o
    h%                    @   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 ]$}t ddt j dD ]}|t d|  }| |tt|f qq	t j	| t j
d} ttj| dd  d S )	Ni   
   r                    ?dtype   )nplogspacelinspacer   expappendcomplexr   eiarraycomplex_r   scexpicheck)datasetrpz r2   Z/var/www/html/scripts/venv/lib/python3.10/site-packages/scipy/special/tests/test_mpmath.pytest_expi_complex#   s   r4   z0.19c                  C   s   g } dD ]/}t dddD ]%}td | ||tt||f W d    n1 s-w   Y  qqt | } tt	j
| dddd	  d S )
N)2   3   r         d   r   r!   r   vIh%<=rtol)r"   r#   r   workdpsr&   floatexpintasarrayr   r+   expnr-   )r.   nxr2   r2   r3   test_expn_large_n3   s   
rE   c                  C   s   g } g d}|D ]7}|D ]2}|D ]-}|d|  }t d tt ||}W d    n1 s0w   Y  | |||f qqqt| } tdd | dddd	  d S )
N)g     Xg      #            ?g      #@g     X@r   x   c                 S      t | j|S Nr+   hyp0f1realvr1   r2   r2   r3   <lambda>U       z$test_hyp0f1_gh5764.<locals>.<lambda>r:   r   r;   r<   )	r   r>   r'   rL   r&   r"   r)   r   r-   )r.   axisrO   rD   yr1   resr2   r2   r3   test_hyp0f1_gh5764D   s"   
	
rU   c                  C   sF   t ddd} t| d}t dd | D }t||tdd d S )	N         rG   c                 S   s   g | ]}t |d qS )rG   r   rL   ).0rO   r2   r2   r3   
<listcomp>^       z'test_hyp0f1_gh_1609.<locals>.<listcomp>-q=r<   )r"   r$   r+   rL   r)   r   astyper?   )vvafmfr2   r2   r3   test_hyp0f1_gh_1609Y   s   rb   z1.1.0c                  C   s   g } t ddD ]6}t dddD ],}| }| ||dtt||df | | d }| ||dtt||df qqdD ]}dD ]}| ||dtt||df qEqAt | } tt	j| dd	d
dd
  d S )N      r   r!   )      %      rF   r   rG   r!   r   )      rF   r   rG   r!         ?r         @r   r!   r      V瞯<-a=r=   atol)r"   aranger$   r&   r?   r   hyperur)   r   r+   r-   )r.   rC   bar2   r2   r3   test_hyperu_around_0f   s    ""
ru   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   rw   ffffff?)r   ry   rx   )r   r!   gffffffr7   )repeatc                 S   sD   g | ]\}}}}||krt ||kr|d k r|dkr||||fqS )r   rz   )round)rZ   rt   rs   crD   r2   r2   r3   r[      s
    
