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    »mœd?z  ã                   @   sŽ  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ƒZG d	d
„ d
ƒZG dd„ dƒZG dd„ dƒZG dd„ dƒZG dd„ dƒZG dd„ dƒZG dd„ dƒZG dd„ dƒ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 )Bé    N)ÚarrayÚsqrt)Úassert_array_almost_equalÚassert_equalÚassert_almost_equalÚassert_allclose)Úraises)Ú	integrate©Úgammac                   @   s,   e Zd Zdd„ Zdd„ Zdd„ Zdd„ Zd	S )
Ú	TestChebyc              	   C   sÖ   t  d¡}t  d¡}tjdd��. t  d¡}t  d¡}t  d¡}t  d¡}W 5 Q R X t|jdgd	ƒ t|jddgd	ƒ t|jddd
gd	ƒ t|jddddgd	ƒ t|jdddddgd	ƒ t|jddddddgd	ƒ d S )Nr   é   Úignore©Úallé   é   é   é   é   éþÿÿÿéýÿÿÿéüÿÿÿéûÿÿÿ)ÚorthÚchebycÚnpÚerrstater   Úc)ÚselfZC0ZC1ZC2ZC3ZC4ZC5© r    ú\/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/scipy/special/tests/test_orthogonal.pyÚtest_chebyc   s    

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

zTestCheby.test_chebycc                 C   s¾   t  d¡}t  d¡}t  d¡}t  d¡}t  d¡}t  d¡}t|jdgdƒ t|jddgdƒ t|jdddgdƒ t|jddd	dgdƒ t|jddd
ddgdƒ t|jddddddgdƒ d S )Nr   r   r   r   r   r   r   éÿÿÿÿr   r   r   )r   Úchebysr   r   )r   ZS0ZS1ZS2ZS3ZS4ZS5r    r    r!   Útest_chebys   s    





zTestCheby.test_chebysc                 C   s¾   t  d¡}t  d¡}t  d¡}t  d¡}t  d¡}t  d¡}t|jdgdƒ t|jddgdƒ t|jdddgdƒ t|jddd	dgdƒ t|jd
ddddgdƒ t|jddddddgdƒ d S )Nr   r   r   r   r   r   r   r#   r   é   iøÿÿÿé   éìÿÿÿ)r   Úchebytr   r   )r   ZT0ZT1ZT2ZT3ZT4ZT5r    r    r!   Útest_chebyt,   s    





zTestCheby.test_chebytc                 C   s¾   t  d¡}t  d¡}t  d¡}t  d¡}t  d¡}t  d¡}t|jdgdƒ t|jddgdƒ t|jdddgdƒ t|jd	dd
dgdƒ t|jdddddgdƒ t|jddddddgdƒ d S )Nr   r   r   r   r   r   r   r#   r&   r   r'   éôÿÿÿé    iàÿÿÿé   )r   Úchebyur   r   )r   ZU0ZU1ZU2ZU3ZU4ZU5r    r    r!   Útest_chebyu:   s    





zTestCheby.test_chebyuN)Ú__name__Ú
__module__Ú__qualname__r"   r%   r*   r/   r    r    r    r!   r      s   r   c                   @   s   e Zd Zdd„ ZdS )Ú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ƒd	ƒ t|jtd| dgƒd	ƒ t|jtd| |d  d| gƒd	ƒ t|jtdt 	|d¡ dd
| |d  dgƒd dƒ t|jtdt 	|d¡ ddt 	|d¡ dd| |d  gƒd dƒ t|jtdt 	|d¡ ddt 	|d¡ ddt 	|d¡ dgƒd dƒ d S )Nr   ç      à?r   çš™™™™™É¿r   r   r   r   r   iúÿÿÿg      @é   r+   g      @r(   é   g      .@)
r   ÚrandomÚanyr   Z
