o
    Eb9%                    @   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 ]$}t ddt j dD ]}|t d|  }| |tt|f qq	t j	| t j
d} ttj| dd  d S )	Ni   
   r                    ?Zdtype   )nplogspacelinspacer   expappendcomplexr   eiarrayZcomplex_r   scexpicheck)datasetrpz r0   A/usr/lib/python3/dist-packages/scipy/special/tests/test_mpmath.pytest_expi_complex#   s   r2   z0.19c                  C   s   g } dD ]/}t dddD ]%}td | ||tt||f W d    n1 s-w   Y  qqt | } tt	j
| dddd	  d S )
N)2   3   r         d   r   r    r   vIh%<=rtol)r!   r"   r   workdpsr%   floatexpintasarrayr   r)   expnr+   )r,   nxr0   r0   r1   test_expn_large_n3   s   
rC   c                  C   s   g } g d}|D ]7}|D ]2}|D ]-}|d|  }t d tt ||}W d    n1 s0w   Y  | |||f qqqt| } tdd | dddd	  d S )
N)g     Xg      #            ?g      #@g     X@r   x   c                 S      t | j|S Nr)   hyp0f1realvr/   r0   r0   r1   <lambda>U       z$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=   )ZvvafZ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    ""
rp   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   rr   ffffff?)r   rt   rs   )r   r    gffffffr5   )repeatc                 S   sD   g | ]\}}}}||krt ||kr|d k r|dkr||||fqS )r   ru   )round)rW   ro   rn   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   rg   绽|=r:   )list	itertoolsproductdictr!   r(   float_r   r)   rz   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   rg   r   )UUUUUU?gUUUUUU?g?g      ?)      ?rE   g      ?gX<ݚ?)r   rt   rg   )r   r   rt   rg   )r   rb   rb   rg   r   )gx&?rr   r^   g333333?)r   r   r   +?)r   r   r   rr   )r   rg   r_   Gz?)rd   rD   rg   r   )r   re   g      
r   )g*4]92@g|O%@gCu?)  ra   r   )r   r         %@r   )rr   r   r          ?)rr   r   r    rc   )r      r_   r   )r   r   r_   rc   )rE   g     prd   gm˟?c                 S   s    g | ]}|t tj| f qS r0   ry   r{   r0   r0   r1   rX           z0test_hyp2f1_real_some_points.<locals>.<listcomp>r   ignoreZinvalidr~   r5   r   r:   )r!   r(   r   errstater   r)   rz   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   ra   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   rz   r{   r   r0   r1   rX         * z-test_hyp2f1_some_points_2.<locals>.<listcomp>r   r~   r5   r   r:   )r!   r(   r   r   r)   rz   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?r_   r   )g      rr   r    g@)r   r   r_   gffffff4@)r   g)\(Gzr   g333333?gffffff?rd   r   r   r   r   r~   r5   &.>Tr;   ignore_inf_sign)r=   r   rz   	Exceptionr%   r!   r(   r   r   r   r)   r+   )r,   ro   rn   rx   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  r_     rd   r   r    r   rg   rr   r   r5   r~   r   r:   )r!   zerosr   randomseedZparetoZrandZrandintr   __version__absmaxr=   rz   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_precZx1Zy1Zx2Z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    rr   rt   g333333?g333333gr   r   rg      r_   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   4  r   ztest_lpmv.<locals>.<listcomp>r   c                 S   s   t | t||S rH   )r)   lpmvr[   r   )r   r   rB   r0   r0   r1   evf7     ztest_lpmv.<locals>.evfr   r   rf   r   +=rj   )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   rr   r    r   rE   gffffffr   g33333Yg3333r     c                 S   s   t t| |S rH   )r=   r   betaro   rn   r0   r0   r1   rN   U      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"   rl   r(   Zbroadcast_arraysreshapeTr   r   r   r   r	   r)   r   Zbetaln)rn   ro   abr   r   r0   r0   r1   	test_betaB  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   r`   r   r    c                 S      g | ]}|t t|fqS r0   r&   r   loggammarW   Zz0r0   r0   r1   rX   w      z3test_loggamma_taylor_transition.<locals>.<listcomp>vIh%,=r:   )LOGGAMMA_TAYLOR_RADIUSr!   r(   r#   r   r   r$   r   flattenr   r)   r   r+   r-   thetadzr/   r,   r0   r0   r1   test_loggamma_taylor_transitionl  s   
r   c                  C   s   t dt td} t ddt j d}t | |\} }| t d|  }t jd| d| f 	 }dd	 |D }t 
|}ttj|ddd
d  d S )Nir   r   r   r`   r   r    c                 S   r   r0   r   r   r0   r0   r1   rX     r   z(test_loggamma_taylor.<locals>.<listcomp>r   r:   )r!   r"   Zlog10r   r#   r   r   r$   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 )Nrr   rg   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   rl   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 )Nrd   rD   gQοrr   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   r_   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 )Nr`   rE   r   r3   r7   c              
   S   s*   g | ]\}}||t tj||d dfqS )Trn   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smallro   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   rd   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   Zouterr$   r   r?   r   r)   r
  r+   )r-   r   r/   r,   r0   r  r1   test_spence_circle  s   r  c                  C   s   t tj} t jt ddd dt dddf }| }t ||\}}|d|  }t ddd	ddd}|t 
|f|j   }t d	d
 |D }tt|ddd|  d  d S )Nr   r   rg   r   r7   r    rr   c                 S   r   r0   )r&   r   sinpir   r0   r0   r1   rX         z$test_sinpi_zeros.<locals>.<listcomp>r   r:   )r!   finfor=   epsr   r"   r   r   rl   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   rg   r   r  r7   r    rE   rr   c                 S   r   r0   )r&   r   cospir   r0   r0   r1   rX   +  r  z$test_cospi_zeros.<locals>.<listcomp>r   r:   )r!   r  r=   r  r   r"   r   r   rl   r   r   r   r   r?   r   r   r+   r  r0   r0   r1   test_cospi_zeros"  s   &
r  c            	   	   C   s   dd } dd }t ddd}t jt dd	d
 dt d	dd
f }g }|D ]}tt|}|D ]}|| }||||||f q1q&t |}t	| |dddd
  d S )Nc                 S      t | |d S Nr   r)   Zellipjumr0   r0   r1   dn7     z"test_dn_quarter_period.<locals>.dnc                 S   s   t tjd| |dS Nr  r  )r=   r   ellipfunr  r0   r0   r1   	mpmath_dn:  r   z)test_dn_quarter_period.<locals>.mpmath_dnr   r    r`   rr   r   r   r8   r   r   r:   )r!   r#   r   r"   r=   r   ellipkr%   r?   r   r+   )	r  r   r  Zdur,   Zm0Zu0Zdu0r.   r0   r0   r1   test_dn_quarter_period5  s   &
r"  c                 C   sh   t |% t | } t | jt j dt j  }t t | |}W d    |S 1 s-w   Y  |S r  )r   r<   ZmpcZceilimagr   lambertwr$   )r/   r   ZunwindrQ   r0   r0   r1   _mpmath_wrightomegaN  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   rr   r   c                 S      g | ]}|t t|d fqS r&  r&   r%  r   r0   r0   r1   rX   g  r  z+test_wrightomega_branch.<locals>.<listcomp>r    :0yE>r:   )r!   r"   Z	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_branchV  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 )
Nrt   r    r   r   c                 S   r'  r(  r)  r   r0   r0   r1   rX   v  r  z,test_wrightomega_region1.<locals>.<listcomp>r   rh   r:   
r!   r#   r   r   r   r?   r   r)   r-  r+   r   r0   r0   r1   test_wrightomega_region1m     
r1  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 )
Nrt   r    rr   r   c                 S   r'  r(  r)  r   r0   r0   r1   rX     r  z,test_wrightomega_region2.<locals>.<listcomp>r   rh   r:   r0  r   r0   r0   r1   test_wrightomega_region2|  r2  r3  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 )
Nrr   r    r&  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   
r4  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   r7  r8  r9  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   r7  r8  r9  r	  r0   r0   r1   rN     rO   z4TestSystematic.test_airyai_complex.<locals>.<lambda>)r   r   r?  r   r@  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   r7  Nr    r9  r	  r0   r0   r1   rN     rO   z2TestSystematic.test_airyai_prime.<locals>.<lambda>c                 S      t j| ddS Nr    )Z
derivativer   r?  r	  r0   r0   r1   rN        r:  r;  r<  r:   c                 S   r7  rE  r9  r	  r0   r0   r1   rN     rO   c                 S   rF  rG  rH  r	  r0   r0   r1   rN     rI  r=  r>  r   r
   r@  r0   r0   r1   test_airyai_prime     

