U
    O8c*P                  
   @   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 dd ZdgZddgZd	dd
gZddddgZdddddgZddddddgZd	ddddddgZddddddddgZdddddddddg	Zdddddddd dd!g
Zeeeeeeeeeeg
ZG d"d# d#ZG d$d% d%ZG d&d' d'ZG d(d) d)ZG d*d+ d+Z G d,d- d-Z!G d.d/ d/Z"G d0d1 d1Z#G d2d3 d3Z$G d4d5 d5Z%G d6d7 d7Z&G d8d9 d9Z'dS ):zTests for chebyshev module.

    )reduceNpolyval)assert_almost_equalassert_raisesassert_equalassert_c                 C   s   t j| ddS )Ngư>)Ztol)chebchebtrimx r   I/tmp/pip-unpacked-wheel-fd_gsd75/numpy/polynomial/tests/test_chebyshev.pytrim   s    r            i      i      i    i8   i@   i   i    	   ii  i   c                   @   s   e Zd Zdd Zdd ZdS )TestPrivatec                 C   sd   t dD ]V}tdgdg|  tj}tdg| dg dg|  tj}t|}t|| qd S )Nr   r   r         ?)rangenparraydoubler	   Z_cseries_to_zseriesr   selfiinptgtresr   r   r   test__cseries_to_zseries!   s
    $
z$TestPrivate.test__cseries_to_zseriesc                 C   sd   t dD ]V}tdg| dg dg|  tj}tdgdg|  tj}t|}t|| qd S )Nr   r!   r   r   )r"   r#   r$   r%   r	   Z_zseries_to_cseriesr   r&   r   r   r   test__zseries_to_cseries(   s
    $
z$TestPrivate.test__zseries_to_cseriesN)__name__
__module____qualname__r,   r-   r   r   r   r   r       s   r    c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestConstantsc                 C   s   t tjddg d S )Nr   r   )r   r	   Z
chebdomainr'   r   r   r   test_chebdomain2   s    zTestConstants.test_chebdomainc                 C   s   t tjdg d S )Nr   )r   r	   Zchebzeror2   r   r   r   test_chebzero5   s    zTestConstants.test_chebzeroc                 C   s   t tjdg d S Nr   )r   r	   Zcheboner2   r   r   r   test_chebone8   s    zTestConstants.test_chebonec                 C   s   t tjddg d S )Nr   r   )r   r	   Zchebxr2   r   r   r   
test_chebx;   s    zTestConstants.test_chebxN)r.   r/   r0   r3   r4   r6   r7   r   r   r   r   r1   0   s   r1   c                   @   s<   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd ZdS )TestArithmeticc                 C   s   t dD ]}t dD ]}d| d| }tt||d }||  d7  < ||  d7  < tdg| dg dg| dg }tt|t||d qqd S Nr   At i=, j=r   r   err_msg)r"   r#   zerosmaxr	   chebaddr   r   r'   r(   jmsgr*   r+   r   r   r   test_chebaddA   s    $zTestArithmetic.test_chebaddc                 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 r9   )r"   r#   r>   r?   r	   Zchebsubr   r   rA   r   r   r   test_chebsubK   s    $zTestArithmetic.test_chebsubc                 C   sv   t tdgdg t tdgddg tddD ]<}dg| dg }dg|d  dddg }t t|| q4d S )Nr   r   r   r!   )r   r	   Zchebmulxr"   )r'   r(   Zserr*   r   r   r   test_chebmulxU   s    zTestArithmetic.test_chebmulxc                 C   s   t dD ]}t dD ]}d| d| }t|| d }|||   d7  < |t||   d7  < tdg| dg dg| dg }tt|t||d qqd S )Nr   r:   r;   r   r!   r   r<   )r"   r#   r>   absr	   chebmulr   r   rA   r   r   r   test_chebmul]   s    $zTestArithmetic.test_chebmulc           
      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<   )r"   r	   r@   ZchebdivrH   r   r   )
r'   r(   rB   rC   cicjr*   Zquoremr+   r   r   r   test_chebdivg   s    zTestArithmetic.test_chebdivc                 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<   )
r"   r#   aranger   r	   rH   r$   Zchebpowr   r   )r'   r(   rB   rC   cr*   r+   r   r   r   test_chebpowr   s    zTestArithmetic.test_chebpowN)	r.   r/   r0   rD   rE   rF   rI   rM   rP   r   r   r   r   r8   ?   s   


r8   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       @      ?i,j->ij
i,j,k->ijk   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   .0rO   r   r   r   
<listcomp>   s     z/TestEvaluation.test_chebval.<locals>.<listcomp>
   r:   r<   rV   r   )r   r	   chebvalsizer#   linspaceTlistr"   r   r>   shape)r'   yr(   rC   r*   r+   Zdimsr   r   r   test_chebval   s    


zTestEvaluation.test_chebvalc           
      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   rV   )r   ra   r   
ValueErrorr	   	chebval2dc2dr   r#   onesr   r`   
r'   x1x2x3y1y2Zy3r*   r+   zr   r   r   test_chebval2d   s    

