a
    hÝEbñH  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   úd/home/ja/django-apps/lartica_env/lib/python3.9/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   s   t tjddgƒ d S )Nr
   r	   )r   r   Z	legdomain©Úselfr   r   r   Útest_legdomain!   s    zTestConstants.test_legdomainc                 C   s   t tjdgƒ d S )Nr   )r   r   Zlegzeror!   r   r   r   Útest_legzero$   s    zTestConstants.test_legzeroc                 C   s   t tjdgƒ d S ©Nr	   )r   r   Zlegoner!   r   r   r   Útest_legone'   s    zTestConstants.test_legonec                 C   s   t tjddgƒ d S )Nr   r	   )r   r   Zlegxr!   r   r   r   Ú	test_legx*   s    zTestConstants.test_legxN)Ú__name__Ú
__module__Ú__qualname__r#   r$   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 ]�}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 ©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   s    $zTestArithmetic.test_legaddc                 C   sž   t dƒD ]�}t dƒD ]‚}d|› d|› �}t t||ƒd ¡}||  d7  < ||  d8  < t dg| dg dg| dg ¡}tt|ƒt|ƒ|d� qqd S r-   )r2   r3   r4   r5   r   Zlegsubr   r   r7   r   r   r   Útest_legsub;   s    $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 ]T}d| d }dg| dg }dg|d  || d|d | g }t t |¡|ƒ q4d S )Nr   r	   r   r   )r   r   Zlegmulxr2   )r"   r8   ÚtmpZserr;   r   r   r   Útest_legmulxE   s    $zTestArithmetic.test_legmulxc           
      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.   r/   r0   )r2   r   Úlegvalr   Úlegmulr   Úlenr   )
r"   r8   Zpol1Zval1r9   r:   Zpol2Zval2Zpol3Zval3r   r   r   Útest_legmulN   s    zTestArithmetic.test_legmulc           
      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.   r/   r   r	   r0   )r2   r   r6   ZlegdivrB   r   r   )
r"   r8   r9   r:   ÚciÚcjr;   ZquoÚremr<   r   r   r   Útest_legdiv\   s    zTestArithmetic.test_legdivc                 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.   r/   r	   r0   )
r2   r3   Úaranger   r   rB   ÚarrayZlegpowr   r   )r"   r8   r9   r:   Úcr;   r<   r   r   r   Útest_legpowg   s    zTestArithmetic.test_legpowN)r(   r)   r*   r3   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)ç       @rO   rO   úi,j->ijú
i,j,k->ijk©r   r   r   r	   )ç      ð?rO   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_legval.<locals>.<listcomp>é
   r.   r0   r   r   )r	   r   r   )r   r   rA   Úsizer3   rM   ÚLlistr2   r   r4   Úshape)r"   Úyr8   r:   r;   r<   Údimsr   r   r   Útest_legval{   s    


z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   r\   r   Ú
ValueErrorr   Úlegval2dÚc2dr   r3   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 r_   )r   r\   r   ra   r   Úlegval3dÚc3dr   r3   rd   r   r[   re   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 )NrP   r`   )r   r   r   r   )r   r\   r3   Úeinsumr   Z	leggrid2drc   r   rd   r   r[   re   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 )NrQ   r`   )r   r   r   r   r   r   )r   r\   r3   rp   r   Z	leggrid3drn   r   rd   r   r[   re   r   r   r   Útest_leggrid3dÀ   s    

zTestEvaluation.test_leggrid3dN)r(   r)   r*   r3   rJ   Zc1drp   rc   rn   Úrandomr   r   r\   r^   rl   ro   rq   rr   r   r   r   r   rN   q   s   rN   c                   @   s$   e Zd Zd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   ç      à?r
   r	   )Úlbnd)Úscl©Úaxisr   r   )ÚmÚk)rz   r{   rv   )rz   r{   rw   ©rz   )r   Ú	TypeErrorr   Úlegintra   r2   r   Úpoly2legÚleg2polyr   rA   Úlist)
r"   r8   r{   r<   rw   Úpolr;   Zlegpolr~   r9   r   r   r   Útest_legintÑ   s€    




z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   s   g | ]}t  |¡‘qS r   ©r   r~   rT   r   r   r   rV   (  rW   z1TestIntegral.test_legint_axis.<locals>.<listcomp>r   rx   c                 S   s   g | ]}t  |¡‘qS r   r†   rT   r   r   r   rV   ,  rW   r	   c                 S   s   g | ]}t j|d d�‘qS )r   )r{   r†   rT   r   r   r   rV   0  rW   r   )r{   ry   )r3   rs   ÚvstackÚTr   r~   r   ©r"   rc   r;   r<   r   r   r   Útest_legint_axis$  s    