$
z.test_hyp2f1_strange_points.<locals>.<listcomp>T)	eliminatec                    s&   g | ]}|t tj|i  f qS r2   r?   r   hyp2f1rZ   r0   kwr2   r3   r[      s   & r   r   r!   r   rl   绽|=r<   )list	itertoolsproductdictr"   r)   float_r   r+   r   r-   ptsr.   r2   r   r3   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   rl   r   )UUUUUU?gUUUUUU?g?g      ?)      ?rG   g      ?gX<ݚ?)r   ry   rl   )r   r   ry   rl   )r   rg   rg   rl   r   )gx&?rw   rc   g333333?)r   r   r   +?)r   r   r   rw   )r   rl   rd   Gz?)ri   rF   rl   r   )r   rj   g      
r   )g*4]92@g|O%@gCu?)  rf   r   )r   r         %@r   )rw   r   r!         ?)rw   r   r!   rh   )r      rd   r   )r   r   rd   rh   )rG   g     pri   gm˟?c                 S   s    g | ]}|t tj| f qS r2   r   r   r2   r2   r3   r[           z0test_hyp2f1_real_some_points.<locals>.<listcomp>r   ignoreinvalidr   r7   r   r<   )r"   r)   r   errstater   r+   r   r-   r   r2   r2   r3   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   )r6   r   )r   gwJ)r   |r   r   )r   r   rf   r   c                 S   s"   t | trt| d | d  S | S )Nr   r!   )
isinstancetupler?   rD   r2   r2   r3   fev   s   
z&test_hyp2f1_some_points_2.<locals>.fevc                    s*   g | ]}t t |ttj| f qS r2   )r   mapr?   r   r   r   r   r2   r3   r[         * z-test_hyp2f1_some_points_2.<locals>.<listcomp>r   r   r7   r   r<   )r"   r)   r   r   r+   r   r-   r   r2   r   r3   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   rc   g?rd   r   )g      rw   r!   g@)r   r   rd   gffffff4@)r   g)\(Gzr   g333333?gffffff?ri   r   r   r   r   r   r7   &.>Tr=   ignore_inf_sign)r?   r   r   	Exceptionr&   r"   r)   r   r   r   r+   r-   )r.   rt   rs   r}   r1   rO   r2   r2   r3   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  rd     ri   r   r!   r   rl   rw   r   r7   r   r   r<   )r"   zerosr   randomseedparetorandrandintr   __version__absmaxr?   r   r   r   r+   r-   )npointsr.   dsr2   r2   r3   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 rJ   )r'   r   erfr   r2   r2   r3   rP      rQ   z"test_erf_complex.<locals>.<lambda>Fr;   
vectorizedr=   c                 S   r   rJ   )r'   r   erfcr   r2   r2   r3   rP     rQ   )r   mpdpsprecr"   meshgridr$   r#   r_ravelr	   r+   r   r   )old_dpsold_precx1y1x2y2pointsr2   r2   r3   test_erf_complex   s   $$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!   rw   ry   g333333?g333333gr   r   rl      rd   r   rc   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murD   r2   r2   r3   mplegenp-  s
   ztest_lpmv.<locals>.mplegenpc                    s*   g | ]}| |d  |d |d f qS )r!   r   r   r2   r   r   r2   r3   r[   6  r   ztest_lpmv.<locals>.<listcomp>r   c                 S   s   t | t||S rJ   )r+   lpmvr^   r   )r   r   rD   r2   r2   r3   evf9     ztest_lpmv.<locals>.evfr   r   rk   r   +=ro   )extendr"   r)   r   r   r   r-   )r   rD   r.   r   r2   r   r3   	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   8r8   r7   r   r   rw   r!   r   rG   gffffffr   g33333Yg3333r     c                 S   s   t t| |S rJ   )r?   r   betart   rs   r2   r2   r3   rP   W      ztest_beta.<locals>.<lambda>Fr   T)r   r=   r   c                 S   s   t ttt| |S rJ   )r?   r   logr   r   r   r2   r2   r3   rP   _      r   )r"   r   r   r   r#   rq   r)   broadcast_arraysreshapeTr   r   r   r   r	   r+   r   betaln)rs   rt   abr   r   r2   r2   r3   	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   re   r   r!   c                 S      g | ]}|t t|fqS r2   r'   r   loggammarZ   z0r2   r2   r3   r[   y      z3test_loggamma_taylor_transition.<locals>.<listcomp>vIh%,=r<   )LOGGAMMA_TAYLOR_RADIUSr"   r)   r$   r   r   r%   r   flattenr   r+   r   r-   r/   thetadzr1   r.   r2   r2   r3   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   re   r   r!   c                 S   r   r2   r   r   r2   r2   r3   r[     r   z(test_loggamma_taylor.<locals>.<listcomp>r   r<   )r"   r#   log10r   r$   r   r   r%   r   r   r)   r   r+   r   r-   r   r2   r2   r3   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 )Nrw   rl   r   r   iVr!   r9   c                 S   r   r2   )r'   r   rgammar   r2   r2   r3   r[     r   z%test_rgamma_zeros.<locals>.<listcomp>r]   r<   )r"   r   r#   copyr   rq   r   dstacksizer   r   r>   r)   r   r+   r  r-   )dxdyr   r   r1   r.   r2   r2   r3   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 )Nri   rF   gQοrw   r   r   gQ?r   r   c                 S   r   r2   r'   r   digammar   r2   r2   r3   r[     r   z&test_digamma_roots.<locals>.<listcomp>r!   r   r<   )r   findrootr  r?   r&   r"   r)   r   r#   r  r   r  r  r   r>   r   r+   r-   )rootrootsr  r  r   r1   r.   r2   r2   r3   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,  r9   r   r   rd   r   (   c                    s   g | ]
}|t  |fqS r2   )r'   r   r  r2   r3   r[     s    z(test_digamma_negreal.<locals>.<listcomp>r!   r;   r<   )r   r   r  r"   r#   r   r   r   r>   rA   r   r+   r-   rD   rS   r1   r.   r2   r  r3   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  r9   )gffffffgg@gffffff@r   r   c                 S   r   r2   r  r   r2   r2   r3   r[     r   z)test_digamma_boundary.<locals>.<listcomp>r   r!   r;   r<   )r"   r#   r)   r   r   r   r>   rA   r   r+   r  r-   r  r2   r2   r3   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 )Nre   rG   r   r5   r9   c              
   S   s*   g | ]\}}||t tj||d dfqS )Trs   regularized)r?   r   gammainc)rZ   a0x0r2   r2   r3   r[     s    z*test_gammainc_boundary.<locals>.<listcomp>r:   r]   r<   )r"   r$   r  r   r   r   r>   zipr)   r   r+   r  r-   )smallrt   rD   r.   r2   r2   r3   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r1   r2   r2   r3   spence  r   z"test_spence_circle.<locals>.spencerG   ri   r   r   r!   r   c                    s   g | ]}| |fqS r2   r2   r   r#  r2   r3   r[     r\   z&test_spence_circle.<locals>.<listcomp>r   r<   )r"   r$   r   outerr%   r   rA   r   r+   r#  r-   )r/   r   r1   r.   r2   r$  r3   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  rl   r   r9   r!   rw   c                 S   r   r2   )r'   r   sinpir   r2   r2   r3   r[         z$test_sinpi_zeros.<locals>.<listcomp>r   r<   )r"   finfor?   epsr   r#   r  r   rq   r   r  r  r   rA   r   r   r-   r+  r  r  r   r   r1   r.   r2   r2   r3   test_sinpi_zeros  s   &
r-  c                  C   s   t tj} t jt ddd dt dddf }| }t ||\}}|d|  }t dddd 	ddd	}|t 
|f|j   }t d
d |D }tt|ddd|  d  d S )Nr   r  rl   r   r'  r9   r!   rG   rw   c                 S   r   r2   )r'   r   cospir   r2   r2   r3   r[   -  r)  z$test_cospi_zeros.<locals>.<listcomp>r   r<   )r"   r*  r?   r+  r   r#   r  r   rq   r   r  r  r   rA   r   r   r-   r,  r2   r2   r3   test_cospi_zeros$  s   &
r/  c            	   	   C   s   dd } dd }t ddd}t jt dd	d
 dt d	dd
f }g }|D ]}tt|}|D ]}|| }||||||f q1q&t |}t	| |dddd
  d S )Nc                 S      t | |d S Nr   r+   ellipjumr2   r2   r3   dn9     z"test_dn_quarter_period.<locals>.dnc                 S   s   t tjd| |dS Nr7  r4  )r?   r   ellipfunr4  r2   r2   r3   	mpmath_dn<  r   z)test_dn_quarter_period.<locals>.mpmath_dnr   r!   re   rw   r
  r   r:   r   r   r<   )r"   r$   r   r#   r?   r   ellipkr&   rA   r   r-   )	r7  r;  r6  dur.   m0u0du0r0   r2   r2   r3   test_dn_quarter_period7  s   &
rA  c                 C   sh   t |% t | } t | jt j dt j  }t t | |}W d    |S 1 s-w   Y  |S r1  )r   r>   mpcceilimagr   lambertwr%   )r1   r   unwindrT   r2   r2   r3   _mpmath_wrightomegaP  s   

rG  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      r5   rw   r   c                 S      g | ]}|t t|d fqS rH  r'   rG  r   r2   r2   r3   r[   i  r)  z+test_wrightomega_branch.<locals>.<listcomp>r!   :0yE>r<   )r"   r#   	nextafterr   infranger&   hstackr   r   rA   r   r+   wrightomegar-   )	rD   picut_abovepicut_belownpicut_abovenpicut_belowirS   r1   r.   r2   r2   r3   test_wrightomega_branchX  s"   
rW  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 )
Nry   r!   r   r   c                 S   rI  rJ  rK  r   r2   r2   r3   r[   x  r)  z,test_wrightomega_region1.<locals>.<listcomp>r   rm   r<   
r"   r$   r   r   r   rA   r   r+   rQ  r-   r  r2   r2   r3   test_wrightomega_region1o     
rY  c                  C   sn   t dd} t dt j d}t | |\} }| d|   }t dd |D }ttj|dddd		  d S )
Nry   r!   rw   r   c                 S   rI  rJ  rK  r   r2   r2   r3   r[     r)  z,test_wrightomega_region2.<locals>.<listcomp>r   rm   r<   rX  r  r2   r2   r3   test_wrightomega_region2~  rZ  r[  c                  C   sn   t dddt ddd} }t | |\} }| d|   }t dd |D }ttj|dddd	  d S )
Nrw   r!   rH  r   c                 S   r   r2   )r'   r   rE  r   r2   r2   r3   r[     r)  z(test_lambertw_smallz.<locals>.<listcomp>r   r;   r<   )	r"   r$   r   r   rA   r   r+   rE  r-   r  r2   r2   r3   test_lambertw_smallz  s   
r\  r8   maxprec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+   airyr"  r2   r2   r3   rP     rQ   z,TestSystematic.test_airyai.<locals>.<lambda>    ח    חAh㈵>r<   c                 S   ra  rb  rc  r"  r2   r2   r3   rP     rQ        @     @@)r   r   airyair
   selfr2   r2   r3   test_airyai  s   

