3
Oédr  ã               @   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jZd dlmZ d dljjZG dd„ deƒZG d	d
„ d
eƒZG dd„ deƒZG dd„ deƒZG dd„ deƒZG dd„ deƒZG dd„ deƒZG dd„ deƒZG dd„ de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>„ Z0d?d@„ Z1d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 jdƒ}t jdƒ}tjdd. t jdƒ}t jdƒ}t jdƒ}t jdƒ}W d 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   úW/var/www/html/virt/lib64/python3.6/site-packages/scipy/special/tests/test_orthogonal.pyÚtest_chebyc   s    




zTestCheby.test_chebycc             C   s¾   t jdƒ}t jdƒ}t jdƒ}t jdƒ}t jdƒ}t jdƒ}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 jdƒ}t jdƒ}t jdƒ}t jdƒ}t jdƒ}t jdƒ}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   é   é   é   r!   r   iøÿÿÿiìÿÿÿ)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 jdƒ}t jdƒ}t jdƒ}t jdƒ}t jdƒ}t jdƒ}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$   r%   é   é    é   r!   r   iôÿÿÿiàÿÿÿ)r   Úchebyur   r   )r   ZU0ZU1ZU2ZU3ZU4ZU5r   r   r   Útest_chebyu:   s    





zTestCheby.test_chebyuN)Ú__name__Ú
__module__Ú__qualname__r    r#   r(   r-   r   r   r   r   r      s   r   c               @   s   e Zd Zdd„ ZdS )ÚTestGegenbauerc             C   s„  dt jjƒ  d }t j|dkƒr$d}tjd|ƒ}tjd|ƒ}tjd|ƒ}tjd|ƒ}tjd|ƒ}tjd|ƒ}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j	|dƒ dd| |d  dgƒd dƒ t|jtdtj	|dƒ ddtj	|dƒ dd| |d  gƒd dƒ t|jtdtj	|dƒ ddtj	|dƒ ddtj	|dƒ dgƒd dƒ d S )Nr   g      à?r   gš™™™™™É?r   r   r   r   r   r+   g      @é   r)   g      @r&   é   g      .@gš™™™™™É¿iúÿÿÿiôÿÿÿiìÿÿÿ)
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   s$    &&&&zTestGegenbauer.test_gegenbauerN)r.   r/   r0   r8   r   r   r   r   r1   I   s   r1   c               @   s   e Zd Zdd„ Zdd„ ZdS )ÚTestHermitec             C   s¾   t jdƒ}t jdƒ}t jdƒ}t jdƒ}t jdƒ}t jdƒ}t|jdgdƒ t|jddgdƒ t|jdddgdƒ t|jddddgdƒ t|jd
dddd	gd	ƒ t|jddddddgd	ƒ d S )Nr   r   r   r   r   r   r   r$   r)   r%   é0   r*   é    éx   r   iôÿÿÿiÐÿÿÿi`ÿÿÿ)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 jdtdƒ dgƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ|ƒ}tjdƒ|ƒtdƒ }	tjdƒ|ƒd }
tjdƒ|ƒdtdƒ  }tjdƒ|ƒd	 }tjdƒ|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 )Ng      ð?r   r   r   r   r   r   g       @g      @r   )r   Úpoly1dr   r   Úhermitenormr=   r   r   )r   Úpsubr>   r?   r@   rA   rB   rC   Zhe0Zhe1Zhe2Zhe3Zhe4Zhe5r   r   r   Útest_hermitenormp   s&    





zTestHermite.test_hermitenormN)r.   r/   r0   rD   rH   r   r   r   r   r9   a   s   r9   c               @   s   e Zd Zdd„ ZdS )Ú_test_sh_legendrec             C   s  t jdd	gƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ|ƒ}tjdƒ|ƒ}	tjdƒ|ƒ}
