test_mathieu_aH  r   zTestCephes.test_mathieu_ac                 C   r   r   )r   r7   	mathieu_br9   r;   r;   r<   test_mathieu_bK  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 )NrQ   r   rz   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?rQ   ry   rC      r   rA            ?)rV   r   r	   mqr"  r;   r;   r<   	ce_smallqR  s   $Hz.TestCephes.test_mathieu_cem.<locals>.ce_smallqd   r(  rh|?+=rK   rU   )	r   r7   mathieu_cemrV   rq   r   r   rf   r   )r:   r  r  r  r;   r;   r<   test_mathieu_cemN  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 )NrQ   r   r   rz   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  rQ   r  r   rC   rA   r  )rV   r   r   r  r;   r;   r<   	se_smallqk  s    Hz.TestCephes.test_mathieu_sem.<locals>.se_smallqr  r  r  r(  r  r  r  )	r   r7   mathieu_semrV   rq   r   r   rf   r   )r:   r  r  r  r;   r;   r<   test_mathieu_semg  s   
*"
zTestCephes.test_mathieu_semc                 C   r1  NrQ   r   r5  )r   r7   mathieu_modcem1r9   r;   r;   r<   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 )
NrQ   r   rA   r  rC   r(  rE   rS   rJ   )	r7   mathieu_modcem2rV   r   r   rf   linspacer  r   r:   r  r  r"  y1fry2r;   r;   r<   test_mathieu_modcem2  s   "&zTestCephes.test_mathieu_modcem2c                 C   r1  r  )r   r7   mathieu_modsem1r9   r;   r;   r<   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 )
NrQ   rA   r  rC   r(  r   rE   rS   rJ   )	r7   mathieu_modsem2rV   r   r   rf   r  r  r   r  r;   r;   r<   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   r7   r  rV   r   r  r  r  r  r  r9   r;   r;   r<   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<   rC   r  rF   r   g.dS?rS   rJ   rQ   gGc?-C6?)rj   r7   r  r   )r:   r`   vr;   r;   r<   test_mathieu_ticket_1847  s
   z#TestCephes.test_mathieu_ticket_1847c                 C   r5   r6   )r7   modfresnelmr9   r;   r;   r<   test_modfresnelm  r>   zTestCephes.test_modfresnelmc                 C   r5   r6   )r7   modfresnelpr9   r;   r;   r<   test_modfresnelp  r>   zTestCephes.test_modfresnelpc                 C   r   r   )r   r7   	modstruver9   r;   r;   r<   test_modstruve  r   zTestCephes.test_modstruvec                 C   r   r   )r   r7   nbdtrr9   r;   r;   r<   
test_nbdtr  r}   zTestCephes.test_nbdtrc                 C   r   r   )r   r7   nbdtrcr9   r;   r;   r<   test_nbdtrc  r}   zTestCephes.test_nbdtrcc                 C   r   r   )r   r7   nbdtrir9   r;   r;   r<   test_nbdtri  r}   zTestCephes.test_nbdtric                 C   r   )NrQ   rD   ry   )r7   nbdtrikr9   r;   r;   r<   test_nbdtrik  r   zTestCephes.test_nbdtrikc                 C   r1  r   )r   r7   nbdtrinr9   r;   r;   r<   test_nbdtrin  r}   zTestCephes.test_nbdtrinc                 C   ra  r   )r   r7   ncfdtrr9   r;   r;   r<   test_ncfdtr  rJ  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 )NrQ   r   r   )ry   rQ   r  rC   r   r  )r   r7   ncfdtrir  r   )r:   fr.  r;   r;   r<   test_ncfdtri  s   zTestCephes.test_ncfdtric                 C   s2   g d}t d|dd}tt d|dd| d S )NrQ   rC   r   rC   r  rp   )r7   r  r   
ncfdtridfd)r:   dfdr.  r;   r;   r<   test_ncfdtridfd     zTestCephes.test_ncfdtridfdc                 C   s6   g d}t |ddd}tt |ddd|dd d S )N)r  rQ   rC   r   g     @rC   r  rp   gh㈵>rJ   )r7   r  r   
ncfdtridfn)r:   dfnr.  r;   r;   r<   test_ncfdtridfn  s   zTestCephes.test_ncfdtridfnc                 C   s2   g d}t dd|d}tt dd|d| d S )N)ry   r  r   rC   r   rp   )r7   r  r   	ncfdtrinc)r:   ncr.  r;   r;   r<   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 )NrQ   r   ry   	   i   r   r   rz   r   r   r   )	r   r7   nctdtrr   rV   r   r   r   r   r9   r;   r;   r<   test_nctdtr  s   zTestCephes.test_nctdtrc                 C   r   )NrQ   ry   r   )r7   	nctdtridfr9   r;   r;   r<   test_nctdtridf  r   zTestCephes.test_nctdtridfc                 C   s   t ddd d S rO  )r7   	nctdtrincr9   r;   r;   r<   test_nctdtrinc  r   zTestCephes.test_nctdtrincc                 C   r   )Nr  r   ry   )r7   nctdtritr9   r;   r;   r<   test_nctdtrit  r   zTestCephes.test_nctdtritc                 C   r1  )Nry   rQ   rz   )r   r7   nrdtrimnr9   r;   r;   r<   test_nrdtrimn  r}   zTestCephes.test_nrdtrimnc                 C   s   t tddddddd d S )Nry   r   r   rT   )r   r7   nrdtrisdr9   r;   r;   r<   test_nrdtrisd  s   
zTestCephes.test_nrdtrisdc                 C      t dddd d S rO  )r7   obl_ang1r9   r;   r;   r<   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 )NrQ   r   rz   r   )r7   obl_ang1_cvr   )r:   resultr;   r;   r<   test_obl_ang1_cv  s   zTestCephes.test_obl_ang1_cvc                 C   rx   NrQ   r   r   )r   r7   obl_cvr9   r;   r;   r<   test_obl_cv	  r}   zTestCephes.test_obl_cvc                 C   r  rO  )r7   obl_rad1r9   r;   r;   r<   test_obl_rad1  r   zTestCephes.test_obl_rad1c                 C      t ddddd d S rO  )r7   obl_rad1_cvr9   r;   r;   r<   test_obl_rad1_cv  r   zTestCephes.test_obl_rad1_cvc                 C   r  rO  )r7   obl_rad2r9   r;   r;   r<   test_obl_rad2  r   zTestCephes.test_obl_rad2c                 C   r   rO  )r7   obl_rad2_cvr9   r;   r;   r<   test_obl_rad2_cv  r   zTestCephes.test_obl_rad2_cvc                 C   r   )NrQ   r   r  )r   r7   pbdvr9   r;   r;   r<   	test_pbdv  r   zTestCephes.test_pbdvc                 C   r  rO  )r7   pbvvr9   r;   r;   r<   	test_pbvv  r  zTestCephes.test_pbvvc                 C   r  rO  )r7   pbwar9   r;   r;   r<   	test_pbwa  r  zTestCephes.test_pbwac                 C   s>   t dd}t|td t g dd}t|g d d S )Nr   rQ   rF   r   rQ   rC   )rQ   rQ   rQ   )r7   pdtrr   rV   r   r   r:   valr;   r;   r<   	test_pdtr!  s   zTestCephes.test_pdtrc                 C   sB   t dd}t|dtd  t g dd}t|g d d S )Nr   rQ   rF   r-  r   )r   r   r   )r7   pdtrcr   rV   r   r   r/  r;   r;   r<   
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 integerry   )r   r  r  r7   pdtri)r:   r  r;   r;   r<   
test_pdtri/  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 )Nry   rQ   r   r  ffffff?)r   #B;r'  )r   r   )r7   pdtrikr   	gammainccr   rV   r   r:   r`   r;   r;   r<   test_pdtrik4  s   zTestCephes.test_pdtrikc                 C   r  rO  )r7   pro_ang1r9   r;   r;   r<   test_pro_ang1;  r   zTestCephes.test_pro_ang1c                 C   s    t tdddddtd d S )NrQ   r   r  )r   r7   pro_ang1_cvr   r9   r;   r;   r<   test_pro_ang1_cv>  s   zTestCephes.test_pro_ang1_cvc                 C   rx   r  )r   r7   pro_cvr9   r;   r;   r<   test_pro_cvB  r}   zTestCephes.test_pro_cvc                 C   r  rR  )r7   pro_rad1r9   r;   r;   r<   test_pro_rad1E  r   zTestCephes.test_pro_rad1c                 C   r   rO  )r7   pro_rad1_cvr9   r;   r;   r<   test_pro_rad1_cvH  r   zTestCephes.test_pro_rad1_cvc                 C   r  rO  )r7   pro_rad2r9   r;   r;   r<   test_pro_rad2K  r   zTestCephes.test_pro_rad2c                 C   r   rO  )r7   pro_rad2_cvr9   r;   r;   r<   test_pro_rad2_cvN  r   zTestCephes.test_pro_rad2_cvc                 C   r5   rh   )r7   psir9   r;   r;   r<   test_psiQ  r>   zTestCephes.test_psic                 C   s   t tdddd d S r6   )r   r7   radianr9   r;   r;   r<   test_radianT  r}   zTestCephes.test_radianc                 C   r   r   )r   r7   rD  r9   r;   r;   r<   test_rgammaW  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            @rA  )r   r7   roundr9   r;   r;   r<   
test_roundZ  s   zTestCephes.test_roundc                 C   r5   rh   )r7   shichir9   r;   r;   r<   test_shichib  r>   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 )NrQ   ry   r   z cosine integral(-inf) is not nan)r7   sicirV   r   r   r   r   r   )r:   sr  r;   r;   r<   	test_sicie  s   

zTestCephes.test_sicic                 C   r   NZ   rz   )r   r7   sindgr9   r;   r;   r<   
test_sindgp  r   zTestCephes.test_sindgc                 C   s.   t tddd tttdtj d S )NrQ   r  ?)r   r7   smirnovr   rV   r   r   r9   r;   r;   r<   test_smirnovs  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 )	NrQ   r  rF   rC         ?      r   g      ȿ)r   r7   	_smirnovpr   rV   r   r   r9   r;   r;   r<   test_smirnovpw  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 )
NrQ   r  r   r  Tendpointr   r   rA   )
r   r7   	_smirnovcr   rV   r   r   r  r   r`  )r:   x10x4r;   r;   r<   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 NrQ   rD   333333?)r   r7   r`  smirnovir   rV   r   r   r9   r;   r;   r<   test_smirnovi     zTestCephes.test_smirnovic                 C   rl  rm  )r   r7   rh  
_smirnovcir   rV   r   r   r9   r;   r;   r<   test_smirnovci  rq  zTestCephes.test_smirnovcic                 C   r   r   )r   r7   spencer9   r;   r;   r<   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 )NrQ   r   ry   rb  rC   gMoF?)r   r7   stdtrr   r9   r;   r;   r<   
test_stdtr     zTestCephes.test_stdtrc                 C   r  )Nffffff?rQ   )r7   stdtridfr9   r;   r;   r<   test_stdtridf  r  zTestCephes.test_stdtridfc                 C   r  )NrQ   ry  )r7   stdtritr9   r;   r;   r<   test_stdtrit  r  zTestCephes.test_stdtritc                 C   r   r   )r   r7   struver9   r;   r;   r<   test_struve  r   zTestCephes.test_struvec                 C   r   r   )r   r7   tandgr9   r;   r;   r<   
test_tandg  r   zTestCephes.test_tandgc                 C   r   r   )r   r7   tklmbdar9   r;   r;   r<   test_tklmbda  r   zTestCephes.test_tklmbdac                 C   r5   rh   )r7   y0r9   r;   r;   r<   test_y0  r>   zTestCephes.test_y0c                 C   r5   rh   )r7   r  r9   r;   r;   r<   test_y1  r>   zTestCephes.test_y1c                 C   rU  rh   )r7   ynr9   r;   r;   r<   test_yn  r  zTestCephes.test_ync                 C   rU  rh   )r7   yvr9   r;   r;   r<   test_yv  r  zTestCephes.test_yvc                 C   rU  rh   )r7   yver9   r;   r;   r<   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$t d%d&t d'd(t d)d*t d+d,t d-d.t d/dt d0d1t d2d3t d4d5t d6d7t d8d9t d:d:g}ttj||d;d< d S )=Ng@g+п皙ٿr   rn  r   r   rz   g      "g      "@g4׵/Yg8EGr?rR  gffffff@ig>@r   g|Pk?r  rQ   ir  r  i   ig     j@  ļBg0"bgpتO#M?gMF>?g5-g`?g	S+?g6U?gǗʿgjD{?/,Gg` 0Gg!^?gnF5o{gI\Y?g7f8goC9	?gyhgEbr?g{g.
?ga~gT-s?gɤ,P&?g|bgޗY3g!ؑ-@gi$bghgy(V@^gһ>g>gx\h<rI   rJ   )r  r2   r7   wofz)r:   r"  wr;   r;   r<   	test_wofz  sr   "zTestCephes.test_wofzN)__name__
__module____qualname__r=   r@   rc   rg   rr   rw   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   markxfailr%  r*  r,  r/  r0  r3  r7  r;  r=  r?  rF  rH  rI  rL  rN  rQ  rT  rW  rY  r[  r]  r`  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$  r&  r(  r*  r,  r1  r3  r6  r<  r>  r@  rB  rD  rF  rH  rJ  rL  rN  rO  rU  rW  rZ  r^  ra  re  rk  rp  rs  ru  rw  r{  r}  r  r  r  r  r  r  r  r  r  r;   r;   r;   r<   r4   6   sv   