zTestSystematic.test_airyaic                 C   s   t dd tjt g d S )Nc                 S   ra  rb  rc  r"  r2   r2   r3   rP     rQ   z4TestSystematic.test_airyai_complex.<locals>.<lambda>)r   r   rj  r   rk  r2   r2   r3   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   ra  Nr!   rc  r"  r2   r2   r3   rP     rQ   z2TestSystematic.test_airyai_prime.<locals>.<lambda>c                 S      t j| ddS Nr!   )
derivativer   rj  r"  r2   r2   r3   rP        re  rf  rg  r<   c                 S   ra  rp  rc  r"  r2   r2   r3   rP     rQ   c                 S   rq  rr  rt  r"  r2   r2   r3   rP     ru  rh  ri  r   r
   rk  r2   r2   r3   test_airyai_prime     

z TestSystematic.test_airyai_primec                 C      t dd dd t g d S )Nc                 S   ra  rp  rc  r"  r2   r2   r3   rP     rQ   z:TestSystematic.test_airyai_prime_complex.<locals>.<lambda>c                 S   rq  rr  rt  r"  r2   r2   r3   rP     ru  r   r   rk  r2   r2   r3   test_airyai_prime_complex     z(TestSystematic.test_airyai_prime_complexc                 C   ro  )Nc                 S   ra  r1  rc  r"  r2   r2   r3   rP     rQ   z,TestSystematic.test_airybi.<locals>.<lambda>c                 S   
   t | S rJ   r   airybir"  r2   r2   r3   rP        
re  rf  rg  r<   c                 S   ra  r1  rc  r"  r2   r2   r3   rP     rQ   c                 S   r}  rJ   r~  r"  r2   r2   r3   rP     r  rh  ri  rv  rk  r2   r2   r3   test_airybi  rx  zTestSystematic.test_airybic                 C   ry  )Nc                 S   ra  r1  rc  r"  r2   r2   r3   rP     rQ   z4TestSystematic.test_airybi_complex.<locals>.<lambda>c                 S   r}  rJ   r~  r"  r2   r2   r3   rP     r  rz  rk  r2   r2   r3   test_airybi_complex  r|  z"TestSystematic.test_airybi_complexc                 C   ro  )Nc                 S   ra  Nrl   rc  r"  r2   r2   r3   rP     rQ   z2TestSystematic.test_airybi_prime.<locals>.<lambda>c                 S   rq  rr  r~  r"  r2   r2   r3   rP     ru  re  rf  rg  r<   c                 S   ra  r  rc  r"  r2   r2   r3   rP     rQ   c                 S   rq  rr  r~  r"  r2   r2   r3   rP     ru  rh  ri  rv  rk  r2   r2   r3   test_airybi_prime  rx  z TestSystematic.test_airybi_primec                 C   ry  )Nc                 S   ra  r  rc  r"  r2   r2   r3   rP     rQ   z:TestSystematic.test_airybi_prime_complex.<locals>.<lambda>c                 S   rq  rr  r~  r"  r2   r2   r3   rP     ru  rz  rk  r2   r2   r3   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 rb  )r   beiHYPERKWr"  r2   r2   r3   rP         z)TestSystematic.test_bei.<locals>.<lambda>rh  ri  )r   r+   r  r   r
   rk  r2   r2   r3   test_bei     

zTestSystematic.test_beic                 C   r  )Nc                 S   r  rb  )r   berr  r"  r2   r2   r3   rP     r  z)TestSystematic.test_ber.<locals>.<lambda>rh  ri  )r   r+   r  r   r
   rk  r2   r2   r3   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 rJ   )r+   	bernoullir   rC   r2   r2   r3   rP         z/TestSystematic.test_bernoulli.<locals>.<lambda>c                 S   s   t tt| S rJ   )r?   r   r  r   r  r2   r2   r3   rP         r   i2  r   r=   rC   )r   r   rk  r2   r2   r3   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 rJ   r   besselir  rN   r2   r2   r3   rP     r  z-TestSystematic.test_besseli.<locals>.<lambda>}Ô%I}Ô%ITgJDrp   )r   r+   ivr   r
   rk  r2   r2   r3   test_besseli  s
   

zTestSystematic.test_besselic                 C   (   t dd tdd tddt g d S )Nc                 S   rI   rJ   )r+   r  rM   rN   r2   r2   r3   rP     rQ   z5TestSystematic.test_besseli_complex.<locals>.<lambda>c                 S   r  rJ   r  rN   r2   r2   r3   rP     r  r  r  r   r   r
   r   rk  r2   r2   r3   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   r  rJ   r   besseljr  rN   r2   r2   r3   rP     r  z-TestSystematic.test_besselj.<locals>.<lambda>r  r  rh  ri  Tr   c                 S   r  rJ   r  rN   r2   r2   r3   rP     r  re  rf  rg  )r   r=   )r   r+   jvr   r
   rk  r2   r2   r3   test_besselj   s   


zTestSystematic.test_besseljc                 C   s$   t dd tdd t t g d S )Nc                 S   rI   rJ   )r+   r  rM   rN   r2   r2   r3   rP     rQ   z5TestSystematic.test_besselj_complex.<locals>.<lambda>c                 S   r  rJ   r  rN   r2   r2   r3   rP     r  r  rk  r2   r2   r3   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   r8   r   Fr]   nan_okr=   )r   r+   kvr   besselkr
   r"   rN  rk  r2   r2   r3   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"   rN  rk  r2   r2   r3   test_besselk_int  r  zTestSystematic.test_besselk_intc                 C   r  )Nc                 S   rI   rJ   )r+   r  rM   rN   r2   r2   r3   rP     rQ   z5TestSystematic.test_besselk_complex.<locals>.<lambda>c                 S   r  rJ   )r   r  r  rN   r2   r2   r3   rP      r  r  r  r  rk  r2   r2   r3   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   besselyr  r   r"   rN  signnanrO   rD   r/   r2   r2   r3   	mpbessely$  s   z.TestSystematic.test_bessely.<locals>.mpbesselyr  r  re  rf    r  )r   r+   yvr   r
   rl  r  r2   r2   r3   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   rN  r  r  r2   r2   r3   r  3  s   
z6TestSystematic.test_bessely_complex.<locals>.mpbesselyc                 S   rI   rJ   )r+   r  rM   rN   r2   r2   r3   rP   :  rQ   z5TestSystematic.test_bessely_complex.<locals>.<lambda>i:  r  r  r  r2   r2   r3   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 rb  )r?   r   r  r   r"   r  r  r2   r2   r3   r  @  s   z2TestSystematic.test_bessely_int.<locals>.mpbesselyc                 S      t t| |S rJ   )r+   ynr   rN   r2   r2   r3   rP   F  r   z1TestSystematic.test_bessely_int.<locals>.<lambda>rz     re  rf  r   r   r   r
   r  r2   r2   r3   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   )rt   rs   nonzero
bad_pointsr2   r3   r   M  s   (z&TestSystematic.test_beta.<locals>.betac                        | |ddS NT)r  r2   r   )r   r2   r3   rP   ]  rQ   z*TestSystematic.test_beta.<locals>.<lambda>r   Tr   r   dy=)r   r   rp   F)r   r+   r   r
   r"   r)   rk  r2   )r  r   r3   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rt   rs   rD   r2   r2   r3   rP   k  r  z-TestSystematic.test_betainc.<locals>.<lambda>)r   r+   r  r   r   r
   rk  r2   r2   r3   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!   rm   )r   r"   r  r?   r|   r&   r   binomial)rC   kr  r  r2   r3   r  q  s   .z+TestSystematic.test_binom.<locals>.binomialc                    r  r  r2   )rC   r  )r  r2   r3   rP     rQ   z+TestSystematic.test_binom.<locals>.<lambda>r   r   r   r   rp   r  )r   r+   binomr
   r"   r)   rk  r2   )r  r  r3   
test_binomn  s   