tjdƒ|ƒ}tjdƒ|ƒ}tjdƒ|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   rE   r   Úsh_legendreÚlegendrer   r   )r   rG   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)r.   r/   r0   rL   r   r   r   r   rI   ˆ   s   rI   c               @   s   e Zd Zdd„ ZdS )Ú_test_sh_chebytc             C   s  t jdd	gƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ|ƒ}tjdƒ|ƒ}	tjdƒ|ƒ}
tjdƒ|ƒ}tjdƒ|ƒ}tjdƒ|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   rE   r   Ú	sh_chebytr'   r   r   )r   rG   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)r.   r/   r0   rO   r   r   r   r   rM   ¡   s   rM   c               @   s   e Zd Zdd„ ZdS )Ú_test_sh_chebyuc             C   s  t jdd
gƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ}tjdƒ|ƒ}tjdƒ|ƒ}	tjdƒ|ƒ}
tjdƒ|ƒ}tjdƒ|ƒ}tjdƒ|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)   r2   r!   )r   rE   r   Ú	sh_chebyur,   r   r   )r   rG   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)r.   r/   r0   rR   r   r   r   r   rP   º   s   rP   c               @   s   e Zd Zdd„ ZdS )Ú_test_sh_jacobic             C   sÊ  dd„ }t jdd
gƒ}dt jjƒ  }|d dt jjƒ   }tjd||ƒ}tjd||ƒ}tjd||ƒ}tjd||ƒ}tjd||ƒ}	tjd||ƒ}
tjd|| |d ƒ|ƒ|d|ƒ }tjd|| |d ƒ|ƒ|d|ƒ }tjd|| |d ƒ|ƒ|d|ƒ }tjd|| |d ƒ|ƒ|d|ƒ }tjd|| |d ƒ|ƒ|d|ƒ }tjd|| |d ƒ|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   s    z0_test_sh_jacobi.test_sh_jacobi.<locals>.<lambda>r   r   r   r   r   r   r   r!   )r   rE   r4   r   Z	sh_jacobiZjacobir   r   )r   ÚconvrG   ÚqrU   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)r.   r/   r0   rY   r   r   r   r   rS   Ó   s   rS   c               @   s   e Zd Zdd„ ZdS )ÚTestCallc             C   sˆ   g }x2t dƒD ]&}|jdd„ dt|d jƒ D ƒƒ qW tjdd: x2|D ]*}t|ƒ}t|dƒtj|j	ƒdƒ|d	 qLW W d Q R X d S )
Nr   c             S   s   g | ]}|j ƒ ‘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)
                )rT   r   )r   g)\Âõ(Ô?)Úerr_msg)
ÚrangeÚextendÚdictÚsplitr   r   Úevalr   rE   Zcoef)r   ÚpolyrT   ÚpstrrU   r   r   r   Ú	test_callñ   s    

zTestCall.test_callN)r.   r/   r0   rg   r   r   r   r   rZ   ð   s   rZ   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jd	dgƒƒ t tjddddtjdd
gƒƒ d S )Nr   F)Zmonicr   g       @Tr   g       Àr!   r   )r   r   Zgenlaguerrer   rE   )r   r   r   r   Útest_regression  s     zTestGenlaguerre.test_regressionN)r.   r/   r0   ri   r   r   r   r   rh     s   rh   çVçž¯Ò<ç›+¡†›„=c                sø   | |dƒ\}}	}
t j|ƒ}||d d …t jf |ƒ}t j||	 |jƒ}dt j|jƒ ƒ }|d d …t jf | | }t|t j|ƒ||ƒ t|	j	ƒ |