zTestEvaluation.test_chebval2dc           
      C   s   | j \}}}| j\}}}tttj|||d d | j || | }t|||| j}t|| t	d}	t|	|	|	| j}t
|jdk d S rc   )r   ra   r   re   r	   	chebval3dc3dr   r#   rh   r   r`   ri   r   r   r   test_chebval3d   s    

zTestEvaluation.test_chebval3dc           
      C   sl   | j \}}}| j\}}}td||}t||| j}t|| td}	t|	|	| j}t	|j
dk d S )NrS   rd   )r   rV   r   rV   )r   ra   r#   einsumr	   Z
chebgrid2drg   r   rh   r   r`   ri   r   r   r   test_chebgrid2d   s    

zTestEvaluation.test_chebgrid2dc           
      C   sr   | j \}}}| j\}}}td|||}t|||| j}t|| td}	t|	|	|	| j}t	|j
dk d S )NrT   rd   )r   rV   r   rV   r   rV   )r   ra   r#   rt   r	   Z
chebgrid3drr   r   rh   r   r`   ri   r   r   r   test_chebgrid3d   s    

zTestEvaluation.test_chebgrid3dN)r.   r/   r0   r#   r$   Zc1drt   rg   rr   randomr   r   ra   rb   rp   rs   ru   rv   r   r   r   r   rQ   |   s   rQ   c                   @   s   e Z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   r   )lbnd)sclaxisr   r   )mk)r}   r~   ry   )r}   r~   rz   r}   )r   	TypeErrorr	   chebintre   r"   r   	poly2cheb	cheb2polyr   r\   list)
r'   r(   r~   r+   rz   Zpolr*   Zchebpolr   rB   r   r   r   test_chebint   s    




zTestIntegral.test_chebintc                 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rV   r   c                 S   s   g | ]}t |qS r   r	   r   rX   r   r   r   rZ   3  s     z2TestIntegral.test_chebint_axis.<locals>.<listcomp>r   r{   c                 S   s   g | ]}t |qS r   r   rX   r   r   r   rZ   7  s     r   c                 S   s   g | ]}t j|d dqS )rV   )r~   r   rX   r   r   r   rZ   ;  s     rV   )r~   r|   )r#   rw   vstackTr	   r   r   r'   rg   r*   r+   r   r   r   test_chebint_axis/  s    

zTestIntegral.test_chebint_axisN)r.   r/   r0   r   r   r   r   r   r   rx      s   Srx   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 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   r!   r   r   r   r   r   )r}   rz   )
r   r   r	   chebderre   r"   r   r   r   r   )r'   r(   r*   r+   rB   r   r   r   test_chebderB  s     zTestDerivative.test_chebderc                 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   rX   r   r   r   rZ   _  s     z4TestDerivative.test_chebder_axis.<locals>.<listcomp>r   r{   c                 S   s   g | ]}t |qS r   r   rX   r   r   r   rZ   c  s     r   )r#   rw   r   r   r	   r   r   r   r   r   r   test_chebder_axis[  s    
z TestDerivative.test_chebder_axisN)r.   r/   r0   r   r   r   r   r   r   r   @  s   r   c                   @   s8   e Zd Zejdd d Zdd Zdd Zdd	 Zd
S )
TestVanderrU   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 )NrV   r   r   r   r   .r   r      )rV   r   r   )
r#   rN   r	   
chebvanderr   r`   r"   r   r\   r$   )r'   r   vr(   coefr   r   r   test_chebvanderl  s    
zTestVander.test_chebvanderc                 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 )Nrd   r   r   )r   r   r   )r   r#   rw   r	   Zchebvander2drf   dotflatr   r   r`   r'   rj   rk   rl   rO   Zvanr*   r+   r   r   r   test_chebvander2d}  s    
zTestVander.test_chebvander2dc                 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   rV   r   r   r   rV   )r   r      )r   r#   rw   r	   Zchebvander3drq   r   r   r   r   r`   r   r   r   r   test_chebvander3d  s    
zTestVander.test_chebvander3dN)	r.   r/   r0   r#   rw   r   r   r   r   r   r   r   r   r   h  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_chebfit.<locals>.fc                 S   s   | d | d  d S )Nr   r   r   r   r   r   r   r   f2  s    z$TestFitting.test_chebfit.<locals>.f2r   r   r   r   )wr   rV   r   r   y              ?y             )r   re   r	   Zchebfitr   r#   r^   r   lenr   r\   r$   r   Z
zeros_likecopy)r'   r   r   r   ra   Zcoef3Zcoef4Zcoef2dr   ZywZwcoef3Zwcoef2dZcoef1Zcoef2r   r   r   test_chebfit  sp    "


