o
    Ö­jÐ}  ã                   @   s˜  d dl Z d dl mZ 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  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raises)ÚarrayÚsqrt)Úassert_array_almost_equalÚassert_equalÚassert_almost_equalÚassert_allclose)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 d   ƒ n1 s/w   Y  t|jdgd	ƒ t|jddgd	ƒ t|jg d
¢d	ƒ t|jg d¢d	ƒ t|jg d¢d	ƒ t|jg d¢d	ƒ d S )Nr   é   Úignore©Úallé   é   é   é   é   )r   r   éþÿÿÿ)r   r   éýÿÿÿr   )r   r   éüÿÿÿr   r   )r   r   éûÿÿÿr   r   r   )ÚorthÚchebycÚnpÚerrstater   Úc)ÚselfÚC0ÚC1ÚC2ÚC3ÚC4ÚC5© r&   ú`/var/www/html/CropPilot/venv/lib/python3.10/site-packages/scipy/special/tests/test_orthogonal.pyÚtest_chebyc   s   




üzTestCheby.test_chebycc                 C   óª   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g d¢dƒ t|jg d	¢dƒ t|jg d
¢dƒ t|jg d¢dƒ d S )Nr   r   r   r   r   r   r   )r   r   éÿÿÿÿ)r   r   r   r   )r   r   r   r   r   )r   r   r   r   r   r   )r   Úchebysr   r   )r   ÚS0ÚS1ÚS2ÚS3ÚS4ÚS5r&   r&   r'   Útest_chebys    ó   





zTestCheby.test_chebysc                 C   r)   )Nr   r   r   r   r   r   r   )r   r   r*   )r   r   r   r   )é   r   iøÿÿÿr   r   )é   r   éìÿÿÿr   r   r   )r   Úchebytr   r   )r   ÚT0ÚT1ÚT2ÚT3ÚT4ÚT5r&   r&   r'   Útest_chebyt.   r3   zTestCheby.test_chebytc                 C   sª   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g d¢dƒ t|jg d	¢dƒ t|jg d
¢dƒ t|jg d¢dƒ d S )Nr   r   r   r   r   r   r   )r   r   r*   )r4   r   r   r   )r5   r   éôÿÿÿr   r   )é    r   iàÿÿÿr   é   r   )r   Úchebyur   r   )r   ÚU0ÚU1ÚU2ÚU3ÚU4ÚU5r&   r&   r'   Útest_chebyu<   r3   zTestCheby.test_chebyuN)Ú__name__Ú
__module__Ú__qualname__r(   r2   r>   rI   r&   r&   r&   r'   r      s
    r   c                   @   s6   e Zd Zdd„ Zej dddg¡dd„ ƒ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      @r6   é   g      .@)
r   ÚrandomÚanyr   Ú
gegenbauerr   r   r   ÚscÚpoch)r   ÚaÚCa0ÚCa1ÚCa2ÚCa3ÚCa4ÚCa5r&   r&   r'   Útest_gegenbauerM   sB   &&ÿÿÿ&ÿÿÿ&ÿÿÿzTestGegenbauer.test_gegenbauerrW   r   r   c                 C   s$   t  d|¡}t|jt dg¡ƒ d S )Nr   ç      ð?)r   rT   r   r   r   Úasarray)r   rW   ÚCn0r&   r&   r'   Útest_n_zero_gh8888b   s   z!TestGegenbauer.test_n_zero_gh8888c                 C   s¾   d}t jt|d�� t dtj¡ W d   ƒ n1 sw   Y  t jt|d�� t dd¡ W d   ƒ n1 s8w   Y  t jt|d�� t dtj ¡ W d   ƒ d S 1 sXw   Y  d S )Nz*`alpha` must be a finite number greater...)Úmatchr   r   ç      à¿r   )Úpytestr   Ú
ValueErrorr   rT   r   ÚnanÚinf)r   Úmessager&   r&   r'   Útest_valid_alphah   s   ÿÿ"ÿzTestGegenbauer.test_valid_alphaN)	rJ   rK   rL   r^   re   ÚmarkÚparametrizerb   rj   r&   r&   r&   r'   rM   K   s
    
