a
    Qezl                    @   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 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.m/Z/ d dl,m0Z0m1Z1m2Z2m3Z3m4Z4 d dl,m5Z5m6Z6 d d	l7m8Z8m9Z9 d d
l:m;Z;m<Z<m=Z= d dl>Z>G dd dZ?G dd dZ@G dd dZAG dd dZBG dd dZCG dd dZDG dd dZEG 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/d0 d0ZQG d1d2 d2ZRG d3d4 d4ZSG d5d6 d6ZTG d7d8 d8ZUG d9d: d:ZVG d;d< d<ZWG d=d> d>ZXG d?d@ d@ZYG dAdB dBZZG dCdD dDZ[G dEdF dFZ\G dGdH dHZ]G dIdJ dJZ^G dKdL dLZ_G dMdN dNZ`G dOdP dPZaG dQdR dRZbG dSdT dTZcdUdV ZddWdX ZeG dYdZ dZZfd[d\ Zgd]d^ Zhd_d` Zidadb Zjdcdd Zkdedf Zle;dgdh Zmdidj Zndkdl Zodmdn Zpdodp Zqdqdr Zrdsdt Zsdudv Ztdwdx Zudydz ZvdS ){    N)arrayisnanr_arangefinfopisincostanexplogzerossqrtasarrayinf
nan_to_numrealarctanfloat_)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)_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^ Z1d_d` Z2dadb Z3dcdd Z4dedf Z5dgdh Z6e7j8j9didjdkdl Z:dmdn Z;dodp Z<dqdr Z=e7j8j9dsdj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$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ Zd|d} Zd~S (  
TestCephesc                 C   s   t d d S Nr   )cephesairyself r5   R/var/www/sunrise/env/lib/python3.9/site-packages/scipy/special/tests/test_basic.py	test_airy4   s    zTestCephes.test_airyc                 C   s   t d d S r0   )r1   airyer3   r5   r5   r6   
test_airye7   s    zTestCephes.test_airyec              	   C   s6  t g d}t g d}t t |d d d f |d d d f ddj}t g dg dg dg dg}ttj| |d	d
 t j	
d t jt dddt j	d d f }t dd}t t |d d d f |d d d f ddj}ttjt|d d df |d d df d |ddd d S )N)gL7A`?   g@   )   皙?   gffffff
@r<   )g޸g	TշJ?g	7?geLF)   g*+ @r   gM{@)gףp=
%@gϔ>@g<wg$@)   g,y3@iK  g5@vIh%<=rtol  i       r   f           ?绽|=atolrD   )npr   broadcast_arraysreshapeTr-   r1   binomravelrandomseedr   r   Zrand)r4   nknkZrknownr5   r5   r6   
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 )NrE   rJ   ,     r   rI   r<   r?   rK   rL   rM   )rO   rU   rV   r   logspacer   r   rP   rQ   rR   r-   r1   rS   )r4   rW   rX   rY   r5   r5   r6   test_binom_2Q   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   sX   t | } t |}t d}t d}td|d D ]}|||  | 9 }||9 }q.t|| S NrJ   )intrangefloat)rW   rX   numZdenir5   r5   r6   	binom_int_   s    
z.TestCephes.test_binom_exact.<locals>.binom_intrE   rJ      r   r<   r?   rM   )rO   	vectorizerU   rV   r   r   rP   rQ   rR   r-   r1   rS   )r4   re   rW   rX   rY   r5   r5   r6   test_binom_exact^   s    