z TestSystematic.test_airyai_primec                 C      t dd dd t g d S )Nc                 S   r7  rE  r9  r	  r0   r0   r1   rN     rO   z:TestSystematic.test_airyai_prime_complex.<locals>.<lambda>c                 S   rF  rG  rH  r	  r0   r0   r1   rN     rI  r   r   r@  r0   r0   r1   test_airyai_prime_complex     z(TestSystematic.test_airyai_prime_complexc                 C   rD  )Nc                 S   r7  r  r9  r	  r0   r0   r1   rN     rO   z,TestSystematic.test_airybi.<locals>.<lambda>c                 S   
   t | S rH   r   Zairybir	  r0   r0   r1   rN        
r:  r;  r<  r:   c                 S   r7  r  r9  r	  r0   r0   r1   rN     rO   c                 S   rQ  rH   rR  r	  r0   r0   r1   rN     rS  r=  r>  rJ  r@  r0   r0   r1   test_airybi  rL  zTestSystematic.test_airybic                 C   rM  )Nc                 S   r7  r  r9  r	  r0   r0   r1   rN     rO   z4TestSystematic.test_airybi_complex.<locals>.<lambda>c                 S   rQ  rH   rR  r	  r0   r0   r1   rN     rS  rN  r@  r0   r0   r1   test_airybi_complex  rP  z"TestSystematic.test_airybi_complexc                 C   rD  )Nc                 S   r7  Nrg   r9  r	  r0   r0   r1   rN     rO   z2TestSystematic.test_airybi_prime.<locals>.<lambda>c                 S   rF  rG  rR  r	  r0   r0   r1   rN     rI  r:  r;  r<  r:   c                 S   r7  rV  r9  r	  r0   r0   r1   rN     rO   c                 S   rF  rG  rR  r	  r0   r0   r1   rN     rI  r=  r>  rJ  r@  r0   r0   r1   test_airybi_prime  rL  z TestSystematic.test_airybi_primec                 C   rM  )Nc                 S   r7  rV  r9  r	  r0   r0   r1   rN     rO   z:TestSystematic.test_airybi_prime_complex.<locals>.<lambda>c                 S   rF  rG  rR  r	  r0   r0   r1   rN     rI  rN  r@  r0   r0   r1   test_airybi_prime_complex  rP  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 r8  )r   beiHYPERKWr	  r0   r0   r1   rN         z)TestSystematic.test_bei.<locals>.<lambda>r=  r>  )r   r)   r[  r   r
   r@  r0   r0   r1   test_bei     

