o
    [qi+                     @   s`  d Z ddlZddlmZ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'yq   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! Z0ee&d"ej1j2d#d$ Z3ee&dd%d& Z4ee&d'd(d) Z5ee&d'd*d+ Z6d,Z7ee&dd-d. Z8ee&dd/d0 Z9ee&dej1j2d1d2 Z:ee&dej1j2d3d4 Z;ee&dd5d6 Z<ee&dd7d8 Z=ee&dej1j2d9d: Z>ee&dej1j2d;d< Z?ee&dd=d> Z@ee&dd?d@ ZAee&ddAdB ZBdCdD ZCej1j2ee&ddEdF ZDej1j2ee&ddGdH ZEej1j2ee&ddIdJ ZFej1j2ee&ddKdL ZGeHdMdMdNZIej1j2ee&dOG dPdQ dQZJdS )Rz4
Test SciPy functions versus mpmath, if available.

    N)assert_assert_allclosesuppress_warnings)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 ]$}t ddt j dD ]}|t d|  }| |tt|f qq	t j	| t j
d} ttj| dd  d S )	Ni   
   r                    ?Zdtype   )nplogspacelinspacer   expappendcomplexr   eiarrayZcdoubler	   scexpicheck)datasetrpz r1   f/home/app/PaddleOCR-VL/.venv_paddleocr/lib/python3.10/site-packages/scipy/special/tests/test_mpmath.pytest_expi_complex#   s   r3   z0.19c                  C   s   g } dD ]/}t dddD ]%}td | ||tt||f W d    n1 s-w   Y  qqt | } tt	j
| dddd	  d S )
N)2   3   r         d   r   r!   r   vIh%<=rtol)r"   r#   r   workdpsr&   floatexpintasarrayr	   r*   expnr,   )r-   nxr1   r1   r2   test_expn_large_n3   s   
rD   c                  C   s   g } g d}|D ]7}|D ]2}|D ]-}|d|  }t d tt ||}W d    n1 s0w   Y  | |||f qqqt| } tdd | dddd	  d S )
N)g     Xg      #            ?g      #@g     X@r   x   c                 S      t | j|S Nr*   hyp0f1realvr0   r1   r1   r2   <lambda>U       z$test_hyp0f1_gh5764.<locals>.<lambda>r9   r   r:   r;   )	r   r=   r'   rK   r&   r"   r)   r	   r,   )r-   ZaxisrN   rC   yr0   resr1   r1   r2   test_hyp0f1_gh5764D   s"   
	
rS   c                  C   sF   t ddd} t| d}t dd | D }t||tdd d S )	N         rF   c                 S   s   g | ]}t |d qS )rF   r   rK   ).0rN   r1   r1   r2   
<listcomp>^       z'test_hyp0f1_gh_1609.<locals>.<listcomp>-q=r;   )r"   r$   r*   rK   r)   r   astyper>   )vvafmfr1   r1   r2   test_hyp0f1_gh_1609Y   s   r`   z1.1.0c                  C   s   g } t ddD ]6}t dddD ],}| }| ||dtt||df | | d }| ||dtt||df qqdD ]}dD ]}| ||dtt||df qEqAt | } tt	j| dd	d
dd
  d S )N      r   r!   )      %      rE   r   rF   r!   r   )      rE   r   rF   r!         ?r         @r   r!   r      V瞯<-a=r<   atol)r"   aranger$   r&   r>   r   hyperur)   r	   r*   r,   )r-   rB   bar1   r1   r2   test_hyperu_around_0f   s    ""
rs   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   ru   ffffff?)r   rw   rv   )r   r!   gffffffr6   )repeatc                 S   sD   g | ]\}}}}||krt ||kr|d k r|dkr||||fqS )r   rx   )round)rX   rr   rq   crC   r1   r1   r2   rY      s
    