gegenbauerr   r   r   ÚscZpoch)r   ÚaZCa0ZCa1ZCa2ZCa3ZCa4ZCa5r    r    r!   Útest_gegenbauerK   sH    &&ÿÿÿ& ÿÿÿ&  ÿÿÿzTestGegenbauer.test_gegenbauerN)r0   r1   r2   r<   r    r    r    r!   r3   I   s   r3   c                   @   s   e Zd Zdd„ Zdd„ ZdS )ÚTestHermitec                 C   s¾   t  d¡}t  d¡}t  d¡}t  d¡}t  d¡}t  d¡}t|jdgdƒ t|jddgdƒ t|jdddgdƒ t|jd	dd
dgdƒ t|jdddddgdƒ t|jddddddgdƒ d S )Nr   r   r   r   r   r   r   r   r&   r+   r'   iÐÿÿÿé   r,   i`ÿÿÿéx   )r   Úhermiter   r   )r   ÚH0ÚH1ÚH2ÚH3ÚH4ÚH5r    r    r!   Útest_hermiteb   s    





zTestHermite.test_hermitec                 C   s2  t  dtdƒ dg¡}t d¡}t d¡}t d¡}t d¡}t d¡}t d¡}t d¡|ƒ}t d¡|ƒtdƒ }	t d¡|ƒd }
t d¡|ƒdtdƒ  }t d¡|ƒd	 }t d¡|ƒd	tdƒ  }t|j|jd
ƒ t|j|	jd
ƒ t|j|
jd
ƒ t|j|jd
ƒ t|j|jd
ƒ t|j|jd
ƒ d S )Nç      ð?r   r   r   r   r   r   ç       @ç      @r   )r   Úpoly1dr   r   Úhermitenormr@   r   r   )r   ÚpsubrA   rB   rC   rD   rE   rF   Zhe0Zhe1Zhe2Zhe3Zhe4Zhe5r    r    r!   Útest_hermitenormp   s&    





zTestHermite.test_hermitenormN)r0   r1   r2   rG   rN   r    r    r    r!   r=   a   s   r=   c                   @   s   e Zd Zdd„ ZdS )Ú_test_sh_legendrec                 C   s  t  ddg¡}t d¡}t d¡}t d¡}t d¡}t d¡}t d¡}t d¡|ƒ}t d¡|ƒ}	t d¡|ƒ}
t d¡|ƒ}t d¡|ƒ}t d¡|ƒ}t|j|jdƒ t|j|	jdƒ t|j|
jdƒ t|j|jdƒ t|j|jd	ƒ t|j|jd	ƒ d S ©
Nr   r#   r   r   r   r   r   r   r>   )r   rK   r   Úsh_legendreÚlegendrer   r   )r   rM   ZPs0ZPs1ZPs2ZPs3ZPs4ZPs5Zpse0Zpse1Zpse2Zpse3Zpse4Zpse5r    r    r!   Útest_sh_legendreŠ   s&    





z"_test_sh_legendre.test_sh_legendreN)r0   r1   r2   rS   r    r    r    r!   rO   ˆ   s   rO   c                   @   s   e Zd Zdd„ ZdS )Ú_test_sh_chebytc                 C   s  t  ddg¡}t d¡}t d¡}t d¡}t d¡}t d¡}t d¡}t d¡|ƒ}t d¡|ƒ}	t d¡|ƒ}
t d¡|ƒ}t d¡|ƒ}t d¡|ƒ}t|j|jdƒ t|j|	jdƒ t|j|
jdƒ t|j|jdƒ t|j|jd	ƒ t|j|jd	ƒ d S rP   )r   rK   r   Ú	sh_chebytr)   r   r   )r   rM   ZTs0ZTs1ZTs2ZTs3ZTs4ZTs5Ztse0Ztse1Ztse2Ztse3Ztse4Ztse5r    r    r!   Útest_sh_chebyt£   s&    





z_test_sh_chebyt.test_sh_chebytN)r0   r1   r2   rV   r    r    r    r!   rT   ¡   s   rT   c                   @   s   e Zd Zdd„ ZdS )Ú_test_sh_chebyuc                 C   s  t  ddg¡}t d¡}t d¡}t d¡}t d¡}t d¡}t d¡}t d¡|ƒ}t d¡|ƒ}	t d¡|ƒ}
t d¡|ƒ}t d¡|ƒ}t d¡|ƒ}t|j|jdƒ t|j|	jdƒ t|j|
jdƒ t|j|jdƒ t|j|jd	ƒ t|j|jd
ƒ d S )Nr   r#   r   r   r   r   r   r   r>   r6   )r   rK   r   Ú	sh_chebyur.   r   r   )r   rM   ZUs0ZUs1ZUs2ZUs3ZUs4ZUs5Zuse0Zuse1Zuse2Zuse3Zuse4Zuse5r    r    r!   Útest_sh_chebyu¼   s&    