rM   c                   @   s   e Zd Zdd„ Zdd„ ZdS )ÚTestHermitec                 C   sª   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g d¢dƒ t|jg d	¢dƒ t|jg d
¢dƒ t|jg d¢dƒ d S )Nr   r   r   r   r   r   r   )r   r   r   )r4   r   r?   r   )r5   r   iÐÿÿÿr   é   rn   )r@   r   i`ÿÿÿr   éx   r   )r   Úhermiter   r   )r   ÚH0ÚH1ÚH2ÚH3ÚH4ÚH5r&   r&   r'   Útest_hermitet   r3   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 )Nr_   r   r   r   r   r   r   ç       @ç      @r   )r   Úpoly1dr   r   Úhermitenormrp   r   r   )r   Úpsubrq   rr   rs   rt   ru   rv   Úhe0Úhe1Úhe2Úhe3Úhe4Úhe5r&   r&   r'   Útest_hermitenorm‚   s&   





zTestHermite.test_hermitenormN)rJ   rK   rL   rw   rƒ   r&   r&   r&   r'   rm   s   s    rm   c                   @   ó   e Zd Zdd„ ZdS )ÚTestShLegendrec                 C   ó  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   rn   )r   rz   r   Úsh_legendreÚlegendrer   r   )r   r|   ÚPs0ÚPs1ÚPs2ÚPs3ÚPs4ÚPs5Úpse0Úpse1Úpse2Úpse3Úpse4Úpse5r&   r&   r'   Útest_sh_legendre›   ó&   





zTestShLegendre.test_sh_legendreN)rJ   rK   rL   r–   r&   r&   r&   r'   r…   š   ó    r…   c                   @   r„   )ÚTestShChebytc                 C   r†   r‡   )r   rz   r   Ú	sh_chebytr7   r   r   )r   r|   ÚTs0ÚTs1ÚTs2ÚTs3ÚTs4ÚTs5Útse0Útse1Útse2Útse3Útse4Útse5r&   r&   r'   Útest_sh_chebyt³   r—   zTestShChebyt.test_sh_chebytN)rJ   rK   rL   r§   r&   r&   r&   r'   r™   ²   r˜   r™   c                   @   r„   )ÚTestShChebyuc                 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   rn   rP   )r   rz   r   Ú	sh_chebyurB   r   r   )r   r|   ÚUs0ÚUs1ÚUs2ÚUs3ÚUs4ÚUs5Úuse0Úuse1Úuse2Úuse3Úuse4Úuse5r&   r&   r'   Útest_sh_chebyuË   r—   zTestShChebyu.test_sh_chebyuN)rJ   rK   rL   r¶   r&   r&   r&   r'   r¨   Ê   r˜   r¨   c                   @   r„   )ÚTestShJacobic                 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convå   s   (z)TestShJacobi.test_sh_jacobi.<locals>.convr   r*   r   r   r   r   r   r   )r   rz   rR   r   Ú	sh_jacobiÚjacobir   r   )r   rº   r|   Úqr¹   ÚG0ÚG1ÚG2ÚG3ÚG4ÚG5Úge0Úge1Úge2Úge3Úge4Úge5r&   r&   r'   Útest_sh_jacobiã   s,   $$$$$$zTestShJacobi.test_sh_jacobiN)rJ   rK   rL   rÊ   r&   r&   r&   r'   r·   â   r˜   r·   c                   @   r„   )ÚTestCallc                 C   s–   g }t dƒD ]}| dd„ dt|d�  ¡ D ƒ¡ qtjdd��! |D ]}t|ƒ}t|dƒt |j	¡dƒ|d	� q#W d   ƒ d S 1 sDw   Y  d S )
Nr   c                 S   s   g | ]}|  ¡ ‘qS r&   )Ústrip)Ú.0Úxr&   r&   r'   Ú
<listcomp>  ó    z&TestCall.test_call.<locals>.<listcomp>aW  
                orth.jacobi(%(n)d,0.3,0.9)
                orth.sh_jacobi(%(n)d,0.3,0.9)
                orth.genlaguerre(%(n)d,0.3)
                orth.laguerre(%(n)d)
                orth.hermite(%(n)d)
                orth.hermitenorm(%(n)d)
                orth.gegenbauer(%(n)d,0.3)
