a
    LfH                  
   @   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ZG dd dZG dd dZG dd dZ G dd dZ!G dd  d Z"G d!d" d"Z#G d#d$ d$Z$G d%d& d&Z%G d'd( d(Z&dS ))zTests for legendre module.

    )reduceNpolyval)assert_almost_equalassert_raisesassert_equalassert_   )r         )r   r      )r   r   ir   #      )r      r   ir   ?   )r   i   r   ir         )r   ir   ;  r   iKr   i  )	r   r   ir   i  r   ir   i#     )
r   r   r   ir   ibF  r   itr   i{/  c                 C   s   t j| ddS )Ngư>)Ztol)leglegtrimx r   ]/var/www/ai-form-bot/venv/lib/python3.9/site-packages/numpy/polynomial/tests/test_legendre.pytrim   s    r   c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestConstantsc                 C   s   t tjddg d S )Nr
   r	   )r   r   Z	legdomainselfr   r   r   test_legdomain!   s    zTestConstants.test_legdomainc                 C   s   t tjdg d S )Nr   )r   r   Zlegzeror!   r   r   r   test_legzero$   s    zTestConstants.test_legzeroc                 C   s   t tjdg d S Nr	   )r   r   Zlegoner!   r   r   r   test_legone'   s    zTestConstants.test_legonec                 C   s   t tjddg d S )Nr   r	   )r   r   Zlegxr!   r   r   r   	test_legx*   s    zTestConstants.test_legxN)__name__
__module____qualname__r#   r$   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 )TestArithmeticr
   r	   d   c                 C   s   t dD ]}t dD ]}d| d| }tt||d }||  d7  < ||  d7  < tdg| dg dg| dg }tt|t||d qqd S Nr   At i=, j=r	   r   err_msg)rangenpzerosmaxr   legaddr   r   r"   ijmsgtgtresr   r   r   test_legadd1   s    $zTestArithmetic.test_legaddc                 C   s   t dD ]}t dD ]}d| d| }tt||d }||  d7  < ||  d8  < tdg| dg dg| dg }tt|t||d qqd S r-   )r2   r3   r4   r5   r   Zlegsubr   r   r7   r   r   r   test_legsub;   s    $zTestArithmetic.test_legsubc                 C   s   t tdgdg t tdgddg tddD ]T}d| d }dg| dg }dg|d  || d|d | g }t t|| q4d S )Nr   r	   r   r   )r   r   Zlegmulxr2   )r"   r8   tmpZserr;   r   r   r   test_legmulxE   s    $zTestArithmetic.test_legmulxc           
      C   s   t dD ]}dg| dg }t| j|}t dD ]x}d| d| }dg| dg }t| j|}t||}t| j|}	tt||| d k| t|	|| |d q2qd S )Nr   r   r	   r.   r/   r0   )r2   r   legvalr   legmulr   lenr   )
r"   r8   Zpol1Zval1r9   r:   Zpol2Zval2Zpol3Zval3r   r   r   test_legmulN   s    zTestArithmetic.test_legmulc           
      C   s   t dD ]}t dD ]z}d| d| }dg| dg }dg| dg }t||}t||\}}tt|||}	tt|	t||d qqd S )Nr   r.   r/   r   r	   r0   )r2   r   r6   ZlegdivrB   r   r   )
r"   r8   r9   r:   cicjr;   Zquoremr<   r   r   r   test_legdiv\   s    zTestArithmetic.test_legdivc                 C   s|   t dD ]n}t dD ]`}d| d| }t|d }ttj|g| tdg}t||}tt	|t	||d qqd S )Nr   r.   r/   r	   r0   )
r2   r3   aranger   r   rB   arrayZlegpowr   r   )r"   r8   r9   r:   cr;   r<   r   r   r   test_legpowg   s    zTestArithmetic.test_legpowN)r(   r)   r*   r3   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Zdd	 Zd
d Zdd Zdd Zdd ZdS )TestEvaluation)       @rO   rO   i,j->ij
i,j,k->ijkr   r   r   r	   )      ?rO   g      @c                    s   t tg dgjd tdd  fddtD }tdD ]<}d| }|| }t dg| dg }t|||d q<td	D ]^}d
g| }t	| t t dgj
| t t ddgj
| t t g dj
| qd S )Nr	   r   r
   c                    s   g | ]}t  |qS r   r   .0rK   r   r   r   
<listcomp>       z.TestEvaluation.test_legval.<locals>.<listcomp>
   r.   r0   r   r   )r	   r   r   )r   r   rA   sizer3   rM   Llistr2   r   r4   shape)r"   yr8   r:   r;   r<   dimsr   r   r   test_legval{   s    