zTestIntegral.test_legint_axisc                 C   s   t t dd¡dƒ d S )N©r	   r   r   r   )r   r   r~   r!   r   r   r   Útest_legint_zerointord4  s    z#TestIntegral.test_legint_zerointordN)r(   r)   r*   rƒ   rŠ   rŒ   r   r   r   r   rt   Ï   s   Srt   c                   @   s$   e Zd Zd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   ru   r
   r   r	   r|   r   )rz   rw   )
r   r}   r   Úlegderra   r2   r   r   r~   r   )r"   r8   r;   r<   r9   r   r   r   Útest_legder:  s     z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 )Nr„   c                 S   s   g | ]}t  |¡‘qS r   ©r   rŽ   rT   r   r   r   rV   W  rW   z3TestDerivative.test_legder_axis.<locals>.<listcomp>r   rx   c                 S   s   g | ]}t  |¡‘qS r   r�   rT   r   r   r   rV   [  rW   r	   )r3   rs   r‡   rˆ   r   rŽ   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   rŽ   )r"   rK   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
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…   )
r3   rI   r   Ú	legvanderr   r[   r2   r   rA   rJ   )r"   r   Úvr8   Úcoefr   r   r   Útest_legvanderg  s    
z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 )Nr`   r	   r   )r	   r   r”   )r   r3   rs   r   Zlegvander2drb   ÚdotÚflatr   r   r[   ©r"   rf   rg   rh   rK   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   r3   rs   r   Zlegvander3drm   r™   rš   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   ra   r   r•   r!   r   r   r   Útest_legvander_negdeg’  s    z TestVander.test_legvander_negdegN)
r(   r)   r*   r3   rs   r   r˜   rœ   rž   rŸ   r   r   r   r   r“   c  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_legfit.<locals>.fc                 S   s   | d | d  d S )Nr…   r   r	   r   r   r   r   r   Úf2œ  s    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   ra   r   Zlegfitr}   r3   rM   r   rC   r   rA   rJ   rˆ   Z
zeros_likeÚcopy)r"   r¡   r¢   r   r\   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    –  s   r    c                   @   s$   e Zd Zdd„ Zdd„ Zdd„ ZdS )ÚTestCompanionc                 C   s"   t ttjg ƒ t ttjdgƒ d S r%   )r   ra   r   Úlegcompanionr!   r   r   r   Útest_raiseså  s    zTestCompanion.test_raisesc                 C   s<   t ddƒD ],}dg| dg }tt |¡j||fkƒ q
d S )Nr	   r   r   )r2   r   r   r§   r[   )r"   r8   r—   r   r   r   Útest_dimensionsé  s    zTestCompanion.test_dimensionsc                 C   s   t t ddg¡d dkƒ d S )Nr	   r   )r   r   ç      à¿)r   r   r§   r!   r   r   r   Útest_linear_rootî  s    zTestCompanion.test_linear_rootN)r(   r)   r*   r¨   r©   r«   r   r   r   r   r¦   ã  s   r¦   c                   @   s   e Zd Zdd„ ZdS )Ú	TestGaussc                 C   s|   t  d¡\}}t  |d¡}t |j| |¡}dt | ¡ ¡ }|d d …d f | | }t|t 	d¡ƒ d}t| 
¡ |ƒ d S )Nr,   éc   r	   rO   )r   Zleggaussr•   r3   r™   rˆ   ÚsqrtZdiagonalr   ÚeyeÚsum)r"   r   r£   r–   ÚvvZvdr;   r   r   r   Útest_100ô  s    zTestGauss.test_100N)r(   r)   r*   r²   r   r   r   r   r¬   ò  s   r¬   c                   @   sL   e Zd Zdd„ Zdd„ Zdd„ Zdd„ Zd	d
„ Zdd„ Zdd„ Z	dd„ Z
dS )ÚTestMiscc              	   C   s¤   t  g ¡}tt|ƒdgƒ tddƒD ]z}t t tj dd| d ¡dd d… ¡}t  |¡}t  	||¡}d}t
t|ƒ|d kƒ tt  |¡d dƒ t||ƒ q$d S )Nr	   r   r   r   r
   )r   Úlegfromrootsr   r   r2   r3   ÚcosrM   ÚpirA   r   rC   r€   )r"   r<   r8   Úrootsr‚   r;   r   r   r   Útest_legfromroots  s    
*
zTestMisc.test_legfromrootsc                 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	   r   rª   r   r
   )r   r   Zlegrootsr2   r3   rM   r´   r   )r"   r8   r;   r<   r   r   r   Útest_legroots  s    z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   ra   r   r   r   )r"   r—   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   r»   r!   r   r   r   Útest_legline_zeroscl)  s    zTestMisc.test_legline_zerosclc                 C   s2   t dƒD ]$}tt dg| dg ¡t| ƒ qd S ©NrX   r   r	   )r2   r   r   r€   rZ   ©r"   r8   r   r   r   Útest_leg2poly,  s    zTestMisc.test_leg2polyc                 C   s2   t dƒD ]$}tt t| ¡dg| dg ƒ qd S r¾   )r2   r   r   r   rZ   r¿   r   r   r   Útest_poly2leg0  s    zTestMisc.test_poly2legc                 C   s*   t  ddd¡}d}t |¡}t||ƒ d S )Nr
   r	   é   rS   )r3   rM   r   Z	legweightr   )r"   r   r;   r<   r   r   r   Útest_weight4  s    
zTestMisc.test_weightN)r(   r)   r*   r¸   r¹   rº   r¼   r½   rÀ   rÁ   rÃ   r   r   r   r   r³     s   r³   )'Ú__doc__Ú	functoolsr   Únumpyr3   Znumpy.polynomial.legendreZ
polynomialZlegendrer   Znumpy.polynomial.polynomialr   Znumpy.testingr   r   r   r   rJ   ZL0ZL1ZL2ZL3ZL4ZL5ZL6ZL7ZL8ZL9rZ   r   r    r+   rN   rt   r�   r“   r    r¦   r¬   r³   r   r   r   r   Ú<module>   s6   C^i+3M