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z_test_sh_chebyu.test_sh_chebyuN)r0   r1   r2   rY   r    r    r    r!   rW   º   s   rW   c                   @   s   e Zd Zdd„ ZdS )Ú_test_sh_jacobic                 C   sÊ  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 ¡|ƒ|d|ƒ }t d|| |d ¡|ƒ|d|ƒ }t d|| |d ¡|ƒ|d|ƒ }t d|| |d ¡|ƒ|d|ƒ }t d|| |d ¡|ƒ|d|ƒ }t d	|| |d ¡|ƒ|d	|ƒ }t|j|jd
ƒ t|j|jd
ƒ t|j|jd
ƒ t|j|jd
ƒ t|	j|jd
ƒ t|
j|jd
ƒ d S )Nc                 S   s(   t | d ƒt | | ƒ t d|  | ƒ S )Nr   r   r
   )ÚnÚpr    r    r!   Ú<lambda>Ö   ó    z0_test_sh_jacobi.test_sh_jacobi.<locals>.<lambda>r   r#   r   r   r   r   r   r   )r   rK   r8   r   Z	sh_jacobiZjacobir   r   )r   ÚconvrM   Úqr\   ZG0ZG1ZG2ZG3ZG4ZG5Zge0Zge1Zge2Zge3Zge4Zge5r    r    r!   Útest_sh_jacobiÔ   s,    $$$$$$z_test_sh_jacobi.test_sh_jacobiN)r0   r1   r2   ra   r    r    r    r!   rZ   Ó   s   rZ   c                   @   s   e Zd Zdd„ ZdS )ÚTestCallc              	   C   s€   g }t dƒD ]&}| dd„ dt|d�  ¡ D ƒ¡ qtjdd��6 |D ]*}t|ƒ}t|dƒt |j	¡dƒ|d	� qFW 5 Q R X d S )
Nr   c                 S   s   g | ]}|  ¡ ‘qS r    )Ústrip)Ú.0Úxr    r    r!   Ú
<listcomp>ô   s     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)
                )r[   r   r   g)\�Âõ(Ô?)Úerr_msg)
ÚrangeÚextendÚdictÚsplitr   r   Úevalr   rK   Zcoef)r   Zpolyr[   Úpstrr\   r    r    r!   Ú	test_callñ   s    
ðÿ
ÿzTestCall.test_callN)r0   r1   r2   rn   r    r    r    r!   rb   ð   s   rb   c                   @   s   e Zd Zdd„ ZdS )ÚTestGenlaguerrec                 C   sx   t tjdddd�dƒdƒ t tjdddd�dƒdƒ t tjdddd�t dd	g¡ƒ t tjdddd�t dd
g¡ƒ d S )Nr   F)Zmonicr   rI   Tç       Àr#   r   r   )r   r   Zgenlaguerrer   rK   )r   r    r    r!   Útest_regression  s     zTestGenlaguerre.test_regressionN)r0   r1   r2   rq   r    r    r    r!   ro     s   ro   çVçž¯Ò<ç‚vIhÂ%,=c                    sø   | |dƒ\}}	}
t  |¡}||d d …t jf |ƒ}t  ||	 |j¡}dt  | ¡ ¡ }|d d …t jf | | }t|t  |¡||ƒ t|	 	¡ |
||ƒ dd„ ‰ t
 ‡ ‡fdd„||¡}t  ˆ |ƒ|	¡}d|d k rÖdn
|d d }t|d ||d	� d S )
NTr   c                 S   s   | d d| d   |  d S )Nr   r   r    ©re   r    r    r!   r]   &  r^   z#verify_gauss_quad.<locals>.<lambda>c                    s   ˆ | ƒˆ| ƒ S ©Nr    rt   ©ÚfÚweight_funcr    r!   r]   '  r^   g�íµ ÷Æ°>é
   r   ©Úrtol)r   ZarangeZnewaxisÚdotÚTr   Zdiagonalr   ÚeyeÚsumr	   ÚquadZvdot)Z	root_funcZ	eval_funcrx   r;   ÚbÚNr{   Úatolre   ÚwÚmur[   ÚvÚvvZvdZresIZresGr    rv   r!   Úverify_gauss_quad  s    
