o
    Ebq                     @   s  d dl Zd dl mZmZ d dlmZmZmZmZ d dl	m
Z d dlmZ d dlmZ d dlmZ d dlm  mZ G dd dZG d	d
 d
ZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZ	dAddZdd Zdd  Z d!d" Z!d#d$ Z"d%d& Z#d'd( Z$d)d* Z%d+d, Z&d-d. Z'd/d0 Z(d1d2 Z)d3d4 Z*d5d6 Z+d7d8 Z,d9d: Z-d;d< Z.d=d> Z/d?d@ Z0dS )B    N)arraysqrt)assert_array_almost_equalassert_equalassert_almost_equalassert_allclose)raises)	integrategammac                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
	TestChebyc                 C   s   t d}t d}tjdd t d}t d}t d}t d}W d    n1 s/w   Y  t|jdgd	 t|jddgd	 t|jg d
d	 t|jg dd	 t|jg dd	 t|jg dd	 d S )Nr      ignoreall               )r   r   )r   r   r   )r   r   r   r   )r   r   r   r   r   )orthchebycnperrstater   c)selfZC0ZC1ZC2ZC3ZC4ZC5 r    E/usr/lib/python3/dist-packages/scipy/special/tests/test_orthogonal.pytest_chebyc   s   




zTestCheby.test_chebycc                 C      t d}t d}t d}t d}t d}t d}t|jdgd t|jddgd t|jg dd t|jg d	d t|jg d
d t|jg dd d S )Nr   r   r   r   r   r   r   )r   r   )r   r   r   r   )r   r   r   r   r   )r   r   r   r   r   r   )r   chebysr   r   )r   ZS0ZS1ZS2ZS3ZS4ZS5r    r    r!   test_chebys      





zTestCheby.test_chebysc                 C   r#   )Nr   r   r   r   r   r   r   )r   r   r$   )r   r   r   r   )   r   ir   r   )   r   r   r   r   )r   chebytr   r   )r   ZT0ZT1ZT2ZT3ZT4ZT5r    r    r!   test_chebyt,   r'   zTestCheby.test_chebytc                 C   s   t d}t d}t d}t d}t d}t d}t|jdgd t|jddgd t|jg dd t|jg d	d t|jg d
d t|jg dd d S )Nr   r   r   r   r   r   r   )r   r   r$   )r(   r   r   r   )r)   r   r   r   )    r   ir      r   )r   chebyur   r   )r   ZU0ZU1ZU2ZU3ZU4ZU5r    r    r!   test_chebyu:   r'   zTestCheby.test_chebyuN)__name__
__module____qualname__r"   r&   r,   r1   r    r    r    r!   r      s
    r   c                   @      e Zd Zdd ZdS )TestGegenbauerc                 C   s  dt j  d }t |dkrd}td|}td|}td|}td|}td|}td|}t|jtdgd	 t|jtd| dgd	 t|jtd| |d  d| gd	 t|jtdt	|d dd
| |d  dgd d t|jtdt	|d ddt	|d dd| |d  gd d t|jtdt	|d ddt	|d ddt	|d dgd d d S )Nr         ?r   皙ɿr   r   r   r   r   ig      @   r-   g      @r*      g      .@)
r   randomanyr   Z
gegenbauerr   r   r   scZpoch)r   aZCa0ZCa1ZCa2ZCa3ZCa4ZCa5r    r    r!   test_gegenbauerK   sB   &&&&zTestGegenbauer.test_gegenbauerN)r2   r3   r4   r?   r    r    r    r!   r6   I       r6   c                   @   s   e Zd Zdd Zdd ZdS )TestHermitec                 C   s   t d}t d}t d}t d}t d}t d}t|jdgd t|jddgd t|jg dd t|jg d	d t|jg d
