o
    V=ºi)K  ã                
   @   s¨  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¢¡d Ze g d	¢¡d Ze g d
¢¡d Ze g d¢¡d Ze g d¢¡d Ze g d¢¡d Ze g d¢¡d Ze g d¢¡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 legendre module.

é    )ÚreduceN©Úpolyval)Úassert_almost_equalÚassert_raisesÚassert_equalÚassert_é   )éÿÿÿÿr   é   é   )r   éýÿÿÿr   é   )r   r   iâÿÿÿr   é#   é   )r   é   r   iºÿÿÿr   é?   )éûÿÿÿr   éi   r   iÅþÿÿr   éç   é   )r   iÝÿÿÿr   é;  r   iKýÿÿr   i­  )	r   r   iûÿÿr   i  r   iÑÿÿr   i#  é€   )
r   r   r   iôíÿÿr   ibF  r   it›ÿÿr   i{/  c                 C   s   t j| dd�S )Ng�íµ ÷Æ°>)Ztol)ÚlegÚlegtrim©Úx© r   újC:\Users\psant\Downloads\PAF backend\school\venv\Lib\site-packages\numpy/polynomial/tests/test_legendre.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 )Nr
   r	   )r   r   Z	legdomain©Úselfr   r   r   Útest_legdomain!   ó   zTestConstants.test_legdomainc                 C   ó   t tjdgƒ d S )Nr   )r   r   Zlegzeror"   r   r   r   Útest_legzero$   ó   zTestConstants.test_legzeroc                 C   r&   ©Nr	   )r   r   Zlegoner"   r   r   r   Útest_legone'   r(   zTestConstants.test_legonec                 C   r!   )Nr   r	   )r   r   Zlegxr"   r   r   r   Ú	test_legx*   r%   zTestConstants.test_legxN)Ú__name__Ú
__module__Ú__qualname__r$   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TestArithmeticr
   r	   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 ©Nr   úAt i=ú, j=r	   r   ©Úerr_msg)ÚrangeÚnpÚzerosÚmaxr   Úlegaddr   r   ©r#   ÚiÚjÚmsgÚtgtÚresr   r   r   Útest_legadd1   ó   $úÿzTestArithmetic.test_legaddc                 C   sž   t dƒD ]H}t dƒD ]A}d|› d|› �}t t||ƒd ¡}||  d7  < ||  d8  < t dg| dg dg| dg ¡}tt|ƒt|ƒ|d� q
qd S r1   )r6   r7   r8   r9   r   Zlegsubr   r   r;   r   r   r   Útest_legsub;   rB   zTestArithmetic.test_legsubc                 C   sŽ   t t dg¡dgƒ t t dg¡ddgƒ tddƒD ]*}d| d }dg| dg }dg|d  || d|d | g }t t |¡|ƒ qd S )Nr   r	   r   r   )r   r   Zlegmulxr6   )r#   r<   ÚtmpZserr?   r   r   r   Útest_legmulxE   s   $üzTestArithmetic.test_legmulxc           
      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 )Nr   r   r	   r2   r3   r4   )r6   r   Úlegvalr   Úlegmulr   Úlenr   )
r#   r<   Zpol1Zval1r=   r>   Zpol2Zval2Zpol3Zval3r   r   r   Útest_legmulN   s   ùýzTestArithmetic.test_legmulc           
      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 )Nr   r2   r3   r   r	   r4   )r6   r   r:   ZlegdivrG   r   r   )
r#   r<   r=   r>   ÚciÚcjr?   ZquoÚremr@   r   r   r   Útest_legdiv\   s   ùÿzTestArithmetic.test_legdivc                 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 )Nr   r2   r3   r	   r4   )
r6   r7   Úaranger   r   rG   ÚarrayZlegpowr   r   )r#   r<   r=   r>   Úcr?   r@   r   r   r   Útest_legpowg   s   ûÿzTestArithmetic.test_legpowN)r,   r-   r.   r7   Úlinspacer   rA   rC   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)ç       @rT   rT   úi,j->ijú
i,j,k->ijk©r   r   r   r	   )ç      ð?rT   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_legval.<locals>.<listcomp>é
   r2   r4   r   r   )r	   r   r   )r   r   rF   Úsizer7   rR   ÚLlistr6   r   r8   Úshape)r#   Úyr<   r>   r?   r@   Údimsr   r   r   Útest_legval{   s   