*$ zTestCephes.test_binom_exactc                 C   s.   g d}t |}ttj|dddd  d S )N))rG   rH   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  i  g*I y)i   i   gI)i  i  gW@N)i  i  g5y)r   rJ   r<   -q=rC   )rO   r   r.   r1   rS   check)r4   Zdatasetr5   r5   r6   test_binom_nooverflow_8346u   s    
z%TestCephes.test_binom_nooverflow_8346c                 C   s   t tdddd d S )NrJ         ?      ?)r   r1   Zbdtrr3   r5   r5   r6   	test_bdtr   s    zTestCephes.test_bdtrc                 C   s   t tdddd d S NrJ      rl   )r   r1   Zbdtrir3   r5   r5   r6   
test_bdtri   s    zTestCephes.test_bdtric                 C   s   t tdddd d S ro   )r   r1   Zbdtrcr3   r5   r5   r6   
test_bdtrc   s    zTestCephes.test_bdtrcc                 C   s   t tdddd d S NrJ   r         @)r   r1   Zbdtrinr3   r5   r5   r6   test_bdtrin   s    zTestCephes.test_bdtrinc                 C   s   t ddd d S ro   )r1   Zbdtrikr3   r5   r5   r6   test_bdtrik   s    zTestCephes.test_bdtrikc                 C   s   t tdd d S Nr           )r   r1   beir3   r5   r5   r6   test_bei   s    zTestCephes.test_beic                 C   s   t tdd d S rw   )r   r1   beipr3   r5   r5   r6   	test_beip   s    zTestCephes.test_beipc                 C   s   t tdd d S Nr   rm   )r   r1   berr3   r5   r5   r6   test_ber   s    zTestCephes.test_berc                 C   s   t tdd d S rw   )r   r1   berpr3   r5   r5   r6   	test_berp   s    zTestCephes.test_berpc                 C   s   t tdddd d S r}   )r   r1   Z
besselpolyr3   r5   r5   r6   test_besselpoly   s    zTestCephes.test_besselpolyc                 C   sF   t tddd ttddtd ttddddd	d
 d S )NrJ   rm   33333YN~h?   g6.8@rB   r   rD   rN   )r   r1   betar   gammar3   r5   r5   r6   	test_beta   s
    zTestCephes.test_betac                 C   s,   t tdddd ttdddd d S )NrJ   rm   r   r   rL   g*?)r   r1   betaincr   r3   r5   r5   r6   test_betainc   s    zTestCephes.test_betaincc                 C   sF   t tddd ttddtd ttddddd	d
 d S )NrJ   rx   r   r   r      gIs	@+=r   r   )r   r1   betalnr   gammalnr3   r5   r5   r6   test_betaln   s
    zTestCephes.test_betalnc                 C   s2   t tdddd ttddddddd	 d S )
NrJ   rm   r   r         ?g"
Yx;gAfc=r   r   )r   r1   
betaincinvr   r3   r5   r5   r6   test_betaincinv   s    zTestCephes.test_betaincinvc                 C   s   t ttdd d S )Nr?   r<   )r   rO   isinfr   r   r3   r5   r5   r6   test_beta_inf   s    zTestCephes.test_beta_infc                 C   s   t tdddd d S NrJ   rm   )r   r1   Zbtdtrr3   r5   r5   r6   
test_btdtr   s    zTestCephes.test_btdtrc                 C   s   t tdddd d S r   )r   r1   Zbtdtrir3   r5   r5   r6   test_btdtri   s    zTestCephes.test_btdtric                 C   s   t tdddd d S NrJ   rt   )r   r1   Zbtdtriar3   r5   r5   r6   test_btdtria   s    zTestCephes.test_btdtriac                 C   s   t tdddd d S r   )r   r1   Zbtdtribr3   r5   r5   r6   test_btdtrib   s    zTestCephes.test_btdtribc                 C   s   t tdd d S r   )r   r1   cbrtr3   r5   r5   r6   	test_cbrt   s    zTestCephes.test_cbrtc                 C   s   t tddd d S NrJ   r   rx   )r   r1   chdtrr3   r5   r5   r6   
test_chdtr   s    zTestCephes.test_chdtrc                 C   s   t tddd d S NrJ   r   rm   )r   r1   chdtrcr3   r5   r5   r6   test_chdtrc   s    zTestCephes.test_chdtrcc                 C   s   t tddd d S NrJ   rx   )r   r1   chdtrir3   r5   r5   r6   test_chdtri   s    zTestCephes.test_chdtric                 C   s   t tddd d S )Nr   rt   )r   r1   Zchdtrivr3   r5   r5   r6   test_chdtriv   s    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   rJ   rx   )      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   rm   gp!P?)g     u@g     r@      $@g j
?)      Y@      +@r   g]?)g     @r   r   g4ۙ?)g     b@r   r   g?)g      d@r   r   rm   r<   rp   ri   rC   r      )r   r1   ZchndtrrO   r   r   r   r   r   r   nan)r4   valuesZcdfr5   r5   r6   test_chndtr   s.    2zTestCephes.test_chndtrc                 C   s   t tdddd d S Nr   rJ   rt   )r   r1   Z	chndtridfr3   r5   r5   r6   test_chndtridf   s    zTestCephes.test_chndtridfc                 C   s   t tdddd d S r   )r   r1   Z	chndtrincr3   r5   r5   r6   test_chndtrinc   s    zTestCephes.test_chndtrincc                 C   s   t tdddd d S Nr   rJ   rx   )r   r1   Zchndtrixr3   r5   r5   r6   test_chndtrix   s    zTestCephes.test_chndtrixc                 C   s   t tdd d S r}   )r   r1   cosdgr3   r5   r5   r6   
test_cosdg  s    zTestCephes.test_cosdgc                 C   s   t tdd d S rw   )r   r1   cosm1r3   r5   r5   r6   
test_cosm1  s    zTestCephes.test_cosm1c                 C   s   t tdd d S N-   rm   )r   r1   cotdgr3   r5   r5   r6   
test_cotdg	  s    zTestCephes.test_cotdgc                 C   s$   t tdd ttdd d S )Nr   rx   gGz?gf?)r   r1   dawsnr   r3   r5   r5   r6   
test_dawsn  s    zTestCephes.test_dawsnc                 C   sV  g d}t dt j d t j}tt||ddd t dt j d t j}tt||ddd t dt j d	 t j}tt||ddd t	t d
rt dt j d t j
}tt||ddd g d}t dt j d t j}tt||ddd t dt j dt j dt j }g d}tt|d|dd d S )N)rJ   r      r<   g-C6
?rm   r>   decimal&.>rf   V瞯<float128ri      )r<   r:            皙?)gg?gsOB?gsaL?g
7I^ʿrp   )rO   r   r   astypefloat32r   r   diricfloat64hasattrr   r   )r4   Zn_oddxZn_evenZoctave_resultr5   r5   r6   
test_diric  s     
 zTestCephes.test_diricc                 C   sH   t d}t g d}tt|d d t jf |j|j|jfk d S )Nr   )rJ   rp   r>   )	rO   r   r   r   r   r   Znewaxisshapesize)r4   r   rW   r5   r5   r6   test_diric_broadcasting)  s    
z"TestCephes.test_diric_broadcastingc                 C   s   t tdd d S r   )r   r1   r    r3   r5   r5   r6   test_ellipe.  s    zTestCephes.test_ellipec                 C   s   t tddd d S r   )r   r1   	ellipeincr3   r5   r5   r6   test_ellipeinc1  s    zTestCephes.test_ellipeincc                 C   s   t dd d S Nr   rJ   )r1   ellipjr3   r5   r5   r6   test_ellipj4  s    zTestCephes.test_ellipjc                 C   s   t tdtd  d S )Nr   r<   )r   r!   r   r3   r5   r5   r6   test_ellipk7  s    zTestCephes.test_ellipkc                 C   s   t tddd d S rw   )r   r1   	ellipkincr3   r5   r5   r6   test_ellipkinc:  s    zTestCephes.test_ellipkincc                 C   s   t tdd d S rw   r   r1   erfr3   r5   r5   r6   test_erf=  s    zTestCephes.test_erfc                 C   s$   d}t t|t|  d d S )Ng#8x@rx   r   r4   r   r5   r5   r6   test_erf_symmetry@  s    zTestCephes.test_erf_symmetryc                 C   s   t tdd d S r}   )r   r1   erfcr3   r5   r5   r6   	test_erfcD  s    zTestCephes.test_erfcc                 C   s   t tdd d S )Nr<   r   )r   r1   exp10r3   r5   r5   r6   
test_exp10G  s    zTestCephes.test_exp10c                 C   s   t tdd d S )Nr<         @)r   r1   exp2r3   r5   r5   r6   	test_exp2J  s    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   rx   r?   )r   r1   expm1rO   r   r   r3   r5   r5   r6   
test_expm1M  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   rJ   r<   r:   r   r?   )r1   r   r   complexrO   r   r   )r4   r   r5   r5   r6   test_expm1_complexS  s"     "$"  "  "   zTestCephes.test_expm1_complexz-The real part of expm1(z) bad at these pointsreasonc                 C   sh   t g d}t t | }|d|  }t g d}t|}t|j|jd t|j|jd d S )N)皙?r   333333?r      r\                 ?)y=Cw?yC7gg)gF<Ug?yQ<D*?yg:><sKy>񸣼$	Um>ly;Vl <@rp   r\   )	rO   r   r   r	   r1   r   r   imagr   )r4   yr   zexpectedfoundr5   r5   r6   test_expm1_complex_hardf  s    
z"TestCephes.test_expm1_complex_hardc                 C   s0   t tdddd ttdddddd	 d S )
NrJ   r   rx   ư>r   
   g2?ri   rC   )r   r1   Zfdtrr   r3   r5   r5   r6   	test_fdtr{  s    zTestCephes.test_fdtrc                 C   s0   t tdddd ttdddddd	 d S )
NrJ   r   rm   r<   r   g    _BgDIXl?ri   rC   )r   r1   Zfdtrcr   r3   r5   r5   r6   
test_fdtrc  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 )NrJ   gV-?gx&1?g
}?g<zO'?r  rC   g׀?r   rp   ri   )r   r1   fdtrir   )r4   pr5   r5   r6   
test_fdtri  s
    zTestCephes.test_fdtrizReturns nan on i686.c                 C   s   t tdddd d S )NrJ   rl   )r   r1   r  r3   r5   r5   r6   test_fdtri_mysterious_failure  s    z(TestCephes.test_fdtri_mysterious_failurec                 C   s   t tdddd d S rs   )r   r1   Zfdtridfdr3   r5   r5   r6   test_fdtridfd  s    zTestCephes.test_fdtridfdc                 C   s   t tdd d S Nr   rx   rx   )r   r1   fresnelr3   r5   r5   r6   test_fresnel  s    zTestCephes.test_fresnelc                 C   s   t tdd d S Nr         8@)r   r1   r   r3   r5   r5   r6   
test_gamma  s    zTestCephes.test_gammac                 C   s   t tddd d S )Nr   rJ   rx   )r   r1   gammainccinvr3   r5   r5   r6   test_gammainccinv  s    zTestCephes.test_gammainccinvc                 C   s   t d d S )Nr  )r1   r   r3   r5   r5   r6   test_gammaln  s    zTestCephes.test_gammalnc                 C   s2   t g dt j}tt|t t| d S )N)      gffffffrJ   g@)rO   r   r   r   r1   Zgammasgnsignrgamma)r4   valsr5   r5   r6   test_gammasgn  s    zTestCephes.test_gammasgnc                 C   s   t tdddd d S r   )r   r1   gdtrr3   r5   r5   r6   	test_gdtr  s    zTestCephes.test_gdtrc                 C   s   t tddtjd d S r   )r   r1   r  rO   r   r3   r5   r5   r6   test_gdtr_inf  s    zTestCephes.test_gdtr_infc                 C   s   t tdddd d S r   )r   r1   Zgdtrcr3   r5   r5   r6   
test_gdtrc  s    zTestCephes.test_gdtrcc                 C   s   t tdddd d S r   )r   r1   Zgdtriar3   r5   r5   r6   test_gdtria  s    zTestCephes.test_gdtriac                 C   s   t ddd d S NrJ   r   )r1   Zgdtribr3   r5   r5   r6   test_gdtrib  s    zTestCephes.test_gdtribc                 C   s   t ddd d S NrJ   r   )r1   Zgdtrixr3   r5   r5   r6   test_gdtrix  s    zTestCephes.test_gdtrixc                 C   s   t dd d S r_   )r1   hankel1r3   r5   r5   r6   test_hankel1  s    zTestCephes.test_hankel1c                 C   s   t dd d S r_   )r1   hankel1er3   r5   r5   r6   test_hankel1e  s    zTestCephes.test_hankel1ec                 C   s   t dd d S r_   )r1   hankel2r3   r5   r5   r6   test_hankel2  s    zTestCephes.test_hankel2c                 C   s   t dd d S r_   )r1   hankel2er3   r5   r5   r6   test_hankel2e  s    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 )NrJ   rm   rp   r:   g㈮?)r   r1   hyp1f1r   r3   r5   r5   r6   test_hyp1f1  s    zTestCephes.test_hyp1f1c                 C   s   t tddddd d S r   )r   r1   hyp2f1r3   r5   r5   r6   test_hyp2f1  s    zTestCephes.test_hyp2f1c                 C   s   t tdd d S r}   )r   r1   i0r3   r5   r5   r6   test_i0  s    zTestCephes.test_i0c                 C   s   t tdd d S r}   )r   r1   i0er3   r5   r5   r6   test_i0e  s    zTestCephes.test_i0ec                 C   s   t tdd d S rw   )r   r1   i1r3   r5   r5   r6   test_i1  s    zTestCephes.test_i1c                 C   s   t tdd d S rw   )r   r1   i1er3   r5   r5   r6   test_i1e  s    zTestCephes.test_i1ec                 C   s   t d d S r_   )r1   it2i0k0r3   r5   r5   r6   test_it2i0k0  s    zTestCephes.test_it2i0k0c                 C   s   t d d S r_   )r1   it2j0y0r3   r5   r5   r6   test_it2j0y0  s    zTestCephes.test_it2j0y0c                 C   s   t d d S r_   )r1   Z
it2struve0r3   r5   r5   r6   test_it2struve0  s    zTestCephes.test_it2struve0c                 C   s   t d d S r_   )r1   Zitairyr3   r5   r5   r6   test_itairy  s    zTestCephes.test_itairyc                 C   s   t tdd d S r  )r   r1   iti0k0r3   r5   r5   r6   test_iti0k0  s    zTestCephes.test_iti0k0c                 C   s   t tdd d S r  )r   r1   itj0y0r3   r5   r5   r6   test_itj0y0  s    zTestCephes.test_itj0y0c                 C   s   t tdd d S rw   )r   r1   Zitmodstruve0r3   r5   r5   r6   test_itmodstruve0  s    zTestCephes.test_itmodstruve0c                 C   s   t tdd d S rw   )r   r1   Z	itstruve0r3   r5   r5   r6   test_itstruve0  s    zTestCephes.test_itstruve0c                 C   s   t tddd d S r   )r   r1   ivr3   r5   r5   r6   test_iv  s    zTestCephes.test_ivc                 C   s   t tddd d S r   )r   r1   iver3   r5   r5   r6   test_ive  s    zTestCephes.test_ivec                 C   s   t tdd d S r}   )r   r1   j0r3   r5   r5   r6   test_j0  s    zTestCephes.test_j0c                 C   s   t tdd d S rw   )r   r1   j1r3   r5   r5   r6   test_j1  s    zTestCephes.test_j1c                 C   s   t tddd d S r}   )r   r1   jnr3   r5   r5   r6   test_jn  s    zTestCephes.test_jnc                 C   s   t tddd d S r}   )r   r1   jvr3   r5   r5   r6   test_jv  s    zTestCephes.test_jvc                 C   s   t tddd d S r}   )r   r1   jver3   r5   r5   r6   test_jve  s    zTestCephes.test_jvec                 C   s   t d d S Nr<   )r1   k0r3   r5   r5   r6   test_k0  s    zTestCephes.test_k0c                 C   s   t d d S rU  )r1   k0er3   r5   r5   r6   test_k0e
  s    zTestCephes.test_k0ec                 C   s   t d d S rU  )r1   k1r3   r5   r5   r6   test_k1  s    zTestCephes.test_k1c                 C   s   t d d S rU  )r1   k1er3   r5   r5   r6   test_k1e  s    zTestCephes.test_k1ec                 C   s   t d d S rU  )r1   keir3   r5   r5   r6   test_kei  s    zTestCephes.test_keic                 C   s   t tdd d S rw   )r   r1   keipr3   r5   r5   r6   	test_keip  s    zTestCephes.test_keipc                 C   s   t d d S rU  )r1   kerr3   r5   r5   r6   test_ker  s    zTestCephes.test_kerc                 C   s   t d d S rU  )r1   kerpr3   r5   r5   r6   	test_kerp  s    zTestCephes.test_kerpc                 C   s   t d d S rU  )r1   kelvinr3   r5   r5   r6   test_kelvin  s    zTestCephes.test_kelvinc                 C   s   t dd d S r_   )r1   knr3   r5   r5   r6   test_kn"  s    zTestCephes.test_knc                 C   s*   t tdd ttttj d S r   )r   r1   Zkolmogir   rO   r   r   r3   r5   r5   r6   test_kolmogi%  s    zTestCephes.test_kolmogic                 C   s   t tdd d S r}   )r   r1   Z
kolmogorovr3   r5   r5   r6   test_kolmogorov)  s    zTestCephes.test_kolmogorovc                 C   s   t tdd d S )Nr          )r   r1   Z_kolmogpr3   r5   r5   r6   test_kolmogp,  s    zTestCephes.test_kolmogpc                 C   s   t tdd d S rw   )r   r1   Z_kolmogcr3   r5   r5   r6   test_kolmogc/  s    zTestCephes.test_kolmogcc                 C   s*   t tdd ttttj d S rw   )r   r1   Z	_kolmogcir   rO   r   r   r3   r5   r5   r6   test_kolmogci2  s    zTestCephes.test_kolmogcic                 C   s   t dd d S r_   )r1   kvr3   r5   r5   r6   test_kv6  s    zTestCephes.test_kvc                 C   s   t dd d S r_   )r1   kver3   r5   r5   r6   test_kve9  s    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   rx   r?   )r1   log1pr   rO   r   r   )r4   ru  r5   r5   r6   
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    n1 s0    Y  d S )	Nr   r?   r   z%invalid value encountered in multiplyrJ   r<   rp   r:   )r1   ru  r   r   rO   r   r   filterRuntimeWarningr   r   r   )r4   ru  csupr5   r5   r6   test_log1p_complexC  s"    
$ ",&"$" zTestCephes.test_log1p_complexc                 C   s   t tdddd d S )Nr   rJ   rm   )r   r1   lpmvr3   r5   r5   r6   	test_lpmvV  s    zTestCephes.test_lpmvc                 C   s   t tddd d S r   )r   r1   Z	mathieu_ar3   r5   r5   r6   test_mathieu_aY  s    zTestCephes.test_mathieu_ac                 C   s   t tddd d S r   )r   r1   Z	mathieu_br3   r5   r5   r6   test_mathieu_b\  s    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 )NrJ   r   rm   rx   c                 S   s   |t jd 9 }| dkr2ddd| td|    S | dkrVt||d td|   S | dkrtd| |td	| d
 d   S t| | |t| d | d	| d   t| d | d	| d      S d S )N   r   g;f?rJ   rl   r<      rp   r:      r   )rO   r   r	   mqr   r5   r5   r6   	ce_smallqc  s    $z.TestCephes.test_mathieu_cem.<locals>.ce_smallqd   r  rh|?r   r   )	r   r1   mathieu_cemrO   rg   r   r   r]   r   )r4   r  r  r  r5   r5   r6   test_mathieu_cem_  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 )NrJ   r   rx   rm   c                 S   s   |t jd 9 }| dkr2t||d td|   S | dkrZtd| |td|  d  S t| | |t| d | d| d   t| d | d| d      S d S )Nr  rJ   r  rp   r<   r:   r  )rO   r   r   r  r5   r5   r6   	se_smallqx  s     z.TestCephes.test_mathieu_sem.<locals>.se_smallqr  r  r  r  r  r   r   )	r   r1   mathieu_semrO   rg   r   r   r]   r   )r4   r  r  r  r5   r5   r6   test_mathieu_semt  s    
*"zTestCephes.test_mathieu_semc                 C   s   t tdddd d S NrJ   r   r  )r   r1   mathieu_modcem1r3   r5   r5   r6   test_mathieu_modcem1  s    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 )
NrJ   r   r:   rt  r<   r  r>   rL   rC   )	r1   mathieu_modcem2rO   r   r   r]   linspacer  r   r4   r  r  r   y1fry2r5   r5   r6   test_mathieu_modcem2  s    "&.zTestCephes.test_mathieu_modcem2c                 C   s   t tdddd d S r  )r   r1   mathieu_modsem1r3   r5   r5   r6   test_mathieu_modsem1  s    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 )
NrJ   r:   rt  r<   r  r   r>   rL   rC   )	r1   mathieu_modsem2rO   r   r   r]   r  r  r   r  r5   r5   r6   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   r1   r  rO   r   r  r  r  r  r  r3   r5   r5   r6   test_mathieu_overflow  s    z TestCephes.test_mathieu_overflowc                 C   sD   t dD ]6}tddd}t|d ddd t|d	 d
dd qd S )N<   r<   r  r?   r   g.dS?rL   rC   rJ   gGc?-C6?)ra   r1   r  r   )r4   rX   vr5   r5   r6   test_mathieu_ticket_1847  s    z#TestCephes.test_mathieu_ticket_1847c                 C   s   t d d S r0   )r1   Zmodfresnelmr3   r5   r5   r6   test_modfresnelm  s    zTestCephes.test_modfresnelmc                 C   s   t d d S r0   )r1   Zmodfresnelpr3   r5   r5   r6   test_modfresnelp  s    zTestCephes.test_modfresnelpc                 C   s   t tddd d S r   )r   r1   Z	modstruver3   r5   r5   r6   test_modstruve  s    zTestCephes.test_modstruvec                 C   s   t tdddd d S r   )r   r1   nbdtrr3   r5   r5   r6   
test_nbdtr  s    zTestCephes.test_nbdtrc                 C   s   t tdddd d S r   )r   r1   nbdtrcr3   r5   r5   r6   test_nbdtrc  s    zTestCephes.test_nbdtrcc                 C   s   t tdddd d S r   )r   r1   nbdtrir3   r5   r5   r6   test_nbdtri  s    zTestCephes.test_nbdtric                 C   s   t ddd d S )NrJ   r=   rl   )r1   Znbdtrikr3   r5   r5   r6   test_nbdtrik  s    zTestCephes.test_nbdtrikc                 C   s   t tdddd d S rs   )r   r1   Znbdtrinr3   r5   r5   r6   test_nbdtrin  s    zTestCephes.test_nbdtrinc                 C   s   t tddddd d S r   )r   r1   ncfdtrr3   r5   r5   r6   test_ncfdtr  s    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 )NrJ   r   rx   )rl   rJ   r  r<   rp   r  )r   r1   Zncfdtrir  r   )r4   fr	  r5   r5   r6   test_ncfdtri  s    zTestCephes.test_ncfdtric                 C   s2   g d}t d|dd}tt d|dd| d S )NrJ   r<   rp   r<   r   rf   )r1   r  r   Z
ncfdtridfd)r4   Zdfdr	  r5   r5   r6   test_ncfdtridfd  s    zTestCephes.test_ncfdtridfdc                 C   s6   g d}t |ddd}tt |ddd|dd d S )N)r   rJ   r<   rp   g     @r<   r   rf   gh㈵>rC   )r1   r  r   Z
ncfdtridfn)r4   dfnr	  r5   r5   r6   test_ncfdtridfn  s    zTestCephes.test_ncfdtridfnc                 C   s2   g d}t dd|d}tt dd|d| d S )N)rl   r  r   r<   rp   rf   )r1   r  r   Z	ncfdtrinc)r4   Zncr	  r5   r5   r6   test_ncfdtrinc  s    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 )NrJ   r   rl   	   i   r   rx   rm   r   r   r   )	r   r1   Znctdtrr   rO   r   r   r   r   r3   r5   r5   r6   test_nctdtr  s    zTestCephes.test_nctdtrc                 C   s   t ddd d S )NrJ   rl   r   )r1   Z	nctdtridfr3   r5   r5   r6   test_nctdtridf  s    zTestCephes.test_nctdtridfc                 C   s   t ddd d S r"  )r1   Z	nctdtrincr3   r5   r5   r6   test_nctdtrinc  s    zTestCephes.test_nctdtrincc                 C   s   t ddd d S )Nr   r   rl   )r1   Znctdtritr3   r5   r5   r6   test_nctdtrit  s    zTestCephes.test_nctdtritc                 C   s   t tdddd d S )Nrl   rJ   rm   )r   r1   Znrdtrimnr3   r5   r5   r6   test_nrdtrimn  s    zTestCephes.test_nrdtrimnc                 C   s   t tddddddd d S )Nrl   rx   r   rM   )r   r1   Znrdtrisdr3   r5   r5   r6   test_nrdtrisd  s    zTestCephes.test_nrdtrisdc                 C   s   t dddd d S r"  )r1   Zobl_ang1r3   r5   r5   r6   test_obl_ang1	  s    zTestCephes.test_obl_ang1c                 C   s2   t ddddd}t|d d t|d d d S )NrJ   r   rm   rx   )r1   Zobl_ang1_cvr   )r4   resultr5   r5   r6   test_obl_ang1_cv  s    zTestCephes.test_obl_ang1_cvc                 C   s   t tdddd d S NrJ   r   r   )r   r1   Zobl_cvr3   r5   r5   r6   test_obl_cv  s    zTestCephes.test_obl_cvc                 C   s   t dddd d S r"  )r1   Zobl_rad1r3   r5   r5   r6   test_obl_rad1  s    zTestCephes.test_obl_rad1c                 C   s   t ddddd d S r"  )r1   Zobl_rad1_cvr3   r5   r5   r6   test_obl_rad1_cv  s    zTestCephes.test_obl_rad1_cvc                 C   s   t dddd d S r"  )r1   Zobl_rad2r3   r5   r5   r6   test_obl_rad2  s    zTestCephes.test_obl_rad2c                 C   s   t ddddd d S r"  )r1   Zobl_rad2_cvr3   r5   r5   r6   test_obl_rad2_cv  s    zTestCephes.test_obl_rad2_cvc                 C   s   t tddd d S )NrJ   r   r  )r   r1   pbdvr3   r5   r5   r6   	test_pbdv   s    zTestCephes.test_pbdvc                 C   s   t dd d S r"  )r1   pbvvr3   r5   r5   r6   	test_pbvv#  s    zTestCephes.test_pbvvc                 C   s   t dd d S r"  )r1   Zpbwar3   r5   r5   r6   	test_pbwa&  s    zTestCephes.test_pbwac                 C   s>   t dd}t|td t g dd}t|g d d S )Nr   rJ   r?   r   rJ   r<   )rJ   rJ   rJ   )r1   Zpdtrr   rO   r   r   r4   valr5   r5   r6   	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   rJ   r?   r  rx   )r   r   r   )r1   Zpdtrcr   rO   r   r   r  r5   r5   r6   
test_pdtrc0  s    zTestCephes.test_pdtrcc                 C   sB   t  (}|td tdd W d    n1 s40    Y  d S )N-floating point number truncated to an integerrl   )r   rw  rx  r1   pdtri)r4   rz  r5   r5   r6   
test_pdtri7  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 )Nrl   rJ   r   r   ffffff?)r   #B;r  )rp   rp   )r1   Zpdtrikr   Z	gammainccr   rO   r   r4   rX   r5   r5   r6   test_pdtrik<  s    zTestCephes.test_pdtrikc                 C   s   t dddd d S r"  )r1   Zpro_ang1r3   r5   r5   r6   test_pro_ang1C  s    zTestCephes.test_pro_ang1c                 C   s    t tdddddtd d S )NrJ   r   r  )r   r1   Zpro_ang1_cvr   r3   r5   r5   r6   test_pro_ang1_cvF  s    zTestCephes.test_pro_ang1_cvc                 C   s   t tdddd d S r  )r   r1   Zpro_cvr3   r5   r5   r6   test_pro_cvJ  s    zTestCephes.test_pro_cvc                 C   s   t dddd d S r$  )r1   Zpro_rad1r3   r5   r5   r6   test_pro_rad1M  s    zTestCephes.test_pro_rad1c                 C   s   t ddddd d S r"  )r1   Zpro_rad1_cvr3   r5   r5   r6   test_pro_rad1_cvP  s    zTestCephes.test_pro_rad1_cvc                 C   s   t dddd d S r"  )r1   Zpro_rad2r3   r5   r5   r6   test_pro_rad2S  s    zTestCephes.test_pro_rad2c                 C   s   t ddddd d S r"  )r1   Zpro_rad2_cvr3   r5   r5   r6   test_pro_rad2_cvV  s    zTestCephes.test_pro_rad2_cvc                 C   s   t d d S r_   )r1   psir3   r5   r5   r6   test_psiY  s    zTestCephes.test_psic                 C   s   t tdddd d S r0   )r   r1   radianr3   r5   r5   r6   test_radian\  s    zTestCephes.test_radianc                 C   s   t tdd d S r   )r   r1   r  r3   r5   r5   r6   test_rgamma_  s    zTestCephes.test_rgammac                 C   sd   t tdd t tdd t tdd t tdd t td	d t td
d d S )N333333@r   333333      g@r   gg            @r  )r   r1   roundr3   r5   r5   r6   
test_roundb  s    zTestCephes.test_roundc                 C   s   t d d S r_   )r1   Zshichir3   r5   r5   r6   test_shichij  s    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 )NrJ   rl   r   z cosine integral(-inf) is not nan)r1   ZsicirO   r   r   r   r   r   )r4   sry  r5   r5   r6   	test_sicim  s    