                orth.chebyt(%(n)d)
                orth.chebyu(%(n)d)
                orth.chebyc(%(n)d)
                orth.chebys(%(n)d)
                orth.sh_chebyt(%(n)d)
                orth.sh_chebyu(%(n)d)
                orth.legendre(%(n)d)
                orth.sh_legendre(%(n)d)
                )r¸   r   r   g)\�Âõ(Ô?)Úerr_msg)
ÚrangeÚextendÚdictÚsplitr   r   Úevalr   rz   Úcoef)r   Úpolyr¸   Úpstrr¹   r&   r&   r'   Ú	test_call  s    
ð
ïÿþ"ÿzTestCall.test_callN)rJ   rK   rL   rÚ   r&   r&   r&   r'   rË      r˜   rË   c                   @   r„   )ÚTestGenlaguerrec                 C   sx   t tjdddd�dƒdƒ t tjdddd�dƒdƒ t tjdddd�t dd	g¡ƒ t tjdddd�t dd
g¡ƒ d S )Nr   F)Úmonicr   rx   Tç       Àr*   r   r   )r   r   Úgenlaguerrer   rz   )r   r&   r&   r'   Útest_regression  s    $zTestGenlaguerre.test_regressionN)rJ   rK   rL   rß   r&   r&   r&   r'   rÛ     r˜   rÛ   çVçž¯Ò<ç‚vIhÂ%,=c                    s  | |dƒ\}}	}
t j|t  d¡d�}||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 rpd	n|d d
 }t|d ||d� d S )NTÚlong)Údtyper   c                 S   s   | d d| d   |  d S )Nr   r   r&   ©rÎ   r&   r&   r'   Úf6  s   zverify_gauss_quad.<locals>.fc                    s   ˆ | ƒˆ| ƒ S ©Nr&   rä   ©rå   Úweight_funcr&   r'   Ú<lambda>8  ó    z#verify_gauss_quad.<locals>.<lambda>g�íµ ÷Æ°>é
   r   ©Úrtol)r   Úarangerã   ÚnewaxisÚdotÚTr   Údiagonalr   ÚeyeÚsumr	   ÚquadÚvdot)Ú	root_funcÚ	eval_funcrè   rW   ÚbÚNrí   ÚatolrÎ   ÚwÚmur¸   ÚvÚvvÚvdÚresIÚresGr&   rç   r'   Úverify_gauss_quad&  s   r  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$d%ƒd	d
dd"d� || d&d'ƒ|d&d'ƒ|d&d'ƒd	d
dƒ || d&d'ƒ|d&d'ƒ|d&d'ƒd	d
ddd� || d&d'ƒ|d&d'ƒ|d&d'ƒd	d
ddd� t d(d)d)¡\}}t d(¡\}}t||d*d*ƒ t||d*d*ƒ t d(d+d+¡\}}t d(d,¡\}}	t||d*d*ƒ t||	d*d*ƒ t ddd-d.¡\}
}t ddd-d/¡\}}}t|
|d*d*ƒ t||d*d*ƒ t |dd-ƒd0d¡\}}t|||d1� tt	tjd2ddƒ tt	tjd3ddƒ tt	tjd-d4dƒ tt	tjd-dd4ƒ tt	tjd-d4d4ƒ d S )5Nc                    ó   ‡ ‡fdd„S )Nc                    ó   t  | ˆ ˆ|¡S ræ   )rU   Úroots_jacobi©r¸   rý   ©rW   rù   r&   r'   ré   ?  rê   z/test_roots_jacobi.<locals>.rf.<locals>.<lambda>r&   r  r&   r  r'   Úrf>  ó   ztest_roots_jacobi.<locals>.rfc                    r  )Nc                    r  ræ   )rU   Úeval_jacobi©r¸   rÎ   r  r&   r'   ré   A  rê   z/test_roots_jacobi.<locals>.ef.<locals>.<lambda>r&   r  r&   r  r'   Úef@  r
  ztest_roots_jacobi.<locals>.efc                    r  )Nc                    s   d|  ˆ  d|  ˆ  S )Nr   r&   rä   r  r&   r'   ré   C  s    z/test_roots_jacobi.<locals>.wf.<locals>.<lambda>r&   r  r&   r  r'   ÚwfB  r
  ztest_roots_jacobi.<locals>.wfrd   ç      è¿ç      ð¿r_   r   é   çê-�™—q=©rû   éd   ç•dyáý¥=rN   çá7ÎQE=çê-�™—�=r   ç‚vIhÂ%L=çÍÌÌÌÌÌì?r   ç‚vIhÂ%<=gá7ÎQU=ç=