$
z.test_hyp2f1_strange_points.<locals>.<listcomp>T)Z	eliminatec                    s&   g | ]}|t tj|i  f qS r1   r>   r   hyp2f1rX   r/   kwr1   r2   rY      s   & r    r   r!   r   rj   绽|=r;   )list	itertoolsproductdictr"   r)   float64r	   r*   r}   r,   ptsr-   r1   r   r2   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   rj   r   )UUUUUU?gUUUUUU?g?g      ?)      ?rF   g      ?gX<ݚ?)r   rw   rj   )r   r   rw   rj   )r   re   re   rj   r   )gx&?ru   ra   g333333?)r   r   r   +?)r   r   r   ru   )r   rj   rb   Gz?)rg   rE   rj   r   )r   rh   g      
r   )g*4]92@g|O%@gCu?)  rd   r   )r   r         %@r   )ru   r   r!         ?)ru   r   r!   rf   )r      rb   r   )r   r   rb   rf   )rF   g     prg   gm˟?c                 S   s    g | ]}|t tj| f qS r1   r|   r~   r1   r1   r2   rY           z0test_hyp2f1_real_some_points.<locals>.<listcomp>r    ignoreinvalidr   r6   r   r;   )r"   r)   r   errstater	   r*   r}   r,   r   r1   r1   r2   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   )r5   r   )r   gwJ)r   |r   r   )r   r   rd   r   c                 S   s"   t | trt| d | d  S | S )Nr   r!   )
isinstancetupler>   rC   r1   r1   r2   fev   s   
z&test_hyp2f1_some_points_2.<locals>.fevc                    s*   g | ]}t t |ttj| f qS r1   )r   mapr>   r   r}   r~   r   r1   r2   rY         * z-test_hyp2f1_some_points_2.<locals>.<listcomp>r    r   r6   r   r;   )r"   r)   r   r	   r*   r}   r,   r   r1   r   r2   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   ra   g?rb   r   )g      ru   r!   g@)r   r   rb   gffffff4@)r   g)\(Gzr   g333333?gffffff?rg   r   r    r   r   r   r6   &.>Tr<   ignore_inf_sign)r>   r   r}   	Exceptionr&   r"   r)   r   r   r	   r*   r,   )r-   rr   rq   r{   r0   rN   r1   r1   r2   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  rb     rg   r   r!   r   rj   ru   r   r6   r   r   r;   )r"   zerosr   randomseedZparetoZrandrandintr   __version__absmaxr>   r}   r   r	   r*   r,   )Znpointsr-   Zdsr1   r1   r2   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 rI   )r'   r   erfr   r1   r1   r2   rO      rP   z"test_erf_complex.<locals>.<lambda>Fr:   
vectorizedr<   c                 S   r   rI   )r'   r   erfcr   r1   r1   r2   rO     rP   )r   mpdpsprecr"   meshgridr$   r#   r_ravelr
   r*   r   r   )old_dpsold_precx1y1Zx2y2Zpointsr1   r1   r2   test_erf_complex   s   $$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!   ru   rw   g333333?g333333gr   r   rj      rb   r   ra   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murC   r1   r1   r2   mplegenp-  s
   ztest_lpmv.<locals>.mplegenpc                    s*   g | ]}| |d  |d |d f qS )r!   r   r   r1   r~   r   r1   r2   rY   6  r   ztest_lpmv.<locals>.<listcomp>r    c                 S   s   t | t||S rI   )r*   lpmvr\   r   )r   r   rC   r1   r1   r2   evf9     ztest_lpmv.<locals>.evfr   r   ri   r   +=rm   )extendr"   r)   r   r   r	   r,   )r   rC   r-   r   r1   r   r2   	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   8r7   r6   r   r   ru   r!   r   rF   gffffffr   g33333Yg3333r     c                 S   s   t t| |S rI   )r>   r   betarr   rq   r1   r1   r2   rO   W      ztest_beta.<locals>.<lambda>Fr   T)r   r<   r   c                 S   s   t ttt| |S rI   )r>   r   logr   r   r   r1   r1   r2   rO   _      r   )r"   r   r   r   r#   ro   r)   Zbroadcast_arraysreshapeTr   r   r   r   r
   r*   r   Zbetaln)rq   rr   abr   r   r1   r1   r2   	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   rc   r   r!   c                 S      g | ]}|t t|fqS r1   r'   r   loggammarX   Zz0r1   r1   r2   rY   y      z3test_loggamma_taylor_transition.<locals>.<listcomp>vIh%,=r;   )LOGGAMMA_TAYLOR_RADIUSr"   r)   r$   r   r   r%   r   flattenr	   r*   r   r,   r.   thetadzr0   r-   r1   r1   r2   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   rc   r   r!   c                 S   r   r1   r   r   r1   r1   r2   rY     r   z(test_loggamma_taylor.<locals>.<listcomp>r   r;   )r"   r#   log10r   r$   r   r   r%   r   r   r)   r	   r*   r   r,   r   r1   r1   r2   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 )Nru   rj   r   r   iVr!   r8   c                 S   r   r1   )r'   r   rgammar   r1   r1   r2   rY     r   z%test_rgamma_zeros.<locals>.<listcomp>r[   r;   )r"   r   r#   copyr   ro   r   dstacksizer   r   r=   r)   r	   r*   r   r,   )dxdyr   r   r0   r-   r1   r1   r2   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 )Nrg   rE   gQοru   r   r   gQ?r   r   c                 S   r   r1   r'   r   digammar   r1   r1   r2   rY     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   r0   r-   r1   r1   r2   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,  r8   r   r   rb   r   (   c                    s   g | ]
}|t  |fqS r1   )r'   r   r   r1   r2   rY         z(test_digamma_negreal.<locals>.<listcomp>r!   r:   r;   )r   r   r   r"   r#   r   r   r   r=   r@   r	   r*   r,   rC   rQ   r0   r-   r1   r  r2   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  r8   )gffffffgg@gffffff@r   r   c                 S   r   r1   r   r   r1   r1   r2   rY     r   z)test_digamma_boundary.<locals>.<listcomp>r   r!   r:   r;   )r"   r#   r)   r   r   r   r=   r@   r	   r*   r   r,   r	  r1   r1   r2   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 )Nrc   rF   r   r4   r8   c              
   S   s*   g | ]\}}||t tj||d dfqS )Trq   regularized)r>   r   gammainc)rX   Za0Zx0r1   r1   r2   rY     s    z*test_gammainc_boundary.<locals>.<listcomp>r9   r[   r;   )r"   r$   r   r   r   r   r=   zipr)   r	   r*   r  r,   )Zsmallrr   rC   r-   r1   r1   r2   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r0   r1   r1   r2   spence  r   z"test_spence_circle.<locals>.spencerF   rg   r   r   r!   r   c                    s   g | ]}| |fqS r1   r1   r   r  r1   r2   rY     rZ   z&test_spence_circle.<locals>.<listcomp>r   r;   )r"   r$   r   outerr%   r   r@   r	   r*   r  r,   )r.   r   r0   r-   r1   r  r2   test_spence_circle  s   r  c                  C   s   t tj} t jt ddd dt dddf }| }t ||\}}|d|  }t ddd	ddd}|t 
|f|j   }t d	d
 |D }tt|ddd|  d  d S )Nr   r   rj   r   r8   r!   ru   c                 S   r   r1   )r'   r   sinpir   r1   r1   r2   rY         z$test_sinpi_zeros.<locals>.<listcomp>r   r;   )r"   finfor>   epsr   r#   r   r   ro   r   r   r   r   r@   r	   r   r,   r  r   r   r   r   r0   r-   r1   r1   r2   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   rj   r   r  r8   r!   rF   ru   c                 S   r   r1   )r'   r   cospir   r1   r1   r2   rY   -  r  z$test_cospi_zeros.<locals>.<listcomp>r   r;   )r"   r  r>   r  r   r#   r   r   ro   r   r   r   r   r@   r	   r   r,   r  r1   r1   r2   test_cospi_zeros$  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mr1   r1   r2   dn9     z"test_dn_quarter_period.<locals>.dnc                 S   s   t tjd| |dS Nr'  r$  )r>   r   ellipfunr$  r1   r1   r2   	mpmath_dn<  r   z)test_dn_quarter_period.<locals>.mpmath_dnr   r!   rc   ru   r   r   r9   r   r   r;   )r"   r$   r   r#   r>   r   ellipkr&   r@   r	   r,   )	r'  r+  r&  Zdur-   Zm0Zu0Zdu0r/   r1   r1   r2   test_dn_quarter_period7  s   &
r-  c                 C   sh   t |% t | } t | jt j dt j  }t t | |}W d    |S 1 s-w   Y  |S r"  )r   r=   Zmpcceilimagr   lambertwr%   )r0   r   ZunwindrR   r1   r1   r2   _mpmath_wrightomegaP  s   

r1  c            	      C   s4  t ddd } t t jt jg}t t jt j g}t t j t jg}t t j t j g}tdD ]4}|t |d t j |t |d t j  |t |d t j |t |d t j  q4t ||||f}t | |\} }| d|  	 }t 
dd |D }ttj|dd	d
d  d S )Nr   r      r4   ru   r   c                 S      g | ]}|t t|d fqS r2  r'   r1  r   r1   r1   r2   rY   i  r  z+test_wrightomega_branch.<locals>.<listcomp>r!   :0yE>r;   )r"   r#   	nextafterr   infranger&   Zhstackr   r   r@   r	   r*   wrightomegar,   )	rC   Zpicut_aboveZpicut_belowZnpicut_aboveZnpicut_belowirQ   r0   r-   r1   r1   r2   test_wrightomega_branchX  s"   
r<  c                  C   sn   t dd} t ddt j }t | |\} }| d|   }t dd |D }ttj|dddd		  d S )
Nrw   r!   r   r   c                 S   r3  r4  r5  r   r1   r1   r2   rY   x  r  z,test_wrightomega_region1.<locals>.<listcomp>r   rk   r;   
r"   r$   r   r   r   r@   r	   r*   r:  r,   r	  r1   r1   r2   test_wrightomega_region1o     
r>  c                  C   sn   t dd} t dt j d}t | |\} }| d|   }t dd |D }ttj|dddd		  d S )
Nrw   r!   ru   r   c                 S   r3  r4  r5  r   r1   r1   r2   rY     r  z,test_wrightomega_region2.<locals>.<listcomp>r   rk   r;   r=  r	  r1   r1   r2   test_wrightomega_region2~  r?  r@  c                  C   sn   t dddt ddd} }t | |\} }| d|   }t dd |D }ttj|dddd	  d S )
Nru   r!   r2  r   c                 S   r   r1   )r'   r   r0  r   r1   r1   r2   rY     r  z(test_lambertw_smallz.<locals>.<listcomp>r   r:   r;   )	r"   r$   r   r   r@   r	   r*   r0  r,   r	  r1   r1   r2   test_lambertw_smallz  s   
rA  r7   ZmaxprecZmaxtermsz0.17c                   @   s  e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zejjd5d6d7d8d9 Z d:d; Z!ejjd5d6d7d<d= Z"d>d? Z#d@dA Z$dBdC Z%dDdE Z&dFdG Z'dHdI Z(dJdK Z)dLdM Z*dNdO Z+dPdQ Z,dRdS Z-dTdU Z.dVdW Z/dXdY Z0dZd[ Z1d\d] Z2d^d_ Z3d`da Z4dbdc Z5ddde Z6dfdg Z7dhdi Z8djdk Z9dldm Z:dndo Z;dpdq Z<drds Z=dtdu Z>dvdw Z?dxdy Z@dzd{ ZAd|d} ZBd~d ZCdd ZDdd ZEdd ZFdd ZGdd ZHdd ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPejjd5ddd ZQdd ZRejjd5ddd ZSeTdd ZUdd ZVdd ZWejjd5dd7dd ZXdd ZYdd ZZdd Z[ejjd5ddd Z\eTdd Z]ejjd5ddd Z^ej_ddd Z`dd Zadd Zbejjd5ddd Zcdd Zddd ZeddĄ ZfeTddƄ ZgddȄ Zhej_dɡdd˄ Zidd̈́ ZjeTddτ Zkddф Zlddӄ ZmddՄ Znddׄ Zoejjd5dd7ddڄ ZpeTdd܄ Zqddބ Zrdd Zsejjd5ddd Ztejjd5dd7dd Zudd Zvejjd5dd7dd Zwdd Zxdd Zyejjdddd Zzdd Z{dd Z|dd Z}dd Z~dd Zdd Zdd  Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zejjd5d%d7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  r1   r1   r2   rO     rP   z,TestSystematic.test_airyai.<locals>.<lambda>    ח    חAh㈵>r;   c                 S   rD  rE  rF  r  r1   r1   r2   rO     rP        @     @@)r   r   airyair   selfr1   r1   r2   test_airyai  s   

