o
    i%                    @   s\  d Z ddlZddlmZmZ ddlmZ ddlZddlZddl	m
Z
 ddlmZ ddlmZmZmZmZ ddlmZmZmZmZmZmZmZmZmZmZ ddlmZm Z m!Z!m"Z"m#Z#m$Z$ zddl%Z%W n e&yo   ed	Z%Y nw ee%d
dd Z'ee%ddd Z(ee%ddd Z)ee%ddd Z*ee%ddd Z+ee%ddd Z,ee%ddd Z-ee%ddd Z.ee%dd d! Z/ee%d"ej0j1d#d$ Z2ee%dd%d& Z3ee%d'd(d) Z4ee%d'd*d+ Z5d,Z6ee%dd-d. Z7ee%dd/d0 Z8ee%dej0j1d1d2 Z9ee%dej0j1d3d4 Z:ee%dd5d6 Z;ee%dd7d8 Z<ee%dej0j1d9d: Z=ee%dej0j1d;d< Z>ee%dd=d> Z?ee%dd?d@ Z@ee%ddAdB ZAdCdD ZBej0j1ee%ddEdF ZCej0j1ee%ddGdH ZDej0j1ee%ddIdJ ZEej0j1ee%ddKdL ZFeGdMdMdNZHej0j1ee%dOG dPdQ dQZIdS )Rz4
Test SciPy functions versus mpmath, if available.

    N)assert_assert_allclose)pi)_pep440)MissingModulecheck_versionFuncDataassert_func_equal)
ArgFixedArg
ComplexArgIntArgassert_mpmath_equalnonfunctional_tooslow
trace_argstime_limitedexception_to_nan
inf_to_nan)_sinpi_cospi_lgam1p_lanczos_sum_expg_scaled_log1pmx	_igam_facmpmathz0.10c               	   C   s   g } t dddD ]$}t ddt j dD ]}|t d|  }| |tt|f qq	t j	| t j
d} ttj| dd  d S )	Ni   
   r                    ?Zdtype   )nplogspacelinspacer   expappendcomplexr   eiarrayZcomplex_r   scexpicheck)datasetrpz r0   n/var/www/html/eduruby.in/lip-sync/lip-sync-env/lib/python3.10/site-packages/scipy/special/tests/test_mpmath.pytest_expi_complex#   s   r2   z0.19c                  C   s   g } dD ]/}t dddD ]%}td | ||tt||f W d    n1 s-w   Y  qqt | } tt	j
| dddd	  d S )
N)2   3   r         d   r   r    r   vIh%<=rtol)r!   r"   r   workdpsr%   floatexpintasarrayr   r)   expnr+   )r,   nxr0   r0   r1   test_expn_large_n3   s   
rC   c                  C   s   g } g d}|D ]7}|D ]2}|D ]-}|d|  }t d tt ||}W d    n1 s0w   Y  | |||f qqqt| } tdd | dddd	  d S )
N)g     Xg      #            ?g      #@g     X@r   x   c                 S      t | j|S Nr)   hyp0f1realvr/   r0   r0   r1   <lambda>U       z$test_hyp0f1_gh5764.<locals>.<lambda>r8   r   r9   r:   )	r   r<   r&   rJ   r%   r!   r(   r   r+   )r,   ZaxisrM   rB   yr/   resr0   r0   r1   test_hyp0f1_gh5764D   s"   
	
rR   c                  C   sF   t ddd} t| d}t dd | D }t||tdd d S )	N         rE   c                 S   s   g | ]}t |d qS )rE   r   rJ   ).0rM   r0   r0   r1   
<listcomp>^       z'test_hyp0f1_gh_1609.<locals>.<listcomp>-q=r:   )r!   r#   r)   rJ   r(   r   astyper=   )vvafmfr0   r0   r1   test_hyp0f1_gh_1609Y   s   r_   z1.1.0c                  C   s   g } t ddD ]6}t dddD ],}| }| ||dtt||df | | d }| ||dtt||df qqdD ]}dD ]}| ||dtt||df qEqAt | } tt	j| dd	d
dd
  d S )N      r   r    )      %      rD   r   rE   r    r   )      rD   r   rE   r          ?r         @r   r    r      V瞯<-a=r;   atol)r!   aranger#   r%   r=   r   hyperur(   r   r)   r+   )r,   rA   bar0   r0   r1   test_hyperu_around_0f   s    ""
rr   1.0.0c                     sx   ddg} | t tjg ddd7 } dd | D } tdd	  fd
d| D }tj|tjd}ttj	|dddd
  d S )N)r   rt   ffffff?)r   rv   ru   )r   r    gffffffr5   )repeatc                 S   sD   g | ]\}}}}||krt ||kr|d k r|dkr||||fqS )r   rw   )round)rW   rq   rp   crB   r0   r0   r1   rX      s
    
$
z.test_hyp2f1_strange_points.<locals>.<listcomp>T)Z	eliminatec                    s&   g | ]}|t tj|i  f qS r0   r=   r   hyp2f1rW   r.   kwr0   r1   rX      s   & r   r   r    r   ri   绽|=r:   )list	itertoolsproductdictr!   r(   float_r   r)   r|   r+   ptsr,   r0   r~   r1   test_hyp2f1_strange_points}   s   
r   z0.13c                  C   sp   g d} dd | D }t j|t jd}t jdd ttj|ddd	d
  W d    d S 1 s1w   Y  d S )N)r    r   ri   r   )UUUUUU?gUUUUUU?g?g      ?)      ?rE   g      ?gX<ݚ?)r   rv   ri   )r   r   rv   ri   )r   rd   rd   ri   r   )gx&?rt   r`   g333333?)r   r   r   +?)r   r   r   rt   )r   ri   ra   Gz?)rf   rD   ri   r   )r   rg   g      
r   )g*4]92@g|O%@gCu?)  rc   r   )r   r         %@r   )rt   r   r          ?)rt   r   r    re   )r      ra   r   )r   r   ra   re   )rE   g     prf   gm˟?c                 S   s    g | ]}|t tj| f qS r0   r{   r}   r0   r0   r1   rX           z0test_hyp2f1_real_some_points.<locals>.<listcomp>r   ignoreinvalidr   r5   r   r:   )r!   r(   r   errstater   r)   r|   r+   r   r0   r0   r1   test_hyp2f1_real_some_points   s   "r   0.14c                     sN   g d} dd   fdd| D }t j|t jd}ttj|ddd	d
  d S )N))p   )r4   r   )r   gwJ)r   |r   r   )r   r   rc   r   c                 S   s"   t | trt| d | d  S | S )Nr   r    )
isinstancetupler=   rB   r0   r0   r1   fev   s   
z&test_hyp2f1_some_points_2.<locals>.fevc                    s*   g | ]}t t |ttj| f qS r0   )r   mapr=   r   r|   r}   r   r0   r1   rX         * z-test_hyp2f1_some_points_2.<locals>.<listcomp>r   r   r5   r   r:   )r!   r(   r   r   r)   r|   r+   r   r0   r   r1   test_hyp2f1_some_points_2   s
   r   c                  C   s   g } dD ]1}dD ],}dD ]'}dD ]"}zt t||||}W n	 ty'   Y qw | |||||f qqqqtj| tjd} tjdd t	t
j| dd	d
dd  W d    d S 1 s]w   Y  d S )N)r   r`   g?ra   r   )g      rt   r    g@)r   r   ra   gffffff4@)r   g)\(Gzr   g333333?gffffff?rf   r   r   r   r   r   r5   &.>Tr;   ignore_inf_sign)r=   r   r|   	Exceptionr%   r!   r(   r   r   r   r)   r+   )r,   rq   rp   rz   r/   rM   r0   r0   r1   test_hyp2f1_real_some   s*   "r   z0.12c                  C   s  d} t | dft j}t jd t jd| |d d df< t jd| |d d df< t jd| |d d df< dt j|  d |d d df< |d d df  d	t jd|  9  < |d d df  d	t jd|  9  < |d d df  d	t jd|  9  < |D ]2}tj	d
k rt
|d d  t
|d krt
|d d  |d< ttjt|d d  |d< qttj|dddd  d S )N  ra     rf   r   r    r   ri   rt   r   r5   r   r   r:   )r!   zerosr   randomseedZparetoZrandrandintr   __version__absmaxr=   r|   r   r   r)   r+   )Znpointsr,   Zdsr0   r0   r1   test_hyp2f1_real_random   s     &&&
  r   c               	   C   s   t jjt jj} }zddt j_ttdddtddd\}}ttdddtddd\}}tj|	 |	 f dtj|	 |	 f   }t
tjd	d
 |ddd t
tjdd
 |ddd W | |t j_t j_d S | |t j_t j_w )NF   r   r          ig?r   c                 S      t t| S rH   )r&   r   erfr   r0   r0   r1   rN      rO   z"test_erf_complex.<locals>.<lambda>Fr9   
vectorizedr;   c                 S   r   rH   )r&   r   erfcr   r0   r0   r1   rN     rO   )r   mpdpsprecr!   meshgridr#   r"   r_ravelr	   r)   r   r   )old_dpsold_precx1y1Zx2y2Zpointsr0   r0   r1   test_erf_complex   s   $$0*r   z0.15c                     sd  g } dD ]o}|  dd|fdd|fdd|fdd|fdd|fdd|fdd|fdd|fdd|fdd	|fd
d|fdd	|fdd|fdd	|fd
d|fdd|fdd|fdd|fd
d|fdd|fdd|fdd|fd
d|fdd|fdd|fdd|fg qdd   fdd| D }tj|tjd}dd }tjdd t||dd
dd d!  W d    d S 1 sw   Y  d S )"N)r   gmư>gL7A`?r    r    rt   rv   g333333?g333333gr   r   ri      ra   r   r`   r   ig @g&@g g&c                 S   s2   |t |kr|dkr|dkrdS dS t| ||S Nr    r   )intr   legenp)numurB   r0   r0   r1   mplegenp-  s
   ztest_lpmv.<locals>.mplegenpc                    s*   g | ]}| |d  |d |d f qS )r    r   r   r0   r}   r   r0   r1   rX   6  r   ztest_lpmv.<locals>.<listcomp>r   c                 S   s   t | t||S rH   )r)   lpmvr[   r   )r   r   rB   r0   r0   r1   evf9     ztest_lpmv.<locals>.evfr   r   rh   r   +=rl   )extendr!   r(   r   r   r   r+   )r   rB   r,   r   r0   r   r1   	test_lpmv  sJ   	"r   c                  C   s  t jd t jt dddt dddt dddt dd	dt dd	dd
 dddddf
 } | }t t |d d d f | d d d f ddj	}t
jjt
jj}}z)dt
j_ttjdd |dddd ttjdd |ddd W ||t
j_t
j_d S ||t
j_t
j_w )Nr   8r6   r5   r   r   rt   r    r   rE   gffffffr   g33333Yg3333r     c                 S   s   t t| |S rH   )r=   r   betarq   rp   r0   r0   r1   rN   W      ztest_beta.<locals>.<lambda>Fr   T)r   r;   r   c                 S   s   t ttt| |S rH   )r=   r   logr   r   r   r0   r0   r1   rN   _      r   )r!   r   r   r   r"   rn   r(   Zbroadcast_arraysreshapeTr   r   r   r   r	   r)   r   Zbetaln)rp   rq   abr   r   r0   r0   r1   	test_betaD  s8   
4*r   g?c                  C   s   t tg d } tddtj d}t| |\} }| td|  }tjd| d| f  }dd |D }t|}t	t
j|ddd	d
  d S )N)gg{Gzr   g{Gz?g?r   r   rb   r   r    c                 S      g | ]}|t t|fqS r0   r&   r   loggammarW   Zz0r0   r0   r1   rX   y      z3test_loggamma_taylor_transition.<locals>.<listcomp>vIh%,=r:   )LOGGAMMA_TAYLOR_RADIUSr!   r(   r#   r   r   r$   r   flattenr   r)   r   r+   r-   thetadzr/   r,   r0   r0   r1   test_loggamma_taylor_transitionn  s   
r   c                  C   s   t dt td} t ddt j d}t | |\} }| t d|  }t jd| d| f 	 }dd	 |D }t 
|}ttj|ddd
d  d S )Nir   r   r   rb   r   r    c                 S   r   r0   r   r   r0   r0   r1   rX     r   z(test_loggamma_taylor.<locals>.<listcomp>r   r:   )r!   r"   log10r   r#   r   r   r$   r   r   r(   r   r)   r   r+   r   r0   r0   r1   test_loggamma_taylor  s   
r   c                  C   s   t jt ddd dt dddf } |  }t | |\} }| d|  }t dddddd}|t |f|j  	 }t
d d	d
 |D }W d    n1 sUw   Y  t |}ttj|dddd  d S )Nrt   ri   r   r   iVr    r7   c                 S   r   r0   )r&   r   rgammar   r0   r0   r1   rX     r   z%test_rgamma_zeros.<locals>.<listcomp>rZ   r:   )r!   r   r"   copyr   rn   r   dstacksizer   r   r<   r(   r   r)   r   r+   )dxdyr   r   r/   r,   r0   r0   r1   test_rgamma_zeros  s   &
r   c               	   C   s  t t jd} t| g}t t jd} |t|  t|}tjdtddd dtddddf }|	 }t
||\}}|d	|  }|t|f|j   }t d
 dd |D }W d    n1 sjw   Y  t|}ttj|dddd  d S )Nrf   rD   gQοrt   r   r   gQ?r   r   c                 S   r   r0   r&   r   digammar   r0   r0   r1   rX     r   z&test_digamma_roots.<locals>.<listcomp>r    r   r:   )r   Zfindrootr   r=   r%   r!   r(   r   r"   r   r   r   r   r   r<   r   r)   r+   )rootrootsr   r   r   r/   r,   r0   r0   r1   test_digamma_roots  s   