	r4   c                   @   <   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd ZdS )TestAiryc                 C   s^   t d}t|tg dd t d}t|tg dd t d}t|tg dd d S )NGz?)g*?gTk'kPĿge+?gyCyt?r  g=
ףp=?)g'$'?geοgL?g
HVV?g
ףp=
׿)gl@D|?gV~׭ͿgU?g3{ɔ?)r    r8   r   r   r  r;   r;   r<   r=     s$   





zTestAiry.test_airyc                 C   s   t d}t d}d gd }tdD ]}|| tdtd  ||< qtddD ]}|| tttdtd   ||< q)t||d d S )Nr   rA   rC   gN贁N{?rG   )	r    r?   r8   rj   r   r   absr   r   )r:   abb1r_   r;   r;   r<   r@     s   


(zTestAiry.test_airyec                 C   s   t d}tddgtddgtddgtdd	gf}t||d
 t d}t|d tg dd t|d tg dd t|d tg dd t|d tg dd d S )NrC   glgoe2+
g(0[g X*JgUfݿg˰zU`?g4c1=C?gCuTrA   r   r   )g&g(.2+
gRg}`g%́r  rQ   )g7;1[ge*JgVwgL g<3r(  )gNݿg3%IQ`?gZyΌ׿gʀ11^?g33tտr   )gqM0=C?g7uTg\G`?gp⍞vg$.m?)r    bi_zerosr   r   )r:   bibiar;   r;   r<   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 )NrQ   gcqg!xLgMSt$?g ~:p?rA   )r    ai_zerosr   r   )r:   air;   r;   r<   test_ai_zeros$  s   
zTestAiry.test_ai_zerosc                 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  rQ   r  rS   rJ   r   rT   rG   )guqgqHkZg4g9Ζ%gB~gL")gLgQO	gMQnGg3:g)}g )r    r  r8   r  r   )r:   r"  zpai_zpxaip_zxai_zaip_z_ai_zpaip_zpai_envelopeaip_enveloper;   r;   r<   test_ai_zeros_big+  "   
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  rQ   r  rS   rJ   r   rT   rG   )gx&gg-2+
gRgg`gu%́g{ )g K;1[g*JgVwg<w gd
3g/{
")r    r  r8   r  r   )r:   r"  r  bi_zpxbip_zxr  bi_zbip_zbi_zpbip_zpbi_envelopebip_enveloper;   r;   r<   test_bi_zeros_bigC  r  zTestAiry.test_bi_zeros_bigN)	r  r  r  r=   r@   r  r  r  r  r;   r;   r;   r<   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  rQ   r   r  )r    genlaguerreassoc_laguerrer   )r:   a1a2r;   r;   r<   test_assoc_laguerre]  s
   z%TestAssocLaguerre.test_assoc_laguerreN)r  r  r  r  r;   r;   r;   r<   r  \      r  c                   @   r  )TestBesselpolyc                 C      d S Nr;   r9   r;   r;   r<   r   f     zTestBesselpoly.test_besselpolyN)r  r  r  r   r;   r;   r;   r<   r  e  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 )NrC   gT?r   )r    r   r   )r:   mbeir;   r;   r<   r   k     
zTestKelvin.test_beic                 C   r  )NrC   gD,X?r   )r    r   r   )r:   mbeipr;   r;   r<   r   o  r  zTestKelvin.test_beipc                 C   r  )NrC   gPA4?r   )r    r   r   )r:   mberr;   r;   r<   r   s  r  zTestKelvin.test_berc                 C   r  )NrC   gii߿r   )r    r   r   )r:   mberpr;   r;   r<   r   w  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@rA   )r    	bei_zerosr   r   )r:   r  r;   r;   r<   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   )r:   bipr;   r;   r<   test_beip_zeros     
zTestKelvin.test_beip_zerosc                 C   r  )Nr   g\@g6ُ@gӟHY'@g>"D0@ggaO;4@rA   )r    	ber_zerosr   r   )r:   r   r;   r;   r<   test_ber_zeros  r  zTestKelvin.test_ber_zerosc                 C   r  )Nr   g '@gs%@gF ^-@gvۅj3@gB7@rA   )r    
berp_zerosr   r   )r:   brpr;   r;   r<   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 )NrC   r   r  )r    r  r   r   r   r  r  r   r   r  r  )r:   mkelvr;   r;   r<   r    s   
zTestKelvin.test_kelvinc                 C   r  )NrC   g>ɿr   )r    r  r   )r:   mkeir;   r;   r<   r    r  zTestKelvin.test_keic                 C   r  )NrC   gr@d"?r   )r    r  r   )r:   mkeipr;   r;   r<   r    r  zTestKelvin.test_keipc                 C   r  )NrC   gܙUr   )r    r  r   )r:   mkerr;   r;   r<   r    r  zTestKelvin.test_kerc                 C   r  )NrC   g^.n3Jr   )r    r  r   )r:   mkerpr;   r;   r<   r    r  zTestKelvin.test_kerpc                 C   r  )Nr   gE>Q@gB= @gPN)@gm91@g
%5@rA   )r    	kei_zerosr   r   )r:   r  r;   r;   r<   test_kei_zeros  r  zTestKelvin.test_kei_zerosc                 C   r  )Nr   gWf,@g?"@gFZ*o+@gOpN2@gEa6@rA   )r    
keip_zerosr   r   )r:   r  r;   r;   r<   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  rA   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   )
r:   tmpberzbeizkerzkeizberpzbeipzkerpzkeipzr;   r;   r<   test_kelvin_zeros  s4   
zTestKelvin.test_kelvin_zerosc                 C   r  )Nr   )r  r  r  r  gD;q3@rA   )r    	ker_zerosr   r   )r:   r  r;   r;   r<   test_ker_zeros  r  zTestKelvin.test_ker_zerosc                 C   r  )Nr   r  rA   )r    
kerp_zerosr   r   )r:   r  r;   r;   r<   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  r;   r;   r;   r<   r  j  s&    		.r  c                   @   r  )TestBernoullic                 C   r  )Nr   )rz   rc  g-!lV?r   g镲r   rA   )r    	bernoullir   r   )r:   brnr;   r;   r<   test_bernoulli  s   
zTestBernoulli.test_bernoulliN)r  r  r  r   r;   r;   r;   r<   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 )NrQ   rz   33333YN~h?   g6.8@rI   r   r  rC   rA   rG   rJ   )r   r    betar   r:  )r:   betbetgr;   r;   r<   	test_beta  s   zTestBeta.test_betac                 C   s   t ttdd d S )NrF   rC   )r   rV   isinfr    r  r9   r;   r;   r<   test_beta_inf  rJ  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 )NrQ   r   r  r  r     gIs	@r  r   r  rC   rA   rI   rJ   )r   r    betalnr   r>  r   r  r  )r:   betlnr  r;   r;   r<   test_betaln   s   zTestBeta.test_betalnN)r  r  r  __doc__r	  r  r  r;   r;   r;   r<   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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  rQ   rQ   )rV   r   r   r    betainc
betaincinvbetainccbetainccinvr  r;   r;   r<   
test_a1_b11  s
   zTestBetaInc.test_a1_b1z
a, b, x, p))rC   rA   g@w?ry   )r  g     `e@rS   g*?)r  r  g"Yx;r  )g   `1?g    ئAg\aY4g    ?)rA   i g-߇)?g;?c                 C   <   t |||}t||dd t |||}t||dd d S )Nr   rJ   g-a=)r    r  r   r  r:   r  r  r   r.  p1x1r;   r;   r<   test_betainc_betaincinvH  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  r9  rb  g`<)      0@rb  g?g<dEA>)g?g7Ê@g/3J?Hz>c                 C   r  )N+<rJ   gV瞯=)r    r  r   r  r  r;   r;   r<   test_betaincc_betainccinv]  s   z%TestBetaInc.test_betaincc_betainccinvza, b, y, ref))cj,@r%  ghHISOa gڭ Y;)g      ,@g      -@g둤g}c]춫;)rS        .@gUv \U,gS^%:)r   g      ?gMoigKB;)r  g    i@g1$-g\_cp:c                 C   s    t |||}t||dd d S )Nr  rJ   )r    r  r   )r:   r  r  r   refr   r;   r;   r<   test_betaincinv_tiny_yo  s   z"TestBetaInc.test_betaincinv_tiny_yfuncargs))r   rC   ry   )r   rC   ry   )r         ry   )r  r   ry   )r  r   333333ӿ)r  r   皙?c              	   C   s|   t jdd. tjt jdd t j|  W d    n1 sw   Y  W d    d S W d    d S 1 s7w   Y  d S )Nraise)domainr/  r   )r    errstater   r   SpecialFunctionErrorr  )r:   r)  r*  r;   r;   r<   test_betainc_domain_errors  s   "z&TestBetaInc.test_betainc_domain_errorsN)r  r  r  r  r  r   r  parametrizer  r$  r(  r    r  r  r  r  r2  r;   r;   r;   r<   r  ,  s,    