zTestEvaluation.test_legvalc           
      C   s   | j \}}}| j\}}}tttj||d d | j || }t||| j}t|| t	d}	t|	|	| j}t
|jdk d S Nr   r   r   )r   r\   r   
ValueErrorr   legval2dc2dr   r3   onesr   r[   
r"   x1x2x3y1y2Zy3r;   r<   zr   r   r   test_legval2d   s    

zTestEvaluation.test_legval2dc           
      C   s   | j \}}}| j\}}}tttj|||d d | j || | }t|||| j}t|| t	d}	t|	|	|	| j}t
|jdk d S r_   )r   r\   r   ra   r   legval3dc3dr   r3   rd   r   r[   re   r   r   r   test_legval3d   s    

zTestEvaluation.test_legval3dc           
      C   sl   | j \}}}| j\}}}td||}t||| j}t|| td}	t|	|	| j}t	|j
dk d S )NrP   r`   )r   r   r   r   )r   r\   r3   einsumr   Z	leggrid2drc   r   rd   r   r[   re   r   r   r   test_leggrid2d   s    

zTestEvaluation.test_leggrid2dc           
      C   sr   | j \}}}| j\}}}td|||}t|||| j}t|| td}	t|	|	|	| j}t	|j
dk 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   test_leggrid3d   s    

zTestEvaluation.test_leggrid3dN)r(   r)   r*   r3   rJ   Zc1drp   rc   rn   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 )TestIntegralc           
   	   C   s2  t ttjdgd t ttjdgd t ttjdgdddg 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	D ]8}dg|d  dg }tjdg||d
}t|ddg qtd	D ]n}|d }dg| dg }|gdg|  d| g }t|}tj|d|gd
}t|}tt	|t	| qtd	D ]N}|d }dg| dg }t|}tj|d|gdd}tt
d|| q@td	D ]r}|d }dg| dg }|gdg|  d| g }t|}tj|d|gdd}t|}tt	|t	| qtd	D ]r}tdd	D ]`}	dg| dg }|d d  }t|	D ]}tj|dd}qJtj||	d}tt	|t	| q"qtd	D ]}tdd	D ]n}	dg| dg }|d d  }t|	D ]}tj|d|gd
}qtj||	tt|	d
}tt	|t	| qqtd	D ]}tdd	D ]r}	dg| dg }|d d  }t|	D ]}tj|d|gdd}qPtj||	tt|	dd}tt	|t	| q(qtd	D ]}tdd	D ]r}	dg| dg }|d d  }t|	D ]}tj|d|gdd}qtj||	tt|	dd}tt	|t	| qqd S )Nr         ?r
   r	   )lbnd)sclaxisr   r   )mk)rz   r{   rv   )rz   r{   rw   rz   )r   	TypeErrorr   legintra   r2   r   poly2legleg2polyr   rA   list)
r"   r8   r{   r<   rw   polr;   Zlegpolr~   r9   r   r   r   test_legint   s    




zTestIntegral.test_legintc                 C   s   t jd}t dd |jD j}tj|dd}t|| t dd |D }tj|dd}t|| t dd |D }tj|d	dd
}t|| d S )Nr      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   vstackTr   r~   r   r"   rc   r;   r<   r   r   r   test_legint_axis$  s    