rˆ   c               	   C   sœ  dd„ } dd„ }dd„ }t }|| ddƒ|ddƒ|ddƒddd	ƒ || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	ƒ || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	dd� || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	ƒ || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	ƒ || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	dd� || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	dd� || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	dd� || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒdddd d� || dd!ƒ|dd!ƒ|dd!ƒddd	dd� || dd!ƒ|dd!ƒ|dd!ƒddd
dd� || dd!ƒ|dd!ƒ|dd!ƒdddd d� || d"d#ƒ|d"d#ƒ|d"d#ƒddd	dd� || d"d#ƒ|d"d#ƒ|d"d#ƒddd
dd� || d"d#ƒ|d"d#ƒ|d"d#ƒdddd d� || d$d%ƒ|d$d%ƒ|d$d%ƒddd	ƒ || d$d%ƒ|d$d%ƒ|d$d%ƒddd
dd� || d$d%ƒ|d$d%ƒ|d$d%ƒddddd� t d&d'd'¡\}}t d&¡\}}t||d(d(ƒ t||d(d(ƒ t d&d)d)¡\}}t d&d*¡\}}	t||d(d(ƒ t||	d(d(ƒ t d	dd+d,¡\}
}t d	dd+d-¡\}}}t|
|d(d(ƒ t||d(d(ƒ t |dd+ƒd.d¡\}}t|||d/� tt	tjd0ddƒ tt	tjd1ddƒ tt	tjd+d2dƒ tt	tjd+dd2ƒ tt	tjd+d2d2ƒ d S )3Nc                    s   ‡ ‡fdd„S )Nc                    s   t  | ˆ ˆ|¡S ru   )r:   Úroots_jacobi©r[   r…   ©r;   r�   r    r!   r]   -  r^   ú5test_roots_jacobi.<locals>.<lambda>.<locals>.<lambda>r    r‹   r    r‹   r!   r]   -  r^   z#test_roots_jacobi.<locals>.<lambda>c                    s   ‡ ‡fdd„S )Nc                    s   t  | ˆ ˆ|¡S ru   )r:   Zeval_jacobi©r[   re   r‹   r    r!   r]   .  r^   rŒ   r    r‹   r    r‹   r!   r]   .  r^   c                    s   ‡ ‡fdd„S )Nc                    s   d|  ˆ  d|  ˆ  S )Nr   r    rt   r‹   r    r!   r]   /  r^   rŒ   r    r‹   r    r‹   r!   r]   /  r^   ç      à¿ç      è¿ç      ð¿rH   r   é   çê-�™—q=©rƒ   éd   ç•dyáý¥=r4   çá7ÎQE=çê-�™—�=r   ç‚vIhÂ%L=çÍÌÌÌÌÌì?r   ç‚vIhÂ%<=gá7ÎQU=ç=
×£p=2@çÍÌÌÌÌL;@g^~zÅ=çÍÌÌÌÌŒG@r5   g     �„@éú   g     ð@ç»½×Ùß|Û=g      €@g     @�@g     @@ç      @çš™™™™9Q@r-   ç        ç›+¡†›„=rJ   g      @r   FTr#   rz   r   çffffff
@r   )
rˆ   r:   r‰   Úroots_legendrer   Úroots_gegenbauerr	   r€   Úassert_raisesÚ
ValueError)ÚrfÚefÚwfÚvgqZxjZwjZxlZwlZxcÚwcre   r„   Úyr†   ÚmÚmuIÚmuI_errr    r    r!   Útest_roots_jacobi,  sº    $ ÿ ÿ$((((($(($ ÿ ÿ(( ÿ(((( ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ$ ÿ ÿr²   c               	   C   s  dd„ } dd„ }dd„ }t }|| ddƒ|ddƒ|ddƒddd	ƒ || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	ƒ || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	ƒ || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	ƒ || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	ƒ || ddƒ|ddƒ|ddƒddd