*
r  c                     s   t tj tddd } tjtddd dtdddf }t| |\} }| d|   }td  fd	d
|D }W d    n1 sIw   Y  t	|}t
tj|dddd  d S )N,  r7   r   r   ra   r   (   c                    s   g | ]
}|t  |fqS r0   )r&   r   r   r0   r1   rX     s    z(test_digamma_negreal.<locals>.<listcomp>r    r9   r:   )r   r   r   r!   r"   r   r   r   r<   r?   r   r)   r+   rB   rP   r/   r,   r0   r  r1   test_digamma_negreal  s   
&
r  c                  C   s   t ddd } t g d}t | |\} }| d|   }td dd |D }W d    n1 s6w   Y  t |}tt	j
|d	d
dd  d S )Nr  r  r7   )gffffffgg@gffffff@r   r   c                 S   r   r0   r   r   r0   r0   r1   rX     r   z)test_digamma_boundary.<locals>.<listcomp>r   r    r9   r:   )r!   r"   r(   r   r   r   r<   r?   r   r)   r   r+   r  r0   r0   r1   test_digamma_boundary  s   
r	  c                  C   s   d} t d|  d|  d}| }t ||\}}| | }}td dd t||D }W d    n1 s<w   Y  t |}t	t
j|ddd	d
  d S )Nrb   rE   r   r3   r7   c              
   S   s*   g | ]\}}||t tj||d dfqS )Trp   regularized)r=   r   gammainc)rW   Za0Zx0r0   r0   r1   rX     s    z*test_gammainc_boundary.<locals>.<listcomp>r8   rZ   r:   )r!   r#   r   r   r   r   r<   zipr(   r   r)   r  r+   )Zsmallrq   rB   r,   r0   r0   r1   test_gammainc_boundary  s   
r  c                     sv   dd  t dd} t ddt }dt | t d|   }t  fd	d
|D }ttj	|dddd
  d S )Nc                 S   s   t tdd|  S Nr   r    )r&   r   polylogr/   r0   r0   r1   spence  r   z"test_spence_circle.<locals>.spencerE   rf   r   r   r    r   c                    s   g | ]}| |fqS r0   r0   r   r  r0   r1   rX     rY   z&test_spence_circle.<locals>.<listcomp>r   r:   )r!   r#   r   outerr$   r   r?   r   r)   r  r+   )r-   r   r/   r,   r0   r  r1   test_spence_circle  s   r  c                  C   s   t tj} t jt ddd dt dddf }| }t ||\}}|d|  }t ddd	ddd}|t 
|f|j   }t d	d
 |D }tt|ddd|  d  d S )Nr   r   ri   r   r7   r    rt   c                 S   r   r0   )r&   r   sinpir   r0   r0   r1   rX         z$test_sinpi_zeros.<locals>.<listcomp>r   r:   )r!   finfor=   epsr   r"   r   r   rn   r   r   r   r   r?   r   r   r+   r  r   r   r   r   r/   r,   r0   r0   r1   test_sinpi_zeros  s   &
r  c                  C   s   t tj} t jt ddd dt dddf }| }t ||\}}|d|  }t dddd 	ddd	}|t 
|f|j   }t d
d |D }tt|ddd|  d  d S )Nr   r   ri   r   r  r7   r    rE   rt   c                 S   r   r0   )r&   r   cospir   r0   r0   r1   rX   -  r  z$test_cospi_zeros.<locals>.<listcomp>r   r:   )r!   r  r=   r  r   r"   r   r   rn   r   r   r   r   r?   r   r   r+   r  r0   r0   r1   test_cospi_zeros$  s   &
r  c            	   	   C   s   dd } dd }t ddd}t jt dd	d
 dt d	dd
f }g }|D ]}tt|}|D ]}|| }||||||f q1q&t |}t	| |dddd
  d S )Nc                 S      t | |d S Nr   r)   Zellipjumr0   r0   r1   dn9     z"test_dn_quarter_period.<locals>.dnc                 S   s   t tjd| |dS Nr%  r"  )r=   r   ellipfunr"  r0   r0   r1   	mpmath_dn<  r   z)test_dn_quarter_period.<locals>.mpmath_dnr   r    rb   rt   r   r   r8   r   r   r:   )r!   r#   r   r"   r=   r   ellipkr%   r?   r   r+   )	r%  r)  r$  Zdur,   Zm0Zu0Zdu0r.   r0   r0   r1   test_dn_quarter_period7  s   &
r+  c                 C   sh   t |% t | } t | jt j dt j  }t t | |}W d    |S 1 s-w   Y  |S r   )r   r<   Zmpcceilimagr   lambertwr$   )r/   r   ZunwindrQ   r0   r0   r1   _mpmath_wrightomegaP  s   