zTestCephes.test_sicic                 C   s   t tdd d S NZ   rm   )r   r1   sindgr3   r5   r5   r6   
test_sindgx  s    zTestCephes.test_sindgc                 C   s.   t tddd tttdtj d S )NrJ   r   ?)r   r1   smirnovr   rO   r   r   r3   r5   r5   r6   test_smirnov{  s    zTestCephes.test_smirnovc                 C   sR   t tddd t tddd t tddd tttdtj d S )	NrJ   r   r?   r<         ?      rp   g      ȿ)r   r1   Z	_smirnovpr   rO   r   r   r3   r5   r5   r6   test_smirnovp  s    zTestCephes.test_smirnovpc                 C   s   t tddd tttdtj tjddddd}ttd|dt	d|  tjddddd}ttd	|dt	d	|  d S )
NrJ   r   r   r   TZendpointrp   r   r:   )
r   r1   	_smirnovcr   rO   r   r   r  r   r  )r4   Zx10Zx4r5   r5   r6   test_smirnovc  s    zTestCephes.test_smirnovcc                 C   sP   t tdtddd t tdtddd tttdtj d S NrJ   r=   333333?)r   r1   r  smirnovir   rO   r   r   r3   r5   r5   r6   test_smirnovi  s    zTestCephes.test_smirnovic                 C   sP   t tdtddd t tdtddd tttdtj d S r  )r   r1   r  Z
_smirnovcir   rO   r   r   r3   r5   r5   r6   test_smirnovci  s    zTestCephes.test_smirnovcic                 C   s   t tdd d S r   )r   r1   Zspencer3   r5   r5   r6   test_spence  s    zTestCephes.test_spencec                 C   s:   t tddd ttddd ttddd d S )NrJ   r   rl   r  r<   gMoF?)r   r1   Zstdtrr   r3   r5   r5   r6   
test_stdtr  s    zTestCephes.test_stdtrc                 C   s   t dd d S )Nffffff?rJ   )r1   Zstdtridfr3   r5   r5   r6   test_stdtridf  s    zTestCephes.test_stdtridfc                 C   s   t dd d S )NrJ   r  )r1   Zstdtritr3   r5   r5   r6   test_stdtrit  s    zTestCephes.test_stdtritc                 C   s   t tddd d S rw   )r   r1   struver3   r5   r5   r6   test_struve  s    zTestCephes.test_struvec                 C   s   t tdd d S r   )r   r1   tandgr3   r5   r5   r6   
test_tandg  s    zTestCephes.test_tandgc                 C   s   t tddd d S r   )r   r1   Ztklmbdar3   r5   r5   r6   test_tklmbda  s    zTestCephes.test_tklmbdac                 C   s   t d d S r_   )r1   y0r3   r5   r5   r6   test_y0  s    zTestCephes.test_y0c                 C   s   t d d S r_   )r1   r  r3   r5   r5   r6   test_y1  s    zTestCephes.test_y1c                 C   s   t dd d S r_   )r1   ynr3   r5   r5   r6   test_yn  s    zTestCephes.test_ync                 C   s   t dd d S r_   )r1   yvr3   r5   r5   r6   test_yv  s    zTestCephes.test_yvc                 C   s   t dd d S r_   )r1   yver3   r5   r5   r6   test_yve  s    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$t d%d&t d'd(t d)d*t d+d,t d-d.t d/dt d0d1t d2d3t d4d5t d6d7t d8d9t d:d:g}ttj||d;d< d S )=Ng@g+п皙ٿr   r  r   r   rm   g      "g      "@g4׵/Yg8EGr?r  gffffff@ig>@rx   g|Pk?r   rJ   irt  r  i   ig     j@  ļBg0"bgpتO#M?gMF>?g5-g`?g	S+?g6U?gǗʿgjD{?/,Gg` 0Gg!^?gnF5o{gI\Y?g7f8goC9	?gyhgEbr?g{g.
?ga~gT-s?gɤ,P&?g|bgޗY3g!ؑ-@gi$bghgy(V@^gһ>g>gx\h<rB   rC   )r   r-   r1   wofz)r4   r   wr5   r5   r6   	test_wofz  sr    "zTestCephes.test_wofzN)__name__
__module____qualname__r7   r9   rZ   r^   rh   rk   rn   rq   rr   ru   rv   rz   r|   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   pytestmarkxfailr  r  r  r
  r  r  r  r  r  r  r  r  r  r   r!  r#  r%  r'  r)  r+  r-  r0  r2  r4  r6  r8  r:  r<  r>  r?  r@  rB  rD  rE  rF  rH  rJ  rL  rN  rP  rR  rT  rW  rY  r[  r]  r_  ra  rc  re  rg  ri  rj  rk  rm  rn  ro  rq  rs  rv  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  r  r	  r  r  r  r  r  r  r  r  r5   r5   r5   r6   r/   3   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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'$'?geοgL?g
HVV?g
ףp=
׿)gl@D|?gV~׭ͿgU?g3{ɔ?)r   r2   r   r   r   r5   r5   r6   r7     s    


zTestAiry.test_airyc                 C   s   t d}t d}d gd }tdD ] }|| tdtd  ||< q&tddD ]*}|| tttdtd   ||< qRt||d d S )Nr   r:   r<   gN贁N{?r@   )	r   r8   r2   ra   r   r   absr   r   )r4   abb1rW   r5   r5   r6   r9     s    


(zTestAiry.test_airyec                 C   s   t d}tddgtddgtddgtdd	gf}t||d
 t d}t|d tg dd t|d tg dd t|d tg dd t|d tg dd d S )Nr<   glgoe2+
g(0[g X*JgUfݿg˰zU`?g4c1=C?gCuTr:   r   r   )g&g(.2+
gRg}`g%́r   rJ   )g7;1[ge*JgVwgL g<3r  )gNݿg3%IQ`?gZyΌ׿gʀ11^?g33tտrp   )gqM0=C?g7uTg\G`?gp⍞vg$.m?)r   bi_zerosr   r   )r4   biZbiar5   r5   r6   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 )NrJ   gcqg!xLgMSt$?g ~:p?r:   )r   ai_zerosr   r   )r4   Zair5   r5   r6   test_ai_zeros   s    
zTestAiry.test_ai_zerosc                 C   s   t d\}}}}t |\}}}}t |\}}	}}dt|d  }
t|d }t||dd t||dd t||
 dddd t|	| dddd t|d d g d	dd t|d d g d
dd d S )NP  rJ   r   rL   rC   r   rM   r@   )guqgqHkZg4g9Ζ%gB~gL")gLgQO	gMQnGg3:g)}g )r   r+  r2   r$  r   )r4   r   zpZai_zpxZaip_zxZai_zZaip_z_Zai_zpZaip_zpZai_envelopeZaip_enveloper5   r5   r6   test_ai_zeros_big'  s"    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-  rJ   r   rL   rC   r   rM   r@   )gx&gg-2+
gRgg`gu%́g{ )g K;1[g*JgVwg<w gd
3g/{
")r   r(  r2   r$  r   )r4   r   r.  Zbi_zpxZbip_zxr/  Zbi_zZbip_zZbi_zpZbip_zpZbi_envelopeZbip_enveloper5   r5   r6   test_bi_zeros_big?  s"    zTestAiry.test_bi_zeros_bigN)	r  r  r  r7   r9   r*  r,  r0  r1  r5   r5   r5   r6   r"    s   

!r"  c                   @   s   e Zd Zdd ZdS )TestAssocLaguerrec                 C   sL   t dd}t ddd}t||dd t ddd}t||dd d S )Nr   rJ   r   r  )r   genlaguerreZassoc_laguerrer   )r4   Za1Za2r5   r5   r6   test_assoc_laguerreY  s
    z%TestAssocLaguerre.test_assoc_laguerreN)r  r  r  r4  r5   r5   r5   r6   r2  X  s   r2  c                   @   s   e Zd Zdd ZdS )TestBesselpolyc                 C   s   d S Nr5   r3   r5   r5   r6   r   b  s    zTestBesselpoly.test_besselpolyN)r  r  r  r   r5   r5   r5   r6   r5  a  s   r5  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zd%S )&
TestKelvinc                 C   s   t d}t|dd d S )Nr<   gT?r   )r   ry   r   )r4   Zmbeir5   r5   r6   rz   g  s    
zTestKelvin.test_beic                 C   s   t d}t|dd d S )Nr<   gD,X?r   )r   r{   r   )r4   Zmbeipr5   r5   r6   r|   k  s    
zTestKelvin.test_beipc                 C   s   t d}t|dd d S )Nr<   gPA4?r   )r   r~   r   )r4   Zmberr5   r5   r6   r   o  s    
zTestKelvin.test_berc                 C   s   t d}t|dd d S )Nr<   gii߿r   )r   r   r   )r4   Zmberpr5   r5   r6   r   s  s    
zTestKelvin.test_berpc                 C   s"   t d}t|tg dd d S )Nr   g&jj@g+"@g(rw+@gU2@g`<6@r:   )r   Z	bei_zerosr   r   )r4   r)  r5   r5   r6   test_bei_zerosw  s    
zTestKelvin.test_bei_zerosc                 C   s"   t d}t|tg dd d S )Nr   )gyWo.@g╲ݏ @gנ{)@gK11@gWc"5@r  )r   Z
beip_zerosr   r   )r4   Zbipr5   r5   r6   test_beip_zeros  s    
zTestKelvin.test_beip_zerosc                 C   s"   t d}t|tg dd d S )Nr   g\@g6ُ@gӟHY'@g>"D0@ggaO;4@r:   )r   Z	ber_zerosr   r   )r4   r~   r5   r5   r6   test_ber_zeros  s    
zTestKelvin.test_ber_zerosc                 C   s"   t d}t|tg dd d S )Nr   g '@gs%@gF ^-@gvۅj3@gB7@r:   )r   Z
berp_zerosr   r   )r4   Zbrpr5   r5   r6   test_berp_zeros  s    
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 )Nr<   r   r  )r   rf  r   r~   ry   rb  r^  r   r{   rd  r`  )r4   Zmkelvr5   r5   r6   rg    s    
zTestKelvin.test_kelvinc                 C   s   t d}t|dd d S )Nr<   g>ɿr   )r   r^  r   )r4   Zmkeir5   r5   r6   r_    s    
zTestKelvin.test_keic                 C   s   t d}t|dd d S )Nr<   gr@d"?r   )r   r`  r   )r4   Zmkeipr5   r5   r6   ra    s    
zTestKelvin.test_keipc                 C   s   t d}t|dd d S )Nr<   gܙUr   )r   rb  r   )r4   Zmkerr5   r5   r6   rc    s    
zTestKelvin.test_kerc                 C   s   t d}t|dd d S )Nr<   g^.n3Jr   )r   rd  r   )r4   Zmkerpr5   r5   r6   re    s    
zTestKelvin.test_kerpc                 C   s"   t d}t|tg dd d S )Nr   gE>Q@gB= @gPN)@gm91@g
%5@r:   )r   Z	kei_zerosr   r   )r4   r^  r5   r5   r6   test_kei_zeros  s    
zTestKelvin.test_kei_zerosc                 C   s"   t d}t|tg dd d S )Nr   gWf,@g?"@gFZ*o+@gOpN2@gEa6@r:   )r   Z
keip_zerosr   r   )r4   r`  r5   r5   r6   test_keip_zeros  s    
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;  r:   r8  )#?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@rA  )r   Zkelvin_zerosr   r   )
r4   tmpZberzZbeizZkerzZkeizZberpzZbeipzZkerpzZkeipzr5   r5   r6   test_kelvin_zeros  s4    
zTestKelvin.test_kelvin_zerosc                 C   s"   t d}t|tg dd d S )Nr   )rC  rD  rE  rF  gD;q3@r:   )r   Z	ker_zerosr   r   )r4   rb  r5   r5   r6   test_ker_zeros  s    
zTestKelvin.test_ker_zerosc                 C   s"   t d}t|tg dd d S )Nr   rG  r:   )r   Z
kerp_zerosr   r   )r4   rd  r5   r5   r6   test_kerp_zeros  s    
zTestKelvin.test_kerp_zerosN)r  r  r  rz   r|   r   r   r9  r:  r<  r>  rg  r_  ra  rc  re  r@  rB  rI  rJ  rK  r5   r5   r5   r6   r7  f  s$   		.r7  c                   @   s   e Zd Zdd ZdS )TestBernoullic                 C   s"   t d}t|tg dd d S )Nr   )rm   r  g-!lV?rx   g镲rx   r:   )r   Z	bernoullir   r   )r4   Zbrnr5   r5   r6   test_bernoulli   s    
zTestBernoulli.test_bernoulliN)r  r  r  rM  r5   r5   r5   r6   rL    s   rL  c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestBetac                 C   s:   t dd}t dt d t d }t||d d S )Nr<   r:   r@   r  )r   r   r   r   )r4   betZbetgr5   r5   r6   r     s    zTestBeta.test_betac                 C   s0   t dd}ttt dd}t||d d S )Nr<   r:   r  )r   r   r   r$  r   r   )r4   ZbetlnrO  r5   r5   r6   r     s    zTestBeta.test_betalnc                 C   s   t ddd}t|dd d S )NrJ   r   r  )r   r   r   )r4   Zbtincr5   r5   r6   r     s    zTestBeta.test_betaincc                 C   s,   t ddd}t dd|}t|dd d S )Nr<   r:   rl   r   )r   r   r   r   )r4   r   compr5   r5   r6   r     s    zTestBeta.test_betaincinvN)r  r  r  r   r   r   r   r5   r5   r5   r6   rN  
  s   rN  c                   @   s   e Zd Zdd Zejdddgejdg d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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sJ d S )Nr  rp   r:         ^@g     @j@Texactx   )rT  
repetition   c                 S   s   g | ]}t jd |ddqS )r\   TrS  )r   comb).0rX   r5   r5   r6   
<listcomp>&      z/TestCombinatorics.test_comb.<locals>.<listcomp>r  r\   r   rN   rJ   l   hU7`S?Q r  2   )r   r   rX  r   r   r   ra   listrO   iinfor`   max)r4   iir  r5   r5   r6   	test_comb   s    zTestCombinatorics.test_combrV  TFlegacy)TFNrX   r  rp   N      @r:   c                 C   s   |d urLt jtdd$ tj||d||d}W d    q`1 s@0    Y  ntj||d||d}|r|rt|| d t| }}d}nt|t| }}t 4}|d ur|t tj||||d}W d    n1 s0    Y  t|| d S )Nz$Using 'legacy' keyword is deprecatedmatchT)rT  rc  rV  rJ   F)rc  rV  )	r  warnsDeprecationWarningr   rX  r`   r   rw  r   )r4   rd  rX   rc  rV  r  rz  r  r5   r5   r6   test_comb_legacy/  s*    &
0z"TestCombinatorics.test_comb_legacyc                 C   sL   d}d}t |}t |}tj||dd}tj||dd}||ksHJ d S )NF   rF   TrS  )rO   int64r   rX  )r4   rW   rX   Znp_nZnp_kZres_npZres_pyr5   r5   r6   test_comb_with_np_int64P  s    