ƒ || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	dd� || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� || ddƒ|ddƒ|ddƒddd	dd� || ddƒ|ddƒ|ddƒddd
dd� || ddƒ|ddƒ|ddƒddddd� t d	ddd ¡\}}t d	ddd!¡\}}}t||d"d"ƒ t||d"d"ƒ t |ddƒd#d¡\}	}
t||	|
d$� tttjd#ddƒ tttjd%ddƒ tttjdddƒ tttjddd&ƒ tttjdd'd&ƒ d S )(Nc                    s   ‡ ‡fdd„S )Nc                    s   t  | ˆ ˆ|¡S ru   )r:   Úroots_sh_jacobirŠ   r‹   r    r!   r]   Š  r^   ú8test_roots_sh_jacobi.<locals>.<lambda>.<locals>.<lambda>r    r‹   r    r‹   r!   r]   Š  r^   z&test_roots_sh_jacobi.<locals>.<lambda>c                    s   ‡ ‡fdd„S )Nc                    s   t  | ˆ ˆ|¡S ru   )r:   Zeval_sh_jacobir�   r‹   r    r!   r]   ‹  r^   r´   r    r‹   r    r‹   r!   r]   ‹  r^   c                    s   ‡ ‡fdd„S )Nc                    s   d|  ˆ ˆ  | ˆd   S )NrH   r    rt   r‹   r    r!   r]   Œ  r^   r´   r    r‹   r    r‹   r!   r]   Œ  r^   rŽ   g      Ð?r¢   rH   r   r‘   r’   r“   r”   r•   r4   rš   r   r–   r—   r   r™   rœ   r›   r�   çš™™™™™É?rŸ   r¡   r    g(Í´#=r˜   r   FTr£   r   rz   r¤   r#   r   )rˆ   r:   r³   r   r	   r€   r§   r¨   )r©   rª   r«   r¬   re   r„   r®   r†   r¯   r°   r±   r    r    r!   Útest_roots_sh_jacobi‰  s`    $ ÿ ÿ$(($(($(($$ ÿ((((( ÿr¶   c            
   	   C   s<  t j} t j}t d¡j}t| ||tj tjdƒ 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	ƒ t	||d	d	ƒ t
 |tj tj¡\}}	t	|||	d
� t  dd¡\}}t  dd¡\}}}t	||d	d	ƒ t	||d	d	ƒ t	t|ƒ|d	d	ƒ ttt jdƒ ttt jdƒ d S )Nr   r‘   rš   r“   r”   r’   FTr£   rz   éÈ   r   r¤   )r:   Zroots_hermiteZeval_hermiter   r@   rx   rˆ   r   Úinfr   r	   r€   r   r§   r¨   ©
ÚrootfÚevalfÚweightfre   r„   r®   r†   r¯   r°   r±   r    r    r!   Útest_roots_hermite½  s&    r½   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   sÐ   t  | |jf¡}t jd t  d|d  ¡ |dd d …f< | dkrÌtdƒ| |dd d …f  |dd d …f< td| ƒD ]X}td| ƒ| ||d d d …f  t|d | ƒ||d d d …f   ||d d …f< qr|S )Nç      Ð¿rŽ   r   r   r   rI   rH   )r   ÚzerosÚsizeÚpiÚexpr   rh   )r[   ZnodesÚHÚkr    r    r!   Úhermite_recursionÛ  s    ((Vz1test_roots_hermite_asy.<locals>.hermite_recursionrr   r£   c                    sX   t  | ¡\}}ˆ | d |ƒ}t|dd d …f t | ¡||ƒ tt|ƒttjƒ||ƒ d S )Nr   r#   )r   Z_roots_hermite_asyr   r   r¿   r   r   rÁ   )r‚   r{   rƒ   re   r„   rÃ   ©rÅ   r    r!   Útestå  s     z$test_roots_hermite_asy.<locals>.testé–   r’   r“   é—   i,  i-  iô  iõ  iç  iè  iÐ  iˆ  )rr   r£   r    )rÇ   r    rÆ   r!   Útest_roots_hermite_asyÙ  s    