zTestSystematic.test_airyaic                 C   s   t dd tjt g d S )Nc                 S   rD  rE  rF  r  r1   r1   r2   rO     rP   z4TestSystematic.test_airyai_complex.<locals>.<lambda>)r   r   rL  r   rM  r1   r1   r2   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   rD  Nr!   rF  r  r1   r1   r2   rO     rP   z2TestSystematic.test_airyai_prime.<locals>.<lambda>c                 S      t j| ddS Nr!   )Z
derivativer   rL  r  r1   r1   r2   rO        rG  rH  rI  r;   c                 S   rD  rR  rF  r  r1   r1   r2   rO     rP   c                 S   rS  rT  rU  r  r1   r1   r2   rO     rV  rJ  rK  r   r   rM  r1   r1   r2   test_airyai_prime     

z TestSystematic.test_airyai_primec                 C      t dd dd t g d S )Nc                 S   rD  rR  rF  r  r1   r1   r2   rO     rP   z:TestSystematic.test_airyai_prime_complex.<locals>.<lambda>c                 S   rS  rT  rU  r  r1   r1   r2   rO     rV  r   r   rM  r1   r1   r2   test_airyai_prime_complex     z(TestSystematic.test_airyai_prime_complexc                 C   rQ  )Nc                 S   rD  r"  rF  r  r1   r1   r2   rO     rP   z,TestSystematic.test_airybi.<locals>.<lambda>c                 S   
   t | S rI   r   Zairybir  r1   r1   r2   rO        
rG  rH  rI  r;   c                 S   rD  r"  rF  r  r1   r1   r2   rO     rP   c                 S   r^  rI   r_  r  r1   r1   r2   rO     r`  rJ  rK  rW  rM  r1   r1   r2   test_airybi  rY  zTestSystematic.test_airybic                 C   rZ  )Nc                 S   rD  r"  rF  r  r1   r1   r2   rO     rP   z4TestSystematic.test_airybi_complex.<locals>.<lambda>c                 S   r^  rI   r_  r  r1   r1   r2   rO     r`  r[  rM  r1   r1   r2   test_airybi_complex  r]  z"TestSystematic.test_airybi_complexc                 C   rQ  )Nc                 S   rD  Nrj   rF  r  r1   r1   r2   rO     rP   z2TestSystematic.test_airybi_prime.<locals>.<lambda>c                 S   rS  rT  r_  r  r1   r1   r2   rO     rV  rG  rH  rI  r;   c                 S   rD  rc  rF  r  r1   r1   r2   rO     rP   c                 S   rS  rT  r_  r  r1   r1   r2   rO     rV  rJ  rK  rW  rM  r1   r1   r2   test_airybi_prime  rY  z TestSystematic.test_airybi_primec                 C   rZ  )Nc                 S   rD  rc  rF  r  r1   r1   r2   rO     rP   z:TestSystematic.test_airybi_prime_complex.<locals>.<lambda>c                 S   rS  rT  r_  r  r1   r1   r2   rO     rV  r[  rM  r1   r1   r2   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 rE  )r   beiHYPERKWr  r1   r1   r2   rO         z)TestSystematic.test_bei.<locals>.<lambda>rJ  rK  )r   r*   rh  r   r   rM  r1   r1   r2   test_bei     

zTestSystematic.test_beic                 C   rf  )Nc                 S   rg  rE  )r   berri  r  r1   r1   r2   rO     rj  z)TestSystematic.test_ber.<locals>.<lambda>rJ  rK  )r   r*   rm  r   r   rM  r1   r1   r2   test_ber  rl  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 rI   )r*   	bernoullir   rB   r1   r1   r2   rO         z/TestSystematic.test_bernoulli.<locals>.<lambda>c                 S   s   t tt| S rI   )r>   r   ro  r   rp  r1   r1   r2   rO         r   i2  r   r<   rB   )r   r   rM  r1   r1   r2   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 rI   r   besseliri  rM   r1   r1   r2   rO      rj  z-TestSystematic.test_besseli.<locals>.<lambda>}Ô%I}Ô%ITgJDrn   )r   r*   ivr   r   rM  r1   r1   r2   test_besseli  s   

zTestSystematic.test_besselic                 C   (   t dd tdd tddt g d S )Nc                 S   rH   rI   )r*   r{  rL   rM   r1   r1   r2   rO     rP   z5TestSystematic.test_besseli_complex.<locals>.<lambda>c                 S   ru  rI   rv  rM   r1   r1   r2   rO     rj  rx  ry  r   r   r   r   rM  r1   r1   r2   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   ru  rI   r   besseljri  rM   r1   r1   r2   rO     rj  z-TestSystematic.test_besselj.<locals>.<lambda>rx  ry  rJ  rK  Tr   c                 S   ru  rI   r  rM   r1   r1   r2   rO     rj  rG  rH  rI  )r   r<   )r   r*   jvr   r   rM  r1   r1   r2   test_besselj  s   


zTestSystematic.test_besseljc                 C   s$   t dd tdd t t g d S )Nc                 S   rH   rI   )r*   r  rL   rM   r1   r1   r2   rO     rP   z5TestSystematic.test_besselj_complex.<locals>.<lambda>c                 S   ru  rI   r  rM   r1   r1   r2   rO      rj  r~  rM  r1   r1   r2   test_besselj_complex  s
   

z#TestSystematic.test_besselj_complexc                 C   s,   t tjtjtddtdtjgddd d S Nr   r7   r   Fr[   nan_okr<   )r   r*   kvr   besselkr   r"   r8  rM  r1   r1   r2   test_besselk$     
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"   r8  rM  r1   r1   r2   test_besselk_int-  r  zTestSystematic.test_besselk_intc                 C   r}  )Nc                 S   rH   rI   )r*   r  rL   rM   r1   r1   r2   rO   8  rP   z5TestSystematic.test_besselk_complex.<locals>.<lambda>c                 S   ru  rI   )r   r  ri  rM   r1   r1   r2   rO   9  rj  rx  ry  r~  rM  r1   r1   r2   test_besselk_complex6  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   besselyri  r   r"   r8  signnanrN   rC   r.   r1   r1   r2   	mpbessely>  s   z.TestSystematic.test_bessely.<locals>.mpbesselyrx  ry  rG  rH    rp  )r   r*   yvr   r   rN  r  r1   r1   r2   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  ri  r   r"   r   r8  r  r  r1   r1   r2   r  O  s   
z6TestSystematic.test_bessely_complex.<locals>.mpbesselyc                 S   rH   rI   )r*   r  rL   rM   r1   r1   r2   rO   W  rP   z5TestSystematic.test_bessely_complex.<locals>.<lambda>i:  rp  r~  r  r1   r1   r2   test_bessely_complexN  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 rE  )r>   r   r  r   r"   r  r  r1   r1   r2   r  ^  s   z2TestSystematic.test_bessely_int.<locals>.mpbesselyc                 S      t t| |S rI   )r*   Zynr   rM   r1   r1   r2   rO   e  r   z1TestSystematic.test_bessely_int.<locals>.<lambda>rx     rG  rH  r   r   r   r   r  r1   r1   r2   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   )rr   rq   nonzero
bad_pointsr1   r2   r   m  s   (z&TestSystematic.test_beta.<locals>.betac                        | |ddS NT)r  r1   r   )r   r1   r2   rO   ~  rP   z*TestSystematic.test_beta.<locals>.<lambda>r   Tr   r   dy=)r   r   rn   F)r   r*   r   r   r"   r)   rM  r1   )r  r   r2   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rr   rq   rC   r1   r1   r2   rO     rj  z-TestSystematic.test_betainc.<locals>.<lambda>)r   r*   r  r   r   r   rM  r1   r1   r2   test_betainc  s   zTestSystematic.test_betaincc                 C   s0   t tjt tdd t t t gdd d S )Nc                 S   s   t j| ||dddS )Nr!   Tr  r  r  r1   r1   r2   rO     rj  z.TestSystematic.test_betaincc.<locals>.<lambda>r   r   )r   r*   Zbetainccr   r   r   rM  r1   r1   r2   test_betaincc  s   
zTestSystematic.test_betainccc                    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 )NrH  r!   rk   )r   r"   r  r>   rz   r&   r   binomial)rB   kr  r  r1   r2   r    s   .z+TestSystematic.test_binom.<locals>.binomialc                    r  r  r1   )rB   r  )r  r1   r2   rO     rP   z+TestSystematic.test_binom.<locals>.<lambda>r   r  r   r   rn   r  )r   r*   Zbinomr   r"   r)   rM  r1   )r  r  r2   
test_binom  s   