z)TestCombinatorics.test_comb_with_np_int64c                 C   sz   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 )Nr<   rp   TrS  r   r?   Fr<   r?   r<   r  rp   rp   r?   rp   )rx   rx   rx   rR  )r   r   rX  r   r3   r5   r5   r6   test_comb_zerosY  s    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  rp   r:        @g     @TrS  i  )r   r   permr   r   r3   r5   r5   r6   	test_perma  s    zTestCombinatorics.test_permc                 C   sz   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 )Nr<   rp   TrS  r   r?   Frn  ro  )rx   rx   rx   rq  )r   r   rr  r   r3   r5   r5   r6   test_perm_zerosf  s    z!TestCombinatorics.test_perm_zerosN)r  r  r  rb  r  r   parametrizerj  rm  rp  rs  rt  r5   r5   r5   r6   rQ    s   	rQ  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   s   t d}d}t|| d S )N   r   )r   r   r   )r4   cbZcbrlr5   r5   r6   r   p  s    
zTestTrigonometric.test_cbrtc                 C   s   t d}d}t||d d S )Ngfffff;@g鎖C@r  )r   r   r   )r4   Zcb1Zcbrl1r5   r5   r6   test_cbrtmoreu  s    
zTestTrigonometric.test_cbrtmorec                 C   s&   t d}ttd }t||d d S )Nr  r   r  r   r   r	   r   r   )r4   ZcdgZcdgrlr5   r5   r6   r   z  s    
zTestTrigonometric.test_cosdgc                 C   s&   t d}ttd }t||d d S NrF         @r  rz  )r4   ZcdgmZcdgmrlr5   r5   r6   test_cosdgmore  s    
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  rJ   r  )r   r   r   r	   r   )r4   csZcsrlr5   r5   r6   r     s     &zTestTrigonometric.test_cosm1c                 C   s*   t d}ttd d }t||d d S )NrF   r|  r?   r  r   r   r
   r   r   )r4   ctZctrlr5   r5   r6   r     s    
zTestTrigonometric.test_cotdgc                 C   s*   t d}ttd d }t||d d S )Nr   r   r?   r  r  )r4   Zct1Zctrl1r5   r5   r6   test_cotdgmore  s    
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   rm      r   r  rx   i   y   i  i;  i  )r   r   r   r3   r5   r5   r6   test_specialpoints  s    z$TestTrigonometric.test_specialpointsc                 C   s&   t tdgd ttdd d S )Nr   rJ   rx   rm   )r   r   Zsincr   r3   r5   r5   r6   	test_sinc  s    zTestTrigonometric.test_sincc                 C   s   t d}t|d d S r  )r   r  r   )r4   Zsnr5   r5   r6   r    s    
zTestTrigonometric.test_sindgc                 C   sH   t d}ttd }t||d t d}ttd }t||d d S )NrF   r|  r  r   r   )r   r  r   r   r   )r4   ZsnmZsnmrlZsnm1Zsnmrl1r5   r5   r6   test_sindgmore  s    

z TestTrigonometric.test_sindgmoreN)r  r  r  r   ry  r   r}  r   r   r  r  r  r  r  r5   r5   r5   r6   rv  o  s   rv  c                   @   s$   e Zd Zdd Zdd Zdd ZdS )	TestTandgc                 C   s&   t d}ttd }t||d d S r{  r   r
  r
   r   r   )r4   tnZtnrlr5   r5   r6   r    s    
zTestTandg.test_tandgc                 C   sH   t d}ttd }t||d t d}ttd }t||d d S )Nr   r   r  r  r   r  )r4   ZtnmZtnmrlZtnm1Ztnmrl1r5   r5   r6   test_tandgmore  s    

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   rx   r  r   rm   r  r   r  r  r  iLr  r  r  r  )r   r   r
  r3   r5   r5   r6   r    s    zTestTandg.test_specialpointsN)r  r  r  r  r  r  r5   r5   r5   r6   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S )	TestEllipc                 C   s   t dtj dS )zRegression test for #912.rl   N)r   r   rO   r   r3   r5   r5   r6   test_ellipj_nan  s    zTestEllip.test_ellipj_nanc                 C   s0   t dd}tdtdddg}t||d d S )Nr   r   rm      )r   r   r   r	   r   )r4   elrelr5   r5   r6   r     s    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   rx   rm   r<   r?   gN?)
r   r!   r   r   r"   rO   r   r   r   r   )r4   elkr5   r5   r6   r     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 )Nr<   r   rf   r\   r  r   gfoKh?r  rx   rm   r   rl   gt?rJ   r=   r   rC   6<R!?r  gfON?)r   r   r   r!   r   r   r   rO   r   r   r   )r4   Zelkincr  alphaphir  r5   r5   r6   r     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  rJ   gV^8j?g,j6Ƅ@r<   )	rO   	nextafterra   appendr   r   r   	full_liker   r4   Zmbadr  r  Zmvalsjr  f1r5   r5   r6   test_ellipkinc_2  s    
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   r<   Fr  rJ   r  rC   )rO   r]   r  r   r   r   r   Zarcsinhr
   r   r   )r4   ZxlogZxlinZxlin2r5   r5   r6   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  rx   r<   rm   r  g?eg@)	r   r    r   r   r   rO   r   r   r   )r4   eler5   r5   r6   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 )Nr<   r   r  4   r  #   g'?r  rx   rm   r   rl   r  r  gL@)r   r   r   r    r   r   r   rO   r   r   r   )r4   Zeleincr  r  r  r  r5   r5   r6   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  rJ   g%?r<   gXo
@r:   )	rO   r  ra   r  r   r   r   r  r   r  r5   r5   r6   test_ellipeinc_2G  s    
zTestEllip.test_ellipeinc_2N)r  r  r  r  r   r   r   r  r  r   r   r  r5   r5   r5   r6   r    s   r  c                   @   sN   e Zd ZdZdd Zdd Zdd Zdd	 Zd
d Ze	j
jdddd ZdS )TestEllipCarlsonzTest for Carlson elliptic integrals ellipr[cdfgj].
    The special values used in these tests can be found in Sec. 3 of Carlson
    (1994), https://arxiv.org/abs/math/9409227
    c                 C   s   t tddd tdtdks"J ttdds4J tdtdtdksLJ 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| ||  qd S )NrJ   rx   r   r   g      @r   r                       r   y
c?
cy=B?CGֿr   y檠f?P9lb?)
r   r#   r   r   r   r   rO   r   r   	enumerater4   argsZexpected_resultsrd   arrr5   r5   r6   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sRJ ttddtddsnJ ttddtddsJ ttddttjj	 d sJ ttddtddsJ t
g d	g d
g dg dg dg dg}t
g d}t|D ]\}}t t| ||  qd S )NrJ   r   r<   r   g`C+?rx   r   r?   )rx   r   rm   r   r   r   r   r  r   rx   r   r  )rx               ?r   )y             r  r  )gfe_?gi+"?gP$M?ytgFU?7?@yR<8*y{62?z)r   r$   r   rO   r   r   r   r   doubletinyr   r  r  r5   r5   r6   test_elliprdq  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s8J ttdddsNJ ttdddsbJ tttdddkszJ ttddtt dsJ tg dg dg d	g d
g dg dg dg}tg d}t|D ]\}}t t| ||  qd S )NrJ   r   r<   gPO?rx   r?   )rm   r   rx   )r   r  rx   )rl   rm   rx   r  r   rx   r  r  )r  r         ?      )geQO?ʞu5J?r  yp\y?kg2ΰ?gHwд?y|pF?-6Fj)	r   r%   r   rO   r   r   r   r   r  r  r5   r5   r6   test_elliprf  s$    zTestEllipCarlson.test_elliprfc                 C   s   t tdddd t tdddd t tdddd ttdtdsLJ ttttddsfJ tg dg dg dg dg dg d	g}ttjd
ddddg}t|D ]\}}t t| ||  qd S )NrJ   r   rl   )rx         0@r  r  r  r  )r  r  r   )rx   g8d`?r   gL+?g}^?y旮0?ʋW?yjN?^?gt?)	r   r&   rO   r   r   r   r   r   r  r  r5   r5   r6   test_elliprg  s*    zTestEllipCarlson.test_elliprgc                 C   s   t tddddd tddtddks*J ttdddds@J ttddddsVJ tdddtdkslJ tg dg dg dg dg d	g d
g dg dg dg	}tg d}t|D ]\}}t t| ||  qd S )NrJ   rx   r   r?   )rx   rm   r   r   )r   r   r   rt   )r   r   r   r  )r   r  rx   r   )r              rm   r   )r   r  rx   r  )r  r  rm   y            ?)r   r   r   r  )r   r   r         )	g @?gviM?ym?\Isؿg'4Ob?go0 ?yW7?xfOA?ybv㿘ܶ.gHQ?gjߡB7E)r   r'   r   r   r   r  r  r5   r5   r6   test_elliprj  s$    		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|>g+<r  r   g   ,@g    x=g   @e:g   `ݽ>g(HR)A)r   r'   r3   r5   r5   r6   test_elliprj_hard  s     z"TestEllipCarlson.test_elliprj_hardN)r  r  r  __doc__r  r  r  r  r  r  r   r!  r  r5   r5   r5   r6   r  X  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   rm   r   r   r?   rx   )rO   r   Zm_n1_1r   r   minZmax_neglog2Z
very_neg_mZconcatenate
ms_up_to_1r3   r5   r5   r6   setup_class  s    

z.TestEllipLegendreCarlsonIdentities.setup_classc                 C   s$   | j }tt|tdd| d dS )z5Test identity:
        K(m) = R_F(0, 1-m, 1)
        rx   rm   N)r  r   r!   r%   r4   r  r5   r5   r6   test_k  s    z)TestEllipLegendreCarlsonIdentities.test_kc                 C   s>   t tj}|dtdt|   }tt|td|d dS )z\Test identity:
        K(m) = R_F(0, 1-m, 1)
        But with the ellipkm1 function
        r   rx   rm   N)	r   r   r  r   rO   r  r   r"   r%   )r4   r  m1r5   r5   r6   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   rx   rm   N)r  r   r    r&   r  r5   r5   r6   test_e  s    z)TestEllipLegendreCarlsonIdentities.test_eN)r  r  r  r  r  r  r  r  r5   r5   r5   r6   r    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   s   t d}t|dd d S )Nr   g);T?r  )r   r   r   )r4   Zerr5   r5   r6   r     s    
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'>@r:   )r   Z	erf_zerosr   r   )r4   ZerzZerzrr5   r5   r6   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	z ||}	||j}
t |	}|	| }	|| }t |
}|
| }
|| }t||	|||d
 t||
|||d
 W d    n1 s0    Y  d S )NrE   r  g{Gz?r<   r   rJ   r   ignoreallr   )	rO   rU   rV   paretorandinterrstater   isfiniter-   )r4   funcZ
other_funcrD   rN   rW   r   r   r   r  Zw_realmaskr5   r5   r6   _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 r_   r1   r   r   r5   r5   r6   <lambda>6  r[  z.TestErf.test_erfc_consistent.<locals>.<lambda>ri   r   r   )r  r1   r   r3   r5   r5   r6   test_erfc_consistent3  s    zTestErf.test_erfc_consistentc                 C   s   | j tjdd dd d S )Nc                 S   s   t | |  t|  S r6  )rO   r   r1   r   r  r5   r5   r6   r  >  r[  z/TestErf.test_erfcx_consistent.<locals>.<lambda>ri   rC   )r  r1   erfcxr3   r5   r5   r6   test_erfcx_consistent;  s
    zTestErf.test_erfcx_consistentc                 C   s   | j tjdd dd d S )Nc                 S   s   dt d|   S )Nr  r   r  r  r5   r5   r6   r  E  r[  z.TestErf.test_erfi_consistent.<locals>.<lambda>ri   rC   )r  r1   erfir3   r5   r5   r6   test_erfi_consistentB  s
    zTestErf.test_erfi_consistentc                 C   s   | j tjdd dd d S )Nc                 S   s&   t td t|  |   t|  S rU  )r   r   rO   r   r1   r  r  r5   r5   r6   r  L  r[  z/TestErf.test_dawsn_consistent.<locals>.<lambda>ri   rC   )r  r1   r   r3   r5   r5   r6   test_dawsn_consistentI  s
    zTestErf.test_dawsn_consistentc                 C   s6   t jt j t jg}t jddg}tt||dd d S )Nr?   rJ   r   rC   )rO   r   r   r   r   r   r4   r  r  r5   r5   r6   test_erf_nan_infP  s    zTestErf.test_erf_nan_infc                 C   s6   t jt j t jg}t jddg}tt||dd d S )Nr<   r   r   rC   )rO   r   r   r   r   r   r  r5   r5   r6   test_erfc_nan_infU  s    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   rC   )rO   r   r   r   r   r  r  r5   r5   r6   test_erfcx_nan_infZ  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   rC   )rO   r   r   r   r   r  r  r5   r5   r6   test_erfi_nan_inf_  s    zTestErf.test_erfi_nan_infc                 C   s6   t jt j t jg}t jddg}tt||dd d S )Nrl  rx   r   rC   )rO   r   r   r   r   r   r  r5   r5   r6   test_dawsn_nan_infd  s    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   rC   )rO   r   r   r   r   r  r  r5   r5   r6   test_wofz_nan_infi  s    zTestErf.test_wofz_nan_infN)r   )r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r5   r5   r5   r6   r    s   	
r  c                   @   s   e Zd Zdd ZdS )	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 ]8}|d rt||  |d| < qxt|| |d| < qxtjdd( t|| | }t	|}	W d    n1 s0    Y  t
|	dd d S )Nr   rJ   r<   r   rC   )rJ   r   r?   r   )rJ   rJ   r   =   ii  iY  i=) il   Q~ l   10[l   $8gC
 l   2l   v}Ju: )r   dr  r  r  rx   r  )r   Zeulerr   r   ra   rb   rO   r  r   r`  r   )
r4   Zeu0Zeu1Zeu2Zeu24Z	mathworldcorrectrX   errZerrmaxr5   r5   r6   
test_eulerp  s"    




