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Zpol1Zval1r/ r0 Zpol2Zval2Zpol3Zval3r r r � test_legmulN s zTestArithmetic.test_legmulc C s� x�t d�D ]�}x�t d�D ]z}d|� d|� �}dg| dg }dg| dg }t�||�}t�||�\}}t�t�||�|�} tt| �t|�|d� qW q W d S )Nr zAt i=z, j=r r )r( )r) r r- Zlegdivr8 r r ) r r. r/ r0 �ci�cjr1 Zquo�remr2 r r r � test_legdiv\ s zTestArithmetic.test_legdivc C s� x~t d�D ]r}xlt d�D ]`}d|� d|� �}t�|d �}ttj|g| t�dg��}t�||�}tt |�t |�|d� qW q W d S )Nr zAt i=z, j=r )r( ) r) r* �aranger r r8 �arrayZlegpowr r )r r. r/ r0 �cr1 r2 r r r � test_legpowg s zTestArithmetic.test_legpowN) r# r$ r% r* �linspacer r3 r4 r6 r: r> rB r r r r r& . s r& c @ s� e Zd Ze�dddg�Ze�dee�Ze�deee�Zej � d�d d Z e e dddg�Z d d � Z d d � Zd d� Zdd� Zdd� ZdS )�TestEvaluationg @zi,j->ijz i,j,k->ijk)r r r r g �?g @c s� t t�g dg�jd� t�dd�� � fdd�tD �}xHtd�D ]<}d|� �}|| }t�� dg| dg �}t|||d� q>W xltd �D ]`}d g| }t� |�� t t�� dg�j |� t t�� ddg�j |� t t�� dddg�j |� q�W d S ) Nr r r c s g | ]}t � |��qS r )r )�.0rA )r r r � <listcomp>� s z.TestEvaluation.test_legval.<locals>.<listcomp>� zAt i=)r( r r ) r r r7 �sizer* rC �Llistr) r r+ �shape)r �yr. r0 r1 r2 Zdimsr )r r � test_legval{ s zTestEvaluation.test_legvalc C s� | j \}}}| j\}}}tttj||d d� | j� || }t�||| j�}t||� t� d�} t�| | | j�}t |j dk� d S )Nr )r r ) r rK r � ValueErrorr �legval2d�c2dr r* �onesr rJ ) r �x1�x2�x3�y1�y2�y3r1 r2 �zr r r � test_legval2d� s z TestEvaluation.test_legval2dc C s� | j \}}}| j\}}}tttj|||d d� | j� || | }t�|||| j�}t||� t� d�} t�| | | | j�}t |j dk� d S )Nr )r r ) r rK r rM r �legval3d�c3dr r* rP r rJ ) r rQ rR rS rT rU rV r1 r2 rW 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 dk� d S )Nzi,j->ij)r r )r r r r ) r rK r* �einsumr Z leggrid2drO r rP r rJ ) r rQ rR rS rT rU rV r1 r2 rW 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 dk� d S )Nz i,j,k->ijk)r r )r r r r r r ) r rK r* r\ r Z leggrid3drZ r rP r rJ ) r rQ rR rS rT rU rV r1 r2 rW r r r �test_leggrid3d� s z TestEvaluation.test_leggrid3dN)r# r$ r% r* r@ Zc1dr\ rO rZ �randomr r rK rL rX r[ r] r^ r r r r rD q s rD c @ s$ e Zd Zdd� Zdd� Zdd� ZdS )� TestIntegralc C sr t ttjdgd� t ttjdgd� t ttjdgdddg� t ttjdgdgd� t ttjdgdgd� t ttjdgdd� xFtdd �D ]8}dg|d dg }tjdg||d �}t|ddg� q�W xztd �D ]n}|d }dg| dg }|gdg| d| g }t�|�}tj|d|gd �}t�|�}tt |�t |�� q�W xZtd �D ]N}|d }dg| dg }t�|�}tj|d|gdd �}tt� d|�|� �qJW x~td �D ]r}|d }dg| dg }|gdg| d| g }t�|�}tj|d|gdd �}t�|�}tt |�t |�� �q�W x�td �D ]z}xrtdd �D ]d} dg| dg }|d d � }x t| �D ]}tj|dd �}�q`W tj|| d �}tt |�t |�� �q6W �q&W x�td �D ]�}x�tdd �D ]r} dg| dg }|d d � }x$t| �D ]}tj|d|gd �}�q�W tj|| t t| ��d �}tt |�t |�� �q�W �q�W x�td �D ]�}x�tdd �D ]v} dg| dg }|d d � }x&t| �D ]}tj|d|gdd �}�q~W tj|| t t| ��dd �}tt |�t |�� �qTW �qDW x�td �D ]�}x�tdd �D ]v} dg| dg }|d d � }x&t| �D ]}tj|d|gdd �}�qW tj|| t t| ��dd �}tt |�t |�� �q�W �q�W d S )Nr g �?r r )�lbnd)�scl)�axisr r )�m�k)rd re ra )rd re rb )rd ) r � TypeErrorr �legintrM r) r �poly2leg�leg2polyr r7 �list) r r. re r2 rb �polr1 Zlegpolrg r/ r r r � test_legint� s� zTestIntegral.test_legintc C s� t j�d�}t �dd� |jD ��j}tj|dd�}t||� t �dd� |D ��}tj|dd�}t||� t �dd� |D ��}tj|d dd �}t||� d S ) N)r � c S s g | ]}t �|��qS r )r rg )rE rA r r r rF ( s z1TestIntegral.test_legint_axis.<locals>.<listcomp>r )rc c S s g | ]}t �|��qS r )r rg )rE rA r r r rF , s r c S s g | ]}t j|d d��qS )r )re )r rg )rE rA r r r rF 0 s r )re rc )r* r_ �vstack�Tr rg r )r rO r1 r2 r r r �test_legint_axis$ s z TestIntegral.test_legint_axisc C s t t�dd�d� d S )N)r r r r )r r rg )r r r r �test_legint_zerointord4 s z#TestIntegral.test_legint_zerointordN)r# r$ r% rl rp rq r r r r r` � s Sr` c @ s$ e Zd Zdd� Zdd� Zdd� ZdS )�TestDerivativec C s. t ttjdgd� t ttjdgd� x@td�D ]4}dg| dg }tj|dd�}tt|�t|�� q.W x^td�D ]R}xLtdd�D ]>}dg| dg }tjtj||d�|d�}t t|�t|�� q�W qpW xbtd�D ]V}xPtdd�D ]B}dg| dg }tjtj||dd�|dd�}t t|�t|�� q�W q�W d S ) Nr g �?r r r )rd r )rd rb ) r rf r �legderrM r) r r rg r )r r. r1 r2 r/ r r r � test_legder: s zTestDerivative.test_legderc C sl t j�d�}t �dd� |jD ��j}tj|dd�}t||� t �dd� |D ��}tj|dd�}t||� d S )N)r rm c S s g | ]}t �|��qS r )r rs )rE rA r r r rF W s z3TestDerivative.test_legder_axis.<locals>.<listcomp>r )rc c S s g | ]}t �|��qS r )r rs )rE rA r r r rF [ s r )r* r_ rn ro r rs r )r rO r1 r2 r r r �test_legder_axisS s z TestDerivative.test_legder_axisc C s d}t t�|d�dg� d S )N)r r r rm rm r )r r rs )r rA r r r � test_legder_orderhigherthancoeff_ s z/TestDerivative.test_legder_orderhigherthancoeffN)r# r$ r% rt ru rv r r r r rr 8 s rr c @ s@ e Zd Zej�d�d d Zdd� Zdd� Zdd � Zd d � Z d S ) � TestVander)r r r r c C s� t �d�}t�|d�}t|jdk� x:td�D ].}dg| dg }t|d|f t�||�� q.W t � ddgddgdd gg�}t�|d�}t|jd k� x:td�D ].}dg| dg }t|d|f t�||�� q�W d S ) Nr )r rm rm r r .r r � )r r rm ) r* r? r � legvanderr rJ r) r r7 r@ )r r �vr. �coefr r r �test_legvanderg s zTestVander.test_legvanderc C sx | j \}}}tj�d�}t�||ddg�}t�|||�}t�||j�}t||� t�|g|gddg�}t |j dk� d S )N)r r r r )r r rx ) r r* r_ r Z legvander2drN �dot�flatr r rJ )r rQ rR rS rA �vanr1 r2 r r r �test_legvander2dx s zTestVander.test_legvander2dc C s� | j \}}}tj�d�}t�|||dddg�}t�||||�}t�||j�}t||� t�|g|g|gdddg�}t |j