U
    gH                     @   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dddgd	 Zedd
ddgd	 Zedddddgd Zeddddddgd Zedddddddgd Zeddddddddgd Zedddddddddg	d Zedddd dd!dd"dd#g
d Zeeeeeeeeeeg
Zd$d% ZG d&d' d'ZG d(d) d)ZG d*d+ d+ZG d,d- d-Z G d.d/ d/Z!G d0d1 d1Z"G d2d3 d3Z#G d4d5 d5Z$G d6d7 d7Z%G d8d9 d9Z&dS ):zTests for legendre module.

    )reduceNpolyval)assert_almost_equalassert_raisesassert_equalassert_            i#         i?   i   i      ii;  iKi  ii  ii#     iibF  iti{/  c                 C   s   t j| ddS )Ngư>)Ztol)leglegtrimx r   H/tmp/pip-unpacked-wheel-2wnnwvus/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,   )r1   r2   r3   r4   r   Zlegsubr   r   r6   r   r   r   test_legsub;   s    $zTestArithmetic.test_legsubc                 C   s   t tdgdg t tdgddg tddD ]T}d| d }dg| dg }dg|d  || d|d | g }t t|| q4d S )Nr   r	   r   r   )r   r   Zlegmulxr1   )r!   r7   tmpZserr:   r   r   r   test_legmulxE   s    $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.   r/   )r1   r   legvalr   legmulr   lenr   )
r!   r7   Zpol1Zval1r8   r9   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	   r/   )r1   r   r5   ZlegdivrA   r   r   )
r!   r7   r8   r9   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	   r/   )
r1   r2   aranger   r   rA   arrayZlegpowr   r   )r!   r7   r8   r9   cr:   r;   r   r   r   test_legpowg   s    zTestArithmetic.test_legpowN)r'   r(   r)   r2   linspacer   r<   r=   r?   rC   rG   rK   r   r   r   r   r*   .   s   

	r*   c                   @   s   e Zd ZedddgZedeeZedeeeZej		dd d Z
ee
dddgZd	d
 Zdd Zdd Zdd Zdd ZdS )TestEvaluation       @i,j->ij
i,j,k->ijkr   r   r   r	         ?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 dddgj
| qd S )Nr	   r   r
   c                    s   g | ]}t  |qS r   r   .0rJ   r   r   r   
<listcomp>   s     z.TestEvaluation.test_legval.<locals>.<listcomp>
   r-   r/   r   r   )r   r   r@   sizer2   rL   Llistr1   r   r3   shape)r!   yr7   r9   r:   r;   Z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   rZ   r   
ValueErrorr   legval2dc2dr   r2   onesr   rY   
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   rZ   r   r^   r   legval3dc3dr   r2   ra   r   rY   rb   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 )NrO   r]   )r   r   r   r   )r   rZ   r2   einsumr   Z	leggrid2dr`   r   ra   r   rY   rb   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 )NrP   r]   )r   r   r   r   r   r   )r   rZ   r2   rm   r   Z	leggrid3drk   r   ra   r   rY   rb   r   r   r   test_leggrid3d   s    

