o
    V=ºi¼J  ã                
   @   sˆ  d Z ddlmZ ddlZddlm  mZ ddl	m
Z
 ddlmZmZmZmZ e dg¡Ze ddg¡Ze g d¢¡Ze g d	¢¡Ze g d
¢¡Ze g d¢¡Ze g d¢¡Ze g d¢¡Ze g d¢¡Ze g d¢¡Zeeeeeeeeeeg
Zdd„ 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$G d"d#„ d#ƒZ%G d$d%„ d%ƒZ&dS )&zTests for hermite module.

é    )ÚreduceN©Úpolyval)Úassert_almost_equalÚassert_raisesÚassert_equalÚassert_é   é   )éþÿÿÿr   é   )r   iôÿÿÿr   é   )é   r   iÐÿÿÿr   é   )r   éx   r   i`ÿÿÿr   é    )iˆÿÿÿr   iÐ  r   i þÿÿr   é@   )r   ipùÿÿr   i   r   iÀúÿÿr   é€   )	i�  r   i€Ëÿÿr   i€4  r   i òÿÿr   é   )
r   i v  r   i Åþÿr   i ½  r   i Üÿÿr   i   c                 C   s   t j| dd�S )Ng�íµ ÷Æ°>)Ztol)ÚhermÚhermtrim©Úx© r   úiC:\Users\psant\Downloads\PAF backend\school\venv\Lib\site-packages\numpy/polynomial/tests/test_hermite.pyÚtrim   s   r   c                   @   s,   e Zd Zdd„ Zdd„ Zdd„ Zdd„ Zd	S )
ÚTestConstantsc                 C   ó   t tjddgƒ d S )Néÿÿÿÿr	   )r   r   Z
hermdomain©Úselfr   r   r   Útest_hermdomain!   ó   zTestConstants.test_hermdomainc                 C   ó   t tjdgƒ d S )Nr   )r   r   Zhermzeror   r   r   r   Útest_hermzero$   ó   zTestConstants.test_hermzeroc                 C   r#   ©Nr	   )r   r   Zhermoner   r   r   r   Útest_hermone'   r%   zTestConstants.test_hermonec                 C   r   )Nr   ç      à?)r   r   Zhermxr   r   r   r   Ú
test_hermx*   r"   zTestConstants.test_hermxN)Ú__name__Ú
__module__Ú__qualname__r!   r$   r'   r)   r   r   r   r   r      s
    r   c                   @   sJ   e Zd Ze ddd¡Zdd„ Zdd„ Zdd	„ Zd
d„ Z	dd„ Z
dd„ ZdS )ÚTestArithmeticéýÿÿÿé   éd   c                 C   sž   t dƒD ]H}t dƒD ]A}d|› d|› �}t t||ƒd ¡}||  d7  < ||  d7  < t dg| dg dg| dg ¡}tt|ƒt|ƒ|d� q
qd S ©Né   úAt i=ú, j=r	   r   ©Úerr_msg)ÚrangeÚnpÚzerosÚmaxr   Úhermaddr   r   ©r    ÚiÚjÚmsgÚtgtÚresr   r   r   Útest_hermadd1   ó   $úÿzTestArithmetic.test_hermaddc                 C   sž   t dƒD ]H}t dƒD ]A}d|› d|› �}t t||ƒd ¡}||  d7  < ||  d8  < t dg| dg dg| dg ¡}tt|ƒt|ƒ|d� q
qd S r1   )r7   r8   r9   r:   r   Zhermsubr   r   r<   r   r   r   Útest_hermsub;   rC   zTestArithmetic.test_hermsubc                 C   sv   t t dg¡dgƒ t t dg¡ddgƒ tddƒD ]}dg| dg }dg|d  |ddg }t t |¡|ƒ qd S )Nr   r	   r(   r2   )r   r   Zhermmulxr7   )r    r=   Zserr@   r   r   r   Útest_hermmulxE   s   ýzTestArithmetic.test_hermmulxc           
      C   s²   t dƒD ]R}dg| dg }t | j|¡}t dƒD ]<}d|› d|› �}dg| dg }t | j|¡}t ||¡}t | j|¡}	tt|ƒ|| d k|ƒ t|	|| |d� qqd S )Nr2   r   r	   r3   r4   r5   )r7   r   Úhermvalr   Úhermmulr   Úlenr   )
r    r=   Zpol1Zval1r>   r?   Zpol2Zval2Zpol3Zval3r   r   r   Útest_hermmulM   s   ùýzTestArithmetic.test_hermmulc           
      C   s–   t dƒD ]D}t dƒD ]=}d|› d|› �}dg| dg }dg| dg }t ||¡}t ||¡\}}t t ||¡|¡}	tt|	ƒt|ƒ|d� q
qd S )Nr2   r3   r4   r   r	   r5   )r7   r   r;   ZhermdivrG   r   r   )
r    r=   r>   r?   ÚciÚcjr@   ZquoÚremrA   r   r   r   Útest_hermdiv[   s   ùÿzTestArithmetic.test_hermdivc                 C   s|   t dƒD ]7}t dƒD ]0}d|› d|› �}t |d ¡}ttj|g| t dg¡ƒ}t ||¡}tt	|ƒt	|ƒ|d� q
qd S )Nr2   r3   r4   r	   r5   )
r7   r8   Úaranger   r   rG   ÚarrayZhermpowr   r   )r    r=   r>   r?   Úcr@   rA   r   r   r   Útest_hermpowf   s   ûÿzTestArithmetic.test_hermpowN)r*   r+   r,   r8   Úlinspacer   rB   rD   rE   rI   rM   rQ   r   r   r   r   r-   .   s    