d t|jg dd d S )Nr   r   r   r   r   r   r   )r   r   r   )r(   r   r-   r   )r)   r   ir      rB   )r.   r   i`r   x   r   )r   hermiter   r   )r   H0H1H2H3H4H5r    r    r!   test_hermiteb   r'   zTestHermite.test_hermitec                 C   s2  t dtd dg}td}td}td}td}td}td}td|}td|td }	td|d }
td|dtd  }td|d	 }td|d	td  }t|j|jd
 t|j|	jd
 t|j|
jd
 t|j|jd
 t|j|jd
 t|j|jd
 d S )N      ?r   r   r   r   r   r          @      @r   )r   poly1dr   r   hermitenormrD   r   r   )r   psubrE   rF   rG   rH   rI   rJ   Zhe0Zhe1Zhe2Zhe3Zhe4Zhe5r    r    r!   test_hermitenormp   s&   





zTestHermite.test_hermitenormN)r2   r3   r4   rK   rR   r    r    r    r!   rA   a   s    rA   c                   @   r5   )_test_sh_legendrec                 C     t ddg}td}td}td}td}td}td}td|}td|}	td|}
td|}td|}td|}t|j|jd t|j|	jd t|j|
jd t|j|jd t|j|jd	 t|j|jd	 d S 
Nr   r$   r   r   r   r   r   r   rB   )r   rO   r   sh_legendrelegendrer   r   )r   rQ   ZPs0ZPs1ZPs2ZPs3ZPs4ZPs5Zpse0Zpse1Zpse2Zpse3Zpse4Zpse5r    r    r!   test_sh_legendre   &   





z"_test_sh_legendre.test_sh_legendreN)r2   r3   r4   rX   r    r    r    r!   rS      r@   rS   c                   @   r5   )_test_sh_chebytc                 C   rT   rU   )r   rO   r   	sh_chebytr+   r   r   )r   rQ   ZTs0ZTs1ZTs2ZTs3ZTs4ZTs5Ztse0Ztse1Ztse2Ztse3Ztse4Ztse5r    r    r!   test_sh_chebyt   rY   z_test_sh_chebyt.test_sh_chebytN)r2   r3   r4   r\   r    r    r    r!   rZ      r@   rZ   c                   @   r5   )_test_sh_chebyuc                 C   s  t ddg}td}td}td}td}td}td}td|}td|}	td|}
td|}td|}td|}t|j|jd t|j|	jd t|j|
jd t|j|jd t|j|jd	 t|j|jd
 d S )Nr   r$   r   r   r   r   r   r   rB   r9   )r   rO   r   	sh_chebyur0   r   r   )r   rQ   ZUs0ZUs1ZUs2ZUs3ZUs4ZUs5Zuse0Zuse1Zuse2Zuse3Zuse4Zuse5r    r    r!   test_sh_chebyu   rY   z_test_sh_chebyu.test_sh_chebyuN)r2   r3   r4   r_   r    r    r    r!   r]      r@   r]   c                   @   r5   )_test_sh_jacobic                 C   s  dd }t ddg}dt j  }|d dt j   }td||}td||}td||}td||}td||}	td	||}
td|| |d ||d| }td|| |d ||d| }td|| |d ||d| }td|| |d ||d| }td|| |d ||d| }td	|| |d ||d	| }t|j|jd
 t|j|jd
 t|j|jd
 t|j|jd
 t|	j|jd
 t|
j|jd
 d S )Nc                 S   s(   t | d t | |  t d|  |  S )Nr   r   r
   )npr    r    r!   <lambda>   s   ( z0_test_sh_jacobi.test_sh_jacobi.<locals>.<lambda>r   r$   r   r   r   r   r   r   )r   rO   r;   r   Z	sh_jacobiZjacobir   r   )r   convrQ   qrb   ZG0ZG1ZG2ZG3ZG4ZG5Zge0Zge1Zge2Zge3Zge4Zge5r    r    r!   test_sh_jacobi   s,   $$$$$$z_test_sh_jacobi.test_sh_jacobiN)r2   r3   r4   rf   r    r    r    r!   r`          r`   c                   @   r5   )TestCallc                 C   s   g }t dD ]}|dd dt|d  D  qtjdd! |D ]}t|}t|dt|j	d|d	 q#W d    d S 1 sDw   Y  d S )
Nr   c                 S   s   g | ]}|  qS r    )strip).0xr    r    r!   