zTestSystematic.test_binomc                 C   (   t dd tdd t t gdd d S )Nc                 S   r  rI   )r*   eval_chebytr   rB   rC   r1   r1   r2   rO     r   z0TestSystematic.test_chebyt_int.<locals>.<lambda>c                 S   ru  rI   )r   chebytri  r  r1   r1   r2   rO     rj  r4   r  r  rM  r1   r1   r2   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 rI   )r   r   r   r  ri  r  r1   r1   r2   rO         z,TestSystematic.test_chebyt.<locals>.<lambda>e   '  rp  )r   r*   r  r   rM  r1   r1   r2   test_chebyt  s   
zTestSystematic.test_chebytc                 C   r  )Nc                 S   r  rI   )r*   eval_chebyur   r  r1   r1   r2   rO     r   z0TestSystematic.test_chebyu_int.<locals>.<lambda>c                 S   ru  rI   )r   chebyuri  r  r1   r1   r2   rO     rj  r4   r  r  rM  r1   r1   r2   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  rI   )r   r   r   r  ri  r  r1   r1   r2   rO     r  z,TestSystematic.test_chebyu.<locals>.<lambda>r  r  )r   r*   r  r   rM  r1   r1   r2   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   rD  rR  r*   Zshichir   r1   r1   r2   chi  rV  z$TestSystematic.test_chi.<locals>.chigU@X   g   V@)r   r   r  r   r   rN  r  r1   r1   r2   test_chi     zTestSystematic.test_chic                 C   8   dd }t |tjtttj dttjdgdd d S )Nc                 S   rD  rR  r  r  r1   r1   r2   r    rV  z,TestSystematic.test_chi_complex.<locals>.chirG  rH  r[   r;   )r   r   r  r   r'   r"   r8  r  r1   r1   r2   test_chi_complex     
zTestSystematic.test_chi_complexc                 C   s"   dd }t |tjtddg d S )Nc                 S   rD  rR  r*   Zsicir   r1   r1   r2   ci  rV  z"TestSystematic.test_ci.<locals>.cirG  rH  )r   r   r  r   rN  r  r1   r1   r2   test_ci  s   zTestSystematic.test_cic                 C   8   dd }t |tjttdtj tdtjgdd d S )Nc                 S   rD  rR  r  r  r1   r1   r2   r    rV  z*TestSystematic.test_ci_complex.<locals>.cirG  rH  r6  r;   )r   r   r  r   r'   r"   r8  r  r1   r1   r2   test_ci_complex  r  zTestSystematic.test_ci_complexc                 C   ,   t tj}tttjt gdd| d d S NFr   r  )	r"   r  r>   r  r   r   r   r  r   rN  r  r1   r1   r2   
test_cospi  s    zTestSystematic.test_cospic                 C      t ttjt gddd d S )NFr:   r  )r   r   r   r  r   rM  r1   r1   r2   test_cospi_complex     
z!TestSystematic.test_cospi_complexc                 C   s"   t tjttjt gddd d S )Nr[   r4   r<   r   )r   r*   r   r   r   r   rM  r1   r1   r2   test_digamma  s   
zTestSystematic.test_digammac                 C   s,   dd }t tjttjt gdd|d d S )Nc                 S   s$   t | jdk t | jdk @ ddS )Nr   gQ?FT)r"   whererL   r   r/  r  r1   r1   r2   param_filter&     $z9TestSystematic.test_digamma_complex.<locals>.param_filterr:   r  r<   r   r  )r   r*   r   r   r   r   )rN  r  r1   r1   r2   test_digamma_complex#  s   
z#TestSystematic.test_digamma_complexc                 C      t tjtjt gdd d S )Nr   r;   )r   r*   exp1r   e1r   rM  r1   r1   r2   test_e12  s   
zTestSystematic.test_e1c                 C   s   t tjtjtttj dttjdgdd t tjtjt	dddd d d f tj
dtd	d
dtd	d
d f d   dd t tjtjt	dddd dd d S )NrG  rH  r  r;   r4      r   r   r   =   r   r   ir  y                )r   r*   r  r   r  r   r'   r"   r8  r$   r   r#   r   rM  r1   r1   r2   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   r1   r1   r2   rO   U  r   z,TestSystematic.test_exprel.<locals>.<lambda>r   c                 S   r  r  r  r   r1   r1   r2   rO   [  r   r[   gW:r   g   mBgyCxDr  r;   )r   r*   Zexprelr   r"   r   r  r   r   r)   r8  r   isinfrM  r1   r1   r2   test_exprelR  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"   r8  rM  r1   r1   r2   test_expm1_complexb  s
   z!TestSystematic.test_expm1_complexc                 C      t tjdd t gdd d S )Nc                 S   s   t | d S rR  r   r   r   r1   r1   r2   rO   m  rP   z3TestSystematic.test_log1p_complex.<locals>.<lambda><   r  )r   r*   log1pr   rM  r1   r1   r2   test_log1p_complexj  s   
z!TestSystematic.test_log1p_complexc                 C   s   t tdd t gddd d S )Nc                 S   s   t | d |  S rR  r  r   r1   r1   r2   rO   u  rr  z-TestSystematic.test_log1pmx.<locals>.<lambda>r  r   )r   r<   )r   r   r   rM  r1   r1   r2   test_log1pmxr  s   
zTestSystematic.test_log1pmxc                 C   r  )Nr  r;   )r   r*   r+   r   r(   r   rM  r1   r1   r2   test_ei{     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 )NrG  rH  r   r;   )	r   r*   r+   r   r(   r   r'   r"   r8  rM  r1   r1   r2   test_ei_complex~  s   
zTestSystematic.test_ei_complexc                 C   s   t tjtjtddg d S )Nr   rq   )r   r*   elliper   r   rM  r1   r1   r2   test_ellipe  r  zTestSystematic.test_ellipec                 C   s$   t tjtjtddtddg d S )NrJ  rK  r   r  r   r*   Z	ellipeincr   r   r   rM  r1   r1   r2   test_ellipeinc  r  zTestSystematic.test_ellipeincc                 C      t tjtjt t g d S rI   r  rM  r1   r1   r2   test_ellipeinc_largephi  r  z&TestSystematic.test_ellipeinc_largephic                 C   s    t tjtjtddt g d S NrJ  rK  r   r*   	ellipkincr   Zellipfr   rM  r1   r1   r2   test_ellipf  s    zTestSystematic.test_ellipfc                 C   r  rI   r  rM  r1   r1   r2   test_ellipf_largephi  r  z#TestSystematic.test_ellipf_largephic                 C   s:   t tjtjtddg t tjdd tddgdd d S )	Nr   r  c                 S   s   t d|  S rR  )r   r,  )r&  r1   r1   r2   rO     rP   z,TestSystematic.test_ellipk.<locals>.<lambda>g        )rr   r   r  )r   r*   r,  r   r   Zellipkm1rM  r1   r1   r2   test_ellipk  s   