||ƒ dd„ ‰ t
j‡ ‡fdd„||ƒ}t jˆ |ƒ|	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   )r]   r   r   r   rV   &  s    z#verify_gauss_quad.<locals>.<lambda>c                s   ˆ | ƒˆ| ƒ S )Nr   )r]   )ÚfÚweight_funcr   r   rV   '  s    gíµ ÷Æ°>é
   r   )Úrtol)r   ZarangeZnewaxisÚdotÚTr   Zdiagonalr   ZeyeÚsumr	   ÚquadZvdot)Z	root_funcZ	eval_funcrm   r7   ÚbÚNro   Úatolr]   ÚwÚmurT   ÚvÚvvZvdZresIZresGr   )rl   rm   r   Úverify_gauss_quad  s    
r{   c           	   C   s”  dd„ } dd„ }dd„ }t }|| d(d)ƒ|d*d+ƒ|d,d-ƒd.ddƒ || d/d0ƒ|d1d2ƒ|d3d4ƒd5dd	d
d || d6d7ƒ|d8d9ƒ|d:d;ƒd<dddd || dd=ƒ|dd>ƒ|dd?ƒd@ddƒ || ddAƒ|ddBƒ|ddCƒdDdd	dd || ddEƒ|ddFƒ|ddGƒdHdddd || ddƒ|ddƒ|ddƒdIdddd || ddƒ|ddƒ|ddƒdJdd	dd || ddƒ|ddƒ|ddƒdKddd
d || ddƒ|ddƒ|ddƒdLddƒ || ddƒ|ddƒ|ddƒdMdd	dd || ddƒ|ddƒ|ddƒdNdddd || ddƒ|ddƒ|ddƒdOddƒ || ddƒ|ddƒ|ddƒdPdd	dd || ddƒ|ddƒ|ddƒdQdddd || ddRƒ|ddSƒ|ddTƒdUdddd || ddVƒ|ddWƒ|ddXƒdYdd	dd || ddZƒ|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jdddƒ\}}tjdƒ\}}t||ddƒ t||ddƒ tjdd d ƒ\}}tjdd!ƒ\}}	t||ddƒ t||	ddƒ tjddd"d#ƒ\}
}tjddd"d$ƒ\}}}t|
|ddƒ t||ddƒ tj|dd"ƒdadƒ\}}t|||d% tt	tjd&ddƒ tt	tjd'ddƒ tt	tjd"dbdƒ tt	tjd"ddcƒ tt	tjd"dddeƒ d S )fNc                s   ‡ ‡fdd„S )Nc                s   t j| ˆ ˆ|ƒS )N)r6   Úroots_jacobi)rT   rx   )r7   rt   r   r   rV   -  s    z5test_roots_jacobi.<locals>.<lambda>.<locals>.<lambda>r   )r7   rt   r   )r7   rt   r   rV   -  s    z#test_roots_jacobi.<locals>.<lambda>c                s   ‡ ‡fdd„S )Nc                s   t j| ˆ ˆ|ƒS )N)r6   Zeval_jacobi)rT   r]   )r7   rt   r   r   rV   .  s    z5test_roots_jacobi.<locals>.<lambda>.<locals>.<lambda>r   )r7   rt   r   )r7   rt   r   rV   .  s    c                s   ‡ ‡fdd„S )Nc                s   d|  ˆ  d|  ˆ  S )Nr   r   )r]   )r7   rt   r   r   rV   /  s    z5test_roots_jacobi.<locals>.<lambda>.<locals>.<lambda>r   )r7   rt   r   )r7   rt   r   rV   /  s    g      à?g      è?g      ð?r   é   gê-™—q=)rv   éd   g•dyáý¥=gá7ÎQE=gê-™—=r   g‚vIhÂ%L=gÍÌÌÌÌÌì?r   g‚vIhÂ%<=gá7ÎQU=g=
×£p=2@gÍÌÌÌÌL;@g^~zÅ=gÍÌÌÌÌŒG@gš™™™™™É?g      @gš™™™™9Q@r+   g        g›+¡†›„=g      @g      @r   FT)ro   r   gffffff
@g      à¿g      è¿g      à¿g      è¿g      à¿g      è¿g      ð¿g      à¿g      è¿g      à¿g      è¿g      à¿g      è¿g      ð¿g      à¿g      è¿g      à¿g      è¿g      à¿g      è¿g      ð¿g      à¿g      à¿g      à¿g      ð¿g      à¿g      à¿g      à¿g      ð¿g      à¿g      à¿g      à¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿gš™™™™™É¿gš™™™™™É¿gš™™™™™É¿g      ð¿gš™™™™™É¿gš™™™™™É¿gš™™™™™É¿g      ð¿gš™™™™™É¿gš™™™™™É¿gš™™™™™É¿g      ð¿g      ð¿g      ð¿g      ð¿r!   r   r   r   r   )