<listcomp>       z&TestCall.test_call.<locals>.<listcomp>aW  
                orth.jacobi(%(n)d,0.3,0.9)
                orth.sh_jacobi(%(n)d,0.3,0.9)
                orth.genlaguerre(%(n)d,0.3)
                orth.laguerre(%(n)d)
                orth.hermite(%(n)d)
                orth.hermitenorm(%(n)d)
                orth.gegenbauer(%(n)d,0.3)
                orth.chebyt(%(n)d)
                orth.chebyu(%(n)d)
                orth.chebyc(%(n)d)
                orth.chebys(%(n)d)
                orth.sh_chebyt(%(n)d)
                orth.sh_chebyu(%(n)d)
                orth.legendre(%(n)d)
                orth.sh_legendre(%(n)d)
                )ra   r   r   g)\(?)err_msg)
rangeextenddictsplitr   r   evalr   rO   Zcoef)r   Zpolyra   Zpstrrb   r    r    r!   	test_call   s    

"zTestCall.test_callN)r2   r3   r4   rt   r    r    r    r!   rh      rg   rh   c                   @   r5   )TestGenlaguerrec                 C   sx   t tjdddddd t tjdddddd t tjddddtdd	g t tjddddtdd
g d S )Nr   F)Zmonicr   rM   T       r$   r   r   )r   r   Zgenlaguerrer   rO   )r   r    r    r!   test_regression  s    $zTestGenlaguerre.test_regressionN)r2   r3   r4   rw   r    r    r    r!   ru     rg   ru   V瞯<vIh%,=c                    s   | |d\}}	}
t |}||d d t jf |}t ||	 |j}dt |  }|d d t jf | | }t|t ||| t|		 |
|| dd  t
 fdd||}t  ||	}d|d k rkdn|d d }t|d ||d	 d S )
NTr   c                 S   s   | d d| d   |  d S )Nr   r   r    rk   r    r    r!   rc   &      z#verify_gauss_quad.<locals>.<lambda>c                    s    | |  S Nr    rz   fweight_funcr    r!   rc   '      gư>
   r   rtol)r   ZarangeZnewaxisdotTr   Zdiagonalr   Zeyesumr	   quadZvdot)Z	root_funcZ	eval_funcr   r>   bNr   atolrk   wmura   vZvvZvdZresIZresGr    r}   r!   verify_gauss_quad  s   
r   c               	   C   s  dd } dd }dd }t }|| dd|dd|ddddd	 || dd|dd|ddddd
dd || dd|dd|ddddddd || dd|dd|ddddd	 || dd|dd|ddddd
dd || dd|dd|ddddddd || dd|dd|ddddd	dd || dd|dd|ddddd
dd || dd|dd|ddddddd || dd|dd|ddddd	 || dd|dd|ddddd
dd || dd|dd|ddddddd || dd|dd|ddddd	 || dd|dd|ddddd
dd || dd|dd|ddddddd || dd|dd|ddddd	dd || dd|dd|ddddd
dd || dd|dd|ddddddd || dd|dd|ddddd	 || dd|dd|ddddd
dd || dd|dd|ddddddd tdd d \}}td\}}t||d!d! t||d!d! tdd"d"\}}tdd#\}}	t||d!d! t||	d!d! td	dd$d%\}
}td	dd$d&\}}}t|
|d!d! t||d!d! t|dd$d'd\}}t|||d( tt	tjd)dd tt	tjd*dd tt	tjd$d+d tt	tjd$dd+ tt	tjd$d+d+ d S ),Nc                        fddS )Nc                       t |  |S r|   )r=   roots_jacobira   r   r>   r   r    r!   rc   -  r   5test_roots_jacobi.<locals>.<lambda>.<locals>.<lambda>r    r   r    r   r!   rc   -      z#test_roots_jacobi.<locals>.<lambda>c                    r   )Nc                    r   r|   )r=   Zeval_jacobira   rk   r   r    r!   rc   .  r   r   r    r   r    r   r!   rc   .  r   c                    r   )Nc                    s   d|    d|    S )Nr   r    rz   r   r    r!   rc   /  s    r   r    r   r    r   r!   rc   /  r                     rL   r      -q=r   d   dy=r7   7QE=-=r   vIh%L=?r   vIh%<=g7QU==