zTestSystematic.test_ellipkc                 C   s.   dd }t tj|tddtddgdd d S )	Nc                 S      t d| |S rE  r   Zellippiphir&  r1   r1   r2   r    rV  z0TestSystematic.test_ellipkinc.<locals>.ellipkincrJ  rK  r   r  Tr  r   r*   r  r   rN  r  r1   r1   r2   test_ellipkinc  s   
zTestSystematic.test_ellipkincc                 C   s*   dd }t tj|t tddgdd d S )Nc                 S   r  rE  r  r  r1   r1   r2   r    rV  z9TestSystematic.test_ellipkinc_largephi.<locals>.ellipkincr   r  Tr  r  r  r1   r1   r2   test_ellipkinc_largephi  s   
z&TestSystematic.test_ellipkinc_largephic                 C   s2   dd }t dd |tddtddd	gd
d d S )Nc                 S   s   | dkrdS t jd| |dS )Nr   snr$  r   r*  r$  r1   r1   r2   r    s   z+TestSystematic.test_ellipfun_sn.<locals>.snc                 S   r!  rE  r#  r$  r1   r1   r2   rO     r   z1TestSystematic.test_ellipfun_sn.<locals>.<lambda>    .    .Ar   r!   r   r6  r;   rW  )rN  r  r1   r1   r2   test_ellipfun_sn  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!  rR  r#  r$  r1   r1   r2   rO     r   z1TestSystematic.test_ellipfun_cn.<locals>.<lambda>c                 S      t jd| |dS )NZcnr$  r  r$  r1   r1   r2   rO     r   r  r  r   r!   r   r6  r;   rW  rM  r1   r1   r2   test_ellipfun_cn     
zTestSystematic.test_ellipfun_cnc                 C   r  )Nc                 S   r!  r"  r#  r$  r1   r1   r2   rO     r   z1TestSystematic.test_ellipfun_dn.<locals>.<lambda>c                 S   r  r)  r  r$  r1   r1   r2   rO     r   r  r  r   r!   r   r6  r;   rW  rM  r1   r1   r2   test_ellipfun_dn  r  zTestSystematic.test_ellipfun_dnc                 C   s   t tjdd t g d S )Nc                 S   r^  rI   r   r   r  r1   r1   r2   rO        
 z)TestSystematic.test_erf.<locals>.<lambda>)r   r*   r   r   rM  r1   r1   r2   test_erf  s   zTestSystematic.test_erfc                 C   r  )Nc                 S   r^  rI   r  r  r1   r1   r2   rO     r  z1TestSystematic.test_erf_complex.<locals>.<lambda>r7   rp  )r   r*   r   r   rM  r1   r1   r2   r     s   zTestSystematic.test_erf_complexc                 C   "   t tjtdd t gdd d S )Nc                 S   r^  rI   r   r   r  r1   r1   r2   rO     r  z*TestSystematic.test_erfc.<locals>.<lambda>r:   r;   )r   r*   r   r   r   rM  r1   r1   r2   	test_erfc     

zTestSystematic.test_erfcc                 C   r!  )Nc                 S   r^  rI   r"  r  r1   r1   r2   rO     r  z2TestSystematic.test_erfc_complex.<locals>.<lambda>r7   rp  )r   r*   r   r   r   rM  r1   r1   r2   test_erfc_complex  r$  z TestSystematic.test_erfc_complexc                 C      t tjtjt gdd d S Nr7   rp  )r   r*   erfir   r   rM  r1   r1   r2   	test_erfi  r  zTestSystematic.test_erfic                 C   r&  r'  )r   r*   r(  r   r   rM  r1   r1   r2   test_erfi_complex  r  z TestSystematic.test_erfi_complexc                 C   r!  )Nc                 S   r^  rI   )r   ncdfr  r1   r1   r2   rO     r  z*TestSystematic.test_ndtr.<locals>.<lambda>r7   rp  )r   r*   ndtrr   r   rM  r1   r1   r2   	test_ndtr  r$  zTestSystematic.test_ndtrc                 C   s0   t tjdd ttddtdddgdd d S )Nc                 S   s   t |  td d S Ng       @)r   r   r"   sqrtr  r1   r1   r2   rO     r   z2TestSystematic.test_ndtr_complex.<locals>.<lambda>r  r   r   rp  )r   r*   r,  r   r'   rM  r1   r1   r2   test_ndtr_complex  s   
z TestSystematic.test_ndtr_complexc                 C   s&   t tjtdd t gdddd d S )Nc                 S   s   t t | S rI   )r   r   r+  r  r1   r1   r2   rO     r   z.TestSystematic.test_log_ndtr.<locals>.<lambda>iX  r  r:   rB   r   r<   )r   r*   log_ndtrr   r   rM  r1   r1   r2   test_log_ndtr  s
   

zTestSystematic.test_log_ndtrc                 C   s6   t tjtdd ttddtdddgdd	d
 d S )Nc                 S   s    t t |  td d S r.  )r   r   r   r"   r/  r  r1   r1   r2   rO     r   z6TestSystematic.test_log_ndtr_complex.<locals>.<lambda>r0  r  r  r8   r   r7   r  rB   r   )r   r*   r3  r   r   r'   rM  r1   r1   r2   test_log_ndtr_complex
  s   

z$TestSystematic.test_log_ndtr_complexc                 C   s"   t dd tjtddgdd d S )Nc                 S   rD  )Nru   )r*   Zeulerrp  r1   r1   r2   rO     rP   z.TestSystematic.test_eulernum.<locals>.<lambda>r!   r  rp  )r   r   Zeulernumr   rM  r1   r1   r2   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   r7   r:      r  )	r   r*   rA   r   r?   r   r   r"   r8  rM  r1   r1   r2   test_expint  r  zTestSystematic.test_expintc                 C      dd }t |tjt g d S )Nc                 S   rD  rE  r*   Zfresnelr   r1   r1   r2   fresnels$  rV  z.TestSystematic.test_fresnels.<locals>.fresnels)r   r   r<  r   )rN  r<  r1   r1   r2   test_fresnels#     zTestSystematic.test_fresnelsc                 C   r:  )Nc                 S   rD  rR  r;  r   r1   r1   r2   fresnelc)  rV  z.TestSystematic.test_fresnelc.<locals>.fresnelc)r   r   r?  r   )rN  r?  r1   r1   r2   test_fresnelc(  r>  zTestSystematic.test_fresnelcc                 C   s   t tjttjt g d S rI   )r   r*   gammar   r   r   rM  r1   r1   r2   
test_gamma-  r  zTestSystematic.test_gammac                 C       t tjttjt gdd d S Nrl   r;   )r   r*   rA  r   r   r   rM  r1   r1   r2   test_gamma_complex0     
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  )r0   rq   r1   r1   r2   rO   <  r   z.TestSystematic.test_gammainc.<locals>.<lambda>r        @Finclusive_ar  r  )r   r*   r  r   rM  r1   r1   r2   test_gammainc8     
zTestSystematic.test_gammaincc                 C   rG  )	Nc                 S   rH  )NT)rr   r  rI  )r0   rr   r1   r1   r2   rO   F  r   z/TestSystematic.test_gammaincc.<locals>.<lambda>r   rJ  FrK  r  r  )r   r*   Z	gammainccr   rM  r1   r1   r2   test_gammainccB  rN  zTestSystematic.test_gammainccc                 C   s"   dd }t tjt|t g d S )Nc                 S   s   t | jS rI   r   r   rL   r  r1   r1   r2   fN  s   z&TestSystematic.test_gammaln.<locals>.f)r   r*   Zgammalnr   r   )rN  rQ  r1   r1   r2   test_gammalnL  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   rM  r1   r1   r2   test_gegenbauerS  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 )
Nry  r   r   r!   r   ru   z1e-50z0.0\4@Iw)	r   r"   r  r   rT  r>   r   r  r8  rB   rr   rC   r.   r1   r1   r2   rT  ]  s   (
z6TestSystematic.test_gegenbauer_int.<locals>.gegenbauerc                 S   s(   t t| ||}t|dkrtjS |S )NrV  )r*   rS  r   r   r"   r8  rW  r1   r1   r2   sc_gegenbauerx  s   z9TestSystematic.test_gegenbauer_int.<locals>.sc_gegenbauerr   r8   g    eg    eAi@  Tr   )rB   r   r   r<   r  r   r  )r   r   r   r   r   r"   r#   )rN  rT  rX  r1   r1   r2   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 rI   )r*   rS  r   rL   rB   rr   rC   r1   r1   r2   rO     rj  z8TestSystematic.test_gegenbauer_complex.<locals>.<lambda>r   r8   )r   r   r   rT  r   r   r   rM  r1   r1   r2   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 rI   )r*   rS  rL   r[  r1   r1   r2   rO     rr  z@TestSystematic.test_gegenbauer_complex_general.<locals>.<lambda>rJ  rK  )r   r   r   rT  r   r   rM  r1   r1   r2   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   ru  rI   )r   hankel1ri  rN   rC   r1   r1   r2   rO     rj  z-TestSystematic.test_hankel1.<locals>.<lambda>@x@xD)r   r*   ra  r   r   rM  r1   r1   r2   test_hankel1  
   