zTestEvaluation.test_leggrid3dN)r'   r(   r)   r2   rI   Zc1drm   r`   rk   randomr   r   rZ   r[   ri   rl   rn   ro   r   r   r   r   rM   q   s   rM   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)rw   rx   rs   )rw   rx   rt   rw   )r   	TypeErrorr   legintr^   r1   r   poly2legleg2polyr   r@   list)
r!   r7   rx   r;   rt   polr:   Zlegpolr{   r8   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{   rS   r   r   r   rU   (  s     z1TestIntegral.test_legint_axis.<locals>.<listcomp>r   ru   c                 S   s   g | ]}t |qS r   r   rS   r   r   r   rU   ,  s     r	   c                 S   s   g | ]}t j|d dqS )r   )rx   r   rS   r   r   r   rU   0  s     r   )rx   rv   )r2   rp   vstackTr   r{   r   r!   r`   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   rq      s   Srq   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   rr   r
   r   r	   ry   r   )rw   rt   )
r   rz   r   legderr^   r1   r   r   r{   r   )r!   r7   r:   r;   r8   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   rS   r   r   r   rU   W  s     z3TestDerivative.test_legder_axis.<locals>.<listcomp>r   ru   c                 S   s   g | ]}t |qS r   r   rS   r   r   r   rU   [  s     r	   )r2   rp   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!   rJ   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 )
TestVanderrQ   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   )
r2   rH   r   	legvanderr   rY   r1   r   r@   rI   )r!   r   vr7   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   r2   rp   r   Zlegvander2dr_   dotflatr   r   rY   r!   rc   rd   re   rJ   Zvanr:   r;   r   r   r   test_legvander2dx  s    
zTestVander.test_legvander2dc                 C   s   | j \}}}tjd}t|||dddg}t||||}t||j}t|| t|g|g|gdddg}t	|j
dk d S )N)r   r   r   r	   r   r   )r	   r      )r   r2   rp   r   Zlegvander3drj   r   r   r   r   rY   r   r   r   r   test_legvander3d  s    
zTestVander.test_legvander3dc                 C   s   t ttjdd d S )Nr   r
   )r   r^   r   r   r    r   r   r   test_legvander_negdeg  s    z TestVander.test_legvander_negdegN)
r'   r(   r)   r2   rp   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ddd
g t ttjdgdgg  tdd}||}t||d}tt|d t	t
||| t||ddddg}tt|d t	t
||| t||d}tt|d t	t
||| t||dddddg}tt|d t	t
||| t||dddddg}tt|d t	t
||| t|t||gjd}t	|t||gj t|t||gjddddg}t	|t||gj t|}| }	d|dd d< d|dd d< tj||	d|d	}
t	|
| tj||	ddddg|d	}
t	|
| tj|t|	|	gjd|d	}t	|t||gj tj|t|	|	gjddddg|d	}t	|t||gj ddddg}t	t||dddg t	t||ddgddg tdd}||}t||d}t	t
||| t||dddg}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   )wr   r   r   r   y              ?y             )r   r^   r   Zlegfitrz   r2   rL   r   rB   r   r@   rI   r   Z
zeros_likecopy)r!   r   r   r   rZ   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$   )r   r^   r   legcompanionr    r   r   r   test_raises  s    zTestCompanion.test_raisesc                 C   s<   t ddD ],}dg| dg }tt|j||fk q
d S )Nr	   r   r   )r1   r   r   r   rY   )r!   r7   r   r   r   r   test_dimensions  s    zTestCompanion.test_dimensionsc                 C   s   t tddgd dk d S )Nr	   r   )r   r         )r   r   r   r    r   r   r   test_linear_root  s    zTestCompanion.test_linear_rootN)r'   r(   r)   r   r   r   r   r   r   r   r     s   r   c                   @   s   e Zd Zdd ZdS )	TestGaussc                 C   s|   t d\}}t |d}t|j| |}dt|  }|d d d f | | }t|t	d d}t|
 | d S )Nr+   c   r	   rN   )r   Zleggaussr   r2   r   r   sqrtZdiagonalr   Zeyesum)r!   r   r   r   vvZvdr:   r   r   r   test_100  s    zTestGauss.test_100N)r'   r(   r)   r   r   r   r   r   r     s   r   c                   @   sL   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dS )TestMiscc              	   C   s   t g }tt|dg tddD ]z}tttj dd| d dd d }t |}t 	||}d}t
t||d k tt |d d t|| q$d S )Nr	   r   r   r   r
   )r   legfromrootsr   r   r1   r2   cosrL   pir@   r   rB   r}   )r!   r;   r7   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legrootsr1   r2   rL   r   r   )r!   r7   r:   r;   r   r   r   test_legroots  s    zTestMisc.test_legrootsc                 C   sf   ddddg}t ttj|d tt||d d  tt|d|d d  tt|ddg d S )Nr   r
   r	   r   r   )r   r^   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 ]$}ttdg| dg t|  qd S NrV   r   r	   )r1   r   r   r}   rX   r!   r7   r   r   r   test_leg2poly,  s    zTestMisc.test_leg2polyc                 C   s2   t dD ]$}ttt| dg| dg  qd S r   )r1   r   r   r|   rX   r   r   r   r   test_poly2leg0  s    zTestMisc.test_poly2legc                 C   s*   t ddd}d}t|}t|| d S )Nr
   r	      rR   )r2   rL   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   Znumpyr2   Znumpy.polynomial.legendreZ
polynomialZlegendrer   Znumpy.polynomial.polynomialr   Znumpy.testingr   r   r   r   rI   ZL0ZL1ZL2ZL3ZL4ZL5ZL6ZL7ZL8ZL9rX   r   r   r*   rM   rq   r   r   r   r   r   r   r   r   r   r   <module>   s6    "C^i+3M