r-   c                   @   s‚   e Zd Ze g d¢¡Ze dee¡Ze deee¡Zej	 	d¡d d Z
ee
g d¢ƒZdd	„ Zd
d„ Zdd„ Zdd„ Zdd„ ZdS )ÚTestEvaluation)g      @ç      ð?g      è?úi,j->ijú
i,j,k->ijk©r/   r2   r
   r	   )rT   g       @g      @c                    sæ   t t g dg¡jdƒ t dd¡‰ ‡ fdd„tD ƒ}tdƒD ]}d|› �}|| }t ˆ dg| dg ¡}t|||d� qtd	ƒD ]/}d
g| }t 	|¡‰ t t ˆ dg¡j
|ƒ t t ˆ ddg¡j
|ƒ t t ˆ g d¢¡j
|ƒ qAd S )Nr	   r   r   c                    s   g | ]}t ˆ |ƒ‘qS r   r   ©Ú.0rP   r   r   r   Ú
<listcomp>€   ó    z/TestEvaluation.test_hermval.<locals>.<listcomp>é
   r3   r5   r/   r
   )r	   r   r   )r   r   rF   Úsizer8   rR   ÚHlistr7   r   r9   Úshape)r    Úyr=   r?   r@   rA   Údimsr   r   r   Útest_hermvalz   s   


ûzTestEvaluation.test_hermvalc           
      C   s‚   | j \}}}| j\}}}tttj||d d… | jƒ || }t ||| j¡}t||ƒ t 	d¡}	t |	|	| j¡}t
|jdkƒ d S ©Nr
   ©r
   r/   )r   r`   r   Ú
ValueErrorr   Ú	hermval2dÚc2dr   r8   Úonesr   r_   ©
r    Úx1Úx2Úx3Úy1Úy2Zy3r@   rA   Úzr   r   r   Útest_hermval2d�   s   

zTestEvaluation.test_hermval2dc           
      C   sŒ   | j \}}}| j\}}}tttj|||d d… | jƒ || | }t |||| j¡}t||ƒ t 	d¡}	t |	|	|	| j¡}t
|jdkƒ d S rc   )r   r`   r   re   r   Ú	hermval3dÚc3dr   r8   rh   r   r_   ri   r   r   r   Útest_hermval3d    s   

zTestEvaluation.test_hermval3dc           
      C   sl   | j \}}}| j\}}}t d||¡}t ||| j¡}t||ƒ t d¡}	t |	|	| j¡}t	|j
dkƒ d S )NrU   rd   )r
   r/   r
   r/   )r   r`   r8   Úeinsumr   Z
hermgrid2drg   r   rh   r   r_   ri   r   r   r   Útest_hermgrid2d±   s   

zTestEvaluation.test_hermgrid2dc           
      C   sr   | j \}}}| j\}}}t d|||¡}t |||| j¡}t||ƒ t d¡}	t |	|	|	| j¡}t	|j
dkƒ d S )NrV   rd   )r
   r/   r
   r/   r
   r/   )r   r`   r8   rt   r   Z
hermgrid3drr   r   rh   r   r_   ri   r   r   r   Útest_hermgrid3d¿   s   