ףp=2@L;@g^~z=̌G@r8         @皙9Q@r/           +=rN   g      @r   FTr$   r   r   ffffff
@r   )
r   r=   r   roots_legendrer   roots_gegenbauerr	   r   assert_raises
ValueError)rfefwfvgqZxjZwjZxlZwlZxcZwcrk   r   yr   mmuImuI_errr    r    r!   test_roots_jacobi,  sp   $$((((($(($ (($(r   c               	   C   s  dd } dd }dd }t }|| dd|dd|ddddd	 || dd|dd|ddddd
dd || dd|dd|ddddddd || dd|dd|ddddd	 || dd|dd|ddddd
dd || dd|dd|ddddddd || dd|dd|ddddd	 || dd|dd|ddddd
dd || dd|dd|ddddddd || dd|dd|ddddd	 || dd|dd|ddddd
dd || dd|dd|ddddddd || dd|dd|ddddd	 || dd|dd|ddddd
 || dd|dd|ddddddd || dd|dd|ddddd	dd || dd|dd|ddddd
dd || dd|dd|ddddddd || dd|dd|ddddd	dd || dd|dd|ddddd
dd || dd|dd|ddddddd td	ddd \}}td	ddd!\}}}t||d"d" t||d"d" t|ddd#d\}	}
t||	|
d$ tttjd#dd tttjd%dd tttjddd tttjddd& tttjdd'd& d S )(Nc                    r   )Nc                    r   r|   )r=   roots_sh_jacobir   r   r    r!   rc   o  r   8test_roots_sh_jacobi.<locals>.<lambda>.<locals>.<lambda>r    r   r    r   r!   rc   o  r   z&test_roots_sh_jacobi.<locals>.<lambda>c                    r   )Nc                    r   r|   )r=   Zeval_sh_jacobir   r   r    r!   rc   p  r   r   r    r   r    r   r!   rc   p  r   c                    r   )Nc                    s   d|     | d   S )NrL   r    rz   r   r    r!   rc   q  r{   r   r    r   r    r   r!   rc   q  r   r   g      ?r   rL   r   r   r   r   r   r   r7   r   r   r   r   r   r   r   r   r   皙?g|=r   r   g(#=r   r   FTr   r   r   r   r$   r   )r   r=   r   r   r	   r   r   r   )r   r   r   r   rk   r   r   r   r   r   r   r    r    r!   test_roots_sh_jacobin  sX   $$(($(($(($$(((((r   c            
   	   C   s<  t j} t j}tdj}t| ||tj tjd t| ||tj tjddd t| ||tj tjddd t dd\}}t dd\}}}t	||d	d	 t	||d	d	 t
|tj tj\}}	t	|||	d
 t dd\}}t dd\}}}t	||d	d	 t	||d	d	 t	t||d	d	 ttt jd ttt jd d S )Nr   r   r   r   r   r   FTr   r      r   r   )r=   Zroots_hermiteZeval_hermiter   rD   r   r   r   infr   r	   r   r   r   r   
rootfevalfweightfrk   r   r   r   r   r   r   r    r    r!   test_roots_hermite  s&   r   c                     s   dd  d fdd	} | ddd	 | d
dd	 | ddd	 | ddd	 | ddd	 | ddd	 | ddd	 | ddd	 | ddd	 | ddd	 d S )Nc                 S   s   t | |jf}t jd t d|d   |dd d f< | dkrftd| |dd d f  |dd d f< td| D ],}td| | ||d d d f  t|d | ||d d d f   ||d d f< q9|S )N      пr   r   r   r   rM   rL   )r   zerossizepiexpr   ro   )ra   ZnodesHkr    r    r!   hermite_recursion  s   ((Vz1test_roots_hermite_asy.<locals>.hermite_recursionrx   r   c                    sX   t | \}} | d |}t|dd d f t| || tt|ttj|| d S )Nr   r$   )r   Z_roots_hermite_asyr   r   r   r   r   r   )r   r   r   rk   r   r   r   r    r!   test  s    z$test_roots_hermite_asy.<locals>.test   r   r      i,  i-  i  i  i  i  i  i  )rx   r   r    )r   r    r   r!   test_roots_hermite_asy  s   