zTestSystematic.test_binomc                 C   (   t dd tdd t t gdd d S )Nc                 S   r  rJ   )r+   eval_chebytr   rC   rD   r2   r2   r3   rP     r   z0TestSystematic.test_chebyt_int.<locals>.<lambda>c                 S   r  rJ   )r   chebytr  r  r2   r2   r3   rP     r  r5   r  r  rk  r2   r2   r3   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 rJ   )r   r   r   r  r  r  r2   r2   r3   rP     r   z,TestSystematic.test_chebyt.<locals>.<lambda>e   '  r  )r   r+   r  r
   rk  r2   r2   r3   test_chebyt  s   
zTestSystematic.test_chebytc                 C   r  )Nc                 S   r  rJ   )r+   eval_chebyur   r  r2   r2   r3   rP     r   z0TestSystematic.test_chebyu_int.<locals>.<lambda>c                 S   r  rJ   )r   chebyur  r  r2   r2   r3   rP     r  r5   r  r  rk  r2   r2   r3   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  rJ   )r   r   r   r  r  r  r2   r2   r3   rP     r   z,TestSystematic.test_chebyu.<locals>.<lambda>r  r  )r   r+   r  r
   rk  r2   r2   r3   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   ra  rp  r+   shichir   r2   r2   r3   chi  ru  z$TestSystematic.test_chi.<locals>.chigU@X   g   V@)r   r   r  r
   r   rl  r  r2   r2   r3   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   ra  rp  r  r"  r2   r2   r3   r    ru  z,TestSystematic.test_chi_complex.<locals>.chire  rf  r]   r<   )r   r   r  r   r'   r"   rN  r  r2   r2   r3   test_chi_complex     
zTestSystematic.test_chi_complexc                 C   s"   dd }t |tjtddg d S )Nc                 S   ra  rp  r+   sicir   r2   r2   r3   ci  ru  z"TestSystematic.test_ci.<locals>.cire  rf  )r   r   r  r
   rl  r  r2   r2   r3   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   ra  rp  r  r"  r2   r2   r3   r    ru  z*TestSystematic.test_ci_complex.<locals>.cire  rf  rL  r<   )r   r   r  r   r'   r"   rN  r  r2   r2   r3   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+  r2   r2   r3   
test_cospi  s
   
zTestSystematic.test_cospic                 C      t ttjt gddd d S )NFr;   r  )r   r   r   r.  r   rk  r2   r2   r3   test_cospi_complex  s   

z!TestSystematic.test_cospi_complexc                 C   s"   t tjttjt gddd d S )Nr]   r5   r=   r   )r   r+   r  r   r   r
   rk  r2   r2   r3   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$   t | jdk t | jdk @ ddS )Nr   gQ?FT)r"   whererM   r   rD  r"  r2   r2   r3   param_filter  s   $z9TestSystematic.test_digamma_complex.<locals>.param_filterr;   r  r=   r   r  )r   r+   r  r   r   r   )rl  r  r2   r2   r3   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  r2   r2   r3   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<   r5      r   r   r   =   r   r   ir  y                )r   r+   r  r   r  r   r'   r"   rN  r$   r   r#   r   rk  r2   r2   r3   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   r2   r2   r3   rP     r   z,TestSystematic.test_exprel.<locals>.<lambda>r   c                 S   r  r  r  r   r2   r2   r3   rP     r   r]   gW:r   g   mBgyCxDr  r<   )r   r+   exprelr
   r"   r   r*  doubler   r)   rN  r   isinfrk  r2   r2   r3   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"   rN  rk  r2   r2   r3   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   r2   r2   r3   rP     rQ   z3TestSystematic.test_log1p_complex.<locals>.<lambda><   r  )r   r+   log1pr   rk  r2   r2   r3   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   r2   r2   r3   rP     r  z-TestSystematic.test_log1pmx.<locals>.<lambda>r  r   )r   r=   )r   r   r
   rk  r2   r2   r3   test_log1pmx
  s   

zTestSystematic.test_log1pmxc                 C   r  )Nr  r<   )r   r+   r,   r   r(   r
   rk  r2   r2   r3   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"   rN  rk  r2   r2   r3   test_ei_complex  s
   
zTestSystematic.test_ei_complexc                 C   s   t tjtjtddg d S )Nr   rs   )r   r+   elliper   r
   rk  r2   r2   r3   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+   	ellipeincr   r!  r
   rk  r2   r2   r3   test_ellipeinc!  s   zTestSystematic.test_ellipeincc                 C      t tjtjt t g d S rJ   r$  rk  r2   r2   r3   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   ellipfr
   rk  r2   r2   r3   test_ellipf+  s   zTestSystematic.test_ellipfc                 C   r'  rJ   r*  rk  r2   r2   r3   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<  )r6  r2   r2   r3   rP   :  rQ   z,TestSystematic.test_ellipk.<locals>.<lambda>g        )rt   r   r  )r   r+   r<  r   r
   ellipkm1rk  r2   r2   r3   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 rb  r   ellippiphir6  r2   r2   r3   r+  ?  ru  z0TestSystematic.test_ellipkinc.<locals>.ellipkincrh  ri  r   r   Tr  r   r+   r+  r
   rl  r+  r2   r2   r3   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   r1  rb  r2  r4  r2   r2   r3   r+  G  ru  z9TestSystematic.test_ellipkinc_largephi.<locals>.ellipkincr   r   Tr  r6  r7  r2   r2   r3   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   snr4  r   r:  r4  r2   r2   r3   r:  O  s   z+TestSystematic.test_ellipfun_sn.<locals>.snc                 S   r0  rb  r2  r4  r2   r2   r3   rP   Y  r   z1TestSystematic.test_ellipfun_sn.<locals>.<lambda>    .    .Ar   r!   r   rL  r<   rv  )rl  r:  r2   r2   r3   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   r0  rp  r2  r4  r2   r2   r3   rP   `  r   z1TestSystematic.test_ellipfun_cn.<locals>.<lambda>c                 S      t jd| |dS )Ncnr4  r;  r4  r2   r2   r3   rP   a  r   r<  r=  r   r!   r   rL  r<   rv  rk  r2   r2   r3   test_ellipfun_cn^  
   
