a
    hÝEb‘H  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   úc/home/ja/django-apps/lartica_env/lib/python3.9/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   s   t tjddgƒ d S )Néÿÿÿÿr	   )r   r   Z
hermdomain©Úselfr   r   r   Útest_hermdomain!   s    zTestConstants.test_hermdomainc                 C   s   t tjdgƒ d S )Nr   )r   r   Zhermzeror   r   r   r   Útest_hermzero$   s    zTestConstants.test_hermzeroc                 C   s   t tjdgƒ d S ©Nr	   )r   r   Zhermoner   r   r   r   Útest_hermone'   s    zTestConstants.test_hermonec                 C   s   t tjddgƒ d S )Nr   ç      à?)r   r   Zhermxr   r   r   r   Ú
test_hermx*   s    zTestConstants.test_hermxN)Ú__name__Ú
__module__Ú__qualname__r    r!   r#   r%   r   r   r   r   r      s   r   c                   @   sJ   e Zd Ze ddd¡Zdd„ Zdd„ Zdd	„ Zd
d„ Z	dd„ Z
dd„ ZdS )ÚTestArithmeticéýÿÿÿé   éd   c                 C   sž   t dƒD ]�}t dƒD ]‚}d|› d|› �}t t||ƒd ¡}||  d7  < ||  d7  < t dg| dg dg| dg ¡}tt|ƒt|ƒ|d� qqd S ©Né   úAt i=ú, j=r	   r   ©Úerr_msg)ÚrangeÚnpÚzerosÚmaxr   Úhermaddr   r   ©r   ÚiÚjÚmsgÚtgtÚresr   r   r   Útest_hermadd1   s    $zTestArithmetic.test_hermaddc                 C   sž   t dƒD ]�}t dƒD ]‚}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 r-   )r3   r4   r5   r6   r   Zhermsubr   r   r8   r   r   r   Útest_hermsub;   s    $zTestArithmetic.test_hermsubc                 C   sv   t t dg¡dgƒ t t dg¡ddgƒ tddƒD ]<}dg| dg }dg|d  |ddg }t t |¡|ƒ q4d S )Nr   r	   r$   r.   )r   r   Zhermmulxr3   )r   r9   Zserr<   r   r   r   Útest_hermmulxE   s    zTestArithmetic.test_hermmulxc           
      C   s²   t dƒD ]¤}dg| dg }t | j|¡}t dƒD ]x}d|› d|› �}dg| dg }t | j|¡}t ||¡}t | j|¡}	tt|ƒ|| d k|ƒ t|	|| |d� q2qd S )Nr.   r   r	   r/   r0   r1   )r3   r   Úhermvalr   Úhermmulr   Úlenr   )
r   r9   Zpol1Zval1r:   r;   Zpol2Zval2Zpol3Zval3r   r   r   Útest_hermmulM   s    zTestArithmetic.test_hermmulc           
      C   s–   t dƒD ]ˆ}t dƒD ]z}d|› d|› �}dg| dg }dg| dg }t ||¡}t ||¡\}}t t ||¡|¡}	tt|	ƒt|ƒ|d� qqd S )Nr.   r/   r0   r   r	   r1   )r3   r   r7   ZhermdivrB   r   r   )
r   r9   r:   r;   ÚciÚcjr<   ZquoÚremr=   r   r   r   Útest_hermdiv[   s    zTestArithmetic.test_hermdivc                 C   s|   t dƒD ]n}t dƒD ]`}d|› d|› �}t |d ¡}ttj|g| t dg¡ƒ}t ||¡}tt	|ƒt	|ƒ|d� qqd S )Nr.   r/   r0   r	   r1   )
r3   r4   Úaranger   r   rB   ÚarrayZhermpowr   r   )r   r9   r:   r;   Úcr<   r=   r   r   r   Útest_hermpowf   s    zTestArithmetic.test_hermpowN)r&   r'   r(   r4   Úlinspacer   r>   r?   r@   rD   rH   rL   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+   r.   r