r/  c            	      C   s4  t ddd } t t jt jg}t t jt j g}t t j t jg}t t j t j g}tdD ]4}|t |d t j |t |d t j  |t |d t j |t |d t j  q4t ||||f}t | |\} }| d|  	 }t 
dd |D }ttj|dd	d
d  d S )Nr   r      r3   rt   r   c                 S      g | ]}|t t|d fqS r0  r&   r/  r   r0   r0   r1   rX   i  r  z+test_wrightomega_branch.<locals>.<listcomp>r    :0yE>r:   )r!   r"   	nextafterr   infranger%   Zhstackr   r   r?   r   r)   wrightomegar+   )	rB   Zpicut_aboveZpicut_belowZnpicut_aboveZnpicut_belowirP   r/   r,   r0   r0   r1   test_wrightomega_branchX  s"   
r:  c                  C   sn   t dd} t ddt j }t | |\} }| d|   }t dd |D }ttj|dddd		  d S )
Nrv   r    r   r   c                 S   r1  r2  r3  r   r0   r0   r1   rX   x  r  z,test_wrightomega_region1.<locals>.<listcomp>r   rj   r:   
r!   r#   r   r   r   r?   r   r)   r8  r+   r  r0   r0   r1   test_wrightomega_region1o     
r<  c                  C   sn   t dd} t dt j d}t | |\} }| d|   }t dd |D }ttj|dddd		  d S )
Nrv   r    rt   r   c                 S   r1  r2  r3  r   r0   r0   r1   rX     r  z,test_wrightomega_region2.<locals>.<listcomp>r   rj   r:   r;  r  r0   r0   r1   test_wrightomega_region2~  r=  r>  c                  C   sn   t dddt ddd} }t | |\} }| d|   }t dd |D }ttj|dddd	  d S )
Nrt   r    r0  r   c                 S   r   r0   )r&   r   r.  r   r0   r0   r1   rX     r  z(test_lambertw_smallz.<locals>.<listcomp>r   r9   r:   )	r!   r#   r   r   r?   r   r)   r.  r+   r  r0   r0   r1   test_lambertw_smallz  s   
r?  r6   ZmaxprecZmaxtermsz0.17c                   @   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$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zejjd3d4d5d6d7 Zd8d9 Z ejjd3d4d5d:d; Z!d<d= Z"d>d? Z#d@dA Z$dBdC Z%dDdE Z&dFdG Z'dHdI Z(dJdK Z)dLdM Z*dNdO Z+dPdQ Z,dRdS Z-dTdU Z.dVdW Z/dXdY Z0dZd[ Z1d\d] Z2d^d_ Z3d`da Z4dbdc Z5ddde Z6dfdg Z7dhdi Z8djdk Z9dldm Z:dndo Z;dpdq Z<drds Z=dtdu Z>dvdw Z?dxdy Z@dzd{ ZAd|d} ZBd~d ZCdd ZDdd ZEdd ZFdd ZGdd ZHdd ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOejjd3ddd ZPdd ZQejjd3ddd ZReSdd ZTdd ZUdd ZVejjd3dd5dd ZWdd ZXdd ZYdd ZZejjd3ddd Z[eSdd Z\ejjd3ddd Z]ej^ddd Z_dd Z`dd Zaejjd3ddd Zbdd Zcdd Zddd ZeeSddĄ ZfddƄ Zgej^dǡddɄ Zhdd˄ ZieSdd̈́ Zjddτ Zkddф Zlddӄ ZmddՄ Znejjd3dd5dd؄ ZoeSddڄ Zpdd܄ Zqddބ Zrejjd3ddd Zsejjd3dd5dd Ztdd Zuejjd3dd5dd Zvdd Zwdd Zxejjdddd Zydd Zzdd Z{dd Z|dd Z}dd Z~dd Zdd Zd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" Zejjd3d#d5d$d% Zd&S ('  TestSystematicc                 C   s<   t dd tjtddgdd t dd tjtdd	g d S )
Nc                 S      t | d S Nr   r)   Zairyr  r0   r0   r1   rN     rO   z,TestSystematic.test_airyai.<locals>.<lambda>    ח    חAh㈵>r:   c                 S   rB  rC  rD  r  r0   r0   r1   rN     rO        @     @@)r   r   airyair
   selfr0   r0   r1   test_airyai  s   

zTestSystematic.test_airyaic                 C   s   t dd tjt g d S )Nc                 S   rB  rC  rD  r  r0   r0   r1   rN     rO   z4TestSystematic.test_airyai_complex.<locals>.<lambda>)r   r   rJ  r   rK  r0   r0   r1   test_airyai_complex  s   z"TestSystematic.test_airyai_complexc                 C   @   t dd dd tddgdd t dd d	d td
dg d S )Nc                 S   rB  Nr    rD  r  r0   r0   r1   rN     rO   z2TestSystematic.test_airyai_prime.<locals>.<lambda>c                 S      t j| ddS Nr    )Z
derivativer   rJ  r  r0   r0   r1   rN        rE  rF  rG  r:   c                 S   rB  rP  rD  r  r0   r0   r1   rN     rO   c                 S   rQ  rR  rS  r  r0   r0   r1   rN     rT  rH  rI  r   r
   rK  r0   r0   r1   test_airyai_prime     

z TestSystematic.test_airyai_primec                 C      t dd dd t g d S )Nc                 S   rB  rP  rD  r  r0   r0   r1   rN     rO   z:TestSystematic.test_airyai_prime_complex.<locals>.<lambda>c                 S   rQ  rR  rS  r  r0   r0   r1   rN     rT  r   r   rK  r0   r0   r1   test_airyai_prime_complex     z(TestSystematic.test_airyai_prime_complexc                 C   rO  )Nc                 S   rB  r   rD  r  r0   r0   r1   rN     rO   z,TestSystematic.test_airybi.<locals>.<lambda>c                 S   
   t | S rH   r   Zairybir  r0   r0   r1   rN        
rE  rF  rG  r:   c                 S   rB  r   rD  r  r0   r0   r1   rN     rO   c                 S   r\  rH   r]  r  r0   r0   r1   rN     r^  rH  rI  rU  rK  r0   r0   r1   test_airybi  rW  zTestSystematic.test_airybic                 C   rX  )Nc                 S   rB  r   rD  r  r0   r0   r1   rN     rO   z4TestSystematic.test_airybi_complex.<locals>.<lambda>c                 S   r\  rH   r]  r  r0   r0   r1   rN     r^  rY  rK  r0   r0   r1   test_airybi_complex  r[  z"TestSystematic.test_airybi_complexc                 C   rO  )Nc                 S   rB  Nri   rD  r  r0   r0   r1   rN     rO   z2TestSystematic.test_airybi_prime.<locals>.<lambda>c                 S   rQ  rR  r]  r  r0   r0   r1   rN     rT  rE  rF  rG  r:   c                 S   rB  ra  rD  r  r0   r0   r1   rN     rO   c                 S   rQ  rR  r]  r  r0   r0   r1   rN     rT  rH  rI  rU  rK  r0   r0   r1   test_airybi_prime  rW  z TestSystematic.test_airybi_primec                 C   rX  )Nc                 S   rB  ra  rD  r  r0   r0   r1   rN     rO   z:TestSystematic.test_airybi_prime_complex.<locals>.<lambda>c                 S   rQ  rR  r]  r  r0   r0   r1   rN     rT  rY  rK  r0   r0   r1   test_airybi_prime_complex  r[  z(TestSystematic.test_airybi_prime_complexc                 C   "   t tjtdd tddg d S )Nc                 S      t jd| fi tS rC  )r   beiHYPERKWr  r0   r0   r1   rN         z)TestSystematic.test_bei.<locals>.<lambda>rH  rI  )r   r)   rf  r   r
   rK  r0   r0   r1   test_bei     

zTestSystematic.test_beic                 C   rd  )Nc                 S   re  rC  )r   berrg  r  r0   r0   r1   rN     rh  z)TestSystematic.test_ber.<locals>.<lambda>rH  rI  )r   r)   rk  r   r
   rK  r0   r0   r1   test_ber  rj  zTestSystematic.test_berc                 C   s&   t dd dd tddgddd d S )Nc                 S   s   t t| t|  S rH   )r)   	bernoullir   rA   r0   r0   r1   rN         z/TestSystematic.test_bernoulli.<locals>.<lambda>c                 S   s   t tt| S rH   )r=   r   rm  r   rn  r0   r0   r1   rN         r   i2  r   r;   rA   )r   r   rK  r0   r0   r1   test_bernoulli  s
   

zTestSystematic.test_bernoullic                 C   s*   t tjtdd tddt gdd d S )Nc                 S      t j| |fi tS rH   r   besselirg  rL   r0   r0   r1   rN     rh  z-TestSystematic.test_besseli.<locals>.<lambda>}Ô%I}Ô%ITgJDrm   )r   r)   ivr   r
   rK  r0   r0   r1   test_besseli  s
   

zTestSystematic.test_besselic                 C   (   t dd tdd tddt g d S )Nc                 S   rG   rH   )r)   ry  rK   rL   r0   r0   r1   rN     rO   z5TestSystematic.test_besseli_complex.<locals>.<lambda>c                 S   rs  rH   rt  rL   r0   r0   r1   rN     rh  rv  rw  r   r   r
   r   rK  r0   r0   r1   test_besseli_complex     
z#TestSystematic.test_besseli_complexc                 C   sZ   t tjtdd tddtddgdd t tjtd	d tddtd
dgddd d S )Nc                 S   rs  rH   r   besseljrg  rL   r0   r0   r1   rN     rh  z-TestSystematic.test_besselj.<locals>.<lambda>rv  rw  rH  rI  Tr   c                 S   rs  rH   r  rL   r0   r0   r1   rN     rh  rE  rF  rG  )r   r;   )r   r)   jvr   r
   rK  r0   r0   r1   test_besselj   s   


zTestSystematic.test_besseljc                 C   s$   t dd tdd t t g d S )Nc                 S   rG   rH   )r)   r  rK   rL   r0   r0   r1   rN     rO   z5TestSystematic.test_besselj_complex.<locals>.<lambda>c                 S   rs  rH   r  rL   r0   r0   r1   rN     rh  r|  rK  r0   r0   r1   test_besselj_complex  s   

z#TestSystematic.test_besselj_complexc                 C   s,   t tjtjtddtdtjgddd d S Nr   r6   r   FrZ   nan_okr;   )r   r)   kvr   besselkr
   r!   r6  rK  r0   r0   r1   test_besselk  
   
zTestSystematic.test_besselkc                 C   s,   t tjtjtddtdtjgddd d S r  )	r   r)   knr   r  r   r
   r!   r6  rK  r0   r0   r1   test_besselk_int  r  zTestSystematic.test_besselk_intc                 C   r{  )Nc                 S   rG   rH   )r)   r  rK   rL   r0   r0   r1   rN     rO   z5TestSystematic.test_besselk_complex.<locals>.<lambda>c                 S   rs  rH   )r   r  rg  rL   r0   r0   r1   rN      rh  rv  rw  r|  rK  r0   r0   r1   test_besselk_complex  r~  z#TestSystematic.test_besselk_complexc                 C   s2   dd }t tjt|tddtddgdd d S )	Nc                 S   sR   t tj| |fi t}t|dkrtjt| }t|dkr'|dkr'tjS |S )NقnQ:Br   )	r=   r   besselyrg  r   r!   r6  signnanrM   rB   r-   r0   r0   r1   	mpbessely$  s   z.TestSystematic.test_bessely.<locals>.mpbesselyrv  rw  rE  rF    rn  )r   r)   yvr   r
   rL  r  r0   r0   r1   test_bessely#  s   	
zTestSystematic.test_besselyc                 C   s,   dd }t dd t|t t gdd d S )Nc                 S   sf   t tj| |fi t}t|dkr1tjdd tjt| }W d    |S 1 s,w   Y  |S )Nr  r   r   )	r&   r   r  rg  r   r!   r   r6  r  r  r0   r0   r1   r  3  s   
z6TestSystematic.test_bessely_complex.<locals>.mpbesselyc                 S   rG   rH   )r)   r  rK   rL   r0   r0   r1   rN   :  rO   z5TestSystematic.test_bessely_complex.<locals>.<lambda>i:  rn  r|  r  r0   r0   r1   test_bessely_complex2  s   