zTestIntegral.test_legint_axisc                 C   s   t tddd d S )Nr	   r   r   r   )r   r   r~   r!   r   r   r   test_legint_zerointord4  s    z#TestIntegral.test_legint_zerointordN)r(   r)   r*   r   r   r   r   r   r   r   rt      s   Srt   c                   @   s$   e Zd Zdd Zdd Zdd ZdS )TestDerivativec                 C   s  t ttjdgd t ttjdgd tdD ]4}dg| dg }tj|dd}tt|t| q,tdD ]N}tddD ]>}dg| dg }tjtj||d|d}t	t|t| qxqjtdD ]R}tddD ]B}dg| dg }tjtj||dd|dd}t	t|t| qqd S )	Nr   ru   r
   r   r	   r|   r   )rz   rw   )
r   r}   r   legderra   r2   r   r   r~   r   )r"   r8   r;   r<   r9   r   r   r   test_legder:  s     zTestDerivative.test_legderc                 C   sl   t jd}t dd |jD j}tj|dd}t|| t dd |D }tj|dd}t|| d S )Nr   c                 S   s   g | ]}t |qS r   r   r   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   r   r   r   r   r   r   r   r   test_legder_axisS  s    
zTestDerivative.test_legder_axisc                 C   s   d}t t|ddg d S )N)r	   r   r   r   r   r   )r   r   r   )r"   rK   r   r   r    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 )
TestVanderrR   r   r	   c                 C   s   t d}t|d}t|jdk tdD ].}dg| dg }t|d|f t|| q,t 	ddgddgdd	gg}t|d}t|jd
k tdD ].}dg| dg }t|d|f t|| qd S )Nr   r   r   r   r	   .r   r      )r   r   r   )
r3   rI   r   	legvanderr   r[   r2   r   rA   rJ   )r"   r   vr8   coefr   r   r   test_legvanderg  s    
zTestVander.test_legvanderc                 C   sx   | j \}}}tjd}t||ddg}t|||}t||j}t|| t|g|gddg}t	|j
dk d S )Nr`   r	   r   )r	   r   r   )r   r3   rs   r   Zlegvander2drb   dotflatr   r   r[   r"   rf   rg   rh   rK   Zvanr;   r<   r   r   r   test_legvander2dx  s    
zTestVander.test_legvander2dc                 C   s   | j \}}}tjd}t|||g d}t||||}t||j}t|| t|g|g|gg d}t	|j
dk d S )N)r   r   r   r   )r	   r      )r   r3   rs   r   Zlegvander3drm   r   r   r   r   r[   r   r   r   r   test_legvander3d  s    
zTestVander.test_legvander3dc                 C   s   t ttjdd d S )Nr   r
   )r   ra   r   r   r!   r   r   r   test_legvander_negdeg  s    z TestVander.test_legvander_negdegN)
r(   r)   r*   r3   rs   r   r   r   r   r   r   r   r   r   r   c  s
   r   c                   @   s   e Zd Zdd ZdS )TestFittingc                 C   s  dd }dd }t ttjdgdgd t ttjdggdgd t ttjg dgd t ttjdgdgggd t ttjddgdgd t ttjdgddgd 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 t ttjdgdgg d
 t ttjdgdgg  tdd}||}t||d}tt|d t	t
||| t||g d}tt|d t	t
||| t||d}tt|d t	t
||| t||g d}tt|d t	t
||| t||g d}tt|d t	t
||| t|t||gjd}t	|t||gj t|t||gjg d}t	|t||gj t|}| }	d|dd d< d|dd d< tj||	d|d	}
t	|
| tj||	g d|d	}
t	|
| tj|t|	|	gjd|d	}t	|t||gj tj|t|	|	gjg d|d	}t	|t||gj g d}t	t||dddg t	t||ddgddg tdd}||}t||d}t	t
||| t||g d}t	t
||| t	|| d S )Nc                 S   s   | | d  | d  S )Nr	   r   r   r   r   r   r   f  s    z"TestFitting.test_legfit.<locals>.fc                 S   s   | d | d  d S )Nr   r   r	   r   r   r   r   r   f2  s    z#TestFitting.test_legfit.<locals>.f2r	   r
   r   r   )w)r   r
   r   r   r   )r   r	   r   r   r   )r   r	   r   r   r   )r   r   r   r	   r   )r	   y              ?r
   y             )r   r   r   )r   ra   r   Zlegfitr}   r3   rM   r   rC   r   rA   rJ   r   Z
zeros_likecopy)r"   r   r   r   r\   Zcoef3Zcoef4Zcoef2dr   ZywZwcoef3Zwcoef2dZcoef1Zcoef2r   r   r   test_legfit  sp    