zTestSystematic.test_ellipfun_cnc                 C   r?  )Nc                 S   r0  r1  r2  r4  r2   r2   r3   rP   g  r   z1TestSystematic.test_ellipfun_dn.<locals>.<lambda>c                 S   r@  r9  r;  r4  r2   r2   r3   rP   h  r   r<  r=  r   r!   r   rL  r<   rv  rk  r2   r2   r3   test_ellipfun_dne  rC  zTestSystematic.test_ellipfun_dnc                 C   s   t tjdd t g d S )Nc                 S   r}  rJ   r   r   r"  r2   r2   r3   rP   n     
 z)TestSystematic.test_erf.<locals>.<lambda>)r   r+   r   r
   rk  r2   r2   r3   test_erfl  s   zTestSystematic.test_erfc                 C   r  )Nc                 S   r}  rJ   rE  r"  r2   r2   r3   rP   s  rF  z1TestSystematic.test_erf_complex.<locals>.<lambda>r8   r  )r   r+   r   r   rk  r2   r2   r3   r   q  r  zTestSystematic.test_erf_complexc                 C   "   t tjtdd t gdd d S )Nc                 S   r}  rJ   r   r   r"  r2   r2   r3   rP   x  rF  z*TestSystematic.test_erfc.<locals>.<lambda>r;   r<   )r   r+   r   r   r
   rk  r2   r2   r3   	test_erfcv     

zTestSystematic.test_erfcc                 C   rH  )Nc                 S   r}  rJ   rI  r"  r2   r2   r3   rP   }  rF  z2TestSystematic.test_erfc_complex.<locals>.<lambda>r8   r  )r   r+   r   r   r   rk  r2   r2   r3   test_erfc_complex{  rK  z TestSystematic.test_erfc_complexc                 C      t tjtjt gdd d S Nr8   r  )r   r+   erfir   r
   rk  r2   r2   r3   	test_erfi  r  zTestSystematic.test_erfic                 C   rM  rN  )r   r+   rO  r   r   rk  r2   r2   r3   test_erfi_complex  r  z TestSystematic.test_erfi_complexc                 C   rH  )Nc                 S   r}  rJ   )r   ncdfr"  r2   r2   r3   rP     rF  z*TestSystematic.test_ndtr.<locals>.<lambda>r8   r  )r   r+   ndtrr   r
   rk  r2   r2   r3   	test_ndtr  rK  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"  r2   r2   r3   rP     r   z2TestSystematic.test_ndtr_complex.<locals>.<lambda>r  r   r   r  )r   r+   rS  r   r'   rk  r2   r2   r3   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 rJ   )r   r   rR  r"  r2   r2   r3   rP     r   z.TestSystematic.test_log_ndtr.<locals>.<lambda>iX  r  r;   rC   r   r=   )r   r+   log_ndtrr   r
   rk  r2   r2   r3   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 rU  )r   r   r   r"   rV  r"  r2   r2   r3   rP     r   z6TestSystematic.test_log_ndtr_complex.<locals>.<lambda>rW  r'  r  r9   r   r8   r  rC   r   )r   r+   rZ  r   r   r'   rk  r2   r2   r3   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   ra  )Nrw   )r+   eulerr  r2   r2   r3   rP     rQ   z.TestSystematic.test_eulernum.<locals>.<lambda>r!   r  r  )r   r   eulernumr   rk  r2   r2   r3   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   r8   r;      r  )	r   r+   rB   r   r@   r   r
   r"   rN  rk  r2   r2   r3   test_expint  r  zTestSystematic.test_expintc                 C      dd }t |tjt g d S )Nc                 S   ra  rb  r+   fresnelr   r2   r2   r3   fresnels  ru  z.TestSystematic.test_fresnels.<locals>.fresnels)r   r   rg  r
   )rl  rg  r2   r2   r3   test_fresnels  
   zTestSystematic.test_fresnelsc                 C   rd  )Nc                 S   ra  rp  re  r   r2   r2   r3   fresnelc  ru  z.TestSystematic.test_fresnelc.<locals>.fresnelc)r   r   rj  r
   )rl  rj  r2   r2   r3   test_fresnelc  ri  zTestSystematic.test_fresnelcc                 C   s   t tjttjt g d S rJ   )r   r+   gammar   r   r
   rk  r2   r2   r3   
test_gamma  s   zTestSystematic.test_gammac                 C       t tjttjt gdd d S Nrn   r<   )r   r+   rl  r   r   r   rk  r2   r2   r3   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  )r1   rs   r2   r2   r3   rP     r   z.TestSystematic.test_gammainc.<locals>.<lambda>r        @Finclusive_ar  r  )r   r+   r  r
   rk  r2   r2   r3   test_gammainc  
   
zTestSystematic.test_gammaincc                 C   rr  )	Nc                 S   rs  )NT)rt   r  rt  )r1   rt   r2   r2   r3   rP     r   z/TestSystematic.test_gammaincc.<locals>.<lambda>r   ru  Frv  r  r  )r   r+   	gammainccr
   rk  r2   r2   r3   test_gammaincc  ry  zTestSystematic.test_gammainccc                 C   s"   dd }t tjt|t g d S )Nc                 S   s   t | jS rJ   r   r   rM   r"  r2   r2   r3   f  s   z&TestSystematic.test_gammaln.<locals>.f)r   r+   gammalnr   r
   )rl  r}  r2   r2   r3   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  r2   r2   r3   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 )
Nr  r   r   r!   r   rw   z1e-50z0.0\4@Iw)	r   r"   r  r   r  r?   r   r  rN  rC   rt   rD   r/   r2   r2   r3   r    s   (
z6TestSystematic.test_gegenbauer_int.<locals>.gegenbauerc                 S   s(   t t| ||}t|dkrtjS |S )Nr  )r+   r  r   r   r"   rN  r  r2   r2   r3   sc_gegenbauer  s   z9TestSystematic.test_gegenbauer_int.<locals>.sc_gegenbauerr   r9   g    eg    eAi@  Tr   )rC   r   r   r=   r  r   r  )r   r   r   r
   r   r"   r#   )rl  r  r  r2   r2   r3   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 rJ   )r+   r  r   rM   rC   rt   rD   r2   r2   r3   rP     r  z8TestSystematic.test_gegenbauer_complex.<locals>.<lambda>r   r9   )r   r   r   r  r   r
   r   rk  r2   r2   r3   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 rJ   )r+   r  rM   r  r2   r2   r3   rP     r  z@TestSystematic.test_gegenbauer_complex_general.<locals>.<lambda>rh  ri  )r   r   r   r  r
   r   rk  r2   r2   r3   test_gegenbauer_complex_general  r  z.TestSystematic.test_gegenbauer_complex_generalc                 C   &   t tjtdd tddt g d S )Nc                 S   r  rJ   )r   hankel1r  rO   rD   r2   r2   r3   rP     s    z-TestSystematic.test_hankel1.<locals>.<lambda>@x@xD)r   r+   r  r   r
   rk  r2   r2   r3   test_hankel1  s   
zTestSystematic.test_hankel1c                 C   r  )Nc                 S   r  rJ   )r   hankel2r  r  r2   r2   r3   rP   !  r  z-TestSystematic.test_hankel2.<locals>.<lambda>r  r  )r   r+   r  r   r
   rk  r2   r2   r3   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  rJ   )r+   eval_hermiter   r  r2   r2   r3   rP   &  r   z-TestSystematic.test_hermite.<locals>.<lambda>r   r  )r   r   r   hermiter   r
   rk  r2   r2   r3   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 rJ   rY   rt   rD   KWr2   r3   rP   1  r  z,TestSystematic.test_hyp0f1.<locals>.<lambda>r  r  r   g     j@r  r  )r   r   r+   rL   r
   rk  r2   r  r3   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   rI   rJ   rK   )rt   r1   r2   r2   r3   rP   :  rQ   z4TestSystematic.test_hyp0f1_complex.<locals>.<lambda>c                 S   r  rJ   )r   rL   r  r  r2   r2   r3   rP   ;  r  r   r   irH   )r   r   r
   r   r'   rk  r2   r2   r3   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 rJ   )r   hyp1f1ZeroDivisionErrorr"   rN  r  r2   r2   r3   mpmath_hyp1f1B  s
   