z#TestSystematic.test_bessely_complexc                 C   s0   dd }t dd t|tddtddg d S )	Nc                 S   s.   t t| |}t|dkr|dkrtjS |S rC  )r=   r   r  r   r!   r  r  r0   r0   r1   r  @  s   z2TestSystematic.test_bessely_int.<locals>.mpbesselyc                 S      t t| |S rH   )r)   Zynr   rL   r0   r0   r1   rN   F  r   z1TestSystematic.test_bessely_int.<locals>.<lambda>rw     rE  rF  r   r   r   r
   r  r0   r0   r1   test_bessely_int?  s
   zTestSystematic.test_bessely_intc                    sV   g  d fdd	t tjfddt t gddd t tjt ddd	d
 d S )NFc                    sj   | dk s|dk rt jS | dk s|dk r/tt| | d dkr/|r/ t| t|f t jS t| |S )Ng   mr   r    )r!   r  r   r=   r%   r   r   )rq   rp   nonzero
bad_pointsr0   r1   r   M  s   (z&TestSystematic.test_beta.<locals>.betac                        | |ddS NT)r  r0   r   )r   r0   r1   rN   ]  rO   z*TestSystematic.test_beta.<locals>.<lambda>r   Tr   r   dy=)r   r   rm   F)r   r)   r   r
   r!   r(   rK  r0   )r  r   r1   r   J  s   


zTestSystematic.test_betac                 C   s,   t tjt tdd t t t g d S )Nc                 S   s   t j| |d|ddS )Nr   T)r  )r   betaincrq   rp   rB   r0   r0   r1   rN   k  rh  z-TestSystematic.test_betainc.<locals>.<lambda>)r   r)   r  r   r   r
   rK  r0   r0   r1   test_betainci  s   zTestSystematic.test_betaincc                    sR   g  d
 fdd	t tjfddt t gdd t tjt ddd	 d S )NFc                    sx   t |dt | d  krtjS | |k r6t t| | tt| |  dk r6|r6 t| t|f tjS t| |S )NrF  r    rj   )r   r!   r  r=   ry   r%   r   binomial)rA   kr  r  r0   r1   r  q  s   .z+TestSystematic.test_binom.<locals>.binomialc                    r  r  r0   )rA   r  )r  r0   r1   rN     rO   z+TestSystematic.test_binom.<locals>.<lambda>r   r   r   r   rm   r  )r   r)   Zbinomr
   r!   r(   rK  r0   )r  r  r1   
test_binomn  s   


zTestSystematic.test_binomc                 C   (   t dd tdd t t gdd d S )Nc                 S   r  rH   )r)   eval_chebytr   rA   rB   r0   r0   r1   rN     r   z0TestSystematic.test_chebyt_int.<locals>.<lambda>c                 S   rs  rH   )r   chebytrg  r  r0   r0   r1   rN     rh  r3   r  r  rK  r0   r0   r1   test_chebyt_int     

zTestSystematic.test_chebyt_intFz'some cases in hyp2f1 not fully accurate)runreasonc                 C   s&   t tjdd tddt gdd d S )Nc                 S      t  ttj| |fi tS rH   )r   r   r   r  rg  r  r0   r0   r1   rN     r   z,TestSystematic.test_chebyt.<locals>.<lambda>e   '  rn  )r   r)   r  r
   rK  r0   r0   r1   test_chebyt  s   
zTestSystematic.test_chebytc                 C   r  )Nc                 S   r  rH   )r)   eval_chebyur   r  r0   r0   r1   rN     r   z0TestSystematic.test_chebyu_int.<locals>.<lambda>c                 S   rs  rH   )r   chebyurg  r  r0   r0   r1   rN     rh  r3   r  r  rK  r0   r0   r1   test_chebyu_int  r  zTestSystematic.test_chebyu_intc                 C   s"   t tjdd tddt g d S )Nc                 S   r  rH   )r   r   r   r  rg  r  r0   r0   r1   rN     r   z,TestSystematic.test_chebyu.<locals>.<lambda>r  r  )r   r)   r  r
   rK  r0   r0   r1   test_chebyu  s   zTestSystematic.test_chebyuc                 C   6   dd }t |tjt g t |tjtg dg d S )Nc                 S   rB  rP  r)   Zshichir   r0   r0   r1   chi  rT  z$TestSystematic.test_chi.<locals>.chigU@X   g   V@)r   r   r  r
   r   rL  r  r0   r0   r1   test_chi     zTestSystematic.test_chic                 C   8   dd }t |tjtttj dttjdgdd d S )Nc                 S   rB  rP  r  r  r0   r0   r1   r    rT  z,TestSystematic.test_chi_complex.<locals>.chirE  rF  rZ   r:   )r   r   r  r   r&   r!   r6  r  r0   r0   r1   test_chi_complex     
zTestSystematic.test_chi_complexc                 C   s"   dd }t |tjtddg d S )Nc                 S   rB  rP  r)   Zsicir   r0   r0   r1   ci  rT  z"TestSystematic.test_ci.<locals>.cirE  rF  )r   r   r  r
   rL  r  r0   r0   r1   test_ci  s
   
zTestSystematic.test_cic                 C   8   dd }t |tjttdtj tdtjgdd d S )Nc                 S   rB  rP  r  r  r0   r0   r1   r    rT  z*TestSystematic.test_ci_complex.<locals>.cirE  rF  r4  r:   )r   r   r  r   r&   r!   r6  r  r0   r0   r1   test_ci_complex  r  zTestSystematic.test_ci_complexc                 C   ,   t tj}tttjt gdd| d d S NFr   r  )	r!   r  r=   r  r   r   r   r  r
   rL  r  r0   r0   r1   
test_cospi  s
   
zTestSystematic.test_cospic                 C      t ttjt gddd d S )NFr9   r  )r   r   r   r  r   rK  r0   r0   r1   test_cospi_complex  s   

z!TestSystematic.test_cospi_complexc                 C   s"   t tjttjt gddd d S )NrZ   r3   r;   r   )r   r)   r   r   r   r
   rK  r0   r0   r1   test_digamma  s   

zTestSystematic.test_digammac                 C   s,   dd }t tjttjt gdd|d d S )Nc                 S   s$   t | jdk t | jdk @ ddS )Nr   gQ?FT)r!   whererK   r   r-  r  r0   r0   r1   param_filter  s   $z9TestSystematic.test_digamma_complex.<locals>.param_filterr9   r  r;   r   r  )r   r)   r   r   r   r   )rL  r  r0   r0   r1   test_digamma_complex  s   

z#TestSystematic.test_digamma_complexc                 C      t tjtjt gdd d S )Nr   r:   )r   r)   exp1r   e1r
   rK  r0   r0   r1   test_e1     
zTestSystematic.test_e1c                 C   s   t tjtjtttj dttjdgdd t tjtjt	dddd d d f tj
dtd	d
dtd	d
d f d   dd t tjtjt	dddd dd d S )NrE  rF  r  r:   r3      r   r   r   =   r   r   ir  y                )r   r)   r  r   r  r   r&   r!   r6  r#   r   r"   r   rK  r0   r0   r1   test_e1_complex  s,   
zTestSystematic.test_e1_complexc                 C   s   t tjdd ttttjj tttjjdg t tjdd t	ddddd	tj
gd
d ttttj
 tttj
 dk d S )Nc                 S       | dkrt | |  S t dS Nr   z1.0r   expm1mpfr   r0   r0   r1   rN     r   z,TestSystematic.test_exprel.<locals>.<lambda>r   c                 S   r  r  r  r   r0   r0   r1   rN     r   rZ   gW:r   g   mBgyCxDr  r:   )r   r)   Zexprelr
   r!   r   r  doubler   r(   r6  r   isinfrK  r0   r0   r1   test_exprel  s   .zTestSystematic.test_exprelc                 C   s.   t tjtjtttj dttjdg d S )N    c    cA)r   r)   r  r   r   r&   r!   r6  rK  r0   r0   r1   test_expm1_complex  s   z!TestSystematic.test_expm1_complexc                 C      t tjdd t gdd d S )Nc                 S   s   t | d S rP  r   r   r   r0   r0   r1   rN     rO   z3TestSystematic.test_log1p_complex.<locals>.<lambda><   r  )r   r)   log1pr   rK  r0   r0   r1   test_log1p_complex     
z!TestSystematic.test_log1p_complexc                 C   s   t tdd t gddd d S )Nc                 S   s   t | d |  S rP  r  r   r0   r0   r1   rN     rp  z-TestSystematic.test_log1pmx.<locals>.<lambda>r  r   )r   r;   )r   r   r
   rK  r0   r0   r1   test_log1pmx
  s   

zTestSystematic.test_log1pmxc                 C   r  )Nr  r:   )r   r)   r*   r   r'   r
   rK  r0   r0   r1   test_ei  s
   
zTestSystematic.test_eic                 C   s2   t tjtjtttj dttjdgdd d S )NrE  rF  r   r:   )	r   r)   r*   r   r'   r   r&   r!   r6  rK  r0   r0   r1   test_ei_complex  s
   
zTestSystematic.test_ei_complexc                 C   s   t tjtjtddg d S )Nr   rp   )r   r)   elliper   r
   rK  r0   r0   r1   test_ellipe     
zTestSystematic.test_ellipec                 C   s$   t tjtjtddtddg d S )NrH  rI  r   r  r   r)   Z	ellipeincr   r  r
   rK  r0   r0   r1   test_ellipeinc!  s   zTestSystematic.test_ellipeincc                 C      t tjtjt t g d S rH   r  rK  r0   r0   r1   test_ellipeinc_largephi&  r  z&TestSystematic.test_ellipeinc_largephic                 C   s    t tjtjtddt g d S NrH  rI  r   r)   	ellipkincr   Zellipfr
   rK  r0   r0   r1   test_ellipf+  s   zTestSystematic.test_ellipfc                 C   r  rH   r  rK  r0   r0   r1   test_ellipf_largephi0  r  z#TestSystematic.test_ellipf_largephic                 C   s:   t tjtjtddg t tjdd tddgdd d S )	Nr   r  c                 S   s   t d|  S rP  )r   r*  )r$  r0   r0   r1   rN   :  rO   z,TestSystematic.test_ellipk.<locals>.<lambda>g        )rq   r   r  )r   r)   r*  r   r
   Zellipkm1rK  r0   r0   r1   test_ellipk5  s   