zTestSystematic.test_beic                 C   rY  )Nc                 S   rZ  r8  )r   berr\  r	  r0   r0   r1   rN     r]  z)TestSystematic.test_ber.<locals>.<lambda>r=  r>  )r   r)   r`  r   r
   r@  r0   r0   r1   test_ber  r_  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   rb  r   rc  r0   r0   r1   rN         r   i2  r   r;   rA   )r   r   r@  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   besselir\  rL   r0   r0   r1   rN     r]  z-TestSystematic.test_besseli.<locals>.<lambda>}Ô%I}Ô%ITgJDrk   )r   r)   ivr   r
   r@  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)   rn  rK   rL   r0   r0   r1   rN     rO   z5TestSystematic.test_besseli_complex.<locals>.<lambda>c                 S   rh  rH   ri  rL   r0   r0   r1   rN     r]  rk  rl  r   r   r
   r   r@  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   rh  rH   r   besseljr\  rL   r0   r0   r1   rN      r]  z-TestSystematic.test_besselj.<locals>.<lambda>rk  rl  r=  r>  Tr   c                 S   rh  rH   rt  rL   r0   r0   r1   rN     r]  r:  r;  r<  )r   r;   )r   r)   jvr   r
   r@  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)   rw  rK   rL   r0   r0   r1   rN     rO   z5TestSystematic.test_besselj_complex.<locals>.<lambda>c                 S   rh  rH   rt  rL   r0   r0   r1   rN     r]  rq  r@  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!   r+  r@  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 rz  )	r   r)   knr   r~  r   r
   r!   r+  r@  r0   r0   r1   test_besselk_int  r  zTestSystematic.test_besselk_intc                 C   rp  )Nc                 S   rG   rH   )r)   r}  rK   rL   r0   r0   r1   rN     rO   z5TestSystematic.test_besselk_complex.<locals>.<lambda>c                 S   rh  rH   )r   r~  r\  rL   r0   r0   r1   rN     r]  rk  rl  rq  r@  r0   r0   r1   test_besselk_complex  rs  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   besselyr\  r   r!   r+  signnanrM   rB   r-   r0   r0   r1   	mpbessely"  s   z.TestSystematic.test_bessely.<locals>.mpbesselyrk  rl  r:  r;    rc  )r   r)   yvr   r
   rA  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  r\  r   r!   r   r+  r  r  r0   r0   r1   r  1  s   
z6TestSystematic.test_bessely_complex.<locals>.mpbesselyc                 S   rG   rH   )r)   r  rK   rL   r0   r0   r1   rN   8  rO   z5TestSystematic.test_bessely_complex.<locals>.<lambda>i:  rc  rq  r  r0   r0   r1   test_bessely_complex0  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 r8  )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   D  r   z1TestSystematic.test_bessely_int.<locals>.<lambda>ru     r:  r;  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   )ro   rn   nonzero
bad_pointsr0   r1   r   K  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   rk   F)r   r)   r   r
   r!   r(   r@  r0   )r  r   r1   r   H  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ro   rn   rB   r0   r0   r1   rN   i  r]  z-TestSystematic.test_betainc.<locals>.<lambda>)r   r)   r  r   r   r
   r@  r0   r0   r1   test_betaincg  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 )Nr;  r    rh   )r   r!   r  r=   rw   r%   r   binomial)rA   kr  r  r0   r1   r  o  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   rk   r  )r   r)   Zbinomr
   r!   r(   r@  r0   )r  r  r1   
test_binoml  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   rh  rH   )r   chebytr\  r  r0   r0   r1   rN     r]  r3   r  r  r@  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  r\  r  r0   r0   r1   rN     r   z,TestSystematic.test_chebyt.<locals>.<lambda>e   '  rc  )r   r)   r  r
   r@  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   rh  rH   )r   chebyur\  r  r0   r0   r1   rN     r]  r3   r  r  r@  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  r\  r  r0   r0   r1   rN     r   z,TestSystematic.test_chebyu.<locals>.<lambda>r  r  )r   r)   r  r
   r@  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   r7  rE  r)   Zshichir   r0   r0   r1   chi  rI  z$TestSystematic.test_chi.<locals>.chigU@X   g   V@)r   r   r  r
   r   rA  r  r0   r0   r1   test_chi     zTestSystematic.test_chic                 C   8   dd }t |tjtttj dttjdgdd d S )Nc                 S   r7  rE  r  r	  r0   r0   r1   r    rI  z,TestSystematic.test_chi_complex.<locals>.chir:  r;  rZ   r:   )r   r   r  r   r&   r!   r+  r  r0   r0   r1   test_chi_complex     
zTestSystematic.test_chi_complexc                 C   s"   dd }t |tjtddg d S )Nc                 S   r7  rE  r)   Zsicir   r0   r0   r1   ci  rI  z"TestSystematic.test_ci.<locals>.cir:  r;  )r   r   r  r
   rA  r  r0   r0   r1   test_ci  s
   