r{   r6   r|   Úroots_legendrer   Úroots_gegenbauerr	   rs   Úassert_raisesÚ
ValueError)ÚrfÚefÚwfÚvgqZxjZwjZxlZwlZxcZwcr]   rw   Úyry   ÚmÚmuIÚmuI_errr   r   r   Útest_roots_jacobi,  sd    $

$((((($(($ 
((
$(
r‹   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jd	dddƒ\}}tjd	ddd ƒ\}}}t||d!d!ƒ t||d!d!ƒ tj|ddƒd"dƒ\}	}
t||	|
d# tttjd"ddƒ tttjd$ddƒ tttjdddƒ tttjddd.ƒ tttjdd/d0ƒ d S )1Nc                s   ‡ ‡fdd„S )Nc                s   t j| ˆ ˆ|ƒS )N)r6   Úroots_sh_jacobi)rT   rx   )r7   rt   r   r   rV   o  s    z8test_roots_sh_jacobi.<locals>.<lambda>.<locals>.<lambda>r   )r7   rt   r   )r7   rt   r   rV   o  s    z&test_roots_sh_jacobi.<locals>.<lambda>c                s   ‡ ‡fdd„S )Nc                s   t j| ˆ ˆ|ƒS )N)r6   Zeval_sh_jacobi)rT   r]   )r7   rt   r   r   rV   p  s    z8test_roots_sh_jacobi.<locals>.<lambda>.<locals>.<lambda>r   )r7   rt   r   )r7   rt   r   rV   p  s    c                s   ‡ ‡fdd„S )Nc                s   d|  ˆ ˆ  | ˆd   S )Ng      ð?r   )r]   )r7   rt   r   r   rV   q  s    z8test_roots_sh_jacobi.<locals>.<lambda>.<locals>.<lambda>r   )r7   rt   r   )r7   rt   r   rV   q  s    g      à?g      Ð?g        g      ð?r   r}   gê-™—q=)rv   r~   g•dyáý¥=g‚vIhÂ%<=r   gá7ÎQE=gê-™—=r   gÍÌÌÌÌÌì?gÍÌÌÌÌL;@g=
×£p=2@gÍÌÌÌÌŒG@gš™™™™™É?g»½×Ùß|Û=gš™™™™9Q@g      @g(Í´#=g‚vIhÂ%L=r   FTg›+¡†›„=r   )ro   gffffff
@g      à¿g      à¿g      à¿g      à¿g      à¿g      à¿g      à¿g      à¿g      à¿r!   r   r!   )r{   r6   rŒ   r   r	   rs   r   r‚   )rƒ   r„   r…   r†   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_sh_jacobin  sP    $

$(($(($(($$
(((((
r   c        
   	   C   s<  t j} t j}tjdƒj}t| ||tj tjdƒ t| ||tj tjddd t| ||tj tjddd t jddƒ\}}t jddƒ\}}}t	||d	d	ƒ t	||d	d	ƒ t
j|tj tjƒ\}}	t	|||	d
 t jddƒ\}}t jddƒ\}}}t	||d	d	ƒ t	||d	d	ƒ t	t|ƒ|d	d	ƒ ttt jdƒ ttt jdƒ d S )Nr   r}   g‚vIhÂ%<=)rv   r~   gê-™—q=FTg›+¡†›„=)ro   éÈ   r   gffffff
@)r6   Zroots_hermiteZeval_hermiter   r=   rm   r{   r   Úinfr   r	   rs   rr   r   r‚   )
ÚrootfÚevalfÚweightfr]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_hermite¢  s&    r“   c                 s’   dd„ ‰ d‡ fdd„	} | ddd	 | d
dd	 | ddd	 | ddd	 | ddd	 | ddd	 | ddd	 | ddd	 | ddd	 | ddd	 d S )Nc             S   sÔ   t j| |jfƒ}t jd t jd	|d  ƒ |dd d …f< | dkrÐtdƒ| |dd d …f  |dd d …f< xftd| ƒD ]X}td| ƒ| ||d d d …f  t|d | ƒ||d d d …f   ||d d …f< qtW |S )