zTestSystematic.test_ellipkc                 C   s.   dd }t tj|tddtddgdd d S )	Nc                 S      t d| |S rC  r   Zellippiphir$  r0   r0   r1   r  ?  rT  z0TestSystematic.test_ellipkinc.<locals>.ellipkincrH  rI  r   r  Tr  r   r)   r  r
   rL  r  r0   r0   r1   test_ellipkinc>  s   
zTestSystematic.test_ellipkincc                 C   s*   dd }t tj|t tddgdd d S )Nc                 S   r  rC  r  r	  r0   r0   r1   r  G  rT  z9TestSystematic.test_ellipkinc_largephi.<locals>.ellipkincr   r  Tr  r  r  r0   r0   r1   test_ellipkinc_largephiF  s   
z&TestSystematic.test_ellipkinc_largephic                 C   s2   dd }t dd |tddtddd	gd
d d S )Nc                 S   s   | dkrdS t jd| |dS )Nr   snr"  r   r(  r"  r0   r0   r1   r  O  s   z+TestSystematic.test_ellipfun_sn.<locals>.snc                 S   r  rC  r!  r"  r0   r0   r1   rN   Y  r   z1TestSystematic.test_ellipfun_sn.<locals>.<lambda>    .    .Ar   r    r   r4  r:   rU  )rL  r  r0   r0   r1   test_ellipfun_snN  s   

zTestSystematic.test_ellipfun_snc                 C   .   t dd dd tddtdddgd	d
 d S )Nc                 S   r  rP  r!  r"  r0   r0   r1   rN   `  r   z1TestSystematic.test_ellipfun_cn.<locals>.<lambda>c                 S      t jd| |dS )NZcnr"  r  r"  r0   r0   r1   rN   a  r   r  r  r   r    r   r4  r:   rU  rK  r0   r0   r1   test_ellipfun_cn^  
   
zTestSystematic.test_ellipfun_cnc                 C   r  )Nc                 S   r  r   r!  r"  r0   r0   r1   rN   g  r   z1TestSystematic.test_ellipfun_dn.<locals>.<lambda>c                 S   r  r'  r  r"  r0   r0   r1   rN   h  r   r  r  r   r    r   r4  r:   rU  rK  r0   r0   r1   test_ellipfun_dne  r  zTestSystematic.test_ellipfun_dnc                 C   s   t tjdd t g d S )Nc                 S   r\  rH   r   r   r  r0   r0   r1   rN   n     
 z)TestSystematic.test_erf.<locals>.<lambda>)r   r)   r   r
   rK  r0   r0   r1   test_erfl  s   zTestSystematic.test_erfc                 C   r  )Nc                 S   r\  rH   r  r  r0   r0   r1   rN   s  r  z1TestSystematic.test_erf_complex.<locals>.<lambda>r6   rn  )r   r)   r   r   rK  r0   r0   r1   r   q  r  zTestSystematic.test_erf_complexc                 C   "   t tjtdd t gdd d S )Nc                 S   r\  rH   r   r   r  r0   r0   r1   rN   x  r  z*TestSystematic.test_erfc.<locals>.<lambda>r9   r:   )r   r)   r   r   r
   rK  r0   r0   r1   	test_erfcv     

zTestSystematic.test_erfcc                 C   r  )Nc                 S   r\  rH   r  r  r0   r0   r1   rN   }  r  z2TestSystematic.test_erfc_complex.<locals>.<lambda>r6   rn  )r   r)   r   r   r   rK  r0   r0   r1   test_erfc_complex{  r  z TestSystematic.test_erfc_complexc                 C      t tjtjt gdd d S Nr6   rn  )r   r)   erfir   r
   rK  r0   r0   r1   	test_erfi  r  zTestSystematic.test_erfic                 C   r!  r"  )r   r)   r#  r   r   rK  r0   r0   r1   test_erfi_complex  r  z TestSystematic.test_erfi_complexc                 C   r  )Nc                 S   r\  rH   )r   ncdfr  r0   r0   r1   rN     r  z*TestSystematic.test_ndtr.<locals>.<lambda>r6   rn  )r   r)   ndtrr   r
   rK  r0   r0   r1   	test_ndtr  r  zTestSystematic.test_ndtrc                 C   s0   t tjdd ttddtdddgdd d S )Nc                 S   s   t |  td d S Ng       @)r   r   r!   sqrtr  r0   r0   r1   rN     r   z2TestSystematic.test_ndtr_complex.<locals>.<lambda>r  r   r   rn  )r   r)   r'  r   r&   rK  r0   r0   r1   test_ndtr_complex  s   
z TestSystematic.test_ndtr_complexc                 C   s&   t tjtdd t gdddd d S )Nc                 S   s   t t | S rH   )r   r   r&  r  r0   r0   r1   rN     r   z.TestSystematic.test_log_ndtr.<locals>.<lambda>iX  r  r9   rA   r   r;   )r   r)   log_ndtrr   r
   rK  r0   r0   r1   test_log_ndtr     

zTestSystematic.test_log_ndtrc                 C   s6   t tjtdd ttddtdddgdd	d
 d S )Nc                 S   s    t t |  td d S r)  )r   r   r   r!   r*  r  r0   r0   r1   rN     r   z6TestSystematic.test_log_ndtr_complex.<locals>.<lambda>r+  r  r  r7   r   r6   r  rA   r   )r   r)   r.  r   r   r&   rK  r0   r0   r1   test_log_ndtr_complex  s   


z$TestSystematic.test_log_ndtr_complexc                 C   s"   t dd tjtddgdd d S )Nc                 S   rB  )Nrt   )r)   Zeulerrn  r0   r0   r1   rN     rO   z.TestSystematic.test_eulernum.<locals>.<lambda>r    r  rn  )r   r   Zeulernumr   rK  r0   r0   r1   test_eulernum  s   
zTestSystematic.test_eulernumc                 C   s,   t tjtjtddtdtjgddd d S )Nr   r6   r9      r  )	r   r)   r@   r   r>   r   r
   r!   r6  rK  r0   r0   r1   test_expint  r  zTestSystematic.test_expintc                 C      dd }t |tjt g d S )Nc                 S   rB  rC  r)   Zfresnelr   r0   r0   r1   fresnels  rT  z.TestSystematic.test_fresnels.<locals>.fresnels)r   r   r8  r
   )rL  r8  r0   r0   r1   test_fresnels  
   zTestSystematic.test_fresnelsc                 C   r6  )Nc                 S   rB  rP  r7  r   r0   r0   r1   fresnelc  rT  z.TestSystematic.test_fresnelc.<locals>.fresnelc)r   r   r;  r
   )rL  r;  r0   r0   r1   test_fresnelc  r:  zTestSystematic.test_fresnelcc                 C   s   t tjttjt g d S rH   )r   r)   gammar   r   r
   rK  r0   r0   r1   
test_gamma  s   zTestSystematic.test_gammac                 C       t tjttjt gdd d S Nrk   r:   )r   r)   r=  r   r   r   rK  r0   r0   r1   test_gamma_complex     
z!TestSystematic.test_gamma_complexc                 C   0   t tjdd tddddtddgddd d S )	Nc                 S      t j| |ddS )NTr
  r   r  )r/   rp   r0   r0   r1   rN     r   z.TestSystematic.test_gammainc.<locals>.<lambda>r        @Finclusive_ar  r  )r   r)   r  r
   rK  r0   r0   r1   test_gammainc  
   
zTestSystematic.test_gammaincc                 C   rC  )	Nc                 S   rD  )NT)rq   r  rE  )r/   rq   r0   r0   r1   rN     r   z/TestSystematic.test_gammaincc.<locals>.<lambda>r   rF  FrG  r  r  )r   r)   Z	gammainccr
   rK  r0   r0   r1   test_gammaincc  rJ  zTestSystematic.test_gammainccc                 C   s"   dd }t tjt|t g d S )Nc                 S   s   t | jS rH   r   r   rK   r  r0   r0   r1   f  s   z&TestSystematic.test_gammaln.<locals>.f)r   r)   Zgammalnr   r
   )rL  rM  r0   r0   r1   test_gammaln  s   zTestSystematic.test_gammaln)r  c                 C   s(   t tjttjtddt t g d S r  )r   r)   eval_gegenbauerr   r   
gegenbauerr
   rK  r0   r0   r1   test_gegenbauer  s   zTestSystematic.test_gegenbauerc                 C   st   dd }dd }t |t|tddtddt gd	dd
dd t |t|tddt ttdddgdd
d d S )Nc                 S   s   t |dkr	tjS | dkrd}n| dkrd| | }nt| ||}t|dkrP|dk rPt|tt|krPt| |td |}t |tdk rPtd}t |d	krYtjS |S )
Nrw  r   r   r    r   rt   z1e-50z0.0\4@Iw)	r   r!   r  r   rP  r=   r   r  r6  rA   rq   rB   r-   r0   r0   r1   rP    s   (
z6TestSystematic.test_gegenbauer_int.<locals>.gegenbauerc                 S   s(   t t| ||}t|dkrtjS |S )NrR  )r)   rO  r   r   r!   r6  rS  r0   r0   r1   sc_gegenbauer  s   z9TestSystematic.test_gegenbauer_int.<locals>.sc_gegenbauerr   r7   g    eg    eAi@  Tr   )rA   r   r   r;   r  r   r  )r   r   r   r
   r   r!   r"   )rL  rP  rT  r0   r0   r1   test_gegenbauer_int  s   
z"TestSystematic.test_gegenbauer_intc                 C   s*   t dd ttjtddt t g d S )Nc                 S   s   t t| |j|S rH   )r)   rO  r   rK   rA   rq   rB   r0   r0   r1   rN     rh  z8TestSystematic.test_gegenbauer_complex.<locals>.<lambda>r   r7   )r   r   r   rP  r   r
   r   rK  r0   r0   r1   test_gegenbauer_complex     z&TestSystematic.test_gegenbauer_complexc                 C   s*   t dd ttjtddt t g d S )Nc                 S      t | j|j|S rH   )r)   rO  rK   rW  r0   r0   r1   rN     rp  z@TestSystematic.test_gegenbauer_complex_general.<locals>.<lambda>rH  rI  )r   r   r   rP  r
   r   rK  r0   r0   r1   test_gegenbauer_complex_general  rY  z.TestSystematic.test_gegenbauer_complex_generalc                 C   &   t tjtdd tddt g d S )Nc                 S   rs  rH   )r   hankel1rg  rM   rB   r0   r0   r1   rN     s    z-TestSystematic.test_hankel1.<locals>.<lambda>@x@xD)r   r)   r]  r   r
   rK  r0   r0   r1   test_hankel1  s   
zTestSystematic.test_hankel1c                 C   r\  )Nc                 S   rs  rH   )r   hankel2rg  r^  r0   r0   r1   rN   !  rh  z-TestSystematic.test_hankel2.<locals>.<lambda>r_  r`  )r   r)   rb  r   r
   rK  r0   r0   r1   test_hankel2  s   
zTestSystematic.test_hankel2z%issues at intermediately large ordersc                 C   s&   t dd ttjtddt g d S )Nc                 S   r  rH   )r)   Zeval_hermiter   r  r0   r0   r1   rN   &  r   z-TestSystematic.test_hermite.<locals>.<lambda>r   r  )r   r   r   Zhermiter   r
   rK  r0   r0   r1   test_hermite$  s   zTestSystematic.test_hermitec                    s:   t ddd ttj fddtddtdd	gd
d d S )Nr   i  r@  c                    s   t j| |fi  S rH   rV   rq   rB   ZKWr0   r1   rN   1  rh  z,TestSystematic.test_hyp0f1.<locals>.<lambda>r  r  r   g     j@r  rn  )r   r   r)   rJ   r
   rK  r0   rf  r1   test_hyp0f1,  s   