zTestSystematic.test_cic                 C   8   dd }t |tjttdtj tdtjgdd d S )Nc                 S   r7  rE  r  r	  r0   r0   r1   r    rI  z*TestSystematic.test_ci_complex.<locals>.cir:  r;  r*  r:   )r   r   r  r   r&   r!   r+  r  r0   r0   r1   test_ci_complex  r  zTestSystematic.test_ci_complexc                 C   (   t tj}tttjt gd|d d S NFr{  )	r!   r  r=   r  r   r   r   r  r
   rA  r  r0   r0   r1   
test_cospi  s
   

zTestSystematic.test_cospic                 C      t ttjt gddd d S )NFr9   r{  )r   r   r   r  r   r@  r0   r0   r1   test_cospi_complex  s   

z!TestSystematic.test_cospi_complexc                 C   s"   t tjttjt gddd d S )NrZ   r3   r;   r   )r   r)   r   r   r   r
   r@  r0   r0   r1   test_digamma  s   

zTestSystematic.test_digammac                 C   s,   dd }t tjttjt gdd|d d S )Nc                 S   s$   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   )rA  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
   r@  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 )Nr:  r;  r  r:   r3      r   r   r   =   r   r   ir  y                )r   r)   r  r   r  r   r&   r!   r+  r#   r   r"   r   r@  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  Zdoubler   r(   r+  r   Zisinfr@  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!   r+  r@  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 rE  r   r   r   r0   r0   r1   rN     rO   z3TestSystematic.test_log1p_complex.<locals>.<lambda><   r  )r   r)   Zlog1pr   r@  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 rE  r  r   r0   r0   r1   rN   
  re  z-TestSystematic.test_log1pmx.<locals>.<lambda>r  r   )r   r;   )r   r   r
   r@  r0   r0   r1   test_log1pmx  s   

zTestSystematic.test_log1pmxc                 C   r  )Nr  r:   )r   r)   r*   r   r'   r
   r@  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 )Nr:  r;  r   r:   )	r   r)   r*   r   r'   r   r&   r!   r+  r@  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   rn   )r   r)   elliper   r
   r@  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 )Nr=  r>  r   r  r   r)   Z	ellipeincr   r  r
   r@  r0   r0   r1   test_ellipeinc  s   zTestSystematic.test_ellipeincc                 C      t tjtjt t g d S rH   r  r@  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 Nr=  r>  r   r)   	ellipkincr   Zellipfr
   r@  r0   r0   r1   test_ellipf)  s   zTestSystematic.test_ellipfc                 C   r  rH   r  r@  r0   r0   r1   test_ellipf_largephi.  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 rE  )r   r!  )r  r0   r0   r1   rN   8  rO   z,TestSystematic.test_ellipk.<locals>.<lambda>g        )ro   r   r  )r   r)   r!  r   r
   Zellipkm1r@  r0   r0   r1   test_ellipk3  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 r8  r   Zellippiphir  r0   r0   r1   r  =  rI  z0TestSystematic.test_ellipkinc.<locals>.ellipkincr=  r>  r   r  Trv  r   r)   r  r
   rA  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  r8  r  r  r0   r0   r1   r  E  rI  z9TestSystematic.test_ellipkinc_largephi.<locals>.ellipkincr   r  Trv  r  r  r0   r0   r1   test_ellipkinc_largephiD  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  M  s   z+TestSystematic.test_ellipfun_sn.<locals>.snc                 S   r  r8  r  r  r0   r0   r1   rN   W  r   z1TestSystematic.test_ellipfun_sn.<locals>.<lambda>    .    .Ar   r    r   r*  r:   rJ  )rA  r  r0   r0   r1   test_ellipfun_snL  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  rE  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   _  r   r  r  r   r    r   r*  r:   rJ  r@  r0   r0   r1   test_ellipfun_cn\  
   
zTestSystematic.test_ellipfun_cnc                 C   r  )Nc                 S   r  r  r  r  r0   r0   r1   rN   e  r   z1TestSystematic.test_ellipfun_dn.<locals>.<lambda>c                 S   r  r  r  r  r0   r0   r1   rN   f  r   r  r  r   r    r   r*  r:   rJ  r@  r0   r0   r1   test_ellipfun_dnc  r	  zTestSystematic.test_ellipfun_dnc                 C   s   t tjdd t g d S )Nc                 S   rQ  rH   r   r   r	  r0   r0   r1   rN   l     
 z)TestSystematic.test_erf.<locals>.<lambda>)r   r)   r   r
   r@  r0   r0   r1   test_erfj  s   zTestSystematic.test_erfc                 C   r  )Nc                 S   rQ  rH   r  r	  r0   r0   r1   rN   q  r  z1TestSystematic.test_erf_complex.<locals>.<lambda>r6   rc  )r   r)   r   r   r@  r0   r0   r1   r   o  r  zTestSystematic.test_erf_complexc                 C   "   t tjtdd t gdd d S )Nc                 S   rQ  rH   r   r   r	  r0   r0   r1   rN   v  r  z*TestSystematic.test_erfc.<locals>.<lambda>r9   r:   )r   r)   r   r   r
   r@  r0   r0   r1   	test_erfct     