	r  c                   @   s   e Zd Zdd Zejdddgejdddegejddd	gejd
ddgdd Zdd Z	dd Z
dd Zdd Z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   rA         ^@g     @j@Texactx   )r7  
repetition   c                 S   s   g | ]
}t jd |ddqS )re   Tr6  )r    comb.0r`   r;   r;   r<   
<listcomp>  s    z/TestCombinatorics.test_comb.<locals>.<listcomp>r  re   r   rU   rQ   l   hU7`S?Q r  2   )r   r    r;  r   r   r   rj   listrV   iinfori   max)r:   iir#  r;   r;   r<   	test_comb  s   zTestCombinatorics.test_combr9  TFlegacyr`   rS  r   N      @rA   c                 C   s   |t ur&tjtdd tj||d||d}W d    n1 s w   Y  n
tj||d||d}|rM|rDt|| d t|}}d}n	t|t|}}t }|t urZ|t tj||||d}W d    n1 smw   Y  t	|| d S )Nz$Using 'legacy' keyword is deprecatedr   T)r7  rF  r9  rQ   F)rF  r9  )
r,   r   warnsDeprecationWarningr    r;  ri   r   r  r   )r:   rG  r`   rF  r9  r  r  r#  r;   r;   r<   test_comb_legacy  s0   
z"TestCombinatorics.test_comb_legacyc                 C   sL   d}d}t |}t |}tj||dd}tj||dd}||ks$J d S )NF   rM   Tr6  )rV   int64r    r;  )r:   r_   r`   np_nnp_kres_npres_pyr;   r;   r<   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 )NrC   r   Tr6  r   rF   FrC   rF   rC   r(  r   r   rF   r   )r   r   r   r5  )r   r    r;  r   r9   r;   r;   r<   test_comb_zeros     z!TestCombinatorics.test_comb_zerosc                 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   rA        @g     @Tr6  i  )r   r    permr   r   r9   r;   r;   r<   	test_perm  s   zTestCombinatorics.test_permc                 C   rS  )NrC   r   Tr6  r   rF   FrT  rU  )r   r   r   rX  )r   r    rY  r   r9   r;   r;   r<   test_perm_zeros  rW  z!TestCombinatorics.test_perm_zerosc                 C   sJ   t jdd tddgddgdd W d    d S 1 sw   Y  d S )Nzuse keyword argumentsr   r(  r   rA   F)r   r   r    r;  r9   r;   r;   r<   test_positional_deprecation  s   "z-TestCombinatorics.test_positional_deprecationN)r  r  r  rE  r   r  r3  r,   rK  rR  rV  rZ  r[  r\  r;   r;   r;   r<   r4    s    	r4  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   )r:   cbcbrlr;   r;   r<   r        
zTestTrigonometric.test_cbrtc                 C      t d}d}t||d d S )Ngfffff;@g鎖C@r  )r    r   r   )r:   cb1cbrl1r;   r;   r<   test_cbrtmore     
zTestTrigonometric.test_cbrtmorec                 C   &   t d}ttd }t||d d S )Nr\  r   r  r    r   r	   r   r   )r:   cdgcdgrlr;   r;   r<   r        
zTestTrigonometric.test_cosdgc                 C   rh  NrM         @r  ri  )r:   cdgmcdgmrlr;   r;   r<   test_cosdgmore  rl  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(  rQ   r  )r    r   r   r	   r   )r:   cscsrlr;   r;   r<   r      s    &zTestTrigonometric.test_cosm1c                 C   *   t d}ttd d }t||d d S )NrM   rn  rF   r  r    r   r
   r   r   )r:   ctctrlr;   r;   r<   r        
zTestTrigonometric.test_cotdgc                 C   rt  )Nr   r  rF   r  ru  )r:   ct1ctrl1r;   r;   r<   test_cotdgmore
  rx  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   rz      r   r\  r   i   y   i  i;  i  )r   r    r   r9   r;   r;   r<   test_specialpoints  s   z$TestTrigonometric.test_specialpointsc                 C   s&   t tdgd ttdd d S )Nr   rQ   r   rz   )r   r    sincr   r9   r;   r;   r<   	test_sinc  s   zTestTrigonometric.test_sincc                 C      t d}t|d d S r[  )r    r]  r   )r:   snr;   r;   r<   r^  #     
zTestTrigonometric.test_sindgc                 C   H   t d}ttd }t||d t d}ttd }t||d d S )NrM   rn  r  r   r  )r    r]  r   r   r   )r:   snmsnmrlsnm1snmrl1r;   r;   r<   test_sindgmore'     

z TestTrigonometric.test_sindgmoreN)r  r  r  r   rf  r   rq  r   r   r{  r  r  r^  r  r;   r;   r;   r<   r]    s    r]  c                   @   $   e Zd Zdd Zdd Zdd ZdS )	TestTandgc                 C   rh  rm  r    r  r
   r   r   )r:   tntnrlr;   r;   r<   r  2  rl  zTestTandg.test_tandgc                 C   r  )Nr   r  r  r  r   r  )r:   tnmtnmrltnm1tnmrl1r;   r;   r<   test_tandgmore7  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   rz   r}  r   r~  r  r  iLr  r  r  r  )r   r    r  r9   r;   r;   r<   r  ?  s   zTestTandg.test_specialpointsN)r  r  r  r  r  r  r;   r;   r;   r<   r  0  s    r  c                   @   sT   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.ry   N)r    r  rV   r   r9   r;   r;   r<   test_ellipj_nanN  s   zTestEllip.test_ellipj_nanc                 C   s0   t dd}tdtdddg}t||d d S )Nr   r   rz      )r    r  r   r	   r   )r:   elrelr;   r;   r<   r  R     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   rz   rC   rF   gN?)
r    r"   r   r   r#   rV   r   r   r   r   )r:   elkr;   r;   r<   r  W  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 )NrC   r   rp   re   r  r   gfoKh?r  r   rz   r   ry   gt?rQ   rD   r  rJ   6<R!?r  gfON?)r    r  r   r"   r   r   r   rV   r   r   r   )r:   elkincr  alphaphir  r;   r;   r<   r	  b  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(  rQ   gV^8j?g,j6Ƅ@rC   )	rV   	nextafterrj   appendr    r  r   	full_liker   r:   mbadr  r  mvalsjr  f1r;   r;   r<   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  rC   Frf  rQ   r  rJ   )rV   rf   r  r   r   r    r  arcsinhr
   r   r   )r:   xlogxlinxlin2r;   r;   r<   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   rC   rz   r  g?eg@)	r    r!   r   r   r   rV   r   r   r   )r:   eler;   r;   r<   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 )NrC   r   r|  4   r  #   g'?r  r   rz   r   ry   r  r  gL@)r    r   r   r!   r   r   r   rV   r   r   r   )r:   eleincr  r  r  r  r;   r;   r<   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(  rQ   g%?rC   gXo
@rA   )	rV   r  rj   r  r    r   r   r  r   r  r;   r;   r<   test_ellipeinc_2  r  zTestEllip.test_ellipeinc_2N)r  r  r  r  r  r  r	  r  r  r   r  r  r;   r;   r;   r<   r  M  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 )NrQ   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   rV   r   r   	enumerater:   r*  expected_resultsrn   arrr;   r;   r<   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 )NrQ   r   rC   r   g`C+?r   r   rF   )r   r   rz   r   r   r  r   r  r   r   r   r  )r               ?r   )y             r  r  )gfe_?gi+"?gP$M?ytgFU?7?@yR<8*y{62?z)r   r%   r   rV   r
  r  r   r   r   tinyr   r  r  r;   r;   r<   test_elliprd  s&   $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 )NrQ   r   rC   gPO?r   rF   )rz   r   r   )r   r  r   )ry   rz   r   r  r   r   r  r  )r  r         ?      )geQO?ʞu5J?r  yp\y?kg2ΰ?gHwд?y|pF?-6Fj)	r   r&   r   rV   r
  r   r  r   r  r  r;   r;   r<   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 )NrQ   r   ry   )r   r!  r!  r  r  r  )r  r  r   )r   g8d`?r  gL+?g}^?y旮0?ʋW?yjN?^?gt?)	r   r'   rV   r
  r   r  r   r   r  r  r;   r;   r<   test_elliprg$  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 )NrQ   r   r   rF   )r   rz   r   r   )r   r   r  r   )r   r   r  r  )r   r  r   r   )r              rz   r   )r   r  r   r  )r  r  rz   y            ?)r   r   r  rc  )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  r;   r;   r<   test_elliprj9  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#  r8  r  g   ,@g    x=g   @e:g   `ݽ>g(HR)A)r   r(   r9   r;   r;   r<   test_elliprj_hardT  s    
z"TestEllipCarlson.test_elliprj_hardN)r  r  r  r  r  r  r  r  r  r   r  r  r  r;   r;   r;   r<   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   rz   r   r   rF   r   )rV   r   m_n1_1r   r   minmax_neglog2
very_neg_mconcatenate
ms_up_to_1r9   r;   r;   r<   setup_classj  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   rz   N)r  r   r"   r&   r:   r  r;   r;   r<   test_kv  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   rz   N)	r   r   r  r   rV   r  r   r#   r&   )r:   r  m1r;   r;   r<   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   rz   N)r  r   r!   r'   r  r;   r;   r<   test_e  s   "z)TestEllipLegendreCarlsonIdentities.test_eN)r  r  r  r  r  r  r  r  r;   r;   r;   r<   r  d  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   )r:   err;   r;   r<   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'>@rA   )r    	erf_zerosr   r   )r:   erzerzrr;   r;   r<   test_erf_zeros  s   
zTestErf.test_erf_zerosr   c                 C   s  t jd d}t jd|dt jdd| d  }t jd|dt jdd| d  }|d|  }t jdd	> ||}	||j}
t |	}|	| }	|| }t |
}|
| }
|| }t||	|||d
 t||
|||d
 W d    d S 1 s{w   Y  d S )NrL   r  g{Gz?rC   r   rQ   r   ignoreallr  )	rV   r\   r]   paretorandintr0  r   isfiniter2   )r:   r)  
other_funcrK   rU   r_   r   r   r"  r  w_realmaskr;   r;   r<   _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 rh   r7   r  r"  r;   r;   r<   <lambda>  s    z.TestErf.test_erfc_consistent.<locals>.<lambda>rt   r  r  )r  r7   r  r9   r;   r;   r<   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  )rV   r   r7   r  r  r;   r;   r<   r    s    z/TestErf.test_erfcx_consistent.<locals>.<lambda>rt   rJ   )r  r7   erfcxr9   r;   r;   r<   test_erfcx_consistent  
   
zTestErf.test_erfcx_consistentc                 C   r  )Nc                 S   s   dt d|   S )Nr  r   r  r  r;   r;   r<   r    s    z.TestErf.test_erfi_consistent.<locals>.<lambda>rt   rJ   )r  r7   erfir9   r;   r;   r<   test_erfi_consistent  r  zTestErf.test_erfi_consistentc                 C   r  )Nc                 S   s&   t td t|  |   t|  S r  )r   r   rV   r   r7   r  r  r;   r;   r<   r    s   & z/TestErf.test_dawsn_consistent.<locals>.<lambda>rt   rJ   )r  r7   r   r9   r;   r;   r<   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 )NrF   rQ   r   rJ   )rV   r   r   r   r    r  r:   rE  r#  r;   r;   r<   test_erf_nan_inf     zTestErf.test_erf_nan_infc                 C   r  )NrC   r   r   rJ   )rV   r   r   r   r    r  r  r;   r;   r<   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   rJ   )rV   r   r   r   r    r  r  r;   r;   r<   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   rJ   )rV   r   r   r   r    r  r  r;   r;   r<   test_erfi_nan_inf  s   zTestErf.test_erfi_nan_infc                 C   r  )Nr  r   r   rJ   )rV   r   r   r   r    r   r  r;   r;   r<   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   rJ   )rV   r   r   r   r    r  r  r;   r;   r<   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  r;   r;   r;   r<   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   rQ   rC   r   rJ   )rQ   r   rF   r   )rQ   rQ   r   =   ii  iY  i=) il   Q~ l   10[l   $8gC
 l   2l   v}Ju: )r   dr  r  r  r   r|  )r    eulerr   r   rj   rk   rV   r0  r   rC  r   )
r:   eu0eu1eu2eu24	mathworldcorrectr`   errerrmaxr;   r;   r<   
test_euler  s$   