zTestSystematic.test_hyp0f1c              	   C   s8   t dd tdd tddttddtddg d S )Nc                 S   rG   rH   rI   )rq   r/   r0   r0   r1   rN   :  rO   z4TestSystematic.test_hyp0f1_complex.<locals>.<lambda>c                 S   rs  rH   )r   rJ   rg  re  r0   r0   r1   rN   ;  rh  r   r   irF   )r   r   r
   r   r&   rK  r0   r0   r1   test_hyp0f1_complex9  s   
z"TestSystematic.test_hyp0f1_complexc              	   C   s<   dd }t tj|tddtddddtddgddd	 d S )
Nc                 S   s*   zt | ||W S  ty   tj Y S w rH   )r   hyp1f1ZeroDivisionErrorr!   r6  r  r0   r0   r1   mpmath_hyp1f1B  s
   
z1TestSystematic.test_hyp1f1.<locals>.mpmath_hyp1f1r  r3   r    FrG  r   )rA   r  )r   r)   ri  r
   )rL  rk  r0   r0   r1   test_hyp1f1A  s   
zTestSystematic.test_hyp1f1c                 C   s8   t tdd tdd tddtddt gdd d S )Nc                 S   rZ  rH   )r)   ri  rK   r  r0   r0   r1   rN   R  rp  z4TestSystematic.test_hyp1f1_complex.<locals>.<lambda>c                 S      t j| ||fi tS rH   )r   ri  rg  r  r0   r0   r1   rN   S  ro  rH  rI  i  rn  )r   r   r   r
   r   rK  r0   r0   r1   test_hyp1f1_complexP  s
   

z"TestSystematic.test_hyp1f1_complexc                 C   s<   t dd tdd tddtddtddt gdd d S )Nc                 S   s   t | j|j|j|S rH   )r)   r|   rK   rq   rp   rz   rB   r0   r0   r1   rN   Z  ro  z4TestSystematic.test_hyp2f1_complex.<locals>.<lambda>c                 S      t j| |||fi tS rH   )r   r|   rg  ro  r0   r0   r1   rN   [  rY   g      Yg      Y@r   rn  r|  rK  r0   r0   r1   test_hyp2f1_complexW  s
   

z"TestSystematic.test_hyp2f1_complexc                 C   s&   t tjtdd t t t g d S )Nc                 S   rm  rH   )r   ro   rg  r  r0   r0   r1   rN   b  ro  z,TestSystematic.test_hyperu.<locals>.<lambda>)r   r)   ro   r   r
   rK  r0   r0   r1   test_hyperu_  s   
zTestSystematic.test_hyperuz:mpmath issue gh-342: unsupported operand mpz, long for powc                 C   s0   dd }t t|tddddtddgdd d S )	Nc                 S   s"   t || t |  t |  S rH   )r   powerr$   r=  re  r0   r0   r1   mp_igam_facg     "z1TestSystematic.test_igam_fac.<locals>.mp_igam_facr   g  ļBFrG  r   r:   )r   r   r
   )rL  rt  r0   r0   r1   test_igam_face  s   
zTestSystematic.test_igam_facc                 C   8   t tjtjtddg t tjtjtddgdd d S NrH  rI  rE  rF  rG  r:   )r   r)   Zj0r   r
   rK  r0   r0   r1   test_j0o  s   


zTestSystematic.test_j0c                 C   rw  rx  )r   r)   Zj1r   r
   rK  r0   r0   r1   test_j1}  s   


zTestSystematic.test_j1c                 C   sR   t tjtdd t t t t g t dd tdd t t t t g d S )Nc                 S   rp  rH   r   jacobirg  ro  r0   r0   r1   rN     rY   z,TestSystematic.test_jacobi.<locals>.<lambda>c                 S      t t| |||S rH   r)   eval_jacobir   )rA   rp   rz   rB   r0   r0   r1   rN     rh  c                 S   rp  rH   r{  ro  r0   r0   r1   rN     rY   )r   r)   r  r   r
   r   rK  r0   r0   r1   test_jacobi  s   

zTestSystematic.test_jacobic                    s:   dd  t dd  fddt t t t gddd d S )	Nc                 S   s   | dkrdS t | |||S )Nr   r   )r   r|  rA   rq   rp   rB   r0   r0   r1   r|    s   z.TestSystematic.test_jacobi_int.<locals>.jacobic                 S   r}  rH   r~  r  r0   r0   r1   rN     rh  z0TestSystematic.test_jacobi_int.<locals>.<lambda>c                    s   t  | |||fi tS rH   )r   rg  r  r|  r0   r1   rN     r    N  r3   r1  r   r   r
   rK  r0   r  r1   test_jacobi_int  s   

zTestSystematic.test_jacobi_intc                 C   s&   dd }t tj|tddgdd d S )Nc                 S   s*   | dkr	t  d S ttjd| fi tS )Nr   r5   )r   r   r   keirg  r   r0   r0   r1   r    s   
z$TestSystematic.test_kei.<locals>.keiꌠ9Y>)ꌠ9Y>)Fr  rn  )r   r)   r  r
   )rL  r  r0   r0   r1   test_kei  s
   
zTestSystematic.test_keic                 C   s&   t tjtdd tddgdd d S )Nc                 S   re  rC  )r   kerrg  r   r0   r0   r1   rN     rh  z)TestSystematic.test_ker.<locals>.<lambda>r  r  r  rn  )r   r)   r  r   r
   rK  r0   r0   r1   test_ker  r0  zTestSystematic.test_kerc                 C   s"   t ttjdd t t g d S )Nc                 S      t tj| |fi tS rH   r   r   Zlaguerrerg  r  r0   r0   r1   rN     rY   z.TestSystematic.test_laguerre.<locals>.<lambda>)r   r   r)   eval_laguerrer
   rK  r0   r0   r1   test_laguerre  s   

zTestSystematic.test_laguerrec                 C   s$   t dd dd t t gdd d S )Nc                 S   r  rH   )r)   r  r   r  r0   r0   r1   rN     r   z2TestSystematic.test_laguerre_int.<locals>.<lambda>c                 S   r  rH   r  r  r0   r0   r1   rN     rY   r  rn  r  rK  r0   r0   r1   test_laguerre_int  s   
z TestSystematic.test_laguerre_intzsee gh-3551 for bad pointsc                 C   s4   t dd dd ttj tjtddgddd d S )	Nc                 S      t | t|jS rH   )r)   r.  r   rK   rB   r  r0   r0   r1   rN     rp  z3TestSystematic.test_lambertw_real.<locals>.<lambda>c                 S   r  rH   )r   r.  r   rK   r  r0   r0   r1   rN     rp  r   r   r9   Fr;   r  )r   r   r!   r6  r   rK  r0   r0   r1   test_lambertw_real  s
   
z!TestSystematic.test_lambertw_realc                    sB   d}t d d fdd}t|tjtd|ddgd	d
 d S )NgGase@r    g  E@c                    s   t jddA |  d   | d  }|t jkr|t|  }n |  d   d| d   }|t|  }||9 }W d    |S W d    |S 1 sJw   Y  |S )Nr   )ZoverrE   )r!   r   r6  r   )rB   ZfacrQ   egr0   r1   r=    s   



z:TestSystematic.test_lanczos_sum_expg_scaled.<locals>.gammar   FrG  r9   r:   )r!   r$   r   r   r=  r
   )rL  Zmaxgammar=  r0   r  r1   test_lanczos_sum_expg_scaled  s   