×£p=2@çÍÌÌÌÌL;@g^~zÅ=çÍÌÌÌÌŒG@rO   g     �„@éú   g     ð@ç»½×Ùß|Û=g      €@g     @�@g     @@ç      @çš™™™™9Q@rA   ç        ç›+¡†›„=ry   g      @r   FTr*   rì   r   çffffff
@r   )
r  rU   r  Úroots_legendrer   Úroots_gegenbauerr	   rõ   Úassert_raisesrf   )r	  r  r  ÚvgqÚxjÚwjÚxlÚwlÚxcÚwcrÎ   rü   Úyrþ   ÚmÚmuIÚmuI_errr&   r&   r'   Útest_roots_jacobi=  s²   $ÿÿ$((((($(($ ÿÿ((ÿ(((( ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ$ ÿ ÿr3  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                    r  )Nc                    r  ræ   )rU   Úroots_sh_jacobir  r  r&   r'   ré   Ÿ  rê   z2test_roots_sh_jacobi.<locals>.rf.<locals>.<lambda>r&   r  r&   r  r'   r	  ž  r
  z test_roots_sh_jacobi.<locals>.rfc                    r  )Nc                    r  ræ   )rU   Úeval_sh_jacobir  r  r&   r'   ré   ¡  rê   z2test_roots_sh_jacobi.<locals>.ef.<locals>.<lambda>r&   r  r&   r  r'   r     r
  z test_roots_sh_jacobi.<locals>.efc                    r  )Nc                    s   d|  ˆ ˆ  | ˆd   S )Nr_   r&   rä   r  r&   r'   ré   £  s    z2test_roots_sh_jacobi.<locals>.wf.<locals>.<lambda>r&   r  r&   r  r'   r  ¢  r
  z test_roots_sh_jacobi.<locals>.wfrd   g      Ð?r"  r_   r   r  r  r  r  r  rN   r  r   r  r  r   r  r  r  r  çš™™™™™É?r  r!  r   g(Í´#=r  r   FTr#  r   rì   r$  r*   r   )r  rU   r4  r   r	   rõ   r'  rf   )r	  r  r  r(  rÎ   rü   r/  rþ   r0  r1  r2  r&   r&   r'   Útest_roots_sh_jacobi�  sX   $ÿÿ$(($(($(($$ÿ(((((ÿr7  c            
   	   C   s<  t j} t j}t d¡j}t| ||tj tjdƒ t| ||tj tjddd� t| ||tj tjddd� t  dd¡\}}t  dd¡\}}}t	||d	d	ƒ t	||d	d	ƒ t
 |tj tj¡\}}	t	|||	d
� t  dd¡\}}t  dd¡\}}}t	||d	d	ƒ t	||d	d	ƒ t	t|ƒ|d	d	ƒ ttt jdƒ ttt jdƒ d S )Nr   r  r  r  r  r  FTr#  rì   éÈ   r   r$  )rU   Úroots_hermiteÚeval_hermiter   rp   rè   r  r   rh   r   r	   rõ   rô   r'  rf   ©
ÚrootfÚevalfÚweightfrÎ   rü   r/  rþ   r0  r1  r2  r&   r&   r'   Útest_roots_hermiteÔ  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   sÐ   t  | |jf¡}t jd t  d|d  ¡ |dd d …f< | dkrftdƒ| |dd d …f  |dd d …f< td| ƒD ],}td| ƒ| ||d d d …f  t|d | ƒ||d d d …f   ||d d …f< q9|S )Nç      Ð¿rd   r   r   r   rx   r_   )r   ÚzerosÚsizeÚpiÚexpr   rÒ   )r¸   ÚnodesÚHÚkr&   r&   r'   Úhermite_recursionò  s   ((Vz1test_roots_hermite_asy.<locals>.hermite_recursionrà   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   Ú_roots_hermite_asyr   r   rA  rô   r   rC  )rú   rí   rû   rÎ   rü   rF  ©rH  r&   r'   Útestü  s    z$test_roots_hermite_asy.<locals>.testé–   r  r  é—   i,  i-  iô  iõ  iç  iè  iÐ  iˆ  )rà   r#  r&   )rK  r&   rJ  r'   Útest_roots_hermite_asyð  s   
rN  c            
   	   C   sì   t j} t j}t d¡j}t| ||tj tjdƒ t| ||tj tjddd� t| ||tj tjddd� t  dd¡\}}t  dd¡\}}}t	||d	d	ƒ t	||d	d	ƒ t
 |tj tj¡\}}	t	|||	d