zTestEuler.test_eulerN)r  r  r  r  r;   r;   r;   r<   r    r  r  c                   @   r  )TestExpc                 C   r^  )NrC   rA   )r    r  r   r:   exexrlr;   r;   r<   r    rb  zTestExp.test_exp2c                 C   rc  )Nr  g;f@r  )r    r  r   r:   exmexmrlr;   r;   r<   test_exp2more  rg  zTestExp.test_exp2morec                 C   r^  )NrC   r  )r    r  r   r  r;   r;   r<   r    rb  zTestExp.test_exp10c                 C   rc  )Nr  gYs@r  )r    r  r   r  r;   r;   r<   test_exp10more  rg  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 )NrC   r   rA   rQ   r  r    r  r   r   r  r;   r;   r<   r        "zTestExp.test_expm1c                 C   r  )NrC    @皙@rQ   r  r  )r:   ex1exrl1r;   r;   r<   test_expm1more%  r  zTestExp.test_expm1moreN)	r  r  r  r  r  r  r  r  r"  r;   r;   r;   r<   r    s    r  c                   @   s
  e Zd Zejdddg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ddgejjde	j
de	dgg dd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ddee	je	je	je	je	je	je	je	jg
ejdedddd Zejdddgejdedddd Zejded d!d"d#d$ Zejdeedd%eed d!d" d&d' Zd(d) Zejde	je	je	je gejdddgejdeddejjdg dgd*ge	j
ge	j
dggg d+dd,d- Z!ejdddgejjddd*d.e	j
dgg d/dd0d1 Z"ejded d!d2d3d4 Z#ejdeedd%eed d!d2 d5d6 Z$ejde	je	je	je gejdddgejdeddejjdg dge	j
ge	j
dggg d7dd8d9 Z%ejdddgejjddd*d.e	j
dgg d/dd:d; Z&ejd<eddejded=d>d?d@dA Z'ejd<eeddd"d>g ejdeedd%eed%dBd2 dCdD Z(ejde	je	je	je gejdddgejdeddejjdg dge	j
ge	j
dggg d7ddEdF Z)ejdg dGejd<eddejjddd*d.e	j
dgg d/ddHdI Z*ejd<dd*e	j
dJgdKdL Z+ejdddgejd<eddMdNdO Z,dPdQ Z-dS )RTestFactorialFunctionsr7  TFc                 C   sN   t tjd|dsJ t tjd|dsJ t tjdd|ds%J d S )NrQ   r6  r   )rV   isscalarr    	factorial
factorial2
factorialk)r:   r7  r;   r;   r<   "test_factorialx_scalar_return_type,  s   z9TestFactorialFunctions.test_factorialx_scalar_return_typer_   )rF   r  c                 C   sB   t tj||dd t tj||dd t tj|d|dd d S )Nr6  r   r   )r   r    r%  r&  r'  )r:   r7  r_   r;   r;   r<   test_factorialx_negative2  s   z/TestFactorialFunctions.test_factorialx_negativec                 C   sf   |rt nt}|tjg d|dg d |tjg d|dg d |tjg dd|dg d d S )N)r@  r   rQ   r6  )r   r   rQ   rQ   r   )r   r   r    r%  r&  r'  )r:   r7  assert_funcr;   r;   r<   test_factorialx_negative_array9  s   z5TestFactorialFunctions.test_factorialx_negative_arraycontentNnat)NaNNoneNaT)idsc                 C   sz  t j||dtju sJ t j||dtju sJ t j|d|dtju s%J |tjurJtjtdd t j|g|d W d    n1 sDw   Y  n1|rltjtdd t j|g|d W d    n1 sfw   Y  nt	t j|g|dd s{J tjtdd t j|g|d W d    n1 sw   Y  tjtdd t j|gd|d W d    d S 1 sw   Y  d S )	Nr6  r   zUnsupported datatype.*r   factorial with `exact=Tr.*r   zfactorial2 does not support.*zfactorialk does not support.*)
r    r%  rV   r   r&  r'  r   r   
ValueErrorr   )r:   r.  r7  r;   r;   r<   test_factorialx_nanD  s(   
"z*TestFactorialFunctions.test_factorialx_nanlevelsrQ   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 )NrQ   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   rQ   r;   r   r`   _nest_mer;   r<   r:  `  s   zDTestFactorialFunctions.test_factorialx_array_shape.<locals>._nest_mec                    s4   t j |dtd}t| t j|t j d S )Nr`   dtype)rV   r   objectr   r   r   )resnucleusr   r:  r7  r;   r<   _checkm  s   zBTestFactorialFunctions.test_factorialx_array_shape.<locals>._checkr   r   r;  r8  rp   Tr6  r(  r   r  rC   rQ   )rV   r   mathr%  r    r&  r'  )r:   r7  r7  rB  r_   exp_nucleusr;   rA  r<   test_factorialx_array_shape]  s   z2TestFactorialFunctions.test_factorialx_array_shaper=  dimr   c                 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   )r=  ndminr8  rp   r(  r  r6  rQ   rH  rC   r   )rV   r   r   r    r%  r&  r'  )r:   rG  r=  r7  r_   r   r;   r;   r<   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 )NrQ   c                    s   |dkr| S  | g|d S r  r;   r8  r9  r;   r<   r:    s   zCTestFactorialFunctions.test_factorialx_array_like.<locals>._nest_mer   r;  r8  rp   r(  r  r6  rI  rC   r   rC  )r   r   r    r%  rV   r   r&  r'  )r:   rK  r7  r_   rE  r,  r;   r9  r<   test_factorialx_array_like  s   z1TestFactorialFunctions.test_factorialx_array_likerM   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 )Nwin32t0=r   Tr6  FrJ   )sysplatformr   rk   r    r%  r   r:   r_   rK   r;   r;   r<   test_factorial_accuracy     
z.TestFactorialFunctions.test_factorial_accuracy   c                 C   s   t |}t|t|d t|t|gdd  tjdkr!dnd}tt|t|d|d tt|t|gdd |d d S )NTr   rN  rO  r   FrJ   )rD  r%  r   r    rP  rQ  r   rk   )r:   r_   r  rK   r;   r;   r<   test_factorial_int_reference  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 t| | t t| gd | tjdd t tj| dd| W d    n1 s.w   Y  tjtdd tj| gdd W d    d S 1 sNw   Y  d S )Nr   Non-integer values.*r   Tr6  r4  )r   r    r%  r   r   r   r5  )r_   r#  r;   r;   r<   rB    s   "zETestFactorialFunctions.test_factorial_float_reference.<locals>._checkr   gr?g(\?gc?g333333@g4s@g333333&@gމOAgfffff@@g	²Gg     K@gC$JOglS@g }WgX@gX>%`g\CSe@gG=r;   )r:   rB  r;   r;   r<   test_factorial_float_reference  s   







z5TestFactorialFunctions.test_factorial_float_referencer-  )[][1]z[1.1][NaN][NaN, 1]c                 C   s  |t jkrtdd |D rtd |dkst|dkr|n|d }t j|||d}d }|s7tj||d}n_t 	|j
t jsft 	|j
t jsftjtdd	 tj||d W d    n1 s`w   Y  n0|rt 	|j
t jstjtd
d	 tj||d W d    n1 sw   Y  ntj||d}dd }|d ur|jr| n|}|jrtj||dng }	t j|	||d}
|||
 d S d S )Nc                 s       | ]}t |V  qd S r  rV   r   r=  r   r;   r;   r<   	<genexpr>      zKTestFactorialFunctions.test_factorial_array_corner_cases.<locals>.<genexpr>impossible combinationr   rQ   rH  r=  r6  Unsupported datatype*r   zfactorial with `exact=.*c                 S   s:   t | t |ksJ dt |  dt | t| | d S )Nztypes not equal: z, )typer   r   r   r;   r;   r<   assert_really_equal  s   ,zUTestFactorialFunctions.test_factorial_array_corner_cases.<locals>.assert_really_equal)rV   rM  anyr   skiplenr   r    r%  
issubdtyper=  integerfloatingr   r5  ndimr[   r   )r:   r.  rG  r7  r=  r_   r  rg  n_flatr'  r#  r;   r;   r<   !test_factorial_array_corner_cases  s6   	
 z8TestFactorialFunctions.test_factorial_array_corner_casesy       @       @)1z1.1z2+2jr0  r1  c                 C   s  |d u s|t ju st t|t jst t|t jrht t|t jrI|rI|t jurItjdd tj	||d}W d    n1 sCw   Y  ntj	||d}|t ju sY|d u r\t jnt	|}t
|| d S tjtdd tj	||d W d    d S 1 sw   Y  d S )NrW  r   r6  rd  )rV   r   rk  re  rl  rm  r   r   r    r%  r   r   r5  r:   r_   r7  r  r   r;   r;   r<   "test_factorial_scalar_corner_cases  s   $
""z9TestFactorialFunctions.test_factorial_scalar_corner_casesr  c                 C   rM  )NrN  g+=r   Tr6  FrJ   )rP  rQ  r   rk   r    r&  r   rR  r;   r;   r<   test_factorial2_accuracy	  rT  z/TestFactorialFunctions.test_factorial2_accuracyc                 C   s|   t tjtt|ddd}t|t|d t|t|gdd  t	t
|t|d t	t
|t|gdd  d S )Nr   r  rQ   TF)	functoolsreduceoperatormulrA  rj   r   r    r&  r   rk   )r:   r_   r  r;   r;   r<   test_factorial2_int_reference	  s
    z4TestFactorialFunctions.test_factorial2_int_reference)rY  rZ  r[  r\  c                 C   s   |t jkrtdd |D rtd |dkst|dkr|n|d }t j|||d}t |jt j	s5|sKt
j||d}|s@|sBtnt}||| d S tjtdd	 t
|d
 W d    d S 1 sdw   Y  d S )Nc                 s   r]  r  r^  r_  r;   r;   r<   r`  3	  ra  zLTestFactorialFunctions.test_factorial2_array_corner_cases.<locals>.<genexpr>rb  r   rQ   rc  r6  factorial2 does not*r   r   )rV   rM  rh  r   ri  rj  r   rk  r=  rl  r    r&  r   r   r   r5  )r:   r.  rG  r7  r=  r_   r  r)  r;   r;   r<   "test_factorial2_array_corner_cases+	  s   
 "z9TestFactorialFunctions.test_factorial2_array_corner_casesc                 C   s   |d u s|t ju st t|t jr1tj||d}|t ju s"|d u r%t jnt|}t|| d S t	j
tdd tj||d W d    d S 1 sKw   Y  d S )Nr6  rz  r   )rV   r   rk  re  rl  r    r&  r%  r   r   r   r5  rr  r;   r;   r<   #test_factorial2_scalar_corner_casesC	  s   $""z:TestFactorialFunctions.test_factorial2_scalar_corner_casesr`   r  re   ic                 C   sV   t ttj||ddtj||dd t tj|g|ddttj|g|dd d S )NTr`   r7  F)r   rk   r    r'  r   )r:   r_   r`   r;   r;   r<   test_factorialk_accuracyP	  s   	z/TestFactorialFunctions.test_factorialk_accuracyr  c                 C   s   t tjtt|d| d}t|t||d t|t|g|dd  t	t
|t||d t	t
|t|g|dd  d S )Nr   rQ   TF)ru  rv  rw  rx  rA  rj   r   r    r'  r   rk   )r:   r_   r`   r  r;   r;   r<   test_factorialk_int_reference^	  s
   "z4TestFactorialFunctions.test_factorialk_int_referencec                 C   s   |t jkrtdd |D rtd |dkst|dkr|n|d }t j|||r+|nt jd}t |j	t j
s:|sGttj|d|d| d S tjtd	d
 tj|d|d W d    d S 1 sbw   Y  d S )Nc                 s   r]  r  r^  r_  r;   r;   r<   r`  v	  ra  zLTestFactorialFunctions.test_factorialk_array_corner_cases.<locals>.<genexpr>rb  r   rQ   rc  r   r6  factorialk does not*r   )rV   rM  rh  r   ri  rj  r   r   rk  r=  rl  r   r    r'  r   r5  )r:   r.  rG  r7  r=  r_   r;   r;   r<   "test_factorialk_array_corner_casesn	  s   
 "z9TestFactorialFunctions.test_factorialk_array_corner_cases)TFNc              	   C   s.  |d u s|t ju st t|t jrT|d u r5tjdd tj|||d}W d    n1 s/w   Y  ntj|||d}|t ju pE|d u }|rKt jnd}t	|| d S tj
tdd2 t }|td tj|||d W d    n1 sxw   Y  W d    d S W d    d S 1 sw   Y  d S )Nzfactorialk will default.*r   r}  rQ   r  zfactorialk will default)rV   r   rk  re  rl  r   r   r    r'  r   r   r5  r   r  rJ  )r:   r_   r`   r7  r  nan_condr#  r  r;   r;   r<   #test_factorialk_scalar_corner_cases	  s$   $"z:TestFactorialFunctions.test_factorialk_scalar_corner_casesrq  c                 C   s@   t jtdd td| W d    d S 1 sw   Y  d S )Nzk must be a positive integer*r   rQ   )r   r   r5  r    r'  r;  r;   r;   r<   test_factorialk_raises_k	  s   "z/TestFactorialFunctions.test_factorialk_raises_kr  c                 C   sB  ||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sFJ 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sJ d S tt |dg}|rtntj}ttj|fi |j| d S )Nr}  rQ   )r/   keysrV   r   r0   r   r    r'  r=  r-   rM  rB  int32rC  r>  getr   )r:   r`   r7  kwr_   r=  r;   r;   r<   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 )
NrQ   rC   r   rG   Fr6  zfactorial with `exact=True.*r   T)	rV   r   r   r   r    r%  r   r   r5  )r:   r   r#  r;   r;   r<   test_factorial_mixed_nan_inputs	  s   "z6TestFactorialFunctions.test_factorial_mixed_nan_inputs).r  r  r  r   r  r3  r(  r*  r-  rV   r   
datetime64r6  rj   rF  ri   int8int16r  rM  uint8uint16uint32uint64rJ  rL  rS  rA  rV  rX  r   
complex128r>  rp  rs  rt  ry  r{  r|  r~  r  r  r  r  r  r  r;   r;   r;   r<   r#  +  s    