   r	   )rO   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 q‚d S )Nr	   r   r   c                    s   g | ]}t ˆ |ƒ‘qS r   r   ©Ú.0rK   r   r   r   Ú
<listcomp>€   ó    z/TestEvaluation.test_hermval.<locals>.<listcomp>é
   r/   r1   r+   r
   )r	   r   r   )r   r   rA   Úsizer4   rM   ÚHlistr3   r   r5   Úshape)r   Úyr9   r;   r<   r=   Údimsr   r   r   Útest_hermvalz   s    


z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   r4   Úonesr   rZ   ©
r   Úx1Úx2Úx3Úy1Úy2Zy3r<   r=   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 r^   )r   r[   r   r`   r   Ú	hermval3dÚc3dr   r4   rc   r   rZ   rd   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 )NrP   r_   )r
   r+   r
   r+   )r   r[   r4   Úeinsumr   Z
hermgrid2drb   r   rc   r   rZ   rd   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 )NrQ   r_   )r
   r+   r
   r+   r
   r+   )r   r[   r4   ro   r   Z
hermgrid3drm   r   rc   r   rZ   rd   r   r   r   Útest_hermgrid3d¿   s    

zTestEvaluation.test_hermgrid3dN)r&   r'   r(   r4   rJ   Zc1dro   rb   rm   Úrandomr   r   r[   r]   rk   rn   rp   rq   r   r   r   r   rN   p   s   rN   c                   @   s   e Zd Zdd„ Zdd„ ZdS )ÚTestIntegralc           
   	   C   s2  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 ]8}dg|d  dg }tjdg||d
�}t|ddgƒ q†td	ƒD ]n}|d }dg| dg }|gdg|  d| g }t |¡}tj|d|gd
�}t |¡}tt	|ƒt	|ƒƒ qÈtd	ƒD ]N}|d }dg| dg }t |¡}tj|d|gdd�}tt 
d|¡|ƒ �q@td	ƒD ]r}|d }dg| dg }|gdg|  d| g }t |¡}tj|d|gdd�}t |¡}tt	|ƒt	|ƒƒ �q˜td	ƒD ]r}tdd	ƒD ]`}	dg| dg }|d d … }t|	ƒD ]}tj|dd�}�qJtj||	d�}tt	|ƒt	|ƒƒ �q"�qtd	ƒD ]€}tdd	ƒD ]n}	dg| dg }|d d … }t|	ƒD ]}tj|d|gd
�}�qÆtj||	tt|	ƒƒd
�}tt	|ƒt	|ƒƒ �qž�q�td	ƒD ]„}tdd	ƒD ]r}	dg| dg }|d d … }t|	ƒD ]}tj|d|gdd�}�qPtj||	tt|	ƒƒdd�}tt	|ƒt	|ƒƒ �q(�qtd	ƒD ]„}tdd	ƒD ]r}	dg| dg }|d d … }t|	ƒD ]}tj|d|gdd�}�qÞtj||	tt|	ƒƒdd�}tt	|ƒt	|ƒƒ �q¶�q¨d S )Nr   r$   r   r	   )Úlbnd)Úscl©Úaxisr
   r.   )ÚmÚk)rx   ry   rt   )rx   ry   ru   ©rx   )r   Ú	TypeErrorr   Úhermintr`   r3   r   Ú	poly2hermÚ	herm2polyr   rA   Úlist)
r   r9   ry   r=   ru   Úpolr<   Zhermpolr|   r:   r   r   r   Útest_hermintÐ   s€    




zTestIntegral.test_hermintc                 C   sš   t j d¡}t  dd„ |jD ƒ¡j}tj|dd�}t||ƒ t  dd„ |D ƒ¡}tj|dd�}t||ƒ t  dd„ |D ƒ¡}tj|d	dd
�}t||ƒ d S )N©r+   r   c                 S   s   g | ]}t  |¡‘qS r   ©r   r|   rS   r   r   r   rU   '  rV   z2TestIntegral.test_hermint_axis.<locals>.<listcomp>r   rv   c                 S   s   g | ]}t  |¡‘qS r   rƒ   rS   r   r   r   rU   +  rV   r	   c                 S   s   g | ]}t j|d d�‘qS )r+   )ry   rƒ   rS   r   r   r   rU   /  rV   r+   )ry   rw   )r4   rr   ÚvstackÚTr   r|   r   ©r   rb   r<   r=   r   r   r   Útest_hermint_axis#  s    