rÊ   c            
   	   C   sì   t j} t j}t d¡j}t| ||tj tjdƒ 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	ƒ t	||d	d	ƒ t
 |tj tj¡\}}	t	|||	d
� ttt jdƒ ttt jdƒ d S )Nr   r‘   rš   r“   r”   r’   FTr£   rz   r   r¤   )r:   Zroots_hermitenormZeval_hermitenormr   rL   rx   rˆ   r   r¸   r   r	   r€   r§   r¨   r¹   r    r    r!   Útest_roots_hermitenormö  s    rË   c               	   C   s”  dd„ } dd„ }dd„ }t }|| dƒ|dƒ|dƒdddƒ || dƒ|dƒ|dƒddd	d
d� || dƒ|dƒ|dƒddddd� || dƒ|dƒ|dƒdddƒ || dƒ|dƒ|dƒddd	dd� || dƒ|dƒ|dƒdddd
d� || dƒ|dƒ|dƒdddƒ || dƒ|dƒ|dƒddd	dd� || dƒ|dƒ|dƒdddd
d� || dƒ|dƒ|dƒdddƒ || dƒ|dƒ|dƒddd	dd� || dƒ|dƒ|dƒdddd
d� || dƒ|dƒ|dƒddddd� || dƒ|dƒ|dƒddd	d
d� || dƒ|dƒ|dƒddddd� || dƒ|dƒ|dƒddddd� || dƒ|dƒ|dƒddd	d
d� || dƒ|dƒ|dƒddddd� || dƒ|dƒ|dƒddddd� || dƒ|dƒ|dƒddd	d
d� || dƒ|dƒ|dƒddddd� || dƒ|dƒ|dƒddddd� || dƒ|dƒ|dƒddd	d
d� || dƒ|dƒ|dƒddddd� || dƒ|dƒ|dƒdddd
d� || dƒ|dƒ|dƒddd	dd� || dƒ|dƒ|dƒddddd� || dƒtj|dƒdddƒ || dƒtj|dƒddd	ƒ || dƒtj|dƒdddd
d� t ddd¡\}}t ddd¡\}}}t||ddƒ t||ddƒ t |dƒdd¡\}	}
t||	|
d� tttjddƒ tttjd dƒ tttjd!d"ƒ d S )#Nc                    s   ‡ fdd„S )Nc                    s   t  | ˆ |¡S ru   )r:   r¦   rŠ   ©r;   r    r!   r]     r^   ú9test_roots_gegenbauer.<locals>.<lambda>.<locals>.<lambda>r    rÌ   r    rÌ   r!   r]     r^   z'test_roots_gegenbauer.<locals>.<lambda>c                    s   ‡ fdd„S )Nc                    s   t  | ˆ |¡S ru   )r:   Zeval_gegenbauerr�   rÌ   r    r!   r]     r^   rÍ   r    rÌ   r    rÌ   r!   r]     r^   c                    s   ‡ fdd„S )Nc                    s   d| d  ˆ d  S )Nr   r   r4   r    rt   rÌ   r    r!   r]     r^   rÍ   r    rÌ   r    rÌ   r!   r]     r^   r¾   r�   rH   r   r‘   r’   r“   r”   r•   çš™™™™™¹?rš   r   ry   é2   éª   g     Pe@gê-�™—A=éî   g     €@rŸ   r   r   FTr£   r#   rz   r¤   r   r�   )	rˆ   r:   Úeval_chebytr¦   r   r	   r€   r§   r¨   ©rº   r»   r¼   r¬   re   r„   r®   r†   r¯   r°   r±   r    r    r!   Útest_roots_gegenbauer
  sV    """"""""""""""""""""""" rÔ   c               	   C   sÐ   t  d¡j} ttjtj| dddƒ ttjtj| dddƒ ttjtj| ddddd� t dd¡\}}t dd	¡\}}}t||d
d
ƒ t||d
d
ƒ t 	| dd¡\}}t|||d� t
ttjdƒ t