zTestSystematic.test_erfcc                 C   r  )Nc                 S   rQ  rH   r  r	  r0   r0   r1   rN   {  r  z2TestSystematic.test_erfc_complex.<locals>.<lambda>r6   rc  )r   r)   r   r   r   r@  r0   r0   r1   test_erfc_complexy  r  z TestSystematic.test_erfc_complexc                 C      t tjtjt gdd d S Nr6   rc  )r   r)   erfir   r
   r@  r0   r0   r1   	test_erfi~  r  zTestSystematic.test_erfic                 C   r  r  )r   r)   r  r   r   r@  r0   r0   r1   test_erfi_complex  r  z TestSystematic.test_erfi_complexc                 C   r  )Nc                 S   rQ  rH   )r   ncdfr	  r0   r0   r1   rN     r  z*TestSystematic.test_ndtr.<locals>.<lambda>r6   rc  )r   r)   ndtrr   r
   r@  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   rc  )r   r)   r  r   r&   r@  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 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   rA   r   )r   r)   log_ndtrr   r
   r@  r0   r0   r1   test_log_ndtr  s   


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   r  )r   r)   r   r   r   r&   r@  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   r7  )Nrr   )r)   Zeulerrc  r0   r0   r1   rN     rO   z.TestSystematic.test_eulernum.<locals>.<lambda>r    r  rc  )r   r   Zeulernumr   r@  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!   r+  r@  r0   r0   r1   test_expint  r  zTestSystematic.test_expintc                 C      dd }t |tjt g d S )Nc                 S   r7  r8  r)   Zfresnelr   r0   r0   r1   fresnels  rI  z.TestSystematic.test_fresnels.<locals>.fresnels)r   r   r(  r
   )rA  r(  r0   r0   r1   test_fresnels  
   zTestSystematic.test_fresnelsc                 C   r&  )Nc                 S   r7  rE  r'  r   r0   r0   r1   fresnelc  rI  z.TestSystematic.test_fresnelc.<locals>.fresnelc)r   r   r+  r
   )rA  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
   r@  r0   r0   r1   
test_gamma  s   zTestSystematic.test_gammac                 C       t tjttjt gdd d S Nri   r:   )r   r)   r-  r   r   r   r@  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/   rn   r0   r0   r1   rN     r   z.TestSystematic.test_gammainc.<locals>.<lambda>r        @Finclusive_ar  r{  )r   r)   r  r
   r@  r0   r0   r1   test_gammainc  
   
zTestSystematic.test_gammaincc                 C   r3  )	Nc                 S   r4  )NT)ro   r  r5  )r/   ro   r0   r0   r1   rN     r   z/TestSystematic.test_gammaincc.<locals>.<lambda>r   r6  Fr7  r  r{  )r   r)   Z	gammainccr
   r@  r0   r0   r1   test_gammaincc  r:  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
   )rA  r=  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
   r@  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 )
Nrl  r   r   r    r   rr   z1e-50z0.0\4@Iw)	r   r!   r  r   r@  r=   r   r  r+  rA   ro   rB   r-   r0   r0   r1   r@    s   (
z6TestSystematic.test_gegenbauer_int.<locals>.gegenbauerc                 S   s(   t t| ||}t|dkrtjS |S )NrB  )r)   r?  r   r   r!   r+  rC  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"   )rA  r@  rD  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)   r?  r   rK   rA   ro   rB   r0   r0   r1   rN     r]  z8TestSystematic.test_gegenbauer_complex.<locals>.<lambda>r   r7   )r   r   r   r@  r   r
   r   r@  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)   r?  rK   rG  r0   r0   r1   rN     re  z@TestSystematic.test_gegenbauer_complex_general.<locals>.<lambda>r=  r>  )r   r   r   r@  r
   r   r@  r0   r0   r1   test_gegenbauer_complex_general  rI  z.TestSystematic.test_gegenbauer_complex_generalc                 C   &   t tjtdd tddt g d S )Nc                 S   rh  rH   )r   hankel1r\  rM   rB   r0   r0   r1   rN     s    z-TestSystematic.test_hankel1.<locals>.<lambda>@x@xD)r   r)   rM  r   r
   r@  r0   r0   r1   test_hankel1  s   
zTestSystematic.test_hankel1c                 C   rL  )Nc                 S   rh  rH   )r   hankel2r\  rN  r0   r0   r1   rN     r]  z-TestSystematic.test_hankel2.<locals>.<lambda>rO  rP  )r   r)   rR  r   r
   r@  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
   r@  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  r5  c                    s   t j| |fi  S rH   rV   ro   rB   ZKWr0   r1   rN   /  r]  z,TestSystematic.test_hyp0f1.<locals>.<lambda>r  r  r   g     j@r  rc  )r   r   r)   rJ   r
   r@  r0   rV  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   )ro   r/   r0   r0   r1   rN   8  rO   z4TestSystematic.test_hyp0f1_complex.<locals>.<lambda>c                 S   rh  rH   )r   rJ   r\  rU  r0   r0   r1   rN   9  r]  r   r   irF   )r   r   r
   r   r&   r@  r0   r0   r1   test_hyp0f1_complex7  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!   r+  r  r0   r0   r1   mpmath_hyp1f1@  s
   