zTestEvaluation.test_hermgrid3dN)r*   r+   r,   r8   rO   Zc1drt   rg   rr   Úrandomr   r   r`   rb   rp   rs   ru   rv   r   r   r   r   rS   p   s    rS   c                   @   ó   e Zd Zdd„ Zdd„ ZdS )ÚTestIntegralc           
   	   C   s.  t ttjdgdƒ t ttjdgdƒ t ttjdgdddgƒ t ttjdgdgd� t ttjdgdgd� t ttjdgdd� tdd	ƒD ]}dg|d  dg }tjdg||d
�}t|ddgƒ qCtd	ƒD ]7}|d }dg| dg }|gdg|  d| g }t |¡}tj|d|gd
�}t |¡}tt	|ƒt	|ƒƒ qdtd	ƒD ]&}|d }dg| dg }t |¡}tj|d|gdd�}tt 
d|¡|ƒ q td	ƒD ]8}|d }dg| dg }|gdg|  d| g }t |¡}tj|d|gdd�}t |¡}tt	|ƒt	|ƒƒ qËtd	ƒD ]9}tdd	ƒD ]0}	dg| dg }|d d … }t|	ƒD ]
}tj|dd�}�q#tj||	d�}tt	|ƒt	|ƒƒ �q�qtd	ƒD ]@}tdd	ƒD ]7}	dg| dg }|d d … }t|	ƒD ]}tj|d|gd
�}�qatj||	tt|	ƒƒd
�}tt	|ƒt	|ƒƒ �qM�qFtd	ƒD ]B}tdd	ƒD ]9}	dg| dg }|d d … }t|	ƒD ]}tj|d|gdd�}�q¦tj||	tt|	ƒƒdd�}tt	|ƒt	|ƒƒ �q’�q‹td	ƒD ]B}tdd	ƒD ]9}	dg| dg }|d d … }t|	ƒD ]}tj|d|gdd�}�qítj||	tt|	ƒƒdd�}tt	|ƒt	|ƒƒ �qÙ�qÒd S )Nr   r(   r   r	   )Úlbnd)Úscl©Úaxisr
   r2   )ÚmÚk)r~   r   rz   )r~   r   r{   ©r~   )r   Ú	TypeErrorr   Úhermintre   r7   r   Ú	poly2hermÚ	herm2polyr   rF   Úlist)
r    r=   r   rA   r{   Úpolr@   Zhermpolr‚   r>   r   r   r   Útest_hermintÐ   sŠ   




ú	ú	ú	úÿzTestIntegral.test_hermintc                 C   sš   t j d¡}t  dd„ |jD ƒ¡j}tj|dd�}t||ƒ t  dd„ |D ƒ¡}tj|dd�}t||ƒ t  dd„ |D ƒ¡}tj|d	dd
�}t||ƒ d S )N©r/   r   c                 S   ó   g | ]}t  |¡‘qS r   ©r   r‚   rX   r   r   r   rZ   '  r[   z2TestIntegral.test_hermint_axis.<locals>.<listcomp>r   r|   c                 S   r‰   r   rŠ   rX   r   r   r   rZ   +  r[   r	   c                 S   s   g | ]	}t j|d d�‘qS )r/   )r   rŠ   rX   r   r   r   rZ   /  s    r/   )r   r}   )r8   rw   ÚvstackÚTr   r‚   r   ©r    rg   r@   rA   r   r   r   Útest_hermint_axis#  s   