Ng      Ð?g      à?r   r   r   g       @g      ð?g      Ð¿g      à¿)r   ÚzerosÚsizeÚpiÚexpr   r`   )rT   ZnodesÚHÚkr   r   r   Úhermite_recursionÀ  s    ((Xz1test_roots_hermite_asy.<locals>.hermite_recursionçVçž¯Ò<ç›+¡†›„=c                sX   t j| ƒ\}}ˆ | d |ƒ}t|dd d …f tj| ƒ||ƒ tt|ƒttjƒ||ƒ d S )Nr   r!   )r   Z_roots_hermite_asyr   r   r”   rr   r   r–   )ru   ro   rv   r]   rw   r˜   )rš   r   r   ÚtestÊ  s     z$test_roots_hermite_asy.<locals>.testé–   gê-™—q=)rv   é—   i,  i-  iô  iõ  iç  iè  iÐ  iˆ  )r›   rœ   r   )r   r   )rš   r   Útest_roots_hermite_asy¾  s    
r    c        
   	   C   sì   t j} t j}tjdƒ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 jddƒ\}}t jddƒ\}}}t	||d	d	ƒ t	||d	d	ƒ t
j|tj tjƒ\}}	t	|||	d
 ttt jdƒ ttt jdƒ d S )Nr   r}   g‚vIhÂ%<=)rv   r~   gê-™—q=FTg›+¡†›„=)ro   r   gffffff
@)r6   Zroots_hermitenormZeval_hermitenormr   rF   rm   r{   r   r   r   r	   rs   r   r‚   )
r   r‘   r’   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_hermitenormÛ  s    r¡   c           	   C   sü  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d0dddd
 || dƒ|dƒ|dƒd1ddd	d
 || dƒ|dƒ|dƒd2dddd
 || dƒtj|dƒd3ddƒ || dƒtj|dƒd4ddƒ || dƒtj|dƒd5ddd	d
 tjdddƒ\}}tjdddƒ\}}}t||ddƒ t||ddƒ tj|dƒd6dƒ\}	}
t||	|
d tttjddƒ tttjddƒ tttjdd7ƒ d S )8Nc                s   ‡ fdd„S )Nc                s   t j| ˆ |ƒS )N)r6   r€   )rT   rx   )r7   r   r   rV   ð  s    z9test_roots_gegenbauer.<locals>.<lambda>.<locals>.<lambda>r   )r7   r   )r7   r   rV   ð  s    z'test_roots_gegenbauer.<locals>.<lambda>c                s   ‡ fdd„S )Nc                s   t j| ˆ |ƒS )N)r6   Zeval_gegenbauer)rT   r]   )r7   r   r   rV   ñ  s    z9test_roots_gegenbauer.<locals>.<lambda>.<locals>.<lambda>r   )r7   r   )r7   r   rV   ñ  s    c                s   ‡ fdd„S )Nc                s   d| d  ˆ d  S )Nr   r   g      à?r   )r]   )r7   r   r   rV   ò  s    z9test_roots_gegenbauer.<locals>.<lambda>.<locals>.<lambda>r   )r7   r   )r7   r   rV   ò  s    g      Ð?g      ð?r   r}   gê-™—q=)rv   r~   g•dyáý¥=gš™™™™™¹?g‚vIhÂ%<=r   rn   é2   r   r   FTg›+¡†›„=)ro   gffffff
@r   g      è?g      Ð¿g      Ð¿g      Ð¿g      ð¿g      Ð¿g      Ð¿g      Ð¿g      ð¿g      Ð¿g      Ð¿g      Ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿g      ð¿r!   g      è¿)	r{   r6   Úeval_chebytr€   r   r	   rs   r   r‚   )r   r‘   r’   r†   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_gegenbauerï  s>    """"""""""" r¤   c           	   C   sÐ   t jdƒ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jddƒ\}}tjddƒ\}}}t||d	d	ƒ t||d	d	ƒ tj	| dd
ƒ\}}t|||d t
ttjdƒ t
ttjdƒ d S )Nr   g      ð?r}   r~   gê-™—q=)rv   FTg›+¡†›„=r   )ro   r   gffffff