z1TestSystematic.test_hyp1f1.<locals>.mpmath_hyp1f1r  r3   r    Fr7  r   )rA   r|  )r   r)   rY  r
   )rA  r[  r0   r0   r1   test_hyp1f1?  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   rJ  rH   )r)   rY  rK   r  r0   r0   r1   rN   P  re  z4TestSystematic.test_hyp1f1_complex.<locals>.<lambda>c                 S      t j| ||fi tS rH   )r   rY  r\  r  r0   r0   r1   rN   Q  rd  r=  r>  i  rc  )r   r   r   r
   r   r@  r0   r0   r1   test_hyp1f1_complexN  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)   rz   rK   ro   rn   rx   rB   r0   r0   r1   rN   X  rd  z4TestSystematic.test_hyp2f1_complex.<locals>.<lambda>c                 S      t j| |||fi tS rH   )r   rz   r\  r_  r0   r0   r1   rN   Y  rY   g      Yg      Y@r   rc  rq  r@  r0   r0   r1   test_hyp2f1_complexU  s
   

z"TestSystematic.test_hyp2f1_complexc                 C   s&   t tjtdd t t t g d S )Nc                 S   r]  rH   )r   rm   r\  r  r0   r0   r1   rN   `  rd  z,TestSystematic.test_hyperu.<locals>.<lambda>)r   r)   rm   r   r
   r@  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$   r-  rU  r0   r0   r1   mp_igam_face     "z1TestSystematic.test_igam_fac.<locals>.mp_igam_facr   g  ļBFr7  r   r:   )r   r   r
   )rA  rd  r0   r0   r1   test_igam_facc  s   
zTestSystematic.test_igam_facc                 C   8   t tjtjtddg t tjtjtddgdd d S Nr=  r>  r:  r;  r<  r:   )r   r)   Zj0r   r
   r@  r0   r0   r1   test_j0m  s   


zTestSystematic.test_j0c                 C   rg  rh  )r   r)   Zj1r   r
   r@  r0   r0   r1   test_j1{  s   


zTestSystematic.test_j1c                 C   sR   t tjtdd t t t t g t dd tdd t t t t g d S )Nc                 S   r`  rH   r   jacobir\  r_  r0   r0   r1   rN     rY   z,TestSystematic.test_jacobi.<locals>.<lambda>c                 S      t t| |||S rH   r)   eval_jacobir   )rA   rn   rx   rB   r0   r0   r1   rN     r]  c                 S   r`  rH   rk  r_  r0   r0   r1   rN     rY   )r   r)   ro  r   r
   r   r@  r0   r0   r1   test_jacobi  s   

zTestSystematic.test_jacobic                    s:   dd  t dd  fddt t t t gddd d S )	Nc                 S   s   | dkrdS t | |||S )Nr   r   )r   rl  rA   ro   rn   rB   r0   r0   r1   rl    s   z.TestSystematic.test_jacobi_int.<locals>.jacobic                 S   rm  rH   rn  rq  r0   r0   r1   rN     r]  z0TestSystematic.test_jacobi_int.<locals>.<lambda>c                    s   t  | |||fi tS rH   )r   r\  rq  rl  r0   r1   rN     r    N  r3   r  r   r   r
   r@  r0   rr  r1   test_jacobi_int  s   

zTestSystematic.test_jacobi_intc                 C   s&   dd }t tj|tddgdd d S )Nc                 S   s*   | dkr	t  d S ttjd| fi tS )Nr   r5   )r   r   r   keir\  r   r0   r0   r1   rv    s   
z$TestSystematic.test_kei.<locals>.keiꌠ9Y>)ꌠ9Y>)Fr  rc  )r   r)   rv  r
   )rA  rv  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   rZ  r8  )r   kerr\  r   r0   r0   r1   rN     r]  z)TestSystematic.test_ker.<locals>.<lambda>rw  rx  r  rc  )r   r)   rz  r   r
   r@  r0   r0   r1   test_ker  s   

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laguerrer\  r  r0   r0   r1   rN     rY   z.TestSystematic.test_laguerre.<locals>.<lambda>)r   r   r)   eval_laguerrer
   r@  r0   r0   r1   test_laguerre  s   

zTestSystematic.test_laguerrec                 C   s$   t dd dd t t gdd d S )Nc                 S   r  rH   )r)   r~  r   r  r0   r0   r1   rN     r   z2TestSystematic.test_laguerre_int.<locals>.<lambda>c                 S   r|  rH   r}  r  r0   r0   r1   rN     rY   rs  rc  rt  r@  r0   r0   r1   test_laguerre_int  s   
z TestSystematic.test_laguerre_intzsee gh-3551 for bad pointsc                 C   s4   t dd dd ttj tjtddgddd d S )	Nc                 S      t | t|jS rH   )r)   r$  r   rK   rB   r  r0   r0   r1   rN     re  z3TestSystematic.test_lambertw_real.<locals>.<lambda>c                 S   r  rH   )r   r$  r   rK   r  r0   r0   r1   rN     re  r   r   r9   Fr;   r|  )r   r   r!   r+  r   r@  r0   r0   r1   test_lambertw_real  s
   