r   c            
   	   C   s   t j} t j}tdj}t| ||tj tjd t| ||tj tjddd t| ||tj tjddd t dd\}}t dd\}}}t	||d	d	 t	||d	d	 t
|tj tj\}}	t	|||	d
 ttt jd ttt jd d S )Nr   r   r   r   r   r   FTr   r   r   r   )r=   Zroots_hermitenormZeval_hermitenormr   rP   r   r   r   r   r   r	   r   r   r   r   r    r    r!   test_roots_hermitenorm  s   r   c               	   C   s  dd } dd }dd }t }|| d|d|dddd || d|d|dddd	d
d || d|d|dddddd || d|d|dddd || d|d|dddd	dd || d|d|ddddd
d || d|d|dddd || d|d|dddd	dd || d|d|ddddd
d || d|d|dddd || d|d|dddd	dd || d|d|ddddd
d || d|d|dddddd || d|d|dddd	d
d || d|d|dddddd || dtj|dddd || dtj|dddd	 || dtj|ddddd
d tddd\}}tddd\}}}t||dd t||dd t|ddd\}	}
t||	|
d tttjdd tttjdd tttjdd d S )Nc                        fddS )Nc                       t |  |S r|   )r=   r   r   r>   r    r!   rc     r   9test_roots_gegenbauer.<locals>.<lambda>.<locals>.<lambda>r    r   r    r   r!   rc         z'test_roots_gegenbauer.<locals>.<lambda>c                    r   )Nc                    r   r|   )r=   Zeval_gegenbauerr   r   r    r!   rc     r   r   r    r   r    r   r!   rc     r   c                    r   )Nc                    s   d| d   d  S )Nr   r   r7   r    rz   r   r    r!   rc     rm   r   r    r   r    r   r!   rc     r   r   r   rL   r   r   r   r   r   r   皙?r   r   r   2   r   r   FTr   r$   r   r   r   r   )	r   r=   eval_chebytr   r   r	   r   r   r   r   r   r   r   rk   r   r   r   r   r   r   r    r    r!   test_roots_gegenbauer  s>   """"""""""" r   c               	   C      t dj} ttjtj| ddd ttjtj| ddd ttjtj| ddddd tdd\}}tdd	\}}}t||d
d
 t||d
d
 t	| dd\}}t|||d t
ttjd t
ttjd d S )Nr   r   rL   r   r   r   r   FTr   r$   r   r   r   r   )r   r+   r   r   r=   roots_chebytr   r   r	   r   r   r   r   rk   r   r   r   r   r   r   r    r    r!   test_roots_chebyt     r   c                  C   sP   t d\} }| d d | dd  }}t||d d d   t| d d d S )N   r   r9   r$   r   )r=   r   r   )rk   r   posnegr    r    r!   test_chebyt_symmetry-  s   r   c                  C      t dj} ttjtj| ddd ttjtj| ddd ttjtj| ddd tdd\}}tdd\}}}t||dd t||dd t	| d	d
\}}t|||d t
ttjd t
ttjd d S )Nr   r   rL   r   r   FTr   r$   r   r   r   r   )r   r0   r   r   r=   Zroots_chebyuZeval_chebyur   r	   r   r   r   r   r    r    r!   test_roots_chebyu3     r   c               	   C   r   )Nr   rv   rM   r   r   r   r   FTr   r   r   r   r   r   )r   r   r   r   r=   Zroots_chebycZeval_chebycr   r	   r   r   r   r   r    r    r!   test_roots_chebycD  r   r   c                  C   r   )Nr   rv   rM   r   r   FTr   r   r   r   r   r   )r   r%   r   r   r=   Zroots_chebysZeval_chebysr   r	   r   r   r   r   r    r    r!   test_roots_chebysU  r   r   c               	   C      t dj} ttjtj| ddd ttjtj| ddd ttjtj| ddddd tdd\}}tdd	\}}}t||d