z+TestSystematic.test_lanczos_sum_expg_scaledc                 C   r  rH   )r   r)   eval_legendrer   legendrer
   rK  r0   r0   r1   test_legendre  s   
zTestSystematic.test_legendrec              
   C   sL   t dd dd t t gdd t dd dd t ttdd	d
g d S )Nc                 S   r  rH   r)   r  r   r  r0   r0   r1   rN     r   z2TestSystematic.test_legendre_int.<locals>.<lambda>c                 S   r  rH   r   r   r  rg  r  r0   r0   r1   rN     rY   r  rn  c                 S   r  rH   r  r  r0   r0   r1   rN     r   c                 S   r  rH   r  r  r0   r0   r1   rN     rY   r  rU  rb   )r   r   r
   r   r!   r"   rK  r0   r0   r1   test_legendre_int  s   
z TestSystematic.test_legendre_intc                 C   sd   dd }dd }dd }t ||tddtddt g t ||tddtddtd	d
gdd d S )Nc                 S   sV   zt || |d d }W n ty   tj Y S w t|dkr)tjt|j }|S )Nr   rt   rt   )#v)	r)   Zlpmn
ValueErrorr!   r  r   r6  r  rK   rA   r$  r/   rM   r0   r0   r1   lpnm  s   
z(TestSystematic.test_legenp.<locals>.lpnmc                 S   s0   t || |}t|dkrtjt|j }|S )Nr  )r)   r   r   r!   r6  r  rK   r  r0   r0   r1   lpnm_2  s   z*TestSystematic.test_legenp.<locals>.lpnm_2c                 S   s   |dks|dkr&t | | kr&|dkr$| dk r|  d } tt|| S dS t|dk r/tjS t|dk r7dnd}ttj| |||d}t|dkrStj	t|j
 }|S )	Nr    rt   r   rj   r   ri   typer  )r   r   rs  r  r   r!   r  r   r   r6  rK   )rA   r$  r/   typrM   r0   r0   r1   r     s   
z*TestSystematic.test_legenp.<locals>.legenpr  r7   rt   r    r   rx  r  )rL  r  r  r   r0   r0   r1   test_legenp  s   

zTestSystematic.test_legenpc                 C      dd }dd }t g d}t g d}|d d d f d|d d d f    }t||tg dtg dt|gd	d
d d S )Nc                 S   :   zt j|j| j|ddd d W S  ty   tj Y S w )Nr   r  r   r  r)   ZclpmnrK   r  r!   r  rA   r$  r/   r0   r0   r1   clpnm  
    
z3TestSystematic.test_legenp_complex_2.<locals>.clpnmc                 S   4   t |dk r	tjS ttjt| jt|j|ddS Nrj   r   r  r   r!   r  r   r   r   r   rK   r  r0   r0   r1   r        "z4TestSystematic.test_legenp_complex_2.<locals>.legenp	rv   r   rD   r   rG  rE   r   rb   g     @@rH  rD   rE   g?r   rv   rt   r   r    r   r   r   r   rq  r!   r(   r   r   r   rL  r  r   rB   rP   r/   r0   r0   r1   test_legenp_complex_2     (
z$TestSystematic.test_legenp_complex_2c                 C   r  )Nc                 S   r  )Nri   r  r   r  r  r  r0   r0   r1   r  /  r  z3TestSystematic.test_legenp_complex_3.<locals>.clpnmc                 S   r  )Nrj   ri   r  r  r  r0   r0   r1   r   5  r  z4TestSystematic.test_legenp_complex_3.<locals>.legenpr  r  r   r  r   r   rq  r  r  r0   r0   r1   test_legenp_complex_3.  r  z$TestSystematic.test_legenp_complex_3z*apparently picks wrong function at |z| > 1c                 C   s4   dd }dd }t ||tddtddt g d S )Nc                 S   s   t || |d d S Nr   r  )r)   lqmnr  r0   r0   r1   lqnmH  s   z(TestSystematic.test_legenq.<locals>.lqnmc                 S   s(   t |dk r	tjS ttj| ||ddS r  )r   r!   r  r   r   legenqr  r0   r0   r1   r  K  s   z*TestSystematic.test_legenq.<locals>.legenqr   r7   r  rL  r  r  r0   r0   r1   test_legenqF  s   zTestSystematic.test_legenqc                 C   s8   dd }dd }t ||tddtddt gdd d S )Nc                 S   s"   t t|jt| j|d d S r  )r)   r  r   rK   r  r0   r0   r1   r  W  ru  z0TestSystematic.test_legenq_complex.<locals>.lqnmc                 S   r  r  )r   r!   r  r   r   r  r   rK   r  r0   r0   r1   r  Z  r  z2TestSystematic.test_legenq_complex.<locals>.legenqr   r7   rn  )r   r   r   r  r0   r0   r1   test_legenq_complexU  s   
z"TestSystematic.test_legenq_complexc                 C   s,   dd }dd }t t|t gdd|d d S )Nc                 S   s    t t | | k| dk@ ddS )Nr   FT)r!   r  floorr   r0   r0   r1   r  f  s    z0TestSystematic.test_lgam1p.<locals>.param_filterc                 S   s   t d|  jS rP  rL  r  r0   r0   r1   	mp_lgam1pj  s   z-TestSystematic.test_lgam1p.<locals>.mp_lgam1pr9   r7   r  )r   r   r
   )rL  r  r  r0   r0   r1   test_lgam1pe  s   

zTestSystematic.test_lgam1pc                 C   s&   dd }t tj|t gdddd d S )Nc                 S   s4   zt | }W |S  ty   ttjtj}Y |S w rH   )r   r   r  r&   r!   r  )r/   rQ   r0   r0   r1   mpmath_loggammat  s   z5TestSystematic.test_loggamma.<locals>.mpmath_loggammaFr   )r  Zdistinguish_nan_and_infr;   )r   r)   r   r   )rL  r  r0   r0   r1   test_loggammas  s   
zTestSystematic.test_loggammac                 C   s(   dd }t |tdd t t g d S )Nc                 S   r  rC  )r)   Zpbdvr^  r0   r0   r1   pcfd  r&  z&TestSystematic.test_pcfd.<locals>.pcfdc                 S   rs  rH   )r   r  rg  r^  r0   r0   r1   rN     rh  z*TestSystematic.test_pcfd.<locals>.<lambda>)r   r   r
   )rL  r  r0   r0   r1   	test_pcfd  s
   

zTestSystematic.test_pcfdzHit's not the same as the mpmath function --- maybe different definition?c                 C   s(   dd }t |dd t t gdd d S )Nc                 S   r  rC  )r)   Zpbvvr^  r0   r0   r1   pcfv  r&  z&TestSystematic.test_pcfv.<locals>.pcfvc                 S   r  rH   )r   r   r   r  rg  r^  r0   r0   r1   rN     r   z*TestSystematic.test_pcfv.<locals>.<lambda>r  rn  rU  )rL  r  r0   r0   r1   	test_pcfv  s
   
zTestSystematic.test_pcfvc                 C   sb   dd }dd }dd }t |tjtddtddgd	d
d t ||tddtddgdd
d d S )Nc                 S   r  rC  r)   Zpbware  r0   r0   r1   pcfw  r&  z&TestSystematic.test_pcfw.<locals>.pcfwc                 S   r  rP  r  re  r0   r0   r1   dpcfw  r&  z'TestSystematic.test_pcfw.<locals>.dpcfwc                 S   s   t t j| |fdS )Nr8   )r   diffr  re  r0   r0   r1   mpmath_dpcfw  r   z.TestSystematic.test_pcfw.<locals>.mpmath_dpcfwr`   ra   g:0yU>r7   rq  g&.!>)r   r   r  r
   )rL  r  r  r  r0   r0   r1   	test_pcfw  s   
zTestSystematic.test_pcfwzCissues at large arguments (atol OK, rtol not) and <eps-close to z=0c                 C   s*   t tjt ttjtddt g d S )Nr   r  )r   r)   Z	polygammar   r   r   r   r
   rK  r0   r0   r1   test_polygamma  s   zTestSystematic.test_polygammac                 C   s&   t tjtjtdtjgdddd d S )Nir  FT)rA   r  r   )r   r)   r   r   r
   r!   r6  rK  r0   r0   r1   test_rgamma  s   
zTestSystematic.test_rgammac                 C   r?  r@  )r   r)   r   r   r   r   rK  r0   r0   r1   test_rgamma_complex  rB  z"TestSystematic.test_rgamma_complexzNsee gh-3551 for bad points on 32 bit systems and gh-8095 for another bad point)r  c                 C   sD   t tjt dkrtj}ndd }ttj|t	 t	 gdd d S )Nrs   c                 S   sN   t | | t| | kr!t | | dkr!t| } t| | |  }t| |S rC  )r=   r   r   r  rf)rq   r$  r0   r0   r1   mppoch  s   (
z&TestSystematic.test_rf.<locals>.mppochr   r  )
r   parser   r   Versionr  r   r)   Zpochr
   )rL  r  r0   r0   r1   test_rf  s   	

zTestSystematic.test_rfc                 C   r  r  )	r!   r  r=   r  r   r   r   r  r
   r  r0   r0   r1   
test_sinpi  s   
zTestSystematic.test_sinpic                 C   r  )NFg+=r  )r   r   r   r  r   rK  r0   r0   r1   test_sinpi_complex  s   

z!TestSystematic.test_sinpi_complexc                 C   r  )Nc                 S   rB  rC  r  r   r0   r0   r1   shi  rT  z$TestSystematic.test_shi.<locals>.shir  )r   r   r  r
   r   rL  r  r0   r0   r1   test_shi  r  zTestSystematic.test_shic                 C   r  )Nc                 S   rB  rC  r  r  r0   r0   r1   r    rT  z,TestSystematic.test_shi_complex.<locals>.shirE  rF  rZ   r:   )r   r   r  r   r&   r!   r6  r  r0   r0   r1   test_shi_complex  r  zTestSystematic.test_shi_complexc                 C   r6  )Nc                 S   rB  rC  r  r   r0   r0   r1   si  rT  z"TestSystematic.test_si.<locals>.si)r   r   r  r
   rL  r  r0   r0   r1   test_si  s   zTestSystematic.test_sic                 C   r  )Nc                 S   rB  rC  r  r  r0   r0   r1   r    rT  z*TestSystematic.test_si_complex.<locals>.sirE  rF  rZ   r:   )r   r   r  r   r&   r!   r6  r  r0   r0   r1   test_si_complex  r  zTestSystematic.test_si_complexc                 C   s,   dd }t tjt|tdtjgdd d S )Nc                 S      t dd|  S r  r   r  r   r0   r0   r1   dilog  r&  z)TestSystematic.test_spence.<locals>.dilogr   r   r:   )r   r)   r  r   r
   r!   r6  rL  r  r0   r0   r1   test_spence  s
   
zTestSystematic.test_spencec                 C   s&   dd }t tjt|t gdd d S )Nc                 S   r  r  r  r  r0   r0   r1   r     r&  z1TestSystematic.test_spence_complex.<locals>.dilogr   r:   )r   r)   r  r   r   r  r0   r0   r1   test_spence_complex  s
   