@g      ð¿g      ð¿g      ð¿r!   )r   r'   rm   r{   r6   Úroots_chebytr£   r   r	   rs   r   r‚   )r’   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_chebyt  s    r¦   c              C   sP   t jdƒ\} }| d d… | dd …  }}t||d d d…  ƒ t| d dƒ d S )Né   rn   r2   r   r   r!   )r6   r¥   r   )r]   rw   ÚposÚnegr   r   r   Útest_chebyt_symmetry-  s    rª   c              C   sÌ   t jdƒ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jddƒ\}}tjddƒ\}}}t||ddƒ t||ddƒ tj	| ddƒ\}}t|||d	 t
ttjd
ƒ t
ttjdƒ d S )Nr   g      ð?r}   r~   FTg›+¡†›„=r   )ro   r   gffffff
@g      ð¿g      ð¿g      ð¿r!   )r   r,   rm   r{   r6   Zroots_chebyuZeval_chebyur   r	   rs   r   r‚   )r’   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_chebyu3  s    r«   c           	   C   sÐ   t jdƒ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jddƒ\}}tjddƒ\}}}t||d	d	ƒ t||d	d	ƒ tj	| dd
ƒ\}}t|||d t
ttjdƒ t
ttjdƒ d S )Nr   g       @r}   r~   gê-™—q=)rv   FTg›+¡†›„=r   )ro   r   gffffff
@g       Àg       Àg       Àr   )r   r   rm   r{   r6   Zroots_chebycZeval_chebycr   r	   rs   r   r‚   )r’   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_chebycD  s    r¬   c              C   sÌ   t jdƒ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jddƒ\}}tjddƒ\}}}t||ddƒ t||ddƒ tj	| ddƒ\}}t|||d	 t
ttjd
ƒ t
ttjdƒ d S )Nr   g       @r}   r~   FTg›+¡†›„=r   )ro   r   gffffff
@g       Àg       Àg       Àr   )r   r"   rm   r{   r6   Zroots_chebysZeval_chebysr   r	   rs   r   r‚   )r’   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_chebysU  s    r­   c           	   C   sÐ   t jdƒ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jddƒ\}}tjdd	ƒ\}}}t||d
d
ƒ t||d
d
ƒ tj	| ddƒ\}}t|||d t
ttjdƒ t
ttjdƒ d S )Nr   g        g      ð?r}   r~   g‚vIhÂ%<=)rv   FTg›+¡†›„=r   r   )ro   gffffff
@)r   rN   rm   r{   r6   Zroots_sh_chebytZeval_sh_chebytr   r	   rs   r   r‚   )r’   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_sh_chebytf  s    
r®   c           	   C   sÐ   t jdƒ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jddƒ\}}tjdd	ƒ\}}}t||d
d
ƒ t||d
d
ƒ tj	| ddƒ\}}t|||d t
ttjdƒ t
ttjdƒ d S )Nr   g        g      ð?r}   r~   g‚vIhÂ%<=)rv   FTg›+¡†›„=r   r   )ro   gffffff
@)r   rQ   rm   r{   r6   Zroots_sh_chebyuZeval_sh_chebyur   r	   rs   r   r‚   )r’   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_sh_chebyux  s    
r¯   c           	   C   sÔ   t jdƒ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jddƒ\}}tjdd	ƒ\}}}t||d
d
ƒ t||d
d
ƒ tj	| ddƒ\}}t|||d t
ttjdƒ t
ttjdƒ d S )Nr   g      ð?r}   g‚vIhÂ%<=)rv   r~   gê-™—q=FTg›+¡†›„=r   )ro   r   gffffff
@g      ð¿g      ð¿g      ð¿r!   )r   rK   rm   r{   r6   r   Zeval_legendrer   r	   rs   r   r‚   )r’   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_legendreŠ  s    