zTestSystematic.test_hankel1c                 C   r`  )Nc                 S   ru  rI   )r   hankel2ri  rb  r1   r1   r2   rO     rj  z-TestSystematic.test_hankel2.<locals>.<lambda>rc  rd  )r   r*   rg  r   r   rM  r1   r1   r2   test_hankel2  rf  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  rI   )r*   Zeval_hermiter   r  r1   r1   r2   rO     r   z-TestSystematic.test_hermite.<locals>.<lambda>r   r  )r   r   r   Zhermiter   r   rM  r1   r1   r2   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  rB  c                    s   t j| |fi  S rI   rW   rr   rC   ZKWr1   r2   rO     rj  z,TestSystematic.test_hyp0f1.<locals>.<lambda>r  r  r   g     j@r  rp  )r   r   r*   rK   r   rM  r1   rk  r2   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   rH   rI   rJ   )rr   r0   r1   r1   r2   rO     rP   z4TestSystematic.test_hyp0f1_complex.<locals>.<lambda>c                 S   ru  rI   )r   rK   ri  rj  r1   r1   r2   rO     rj  r   r   irG   )r   r   r   r   r'   rM  r1   r1   r2   test_hyp0f1_complex  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 rI   )r   hyp1f1ZeroDivisionErrorr"   r8  r  r1   r1   r2   mpmath_hyp1f1  s
   
z1TestSystematic.test_hyp1f1.<locals>.mpmath_hyp1f1r  r4   r!   FrK  r   )rB   r  )r   r*   rn  r   )rN  rp  r1   r1   r2   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   r^  rI   )r*   rn  rL   r  r1   r1   r2   rO     rr  z4TestSystematic.test_hyp1f1_complex.<locals>.<lambda>c                 S      t j| ||fi tS rI   )r   rn  ri  r  r1   r1   r2   rO     rq  rJ  rK  i  rp  )r   r   r   r   r   rM  r1   r1   r2   test_hyp1f1_complex  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 rI   )r*   r}   rL   rr   rq   r{   rC   r1   r1   r2   rO     rq  z4TestSystematic.test_hyp2f1_complex.<locals>.<lambda>c                 S      t j| |||fi tS rI   )r   r}   ri  rt  r1   r1   r2   rO     rZ   g      Yg      Y@r   rp  r~  rM  r1   r1   r2   test_hyp2f1_complex  s   

z"TestSystematic.test_hyp2f1_complexc                 C   s&   t tjtdd t t t g d S )Nc                 S   rr  rI   )r   rp   ri  r  r1   r1   r2   rO     rq  z,TestSystematic.test_hyperu.<locals>.<lambda>)r   r*   rp   r   r   rM  r1   r1   r2   test_hyperu  s
   
zTestSystematic.test_hyperuz:mpmath issue gh-342: unsupported operand mpz, long for powc                 C   s2   dd }t t|tddddtddgddd	 d S )
Nc                 S   s"   t || t |  t |  S rI   )r   powerr%   rA  rj  r1   r1   r2   mp_igam_fac     "z1TestSystematic.test_igam_fac.<locals>.mp_igam_facr   g  ļBFrK  r      r  )r   r   r   )rN  ry  r1   r1   r2   test_igam_fac  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 NrJ  rK  rG  rH  rI  r;   )r   r*   Zj0r   r   rM  r1   r1   r2   test_j0  s    zTestSystematic.test_j0c                 C   r}  r~  )r   r*   Zj1r   r   rM  r1   r1   r2   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   ru  rI   r   jacobiri  rt  r1   r1   r2   rO     rZ   z,TestSystematic.test_jacobi.<locals>.<lambda>c                 S      t t| |||S rI   r*   eval_jacobir   )rB   rq   r{   rC   r1   r1   r2   rO     rj  c                 S   ru  rI   r  rt  r1   r1   r2   rO     rZ   )r   r*   r  r   r   r   rM  r1   r1   r2   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  rB   rr   rq   rC   r1   r1   r2   r  #  s   z.TestSystematic.test_jacobi_int.<locals>.jacobic                 S   r  rI   r  r  r1   r1   r2   rO   )  rj  z0TestSystematic.test_jacobi_int.<locals>.<lambda>c                    s   t  | |||fi tS rI   )r   ri  r  r  r1   r2   rO   *  r    N  r4   r5  r   r   r   rM  r1   r  r2   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   r6   )r   r   r   keiri  r   r1   r1   r2   r  1  s   
z$TestSystematic.test_kei.<locals>.keiꌠ9Y>)ꌠ9Y>)Fr  rp  )r   r*   r  r   )rN  r  r1   r1   r2   test_kei0  s   zTestSystematic.test_keic                 C   s&   t tjtdd tddgdd d S )Nc                 S   rg  rE  )r   kerri  r   r1   r1   r2   rO   ;  rj  z)TestSystematic.test_ker.<locals>.<lambda>r  r  r  rp  )r   r*   r  r   r   rM  r1   r1   r2   test_ker8  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 rI   r   r   Zlaguerreri  r  r1   r1   r2   rO   D  rZ   z.TestSystematic.test_laguerre.<locals>.<lambda>)r   r   r*   eval_laguerrer   rM  r1   r1   r2   test_laguerre@  s
   
zTestSystematic.test_laguerrec                 C   s$   t dd dd t t gdd d S )Nc                 S   r  rI   )r*   r  r   r  r1   r1   r2   rO   J  r   z2TestSystematic.test_laguerre_int.<locals>.<lambda>c                 S   r  rI   r  r  r1   r1   r2   rO   K  rZ   r  rp  r  rM  r1   r1   r2   test_laguerre_intH  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 rI   )r*   r0  r   rL   rC   r  r1   r1   r2   rO   S  rr  z3TestSystematic.test_lambertw_real.<locals>.<lambda>c                 S   r  rI   )r   r0  r   rL   r  r1   r1   r2   rO   T  rr  r   r   r:   Fr<   r  )r   r   r"   r8  r   rM  r1   r1   r2   test_lambertw_realP  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overrF   )r"   r   r8  r   )rC   ZfacrR   egr1   r2   rA  ^  s   



z:TestSystematic.test_lanczos_sum_expg_scaled.<locals>.gammar   FrK  r:   r;   )r"   r%   r   r   rA  r   )rN  ZmaxgammarA  r1   r  r2   test_lanczos_sum_expg_scaledY  s   