zTestIntegral.test_hermint_axisN)r&   r'   r(   r�   r‡   r   r   r   r   rs   Î   s   Srs   c                   @   s   e Zd Zdd„ Zdd„ ZdS )ÚTestDerivativec                 C   s  t ttjdgdƒ t ttjdgdƒ tdƒD ]4}dg| dg }tj|dd�}tt|ƒt|ƒƒ q,tdƒD ]N}tddƒD ]>}dg| dg }tjtj||d�|d�}t	t|ƒt|ƒƒ qxqjtdƒD ]R}tddƒD ]B}dg| dg }tjtj||dd�|dd�}t	t|ƒt|ƒƒ qÐqÂd S )	Nr   r$   r   r.   r	   rz   r
   )rx   ru   )
r   r{   r   Úhermderr`   r3   r   r   r|   r   )r   r9   r<   r=   r:   r   r   r   Útest_hermder6  s     z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 )Nr‚   c                 S   s   g | ]}t  |¡‘qS r   ©r   r‰   rS   r   r   r   rU   S  rV   z4TestDerivative.test_hermder_axis.<locals>.<listcomp>r   rv   c                 S   s   g | ]}t  |¡‘qS r   r‹   rS   r   r   r   rU   W  rV   r	   )r4   rr   r„   r…   r   r‰   r   r†   r   r   r   Útest_hermder_axisO  s    
z TestDerivative.test_hermder_axisN)r&   r'   r(   rŠ   rŒ   r   r   r   r   rˆ   4  s   rˆ   c                   @   s8   e Zd Zej d¡d d Zdd„ Zdd„ Zdd	„ Zd
S )Ú
TestVanderrR   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 qšd S )Nr+   r‚   r   r   r	   .r
   r.   é   )r+   r
   r   )
r4   rI   r   Ú
hermvanderr   rZ   r3   r   rA   rJ   )r   r   Úvr9   Úcoefr   r   r   Útest_hermvander`  s    
z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 )Nr_   r	   r
   )r	   r.   rŽ   )r   r4   rr   r   Zhermvander2dra   ÚdotÚflatr   r   rZ   ©r   re   rf   rg   rK   Zvanr<   r=   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	   r.   é   )r   r4   rr   r   Zhermvander3drl   r“   r”   r   r   rZ   r•   r   r   r   Útest_hermvander3d~  s    
zTestVander.test_hermvander3dN)	r&   r'   r(   r4   rr   r   r’   r–   r˜   r   r   r   r   r�   \  s   r�   c                   @   s   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�  s    z#TestFitting.test_hermfit.<locals>.fc                 S   s   | d | d  d S )Nr   r
   r	   r   r   r   r   r   Úf2’  s    z$TestFitting.test_hermfit.<locals>.f2r	   r   r   r
   )Úw)r
   r   rŽ   r+   r   )r   r	   r
   r+   r.   )r   r	   r
   r+   r   )r
   r+   r   r	   r   )r	   y              ð?r   y       €      ð¿r$   )r   r
   r   )r   r`   r   Zhermfitr{   r4   rM   r   rC   r   rA   rJ   r…   Z
zeros_likeÚcopy)r   rš   r›   r   r[   Zcoef3Zcoef4Zcoef2drœ   ZywZwcoef3Zwcoef2dZcoef1Zcoef2r   r   r   Útest_hermfitŽ  sp    