r°   c           	   C   sÔ   t jdƒ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jdd	ƒ\}}tjdd
ƒ\}}}t||ddƒ t||ddƒ tj	| ddƒ\}}t|||d t
ttjdƒ t
ttjdƒ d S )Nr   g        g      ð?r}   g‚vIhÂ%<=)rv   r~   gê-™—q=FTg›+¡†›„=r   r   )ro   gffffff
@)r   rJ   rm   r{   r6   Zroots_sh_legendreZeval_sh_legendrer   r	   rs   r   r‚   )r’   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_sh_legendre  s    

r±   c           	   C   sÜ   t jdƒ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jddƒ\}}tjdd	ƒ\}}}t	||d
d
ƒ t	||d
d
ƒ t
j| dtjƒ\}}t	|||d tttjdƒ tttjdƒ d S )Nr   g        r}   g‚vIhÂ%<=)rv   r~   gê-™—q=FTg›+¡†›„=r   )ro   gffffff
@)r   Zlaguerrerm   r{   r6   Zroots_laguerreZeval_laguerrer   r   r   r	   rs   r   r‚   )r’   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_laguerre°  s    

r²   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jdddƒ\}}tjdddƒ\}}}t||ddƒ t||ddƒ tj|dƒdtjƒ\}	}
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 j| ˆ |ƒS )N)r6   Úroots_genlaguerre)rT   rx   )r7   r   r   rV   Ä  s    z:test_roots_genlaguerre.<locals>.<lambda>.<locals>.<lambda>r   )r7   r   )r7   r   rV   Ä  s    z(test_roots_genlaguerre.<locals>.<lambda>c                s   ‡ fdd„S )Nc                s   t j| ˆ |ƒS )N)r6   Zeval_genlaguerre)rT   r]   )r7   r   r   rV   Å  s    z:test_roots_genlaguerre.<locals>.<lambda>.<locals>.<lambda>r   )r7   r   )r7   r   rV   Å  s    c                s   ‡ fdd„S )Nc                s   | ˆ  t j|  ƒ S )N)r   r—   )r]   )r7   r   r   rV   Æ  s    z:test_roots_genlaguerre.<locals>.<lambda>.<locals>.<lambda>r   )r7   r   )r7   r   rV   Æ  s    g      à?g        r   r}   g‚vIhÂ%<=)rv   r~   gê-™—q=gš™™™™™¹?g›+¡†›„F=r   g‹N¼£îý<=rn   r¢   g›+¡†›„=g‚vIhÂ%L=)ro   rv   r   FTg       @)ro   r   gffffff
@r   gš™™™™™ñ?g      à¿g      à¿g      à¿g      à¿g      à¿g      à¿g      à¿g      à¿g      à¿gš™™™™™ñ¿)
r{   r   r   r6   r³   r   r	   rs   r   r‚   )r   r‘   r’   r†   r]   rw   r‡   ry   rˆ   r‰   rŠ   r   r   r   Útest_roots_genlaguerreÃ  s8     $$ $$ $$ $$ $&r´   c               C   s   t jdƒdƒ d S )NéA   gš™™™™™É?)r6   r'   r   r   r   r   Útest_gh_6721ê  s    r¶   )rj   rk   )2Znumpyr   r   r   Znumpy.testingr   r   r   r   Zpytestr   r   Zscipyr	   Zscipy.specialZspecialr6   r
   Zscipy.special.orthogonalZ
orthogonalr   Úobjectr   r1   r9   rI   rM   rP   rS   rZ   rh   r{   r‹   r   r“   r    r¡   r¤   r¦   rª   r«   r¬   r­   r®   r¯   r°   r±   r²   r´   r¶   r   r   r   r   Ú<module>   sF   
<'	
B4-'