zTestIntegral.test_hermint_axisN)r*   r+   r,   r‡   rŽ   r   r   r   r   ry   Î   s    Sry   c                   @   rx   )ÚTestDerivativec                 C   s  t ttjdgdƒ t ttjdgdƒ tdƒD ]}dg| dg }tj|dd�}tt|ƒt|ƒƒ qtdƒD ]'}tddƒD ]}dg| dg }tjtj||d�|d�}t	t|ƒt|ƒƒ q<q5tdƒD ])}tddƒD ]!}dg| dg }tjtj||dd�|dd�}t	t|ƒt|ƒƒ qhqad S )	Nr   r(   r   r2   r	   r€   r
   )r~   r{   )
r   r�   r   Úhermderre   r7   r   r   r‚   r   )r    r=   r@   rA   r>   r   r   r   Útest_hermder6  s&   ýýÿzTestDerivative.test_hermderc                 C   sl   t j d¡}t  dd„ |jD ƒ¡j}tj|dd�}t||ƒ t  dd„ |D ƒ¡}tj|dd�}t||ƒ d S )Nrˆ   c                 S   r‰   r   ©r   r�   rX   r   r   r   rZ   S  r[   z4TestDerivative.test_hermder_axis.<locals>.<listcomp>r   r|   c                 S   r‰   r   r’   rX   r   r   r   rZ   W  r[   r	   )r8   rw   r‹   rŒ   r   r�   r   r�   r   r   r   Útest_hermder_axisO  s   
z TestDerivative.test_hermder_axisN)r*   r+   r,   r‘   r“   r   r   r   r   r�   4  s    r�   c                   @   s8   e Zd Zej d¡d d Zdd„ Zdd„ Zdd	„ Zd
S )Ú
TestVanderrW   r
   r	   c                 C   sÎ   t  d¡}t |d¡}t|jdkƒ tdƒD ]}dg| dg }t|d|f t ||¡ƒ qt  	ddgddgdd	gg¡}t |d¡}t|jd
kƒ tdƒD ]}dg| dg }t|d|f t ||¡ƒ qMd S )Nr/   rˆ   r   r   r	   .r
   r2   é   )r/   r
   r   )
r8   rN   r   Ú
hermvanderr   r_   r7   r   rF   rO   )r    r   Úvr=   Úcoefr   r   r   Útest_hermvander`  s   
þzTestVander.test_hermvanderc                 C   sx   | j \}}}tj d¡}t ||ddg¡}t |||¡}t ||j¡}t||ƒ t |g|gddg¡}t	|j
dkƒ d S )Nrd   r	   r
   )r	   r2   r•   )r   r8   rw   r   Zhermvander2drf   ÚdotÚflatr   r   r_   ©r    rj   rk   rl   rP   Zvanr@   rA   r   r   r   Útest_hermvander2dq  s   
zTestVander.test_hermvander2dc                 C   s€   | j \}}}tj d¡}t |||g d¢¡}t ||||¡}t ||j¡}t||ƒ t |g|g|gg d¢¡}t	|j
dkƒ d S )N)r
   r/   r   )r	   r
   r/   )r	   r2   é   )r   r8   rw   r   Zhermvander3drq   rš   r›   r   r   r_   rœ   r   r   r   Útest_hermvander3d~  s   
zTestVander.test_hermvander3dN)	r*   r+   r,   r8   rw   r   r™   r�   rŸ   r   r   r   r   r”   \  s
    r”   c                   @   ó   e Zd Zdd„ ZdS )ÚTestFittingc                 C   s  dd„ }dd„ }t ttjdgdgdƒ t ttjdggdgdƒ t ttjg dgdƒ t ttjdgdgggdƒ t ttjddgdgdƒ t ttjdgddgdƒ t ttjdgdgddggd	� t ttjdgdgdddgd	� t ttjdgdgdgƒ t ttjdgdgg d
¢ƒ t ttjdgdgg ƒ t dd¡}||ƒ}t ||d¡}tt|ƒdƒ t	t 
||¡|ƒ t ||g d¢¡}tt|ƒdƒ t	t 
||¡|ƒ t ||d¡}tt|ƒdƒ t	t 
||¡|ƒ t ||g d¢¡}tt|ƒdƒ t	t 
||¡|ƒ t ||g d¢¡}tt|ƒdƒ t	t 
||¡|ƒ t |t ||g¡jd¡}t	|t ||g¡jƒ t |t ||g¡jg d¢¡}t	|t ||g¡jƒ t |¡}| ¡ }	d|dd d…< d|dd d…< tj||	d|d	�}
t	|
|ƒ tj||	g d¢|d	�}
t	|
|ƒ tj|t |	|	g¡jd|d	�}t	|t ||g¡jƒ tj|t |	|	g¡jg d¢|d	�}t	|t ||g¡jƒ g d¢}t	t ||d¡ddgƒ t	t ||ddg¡ddgƒ t dd¡}||ƒ}t ||d¡}t	t 
||¡|ƒ t ||g d¢¡}t	t 
||¡|ƒ t	||ƒ d S )Nc                 S   s   | | d  | d  S )Nr	   r
   r   r   r   r   r   Úf�  r"   z#TestFitting.test_hermfit.<locals>.fc                 S   s   | d | d  d S )Nr   r
   r	   r   r   r   r   r   Úf2’  r"   z$TestFitting.test_hermfit.<locals>.f2r	   r   r   r
   )Úw)r
   r   r•   r/   r   )r   r	   r
   r/   r2   )r   r	   r
   r/   r   )r
   r/   r   r	   r   )r	   y              ð?r   y       €      ð¿r(   )r   r
   r   )r   re   r   Zhermfitr�   r8   rR   r   rH   r   rF   rO   rŒ   Z
zeros_likeÚcopy)r    r¢   r£   r   r`   Zcoef3Zcoef4Zcoef2dr¤   ZywZwcoef3Zwcoef2dZcoef1Zcoef2r   r   r   Útest_hermfitŽ  sp   