"zTestFitting.test_legfitN)r(   r)   r*   r   r   r   r   r   r     s   r   c                   @   s$   e Zd Zdd Zdd Zdd ZdS )TestCompanionc                 C   s"   t ttjg  t ttjdg d S r%   )r   ra   r   legcompanionr!   r   r   r   test_raises  s    zTestCompanion.test_raisesc                 C   s<   t ddD ],}dg| dg }tt|j||fk q
d S )Nr	   r   r   )r2   r   r   r   r[   )r"   r8   r   r   r   r   test_dimensions  s    zTestCompanion.test_dimensionsc                 C   s   t tddgd dk d S )Nr	   r   )r   r         )r   r   r   r!   r   r   r   test_linear_root  s    zTestCompanion.test_linear_rootN)r(   r)   r*   r   r   r   r   r   r   r   r     s   r   c                   @   s   e Zd Zdd ZdS )	TestGaussc                 C   s|   t d\}}t |d}t|j| |}dt|  }|d d d f | | }t|t	d d}t|
 | d S )Nr,   c   r	   rO   )r   Zleggaussr   r3   r   r   sqrtZdiagonalr   eyesum)r"   r   r   r   ZvvZvdr;   r   r   r   test_100  s    zTestGauss.test_100N)r(   r)   r*   r   r   r   r   r   r     s   r   c                   @   sL   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dS )TestMiscc              	   C   s   t g }tt|dg tddD ]z}tttj dd| d dd d }t |}t 	||}d}t
t||d k tt |d d t|| q$d S )Nr	   r   r   r   r
   )r   legfromrootsr   r   r2   r3   cosrM   pirA   r   rC   r   )r"   r<   r8   rootsr   r;   r   r   r   test_legfromroots  s    
*
zTestMisc.test_legfromrootsc                 C   sl   t tdgg  t tddgdg tddD ]4}tdd|}tt|}t t|t| q2d S )Nr	   r   r   r   r
   )r   r   Zlegrootsr2   r3   rM   r   r   )r"   r8   r;   r<   r   r   r   test_legroots  s    zTestMisc.test_legrootsc                 C   sb   g d}t ttj|d tt||d d  tt|d|d d  tt|ddg d S )N)r   r
   r	   r   r
   r	   r   r   r   )r   ra   r   r   r   )r"   r   r   r   r   test_legtrim  s
    zTestMisc.test_legtrimc                 C   s   t tddddg d S )Nr   r   r   r   Zlegliner!   r   r   r   test_legline&  s    zTestMisc.test_leglinec                 C   s   t tdddg d S )Nr   r   r   r!   r   r   r   test_legline_zeroscl)  s    zTestMisc.test_legline_zerosclc                 C   s2   t dD ]$}ttdg| dg t|  qd S NrX   r   r	   )r2   r   r   r   rZ   r"   r8   r   r   r   test_leg2poly,  s    zTestMisc.test_leg2polyc                 C   s2   t dD ]$}ttt| dg| dg  qd S r   )r2   r   r   r   rZ   r   r   r   r   test_poly2leg0  s    zTestMisc.test_poly2legc                 C   s*   t ddd}d}t|}t|| d S )Nr
   r	      rS   )r3   rM   r   Z	legweightr   )r"   r   r;   r<   r   r   r   test_weight4  s    
zTestMisc.test_weightN)r(   r)   r*   r   r   r   r   r   r   r   r   r   r   r   r   r     s   r   )'__doc__	functoolsr   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   r   r   r   r   r   <module>   s6   C^i+3M