&zTestEuler.test_eulerN)r  r  r  r  r5   r5   r5   r6   r  o  s   r  c                   @   s<   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd ZdS )TestExpc                 C   s   t d}d}t|| d S )Nr<   r:   )r   r   r   r4   exZexrlr5   r5   r6   r     s    
zTestExp.test_exp2c                 C   s   t d}d}t||d d S )N      @g;f@r  )r   r   r   r4   ZexmZexmrlr5   r5   r6   test_exp2more  s    
zTestExp.test_exp2morec                 C   s   t d}d}t|| d S )Nr<   r  )r   r   r   r  r5   r5   r6   r     s    
zTestExp.test_exp10c                 C   s   t d}d}t||d d S )Nr  gYs@r  )r   r   r   r  r5   r5   r6   test_exp10more  s    
zTestExp.test_exp10morec                 C   sN   t dt dt df}tdd tdd tdd f}t||d d S )Nr<   rp   r:   rJ   r  r   r   r   r   r  r5   r5   r6   r     s    "zTestExp.test_expm1c                 C   sN   t dt dt df}tdd tdd tdd f}t||d d S )Nr<    @皙@rJ   r  r  )r4   Zex1Zexrl1r5   r5   r6   test_expm1more  s    "zTestExp.test_expm1moreN)	r  r  r  r   r  r   r  r   r  r5   r5   r5   r6   r    s   r  c                   @   s  e Zd Zejdddgdd Zejdg dejdddgdd	 Zejdddgd
d Zejdddgejjde	j
de	dgg dddd Zejdeddejdddgdd Zejdddgejdedddd Zejdddgejdedddd Zejdedd d!d"d# Zejdeedd$eedd d! d%d& Zejdddg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$eedd d2 d5d6 Zejd)e	je	je	jegejdddgejdeddejjdg dge	j
ge	j
dggg d7dd8d9 Zejdddgejjddd*d.e	j
dgg d/dd:d; Zejd<eeddd!d=g ejdeedd$eed$d>d2 d?d@ Zejd)e	je	je	jegejdeddejjdg dge	j
ge	j
dggg d7ddAdB Z ejdddgejd<eddejjddd*d.e	j
dgg d/ddCdD Z!ejd<dd*e	j
dEgdFdG Z"ejd<eddHdIdJ Z#dKdL Z$dS )MTestFactorialFunctionsrT  TFc                 C   sN   t tjd|dsJ t tjd|ds0J t tjddddsJJ d S )NrJ   rS  rp   T)rO   Zisscalarr   	factorial
factorial2
factorialk)r4   rT  r5   r5   r6   "test_factorialx_scalar_return_type  s    z9TestFactorialFunctions.test_factorialx_scalar_return_typerW   )r?   rt  c                 C   sB   t tj||dd t tj||dd t tj|dddd d S )NrS  r   rp   T)r   r   r  r  r  )r4   rT  rW   r5   r5   r6   test_factorialx_negative  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dg d d S )N)r  r   rJ   rS  )r   r   rJ   rJ   rp   T)r   r   r   r  r  r  )r4   rT  assert_funcr5   r5   r6   test_factorialx_negative_array  s    z5TestFactorialFunctions.test_factorialx_negative_arraycontentNZnat)NaNNoneZNaT)idsc                 C   s  t j||dtju sJ t j||dtju s0J t j|dddtju sJJ |tjurtjtdd  t j|g|d W d    n1 s0    Y  nr|rtj	t
dd. tt j|g|dd sJ W d    n1 s0    Y  n tt j|g|dd sJ tjtdd  t j|g|d W d    n1 s<0    Y  tjtd	d" t j|gddd W d    n1 s~0    Y  d S )
NrS  rp   TzUnsupported datatype.*rf  Non-integer array.*r   zfactorial2 does not support.*zfactorialk does not support.*)r   r  rO   r   r  r  r  r   
ValueErrorrh  ri  r   )r4   r  rT  r5   r5   r6   test_factorialx_nan  s    
0> 0z*TestFactorialFunctions.test_factorialx_nanlevelsrJ   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ddgd}|tj||d|d  |tj||d|d  |tj|ddd|d  d S )NrJ   c                    s"   |dkr| S  | | g|d S 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   rJ   Nr5   r   rX   _nest_mer5   r6   r    s    zDTestFactorialFunctions.test_factorialx_array_shape.<locals>._nest_mec                    s4   t j |dtd}t| t j|t j d S )NrX   dtype)rO   r   objectr   r   r   )resZnucleusr   r  r  r5   r6   _check  s    zBTestFactorialFunctions.test_factorialx_array_shape.<locals>._checkr   r   r  rU  rf   TrS  r  rp   r  r<   )rJ   )rO   r   mathr  r   r  r  )r4   r  rT  r  rW   exp_nucleusr5   r  r6   test_factorialx_array_shape  s    z2TestFactorialFunctions.test_factorialx_array_shape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dt j|d
 |d d S )Nr   ndminrU  rf   r  r  rS  rJ   r<   rp   T)rO   r   r   r   r  r  r  )r4   r  rT  rW   r   r5   r5   r6   test_factorialx_array_dimension  s    z6TestFactorialFunctions.test_factorialx_array_dimensionlevelc                    s   d fdd	  dg|d d}dddd	}|r4t nt}|tj||d
tj|d |d |tj||d
tj|d |d |tj|ddd
tj|d |d d S )NrJ   c                    s    |dkr| S  | g|d S d S r   r5   r  r  r5   r6   r  
  s    zCTestFactorialFunctions.test_factorialx_array_like.<locals>._nest_mer   r  rU  rf   r  r  rS  r  r<   rp   T)rJ   )r   r   r   r  rO   r   r  r  )r4   r  rT  rW   r  r  r5   r  r6   test_factorialx_array_like  s    z1TestFactorialFunctions.test_factorialx_array_likerF   r  r  c                 C   sh   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   TrS  FrC   )sysplatformr   rb   r   r  r   r4   rW   rD   r5   r5   r6   test_factorial_accuracy  s    z.TestFactorialFunctions.test_factorial_accuracy   c                 C   s   t |}t|t|d t|t|gdd  tjdkrBdnd}tt|t|d|d tt|t|gdd |d d S )NTr   r  r   r   FrC   )r  r  r   r   r!  r"  r   rb   )r4   rW   r  rD   r5   r5   r6   test_factorial_int_reference'  s    
z3TestFactorialFunctions.test_factorial_int_referencec                    sj    fdd}|dd |dd |dd |d	d
 |dd |dd |dd |dd |dd d S )Nc                    s.   t tj|  d| t t| gd | d S )NrS  r   )r   r   r  )rW   r  rS  r5   r6   r  7  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=r5   )r4   rT  r  r5   rS  r6   test_factorial_float_reference5  s    







z5TestFactorialFunctions.test_factorial_float_referencer  皙?)[][1]z[1.1][NaN][NaN, 1]c                 C   sr  |t jkr&tdd |D r&td |dks:t|dkr>|n|d }t j|||d}d }|sptj||d}nrt 	|j
t jst 	|j
t jstjtdd	 tj||d W d    n1 s0    Y  n|r|t 	|j
t js||jr|t |t |  |t |  t jr|tjtd
d	< tj||d}t t |rTt jnt j}W d    n1 sp0    Y  nf|rt 	|j
t jstjtdd	 tj||d W d    n1 s0    Y  ntj||d}dd }|d urnt H}|t |jr| n|}	|jr0tj|	|dng }
W d    n1 sJ0    Y  t j|
||d}||| d S )Nc                 s   s   | ]}t |V  qd S r6  rO   r   rY  r   r5   r5   r6   	<genexpr>R  r[  zKTestFactorialFunctions.test_factorial_array_corner_cases.<locals>.<genexpr>impossible combinationr   rJ   r  r  rS  Unsupported datatype*rf  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   r5   r5   r6   assert_really_equaln  s    ,zUTestFactorialFunctions.test_factorial_array_corner_cases.<locals>.assert_really_equal)rO   rl  anyr  skiplenr   r   r  
issubdtyper  integerfloatingr   r	  r   Zallcloser   r   rh  ri  r   int_r   rw  ndimrT   )r4   r  r  rT  r  rW   r  r5  rz  Zn_flatrr  r5   r5   r6   !test_factorial_array_corner_casesI  s<    	
 0 *@0

:z8TestFactorialFunctions.test_factorial_array_corner_casesy       @       @)1z1.1z2+2jr  r  c                 C   s   |d u s6|t ju s6t t|t js6t t|t jrrtj||d}|t ju sV|d u r\t jnt|}t|| n<t	j
tdd tj||d W d    n1 s0    Y  d S )NrS  r2  rf  )rO   r   r9  r3  r:  r;  r   r  r   r  r   r	  r4   rW   rT  r  r   r5   r5   r6   "test_factorial_scalar_corner_cases}  s    $"z9TestFactorialFunctions.test_factorial_scalar_corner_casesr   c                 C   sh   t jdkrdnd}tttj|ddtj|dd|d ttj|gddttj|gdd|d d S )Nr  g+=r   TrS  FrC   )r!  r"  r   rb   r   r  r   r#  r5   r5   r6   test_factorial2_accuracy  s    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   rt  rJ   TF)	functoolsreduceoperatormulr^  ra   r   r   r  r   rb   )r4   rW   r  r5   r5   r6   test_factorial2_int_reference  s
    z4TestFactorialFunctions.test_factorial2_int_reference)r)  r*  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	sj|st
j||d}|s|stnt}||| n:tjtdd	 t
|d
 W d    n1 s0    Y  d S )Nc                 s   s   | ]}t |V  qd S r6  r-  r.  r5   r5   r6   r/    r[  zLTestFactorialFunctions.test_factorial2_array_corner_cases.<locals>.<genexpr>r0  r   rJ   r1  rS  factorial2 does not*rf  rp   )rO   rl  r6  r  r7  r8  r   r9  r  r:  r   r  r   r   r   r	  )r4   r  r  rT  r  rW   r  r  r5   r5   r6   "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r`tj||d}|t ju sD|d u rJt jnt|}t|| n<t	j
tdd tj||d W d    n1 s0    Y  d S )NrS  rI  rf  )rO   r   r9  r3  r:  r   r  r  r   r  r   r	  rA  r5   r5   r6   #test_factorial2_scalar_corner_cases  s    $"z:TestFactorialFunctions.test_factorial2_scalar_corner_casesrX   r\   r  c                 C   sP   t tjtt|d| d}t|t||d t|t|g|dd  d S )Nr   rJ   T)	rD  rE  rF  rG  r^  ra   r   r   r  )r4   rW   rX   r  r5   r5   r6   test_factorialk_int_reference  s    z4TestFactorialFunctions.test_factorialk_int_referencec                 C   s   |t jkr&tdd |D r&td |dks:t|dkr>|n|d }t j|||d}t |jt j	sj|s~t
t|d| n:tjtdd	 t|d W d    n1 s0    Y  d S )
Nc                 s   s   | ]}t |V  qd S r6  r-  r.  r5   r5   r6   r/    r[  zLTestFactorialFunctions.test_factorialk_array_corner_cases.<locals>.<genexpr>r0  r   rJ   r1  rp   factorialk does not*rf  )rO   rl  r6  r  r7  r8  r   r9  r  r:  r   r   r  r   r	  )r4   r  r  r  rW   r5   r5   r6   "test_factorialk_array_corner_cases  s    
 z9TestFactorialFunctions.test_factorialk_array_corner_casesc                 C   s   |s@t t  tj|||d W d    q1 s40    Y  n|d u sd|tju sdtt|tj	rtj
||d}|tju p|d u }|rtjntj||d}t|| n>t jtdd  tj|||d W d    n1 s0    Y  d S )N)rX   rT  rS  r  rM  rf  )r  r   NotImplementedErrorr   r  rO   r   r9  r3  r:  r  r   r	  )r4   rW   rX   rT  r  Znan_condr  r5   r5   r6   #test_factorialk_scalar_corner_cases  s    0$z:TestFactorialFunctions.test_factorialk_scalar_corner_casesr@  c                 C   s>   t jtdd td| W d    n1 s00    Y  d S )Nzk must be a positive integer*rf  rJ   )r  r   r	  r   r  r  r5   r5   r6   test_factorialk_raises_k	  s    z/TestFactorialFunctions.test_factorialk_raises_kr  c                 C   s   |t  v rtt| g}tt||jtj	 tt|d |jtj
 t|d |ttjjksnJ tt | g}tt||jtj
 tt|d |jt t|d |ttj
jksJ ntttdg|jt d S r_   )r*   keysrO   r   r+   r   r   r  r  r<  rl  r_  int32r`  r  )r4   rX   rW   r5   r5   r6   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tj|d	d| W d    n1 s|0    Y  d S )
NrJ   r<   rp   r@   FrS  r  rf  T)	rO   r   r   r   r   r  r  rh  ri  )r4   r   r  r5   r5   r6   test_factorial_mixed_nan_inputs	  s
    z6TestFactorialFunctions.test_factorial_mixed_nan_inputs)%r  r  r  r  r   ru  r  r   r  rO   r   Z
datetime64r
  ra   r  r  r  r$  r^  r&  r'  rl  r   
complex128r  r?  rB  rC  rH  rJ  rK  rL  rN  rP  rQ  rT  rU  r5   r5   r5   r6   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)rl   gN?ց[?)y      ?        rX  rY  )y       ?yn<ӿj<Cy)BR;߿ux7Q?)y      yھ|}-2?y/?!ۿ)r|  GM?pBR?)y      @        rZ  r[  )y              @y       GMܿy        pBR?)y              gGMܿgpBR߿)y             y        GM?y       pBR߿rl   r  c                 C   s&   t t|}t|t ||gd d S )Nr  )r   r   r  r   )r4   r   r  ry  frsr5   r5   r6   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?rp   )y.1?ǘ?yʡE6@:#J{/?yq-
@y&1?yh o@߾3?yW2q@qh?r   rJ   r  )r   fresnel_zerosr   r   r  )r4   szoczoZvals1Zvals2r5   r5   r6   test_fresnel_zerosE	  s    