"zTestFitting.test_hermfitN)r*   r+   r,   r¦   r   r   r   r   r¡   Œ  ó    r¡   c                   @   s$   e Zd Zdd„ Zdd„ Zdd„ ZdS )ÚTestCompanionc                 C   s"   t ttjg ƒ t ttjdgƒ d S r&   )r   re   r   Úhermcompanionr   r   r   r   Útest_raisesÛ  s   zTestCompanion.test_raisesc                 C   s<   t ddƒD ]}dg| dg }tt |¡j||fkƒ qd S )Nr	   r2   r   )r7   r   r   r©   r_   )r    r=   r˜   r   r   r   Útest_dimensionsß  s   þzTestCompanion.test_dimensionsc                 C   s   t t ddg¡d dkƒ d S )Nr	   r
   )r   r   g      Ð¿)r   r   r©   r   r   r   r   Útest_linear_rootä  s   zTestCompanion.test_linear_rootN)r*   r+   r,   rª   r«   r¬   r   r   r   r   r¨   Ù  s    r¨   c                   @   r    )Ú	TestGaussc                 C   s„   t  d¡\}}t  |d¡}t |j| |¡}dt | ¡ ¡ }|d d …d f | | }t|t 	d¡ƒ t tj
¡}t| ¡ |ƒ d S )Nr0   éc   r	   )r   Z	hermgaussr–   r8   rš   rŒ   ÚsqrtZdiagonalr   ZeyeÚpiÚsum)r    r   r¤   r—   ÚvvZvdr@   r   r   r   Útest_100ê  s   zTestGauss.test_100N)r*   r+   r,   r³   r   r   r   r   r­   è  r§   r­   c                   @   sD   e Zd Zdd„ Zdd„ Zdd„ Zdd„ Zd	d
„ Zdd„ Zdd„ Z	dS )ÚTestMiscc              	   C   s¤   t  g ¡}tt|ƒdgƒ tddƒD ]=}t t tj dd| d ¡dd d… ¡}t  |¡}t  	||¡}d}t
t|ƒ|d kƒ tt  |¡d dƒ t||ƒ qd S )Nr	   r2   r   r
   r   )r   Úhermfromrootsr   r   r7   r8   ÚcosrR   r°   rF   r   rH   r„   )r    rA   r=   Úrootsr†   r@   r   r   r   Útest_hermfromrootsý  s   
*
ùzTestMisc.test_hermfromrootsc                 C   sl   t t dg¡g ƒ t t ddg¡dgƒ tddƒD ]}t dd|¡}t t |¡¡}t t|ƒt|ƒƒ qd S )Nr	   g      à¿r
   r2   r   )r   r   Z	hermrootsr7   r8   rR   rµ   r   )r    r=   r@   rA   r   r   r   Útest_hermroots	  s   ýzTestMisc.test_hermrootsc                 C   sb   g d¢}t ttj|dƒ tt |¡|d d… ƒ tt |d¡|d d… ƒ tt |d¡dgƒ d S )N)r
   r   r	   r   r   r	   r.   r
   r   )r   re   r   r   r   )r    r˜   r   r   r   Útest_hermtrim  s
   zTestMisc.test_hermtrimc                 C   s   t t dd¡ddgƒ d S )Nr/   r   r
   )r   r   Zhermliner   r   r   r   Útest_hermline  s   zTestMisc.test_hermlinec                 C   s2   t dƒD ]}tt dg| dg ¡t| ƒ qd S ©Nr\   r   r	   )r7   r   r   r„   r^   ©r    r=   r   r   r   Útest_herm2poly  ó   "ÿzTestMisc.test_herm2polyc                 C   s2   t dƒD ]}tt t| ¡dg| dg ƒ qd S r¼   )r7   r   r   rƒ   r^   r½   r   r   r   Útest_poly2herm#  r¿   zTestMisc.test_poly2hermc                 C   s6   t  ddd¡}t  |d  ¡}t |¡}t||ƒ d S )Néûÿÿÿr2   é   r
   )r8   rR   Úexpr   Z
hermweightr   )r    r   r@   rA   r   r   r   Útest_weight'  s   
zTestMisc.test_weightN)
r*   r+   r,   r¸   r¹   rº   r»   r¾   rÀ   rÄ   r   r   r   r   r´   û  s    r´   )'Ú__doc__Ú	functoolsr   Znumpyr8   Znumpy.polynomial.hermiteZ
polynomialZhermiter   Znumpy.polynomial.polynomialr   Znumpy.testingr   r   r   r   rO   ZH0ZH1ZH2ZH3ZH4ZH5ZH6ZH7ZH8ZH9r^   r   r   r-   rS   ry   r�   r”   r¡   r¨   r­   r´   r   r   r   r   Ú<module>   s8    B^f(0M