ttjdƒ d S )Nr   r�   rH   r‘   r”   r’   r“   FTr£   r#   r   rz   r   r¤   )r   r)   rx   rˆ   r:   Úroots_chebytrÒ   r   r	   r€   r§   r¨   ©r¼   re   r„   r®   r†   r¯   r°   r±   r    r    r!   Útest_roots_chebytG  s    r×   c                  C   sP   t  d¡\} }| d d… | dd …  }}t||d d d…  ƒ t| d dƒ d S )Né   ry   r6   r#   r   )r:   rÕ   r   )re   r„   ÚposÚnegr    r    r!   Útest_chebyt_symmetryX  s    rÛ   c                  C   sÌ   t  d¡j} ttjtj| dddƒ ttjtj| dddƒ ttjtj| dddƒ t dd¡\}}t dd¡\}}}t||ddƒ t||ddƒ t 	| d	d
¡\}}t|||d� t
ttjdƒ t
ttjdƒ d S )Nr   r�   rH   r‘   r”   FTr£   r#   r   rz   r   r¤   )r   r.   rx   rˆ   r:   Zroots_chebyuZeval_chebyur   r	   r€   r§   r¨   rÖ   r    r    r!   Útest_roots_chebyu^  s    rÜ   c               	   C   sÐ   t  d¡j} ttjtj| dddƒ ttjtj| dddƒ ttjtj| ddddd� t dd¡\}}t dd	¡\}}}t||d
d
ƒ t||d
d
ƒ t 	| dd¡\}}t|||d� t
ttjdƒ t
ttjdƒ d S )Nr   rp   rI   r‘   r”   r’   r“   FTr£   r   r   rz   r   r¤   )r   r   rx   rˆ   r:   Zroots_chebycZeval_chebycr   r	   r€   r§   r¨   rÖ   r    r    r!   Útest_roots_chebyco  s    rÝ   c                  C   sÌ   t  d¡j} ttjtj| dddƒ ttjtj| dddƒ ttjtj| dddƒ t dd¡\}}t dd¡\}}}t||ddƒ t||ddƒ t 	| d	d
¡\}}t|||d� t
ttjdƒ t
ttjdƒ d S )Nr   rp   rI   r‘   r”   FTr£   r   r   rz   r   r¤   )r   r$   rx   rˆ   r:   Zroots_chebysZeval_chebysr   r	   r€   r§   r¨   rÖ   r    r    r!   Útest_roots_chebys€  s    rÞ   c               	   C   sÐ   t  d¡j} ttjtj| dddƒ ttjtj| dddƒ ttjtj| ddddd� t dd¡\}}t dd	¡\}}}t||d
d
ƒ t||d
d
ƒ t 	| dd¡\}}t|||d� t
ttjdƒ t
ttjdƒ d S ©Nr   r¢   rH   r‘   r”   rš   r“   FTr£   r   r   rz   r¤   )r   rU   rx   rˆ   r:   Zroots_sh_chebytZeval_sh_chebytr   r	   r€   r§   r¨   rÖ   r    r    r!   Útest_roots_sh_chebyt‘  s     ÿrà   c               	   C   sÐ   t  d¡j} ttjtj| dddƒ ttjtj| dddƒ ttjtj| ddddd� t dd¡\}}t dd	¡\}}}t||d
d
ƒ t||d
d
ƒ t 	| dd¡\}}t|||d� t
ttjdƒ t
ttjdƒ d S rß   )r   rX   rx   rˆ   r:   Zroots_sh_chebyuZeval_sh_chebyur   r	   r€   r§   r¨   rÖ   r    r    r!   Útest_roots_sh_chebyu£  s     ÿrá   c               	   C   sÔ   t  d¡j} ttjtj| dddƒ 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ƒ t||ddƒ t 	| dd¡\}}t|||d� t
ttjdƒ t
ttjdƒ d S )Nr   r�   rH   r‘   rš   r“   r”   r’   FTr£   r#   r   rz   r   r¤   )r   rR   rx   rˆ   r:   r¥   Zeval_legendrer   r	   r€   r§   r¨   rÖ   r    r    r!   Útest_roots_legendreµ  s$     ÿ ÿrâ   c               	   C   sÔ   t  d¡j} ttjtj| dddƒ ttjtj| ddddd� ttjtj| ddddd� t dd	¡\}}t dd