ûzTestEvaluation.test_legvalc           
      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   ra   r   Ú
ValueErrorr   Úlegval2dÚc2dr   r7   Úonesr   r`   ©
r#   Úx1Úx2Úx3Úy1Úy2Zy3r?   r@   Úzr   r   r   Útest_legval2d�   s   

zTestEvaluation.test_legval2dc           
      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 rd   )r   ra   r   rf   r   Úlegval3dÚc3dr   r7   ri   r   r`   rj   r   r   r   Útest_legval3d¡   s   

zTestEvaluation.test_legval3dc           
      C   sl   | j \}}}| j\}}}t d||¡}t ||| j¡}t||ƒ t d¡}	t |	|	| j¡}t	|j
dkƒ d S )NrU   re   )r   r   r   r   )r   ra   r7   Úeinsumr   Z	leggrid2drh   r   ri   r   r`   rj   r   r   r   Útest_leggrid2d²   s   

zTestEvaluation.test_leggrid2dc           
      C   sr   | j \}}}| j\}}}t d|||¡}t |||| j¡}t||ƒ t d¡}	t |	|	|	| j¡}t	|j
dkƒ d S )NrV   re   )r   r   r   r   r   r   )r   ra   r7   ru   r   Z	leggrid3drs   r   ri   r   r`   rj   r   r   r   Útest_leggrid3dÀ   s   

zTestEvaluation.test_leggrid3dN)r,   r-   r.   r7   rO   Zc1dru   rh   rs   Úrandomr   r   ra   rc   rq   rt   rv   rw   r   r   r   r   rS   q   s    rS   c                   @   ó$   e Zd Zd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   ç      à?r
   r	   )Úlbnd)Úscl©Úaxisr   r   )ÚmÚk)r€   r�   r|   )r€   r�   r}   ©r€   )r   Ú	TypeErrorr   Úlegintrf   r6   r   Úpoly2legÚleg2polyr   rF   Úlist)
r#   r<   r�   r@   r}   Úpolr?   Zlegpolr„   r=   r   r   r   Útest_legintÑ   sŠ   




ú	ú	ú	úÿzTestIntegral.test_legintc                 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   é   c                 S   ó   g | ]}t  |¡‘qS r   ©r   r„   rY   r   r   r   r[   (  r\   z1TestIntegral.test_legint_axis.<locals>.<listcomp>r   r~   c                 S   rŒ   r   r�   rY   r   r   r   r[   ,  r\   r	   c                 S   s   g | ]	}t j|d d�‘qS )r   )r�   r�   rY   r   r   r   r[   0  s    r   )r�   r   )r7   rx   ÚvstackÚTr   r„   r   ©r#   rh   r?   r@   r   r   r   Útest_legint_axis$  s   

zTestIntegral.test_legint_axisc                 C   s   t t dd¡dƒ d S )N©r	   r   r   r   )r   r   r„   r"   r   r   r   Útest_legint_zerointord4  s   z#TestIntegral.test_legint_zerointordN)r,   r-   r.   r‰   r‘   r“   r   r   r   r   rz   Ï   s    Srz   c                   @   ry   )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
   r   r	   r‚   r   )r€   r}   )
r   rƒ   r   Úlegderrf   r6   r   r   r„   r   )r#   r<   r?   r@   r=   r   r   r   Útest_legder:  s&   ýýÿzTestDerivative.test_legderc                 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 )NrŠ   c                 S   rŒ   r   ©r   r•   rY   r   r   r   r[   W  r\   z3TestDerivative.test_legder_axis.<locals>.<listcomp>r   r~   c                 S   rŒ   r   r—   rY   r   r   r   r[   [  r\   r	   )r7   rx   rŽ   r�   r   r•   r   r�   r   r   r   Útest_legder_axisS  s   
zTestDerivative.test_legder_axisc                 C   s   d}t t |d¡dgƒ d S )N)r	   r   r   r‹   r‹   r   )r   r   r•   )r#   rP   r   r   r   Ú test_legder_orderhigherthancoeff_  s   z/TestDerivative.test_legder_orderhigherthancoeffN)r,   r-   r.   r–   r˜   r™   r   r   r   r   r”   8  s    r”   c                   @   s@   e Zd Zej d¡d d Z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   rŠ   r‹   r   r	   .r   r   é   )r   r   r‹   )
r7   rN   r   Ú	legvanderr   r`   r6   r   rF   rO   )r#   r   Úvr<   Úcoefr   r   r   Útest_legvanderg  s   
þzTestVander.test_legvanderc                 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 )Nre   r	   r   )r	   r   r›   )r   r7   rx   r   Zlegvander2drg   ÚdotÚflatr   r   r`   ©r#   rk   rl   rm   rP   Zvanr?   r@   r   r   r   Útest_legvander2dx  s   
zTestVander.test_legvander2dc                 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   é   )r   r7   rx   r   Zlegvander3drr   r    r¡   r   r   r`   r¢   r   r   r   Útest_legvander3d…  s   
zTestVander.test_legvander3dc                 C   s   t ttjddƒ d S )Nr’   r
   )r   rf   r   rœ   r"   r   r   r   Útest_legvander_negdeg’  r%   z TestVander.test_legvander_negdegN)
r,   r-   r.   r7   rx   r   rŸ   r£   r¥   r¦   r   r   r   r   rš   c  s    rš   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_legfit.<locals>.fc                 S   s   | d | d  d S )Nr‹   r   r	   r   r   r   r   r   Úf2œ  r%   z#TestFitting.test_legfit.<locals>.f2r	   r
   r   r   )Úw)r   r
   r›   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   rf   r   Zlegfitrƒ   r7   rR   r   rH   r   rF   rO   r�   Z
zeros_likeÚcopy)r#   r©   rª   r   ra   Zcoef3Zcoef4Zcoef2dr«   ZywZwcoef3Zwcoef2dZcoef1Zcoef2r   r   r   Útest_legfit˜  sp   