#




r#  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)ry   gN?ց[?)y      ?        r  r  )y       ?yn<ӿj<Cy)BR;߿ux7Q?)y      yھ|}-2?y/?!ۿ)rn  GM?pBR?)y      @        r  r  )y              @y       GMܿy        pBR?)y              gGMܿgpBR߿)y             y        GM?y       pBR߿ry   rc  c                 C   s&   t t|}t|t ||gd d S )Nr  )r   r    r6  r   )r:   r"  rY  r  frsr;   r;   r<   test_fresnel_values	  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   rQ   r|  )r    fresnel_zerosr   r   r6  )r:   szoczovals1vals2r;   r;   r<   test_fresnel_zeros	  s   

zTestFresnel.test_fresnel_zerosc                 C   s(   t d\}}t d}t||d d S )NrG   r  )r    r  fresnelc_zerosr   )r:   r  r  frcr;   r;   r<   test_fresnelc_zeros	     
zTestFresnel.test_fresnelc_zerosc                 C   s(   t d\}}t d}t||d d S )Nr   r  )r    r  fresnels_zerosr   )r:   r  r  r  r;   r;   r<   test_fresnels_zeros	  r  zTestFresnel.test_fresnels_zerosN)r  r  r  r   r  r3  rV   r   r  r  r  r  r;   r;   r;   r<   r  	  s$    

r  c                   @   sL   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
dS )	TestGammac                 C   r  r8  )r    r:  r   )r:   gamr;   r;   r<   r;  
  r  zTestGamma.test_gammac                 C   s(   t d}tt d}t||d d S )Nr   r  )r    r>  r   r:  r   )r:   gamlnlngamr;   r;   r<   r?  
     
zTestGamma.test_gammalnc                 C   s(   t dd}t dd}t||d d S )Nry   r  )r    r<  gammaincinvr   )r:   gccinvgcinvr;   r;   r<   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 )
NrD   rQ   r(  g?g`	\;r   r@  gmb<g      &@)r    r  gammaincr   r:   r   r   r;   r;   r<   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?rQ   g^F    ?rD   rt   rJ   )rV   r  r    r  r  r   )r:   ptsxpr   r   r;   r;   r<   test_975
  s   zTestGamma.test_975c                 C   s(   t d}dt d }t||d d S )Nr  rQ   )r    rD  r:  r   )r:   rgamrlgamr;   r;   r<   rO  (
  r  zTestGamma.test_rgammac                 C   s(   t ttd ttdd d S )NrF   r   )r   rV   r
  r    r:  r   rD  r9   r;   r;   r<   test_infinity-
  s   zTestGamma.test_infinityN)r  r  r  r;  r?  r=  r1   r  r  rO  r  r;   r;   r;   r<   r   
  s    

r  c                   @   sL   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S )
TestHankelc                 C   "   t tddtdd d d S Nr)  rC   r   r|  )r   r    rV  r9   r;   r;   r<   
test_negv14
     "zTestHankel.test_negv1c                 C   8   t dd}t ddt ddd  }t||d d S NrQ   r  r   r  )r    rV  r  r  r   )r:   hank1hankrlr;   r;   r<   rW  7
     zTestHankel.test_hankel1c                 C   r  r  )r   r    rX  r9   r;   r;   r<   test_negv1e<
  r  zTestHankel.test_negv1ec                 C   0   t dd}t ddtd }t||d d S )NrQ   r  y       r  )r    rX  rV  r   r   )r:   hank1ehankrler;   r;   r<   rY  ?
  r  zTestHankel.test_hankel1ec                 C   r  r  )r   r    rZ  r9   r;   r;   r<   
test_negv2D
  r  zTestHankel.test_negv2c                 C   8   t dd}t ddt ddd  }t||d d S r  )r    rZ  r  r  r   )r:   hank2hankrl2r;   r;   r<   r[  G
  r  zTestHankel.test_hankel2c                 C   r  r  )r   r    r\  r9   r;   r;   r<   
test_neg2eL
  r  zTestHankel.test_neg2ec                 C   s(   t dd}t dd}t||d d S )NrQ   r  r  )r    r\  r   )r:   hank2ehankrl2er;   r;   r<   test_hankl2eO
  r  zTestHankel.test_hankl2eN)r  r  r  r  rW  r  rY  r  r[  r  r  r;   r;   r;   r<   r  2
  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   )r:   h1h1realr;   r;   r<   	test_h1vpV
  r  zTestHyper.test_h1vpc                 C   r  r  )r    h2vpr  r  r   )r:   h2h2realr;   r;   r<   	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  ry   Qvo?rt   rJ   r   rz   r   r   )g      rF   r   rQ   r  )g̷?g3|t-Ք?rz   go?g{h?r  ry   r  r  )r   rQ   ry   )rz   gc?r  rC   r   rQ   )
r   r    hyp0f1rV   r   r   r  vstackassert_raisesr5  )r:   r   r#  r  x2r;   r;   r<   test_hyp0f1`
  s"   zTestHyper.test_hyp0f1c                 C   s   t dd}t|d d S )N皙?      ?      ?y;EG?uM?)r    r  r   )r:   r?  r;   r;   r<   test_hyp0f1_gh5764z
  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$g d%g d&g d'g d(g d)g d*g d+g d,g d-g d.g d/g d0g d1g d2g d3g d4g d5g d6g d7g d8g d9g d:g d;g d<g d=g d>g d?g d@g dAg dBg dCg dDg dEg dFg dGg dHg dIg dJg dKg dLg dMg dNg dOg dPg dQg dRg dSg dTg dUg dVg dWg dXg dYg dZg d[g d\g d]g d^g d_g d`g dag dbg dcg ddg deg dfg dgg dh}|D ]\}}}}t |||}tt|| | dik  qd S )jNr  r  g?rE   )g{*= g˱a)g5=gvX@)g)AI@gDAhg$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$9?)glkC9g<tF8gp?g ?r  )r    r_  r   r   r   r  )r:   hyp1ref_datar  r  r  r#  r  r;   r;   r<   r`  
  s  	
 !"#$%&'()*+,-./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 )Nry   r  g7B.g|:B.r  r    r_  r   )r:   r  hyp2r;   r;   r<   test_hyp1f1_gh2957
  s   zTestHyper.test_hyp1f1_gh2957c                 C   s   t ddd}t|dd d S )Nry   r  ig<`?r  r  )r:   hypr;   r;   r<   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$d%g}t|D ]\}\}}}}}t	||||}t
||dd&| d' qd S )(Nry   rQ   r  |Gz?r  g?g|Gzr   r   rC   r  r  )r   rS  r  r  gYi2?r)  r   g433333?rA   r  r   rF   r  r   g      ?r   rH  g      gUUUUUUտg  @gUUUUUU?g)r  rc  rz         $gEciH!@)r  r   rQ   r7  gzG?)rC   r)  rQ   r7  gy&1|)r^  r   rQ   r7  g"nN%@?)rC   r+  rQ   r7  g!J)r(  |      %@r  gzS;)r(  r  g      %r  g[B.VP<test #%derr_msg)r   r   r   r	   r    r:  r   r   r  rb  r   )	r:   r   rn   r  r  r  r   r  cvr;   r;   r<   rc  
  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 )NrQ   r  r  g D?rE   )r  rn  333333?g)r  g	@r  g	ry   rC   r  )	r    hyperur   r   r   r   r_  r:  r   )r:   val1r  r  r"  hypuhprlr;   r;   r<   test_hyperu"  s   $zTestHyper.test_hyperuc                 C   s   t tddddd d S )NrQ   r  g3333334@g(¨?r  )r   r    r  r9   r;   r;   r<   test_hyperu_gh2287/  s   zTestHyper.test_hyperu_gh2287N)r  r  r  r  r  r  r  r`  r  r  rc  r  r  r;   r;   r;   r<   r  U
  s    t$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` Z2ddddeZ3e4j5j6e78 dfkdgdhdidj Z9e4j5j6e78 dfkdgdhdkdl Z:dmdn Z;dodp Z<e4j5j=dqdr Z>dsdt Z?dudv Z@dwdx ZAdydz ZBd{d| ZCd}d~ ZDdd ZEdddZFdd ZGdd ZHdd ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQdd ZRdd ZSdd ZTdcS )
TestBesselc                 C   &   t td}t|t ddgd d S )Nr   gbɃ?gΝJ ֿr  )r   r    rv  r   )r:   it0r;   r;   r<   rw  5     
zTestBessel.test_itj0y0c                 C   r  )Nr   gbqTtt?g/]ooۿr  )r   r    rn  r   )r:   it2r;   r;   r<   ro  =  r  zTestBessel.test_it2j0y0c                 C      t tddtdd d S Nr   rC   r)  )r   r    r|  r9   r;   r;   r<   test_negv_ivE     zTestBessel.test_negv_ivc                 C   &   t d}t dd}t||d d S Nr  r   r  )r    r  r  r   r:   ozozrr;   r;   r<   r  H  rl  zTestBessel.test_j0c                 C   r  Nr  rQ   r  )r    r  r  r   r:   o1o1rr;   r;   r<   r  M  rl  zTestBessel.test_j1c                 C      t dd}t|dd d S )NrQ   r   ;x?r  )r    r  r   )r:   jnnrr;   r;   r<   r  R     zTestBessel.test_jnc                 C   r  r  )r   r    r  r9   r;   r;   r<   test_negv_jvV  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˿+>)r  rS   g)%->)g@rS   g5c)!9)r  r  g%,Ϳr  r  r  )r  r    r  r   )r:   r   rn   r  r   r   ycr;   r;   r<   r  Y  s   zTestBessel.test_jvc                 C   r  r  )r   r    r  r9   r;   r;   r<   test_negv_jved  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 )NrQ   r   r  r  ?      ?)r    r  r   r  r   r  r!  )r:   jvexpjvexp1r"  jvexprr;   r;   r<   r  g  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   rQ   )go@.=@gzj,[@glN!@g5/ D'@gh>-@rA   gW@g0@gQX$@g*@g8*5{x0@rP   )gEk[@g~Cju]@gYrʝ^@g, `@gf	`@rI   rJ   -  )gts@g&ǭr3t@gWt@g,$Y&u@gu@)r    jn_zerosr   r   r   )r:   jn0jn1jn102jn301r;   r;   r<   test_jn_zeroso  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   rd   i  g;@rI   rJ   i  g8v@i+  gׂMm@r(  gxi@g	,@gи{>@i  r   )gUDX@g!@g*HS@gz5 @g@2;@r  )r    r  r   r   )r:   r  jn10jn3010r;   r;   r<   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 )NrQ   rC   r;   )r_   r   r  r;   r<   jnp      z(TestBessel.test_jnjnp_zeros.<locals>.jnprQ   rM   r   r'  r?  zInvalid t return for nt=%d)r    r  rj   jnjnp_zeroszipr   AssertionError)
r:   r$  ntr"  r_   r  tzznnttr;   r#  r<   test_jnjnp_zeros  s   zTestBessel.test_jnjnp_zerosc                 C   sF   t dd}t|tg dd t dd}tt d|ddd d S )	NrQ   r   g(yu?gOXeS@ga!@gxi'@g'Nw(-@rA     r   r   r?  )r    	jnp_zerosr   r   r   r  )r:   r$  r;   r;   r<   test_jnp_zeros  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 )NrQ   r   r  r/  )"@g+@g-9(1!@gȘ'@g>tA}-@)g0v@gjt@gH.?$@g}"O*@gGŧp0@)r    
jnyn_zerosr   r   )r:   jnzr;   r;   r<   test_jnyn_zeros  s   