z!TestSystematic.test_lambertw_realc                    sB   d}t d d fdd}t|tjtd|ddgd	d
 d S )NgGase@r    g  E@c                    s   t jddA |  d   | d  }|t jkr|t|  }n |  d   d| d   }|t|  }||9 }W d    |S W d    |S 1 sJw   Y  |S )Nr   )ZoverrE   )r!   r   r+  r   )rB   ZfacrQ   egr0   r1   r-    s   



z:TestSystematic.test_lanczos_sum_expg_scaled.<locals>.gammar   Fr7  r9   r:   )r!   r$   r   r   r-  r
   )rA  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
   r@  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  r\  r  r0   r0   r1   rN     rY   rs  rc  c                 S   r  rH   r  r  r0   r0   r1   rN     r   c                 S   r|  rH   r  r  r0   r0   r1   rN     rY   r   rE  r`   )r   r   r
   r   r!   r"   r@  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   rr   rr   )#v)	r)   Zlpmn
ValueErrorr!   r  r   r+  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!   r+  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$| dk r|  d } tt|| S dS t|dk r/tjS t|dk r7dnd}ttj| |||d}t|dkrStj	t|j
 }|S )	Nr    rr   r   rh   r   rg   typer  )r   r   rc  r  r   r!   r  r   r   r+  rK   )rA   r  r/   typrM   r0   r0   r1   r     s   
z*TestSystematic.test_legenp.<locals>.legenpr  r7   rr   r    r   rm  rt  )rA  r  r  r   r0   r0   r1   test_legenp  s   

zTestSystematic.test_legenpc                 C      dd }dd }t g d}t g d}|d d d f d|d d d f    }t||tg dtg dt|gd	d
d d S )Nc                 S   :   zt j|j| j|ddd d W S  ty   tj Y S w )Nr   r  r   r  r)   ZclpmnrK   r  r!   r  rA   r  r/   r0   r0   r1   clpnm  
    
z3TestSystematic.test_legenp_complex_2.<locals>.clpnmc                 S   4   t |dk r	tjS ttjt| jt|j|ddS Nrh   r   r  r   r!   r  r   r   r   r   rK   r  r0   r0   r1   r        "z4TestSystematic.test_legenp_complex_2.<locals>.legenp	rt   r   rD   r   r<  rE   r   r`   g     @@r=  rD   rE   g?r   rt   rr   r   r    r   r   r   r   rf  r!   r(   r   r   r   rA  r  r   rB   rP   r/   r0   r0   r1   test_legenp_complex_2     (
z$TestSystematic.test_legenp_complex_2c                 C   r  )Nc                 S   r  )Nrg   r  r   r  r  r  r0   r0   r1   r  -  r  z3TestSystematic.test_legenp_complex_3.<locals>.clpnmc                 S   r  )Nrh   rg   r  r  r  r0   r0   r1   r   3  r  z4TestSystematic.test_legenp_complex_3.<locals>.legenpr  r  r   r  r   r   rf  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   lqnmF  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  I  s   z*TestSystematic.test_legenq.<locals>.legenqr   r7   rt  rA  r  r  r0   r0   r1   test_legenqD  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  U  re  z0TestSystematic.test_legenq_complex.<locals>.lqnmc                 S   r  r  )r   r!   r  r   r   r  r   rK   r  r0   r0   r1   r  X  r  z2TestSystematic.test_legenq_complex.<locals>.legenqr   r7   rc  )r   r   r   r  r0   r0   r1   test_legenq_complexS  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  Zfloorr   r0   r0   r1   r  d  s    z0TestSystematic.test_lgam1p.<locals>.param_filterc                 S   s   t d|  jS rE  r<  r	  r0   r0   r1   	mp_lgam1ph  s   z-TestSystematic.test_lgam1p.<locals>.mp_lgam1pr9   r7   r  )r   r   r
   )rA  r  r  r0   r0   r1   test_lgam1pc  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_loggammar  s   z5TestSystematic.test_loggamma.<locals>.mpmath_loggammaFr   )r|  Zdistinguish_nan_and_infr;   )r   r)   r   r   )rA  r  r0   r0   r1   test_loggammaq  s   
zTestSystematic.test_loggammac                 C   s(   dd }t |tdd t t g d S )Nc                 S   r  r8  )r)   ZpbdvrN  r0   r0   r1   pcfd  r  z&TestSystematic.test_pcfd.<locals>.pcfdc                 S   rh  rH   )r   r  r\  rN  r0   r0   r1   rN     r]  z*TestSystematic.test_pcfd.<locals>.<lambda>)r   r   r
   )rA  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  r8  )r)   ZpbvvrN  r0   r0   r1   pcfv  r  z&TestSystematic.test_pcfv.<locals>.pcfvc                 S   r  rH   )r   r   r   r  r\  rN  r0   r0   r1   rN     r   z*TestSystematic.test_pcfv.<locals>.<lambda>r  rc  rJ  )rA  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  r8  r)   ZpbwarU  r0   r0   r1   pcfw  r  z&TestSystematic.test_pcfw.<locals>.pcfwc                 S   r  rE  r  rU  r0   r0   r1   dpcfw  r  z'TestSystematic.test_pcfw.<locals>.dpcfwc                 S   s   t t j| |fdS )Nr8   )r   Zdiffr  rU  r0   r0   r1   mpmath_dpcfw  r   z.TestSystematic.test_pcfw.<locals>.mpmath_dpcfwr^   r_   g:0yU>r7   rf  g&.!>)r   r   r  r
   )rA  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
   r@  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!   r+  r@  r0   r0   r1   test_rgamma  s   
zTestSystematic.test_rgammac                 C   r/  r0  )r   r)   r   r   r   r   r@  r0   r0   r1   test_rgamma_complex  r2  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 )Nrq   c                 S   sN   t | | t| | kr!t | | dkr!t| } t| | |  }t| |S r8  )r=   r   r   r  rf)ro   r  r0   r0   r1   mppoch  s   (
z&TestSystematic.test_rf.<locals>.mppochr   r  )
r   parser   r   ZVersionr  r   r)   Zpochr
   )rA  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   r@  r0   r0   r1   test_sinpi_complex  s   

