B
    F0dH                 @   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Zedd
ddgZedddddgZeddddddgZedddddddgZeddddddddgZedddddddddg	Zedddd dd!dd"dd#g
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 hermite module.

    )reduceN)polyval)assert_almost_equalassert_raisesassert_equalassert_         i      i   x   i`    ii  i @   ipi   i   i  ii4  i    i v  i i   i i   c             C   s   t j| ddS )Ngư>)Ztol)hermhermtrim)x r   U/var/www/html/venv/lib/python3.7/site-packages/numpy/polynomial/tests/test_hermite.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   Z
hermdomain)selfr   r   r   test_hermdomain!   s    zTestConstants.test_hermdomainc             C   s   t tjdg d S )Nr   )r   r   Zhermzero)r   r   r   r   test_hermzero$   s    zTestConstants.test_hermzeroc             C   s   t tjdg d S )Nr   )r   r   Zhermone)r   r   r   r   test_hermone'   s    zTestConstants.test_hermonec             C   s   t tjddg d S )Nr   g      ?)r   r   Zhermx)r   r   r   r   
test_hermx*   s    zTestConstants.test_hermxN)__name__
__module____qualname__r   r   r   r    r   r   r   r   r      s   r   c               @   sJ   e Zd ZedddZdd Zdd Zdd	 Zd
d Z	dd Z
dd ZdS )TestArithmetic   d   c             C   s   xt dD ]}xt dD ]}d| d| }tt||d }||  d7  < ||  d7  < tdg| dg dg| dg }tt|t||d qW q
W d S )N   zAt i=z, j=r   r   )err_msg)rangenpzerosmaxr   hermaddr   r   )r   ijmsgtgtresr   r   r   test_hermadd1   s    $zTestArithmetic.test_hermaddc             C   s   xt dD ]}xt 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W q
W d S )Nr(   zAt i=z, j=r   r   )r)   )r*   r+   r,   r-   r   Zhermsubr   r   )r   r/   r0   r1   r2   r3   r   r   r   test_hermsub;   s    $zTestArithmetic.test_hermsubc             C   sz   t tdgdg t tdgddg xJtddD ]<}dg| dg }dg|d  |ddg }t t|| q6W d S )Nr   r   g      ?r(   )r   r   Zhermmulxr*   )r   r/   Zserr2   r   r   r   test_hermmulxE   s    zTestArithmetic.test_hermmulxc       
      C   s   xt dD ]}dg| dg }t| j|}xt dD ]x}d| d| }dg| dg }t| j|}t||}t| j|}	tt||| d k| t|	|| |d q6W q
W d S )Nr(   r   r   zAt i=z, j=)r)   )r*   r   hermvalr   hermmulr   lenr   )
r   r/   Zpol1Zval1r0   r1   Zpol2Zval2Zpol3Zval3r   r   r   test_hermmulM   s    zTestArithmetic.test_hermmulc       
      C   s   xt dD ]}xt dD ]z}d| d| }dg| dg }dg| dg }t||}t||\}}tt|||}	tt|	t||d qW q
W d S )Nr(   zAt i=z, j=r   r   )r)   )r*   r   r.   Zhermdivr8   r   r   )
r   r/   r0   r1   cicjr2   Zquoremr3   r   r   r   test_hermdiv[   s    zTestArithmetic.test_hermdivc             C   s   x~t dD ]r}xlt dD ]`}d| d| }t|d }ttj|g| tdg}t||}tt	|t	||d qW q
W d S )Nr(   zAt i=z, j=r   )r)   )
r*   r+   aranger   r   r8   arrayZhermpowr   r   )r   r/   r0   r1   cr2   r3   r   r   r   test_hermpowf   s    zTestArithmetic.test_hermpowN)r!   r"   r#   r+   linspacer   r4   r5   r6   r:   r>   rB   r   r   r   r   r$   .   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 )TestEvaluationg      @g      ?g      ?zi,j->ijz
i,j,k->ijk)r&   r(   r	   r   g       @g      @c                s   t tg dgjd tdd  fddtD }xHtdD ]<}d| }|| }t dg| dg }t|||d q>W xltd	D ]`}d
g| }t	| t t dgj
| t t ddgj
| t t dddgj
| qW d S )Nr   r   r   c                s   g | ]}t  |qS r   )r   ).0rA   )r   r   r   
<listcomp>   s    z/TestEvaluation.test_hermval.<locals>.<listcomp>
   zAt i=)r)   r&   r	   )r   r   r7   sizer+   rC   Hlistr*   r   r,   shape)r   yr/   r1   r2   r3   Zdimsr   )r   r   test_hermvalz   s    


zTestEvaluation.test_hermvalc       
      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   rK   r   
ValueErrorr   	hermval2dc2dr   r+   onesr   rJ   )
r   x1x2x3y1y2y3r2   r3   zr   r   r   test_hermval2d   s    