zTestBessel.test_jnyn_zerosc                 C   s8   t dd}t ddt dd d }t||d d S )NrC   rQ   r   r(  )r    r  r  r   )r:   jvprimjv0r;   r;   r<   test_jvp  r  zTestBessel.test_jvpc                 C   r  r  )r    r  r  r   )r:   ozkozkrr;   r;   r<   r    rl  zTestBessel.test_k0c                 C   r  r  )r    r  r  r   )r:   ozkeozkerr;   r;   r<   r    rl  zTestBessel.test_k0ec                 C   r  r  )r    r  r  r   )r:   o1ko1krr;   r;   r<   r    rl  zTestBessel.test_k1c                 C   r  r  )r    r  r  r   )r:   o1keo1kerr;   r;   r<   r    rl  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   rQ   r   rC   r   r  r   rA   r   rG   r  r  g      H@)rV   r\   r    jacobir   r  r   )
r:   r  r  P0P1P2P3cpp2cp3cr;   r;   r<   test_jacobi  s    &B2D8XzTestBessel.test_jacobic                 C   r  )Nr   r   _2?r  )r    r  r   )r:   kn1r;   r;   r<   r    r  zTestBessel.test_knc                 C   r  Nr   r  rR  r   r    r  r9   r;   r;   r<   test_negv_kv  r  zTestBessel.test_negv_kvc                 C   r  )Nr   r   rK  r(  r    r  r   )r:   kv0r;   r;   r<   test_kv0  r  zTestBessel.test_kv0c                 C   r  )NrQ   r   gKދ@r(  rP  )r:   kv1r;   r;   r<   test_kv1  r  zTestBessel.test_kv1c                 C   r  )NrC   r   g)lHH@r(  rP  )r:   kv2r;   r;   r<   test_kv2  r  zTestBessel.test_kv2c                 C   r   )N    rQ   g.Ք"H)r   r    r  r9   r;   r;   r<   test_kn_largeorder  r   zTestBessel.test_kn_largeorderc                 C   s   t tddd d S )Nr   g =`XCrN  r9   r;   r;   r<   test_kv_largearg  r   zTestBessel.test_kv_largeargc                 C   r  rM  )r   r    r  r9   r;   r;   r<   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  r  )r    r  r  r   r   )r:   kve1rS  r"  kve2rU  r;   r;   r<   r    s   zTestBessel.test_kvec                 C   s*   d}t td| tjd|ddd d S )Nr  rQ   r   r_   r(  )r   r    r  kvp)r:   r"  r;   r;   r<   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  rQ   r]  r(  r    r  r^  r   r:   r  r"  xcr   r;   r;   r<   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  rC   rQ   r]  r(  r`  ra  r;   r;   r<   test_kvp_n2(  s
   <zTestBessel.test_kvp_n2c                 C   r  r  )r    r  r  r   r  r;   r;   r<   r  /  rl  zTestBessel.test_y0c                 C   r  r  )r    r  r  r   r  r;   r;   r<   r  4  rl  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 )NrC   rQ   r  r   r  )r    y0_zerosr   r   r  r  )r:   yoypozozpor  allvalr;   r;   r<   test_y0_zeros9  s    zTestBessel.test_y0_zerosc                 C   s*   t d}t|tdgtdgfd d S )NrQ   r3  gѮBO?r   )r    y1_zerosr   r   )r:   r  r;   r;   r<   test_y1_zerosA  s   
 zTestBessel.test_y1_zerosc                 C   s.   t jddd}t|tdgtdgfd d S )NrQ   re  yL
F%u?!rh?y;OnгY?r   )r    	y1p_zerosr   r   )r:   y1pr;   r;   r<   test_y1p_zerosE  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 )
NrA   rC   g3@g(A&"@r   r0  )g]E.+"|@gH(|@gff|}@g&b`~@gHO_~@r   rJ   )r    yn_zerosr   r   r   )r:   anr;   r;   r<   test_yn_zerosM  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   rC   gQhվ@gzN@rG   +   r   r   r?  r0  r   )r    	ynp_zerosr   r   r   r  r:   aor;   r;   r<   test_ynp_zerosX  s   zTestBessel.test_ynp_zerosc                 C   s&   t dd}tt d|ddd d S )Nr0  r   r   r  r?  )r    rv  r   r  rw  r;   r;   r<   test_ynp_zeros_large_order`  s   z%TestBessel.test_ynp_zeros_large_orderc                 C   r  NrQ   r   5,1
r  )r    r  r   )r:   yn2nr;   r;   r<   r  d  r  zTestBessel.test_ync                 C   r  r  )r   r    r  r9   r;   r;   r<   test_negv_yvh  r  zTestBessel.test_negv_yvc                 C   r  r{  )r    r  r   )r:   yv2r;   r;   r<   r  k  r  zTestBessel.test_yvc                 C   r  r  )r   r    r  r9   r;   r;   r<   test_negv_yveo  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 )NrQ   r   r|  r  r  rF   )r    r  r   r  r   )r:   yve2yve2ryve22r;   r;   r<   r  r  s
   zTestBessel.test_yvec                 C   s8   t ddt dd d }t dd}t||d d S )NrQ   r   r   r   rC   r(  )r    r  r  r   )r:   yvpryvp1r;   r;   r<   test_yvpy     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   rc  r   rz   {G(@r5  r  )ir  rF   rz   r        i@g     y@g     Ă@g@  i'  Nry   ir  rS  )	itertoolsproductr   )r:   r  r"  r;   r;   r<   _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  rK   rU   )	r  ri   rV   r
  r   r  r   r!  r   )r:   r  f2rK   rU   ri  r  r"  c1c2c3r;   r;   r<   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 )NrS   u5% r  )r  r    r  r  r9   r;   r;   r<   test_jv_cephes_vs_amos     z!TestBessel.test_jv_cephes_vs_amosc                 C   r  )Nr  r  r  r  r    r  r  r9   r;   r;   r<   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 )Nr@  )r  )r  r"  r;   r;   r<   skipper  s   zDTestBessel.test_yv_cephes_vs_amos_only_small_orders.<locals>.skipperr  r  )rK   rU   ri  r  )r:   r  r;   r;   r<   (test_yv_cephes_vs_amos_only_small_orders  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  )rV   r0  r  r    r|  r9   r;   r;   r<   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 rQ   ry   rF   rC   )r   r   r  r   r  r  r  r  gYngH׊>)rV   r\   r]   r  r  r   rM  r0  r    r|  r   r  r   argmaxr   )	r:   rG  r  r   imskr  r  dcr`   r;   r;   r<    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  r9   r;   r;   r<   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   rA   gP?r  r  g~Omʒ?gY8E@@gKSn)r   r    r  r9   r;   r;   r<   test_ticket_623  rx  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 BesselsrF   rQ   gl)ܿr  gPj?gk?g%E*2ig敋?gw--`?gÉB?gW?rc  g޴?gz|?a?gpx%?y      ?              ?      ?yYD?`{1wy6x?B]#Ӯ?y ?b>?y.}9d?8kؿy      ?333333?r,  y333333?      ?r   N)r   r    r  r  r|  r  r  r   r  r~  r  rV  rZ  r9   r;   r;   r<   test_ticket_853  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 domainsry   rF   rQ   r   rC   rA   N)r   r   r    r  r|  r  r  r  r~  r  r  r?   r  rh  r9   r;   r;   r<   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  rV   r   r  r9   r;   r;   r<   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 overflowrQ   i  g~rN   i`  g ?los~Nr   r    r|  r9   r;   r;   r<   test_ticket_503  s   zTestBessel.test_ticket_503c                 C   r   )Nrc  rQ   r  r  r9   r;   r;   r<   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   rC   ry   rQ   rF   r(  )r   r   r   r   r    r>  r   r   r   r  rC  r   epssumr:   r  r"  r_   r`   rr  r;   r;   r<   	iv_series%  s   8*zTestBessel.iv_seriesc                 C   4   dD ]}|  d|\}}tt||||d qd S )Nrz   r   r  r   rU   r  )r  r   r    rd  r:   r"  valuer  r;   r;   r<   test_i0_series-     zTestBessel.test_i0_seriesc                 C   r  )Nr  rQ   r  )r  r   r    rh  r  r;   r;   r<   test_i1_series2  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   rz   r  r5  )rz   r   r  y             @r  )r  r   r    r|  r:   r  r"  r  r  r;   r;   r<   test_iv_series7  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   rz   rS   r  g0oO?ry   g!?grb?r  gpH?r   gC~?r   ggo?r  r  r  )r  r    rd  r   r   r:   r   rn   r   r  r  r;   r;   r<   re  =  s   	zTestBessel.test_i0c                 C   r  r  )r    rf  r~  r   )r:   oizeoizerr;   r;   r<   rg  K  rl  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   rS   gj|=r  gȕ![1?ry   g;͘?rz   gRΜ?r   g|?r   g}f?r  r  r  )r  r    rh  r   r   r  r;   r;   r<   ri  P  s   zTestBessel.test_i1c                 C   r  r  )r    rj  r~  r   )r:   oi1eoi1err;   r;   r<   rk  ]  rl  zTestBessel.test_i1ec                 C   s&   t td}t|t ddgd d S )Nr   gїJB?@g*u?)r   r    rt  r   )r:   iti0r;   r;   r<   ru  b  r  zTestBessel.test_iti0k0c                 C   s"   t d}t|tddgd d S )Nr  gݳɄ|T?gVƥ
@rG   )r    rl  r   r   )r:   it2kr;   r;   r<   rm  j  s   

zTestBessel.test_it2i0k0c                 C   s$   t ddtd }t|dd d S )Nr   r  皙gv M?r(  )r    r|  r   r   )r:   iv1r;   r;   r<   r}  r  s   zTestBessel.test_ivc                 C   r  r  )r   r    r~  r9   r;   r;   r<   test_negv_ivev  r  zTestBessel.test_negv_ivec                 C   r  )Nr   r  r  r(  )r    r~  r|  r   r   )r:   ive1r  r;   r;   r<   r  y  r  zTestBessel.test_ivec                 C   s    t tddtddd d S )NrQ   rC   r   r(  )r   r    r|  ivpr9   r;   r;   r<   	test_ivp0~  r%  zTestBessel.test_ivp0c                 C   s8   t ddt dd d }t dd}t||d d S )Nr   rC   rQ   r(  )r    r|  r  r   r  r;   r;   r<   test_ivp  r  zTestBessel.test_ivp)r  r   N)r  )Ur  r  r  rw  ro  r   r  r  r  r  r  r  r  r  r"  r.  r2  r6  r9  r  r  r  r  rJ  r  rO  rR  rT  rV  rX  rY  rZ  r  r_  rc  rd  r  r  rl  rn  rq  rt  ry  rz  r  r~  r  r  r  r  r  r  r   r  r  rQ  machiner  r  r  r  slowr  r  r  r  r  r  r  r  r  r  r  r  re  rg  ri  rk  ru  rm  r}  r  r  r  r  r;   r;   r;   r<   r  4  s    
	