z+TestSystematic.test_lanczos_sum_expg_scaledc                 C   r  rI   )r   r*   eval_legendrer   legendrer   rM  r1   r1   r2   test_legendrep  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  rI   r*   r  r   r  r1   r1   r2   rO   v  r   z2TestSystematic.test_legendre_int.<locals>.<lambda>c                 S   r  rI   r   r   r  ri  r  r1   r1   r2   rO   w  rZ   r  rp  c                 S   r  rI   r  r  r1   r1   r2   rO   ~  r   c                 S   r  rI   r  r  r1   r1   r2   rO     rZ   r  rY  rc   )r   r   r   r   r"   r#   rM  r1   r1   r2   test_legendre_intt  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   s   z&t  }|jtd t|| |d d }W d    n1 s w   Y  W n ty2   tj Y S w t|dkrBtj	t
|j }|S )Ncategoryr   ru   ru   )#v)r   filterDeprecationWarningr*   Zlpmn
ValueErrorr"   r  r   r8  r  rL   )rB   r&  r0   suprN   r1   r1   r2   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"   r8  r  rL   )rB   r&  r0   rN   r1   r1   r2   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!   ru   r   rk   r   rj   typer  )r   r   rx  r  r   r"   r  r   r   r8  rL   )rB   r&  r0   typrN   r1   r1   r2   r     s   
z*TestSystematic.test_legenp.<locals>.legenpr  r8   ru   r!   r   rz  r  )rN  r  r  r   r1   r1   r2   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   r   z,t  }|jtd tj|j| j|ddd d W  d    W S 1 s%w   Y  W d S  ty8   tj Y S w )Nr  r   r  r   r  	r   r  r  r*   ZclpmnrL   r  r"   r  rB   r&  r0   r  r1   r1   r2   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 Nrk   r   r  r   r"   r  r   r   r   r   rL   rB   r&  r0   r1   r1   r2   r        "z4TestSystematic.test_legenp_complex_2.<locals>.legenp	rw   r   rE   r   rI  rF   r   rc   g     @@rJ  rE   rF   g?r   rw   ru   r   r!   r   r   r   r   rs  r"   r)   r   r   r   rN  r  r   rC   rQ   r0   r1   r1   r2   test_legenp_complex_2     (


z$TestSystematic.test_legenp_complex_2c                 C   r  )Nc                 S   r  )Nr  rj   r  r   r  r  r  r1   r1   r2   r    r  z3TestSystematic.test_legenp_complex_3.<locals>.clpnmc                 S   r  )Nrk   rj   r  r  r  r1   r1   r2   r     r  z4TestSystematic.test_legenp_complex_3.<locals>.legenpr  r  r   r  r   r   rs  r  r  r1   r1   r2   test_legenp_complex_3  r  z$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  r1   r1   r2   lqnm  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  r1   r1   r2   r    s   z*TestSystematic.test_legenq.<locals>.legenqr   r8   r  rN  r  r  r1   r1   r2   test_legenq  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   rL   r  r1   r1   r2   r    rz  z0TestSystematic.test_legenq_complex.<locals>.lqnmc                 S   r  r  )r   r"   r  r   r   r  r   rL   r  r1   r1   r2   r  
  r  z2TestSystematic.test_legenq_complex.<locals>.legenqr   r8   rp  )r   r   r   r  r1   r1   r2   test_legenq_complex  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   r1   r1   r2   r    s    z0TestSystematic.test_lgam1p.<locals>.param_filterc                 S   s   t d|  jS rR  rP  r  r1   r1   r2   	mp_lgam1p  s   z-TestSystematic.test_lgam1p.<locals>.mp_lgam1pr:   r8   r  )r   r   r   )rN  r  r  r1   r1   r2   test_lgam1p  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 rI   )r   r   r  r'   r"   r  )r0   rR   r1   r1   r2   mpmath_loggamma*  s   z5TestSystematic.test_loggamma.<locals>.mpmath_loggammaFr   )r  Zdistinguish_nan_and_infr<   )r   r*   r   r   )rN  r  r1   r1   r2   test_loggamma)  s   
zTestSystematic.test_loggammac                 C   s(   dd }t |tdd t t g d S )Nc                 S   r!  rE  )r*   Zpbdvrb  r1   r1   r2   pcfd<  r(  z&TestSystematic.test_pcfd.<locals>.pcfdc                 S   ru  rI   )r   r  ri  rb  r1   r1   r2   rO   @  rj  z*TestSystematic.test_pcfd.<locals>.<lambda>)r   r   r   )rN  r  r1   r1   r2   	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!  rE  )r*   Zpbvvrb  r1   r1   r2   pcfvG  r(  z&TestSystematic.test_pcfv.<locals>.pcfvc                 S   r  rI   )r   r   r   r  ri  rb  r1   r1   r2   rO   K  r   z*TestSystematic.test_pcfv.<locals>.<lambda>r  rp  rW  )rN  r  r1   r1   r2   	test_pcfvD  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!  rE  r*   Zpbwarj  r1   r1   r2   pcfwQ  r(  z&TestSystematic.test_pcfw.<locals>.pcfwc                 S   r!  rR  r  rj  r1   r1   r2   dpcfwT  r(  z'TestSystematic.test_pcfw.<locals>.dpcfwc                 S   s   t t j| |fdS )Nr9   )r   diffr  rj  r1   r1   r2   mpmath_dpcfwW  r   z.TestSystematic.test_pcfw.<locals>.mpmath_dpcfwra   rb   g:0yU>r8   rs  g&.!>)r   r   r  r   )rN  r  r  r  r1   r1   r2   	test_pcfwP  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   rM  r1   r1   r2   test_polygammal  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)rB   r  r   )r   r*   r   r   r   r"   r8  rM  r1   r1   r2   test_rgammav  s   
zTestSystematic.test_rgammac                 C   rC  rD  )r   r*   r   r   r   r   rM  r1   r1   r2   test_rgamma_complex  rF  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 )Nrt   c                 S   sN   t | | t| | kr!t | | dkr!t| } t| | |  }t| |S rE  )r>   r   r   r  rf)rr   r&  r1   r1   r2   mppoch  s   (
z&TestSystematic.test_rf.<locals>.mppochr   r  )
r   parser   r   Versionr  r   r*   Zpochr   )rN  r  r1   r1   r2   test_rf  s   	zTestSystematic.test_rfc                 C   r  r  )	r"   r  r>   r  r   r   r   r  r   r  r1   r1   r2   
test_sinpi  s   
zTestSystematic.test_sinpic                 C   r  )NFg+=r  )r   r   r   r  r   rM  r1   r1   r2   test_sinpi_complex  r  z!TestSystematic.test_sinpi_complexc                 C   r  )Nc                 S   rD  rE  r  r   r1   r1   r2   shi  rV  z$TestSystematic.test_shi.<locals>.shir  )r   r   r  r   r   rN  r  r1   r1   r2   test_shi  r  zTestSystematic.test_shic                 C   r  )Nc                 S   rD  rE  r  r  r1   r1   r2   r    rV  z,TestSystematic.test_shi_complex.<locals>.shirG  rH  r[   r;   )r   r   r  r   r'   r"   r8  r  r1   r1   r2   test_shi_complex  r  zTestSystematic.test_shi_complexc                 C   r:  )Nc                 S   rD  rE  r  r   r1   r1   r2   si  rV  z"TestSystematic.test_si.<locals>.si)r   r   r  r   rN  r  r1   r1   r2   test_si  r>  zTestSystematic.test_sic                 C   r  )Nc                 S   rD  rE  r  r  r1   r1   r2   r    rV  z*TestSystematic.test_si_complex.<locals>.sirG  rH  r[   r;   )r   r   r  r   r'   r"   r8  r  r1   r1   r2   test_si_complex  r  zTestSystematic.test_si_complexc                 C   s,   dd }t tjt|tdtjgdd d S )Nc                 S      t dd|  S r  r   r  r   r1   r1   r2   dilog  r(  z)TestSystematic.test_spence.<locals>.dilogr   r   r;   )r   r*   r  r   r   r"   r8  rN  r  r1   r1   r2   test_spence  s   
zTestSystematic.test_spencec                 C   s&   dd }t tjt|t gdd d S )Nc                 S   r  r  r  r  r1   r1   r2   r    r(  z1TestSystematic.test_spence_complex.<locals>.dilogr   r;   )r   r*   r  r   r   r  r1   r1   r2   test_spence_complex  s   
z"TestSystematic.test_spence_complexc              
   C   sJ   dd }t |tjtddtddtdtdtddt dgddd	d
 d S )Nc                 S   sT   || krt jS t }|jtd t|| ||W  d    S 1 s#w   Y  d S )Nr  )r"   r  r   r  r  r*   Zsph_harm)lr&  r   r  r  r1   r1   r2   	spherharm  s   $z0TestSystematic.test_spherharm.<locals>.spherharmr   r8   r   r   r6  ip  rT   )rn   rB   r   )r   r   r  r   r   r   )rN  r  r1   r1   r2   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     rJ  r   &.>r;   )r   r*   Zstruver   r   Zstruvehr   rM  r1   r1   r2   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)rN   r0   r   r1   r1   r2   
mp_struvel  s   z/TestSystematic.test_struvel.<locals>.mp_struvelr  rJ  r   r  Tr   )r   r*   Z	modstruver   r   )rN  r  r1   r1   r2   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   r0  r%   r  r   r1   r1   r2   mpmath_wrightomega_real  s   zETestSystematic.test_wrightomega_real.<locals>.mpmath_wrightomega_realrx   gPKDg+<r   F)r<   rn   r  )r   r*   r:  r   )rN  r  r1   r1   r2   test_wrightomega_real  s   