zTestEvaluation.test_hermval2dc       
      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   rK   r   rM   r   	hermval3dc3dr   r+   rP   r   rJ   )
r   rQ   rR   rS   rT   rU   rV   r2   r3   rW   r   r   r   test_hermval3d   s    

zTestEvaluation.test_hermval3dc       
      C   sl   | j \}}}| j\}}}td||}t||| j}t|| td}	t|	|	| j}t	|j
dk d S )Nzi,j->ij)r	   r&   )r	   r&   r	   r&   )r   rK   r+   einsumr   Z
hermgrid2drO   r   rP   r   rJ   )
r   rQ   rR   rS   rT   rU   rV   r2   r3   rW   r   r   r   test_hermgrid2d   s    

zTestEvaluation.test_hermgrid2dc       
      C   sr   | j \}}}| j\}}}td|||}t|||| j}t|| td}	t|	|	|	| j}t	|j
dk d S )Nz
i,j,k->ijk)r	   r&   )r	   r&   r	   r&   r	   r&   )r   rK   r+   r\   r   Z
hermgrid3drZ   r   rP   r   rJ   )
r   rQ   rR   rS   rT   rU   rV   r2   r3   rW   r   r   r   test_hermgrid3d   s    

zTestEvaluation.test_hermgrid3dN)r!   r"   r#   r+   r@   Zc1dr\   rO   rZ   randomr   r   rK   rL   rX   r[   r]   r^   r   r   r   r   rD   p   s   rD   c               @   s   e Zd Zdd Zdd ZdS )TestIntegralc       
   	   C   sr  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 xFtdd	D ]8}dg|d  dg }tjdg||d
}t|ddg qW xztd	D ]n}|d }dg| dg }|gdg|  d| g }t|}tj|d|gd
}t|}tt	|t	| qW xZtd	D ]N}|d }dg| dg }t|}tj|d|gdd}tt
d|| qJW x~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	| qW xtd	D ]z}xrtdd	D ]d}	dg| dg }|d d  }x t|	D ]}tj|dd}q`W tj||	d}tt	|t	| q6W q&W xtd	D ]}xtdd	D ]r}	dg| dg }|d d  }x$t|	D ]}tj|d|gd
}qW tj||	tt|	d
}tt	|t	| qW qW xtd	D ]}xtdd	D ]v}	dg| dg }|d d  }x&t|	D ]}tj|d|gdd}q~W tj||	tt|	dd}tt	|t	| qTW qDW xtd	D ]}xtdd	D ]v}	dg| dg }|d d  }x&t|	D ]}tj|d|gdd}qW tj||	tt|	dd}tt	|t	| qW qW d S )Nr   g      ?r   r   )lbnd)scl)axisr	   r(   )mk)rd   re   ra   )rd   re   rb   )rd   )r   	TypeErrorr   hermintrM   r*   r   	poly2herm	herm2polyr   r7   list)
r   r/   re   r3   rb   polr2   Zhermpolrg   r0   r   r   r   test_hermint   s    




zTestIntegral.test_hermintc             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&   r   c             S   s   g | ]}t |qS r   )r   rg   )rE   rA   r   r   r   rF   '  s    z2TestIntegral.test_hermint_axis.<locals>.<listcomp>r   )rc   c             S   s   g | ]}t |qS r   )r   rg   )rE   rA   r   r   r   rF   +  s    r   c             S   s   g | ]}t j|d dqS )r&   )re   )r   rg   )rE   rA   r   r   r   rF   /  s    r&   )re   rc   )r+   r_   vstackTr   rg   r   )r   rO   r2   r3   r   r   r   test_hermint_axis#  s    