"zTestFitting.test_legfitN)r,   r-   r.   r­   r   r   r   r   r¨   –  ó    r¨   c                   @   ry   )ÚTestCompanionc                 C   s"   t ttjg ƒ t ttjdgƒ d S r)   )r   rf   r   Úlegcompanionr"   r   r   r   Útest_raiseså  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   )r6   r   r   r°   r`   )r#   r<   rž   r   r   r   Útest_dimensionsé  s   þzTestCompanion.test_dimensionsc                 C   s   t t ddg¡d dkƒ d S )Nr	   r   )r   r   ç      à¿)r   r   r°   r"   r   r   r   Útest_linear_rootî  s   zTestCompanion.test_linear_rootN)r,   r-   r.   r±   r²   r´   r   r   r   r   r¯   ã  s    r¯   c                   @   r§   )Ú	TestGaussc                 C   s|   t  d¡\}}t  |d¡}t |j| |¡}dt | ¡ ¡ }|d d …d f | | }t|t 	d¡ƒ d}t| 
¡ |ƒ d S )Nr0   éc   r	   rT   )r   Zleggaussrœ   r7   r    r�   ÚsqrtZdiagonalr   ZeyeÚsum)r#   r   r«   r�   ÚvvZvdr?   r   r   r   Útest_100ô  s   zTestGauss.test_100N)r,   r-   r.   rº   r   r   r   r   rµ   ò  r®   rµ   c                   @   sL   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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	   r   r   r   r
   )r   Úlegfromrootsr   r   r6   r7   ÚcosrR   ÚpirF   r   rH   r†   )r#   r@   r<   Úrootsrˆ   r?   r   r   r   Útest_legfromroots  s   
*
ùzTestMisc.test_legfromrootsc                 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	   r   r³   r   r
   )r   r   Zlegrootsr6   r7   rR   r¼   r   )r#   r<   r?   r@   r   r   r   Útest_legroots  s   ýzTestMisc.test_legrootsc                 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   rf   r   r   r   )r#   rž   r   r   r   Útest_legtrim  s
   zTestMisc.test_legtrimc                 C   s   t t dd¡ddgƒ d S )Nr   r‹   ©r   r   Zlegliner"   r   r   r   Útest_legline&  s   zTestMisc.test_leglinec                 C   s   t t dd¡dgƒ d S )Nr   r   rÃ   r"   r   r   r   Útest_legline_zeroscl)  s   zTestMisc.test_legline_zerosclc                 C   s2   t dƒD ]}tt dg| dg ¡t| ƒ qd S ©Nr]   r   r	   )r6   r   r   r†   r_   ©r#   r<   r   r   r   Útest_leg2poly,  ó   "ÿzTestMisc.test_leg2polyc                 C   s2   t dƒD ]}tt t| ¡dg| dg ƒ qd S rÆ   )r6   r   r   r…   r_   rÇ   r   r   r   Útest_poly2leg0  rÉ   zTestMisc.test_poly2legc                 C   s*   t  ddd¡}d}t |¡}t||ƒ d S )Nr
   r	   é   rX   )r7   rR   r   Z	legweightr   )r#   r   r?   r@   r   r   r   Útest_weight4  s   
zTestMisc.test_weightN)r,   r-   r.   rÀ   rÁ   rÂ   rÄ   rÅ   rÈ   rÊ   rÌ   r   r   r   r   r»     s    r»   )'Ú__doc__Ú	functoolsr   Znumpyr7   Znumpy.polynomial.legendreZ
polynomialZlegendrer   Znumpy.polynomial.polynomialr   Znumpy.testingr   r   r   r   rO   ZL0ZL1ZL2ZL3ZL4ZL5ZL6ZL7ZL8ZL9r_   r   r    r/   rS   rz   r”   rš   r¨   r¯   rµ   r»   r   r   r   r   Ú<module>   s8    C^i+3M