� ttt jdƒ ttt jdƒ d S )Nr   r  r  r  r  r  FTr#  rì   r   r$  )rU   Úroots_hermitenormÚeval_hermitenormr   r{   rè   r  r   rh   r   r	   rõ   r'  rf   r;  r&   r&   r'   Útest_roots_hermitenorm  s   rQ  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$ƒ d S )%Nc                    ó   ‡ fdd„S )Nc                    ó   t  | ˆ |¡S ræ   )rU   r&  r  ©rW   r&   r'   ré   #  ó    z6test_roots_gegenbauer.<locals>.rootf.<locals>.<lambda>r&   rT  r&   rT  r'   r<  "  ó   z$test_roots_gegenbauer.<locals>.rootfc                    rR  )Nc                    rS  ræ   )rU   Úeval_gegenbauerr  rT  r&   r'   ré   %  rU  z6test_roots_gegenbauer.<locals>.evalf.<locals>.<lambda>r&   rT  r&   rT  r'   r=  $  rV  z$test_roots_gegenbauer.<locals>.evalfc                    rR  )Nc                    s   d| d  ˆ d  S )Nr   r   rN   r&   rä   rT  r&   r'   ré   '  rÐ   z8test_roots_gegenbauer.<locals>.weightf.<locals>.<lambda>r&   rT  r&   rT  r'   r>  &  rV  z&test_roots_gegenbauer.<locals>.weightfr@  r  r_   r   r  r  r  r  r  çš™™™™™¹?r  r   rë   é2   éª   g     Pe@gê-�™—A=éî   g     €@r  r   r   FTr#  r*   rì   r$  r   r  )	r  rU   Úeval_chebytr&  r   r	   rõ   r'  rf   ©r<  r=  r>  r(  rÎ   rü   r/  rþ   r0  r1  r2  r&   r&   r'   Útest_roots_gegenbauer!  sV   """"""""""""""""""""""" r^  c               	   C   óÐ   t  d¡j} ttjtj| dddƒ ttjtj| dddƒ ttjtj| ddddd� t dd¡\}}t dd	¡\}}}t||d
d
ƒ t||d
d
ƒ t 	| dd¡\}}t|||d� t
ttjdƒ t
ttjdƒ d S )Nr   r  r_   r  r  r  r  FTr#  r*   r   rì   r   r$  )r   r7   rè   r  rU   Úroots_chebytr\  r   r	   rõ   r'  rf   ©r>  rÎ   rü   r/  rþ   r0  r1  r2  r&   r&   r'   Útest_roots_chebyta  ó   ÿrb  c                  C   sP   t  d¡\} }| d d… | dd … }}t||d d d…  ƒ t| d dƒ d S )Né   rë   rP   r*   r   )rU   r`  r   )rÎ   rü   ÚposÚnegr&   r&   r'   Útest_chebyt_symmetrys  s   rg  c                  C   óÌ   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  r_   r  r  FTr#  r*   r   rì   r   r$  )r   rB   rè   r  rU   Úroots_chebyuÚeval_chebyur   r	   rõ   r'  rf   ra  r&   r&   r'   Útest_roots_chebyuy  ó   rk  c               	   C   r_  )Nr   rÝ   rx   r  r  r  r  FTr#  r   r   rì   r   r$  )r   r   rè   r  rU   Úroots_chebycÚeval_chebycr   r	   rõ   r'  rf   ra  r&   r&   r'   Útest_roots_chebycŠ  rc  ro  c                  C   rh  )Nr   rÝ   rx   r  r  FTr#  r   r   rì   r   r$  )r   r+   rè   r  rU   Úroots_chebysÚeval_chebysr   r	   rõ   r'  rf   ra  r&   r&   r'   Útest_roots_chebysœ  rl  rr  c               	   C   óÐ   t  d¡j} ttjtj| dddƒ ttjtj| dddƒ ttjtj| ddddd� t dd¡\}}t dd	¡\}}}t||d
d
ƒ t||d
d
ƒ t 	| dd¡\}}t|||d� t
ttjdƒ t