z$TestSystematic.test_wrightomega_realc                 C   s    t tjdd t gddd d S )Nc                 S   s
   t | dS )Nr2  )r1  r  r1   r1   r2   rO   %  r  z1TestSystematic.test_wrightomega.<locals>.<lambda>r   Fr  )r   r*   r:  r   rM  r1   r1   r2   test_wrightomega"  s   
zTestSystematic.test_wrightomegac                 C   s.   t tjttjtddddtdddg d S )Nr!       _BF)rr   rq   rL  r   rr   rL  )r   r*   zetar   r   r   rM  r1   r1   r2   test_hurwitz_zeta+  s
   z TestSystematic.test_hurwitz_zetac                 C   s$   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 rR  r   r  r8  r   r1   r1   r2   rO   5  rZ   z2TestSystematic.test_riemann_zeta.<locals>.<lambda>r  r8   Frl   r  )r   r*   r  r   rM  r1   r1   r2   test_riemann_zeta2  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 rR  r  r   r1   r1   r2   rO   >  r  z+TestSystematic.test_zetac.<locals>.<lambda>r  r8   F-   rl   )r  r   r<   )r   r*   Zzetacr   rM  r1   r1   r2   
test_zetac;  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 rE  r   r   r  r   Zpowm1)rC   lmbdar1   r1   r2   	mp_boxcoxG  s
   z-TestSystematic.test_boxcox.<locals>.mp_boxcoxr   Fr   r7   r  r:   r2  )r   r*   Zboxcoxr   r   )rN  r
  r1   r1   r2   test_boxcoxE  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  )rC   r	  oner1   r1   r2   mp_boxcox1pZ  s   z1TestSystematic.test_boxcox1p.<locals>.mp_boxcox1pru   Fr   r7   r  r:   r2  )r   r*   Zboxcox1pr   r   )rN  r  r1   r1   r2   test_boxcox1pX  s   	
zTestSystematic.test_boxcox1pc                 C   s>   dd }t dd t|tddtddgd	d d
d fd d S )Nc                 S   L   t |}t | t dd  |t d| t j  }|jdkr$|jS |S Nr!   r   r   r   	mpmathifyr  r  r/  r   r/  rL   rB   r0   argoutr1   r1   r2   mp_spherical_jnm     

z9TestSystematic.test_spherical_jn.<locals>.mp_spherical_jnc                 S   r  rI   )r*   spherical_jnr   rB   r0   r1   r1   r2   rO   w  r   z2TestSystematic.test_spherical_jn.<locals>.<lambda>r   r7   rG  rH  r  c                 S   s   t | dkS )Ng#B;)r"   r   r  r1   r1   r2   rO   |  rP   )r   r  r  rN  r  r1   r1   r2   test_spherical_jnl  s   	

z TestSystematic.test_spherical_jnc                 C   ,   dd }t dd t|tddt g d S )Nc                 S   r  r  r  r  r1   r1   r2   r    r  zATestSystematic.test_spherical_jn_complex.<locals>.mp_spherical_jnc                 S      t t| j|S rI   )r*   r  r   rL   r  r1   r1   r2   rO     rr  z:TestSystematic.test_spherical_jn_complex.<locals>.<lambda>r   r7   r   r   r   r   r  r1   r1   r2   test_spherical_jn_complex     	z(TestSystematic.test_spherical_jn_complexc                 C   s4   dd }t dd t|tddtddgd	d
 d S )Nc                 S   r  r  r   r  r  r  r/  r   r/  rL   r  r1   r1   r2   mp_spherical_yn  r  z9TestSystematic.test_spherical_yn.<locals>.mp_spherical_ync                 S   r  rI   )r*   spherical_ynr   r  r1   r1   r2   rO     r   z2TestSystematic.test_spherical_yn.<locals>.<lambda>r   r7   g    _r  r8   r  r  rN  r"  r1   r1   r2   test_spherical_yn  s   	
z TestSystematic.test_spherical_ync                 C   r  )Nc                 S   r  r  r!  r  r1   r1   r2   r"    r  zATestSystematic.test_spherical_yn_complex.<locals>.mp_spherical_ync                 S   r  rI   )r*   r#  r   rL   r  r1   r1   r2   rO     rr  z:TestSystematic.test_spherical_yn_complex.<locals>.<lambda>r   r7   r  r$  r1   r1   r2   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  rw  r  r/  r   r/  rL   r  r1   r1   r2   mp_spherical_in  r  z9TestSystematic.test_spherical_in.<locals>.mp_spherical_inc                 S   r  rI   )r*   spherical_inr   r  r1   r1   r2   rO     r   z2TestSystematic.test_spherical_in.<locals>.<lambda>r   r7   g訰6r  r  rN  r(  r1   r1   r2   test_spherical_in  s   	
z TestSystematic.test_spherical_inc                 C   r  )Nc                 S   r  r  r'  r  r1   r1   r2   r(    r  zATestSystematic.test_spherical_in_complex.<locals>.mp_spherical_inc                 S   r  rI   )r*   r)  r   rL   r  r1   r1   r2   rO     rr  z:TestSystematic.test_spherical_in_complex.<locals>.<lambda>r   r7   r  r*  r1   r1   r2   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   sR   t |}t | t dd  |t d| t j  }t |jdkr'|jS |S r  r   r  r  r  r/  r   r/  rL   r  r1   r1   r2   mp_spherical_kn  s   
z9TestSystematic.test_spherical_kn.<locals>.mp_spherical_knc                 S   r  rI   )r*   spherical_knr   r  r1   r1   r2   rO     r   z2TestSystematic.test_spherical_kn.<locals>.<lambda>r   rT   r8   r  r  rN  r.  r1   r1   r2   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  r1   r1   r2   r.    r  zATestSystematic.test_spherical_kn_complex.<locals>.mp_spherical_knc                 S   r  rI   )r*   r/  r   rL   r  r1   r1   r2   rO     rr  z:TestSystematic.test_spherical_kn_complex.<locals>.<lambda>r   r7   r  r  r0  r1   r1   r2   test_spherical_kn_complex  s   	
z(TestSystematic.test_spherical_kn_complexN)__name__
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scipy._libr   Zscipy.specialZspecialr*   Zscipy.special._testutilsr   r   r	   r
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