"zTestFitting.test_hermfitN)r&   r'   r(   rž   r   r   r   r   r™   Œ  s   r™   c                   @   s$   e Zd Zdd„ Zdd„ Zdd„ ZdS )ÚTestCompanionc                 C   s"   t ttjg ƒ t ttjdgƒ d S r"   )r   r`   r   Úhermcompanionr   r   r   r   Útest_raisesÛ  s    zTestCompanion.test_raisesc                 C   s<   t ddƒD ],}dg| dg }tt |¡j||fkƒ q
d S )Nr	   r.   r   )r3   r   r   r    rZ   )r   r9   r‘   r   r   r   Útest_dimensionsß  s    zTestCompanion.test_dimensionsc                 C   s   t t ddg¡d dkƒ d S )Nr	   r
   )r   r   g      Ð¿)r   r   r    r   r   r   r   Útest_linear_rootä  s    zTestCompanion.test_linear_rootN)r&   r'   r(   r¡   r¢   r£   r   r   r   r   rŸ   Ù  s   rŸ   c                   @   s   e Zd Zdd„ ZdS )Ú	TestGaussc                 C   s„   t  d¡\}}t  |d¡}t |j| |¡}dt | ¡ ¡ }|d d …d f | | }t|t 	d¡ƒ t tj
¡}t| ¡ |ƒ d S )Nr,   éc   r	   )r   Z	hermgaussr�   r4   r“   r…   ÚsqrtZdiagonalr   ÚeyeÚpiÚsum)r   r   rœ   r�   ÚvvZvdr<   r   r   r   Útest_100ê  s    zTestGauss.test_100N)r&   r'   r(   r«   r   r   r   r   r¤   è  s   r¤   c                   @   sD   e Zd Zdd„ Zdd„ Zdd„ Zdd„ Zd	d
„ Zdd„ Zdd„ Z	dS )ÚTestMiscc              	   C   s¤   t  g ¡}tt|ƒdgƒ tddƒD ]z}t t tj dd| d ¡dd d… ¡}t  |¡}t  	||¡}d}t
t|ƒ|d kƒ tt  |¡d dƒ t||ƒ q$d S )Nr	   r.   r   r
   r   )r   Úhermfromrootsr   r   r3   r4   ÚcosrM   r¨   rA   r   rC   r~   )r   r=   r9   Úrootsr€   r<   r   r   r   Útest_hermfromrootsý  s    
*
zTestMisc.test_hermfromrootsc                 C   sl   t t dg¡g ƒ t t ddg¡dgƒ tddƒD ]4}t dd|¡}t t |¡¡}t t|ƒt|ƒƒ q2d S )Nr	   g      à¿r
   r.   r   )r   r   Z	hermrootsr3   r4   rM   r­   r   )r   r9   r<   r=   r   r   r   Útest_hermroots	  s    z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   r`   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 ]$}tt dg| dg ¡t| ƒ qd S ©NrW   r   r	   )r3   r   r   r~   rY   ©r   r9   r   r   r   Útest_herm2poly  s    zTestMisc.test_herm2polyc                 C   s2   t dƒD ]$}tt t| ¡dg| dg ƒ qd S r´   )r3   r   r   r}   rY   rµ   r   r   r   Útest_poly2herm#  s    zTestMisc.test_poly2hermc                 C   s6   t  ddd¡}t  |d  ¡}t |¡}t||ƒ d S )Néûÿÿÿr.   é   r
   )r4   rM   Úexpr   Z
hermweightr   )r   r   r<   r=   r   r   r   Útest_weight'  s    
zTestMisc.test_weightN)
r&   r'   r(   r°   r±   r²   r³   r¶   r·   r»   r   r   r   r   r¬   û  s   r¬   )'Ú__doc__Ú	functoolsr   Únumpyr4   Znumpy.polynomial.hermiteZ
polynomialZhermiter   Znumpy.polynomial.polynomialr   Znumpy.testingr   r   r   r   rJ   ZH0ZH1ZH2ZH3ZH4ZH5ZH6ZH7ZH8ZH9rY   r   r   r)   rN   rs   rˆ   r�   r™   rŸ   r¤   r¬   r   r   r   r   Ú<module>   s6   B^f(0M