z!TestSystematic.test_sinpi_complexc                 C   r  )Nc                 S   r7  r8  r  r   r0   r0   r1   shi  rI  z$TestSystematic.test_shi.<locals>.shir  )r   r   r  r
   r   rA  r  r0   r0   r1   test_shi  r  zTestSystematic.test_shic                 C   r  )Nc                 S   r7  r8  r  r	  r0   r0   r1   r    rI  z,TestSystematic.test_shi_complex.<locals>.shir:  r;  rZ   r:   )r   r   r  r   r&   r!   r+  r  r0   r0   r1   test_shi_complex  r  zTestSystematic.test_shi_complexc                 C   r&  )Nc                 S   r7  r8  r  r   r0   r0   r1   si  rI  z"TestSystematic.test_si.<locals>.si)r   r   r  r
   rA  r  r0   r0   r1   test_si  s   zTestSystematic.test_sic                 C   r  )Nc                 S   r7  r8  r  r	  r0   r0   r1   r    rI  z*TestSystematic.test_si_complex.<locals>.sir:  r;  rZ   r:   )r   r   r  r   r&   r!   r+  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!   r+  rA  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   r*  ip  rS   )rk   rA   r   )r   r   r  r   r
   r   )rA  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     r6  r   &.>r:   )r   r)   Zstruver   r   Zstruvehr
   r@  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  r6  r   r  Tr   )r   r)   Z	modstruver   r
   )rA  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_realru   gPKDg+<r   F)r;   rk   r|  )r   r)   r-  r
   )rA  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 )Nr&  )r%  r	  r0   r0   r1   rN   :  r  z1TestSystematic.test_wrightomega.<locals>.<lambda>r   Fr  )r   r)   r-  r   r@  r0   r0   r1   test_wrightomega8  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)ro   rn   r8  r   ro   r8  )r   r)   zetar   r   r
   r@  r0   r0   r1   test_hurwitz_zeta=  s   
z TestSystematic.test_hurwitz_zetac                 C   s"   t tjtjtddgddd d S )Nr  r7   Fr9   r{  )r   r)   r  r   r
   r@  r0   r0   r1   test_riemann_zetaC  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   t | d S rE  )r   r  r   r0   r0   r1   rN   N  rO   z+TestSystematic.test_zetac.<locals>.<lambda>r  r7   F-   r9   )r|  r   r;   )r   r)   Zzetacr
   r@  r0   r0   r1   
test_zetacL  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 r8  r   r   r  r   Zpowm1)rB   lmbdar0   r0   r1   	mp_boxcoxT  s
   z-TestSystematic.test_boxcox.<locals>.mp_boxcoxr   Fr  r6   r  r9   rA   r   r;   )r   r)   Zboxcoxr   r
   )rA  r  r0   r0   r1   test_boxcoxR  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  Zoner0   r0   r1   mp_boxcox1pe  s   z1TestSystematic.test_boxcox1p.<locals>.mp_boxcox1prr   Fr  r6   r  r9   r  )r   r)   Zboxcox1pr   r
   )rA  r  r0   r0   r1   test_boxcox1pc  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   	mpmathifyru  r  r  r   r#  rK   rA   r/   argoutr0   r0   r1   mp_spherical_jnv     

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   r:  r;  r   r  r  rA  r  r0   r0   r1   test_spherical_jnu     	
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     re  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  rA  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     re  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  rj  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  rA  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     re  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  rA  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     re  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__rB  rC  rK  rO  rT  rU  rW  rX  r^  ra  rg  ro  rr  rx  ry  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!  r"  r#  r%  r)  r,  r.  r1  r9  r;  r>  rA  rF  rH  r   rK  rQ  rS  rT  rW  rX  r\  r^  ra  rb  Zxfail_on_32bitrf  ri  rj  rp  ru  ry  r{  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r	  r  r  r  r  r0   r0   r0   r1   r6    sD   





		
	
0







	






3






		
		r6  )J__doc__Z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]   rp   r   r   r   r   r  Zslowr   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r"  r%  r/  r1  r3  r4  r   r\  r6  r0   r0   r0   r1   <module>   s    0 










7
&