ttjdƒ d S ©Nr   r"  r_   r  r  r  r  FTr#  r   r   rì   r$  )r   rš   rè   r  rU   Úroots_sh_chebytÚeval_sh_chebytr   r	   rõ   r'  rf   ra  r&   r&   r'   Útest_roots_sh_chebyt­  ó   ÿrw  c               	   C   rs  rt  )r   r©   rè   r  rU   Úroots_sh_chebyuÚeval_sh_chebyur   r	   rõ   r'  rf   ra  r&   r&   r'   Útest_roots_sh_chebyu¿  rx  r{  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  r_   r  r  r  r  r  FTr#  r*   r   rì   r   r$  )r   r‰   rè   r  rU   r%  Úeval_legendrer   r	   rõ   r'  rf   ra  r&   r&   r'   Útest_roots_legendreÑ  ó    ÿÿr}  c               	   C   sÔ   t  d¡j} ttjtj| dddƒ ttjtj| ddddd� ttjtj| ddddd� t dd	¡\}}t dd
¡\}}}t||ddƒ t||ddƒ t 	| dd¡\}}t|||d� t
ttjdƒ t
ttjdƒ d S )Nr   r"  r_   r  r  r  r  r  FTr#  r   r   rì   r$  )r   rˆ   rè   r  rU   Úroots_sh_legendreÚeval_sh_legendrer   r	   rõ   r'  rf   ra  r&   r&   r'   Útest_roots_sh_legendreä  r~  r�  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  r  r  r  r  FTr#  r   rì   r$  )r   Úlaguerrerè   r  rU   Úroots_laguerreÚeval_laguerrer   rh   r   r	   rõ   r'  rf   ra  r&   r&   r'   Útest_roots_laguerre÷  s    ÿÿr…  c               
   C   sÂ  dd„ } dd„ }dd„ }t }|| dƒ|dƒ|dƒdtjd	ƒ || dƒ|dƒ|dƒdtjd
dd� || dƒ|dƒ|dƒdtjddd� || dƒ|dƒ|dƒdtjd	ƒ || dƒ|dƒ|dƒdtjd
dd� || dƒ|dƒ|dƒdtjddd� || dƒ|dƒ|dƒdtjd	ƒ || dƒ|dƒ|dƒdtjd
dd� || dƒ|dƒ|dƒdtjddd� || dƒ|dƒ|dƒdtjd	ƒ || dƒ|dƒ|dƒdtjd
dd� || dƒ|dƒ|dƒdtjddd� || dƒ|dƒ|dƒdtjd	ƒ || dƒ|dƒ|dƒdtjd
dd� || dƒ|dƒ|dƒdtjdddd� t d	dd¡\}}t d	dd¡\}}}t||ddƒ t||ddƒ t |dƒdtj¡\}	}
t||	|
d� tt	tjddƒ tt	tjddƒ tt	tjdd ƒ d S )!Nc                    rR  )Nc                    rS  ræ   )rU   Úroots_genlaguerrer  rT  r&   r'   ré     rU  z7test_roots_genlaguerre.<locals>.rootf.<locals>.<lambda>r&   rT  r&   rT  r'   r<    rV  z%test_roots_genlaguerre.<locals>.rootfc                    rR  )Nc                    rS  ræ   )rU   Úeval_genlaguerrer  rT  r&   r'   ré     rU  z7test_roots_genlaguerre.<locals>.evalf.<locals>.<lambda>r&   rT  r&   rT  r'   r=    rV  z%test_roots_genlaguerre.<locals>.evalfc                    rR  )Nc                    s   | ˆ  t  |  ¡ S ræ   )r   rD  rä   rT  r&   r'   ré     rÐ   z9test_roots_genlaguerre.<locals>.weightf.<locals>.<lambda>r&   rT  r&   rT  r'   r>    rV  z'test_roots_genlaguerre.<locals>.weightfrd   r"  r   r  r  r  r  r  rX  g›+¡†›„F=r   g‹N¼£îý<=rë   rY  r#  r  )rí   rû   r   FTrx   rì   r   r$  r   gš™™™™™ñ¿)
r  r   rh   rU   r†  r   r	   rõ   r'  rf   r]  r&   r&   r'   Útest_roots_genlaguerre
  s8    $$ $$ $$ $$ $&rˆ  c                   C   s   t  d¡dƒ d S )NéA   r6  )rU   r7   r&   r&   r&   r'   Útest_gh_67214  s   rŠ  )rà   rá   )1re   r   r'  Únumpyr   r   r   Únumpy.testingr   r   r   r   Úscipyr	   Úscipy.specialÚspecialrU   r   Úscipy.special._orthogonalÚ_orthogonalr   r   rM   rm   r…   r™   r¨   r·   rË   rÛ   r  r3  r7  r?  rN  rQ  r^  rb  rg  rk  ro  rr  rw  r{  r}  r�  r…  rˆ  rŠ  r&   r&   r&   r'   Ú<module>   sL    <('	
ÿ`7@*