2
r  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   rQ   rC   r   rA   r   r  rF   )rQ   r@  rC   r   )rF   r  irG   rn  )rQ   iH   ir   r9  )rF   r   i8iX  ir8  r5  )r    laguerrer   r  r   )r:   lag0lag1lag2lag3lag4lag5r;   r;   r<   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   rQ   rC   r   rF   r  rz   r   r)  rn  )rV   r\   r    r  r   r  r   r   )r:   r`   r  r  r  r  r;   r;   r<   test_genlaguerre  s   $>zTestLaguerre.test_genlaguerreN)r  r  r  r  r  r;   r;   r;   r<   r    s    r  c                   @   sR   e Zd Zdd Zejdg dejdg dejdg dd	d
 ZdS )TestLegendrec                 C   s   t d}t d}t d}t d}t d}t d}t|jdg t|jddg t|jtg dd d	d
 t|jtg dd  t|jtg dd  t|jtg dd  d S )Nr   rQ   rC   r   rA   r   )r   r   rF   r   r  r   )r   r   r)  r   )r  r   r  r   r   r   )?   r   ir   rp   r   )r    legendrer   r  r   r   )r:   leg0leg1leg2leg3leg4leg5r;   r;   r<   test_legendre  s   





zTestLegendre.test_legendrer_   )rQ   rC   r   rA   r   zr)g?g{ɚ)@gue#gbLd?g7f?zi)go^#@g"1?g7ܘ~ @g^26g6n"c                 C   sZ   t |||d  }t d|||d  }t|d |d d  t|d |d d  d S )Nr   r   rQ   )r    lpnclpmnr   )r:   r_   r  r  reslpnresclpmnr;   r;   r<   test_lpn_against_clpmn  s   z#TestLegendre.test_lpn_against_clpmnN)r  r  r  r  r   r  r3  r  r;   r;   r;   r<   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 )NrQ   r  r   rC   r  r   r  )r    lmbdar   r  r  r  r   )r:   lamlamrr;   r;   r<   
test_lmbda  s
   "6zTestLambda.test_lmbdaN)r  r  r  r  r;   r;   r;   r<   r    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   )r:   l1pl1prlr;   r;   r<   r       zTestLog1p.test_log1pc                 C   sB   t dt dt df}tdtdtdf}t||d d S )NrQ   r-  r  rC   r  r  r  r  )r:   l1pml1pmrlr;   r;   r<   test_log1pmore  r  zTestLog1p.test_log1pmoreN)r  r  r  r  r  r;   r;   r;   r<   r    s    r  c                   @   st   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S )TestLegendreFunctionsc                 C   s   d}t dd|d}t|td|dd| | d  gdt|| d d| t|| d  gddd|| d  ggtddd| gd|t|| d  dd| | d  t|| d  gddd| ggfd	 d S )
Ny      ?333333?rC   r   rz   ry   rQ   r   rG   rE   )r    r  r   r   r   )r:   r"  clpr;   r;   r<   
test_clpmn  s   (8z TestLegendreFunctions.test_clpmnc              	   C   s   d}d}d}d}t |||d|  dd ||f }t |||d|  dd ||f }tt||gtt |||t |||gd d S )	NrS   rQ   r   ry   r   rC   r   rE   )r    r  r   r   r  r:   r  r  r_   r   clp_plus	clp_minusr;   r;   r<   test_clpmn_close_to_real_2  s   $$z0TestLegendreFunctions.test_clpmn_close_to_real_2c              	   C   s   d}d}d}d}t |||d|  dd ||f }t |||d|  dd ||f }tt||gtt |||td| tj  t |||td| tj  gd	 d S )
NrS   rQ   r   ry   r   r   y             y              ?rE   )r    r  r   r   r  rV   r   r   r  r;   r;   r<   test_clpmn_close_to_real_3  s   $$" z0TestLegendreFunctions.test_clpmn_close_to_real_3c              
   C   sj   d}d}d}d}dD ](}t t|||d|  |d ||f t|||d|  |d ||f d q
d S )Nr"  rQ   r   rC   r   r   rG   )r   r    r  )r:   r  r  r_   r   re  r;   r;   r<   test_clpmn_across_unit_circle  s   $$z3TestLegendreFunctions.test_clpmn_across_unit_circlec              
   C   s   dD ]A}t dD ]:}t d|D ]2}t|||}tt|d ddd f   t|||}tt|d ddd f   qqqd S )N)rQ   rF   rA   rQ   )rj   r    r  r   rV   r
  r  lpmn)r:   r"  r_   r  lpr;   r;   r<   test_inf  s   "$zTestLegendreFunctions.test_infc                 C   s   g d}d}d}dD ]9}|D ]4}dD ]/}t |||d|  |d t |||d|  |d  | }tt ||||d |d	d
 qqq
d S )N)r  y            ?y            y      ?      r  r  r  r  rC   r   r  )r   y        MbP?ry   r   rQ   r  rJ   )r    r  r   )r:   zvalsr  r_   re  r"  happrox_derivativer;   r;   r<   test_deriv_clpmn  s$   z&TestLegendreFunctions.test_deriv_clpmnc                 C   s6   t ddd}t|tg dgtg dgfd d S )Nr   rC   ry   rz   ry         r   rz   r  rA   )r    r  r   r   r:   r  r;   r;   r<   	test_lpmn   s   zTestLegendreFunctions.test_lpmnc                 C   0   t dd}t|tg dtg dfd d S )NrC   ry   r  r  rA   )r    r  r   r   )r:   lpnfr;   r;   r<   test_lpn)  s   
zTestLegendreFunctions.test_lpnc                 C   s   t ddd}t|dd t ddd}t|dd tjd	d
 t ddd}W d    n1 s2w   Y  t|dkp@t| d S )Nr   rC   ry   r  rE   (   r   gI?r  r  rF   )r    r  r   rV   r0  r   r   r  r;   r;   r<   r  2  s   zTestLegendreFunctions.test_lpmvc                 C   sN   t ddd}t dd}t|d d |d d t|d d |d d d S )Nr   rC   ry   rA   rQ   )r    lqmnlqnr   )r:   lqmnflqfr;   r;   r<   	test_lqmn>  s   zTestLegendreFunctions.test_lqmnc                 C   sR   d}d}|| || fD ]}t dd|d d }d|| d  }t|| qdS )znalgorithm for real arguments changes at 1.0001
           test against analytical result for m=2, n=1
        gqh ?h㈵>rC   rQ   r   )rF   rF   N)r    r  r   )r:   x0deltar   lqr#  r;   r;   r<   test_lqmn_gt1D  s   z#TestLegendreFunctions.test_lqmn_gt1c                 C   sX   t ddd\}}t|jd t|jd t ddd\}}t|jd t|jd d S )NrA   r-  )r   r   r   )r   rQ   )r    r  r   r   )r:   r  r  r;   r;   r<   test_lqmn_shapeO  s   z%TestLegendreFunctions.test_lqmn_shapec                 C   r  )NrC   ry   )gk+ݓ?g=yX5gW2)g|a2U?g~jt?gڊerA   )r    r  r   r   )r:   r  r;   r;   r<   test_lqnX  s   
zTestLegendreFunctions.test_lqnN)r  r  r  r  r   r  r  r  r
  r  r  r  r  r  r  r  r;   r;   r;   r<   r    s    					r  c                   @   r  )TestMathieuc                 C   r  r  r;   r9   r;   r;   r<   r  `  r  zTestMathieu.test_mathieu_ac                 C   r  )NrC   r   )r    r*   r9   r;   r;   r<   test_mathieu_even_coefc  r  z"TestMathieu.test_mathieu_even_coefc                 C   r  r  r;   r9   r;   r;   r<   test_mathieu_odd_coefg  s   z!TestMathieu.test_mathieu_odd_coefN)r  r  r  r  r!  r"  r;   r;   r;   r<   r   ^  s    r   c                   @   r  )TestFresnelIntegralc                 C   r  r  r;   r9   r;   r;   r<   r  n  r  z$TestFresnelIntegral.test_modfresnelpc                 C   r  r  r;   r9   r;   r;   r<   r  q  r  z$TestFresnelIntegral.test_modfresnelmN)r  r  r  r  r  r;   r;   r;   r<   r#  l  s    r#  c                   @   r  )TestOblCvSeqc                 C   &   t ddd}t|tg dd d S )Nr   r   rQ   )g~T~Oֿgt_J?gm{@g@j'&@r   )r    
obl_cv_seqr   r   )r:   oblr;   r;   r<   test_obl_cv_seqv     zTestOblCvSeq.test_obl_cv_seqN)r  r  r  r(  r;   r;   r;   r<   r$  u  r  r$  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 )NrQ   r  gQ?gx$(~?gx$(~g(\?rA   )r    pbdn_seqr   r   )r:   pbr;   r;   r<   test_pbdn_seq  s   z#TestParabolicCylinder.test_pbdn_seqc                 C   s4   t dd dt ddd  t ddd   d S )NrQ   r   r  r   )r    r'  r9   r;   r;   r<   r(    s   (zTestParabolicCylinder.test_pbdvc                 C   s<   t dd}t dd}t|t|d t|d fd d S )NrQ   r  r   rA   )r    r+  pbdv_seqr   r   )r:   pbnpbvr;   r;   r<   test_pbdv_seq  s   $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   rC   ry   r   r   r  r  gGz$@gq=
ףp4@gHQ9rt   rJ   g(\#gQ@gkS a>)rV   r  r   r   r    r:  r   r'  )r:   etar"  r;   r;   r<   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@  rA   r  r  r(  r   r"  r   r   rQ   r'  r  )rV   r  r    r'  r  r   r:   r   r2  r.  r  dpr;   r;   r<   test_pbdv_gradient     0z(TestParabolicCylinder.test_pbdv_gradientc                 C   r4  r5  )rV   r  r    r)  r  r   r6  r;   r;   r<   test_pbvv_gradient  r9  z(TestParabolicCylinder.test_pbvv_gradientc                 C   s<   t dd\}}t|tg d t|tg d d S )NrC   r   )g:4@g1{н?g7,%n?)gX@g=<'?gʠ?)r    pbvv_seqr   rV   r   )r:   res1res2r;   r;   r<   test_pbvv_seq  s   z#TestParabolicCylinder.test_pbvv_seqN)
r  r  r  r-  r(  r1  r3  r8  r:  r>  r;   r;   r;   r<   r*  ~  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 )NrC   rQ   r   gX];r(  gOV,@@)rC   r   g  8Br   r-  r  )g2}jg.M?g}2;ο)r    	polygammar   rK  rV   r  )r:   poly2poly3r   r_   r#  r;   r;   r<   test_polygamma  s"   zTestPolygamma.test_polygammaN)r  r  r  rC  r;   r;   r;   r<   r?    s    r?  c                   @   r  )TestProCvSeqc                 C   r%  )Nr   r   rQ   )g"~j?g6?Ң@g)u8F"@g2g)@r   )r    
pro_cv_seqr   r   )r:   prolr;   r;   r<   test_pro_cv_seq  r)  zTestProCvSeq.test_pro_cv_seqN)r  r  r  rG  r;   r;   r;   r<   rD    r  rD  c                   @   r  )TestPsic                 C   r  )NrQ   goxr  )r    rK  r   )r:   psr;   r;   r<   rL    r  zTestPsi.test_psiN)r  r  r  rL  r;   r;   r;   r<   rH    r  rH  c                   @   r  )
TestRadianc                 C   s"   t ddd}t|td d d S )Nr\  r   r   r   r    rM  r   r   )r:   radr;   r;   r<   rN    s   zTestRadian.test_radianc                 C   s&   t ddd}t|td d d d S )Nr\  rQ   r  rC   gC?r   rK  )r:   rad1r;   r;   r<   test_radianmore  s   zTestRadian.test_radianmoreN)r  r  r  rN  rN  r;   r;   r;   r<   rJ    s    rJ  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)rC   r   T)
derivativer   rQ   r  )rV   emptyrj   r    spherical_jnr   
riccati_jn)r:   rG  r   Sr_   r  jpr;   r;   r<   test_riccati_jn     zTestRiccati.test_riccati_jnc                 C   rP  rQ  )rV   rS  rj   r    spherical_ynr   
riccati_yn)r:   rG  r   Cr_   r   ypr;   r;   r<   test_riccati_yn  rY  zTestRiccati.test_riccati_ynN)r  r  r  rX  r^  r;   r;   r;   r<   rO    s    
rO  c                   @   r  )	TestRoundc              	   C   s@   t tttdtdtdtdf}d}t|| d S )Ng333333$@g$@r  g333333%@)r(  r(  r(  r  )rA  mapri   r    rT  r   )r:   rndrndrlr;   r;   r<   rU    s   
zTestRound.test_roundN)r  r  r  rU  r;   r;   r;   r<   r_    r  r_  c                  C   s  t j} tj}tj}tj}tj}tj}t| ddddd||  t| ddd|d d|dd	|   ||d d	   t| ddd|d d|dd	|    t| dd||d d|d
d	|   |dd	| d   ||d	 d	   t| dd|d |d d|dd	|   |dd	| d d   ||d d	  d||d d	  d   t| dd|d |d d|dd	|   |dd| d d   ||d d   d S )Nr   ry   r  rC   r   rA   r  r&  r   rp   r   r  r   r  r   g      @rQ   r   rn  g      ?g     A@)	r    sph_harmrV   r   r   r   r   r	   r   )shr   r   r   r   r	   r;   r;   r<   test_sph_harm  sP   
re  c                  C   s   t t j} ttddddj|  ttdgdddj|  ttddgddj|  ttdddgdj|  ttddddgj|  ttdgdgdgdgj|  d S r6   )rV   r=  r  r   r    rc  )dtr;   r;   r<   "test_sph_harm_ufunc_loop_selection*  s   $rg  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   rF   ry   rC   rQ   r  )	r   r    r:  r  rC  r   r   r  r  r  r;   r;   r<   _series6  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  (\rQ  rF   r   rQ   rP  r     )rQ   r(  r   r  rM   r   r  N)ri  r   r    r~  r  r;   r;   r<   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 )Nrj  r  g;cv=?r"  rJ   gQ g< j?r  rR  r  g?rt   g       igzz?r  i)   r  r  r  gffffffrF   g333333$)r   r    r~  r   r   r   r9   r;   r;   r<   test_some_valuesD  s   zTestStruve.test_some_valuesc                 C   sR   t tddtdd t tddtdd t tddtdd dS )zRegression test for #679r   g3@g*   4@r+  g333333N)r   r    r~  r9   r;   r;   r<   test_regression_679Q  s   