zTestIntegral.test_hermint_axisN)r!   r"   r#   rl   ro   r   r   r   r   r`      s   Sr`   c               @   s   e Z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 x@tdD ]4}dg| dg }tj|dd}tt|t| q.W x^tdD ]R}xLtddD ]>}dg| dg }tjtj||d|d}t	t|t| qW qpW xbtdD ]V}xPtddD ]B}dg| dg }tjtj||dd|dd}t	t|t| qW qW d S )	Nr   g      ?r   r(   r   )rd   r	   )rd   rb   )
r   rf   r   hermderrM   r*   r   r   rg   r   )r   r/   r2   r3   r0   r   r   r   test_hermder6  s     zTestDerivative.test_hermderc             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 )N)r&   r   c             S   s   g | ]}t |qS r   )r   rq   )rE   rA   r   r   r   rF   S  s    z4TestDerivative.test_hermder_axis.<locals>.<listcomp>r   )rc   c             S   s   g | ]}t |qS r   )r   rq   )rE   rA   r   r   r   rF   W  s    r   )r+   r_   rm   rn   r   rq   r   )r   rO   r2   r3   r   r   r   test_hermder_axisO  s    
z TestDerivative.test_hermder_axisN)r!   r"   r#   rr   rs   r   r   r   r   rp   4  s   rp   c               @   s8   e Zd Zejdd d Zdd Zdd Zdd	 Zd
S )
TestVander)r&   r(   r	   r   c             C   s   t d}t|d}t|jdk x:tdD ].}dg| dg }t|d|f t|| q.W t 	ddgddgdd	gg}t|d}t|jd
k x:tdD ].}dg| dg }t|d|f t|| qW d S )Nr&   )r&   r   r   r   r   .r	   r(      )r&   r	   r   )
r+   r?   r   
hermvanderr   rJ   r*   r   r7   r@   )r   r   vr/   coefr   r   r   test_hermvander`  s    
zTestVander.test_hermvanderc             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 )N)r	   r&   r   r	   )r   r(   ru   )r   r+   r_   r   Zhermvander2drN   dotflatr   r   rJ   )r   rQ   rR   rS   rA   vanr2   r3   r   r   r   test_hermvander2dq  s    
zTestVander.test_hermvander2dc             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   r+   r_   r   Zhermvander3drY   rz   r{   r   r   rJ   )r   rQ   rR   rS   rA   r|   r2   r3   r   r   r   test_hermvander3d~  s    
zTestVander.test_hermvander3dN)	r!   r"   r#   r+   r_   r   ry   r}   r   r   r   r   r   rt   \  s   rt   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_hermfit.<locals>.fc             S   s   | d | d  d S )Nr   r	   r   r   )r   r   r   r   f2  s    z$TestFitting.test_hermfit.<locals>.f2r   r   r   r	   )wru   r&   r   r(   y              ?y             g      ?)r   rM   r   Zhermfitrf   r+   rC   r   r9   r   r7   r@   rn   Z
zeros_likecopy)r   r   r   r   rK   Zcoef3Zcoef4Zcoef2dr   ZywZwcoef3Zwcoef2dZcoef1Zcoef2r   r   r   test_hermfit  sp    "


&zTestFitting.test_hermfitN)r!   r"   r#   r   r   r   r   r   r     s   r   c               @   s$   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 )Nr   )r   rM   r   hermcompanion)r   r   r   r   test_raises  s    zTestCompanion.test_raisesc             C   s@   x:t ddD ],}dg| dg }tt|j||fk qW d S )Nr   r(   r   )r*   r   r   r   rJ   )r   r/   rx   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   g      п)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 ttj
}t| | d S )Nr'   c   r   )r   Z	hermgaussrv   r+   rz   rn   sqrtZdiagonalr   eyepisum)r   r   r   rw   vvZvdr2   r   r   r   test_100  s    zTestGauss.test_100N)r!   r"   r#   r   r   r   r   r   r     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 )TestMiscc          	   C   s   t g }tt|dg xt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&W d S )Nr   r(   r   r	   r   )r   hermfromrootsr   r   r*   r+   cosrC   r   r7   r   r9   ri   )r   r3   r/   rootsrk   r2   r   r   r   test_hermfromroots  s    
*
zTestMisc.test_hermfromrootsc             C   sp   t tdgg  t tddgdg xBtddD ]4}tdd|}tt|}t t|t| q4W d S )Nr   g      r	   r(   r   )r   r   Z	hermrootsr*   r+   rC   r   r   )r   r/   r2   r3   r   r   r   test_hermroots	  s    zTestMisc.test_hermrootsc             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   rM   r   r   r   )r   rx   r   r   r   test_hermtrim  s
    zTestMisc.test_hermtrimc             C   s   t tddddg d S )Nr&   r   r	   )r   r   Zhermline)r   r   r   r   test_hermline  s    zTestMisc.test_hermlinec             C   s6   x0t dD ]$}ttdg| dg t|  q
W d S )NrG   r   r   )r*   r   r   ri   rI   )r   r/   r   r   r   test_herm2poly  s    zTestMisc.test_herm2polyc             C   s6   x0t dD ]$}ttt| dg| dg  q
W d S )NrG   r   r   )r*   r   r   rh   rI   )r   r/   r   r   r   test_poly2herm#  s    zTestMisc.test_poly2hermc             C   s6   t ddd}t |d  }t|}t|| d S )Nr(      r	   )r+   rC   expr   Z
hermweightr   )r   r   r2   r3   r   r   r   test_weight'  s    
zTestMisc.test_weightN)
r!   r"   r#   r   r   r   r   r   r   r   r   r   r   r   r     s   r   )'__doc__	functoolsr   numpyr+   Znumpy.polynomial.hermiteZ
polynomialZhermiter   Znumpy.polynomial.polynomialr   Znumpy.testingr   r   r   r   r@   ZH0ZH1ZH2ZH3ZH4ZH5ZH6ZH7ZH8ZH9rI   r   r   r$   rD   r`   rp   rt   r   r   r   r   r   r   r   r   <module>   s6   B^f(0M