z"TestSystematic.test_spence_complexc              
   C   sJ   dd }t |tjtddtddtdtdtddt dgddd	d
 d S )Nc                 S   s   || krt jS t|| ||S rH   )r!   r  r)   Zsph_harm)lr$  r   r
  r0   r0   r1   	spherharm  s   z0TestSystematic.test_spherharm.<locals>.spherharmr   r7   r   r   r4  ip  rS   )rm   rA   r   )r   r   r  r   r
   r   )rL  r  r0   r0   r1   test_spherharm  s   
zTestSystematic.test_spherharmc                 C   s,   t tjttjtddtddgdd d S )N     rF  r   &.>r:   )r   r)   Zstruver   r   Zstruvehr
   rK  r0   r0   r1   test_struveh  s
   
zTestSystematic.test_struvehc                 C   s4   dd }t tjt|tddtddgddd d S )	Nc                 S   s\   | dk r(||  k r(t | dkr(tjj}zdtj_t| |W |tj_S |tj_w t| |S )Nr   r  r  )r   r   r   r   Zstruvel)rM   r/   r   r0   r0   r1   
mp_struvel  s   z/TestSystematic.test_struvel.<locals>.mp_struvelr  rF  r   r  Tr   )r   r)   Z	modstruver   r
   )rL  r  r0   r0   r1   test_struvel  s   
zTestSystematic.test_struvelc                 C   s*   dd }t tj|tddgdddd d S )	Nc                 S   s   t t | t dS )Nz-0.5)r   r.  r$   r  r   r0   r0   r1   mpmath_wrightomega_real+  s   zETestSystematic.test_wrightomega_real.<locals>.mpmath_wrightomega_realrw   gPKDg+<r   F)r;   rm   r  )r   r)   r8  r
   )rL  r  r0   r0   r1   test_wrightomega_real*  s   

z$TestSystematic.test_wrightomega_realc                 C   s    t tjdd t gddd d S )Nc                 S   s
   t | dS )Nr0  )r/  r  r0   r0   r1   rN   <  r  z1TestSystematic.test_wrightomega.<locals>.<lambda>r   Fr  )r   r)   r8  r   rK  r0   r0   r1   test_wrightomega:  s   

zTestSystematic.test_wrightomegac                 C   s.   t tjttjtddddtdddg d S )Nr        _BF)rq   rp   rH  r   rq   rH  )r   r)   zetar   r   r
   rK  r0   r0   r1   test_hurwitz_zeta?  s   
z TestSystematic.test_hurwitz_zetac                 C   s$   t tjdd tddgddd d S )Nc                 S   s   | dkr	t | S t jS rP  r   r  r6  r   r0   r0   r1   rN   H  rY   z2TestSystematic.test_riemann_zeta.<locals>.<lambda>r  r7   Frk   r  )r   r)   r  r
   rK  r0   r0   r1   test_riemann_zetaE  s   

z TestSystematic.test_riemann_zetac                 C   s&   t tjdd tddgdddd d S )	Nc                 S   s   | dkrt | d S t jS rP  r  r   r0   r0   r1   rN   P  s   z+TestSystematic.test_zetac.<locals>.<lambda>r  r7   F-   rk   )r  r   r;   )r   r)   Zzetacr
   rK  r0   r0   r1   
test_zetacN  s
   

zTestSystematic.test_zetacc                 C   4   dd }t tjt|tdddt gdddd	 d S )
Nc                 S   s>   t j| } t j|}|dkrt j| S t j| || S rC  r   r   r  r   Zpowm1)rB   lmbdar0   r0   r1   	mp_boxcoxW  s
   z-TestSystematic.test_boxcox.<locals>.mp_boxcoxr   Fr  r6   r  r9   r-  )r   r)   Zboxcoxr   r
   )rL  r  r0   r0   r1   test_boxcoxU  s   
zTestSystematic.test_boxcoxc                 C   r  )
Nc                 S   sR   t j| } t j|}t jd}|dkrt j||  S t j||  || S r   r  )rB   r  oner0   r0   r1   mp_boxcox1ph  s   z1TestSystematic.test_boxcox1p.<locals>.mp_boxcox1prt   Fr  r6   r  r9   r-  )r   r)   Zboxcox1pr   r
   )rL  r  r0   r0   r1   test_boxcox1pf  s   	
zTestSystematic.test_boxcox1pc                 C   4   dd }t dd t|tddtddgd	d
 d S )Nc                 S   L   t |}t | t dd  |t d| t j  }|jdkr$|jS |S Nr    r   r   r   	mpmathifyr  r  r*  r   r-  rK   rA   r/   argoutr0   r0   r1   mp_spherical_jny     

z9TestSystematic.test_spherical_jn.<locals>.mp_spherical_jnc                 S   r  rH   )r)   spherical_jnr   rA   r/   r0   r0   r1   rN     r   z2TestSystematic.test_spherical_jn.<locals>.<lambda>r   r6   rE  rF  r  r  r  rL  r  r0   r0   r1   test_spherical_jnx     	
z TestSystematic.test_spherical_jnc                 C   ,   dd }t dd t|tddt g d S )Nc                 S   r  r  r  r	  r0   r0   r1   r    r  zATestSystematic.test_spherical_jn_complex.<locals>.mp_spherical_jnc                 S      t t| j|S rH   )r)   r  r   rK   r  r0   r0   r1   rN     rp  z:TestSystematic.test_spherical_jn_complex.<locals>.<lambda>r   r6   r   r   r   r   r  r0   r0   r1   test_spherical_jn_complex  
   	z(TestSystematic.test_spherical_jn_complexc                 C   r  )Nc                 S   r  r  r   r  r  r  r*  r   r-  rK   r	  r0   r0   r1   mp_spherical_yn  r  z9TestSystematic.test_spherical_yn.<locals>.mp_spherical_ync                 S   r  rH   )r)   spherical_ynr   r  r0   r0   r1   rN     r   z2TestSystematic.test_spherical_yn.<locals>.<lambda>r   r6   g    _r  r7   r  r  rL  r  r0   r0   r1   test_spherical_yn  r  z TestSystematic.test_spherical_ync                 C   r  )Nc                 S   r  r  r  r	  r0   r0   r1   r    r  zATestSystematic.test_spherical_yn_complex.<locals>.mp_spherical_ync                 S   r  rH   )r)   r  r   rK   r  r0   r0   r1   rN     rp  z:TestSystematic.test_spherical_yn_complex.<locals>.<lambda>r   r6   r  r  r0   r0   r1   test_spherical_yn_complex  r  z(TestSystematic.test_spherical_yn_complexc                 C   s2   dd }t dd t|tddt gddd d S )	Nc                 S   r  r  r   r  ru  r  r*  r   r-  rK   r	  r0   r0   r1   mp_spherical_in  r  z9TestSystematic.test_spherical_in.<locals>.mp_spherical_inc                 S   r  rH   )r)   spherical_inr   r  r0   r0   r1   rN     r   z2TestSystematic.test_spherical_in.<locals>.<lambda>r   r6   g訰6r  r  rL  r  r0   r0   r1   test_spherical_in  s   	
z TestSystematic.test_spherical_inc                 C   r  )Nc                 S   r  r  r  r	  r0   r0   r1   r    r  zATestSystematic.test_spherical_in_complex.<locals>.mp_spherical_inc                 S   r  rH   )r)   r   r   rK   r  r0   r0   r1   rN     rp  z:TestSystematic.test_spherical_in_complex.<locals>.<lambda>r   r6   r  r!  r0   r0   r1   test_spherical_in_complex  r  z(TestSystematic.test_spherical_in_complexc                 C   s0   dd }t dd t|tddt gdd d S )	Nc                 S   sN   t | t dd  |t t jdt |   }t |jdkr%|jS |S r  )r   r  r  r*  r   r  r-  rK   )rA   r/   r  r0   r0   r1   mp_spherical_kn  s   z9TestSystematic.test_spherical_kn.<locals>.mp_spherical_knc                 S   r  rH   )r)   spherical_knr   r  r0   r0   r1   rN     r   z2TestSystematic.test_spherical_kn.<locals>.<lambda>r   rS   r7   r  r  rL  r$  r0   r0   r1   test_spherical_kn  s   
z TestSystematic.test_spherical_knz.Accuracy issues near z = -1 inherited from kv.c                 C   s0   dd }t dd t|tddt gdd d S )Nc                 S   r  r  )r   r  r  r  r*  r   r-  rK   r	  r0   r0   r1   r$    r  zATestSystematic.test_spherical_kn_complex.<locals>.mp_spherical_knc                 S   r  rH   )r)   r%  r   rK   r  r0   r0   r1   rN     rp  z:TestSystematic.test_spherical_kn_complex.<locals>.<lambda>r   r6   r  r  r&  r0   r0   r1   test_spherical_kn_complex  s   	
z(TestSystematic.test_spherical_kn_complexN)__name__
__module____qualname__rM  rN  rV  rZ  r_  r`  rb  rc  ri  rl  rr  rz  r}  r  r  r  r  r  r  r  r  r   r  r  r  pytestmarkZxfailr  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/  r2  r3  r5  r9  r<  r>  rA  rI  rK  rN  rQ  rV  rX  r   r[  ra  rc  rd  rg  rh  rl  rn  rq  rr  Zxfail_on_32bitrv  ry  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  r   r  r  r  r  r  r"  r#  r'  r(  r0   r0   r0   r1   rA    sD   





		
	
0







	






3






		
		rA  )J__doc__numpyr!   Znumpy.testingr   r   r   r,  r   Z
scipy._libr   Zscipy.specialZspecialr)   Zscipy.special._testutilsr   r   r   r	   Zscipy.special._mptestutilsr
   r   r   r   r   r   r   r   r   r   Zscipy.special._ufuncsr   r   r   r   r   r   r   ImportErrorr2   rC   rR   r_   rr   r   r   r   r   r-  Zslowr   r   r   r   r   r   r   r   r  r  r	  r  r  r  r  r+  r/  r:  r<  r>  r?  r   rg  rA  r0   r0   r0   r1   <module>   s    0 










7
&