z1TestSystematic.test_hyp1f1.<locals>.mpmath_hyp1f1r  r5   r!   Frv  r   )rC   r  )r   r+   r  r
   )rl  r  r2   r2   r3   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   r  rJ   )r+   r  rM   r  r2   r2   r3   rP   R  r  z4TestSystematic.test_hyp1f1_complex.<locals>.<lambda>c                 S      t j| ||fi tS rJ   )r   r  r  r  r2   r2   r3   rP   S  r  rh  ri  i  r  )r   r   r   r
   r   rk  r2   r2   r3   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 rJ   )r+   r   rM   rt   rs   r}   rD   r2   r2   r3   rP   Z  r  z4TestSystematic.test_hyp2f1_complex.<locals>.<lambda>c                 S      t j| |||fi tS rJ   )r   r   r  r  r2   r2   r3   rP   [  r\   g      Yg      Y@r   r  r  rk  r2   r2   r3   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   r  rJ   )r   rr   r  r  r2   r2   r3   rP   b  r  z,TestSystematic.test_hyperu.<locals>.<lambda>)r   r+   rr   r   r
   rk  r2   r2   r3   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 rJ   )r   powerr%   rl  r  r2   r2   r3   mp_igam_facg     "z1TestSystematic.test_igam_fac.<locals>.mp_igam_facr   g  ļBFrv  r   r<   )r   r   r
   )rl  r  r2   r2   r3   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+   j0r   r
   rk  r2   r2   r3   test_j0o  s   


zTestSystematic.test_j0c                 C   r  r  )r   r+   j1r   r
   rk  r2   r2   r3   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  rJ   r   jacobir  r  r2   r2   r3   rP     r\   z,TestSystematic.test_jacobi.<locals>.<lambda>c                 S      t t| |||S rJ   r+   eval_jacobir   )rC   rs   r}   rD   r2   r2   r3   rP     r  c                 S   r  rJ   r  r  r2   r2   r3   rP     r\   )r   r+   r  r   r
   r   rk  r2   r2   r3   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  rC   rt   rs   rD   r2   r2   r3   r    s   z.TestSystematic.test_jacobi_int.<locals>.jacobic                 S   r  rJ   r  r  r2   r2   r3   rP     r  z0TestSystematic.test_jacobi_int.<locals>.<lambda>c                    s   t  | |||fi tS rJ   )r   r  r  r  r2   r3   rP     r    N  r5   r]  r   r   r
   rk  r2   r  r3   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   r7   )r   r   r   keir  r   r2   r2   r3   r    s   
z$TestSystematic.test_kei.<locals>.keiꌠ9Y>)ꌠ9Y>)Fr  r  )r   r+   r  r
   )rl  r  r2   r2   r3   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   r  rb  )r   kerr  r   r2   r2   r3   rP     r  z)TestSystematic.test_ker.<locals>.<lambda>r  r  r  r  )r   r+   r  r   r
   rk  r2   r2   r3   test_ker  r\  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 rJ   r   r   laguerrer  r  r2   r2   r3   rP     r\   z.TestSystematic.test_laguerre.<locals>.<lambda>)r   r   r+   eval_laguerrer
   rk  r2   r2   r3   test_laguerre  s   

zTestSystematic.test_laguerrec                 C   s$   t dd dd t t gdd d S )Nc                 S   r  rJ   )r+   r  r   r  r2   r2   r3   rP     r   z2TestSystematic.test_laguerre_int.<locals>.<lambda>c                 S   r  rJ   r  r  r2   r2   r3   rP     r\   r  r  r  rk  r2   r2   r3   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 rJ   )r+   rE  r   rM   rD   r  r2   r2   r3   rP     r  z3TestSystematic.test_lambertw_real.<locals>.<lambda>c                 S   r  rJ   )r   rE  r   rM   r  r2   r2   r3   rP     r  r   r   r;   Fr=   r  )r   r   r"   rN  r   rk  r2   r2   r3   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   )overrG   )r"   r   rN  r   )rD   facrT   egr2   r3   rl    s   



z:TestSystematic.test_lanczos_sum_expg_scaled.<locals>.gammar   Frv  r;   r<   )r"   r%   r   r   rl  r
   )rl  maxgammarl  r2   r  r3   test_lanczos_sum_expg_scaled  s   