d
 t||d
d
 t	| dd\}}t|||d t
ttjd t
ttjd d S Nr   r   rL   r   r   r   r   FTr   r   r   r   r   )r   r[   r   r   r=   Zroots_sh_chebytZeval_sh_chebytr   r	   r   r   r   r   r    r    r!   test_roots_sh_chebytf     r   c               	   C   r   r   )r   r^   r   r   r=   Zroots_sh_chebyuZeval_sh_chebyur   r	   r   r   r   r   r    r    r!   test_roots_sh_chebyux  r   r   c               	   C   s   t dj} ttjtj| ddd ttjtj| ddddd ttjtj| ddddd tdd	\}}tdd
\}}}t||dd t||dd t	| dd\}}t|||d t
ttjd t
ttjd d S )Nr   r   rL   r   r   r   r   r   FTr   r$   r   r   r   r   )r   rW   r   r   r=   r   Zeval_legendrer   r	   r   r   r   r   r    r    r!   test_roots_legendre      r   c               	   C   s   t dj} ttjtj| ddd ttjtj| ddddd ttjtj| ddddd tdd	\}}tdd
\}}}t||dd t||dd t	| dd\}}t|||d t
ttjd t
ttjd d S )Nr   r   rL   r   r   r   r   r   FTr   r   r   r   r   )r   rV   r   r   r=   Zroots_sh_legendreZeval_sh_legendrer   r	   r   r   r   r   r    r    r!   test_roots_sh_legendre  r   r   c               	   C   s   t dj} ttjtj| dtjd ttjtj| dtjddd ttjtj| dtjddd tdd\}}tdd	\}}}t	||d
d
 t	||d
d
 t
| dtj\}}t	|||d tttjd tttjd d S )Nr   r   r   r   r   r   r   FTr   r   r   r   )r   Zlaguerrer   r   r=   Zroots_laguerreZeval_laguerrer   r   r   r	   r   r   r   r   r    r    r!   test_roots_laguerre  s    r   c               
   C   s  dd } dd }dd }t }|| d|d|ddtjd || d|d|ddtjdd	d
 || d|d|ddtjddd
 || d|d|ddtjd || d|d|ddtjdd	d
 || d|d|ddtjddd
 || d|d|ddtjd || d|d|ddtjdd	d
 || d|d|ddtjddd
 || d|d|ddtjd || d|d|ddtjdd	d
 || d|d|ddtjddd
 || d|d|ddtjd || d|d|ddtjdd	d
 || d|d|ddtjdddd tddd\}}tddd\}}}t||dd t||dd t|ddtj\}	}
t||	|
d tt	tjdd tt	tjdd tt	tjdd d S )Nc                    r   )Nc                    r   r|   )r=   roots_genlaguerrer   r   r    r!   rc     r   :test_roots_genlaguerre.<locals>.<lambda>.<locals>.<lambda>r    r   r    r   r!   rc     r   z(test_roots_genlaguerre.<locals>.<lambda>c                    r   )Nc                    r   r|   )r=   Zeval_genlaguerrer   r   r    r!   rc     r   r   r    r   r    r   r!   rc     r   c                    r   )Nc                    s   |   t |   S r|   )r   r   rz   r   r    r!   rc     rm   r   r    r   r    r   r!   rc     r   r   r   r   r   r   r   r   r   r   g+F=r   gN<=r   r   r   r   )r   r   r   FTrM   r   r   r   r   g)
r   r   r   r=   r   r   r	   r   r   r   r   r    r    r!   test_roots_genlaguerre  s8    $$ $$ $$ $$ $&r   c                   C   s   t dd d S )NA   r   )r=   r+   r    r    r    r!   test_gh_6721  s   r   )rx   ry   )1Znumpyr   r   r   Znumpy.testingr   r   r   r   Zpytestr   r   Zscipyr	   Zscipy.specialZspecialr=   r   Zscipy.special._orthogonalZ_orthogonalr   r   r6   rA   rS   rZ   r]   r`   rh   ru   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r    r    r!   <module>   sJ    <'	
B4-'