¡\}}}t||ddƒ t||ddƒ t 	| dd¡\}}t|||d� t
ttjdƒ t
ttjdƒ d S )Nr   r¢   rH   r‘   rš   r“   r”   r’   FTr£   r   r   rz   r¤   )r   rQ   rx   rˆ   r:   Zroots_sh_legendreZeval_sh_legendrer   r	   r€   r§   r¨   rÖ   r    r    r!   Útest_roots_sh_legendreÈ  s$     ÿ ÿrã   c               	   C   sÜ   t  d¡j} ttjtj| dtjdƒ 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
ƒ t	||d
d
ƒ t
 | dtj¡\}}t	|||d� tttjdƒ tttjdƒ d S )Nr   r¢   r‘   rš   r“   r”   r’   FTr£   r   rz   r¤   )r   Zlaguerrerx   rˆ   r:   Zroots_laguerreZeval_laguerrer   r¸   r   r	   r€   r§   r¨   rÖ   r    r    r!   Útest_roots_laguerreÛ  s$     ÿ ÿrä   c               
   C   sÂ  dd„ } dd„ }dd„ }t }|| dƒ|dƒ|dƒdtjdƒ || dƒ|dƒ|dƒdtjdd	d
� || dƒ|dƒ|dƒdtjddd
� || dƒ|dƒ|dƒdtjdƒ || dƒ|dƒ|dƒdtjdd	d
� || dƒ|dƒ|dƒdtjddd
� || dƒ|dƒ|dƒdtjdƒ || dƒ|dƒ|dƒdtjdd	d
� || dƒ|dƒ|dƒdtjddd
� || dƒ|dƒ|dƒdtjdƒ || dƒ|dƒ|dƒdtjdd	d
� || dƒ|dƒ|dƒdtjddd
� || dƒ|dƒ|dƒdtjdƒ || dƒ|dƒ|dƒdtjdd	d
� || dƒ|dƒ|dƒdtjdddd� t ddd¡\}}t ddd¡\}}}t||ddƒ t||ddƒ t |dƒdtj¡\}	}
t||	|
d� tt	tjddƒ tt	tjddƒ tt	tjddƒ d S )Nc                    s   ‡ fdd„S )Nc                    s   t  | ˆ |¡S ru   )r:   Úroots_genlaguerrerŠ   rÌ   r    r!   r]   ï  r^   ú:test_roots_genlaguerre.<locals>.<lambda>.<locals>.<lambda>r    rÌ   r    rÌ   r!   r]   ï  r^   z(test_roots_genlaguerre.<locals>.<lambda>c                    s   ‡ fdd„S )Nc                    s   t  | ˆ |¡S ru   )r:   Zeval_genlaguerrer�   rÌ   r    r!   r]   ð  r^   ræ   r    rÌ   r    rÌ   r!   r]   ð  r^   c                    s   ‡ fdd„S )Nc                    s   | ˆ  t  |  ¡ S ru   )r   rÂ   rt   rÌ   r    r!   r]   ñ  r^   ræ   r    rÌ   r    rÌ   r!   r]   ñ  r^   rŽ   r¢   r   r‘   rš   r“   r”   r’   rÎ   g›+¡†›„F=r   g‹N¼£îý<=ry   rÏ   r£   r˜   )r{   rƒ   r   FTrI   rz   r   r¤   r   gš™™™™™ñ¿)
rˆ   r   r¸   r:   rå   r   r	   r€   r§   r¨   rÓ   r    r    r!   Útest_roots_genlaguerreî  s8     $$ $$ $$ $$ $&rç   c                   C   s   t  d¡dƒ d S )NéA   rµ   )r:   r)   r    r    r    r!   Útest_gh_6721  s    ré   )rr   rs   )1Únumpyr   r   r   Znumpy.testingr   r   r   r   Zpytestr   r§   Zscipyr	   Zscipy.specialÚspecialr:   r   Zscipy.special._orthogonalZ_orthogonalr   r   r3   r=   rO   rT   rW   rZ   rb   ro   rˆ   r²   r¶   r½   rÊ   rË   rÔ   r×   rÛ   rÜ   rÝ   rÞ   rà   rá   râ   rã   rä   rç   ré   r    r    r    r!   Ú<module>   sJ   <'	   ÿ
]4='