zTestFresnel.test_fresnel_zerosc                 C   s(   t d\}}t d}t||d d S )Nr@   r  )r   r^  Zfresnelc_zerosr   )r4   r_  r`  Zfrcr5   r5   r6   test_fresnelc_zerosX	  s    
zTestFresnel.test_fresnelc_zerosc                 C   s(   t d\}}t d}t||d d S )Nr   r  )r   r^  Zfresnels_zerosr   )r4   r_  r`  r\  r5   r5   r6   test_fresnels_zeros]	  s    
zTestFresnel.test_fresnels_zerosN)r  r  r  r  r   ru  rO   r   r]  ra  rb  rc  r5   r5   r5   r6   rW  	  s"   

rW  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   s   t d}t|d d S r  )r   r   r   )r4   Zgamr5   r5   r6   r  d	  s    
zTestGamma.test_gammac                 C   s(   t d}tt d}t||d d S )Nrp   r  )r   r   r   r   r   )r4   ZgamlnZlngamr5   r5   r6   r  h	  s    
zTestGamma.test_gammalnc                 C   s(   t dd}t dd}t||d d S )Nrl   r  )r   r  gammaincinvr   )r4   ZgccinvZgcinvr5   r5   r6   r  m	  s    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 )
Nr=   rJ   r  g?g`	\;r   r]  gmb<g      &@)r   re  gammaincr   r4   r   r   r5   r5   r6   test_gammaincinvr	  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?rJ   g^F    ?r=   ri   rC   )rO   r  r   re  rf  r   )r4   ZptsZxpr   r   r5   r5   r6   test_975~	  s    zTestGamma.test_975c                 C   s(   t d}dt d }t||d d S )Nr  rJ   )r   r  r   r   )r4   ZrgamZrlgamr5   r5   r6   r  	  s    
zTestGamma.test_rgammac                 C   s(   t ttd ttdd d S )Nr?   r   )r   rO   r   r   r   r   r  r3   r5   r5   r6   test_infinity	  s    zTestGamma.test_infinityN)r  r  r  r  r  r  r,   rh  ri  r  rj  r5   r5   r5   r6   rd  c	  s   

rd  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   s"   t tddtdd d d S Nr  r<   rp   r  )r   r   r&  r3   r5   r5   r6   
test_negv1	  s    zTestHankel.test_negv1c                 C   s8   t dd}t ddt ddd  }t||d d S NrJ   r   r   r  )r   r&  rQ  r  r   )r4   Zhank1Zhankrlr5   r5   r6   r'  	  s    zTestHankel.test_hankel1c                 C   s"   t tddtdd d d S rl  )r   r   r(  r3   r5   r5   r6   test_negv1e	  s    zTestHankel.test_negv1ec                 C   s0   t dd}t ddtd }t||d d S )NrJ   r   y       r  )r   r(  r&  r   r   )r4   Zhank1eZhankrler5   r5   r6   r)  	  s    zTestHankel.test_hankel1ec                 C   s"   t tddtdd d d S rl  )r   r   r*  r3   r5   r5   r6   
test_negv2	  s    zTestHankel.test_negv2c                 C   s8   t dd}t ddt ddd  }t||d d S rn  )r   r*  rQ  r  r   )r4   Zhank2Zhankrl2r5   r5   r6   r+  	  s    zTestHankel.test_hankel2c                 C   s"   t tddtdd d d S rl  )r   r   r,  r3   r5   r5   r6   
test_neg2e	  s    zTestHankel.test_neg2ec                 C   s(   t dd}t dd}t||d d S )NrJ   r   r  )r   r,  r   )r4   Zhank2eZhankrl2er5   r5   r6   test_hankl2e	  s    zTestHankel.test_hankl2eN)r  r  r  rm  r'  ro  r)  rp  r+  rq  rr  r5   r5   r5   r6   rk  	  s   rk  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   s8   t dd}t ddt ddd  }t||d d S rn  )r   Zh1vpjvpyvpr   )r4   h1Zh1realr5   r5   r6   	test_h1vp	  s    zTestHyper.test_h1vpc                 C   s8   t dd}t ddt ddd  }t||d d S rn  )r   Zh2vprt  ru  r   )r4   h2Zh2realr5   r5   r6   	test_h2vp	  s    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  rl   Qvo?ri   rC   r   rm   r   r   )g      r?   r   rJ   r  )g̷?g3|t-Ք?rm   go?g{h?r   rl   r  r  )r   rJ   rl   )rm   gc?rz  r<   rp   rJ   )
r   r   hyp0f1rO   r   r   r   	row_stackassert_raisesr	  )r4   r   r  x1Zx2r5   r5   r6   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   )r4   r  r5   r5   r6   test_hyp0f1_gh5764	  s    zTestHyper.test_hyp0f1_gh5764c              f   C   s  t ddd}t|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 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$g d%g d&g d'g d(g d)g d*g d+g d,g d-g d.g d/g d0g d1g d2g d3g d4g d5g d6g d7g d8g d9g d:g d;g d<g d=g d>g d?g d@g dAg dBg dCg dDg dEg dFg dGg dHg dIg dJg dKg dLg dMg dNg dOg dPg dQg dRg dSg dTg dUg dVg dWg dXg dYg dZg d[g d\g d]g d^g d_g d`g dag dbg dcg ddg deg dfg dgg dhgd}|D ]4\}}}}t |||}tt|| | dik  q~d S )jNr   r   g?r>   )g{*= g˱a)g5=gvX@)g)AI@gDAhg$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$9?)glkC9g<tF8gp?g ?r  )r   r/  r   r   r   r$  )r4   hyp1Zref_datar%  r&  ry  r  r  r5   r5   r6   r0  	  s    ezTestHyper.test_hyp1f1c                 C   s,   t ddd}t ddd}t||d d S )Nrl   r  g7B.g|:B.r  r   r/  r   )r4   r  Zhyp2r5   r5   r6   test_hyp1f1_gh2957V
  s    zTestHyper.test_hyp1f1_gh2957c                 C   s   t ddd}t|dd d S )Nrl   r  ig<`?r  r  )r4   Zhypr5   r5   r6   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$d%g}t|D ]8\}\}}}}}t	||||}t
||dd&| d' qPd S )(Nrl   rJ   r  |Gz?r  g?g|Gzrt   r   r<   r  r  )rp   r  r  r  gYi2?r  rp   g433333?r:   r  r   r?   g      ?r   g      ?r   re  g      gUUUUUUտg  @gUUUUUU?g)r  r  rm         $gEciH!@)rt  rp   rJ   r  gzG?)r<   r  rJ   r  gy&1|)r.  rp   rJ   r  g"nN%@?)r<   r  rJ   r  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  r1  r   )	r4   r   rd   r%  r&  ry  r   r  cvr5   r5   r6   r2  _
  sL    0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 )NrJ   r   r  g D?r>   )r   r  333333?g)r  g	@r  g	rl   r<   r  )	r   hyperur   r   r   r   r/  r   r   )r4   Zval1r%  r&  r   ZhypuZhprlr5   r5   r6   test_hyperu~
  s    $zTestHyper.test_hyperuc                 C   s   t tddddd d S )NrJ   r  g3333334@g(¨?r  )r   r   r  r3   r5   r5   r6   test_hyperu_gh2287
  s    zTestHyper.test_hyperu_gh2287N)r  r  r  rw  ry  r  r  r0  r  r  r2  r  r  r5   r5   r5   r6   rs  	  s   rrs  c                   @   s  e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ 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   s&   t td}t|t ddgd d S )Nr   gbɃ?gΝJ ֿr  )r   r   rC  r   )r4   Zit0r5   r5   r6   rD  
  s    zTestBessel.test_itj0y0c                 C   s&   t td}t|t ddgd d S )Nr   gbqTtt?g/]ooۿr  )r   r   r=  r   )r4   Zit2r5   r5   r6   r>  
  s    zTestBessel.test_it2j0y0c                 C   s   t tddtdd d S Nrp   r<   r  )r   r   rG  r3   r5   r5   r6   test_negv_iv
  s    zTestBessel.test_negv_ivc                 C   s&   t d}t dd}t||d d S Nr   r   r  )r   rK  rO  r   r4   ZozZozrr5   r5   r6   rL  
  s    
zTestBessel.test_j0c                 C   s&   t d}t dd}t||d d S Nr   rJ   r  )r   rM  rO  r   r4   Zo1Zo1rr5   r5   r6   rN  
  s    
zTestBessel.test_j1c                 C   s   t dd}t|dd d S )NrJ   r   ;x?r  )r   rO  r   )r4   Zjnnrr5   r5   r6   rP  
  s    zTestBessel.test_jnc                 C   s"   t tddtdd d d S rl  )r   r   rQ  r3   r5   r5   r6   test_negv_jv
  s    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  rL   g)%->)g@rL   g5c)!9)r  r   g%,Ϳr  r  r  )r  r   rQ  r   )r4   r   rd   r  r   r   Zycr5   r5   r6   rR  
  s    zTestBessel.test_jvc                 C   s"   t tddtdd d d S rl  )r   r   rS  r3   r5   r5   r6   test_negv_jve
  s    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 )NrJ   r   r  r  ?      ?)r   rS  r   rQ  r   r$  r   )r4   ZjvexpZjvexp1r   Zjvexprr5   r5   r6   rT  
  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   rJ   )go@.=@gzj,[@glN!@g5/ D'@gh>-@r:   gW@g0@gQX$@g*@g8*5{x0@rI   )gEk[@g~Cju]@gYrʝ^@g, `@gf	`@rB   rC   -  )gts@g&ǭr3t@gWt@g,$Y&u@gu@)r   jn_zerosr   r   r   )r4   jn0Zjn1Zjn102Zjn301r5   r5   r6   test_jn_zeros
  s     zTestBessel.test_jn_zerosc                 C   s   t dd}t|d ddd t|d ddd t|d	 d
dd t dd}t|d ddd t|d ddd t|d	 ddd t dd}t|tg ddd d S )Nr   r[   i  g;@rB   rC   i  g8v@i+  gׂMm@r  gxi@g	,@gи{>@i  r   )gUDX@g!@g*HS@gz5 @g@2;@r  )r   r  r   r   )r4   r  Zjn10Zjn3010r5   r5   r6   test_jn_zeros_slow
  s    zTestBessel.test_jn_zeros_slowc           
         s   t j  fdd}tddD ]v}t |\}}}}t|||D ]R\}}}	|	dkrft ||ddd q>|	dkrt|||ddd q>td| q>qd S )	Nc                    s     | d | | d | d S )NrJ   r<   r5   )rW   r   rO  r5   r6   jnp
  s    z(TestBessel.test_jnjnp_zeros.<locals>.jnprJ   rF   r   r  r\  zInvalid t return for nt=%d)r   rO  ra   Zjnjnp_zeroszipr   AssertionError)
r4   r  ntr   rW   r  tzznnttr5   r  r6   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 )	NrJ   r   g(yu?gOXeS@ga!@gxi'@g'Nw(-@r:     r   r   r\  )r   Z	jnp_zerosr   r   r   rt  )r4   r  r5   r5   r6   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 )NrJ   r   r  r  )"@g+@g-9(1!@gȘ'@g>tA}-@)g0v@gjt@gH.?$@g}"O*@gGŧp0@)r   Z
jnyn_zerosr   r   )r4   Zjnzr5   r5   r6   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 )Nr<   rJ   rp   r  )r   rt  rQ  r   )r4   ZjvprimZjv0r5   r5   r6   test_jvp!  s    zTestBessel.test_jvpc                 C   s&   t d}t dd}t||d d S r  )r   rV  rp  r   )r4   ZozkZozkrr5   r5   r6   rW  &  s    
zTestBessel.test_k0c                 C   s&   t d}t dd}t||d d S r  )r   rX  rr  r   )r4   ZozkeZozkerr5   r5   r6   rY  +  s    
zTestBessel.test_k0ec                 C   s&   t d}t dd}t||d d S r  )r   rZ  rp  r   )r4   Zo1kZo1krr5   r5   r6   r[  0  s    
zTestBessel.test_k1c                 C   s&   t d}t dd}t||d d S r  )r   r\  rr  r   )r4   Zo1keZo1kerr5   r5   r6   r]  5  s    
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   rJ   r   r<   rp   r  r   r:   r   r@   r  r  g      H@)rO   rU   r   Zjacobir   ry  r   )
r4   r%  r&  ZP0ZP1ZP2ZP3cpZp2cZp3cr5   r5   r6   test_jacobi:  s     &B2D8XzTestBessel.test_jacobic                 C   s   t dd}t|dd d S )Nr   r   _2?r  )r   rh  r   )r4   Zkn1r5   r5   r6   ri  L  s    zTestBessel.test_knc                 C   s   t tddtdd d S Nr   r  r  r   r   rp  r3   r5   r5   r6   test_negv_kvP  s    zTestBessel.test_negv_kvc                 C   s   t dd}t|dd d S )Nr   r   r  r  r   rp  r   )r4   Zkv0r5   r5   r6   test_kv0S  s    zTestBessel.test_kv0c                 C   s   t dd}t|dd d S )NrJ   r   gKދ@r  r  )r4   kv1r5   r5   r6   test_kv1W  s    zTestBessel.test_kv1c                 C   s   t dd}t|dd d S )Nr<   r   g)lHH@r  r  )r4   kv2r5   r5   r6   test_kv2[  s    zTestBessel.test_kv2c                 C   s   t tddd d S )N    rJ   g.Ք"H)r   r   rh  r3   r5   r5   r6   test_kn_largeorder_  s    zTestBessel.test_kn_largeorderc                 C   s   t tddd d S )Nr   g =`XCr  r3   r5   r5   r6   test_kv_largeargb  s    zTestBessel.test_kv_largeargc                 C   s   t tddtdd d S r  )r   r   rr  r3   r5   r5   r6   test_negv_kvee  s    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   rr  rp  r   r   )r4   Zkve1r  r   Zkve2r  r5   r5   r6   rs  h  s    zTestBessel.test_kvec                 C   s*   d}t td| tjd|ddd d S )Nr  rJ   r   rW   r  )r   r   rp  kvp)r4   r   r5   r5   r6   test_kvp_v0n1q  s    zTestBessel.test_kvp_v0n1c                 C   sN   d}d}t |d | || t ||  }t j||dd}t||d d S )Nr   r  rJ   r  r  r   rp  r  r   r4   r  r   Zxcr   r5   r5   r6   test_kvp_n1u  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  r<   rJ   r  r  r  r  r5   r5   r6   test_kvp_n2|  s
    <zTestBessel.test_kvp_n2c                 C   s&   t d}t dd}t||d d S r  )r   r  r  r   r  r5   r5   r6   r    s    
zTestBessel.test_y0c                 C   s&   t d}t dd}t||d d S r  )r   r  r  r   r  r5   r5   r6   r    s    
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 )Nr<   rJ   r   rx   r   )r   Zy0_zerosr   r   r$  r  )r4   ZyoZypoZzoZzpor  Zallvalr5   r5   r6   test_y0_zeros  s    zTestBessel.test_y0_zerosc                 C   s*   t d}t|tdgtdgfd d S )NrJ   r  gѮBO?r   )r   Zy1_zerosr   r   )r4   r  r5   r5   r6   test_y1_zeros  s    
zTestBessel.test_y1_zerosc                 C   s.   t jddd}t|tdgtdgfd d S )NrJ   r  yL
F%u?!rh?y;OnгY?rp   )r   Z	y1p_zerosr   r   )r4   Zy1pr5   r5   r6   test_y1p_zeros  s    zTestBessel.test_y1p_zerosc                 C   sB   t dd}t|tddgd t dd}t|g ddd	 d S )
Nr:   r<   g3@g(A&"@r   r  )g]E.+"|@gH(|@gff|}@g&b`~@gHO_~@r   rC   )r   Zyn_zerosr   r   r   )r4   Zanr5   r5   r6   test_yn_zeros  s    
zTestBessel.test_yn_zerosc                 C   sh   t dd}t|tddgd t dd}tt d|ddd	 t d
d}tt d
|ddd	 d S )Nr   r<   gQhվ@gzN@r@   +   r   r   r\  r  r   )r   	ynp_zerosr   r   r   ru  r4   Zaor5   r5   r6   test_ynp_zeros  s    zTestBessel.test_ynp_zerosc                 C   s&   t dd}tt d|ddd d S )Nr  r   r   r   r\  )r   r  r   ru  r  r5   r5   r6   test_ynp_zeros_large_order  s    z%TestBessel.test_ynp_zeros_large_orderc                 C   s   t dd}t|dd d S NrJ   r   5,1
r  )r   r  r   )r4   Zyn2nr5   r5   r6   r    s    zTestBessel.test_ync                 C   s"   t tddtdd d d S rl  )r   r   r  r3   r5   r5   r6   test_negv_yv  s    zTestBessel.test_negv_yvc                 C   s   t dd}t|dd d S r  )r   r  r   )r4   Zyv2r5   r5   r6   r    s    zTestBessel.test_yvc                 C   s"   t tddtdd d d S rl  )r   r   r  r3   r5   r5   r6   test_negv_yve  s    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 )NrJ   r   r  r  r  r?   )r   r  r   r  r   )r4   Zyve2Zyve2rZyve22r5   r5   r6   r    s
    zTestBessel.test_yvec                 C   s8   t ddt dd d }t dd}t||d d S )NrJ   r   rp   r   r<   r  )r   r  ru  r   )r4   ZyvprZyvp1r5   r5   r6   test_yvp  s    zTestBessel.test_yvpc                 c   sD   g d}g d}t ||E dH  t dtdd dgE dH  dS )z>Yield points at which to compare Cephes implementation to AMOS)ir         4r  r   r  rx   rm   {G(@rR  r  )ir  r?   rm   r        i@g     y@g     Ă@g@  i'  Nrl   ir  r  )	itertoolsproductr   )r4   r  r   r5   r5   r6   _cephes_vs_amos_points  s    z!TestBessel._cephes_vs_amos_pointsdy=r   Nc                 C   s   |   D ]\}}|d ur$|||r$q||||||d |t||  }}	}
t|rrtt|	dk||f qt|rt|	jdk||f qt||	||f||d |t|krt|
|	||f||d qd S )Nr   u <7~r   )r  rD   rN   )	r  r`   rO   r   r   r$  r   r   r   )r4   r  f2rD   rN   r7  r  r   c1c2c3r5   r5   r6   check_cephes_vs_amos  s    *