z+TestSystematic.test_lanczos_sum_expg_scaledc                 C   r'  rJ   )r   r+   eval_legendrer   legendrer
   rk  r2   r2   r3   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  rJ   r+   r  r   r  r2   r2   r3   rP     r   z2TestSystematic.test_legendre_int.<locals>.<lambda>c                 S   r  rJ   r   r   r  r  r  r2   r2   r3   rP     r\   r  r  c                 S   r  rJ   r  r  r2   r2   r3   rP     r   c                 S   r  rJ   r  r  r2   r2   r3   rP     r\   r  r  re   )r   r   r
   r   r"   r#   rk  r2   r2   r3   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   rw   rw   )#v)	r+   lpmn
ValueErrorr"   r  r   rN  r  rM   rC   r6  r1   rO   r2   r2   r3   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"   rN  r  rM   r  r2   r2   r3   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!   rw   r   rm   r   rl   typer  )r   r   r  r  r   r"   r  r   r   rN  rM   )rC   r6  r1   typrO   r2   r2   r3   r     s   
z*TestSystematic.test_legenp.<locals>.legenpr'  r9   rw   r!   r   r  r  )rl  r  r  r   r2   r2   r3   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+   clpmnrM   r  r"   r  rC   r6  r1   r2   r2   r3   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 Nrm   r   r  r   r"   r  r   r   r   r   rM   r  r2   r2   r3   r        "z4TestSystematic.test_legenp_complex_2.<locals>.legenp	ry   r   rF   r   rg  rG   r   re   g     @@rh  rF   rG   g?r   ry   rw   r   r!   r   r   r   r   r  r"   r)   r   r   r   rl  r  r   rD   rS   r1   r2   r2   r3   test_legenp_complex_2     (
z$TestSystematic.test_legenp_complex_2c                 C   r  )Nc                 S   r  )Nrl   r  r   r  r  r  r2   r2   r3   r  /  r  z3TestSystematic.test_legenp_complex_3.<locals>.clpnmc                 S   r  )Nrm   rl   r  r  r  r2   r2   r3   r   5  r  z4TestSystematic.test_legenp_complex_3.<locals>.legenpr  r  r   r  r   r   r  r  r  r2   r2   r3   test_legenp_complex_3.  r  z$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  r2   r2   r3   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  r2   r2   r3   r  K  s   z*TestSystematic.test_legenq.<locals>.legenqr   r9   r  rl  r  r  r2   r2   r3   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   rM   r  r2   r2   r3   r  W  r  z0TestSystematic.test_legenq_complex.<locals>.lqnmc                 S   r  r  )r   r"   r  r   r   r  r   rM   r  r2   r2   r3   r  Z  r  z2TestSystematic.test_legenq_complex.<locals>.legenqr   r9   r  )r   r   r   r  r2   r2   r3   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   r2   r2   r3   r  f  s    z0TestSystematic.test_lgam1p.<locals>.param_filterc                 S   s   t d|  jS rp  r|  r"  r2   r2   r3   	mp_lgam1pj  s   z-TestSystematic.test_lgam1p.<locals>.mp_lgam1pr;   r9   r   )r   r   r
   )rl  r  r  r2   r2   r3   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 rJ   )r   r   r  r'   r"   r  )r1   rT   r2   r2   r3   mpmath_loggammat  s   z5TestSystematic.test_loggamma.<locals>.mpmath_loggammaFr   )r  distinguish_nan_and_infr=   )r   r+   r   r   )rl  r  r2   r2   r3   test_loggammas  s   
zTestSystematic.test_loggammac                 C   s(   dd }t |tdd t t g d S )Nc                 S   r0  rb  )r+   pbdvr  r2   r2   r3   pcfd  r8  z&TestSystematic.test_pcfd.<locals>.pcfdc                 S   r  rJ   )r   r  r  r  r2   r2   r3   rP     r  z*TestSystematic.test_pcfd.<locals>.<lambda>)r   r   r
   )rl  r  r2   r2   r3   	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   r0  rb  )r+   pbvvr  r2   r2   r3   pcfv  r8  z&TestSystematic.test_pcfv.<locals>.pcfvc                 S   r  rJ   )r   r   r   r  r  r  r2   r2   r3   rP     r   z*TestSystematic.test_pcfv.<locals>.<lambda>r  r  rv  )rl  r  r2   r2   r3   	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   r0  rb  r+   pbwar  r2   r2   r3   pcfw  r8  z&TestSystematic.test_pcfw.<locals>.pcfwc                 S   r0  rp  r
  r  r2   r2   r3   dpcfw  r8  z'TestSystematic.test_pcfw.<locals>.dpcfwc                 S   s   t t j| |fdS )Nr:   )r   diffr  r  r2   r2   r3   mpmath_dpcfw  r   z.TestSystematic.test_pcfw.<locals>.mpmath_dpcfwrc   rd   g:0yU>r9   r  g&.!>)r   r   r  r
   )rl  r  r  r  r2   r2   r3   	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+   	polygammar   r   r   r   r
   rk  r2   r2   r3   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)rC   r  r   )r   r+   r  r   r
   r"   rN  rk  r2   r2   r3   test_rgamma  s   
zTestSystematic.test_rgammac                 C   rn  ro  )r   r+   r  r   r   r   rk  r2   r2   r3   test_rgamma_complex  rq  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 )Nrv   c                 S   sN   t | | t| | kr!t | | dkr!t| } t| | |  }t| |S rb  )r?   r   r   r  rf)rt   r6  r2   r2   r3   mppoch  s   (
z&TestSystematic.test_rf.<locals>.mppochr   r  )
r   parser   r   Versionr  r   r+   pochr
   )rl  r  r2   r2   r3   test_rf  s   	

zTestSystematic.test_rfc                 C   r  r  )	r"   r*  r?   r+  r   r   r   r(  r
   r  r2   r2   r3   
test_sinpi  s   
zTestSystematic.test_sinpic                 C   r  )NFg+=r  )r   r   r   r(  r   rk  r2   r2   r3   test_sinpi_complex  s   

z!TestSystematic.test_sinpi_complexc                 C   r  )Nc                 S   ra  rb  r  r   r2   r2   r3   shi  ru  z$TestSystematic.test_shi.<locals>.shir  )r   r   r  r
   r   rl  r  r2   r2   r3   test_shi  r  zTestSystematic.test_shic                 C   r  )Nc                 S   ra  rb  r  r"  r2   r2   r3   r    ru  z,TestSystematic.test_shi_complex.<locals>.shire  rf  r]   r<   )r   r   r  r   r'   r"   rN  r  r2   r2   r3   test_shi_complex  r  zTestSystematic.test_shi_complexc                 C   rd  )Nc                 S   ra  rb  r  r   r2   r2   r3   si  ru  z"TestSystematic.test_si.<locals>.si)r   r   r!  r
   rl  r!  r2   r2   r3   test_si  s   zTestSystematic.test_sic                 C   r  )Nc                 S   ra  rb  r  r"  r2   r2   r3   r!    ru  z*TestSystematic.test_si_complex.<locals>.sire  rf  r]   r<   )r   r   r!  r   r'   r"   rN  r"  r2   r2   r3   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   r2   r2   r3   dilog  r8  z)TestSystematic.test_spence.<locals>.dilogr   r   r<   )r   r+   r#  r   r
   r"   rN  rl  r'  r2   r2   r3   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"  r2   r2   r3   r'     r8  z1TestSystematic.test_spence_complex.<locals>.dilogr   r<   )r   r+   r#  r   r   r(  r2   r2   r3   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 rJ   )r"   r  r+   sph_harm)lr6  r   r5  r2   r2   r3   	spherharm  s   z0TestSystematic.test_spherharm.<locals>.spherharmr   r9   r   r   rL  ip  rV   )rp   rC   r   )r   r   r-  r   r
   r   )rl  r-  r2   r2   r3   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     ru  r   &.>r<   )r   r+   struver   r   struvehr
   rk  r2   r2   r3   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   struvel)rO   r1   r   r2   r2   r3   
mp_struvel  s   z/TestSystematic.test_struvel.<locals>.mp_struvelr/  ru  r   r0  Tr   )r   r+   	modstruver   r
   )rl  r5  r2   r2   r3   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   rE  r%   r  r   r2   r2   r3   mpmath_wrightomega_real+  s   zETestSystematic.test_wrightomega_real.<locals>.mpmath_wrightomega_realrz   gPKDg+<r   F)r=   rp   r  )r   r+   rQ  r
   )rl  r8  r2   r2   r3   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 )NrH  )rG  r"  r2   r2   r3   rP   <  rF  z1TestSystematic.test_wrightomega.<locals>.<lambda>r   Fr  )r   r+   rQ  r   rk  r2   r2   r3   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)rt   rs   rw  r   rt   rw  )r   r+   zetar   r   r
   rk  r2   r2   r3   test_hurwitz_zeta?  s   
z TestSystematic.test_hurwitz_zetac                 C   s$   t tjdd tddgddd d S )Nc                 S   s   | dkr	t | S t jS rp  r   r=  rN  r   r2   r2   r3   rP   H  r\   z2TestSystematic.test_riemann_zeta.<locals>.<lambda>r'  r9   Frn   r  )r   r+   r=  r
   rk  r2   r2   r3   test_riemann_zetaE  s   