&zTestFitting.test_chebfitN)r.   r/   r0   r   r   r   r   r   r     s   r   c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestInterpolatec                 C   s   ||d  |d  S r   r   )r'   r   r   r   r   r     s    zTestInterpolate.fc                 C   s(   t ttj| jd t ttj| jd d S )Nr   g      $@)r   re   r	   chebinterpolater   r   r2   r   r   r   test_raises  s    zTestInterpolate.test_raisesc                 C   s2   t ddD ]"}tt| j|j|d fk q
d S )Nr   r   )r"   r   r	   r   r   r`   )r'   degr   r   r   test_dimensions  s    zTestInterpolate.test_dimensionsc                 C   sj   dd }t ddd}tddD ]D}td|d D ]0}t|||f}tt|||||dd q2q d S )	Nc                 S   s   | | S )Nr   )r   pr   r   r   powx  s    z0TestInterpolate.test_approximation.<locals>.powxr   r   r[   r      )decimal)r#   r^   r"   r	   r   r   r\   )r'   r   r   r   r   rO   r   r   r   test_approximation  s    z"TestInterpolate.test_approximationN)r.   r/   r0   r   r   r   r   r   r   r   r   r     s   r   c                   @   s$   e Zd Zdd Zdd Zdd ZdS )TestCompanionc                 C   s"   t ttjg  t ttjdg d S r5   )r   re   r	   chebcompanionr2   r   r   r   r      s    zTestCompanion.test_raisesc                 C   s<   t ddD ],}dg| dg }tt|j||fk q
d S )Nr   r   r   )r"   r   r	   r   r`   )r'   r(   r   r   r   r   r     s    zTestCompanion.test_dimensionsc                 C   s   t tddgd dk d S )Nr   r   )r   r         )r   r	   r   r2   r   r   r   test_linear_root	  s    zTestCompanion.test_linear_rootN)r.   r/   r0   r   r   r   r   r   r   r   r     s   r   c                   @   s   e Zd Zdd ZdS )	TestGaussc                 C   s~   t d\}}t |d}t|j| |}dt|  }|d d d f | | }t|t	d tj
}t| | d S )Nd   c   r   )r	   Z	chebgaussr   r#   r   r   sqrtZdiagonalr   Zeyepisum)r'   r   r   r   vvZvdr*   r   r   r   test_100  s    zTestGauss.test_100N)r.   r/   r0   r   r   r   r   r   r     s   r   c                   @   sT   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd ZdS )TestMiscc              	   C   s   t g }tt|dg tddD ]f}tttj dd| d dd d }dg| dg }t |d|d   }tt|t| q$d S )Nr   r   r   r   )	r	   chebfromrootsr   r   r"   r#   cosr^   r   )r'   r+   r(   rootsr*   r   r   r   test_chebfromroots"  s    
*zTestMisc.test_chebfromrootsc                 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	chebrootsr"   r#   r^   r   r   )r'   r(   r*   r+   r   r   r   test_chebroots+  s    zTestMisc.test_chebrootsc                 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   re   r	   r
   r   )r'   r   r   r   r   test_chebtrim3  s
    zTestMisc.test_chebtrimc                 C   s   t tddddg d S )NrV   r   )r   r	   Zchebliner2   r   r   r   test_chebline>  s    zTestMisc.test_cheblinec                 C   s2   t dD ]$}ttdg| dg t|  qd S Nr[   r   r   )r"   r   r	   r   r_   r'   r(   r   r   r   test_cheb2polyA  s    zTestMisc.test_cheb2polyc                 C   s2   t dD ]$}ttt| dg| dg  qd S r   )r"   r   r	   r   r_   r   r   r   r   test_poly2chebE  s    zTestMisc.test_poly2chebc                 C   sN   t ddddd }dt d| t d|   }t|}t|| d S )Nr   r      rW   )r#   r^   r   r	   Z
chebweightr   )r'   r   r*   r+   r   r   r   test_weightI  s     
zTestMisc.test_weightc                 C   s   t ttjd t ttjd dg}ttd| ddg}ttd| dddg}ttd	| d
dddg}ttd| d S )NrR   r   r   g;fg;f?r   gLXzgLXz?rV   g( 1kgŜ}ؿgŜ}?g( 1k?r   )r   re   r	   Zchebpts1r   r'   r*   r   r   r   test_chebpts1O  s    
zTestMisc.test_chebpts1c                 C   s   t ttjd t ttjd ddg}ttd| dddg}ttd| ddddg}ttd	| d
ddddg}ttd| d S )NrR   r   r   r   r   rV   r   r!   r   g      gKfgKf?rW   r   )r   re   r	   Zchebpts2r   r   r   r   r   test_chebpts2^  s    
zTestMisc.test_chebpts2N)r.   r/   r0   r   r   r   r   r   r   r   r   r   r   r   r   r   r      s   	r   )(__doc__	functoolsr   Znumpyr#   Znumpy.polynomial.chebyshevZ
polynomialZ	chebyshevr	   Znumpy.polynomial.polynomialr   Znumpy.testingr   r   r   r   r   ZT0ZT1ZT2ZT3ZT4ZT5ZT6ZT7ZT8ZT9r_   r    r1   r8   rQ   rx   r   r   r   r   r   r   r   r   r   r   r   <module>   s:   
=^f(0M