zTestBessel.check_cephes_vs_amosppc64lezfails on ppc64ler   c                 C   s   | j tjtjddd d S )NrL   u5% r   )r  r   rQ  rO  r3   r5   r5   r6   test_jv_cephes_vs_amos  s    z!TestBessel.test_jv_cephes_vs_amosc                 C   s   | j tjtjddd d S )Nr  r  r   r  r   r  r  r3   r5   r5   r6   test_yv_cephes_vs_amos  s    z!TestBessel.test_yv_cephes_vs_amosc                 C   s$   dd }| j tjtjdd|d d S )Nc                 S   s   t | dkS )Nr]  )r$  )r  r   r5   r5   r6   skipper  s    zDTestBessel.test_yv_cephes_vs_amos_only_small_orders.<locals>.skipperr  r  )rD   rN   r7  r  )r4   r  r5   r5   r6   (test_yv_cephes_vs_amos_only_small_orders  s    z3TestBessel.test_yv_cephes_vs_amos_only_small_ordersc                 C   sF   t jdd& | jtjtjddd W d    n1 s80    Y  d S )Nr  r  g:0y5>r  r   )rO   r  r  r   rG  r3   r5   r5   r6   test_iv_cephes_vs_amos  s    z!TestBessel.test_iv_cephes_vs_amosc           	   
   C   sz  d}t jd t jd|dt jjd|d  }t jd|dt jjd|d  }t jjd|dd	k}|| t||< t jd
d t	||}t	||d }t j
|t|dk< t j
|t|dk< d	|t|dk < d	|t|dk < t|| d }d	|t |< W d    n1 s0    Y  t |}t|| dk || || t	|| || t	|| || d f d S )Ni@B rJ   rl   r?   r<   )r   r   r  r   r  r  r   r  gYngH׊>)rO   rU   rV   r  r  r   r`   r  r   rG  r   r$  r   Zargmaxr   )	r4   rd  r  r   Zimskr  r  dcrX   r5   r5   r6    test_iv_cephes_vs_amos_mass_test  s"    "".
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   rp  rh  r3   r5   r5   r6   test_kv_cephes_vs_amos  s    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 )	Nrp   r:   gP?r  r  g~Omʒ?gY8E@@gKSn)r   r   rQ  r3   r5   r5   r6   test_ticket_623  s    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 Besselsr?   rJ   gl)ܿrt  gPj?gk?g%E*2ig敋?gw--`?gÉB?gW?r  g޴?gz|?a?gpx%?y      ?              ?      ?yYD?`{1wy6x?B]#Ӯ?y ?b>?y.}9d?8kؿy      ?333333?g333333ӿy333333?      ?r   N)r   r   rQ  r  rG  rp  rS  r   r  rI  rr  r&  r*  r3   r5   r5   r6   test_ticket_853  sD    """"*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 domainsrl   r?   rJ   r   r<   r:   N)r   r   r   rQ  rG  r  rp  rS  rI  r  rr  r8   r  r6  r3   r5   r5   r6   test_ticket_854K  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   rp  rO   r   rr  r3   r5   r5   r6   test_gh_7909\  s    zTestBessel.test_gh_7909c                 C   s(   t tddd t tddd dS )zReal-valued Bessel I overflowrJ   i  g~rG   i`  g ?los~Nr   r   rG  r3   r5   r5   r6   test_ticket_503`  s    zTestBessel.test_ticket_503c                 C   s   t tddd d S )Nr  rJ   r  r  r3   r5   r5   r6   test_iv_hyperg_polese  s    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   r<   rl   rJ   r?   r  )r   r   r   r   r   r   r   r   r   r$  r`  r   epssumr4   r  r   rW   rX   r>  r  r5   r5   r6   	iv_seriesh  s    8*zTestBessel.iv_seriesc                 C   s4   dD ]*}|  d|\}}tt||||d qd S )Nrm   r   r  r   rN   r  )r  r   r   r3  r4   r   valuer  r5   r5   r6   test_i0_seriesp  s    zTestBessel.test_i0_seriesc                 C   s4   dD ]*}|  d|\}}tt||||d qd S )Nr  rJ   r  )r  r   r   r7  r  r5   r5   r6   test_i1_seriesu  s    zTestBessel.test_i1_seriesc                 C   sD   dD ]:}dD ]0}|  ||\}}tt||||||fd qqd S )N)r  r  r   rx   rm   r  rR  )rm   r   r  y             @r  )r  r   r   rG  r4   r  r   r  r  r5   r5   r6   test_iv_seriesz  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 ]4\}\}}t|t|  }t||dd| d q<d S )Nrx   rm   rL   r   g0oO?rl   g!?grb?r  gpH?rt   gC~?r   ggo?r  r  r  )r  r   r3  r   r   r4   r   rd   r   r  r  r5   r5   r6   r4    s    	zTestBessel.test_i0c                 C   s&   t d}t dd}t||d d S r  )r   r5  rI  r   )r4   ZoizeZoizerr5   r5   r6   r6    s    
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 ]4\}\}}t|t|  }t||dd| d q6d S )Nrx   rL   gj|=r   gȕ![1?rl   g;͘?rm   gRΜ?rt   g|?r   g}f?r  r  r  )r  r   r7  r   r   r  r5   r5   r6   r8    s    zTestBessel.test_i1c                 C   s&   t d}t dd}t||d d S r  )r   r9  rI  r   )r4   Zoi1eZoi1err5   r5   r6   r:    s    
zTestBessel.test_i1ec                 C   s&   t td}t|t ddgd d S )Nr   gїJB?@g*u?)r   r   rA  r   )r4   Ziti0r5   r5   r6   rB    s    zTestBessel.test_iti0k0c                 C   s"   t d}t|tddgd d S )Nr   gݳɄ|T?gVƥ
@r@   )r   r;  r   r   )r4   Zit2kr5   r5   r6   r<    s    
zTestBessel.test_it2i0k0c                 C   s$   t ddtd }t|dd d S )Nr   r   皙gv M?r  )r   rG  r   r   )r4   iv1r5   r5   r6   rH    s    zTestBessel.test_ivc                 C   s   t tddtdd d S r  )r   r   rI  r3   r5   r5   r6   test_negv_ive  s    zTestBessel.test_negv_ivec                 C   s0   t dd}t ddtd }t||d d S )Nr   r   r  r  )r   rI  rG  r   r   )r4   Zive1r  r5   r5   r6   rJ    s    zTestBessel.test_ivec                 C   s    t tddtddd d S )NrJ   r<   r   r  )r   r   rG  ivpr3   r5   r5   r6   	test_ivp0  s    zTestBessel.test_ivp0c                 C   s8   t ddt dd d }t dd}t||d d S )Nr   r<   rJ   r  )r   rG  r  r   rg  r5   r5   r6   test_ivp  s    zTestBessel.test_ivp)r  r   N)r   )Ur  r  r  rD  r>  r  rL  rN  rP  r  rR  r  rT  r  r  r  r  r  r  rW  rY  r[  r]  r  ri  r  r  r  r  r  r  r  rs  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  machiner  r  r  r  Zslowr  r  r  r  r  r  r  r  r  r	  r
  r  r4  r6  r8  r:  rB  r<  rH  r  rJ  r  r  r5   r5   r5   r6   r  
  s   
	



,
r  c                   @   s   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   rJ   r<   rp   r:   r   r  r?   )rJ   r  r<   r   )r?   r  ir@   r|  )rJ   iH   ir   r  )r?   r   i8iX  irU  rR  )r   Zlaguerrer   ry  r   )r4   lag0lag1lag2lag3Zlag4Zlag5r5   r5   r6   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   rJ   r<   rp   r?   rt  rm   r   r  r|  )rO   rU   r   r3  r   ry  r   r   )r4   rX   r  r  r  r  r5   r5   r6   test_genlaguerre  s    .zTestLaguerre.test_genlaguerreN)r  r  r  r  r  r5   r5   r5   r6   r    s   r  c                   @   s   e Zd Z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   rJ   r<   rp   r:   r   )rp   r   r?   r   r  r   )r   r   r  r   )r  r   r  r   rp   r   )?   r   ir   rf   r   )r   Zlegendrer   ry  r   r   )r4   Zleg0Zleg1Zleg2Zleg3Zleg4Zleg5r5   r5   r6   test_legendre  s    