z TestSystematic.test_riemann_zetac                 C   s&   t tjdd tddgdddd d S )	Nc                 S   s   | dkrt | d S t jS rp  r?  r   r2   r2   r3   rP   P  s   z+TestSystematic.test_zetac.<locals>.<lambda>r'  r9   F-   rn   )r  r   r=   )r   r+   zetacr
   rk  r2   r2   r3   
test_zetacN  s
   

zTestSystematic.test_zetacc                 C   4   dd }t tjt|tdddt gdddd	 d S )
Nc                 S   s>   t j| } t j|}|dkrt j| S t j| || S rb  r   r   r  r   powm1)rD   lmbdar2   r2   r3   	mp_boxcoxW  s
   z-TestSystematic.test_boxcox.<locals>.mp_boxcoxr   Fr<  r8   r  r;   rY  )r   r+   boxcoxr   r
   )rl  rH  r2   r2   r3   test_boxcoxU  s   
zTestSystematic.test_boxcoxc                 C   rD  )
Nc                 S   sR   t j| } t j|}t jd}|dkrt j||  S t j||  || S r   rE  )rD   rG  oner2   r2   r3   mp_boxcox1ph  s   z1TestSystematic.test_boxcox1p.<locals>.mp_boxcox1prw   Fr<  r8   r  r;   rY  )r   r+   boxcox1pr   r
   )rl  rL  r2   r2   r3   test_boxcox1pf  s   	
zTestSystematic.test_boxcox1pc                 C   4   dd }t dd t|tddtddgd	d
 d S )Nc                 S   L   t |}t | t dd  |t d| t j  }|jdkr$|jS |S Nr!   r   r   r   	mpmathifyr  r  rV  r   rD  rM   rC   r1   argoutr2   r2   r3   mp_spherical_jny     

z9TestSystematic.test_spherical_jn.<locals>.mp_spherical_jnc                 S   r  rJ   )r+   spherical_jnr   rC   r1   r2   r2   r3   rP     r   z2TestSystematic.test_spherical_jn.<locals>.<lambda>r   r8   re  rf  r  r  r  rl  rW  r2   r2   r3   test_spherical_jnx     	
z TestSystematic.test_spherical_jnc                 C   ,   dd }t dd t|tddt g d S )Nc                 S   rP  rQ  rR  rT  r2   r2   r3   rW    rX  zATestSystematic.test_spherical_jn_complex.<locals>.mp_spherical_jnc                 S      t t| j|S rJ   )r+   rY  r   rM   rZ  r2   r2   r3   rP     r  z:TestSystematic.test_spherical_jn_complex.<locals>.<lambda>r   r8   r   r   r   r   r[  r2   r2   r3   test_spherical_jn_complex  
   	z(TestSystematic.test_spherical_jn_complexc                 C   rO  )Nc                 S   rP  rQ  r   rS  r  r  rV  r   rD  rM   rT  r2   r2   r3   mp_spherical_yn  rX  z9TestSystematic.test_spherical_yn.<locals>.mp_spherical_ync                 S   r  rJ   )r+   spherical_ynr   rZ  r2   r2   r3   rP     r   z2TestSystematic.test_spherical_yn.<locals>.<lambda>r   r8   g    _r;  r9   r  r  rl  rd  r2   r2   r3   test_spherical_yn  r]  z TestSystematic.test_spherical_ync                 C   r^  )Nc                 S   rP  rQ  rc  rT  r2   r2   r3   rd    rX  zATestSystematic.test_spherical_yn_complex.<locals>.mp_spherical_ync                 S   r_  rJ   )r+   re  r   rM   rZ  r2   r2   r3   rP     r  z:TestSystematic.test_spherical_yn_complex.<locals>.<lambda>r   r8   r`  rf  r2   r2   r3   test_spherical_yn_complex  rb  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   rP  rQ  r   rS  r  r  rV  r   rD  rM   rT  r2   r2   r3   mp_spherical_in  rX  z9TestSystematic.test_spherical_in.<locals>.mp_spherical_inc                 S   r  rJ   )r+   spherical_inr   rZ  r2   r2   r3   rP     r   z2TestSystematic.test_spherical_in.<locals>.<lambda>r   r8   g訰6r  r  rl  rj  r2   r2   r3   test_spherical_in  s   	
z TestSystematic.test_spherical_inc                 C   r^  )Nc                 S   rP  rQ  ri  rT  r2   r2   r3   rj    rX  zATestSystematic.test_spherical_in_complex.<locals>.mp_spherical_inc                 S   r_  rJ   )r+   rk  r   rM   rZ  r2   r2   r3   rP     r  z:TestSystematic.test_spherical_in_complex.<locals>.<lambda>r   r8   r`  rl  r2   r2   r3   test_spherical_in_complex  rb  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 rQ  )r   r  r  rV  r   rS  rD  rM   )rC   r1   rV  r2   r2   r3   mp_spherical_kn  s   z9TestSystematic.test_spherical_kn.<locals>.mp_spherical_knc                 S   r  rJ   )r+   spherical_knr   rZ  r2   r2   r3   rP     r   z2TestSystematic.test_spherical_kn.<locals>.<lambda>r   rV   r9   r  r  rl  ro  r2   r2   r3   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   rP  rQ  )r   rS  r  r  rV  r   rD  rM   rT  r2   r2   r3   ro    rX  zATestSystematic.test_spherical_kn_complex.<locals>.mp_spherical_knc                 S   r_  rJ   )r+   rp  r   rM   rZ  r2   r2   r3   rP     r  z:TestSystematic.test_spherical_kn_complex.<locals>.<lambda>r   r8   r  r`  rq  r2   r2   r3   test_spherical_kn_complex  s   	
z(TestSystematic.test_spherical_kn_complexN)__name__
__module____qualname__rm  rn  rw  r{  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  pytestmarkxfailr  r  r  r  r  r  r  r  r  r  r  r  r
  r  r  r  r  r  r  r"  r&  r(  r-  r.  r0  r8  r9  r>  rB  rD  rG  r   rJ  rL  rP  rQ  rT  rX  r[  r^  ra  rc  rh  rk  rm  rp  rx  r{  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r  xfail_on_32bitr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r	  r  r  r  r  r  r  r  r  r   r#  r$  r)  r*  r.  r3  r7  r9  r:  r>  r@  rC  rJ  rN  r\  ra  rg  rh  rm  rn  rr  rs  r2   r2   r2   r3   r`    sD   





		
	
0







	






3






		
		r`  )J__doc__numpyr"   numpy.testingr   r   r   rw  r   
scipy._libr   scipy.specialspecialr+   scipy.special._testutilsr   r   r   r	   scipy.special._mptestutilsr
   r   r   r   r   r   r   r   r   r   scipy.special._ufuncsr   r   r   r   r   r   r   ImportErrorr4   rE   rU   rb   ru   r   r   r   r   rx  slowr   r   r   r   r   r   r  r	  r  r  r  r  r&  r-  r/  rA  rG  rW  rY  r[  r\  r   r  r`  r2   r2   r2   r3   <module>   s    0 










7
&