zTestStruve.test_regression_679N)r  )r  r  r  ri  rl  rn  ro  r;   r;   r;   r<   rh  5  s
    
rh  c                   C   r   )Nrn  r   gdX	
?)r   r    r   r;   r;   r;   r<   test_chi2_smalldf[  r   rp  c                   C   s   t tdtjd d S )Nry  rz   )r   r    r   rV   r   r;   r;   r;   r<   test_ch2_inf_  r}   rq  c                   C   r   )Nrn  r   yj_?)r   r    r   r;   r;   r;   r<   test_chi2c_smalldfc  r   rs  c                   C   r   )Nrn  rr  r   )r   r    r   r;   r;   r;   r<   test_chi2_inv_smalldfg  r   rt  c                  C   s  d} t dtdtd d| d d}d}d}t tdgd	ggg d
d||g|d	|gg| d d}t tdd|| d t tdd|| d t tdd| | d t tddd| d t tddd| d t tddd| d t tddd| d t tddd| d t tddd| d t tddd| d td}t t|j|jd | d t td!|j |jd"| d t t|jd	|j d#| d ttd$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 )'NrI   rQ   rC   gDSYC?rJ   gQ_?g?@g>;,
i}@r   )rQ   r   r   g=O?rF   r  r   rG   gXs*@r  g   V4oAgO1eAgꌠ9Y>)FgEg^ 9^;gd-?gP.5_gsTNNeg6dgu?j/ g]XC}KdgѧRg"!x{{ rz   g][#!Rrb  gٍS1gN_ r   c   r(  )r   r    agmrV   r   r   r  rC  r   r   r   )rK   agm13agm15agm35agm12fir;   r;   r<   test_agm_simplek  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 )Nr4  rQ   r  g?rC   gffffff@)r   r  r  r   r    expnr  r  r  r5  r  r  r`  ro  )r  r;   r;   r<   test_legacy  s   "r~  c                   C   s   t tjtjdd d S )NrQ   y        .B}T)r  r    r1  r|  r;   r;   r;   r<   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   )rV   r0  r   r   rf  r;   r;   r<   xfunc     $ztest_xlogy.<locals>.xfuncr   r   r   rz   r   r<  )r   r   )rQ   r   rQ   rI   r  )
rV   r   r   r   rk   r   rq   r2   r    xlogy)r  z1z2w1w2r;   r;   r<   
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  )rV   r0  r   r  rf  r;   r;   r<   r    r  ztest_xlog1py.<locals>.xfuncr  r   r  )rQ   gKH9r<  rQ   rI   r  )	rV   r   r   r   rk   rq   r2   r    xlog1py)r  r  r  r;   r;   r<   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 r6   )rV   r   r    r  )r   r;   r;   r<   r    s   ztest_entr.<locals>.xfuncr   ry   rz   rF   rQ   r<  otypesrI   r  )rV   r   r  r  r  r   rk   rq   r   r2   r    entr)r  r   signsr  sgnr  r"  r  r;   r;   r<   	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 r6   )rV   r   isposinfr    r  rf  r;   r;   r<   r    s    ztest_kl_div.<locals>.xfuncr   ry   rz   rF   rQ   r<  r  r   rI   r  )r  r  r  rV   r   rk   rq   r   r2   r    kl_div
r  r   r  r  sgnavasgnbvbr"  r  r;   r;   r<   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 r6   )r    r  rV   r   rf  r;   r;   r<   r    s
   ztest_rel_entr.<locals>.xfuncr  rF   rQ   r<  r  r   rI   r  )r  r  r  rV   r   rk   rq   r   r2   r    rel_entrr  r;   r;   r<   test_rel_entr  s   0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 )NrF   r  rC   ry   r  r   c                 S   s@   | dk rt jS t || k rdt | S | t |d|    S )Nr   ry   )rV   r   r  squarer  r  r;   r;   r<   r    s
   ztest_huber.<locals>.xfuncr(  r  r   rQ   rI   r  )r   r    huberrV   r   r   r  r\   randnrq   r   r2   r  r"  r  r;   r;   r<   
test_huber  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   rC   rQ   )rV   r   r   r  r;   r;   r<   r  &  s
   "z test_pseudo_huber.<locals>.xfuncr(  rC   r   ry   r  rQ   rI   r  )
rV   r   r\   r  tolistrq   r   r2   r    pseudo_huberr  r;   r;   r<   test_pseudo_huber%  s   (0r  c                  C   s*   d} d}t | |}d}t||dd d S )Nrz   gC]r2<gs.-De8rI   rJ   )r    r  r   )r  r  r   r#  r;   r;   r<   test_pseudo_huber_small_r3  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   rN   )r   rI  r  r)   r*   r;   r;   r;   r<   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TestStirling2rQ   r   )r   rQ   rQ   )r   rQ   r   rQ   )r   rQ   rE   rG   rQ   )r   rQ   rp   r   r(  rQ   )r   rQ      r\  A   rp   rQ   )r   rQ   r  r  i^     r  rQ   )	r   rQ      i  i    i
     rQ   )
r   rQ      i  iZ  i'  iV
  i  $   rQ   )r   rQ   rs   r$  i9  i  i+Y    i  r   rQ   zis_exact, comp, kwargsTFrK   rt   c                 C   sR   t dt| jD ]}tt |d }| j| }||t|g||dfi | qd S )NrQ   r6  )rj   rj  tablerA  r+   )r:   is_exactcompkwargsr_   k_valuesrowr;   r;   r<   test_table_casesX  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   r6  rA   rC   r   r   r   )r+   r  r:   r  r  r  r;   r;   r<   test_valid_single_integerb  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 )NrF   r6  r   rC   r+   r  r;   r;   r<   test_negative_integern  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   rA   r6  )r  r+   r   )r:   r  r  r  ansr;   r;   r<   test_array_inputsx  s&   


zTestStirling2.test_array_inputsrI   c                 C   s8   g d}g d}g d}|t |||d|fi | d S )N)r   rQ   r   r   r  r  r  )rF   r   r   r   r  r(  r(  )r  r   rC   r   r   rE   r   r6  r  r:   r  r  r  r  r_   r`   r;   r;   r<   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   Tr6  rC   c                    s,   g | ]}t  |d   d  | d  qS )rC   rQ   )rD  r;  r<  r]  r;   r<   r>    s   , z5TestStirling2.test_correct_parity.<locals>.<listcomp>N)rV   r   r   r+   )r:   Kr;   r]  r<   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   rM   rB   rA   Tr6  l	   D,"SBXp!N l   wY)H_1e_*   ru     )r   r   r+   )r:   r  r_   r`   r;   r;   r<   test_big_numbers  s   zTestStirling2.test_big_numbersrG  rH  r   y      @      ?12r  )rS  r   2Nr  c                 C   s>   t t t|||d W d    d S 1 sw   Y  d S )Nr6  )r   r   	TypeErrorr+   )r:   rG  r  r  r;   r;   r<   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 )NrA   rQ   rA   rA   rA   rA   r<  rQ   rC   r   rA   r6  )r   r  r>  r   r   r  r   r+   )r:   r  r  r_   r`   r;   r;   r<   !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 )NrA   rQ   r  r<  r  Fr6  )r   r  r.   r+   r  r;   r;   r<   #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)rQ   rp   r   r(  )rQ   rE   rG   rQ   )r   r   r   r   r  r  r6  rA   )r   rQ   rC   r   rA   r   c                 S   s   g | ]}g d qS ))r   rQ   rE   rG   rQ   r   r;   )r=  r  r;   r;   r<   r>    s    zDTestStirling2.test_broadcasting_arrays_correctly.<locals>.<listcomp>r   F)r   r+   rj   r  r;   r;   r<   "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   rQ   Tr6  Fr  )rA  rj   r+   rV   rC  r  )r:   r   r_   	k_entriesdenomrl   r;   r;   r<   test_temme_rel_max_error  s   z&TestStirling2.test_temme_rel_max_errorN)r  r  r  r  r   r  r3  r   r   r  r  r  r  r  r  r  rV   r   r  r  r  r  r  r;   r;   r;   r<   r  I  sr    





	

r  )ru  r  rw  rQ  rP  numpyrV   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_ufuncsr7   scipy.specialr!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   scipy._lib.deprecationr,   scipy._lib._utilr-   r.   scipy.special._basicr/   r0   scipy.special._testutilsr1   r2   r3   rD  r4   r  r  r  r  r  r  r  r4  r]  r  r  r  r  r  r  r  r#  r  r  r  r  r  r  r  r  r  r  r   r#  r$  r*  r?  rD  rH  rJ  rO  r_  re  rg  rh  rp  rq  rs  rt  r|  r~  r  r  r  r  r  r  r  r  r  r  r  r;   r;   r;   r<   <module>   s   X,       3z	 jUE  ,b    D2# `    W"
 		7	
&=
	