zTestLegendre.test_legendreN)r  r  r  r  r5   r5   r5   r6   r    s   r  c                   @   s   e Zd Zdd ZdS )
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 )NrJ   r   r   r<   rt  r   r  )r   Zlmbdar   rO  rt  rQ  r   )r4   ZlamZlamrr5   r5   r6   
test_lmbda  s
    "6zTestLambda.test_lmbdaN)r  r  r  r!  r5   r5   r5   r6   r     s   r   c                   @   s   e Zd Zdd Zdd ZdS )	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   ru  r   r   )r4   Zl1pZl1prlr5   r5   r6   rv    s    zTestLog1p.test_log1pc                 C   sB   t dt dt df}tdtdtdf}t||d d S )NrJ   r(  r  r<   r  r  r  r#  )r4   Zl1pmZl1pmrlr5   r5   r6   test_log1pmore  s    zTestLog1p.test_log1pmoreN)r  r  r  rv  r$  r5   r5   r5   r6   r"    s   r"  c                   @   st   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd ZdS )TestLegendreFunctionsc                 C   s   d}t dd|d}t|td|dd| | d  gdt|| d d| t|| d  gddd|| d  ggtddd| gd|t|| d  dd| | d  t|| d  gddd| ggfd	 d S )
Ny      ?333333?r<   rp   rm   rl   rJ   rx   r@   r>   )r   clpmnr   r   r   )r4   r   Zclpr5   r5   r6   
test_clpmn  s    (8z TestLegendreFunctions.test_clpmnc              	   C   s   d}d}d}d}t |||d|  dd ||f }t |||d|  dd ||f }tt||gtt |||t |||gd d S )	NrL   rJ   rp   rl   r   r<   r   r>   )r   r&  r   r   r|  r4   r  r  rW   r   Zclp_plusZ	clp_minusr5   r5   r6   test_clpmn_close_to_real_2  s    $$z0TestLegendreFunctions.test_clpmn_close_to_real_2c              	   C   s   d}d}d}d}t |||d|  dd ||f }t |||d|  dd ||f }tt||gtt |||td| tj  t |||td| tj  gd	 d S )
NrL   rJ   rp   rl   r   r   y             y              ?r>   )r   r&  r   r   r|  rO   r   r   r(  r5   r5   r6   test_clpmn_close_to_real_3  s    $$" z0TestLegendreFunctions.test_clpmn_close_to_real_3c              
   C   sj   d}d}d}d}dD ]P}t t|||d|  |d ||f t|||d|  |d ||f d qd S )NHz>rJ   r   r<   rp   r   r@   )r   r   r&  )r4   r  r  rW   r   r3  r5   r5   r6   test_clpmn_across_unit_circle'  s    $$z3TestLegendreFunctions.test_clpmn_across_unit_circlec              
   C   s   dD ]}t dD ]t}t d|D ]d}t|||}tt|d ddd f   t|||}tt|d ddd f   qqqd S )N)rJ   r?   r:   rJ   )ra   r   r&  r   rO   r   r  lpmn)r4   r   rW   r  lpr5   r5   r6   test_inf0  s    "zTestLegendreFunctions.test_infc                 C   s   g d}d}d}dD ]r}|D ]h}dD ]^}t |||d|  |d t |||d|  |d  | }tt ||||d |d	d
 q$qqd S )N)r  y            ?y            y      ?      r  r  r  r  r<   rp   r,  )r   y        MbP?rl   r   rJ   r  rC   )r   r&  r   )r4   Zzvalsr  rW   r3  r   hZapprox_derivativer5   r5   r6   test_deriv_clpmn9  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   r<   rl   rm   rl         rx   rm   r  r:   )r   r.  r   r   r4   r/  r5   r5   r6   	test_lpmnH  s    zTestLegendreFunctions.test_lpmnc                 C   s0   t dd}t|tg dtg dfd d S )Nr<   rl   r3  r5  r:   )r   Zlpnr   r   )r4   Zlpnfr5   r5   r6   test_lpnQ  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 sd0    Y  t|dkpt| d S )Nr   r<   rl   r4  r>   (   r   gI?r  r  r?   )r   r|  r   rO   r  r   r   r6  r5   r5   r6   r}  Z  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   r<   rl   r:   rJ   )r   lqmnlqnr   )r4   Zlqmnflqfr5   r5   r6   	test_lqmnf  s    zTestLegendreFunctions.test_lqmnc                 C   sR   d}d}|| || fD ]4}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 ?gh㈵>r<   rJ   r   )r?   r?   N)r   r:  r   )r4   Zx0deltar   Zlqr  r5   r5   r6   test_lqmn_gt1l  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 )Nr:   r(  )r   r   r   )r   rJ   )r   r:  r   r   )r4   r%  r&  r5   r5   r6   test_lqmn_shapew  s    z%TestLegendreFunctions.test_lqmn_shapec                 C   s0   t dd}t|tg dtg dfd d S )Nr<   rl   )gk+ݓ?g=yX5gW2)g|a2U?g~jt?gڊer:   )r   r;  r   r   )r4   r<  r5   r5   r6   test_lqn  s    
zTestLegendreFunctions.test_lqnN)r  r  r  r'  r)  r*  r-  r0  r2  r7  r8  r}  r=  r?  r@  rA  r5   r5   r5   r6   r%    s   					r%  c                   @   s$   e Zd Zdd Zdd Zdd ZdS )TestMathieuc                 C   s   d S r6  r5   r3   r5   r5   r6   r~    s    zTestMathieu.test_mathieu_ac                 C   s   t dd d S )Nr<   r   )r   r)   r3   r5   r5   r6   test_mathieu_even_coef  s    z"TestMathieu.test_mathieu_even_coefc                 C   s   d S r6  r5   r3   r5   r5   r6   test_mathieu_odd_coef  s    z!TestMathieu.test_mathieu_odd_coefN)r  r  r  r~  rC  rD  r5   r5   r5   r6   rB    s   rB  c                   @   s   e Zd Zdd Zdd ZdS )TestFresnelIntegralc                 C   s   d S r6  r5   r3   r5   r5   r6   r    s    z$TestFresnelIntegral.test_modfresnelpc                 C   s   d S r6  r5   r3   r5   r5   r6   r    s    z$TestFresnelIntegral.test_modfresnelmN)r  r  r  r  r  r5   r5   r5   r6   rE    s   rE  c                   @   s   e Zd Zdd ZdS )TestOblCvSeqc                 C   s&   t ddd}t|tg dd d S )Nr   rp   rJ   )g~T~Oֿgt_J?gm{@g@j'&@r   )r   Z
obl_cv_seqr   r   )r4   Zoblr5   r5   r6   test_obl_cv_seq  s    zTestOblCvSeq.test_obl_cv_seqN)r  r  r  rG  r5   r5   r5   r6   rF    s   rF  c                   @   s<   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd ZdS )TestParabolicCylinderc                 C   s0   t dd}t|tddgtddgfd d S )NrJ   r   gQ?gx$(~?gx$(~g(\?r:   )r   pbdn_seqr   r   )r4   Zpbr5   r5   r6   test_pbdn_seq  s    z#TestParabolicCylinder.test_pbdn_seqc                 C   s4   t dd dt ddd  t ddd   d S )NrJ   r   r   r   )r   r  r3   r5   r5   r6   r    s    zTestParabolicCylinder.test_pbdvc                 C   s<   t dd}t dd}t|t|d t|d fd d S )NrJ   r   r   r:   )r   rI  Zpbdv_seqr   r   )r4   ZpbnZpbvr5   r5   r6   test_pbdv_seq  s    z#TestParabolicCylinder.test_pbdv_seqc                 C   s   t ddd}d|d  t t j tdd|   }tt|dd |ddd	 ttd
dd ddd ttddd ddd d S )Nr  r  r   r<   rl   rx   r   r   r   gGz$@gq=
ףp4@gHQ9ri   rC   g(\#gQ@gkS a>)rO   r  r   r   r   r   r   r  )r4   etar   r5   r5   r6   test_pbdv_points  s
    *z&TestParabolicCylinder.test_pbdv_pointsc                 C   s   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  r:   r  r  r  r   r+  r   r   rJ   r  r   )rO   r  r   r  r$  r   r4   r   rL  r	  r  Zdpr5   r5   r6   test_pbdv_gradient  s    0z(TestParabolicCylinder.test_pbdv_gradientc                 C   s   t dddd d d f }t dddd d d f }t||}ddt|  }t||| d t||| d  | d	 }t|d
 |ddd d S rN  )rO   r  r   r  r$  r   rO  r5   r5   r6   test_pbvv_gradient  s    0z(TestParabolicCylinder.test_pbvv_gradientN)	r  r  r  rJ  r  rK  rM  rP  rQ  r5   r5   r5   r6   rH    s   
	rH  c                   @   s   e Zd Zdd ZdS )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 )Nr<   rJ   rp   gX];r  gOV,@@)r<   rp   g  8Br   r  r{  )g2}jg.M?g}2;ο)r   Z	polygammar   r  rO   r}  )r4   Zpoly2Zpoly3r   rW   r  r5   r5   r6   test_polygamma  s"    zTestPolygamma.test_polygammaN)r  r  r  rS  r5   r5   r5   r6   rR    s   rR  c                   @   s   e Zd Zdd ZdS )TestProCvSeqc                 C   s&   t ddd}t|tg dd d S )Nr   rp   rJ   )g"~j?g6?Ң@g)u8F"@g2g)@r   )r   Z
pro_cv_seqr   r   )r4   Zprolr5   r5   r6   test_pro_cv_seq  s    zTestProCvSeq.test_pro_cv_seqN)r  r  r  rU  r5   r5   r5   r6   rT    s   rT  c                   @   s   e Zd Zdd ZdS )TestPsic                 C   s   t d}t|dd d S )NrJ   goxr  )r   r  r   )r4   Zpsr5   r5   r6   r    s    
zTestPsi.test_psiN)r  r  r  r  r5   r5   r5   r6   rV    s   rV  c                   @   s   e Zd Zdd Zdd ZdS )
TestRadianc                 C   s"   t ddd}t|td d d S )Nr  r   r   r   r   r  r   r   )r4   Zradr5   r5   r6   r    s    zTestRadian.test_radianc                 C   s&   t ddd}t|td d d d S )Nr  rJ   r  r<   gC?r   rX  )r4   Zrad1r5   r5   r6   test_radianmore  s    zTestRadian.test_radianmoreN)r  r  r  r  rY  r5   r5   r5   r6   rW    s   rW  c                   @   s   e Zd Zdd Zdd ZdS )TestRiccatic                 C   s|   d\}}t ||f}t|D ]D}t||}tj||dd}|| |d|f< || | |d|f< qt|t||d d S N)r<   r   T)Z
derivativer   rJ   r  )rO   emptyra   r   Zspherical_jnr   Z
riccati_jn)r4   rd  r   SrW   r  Zjpr5   r5   r6   test_riccati_jn  s    zTestRiccati.test_riccati_jnc                 C   s|   d\}}t ||f}t|D ]D}t||}tj||dd}|| |d|f< || | |d|f< qt|t||d d S r[  )rO   r\  ra   r   Zspherical_ynr   Z
riccati_yn)r4   rd  r   CrW   r   Zypr5   r5   r6   test_riccati_yn  s    zTestRiccati.test_riccati_ynN)r  r  r  r^  r`  r5   r5   r5   r6   rZ    s   
rZ  c                   @   s   e Zd Zdd ZdS )	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   )r^  mapr`   r   r  r   )r4   ZrndZrndrlr5   r5   r6   r    s    .zTestRound.test_roundN)r  r  r  r  r5   r5   r5   r6   ra    s   ra  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   rl   rt  r<   rx   r:   r   g      .@r   rf   r   r   r   g      ?rt   g      @rJ   r   r|  g      ?g     A@)	r   sph_harmrO   r   r   r   r   r	   r   )shr   r   r   r   r	   r5   r5   r6   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 r0   )rO   r  rV  r   r   rc  )dtr5   r5   r6   "test_sph_harm_ufunc_loop_selectionF  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   r?   rl   r<   rJ   r  )	r   r   r   r$  r`  r   r   r  r  r  r5   r5   r6   _seriesR  s    
@zTestStruve._seriesc                 C   sH   dD ]>}dD ]4}|  ||\}}tt|||d|d||ff qqdS )z-Check Struve function versus its power series)
ir  (\r  r?   r   rJ   r  r     )rJ   r  r   r  rF   r   r   N)ri  r   r   r  r  r5   r5   r6   test_vs_seriesY  s    zTestStruve.test_vs_seriesc                 C   s   t tddddd t tddddd t td	d
ddd t tddddd ttddtdd  ttddtdd  ttddtdd
  ttddtdd
  tttdd tttdd d S )Nrj  r  g;cv=?r+  rC   gQ g< j?r  r  r   g?ri   g       igzz?r  i)   r  r  r   gffffffr?   g333333$)r   r   r  r   r   r   r3   r5   r5   r6   test_some_values`  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  r3   r5   r5   r6   test_regression_679m  s    zTestStruve.test_regression_679N)r  )r  r  r  ri  rl  rn  ro  r5   r5   r5   r6   rh  Q  s   
rh  c                   C   s   t tddd d S )Nr  rp   gdX	
?)r   r   r   r5   r5   r5   r6   test_chi2_smalldft  s    rp  c                   C   s   t tdtjd d S )Nr  rm   )r   r   r   rO   r   r5   r5   r5   r6   test_ch2_infx  s    rq  c                   C   s   t tddd d S )Nr  rp   yj_?)r   r   r   r5   r5   r5   r6   test_chi2c_smalldf|  s    rs  c                   C   s   t tddd d S )Nr  rr  rp   )r   r   r   r5   r5   r5   r6   test_chi2_inv_smalldf  s    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 )'NrB   rJ   r<   gDSYC?rC   gQ_?g?@g>;,
i}@rp   )rJ   rp   r   g=O?r?   rt  r   r@   gXs*@r  g   V4oAgO1eAgꌠ9Y>)FgEg^ 9^;gd-?gP.5_gsTNNeg6dgu?j/ g]XC}KdgѧRg"!x{{ rm   g][#!Rr  gٍS1gN_ r   c   r  )r   r   ZagmrO   r   r   r  r`  r   r   r   )rD   Zagm13Zagm15Zagm35Zagm12fir5   r5   r6   test_agm_simple  sr    
rw  c                  C   s0  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    n1 s"0    Y  d S )Nr  rJ   r   g?r<   gffffff@)r   rw  rx  r   r   Zexpnr  r  r  r  rh  r  r  r   )rz  r5   r5   r6   test_legacy  s    
rx  c                   C   s   t tjtjdd d S )NrJ   y        .B}T)r~  r   ZSpecialFunctionErrorrG  r5   r5   r5   r6   test_error_raising  s    ry  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   sp   t jddP | dkr2t |s2| W  d    S | t | W  d    S W d    n1 sb0    Y  d S Nr  )invalidr   )rO   r  r   r   r4  r5   r5   r6   xfunc  s    ztest_xlogy.<locals>.xfuncr   r   r   rm   r   r  )r   r   )rJ   r   rJ   rB   r   )
rO   r   r   r   rb   r   rg   r-   r   xlogy)r|  z1Zz2w1Zw2r5   r5   r6   
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   sp   t jddP | dkr2t |s2| W  d    S | t | W  d    S W d    n1 sb0    Y  d S rz  )rO   r  r   ru  r4  r5   r5   r6   r|    s    ztest_xlog1py.<locals>.xfuncr}  r   r~  )rJ   gKH9r  rJ   rB   r   )	rO   r   r   r   rb   rg   r-   r   Zxlog1py)r|  r  r  r5   r5   r6   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 d S r0   )rO   r   r   r  )r   r5   r5   r6   r|    s    ztest_entr.<locals>.xfuncr   rl   rm   r?   rJ   r  ZotypesrB   r   )rO   r   r  r  r  r   rb   rg   r   r-   r   Zentr)r|  r   signsr  Zsgnr  r   r  r5   r5   r6   	test_entr  s    r  c            
      C   s   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   sh   | dk s |dk s |dkr&| dkr&t jS t | s:t |r@t jS | dkrL|S t| | | |  | S d S r0   )rO   r   Zisposinfr   r  r4  r5   r5   r6   r|    s     ztest_kl_div.<locals>.xfuncr   rl   rm   r?   rJ   r  r  r   rB   r   )r  r  r  rO   r   rb   rg   r   r-   r   Zkl_div
r|  r   r  r  ZsgnavaZsgnbZvbr   r  r5   r5   r6   test_kl_div  s    0r  c            
      C   s   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   s>   | dkr |dkr t | | | S | dkr4|dkr4dS tjS d S r0   )r   r  rO   r   r4  r5   r5   r6   r|    s
    ztest_rel_entr.<locals>.xfuncr  r?   rJ   r  r  r   rB   r   )r  r  r  rO   r   rb   rg   r   r-   r   Zrel_entrr  r5   r5   r6   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 )Nr?   r  r<   rl   r  r   c                 S   sD   | dk rt jS t || k r*dt | S | t |d|    S d S )Nr   rl   )rO   r   r$  squarer>  r>  r5   r5   r6   r|  1  s
    ztest_huber.<locals>.xfuncr  r  r   rJ   rB   r   )r   r   ZhuberrO   r   r   r  rU   randnrg   r   r-   r|  r   r  r5   r5   r6   
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 d S )Nr   r<   rJ   )rO   r   r   r  r5   r5   r6   r|  ?  s
    z test_pseudo_huber.<locals>.xfuncr  r<   r   rl   r  rJ   rB   r   )
rO   r   rU   r  tolistrg   r   r-   r   pseudo_huberr  r5   r5   r6   test_pseudo_huber>  s    (0r  c                  C   s*   d} d}t | |}d}t||dd d S )Nrm   gC]r2<gs.-De8rB   rC   )r   r  r   )r>  r>  r   r  r5   r5   r6   test_pseudo_huber_small_rL  s
    r  c                   C   st   t jtdd tdd W d    n1 s.0    Y  t jtdd tdd W d    n1 sf0    Y  d S )NzToo many predicted coefficientsrf  rG   )r  rh  rx  r(   r)   r5   r5   r5   r6   test_runtime_warningY  s    (r  )wrD  r  rF  r"  r!  numpyrO   r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r  r   r~  Znumpy.testingr   r   r   r   r   r   r   r   r   Zscipyr   Zscipy.special._ufuncsZ_ufuncsr1   Zscipy.specialr    r!   r"   r#   r$   r%   r&   r'   r(   r)   Zscipy.special._basicr*   r+   Zscipy.special._testutilsr,   r-   r.   r  r/   r"  r2  r5  r7  rL  rN  rQ  rv  r  r  r  r  r  r  r  r  rW  rd  rk  rs  r  r  r  r   r"  r%  rB  rE  rF  rH  rR  rT  rV  rW  rZ  ra  re  rg  rh  rp  rq  rs  rt  rw  rx  ry  r  r  r  r  r  r  r  r  r  r5   r5   r5   r6   <module>   s   T,       >n	 PE  +b   yD2# Y    6 		.	
#=