dk� d S )N)r r rm r r r )r r � ) r r* r_ r Z legvander3drY r} r~ r r rJ )r rQ rR rS rA r r1 r2 r r r �test_legvander3d� s zTestVander.test_legvander3dc C s t ttjdd� d S )N)r r r r )r rM r ry )r r r r �test_legvander_negdeg� s z TestVander.test_legvander_negdegN) r# r$ r% r* r_ r r| r� r� r� r r r r rw c s rw c @ s e Zd Zdd� ZdS )� TestFittingc C s& dd� }dd� }t ttjdgdgd� t ttjdggdgd� t ttjg dgd� t ttjdgdgggd� t ttjddgdgd� t ttjdgddgd� t ttjdgdgddggd � t ttjdgdgdddgd � t ttjdgdgdg� t ttjdgdgddd g� t ttjdgdgg � t�dd�}||�}t�||d �}tt|�d � t t� ||�|� t�||dddd g�}tt|�d � t t� ||�|� t�||d �}tt|�d � t t� ||�|� t�||dddd d g�}tt|�d � t t� ||�|� t�||dd d ddg�}tt|�d � t t� ||�|� t�|t� ||g�j d �}t |t� ||g�j � t�|t� ||g�j dddd g�}t |t� ||g�j � t� |�}|�� } d|dd d�< d|dd d�< tj|| d |d �} t | |� tj|| dddd g|d �} t | |� tj|t� | | g�j d |d �} t | t� ||g�j � tj|t� | | g�j dddd g|d �} t | t� ||g�j � ddddg}t t�||d�ddg� t t�||ddg�ddg� t�dd�}||�}t�||d �} t t� || �|� t�||ddd 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 )Nrm r r r )r r r r �f2� s z#TestFitting.test_legfit.<locals>.f2r r r r )�wrx r rm r y �?y � �)r rM r Zlegfitrf r* rC r r9 r r7 r@ ro Z zeros_like�copy)r r� r� r rK Zcoef3Zcoef4Zcoef2dr� ZywZwcoef3Zwcoef2dZcoef1Zcoef2r r r � test_legfit� sp " & zTestFitting.test_legfitN)r# r$ r% r� r r r r r� � s r� c @ s$ e Zd Zdd� Zdd� Zdd� ZdS )� TestCompanionc C s" t ttjg � t ttjdg� d S )Nr )r rM r � legcompanion)r r r r � test_raises� s zTestCompanion.test_raisesc C s@ x:t dd�D ],}dg| dg }tt�|�j||fk� q W d S )Nr r r )r) r r r� rJ )r r. r{ r r r �test_dimensions� s z TestCompanion.test_dimensionsc C s t t�ddg�d dk� d S )Nr r )r r g �)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 Zd Zdd� ZdS )� TestGaussc C s| t �d�\}}t �|d�}t�|j| |�}dt�|�� � }|d d �d f | | }t|t� d�� d}t|� � |� d S )Nr' �c r g @) r Zleggaussry r* r} ro �sqrtZdiagonalr �eye�sum)r r r� rz �vvZvdr1 r r r �test_100� s zTestGauss.test_100N)r# r$ r% r� r r r r r� � s r� c @ sL e Zd Zdd� Zdd� Zdd� Zdd� Zd d � Zd d � Zd d� Z dd� Z dS )�TestMiscc C s� t �g �}tt|�dg� x�tdd�D ]z}t�t�tj dd| d �dd d� �}t �|�}t � ||�}d}t t |�|d k� tt � |�d d� t||� q&W d S )Nr r r r r ) r � legfromrootsr r r) r* �cosrC �pir7 r r9 ri )r r2 r. �rootsrk r1 r r r �test_legfromroots s * zTestMisc.test_legfromrootsc C sp t t�dg�g � t t�ddg�dg� xBtdd�D ]4}t�dd|�}t�t�|��}t t|�t|�� q4W d S )Nr r g �r r )r r Zlegrootsr) r* rC r� r )r r. r1 r2 r r r � test_legroots s zTestMisc.test_legrootsc C sf ddddg}t ttj|d� tt�|�|d d� � tt�|d�|d d� � tt�|d�dg� d S )Nr r r r r )r rM r r r )r r{ r r r � test_legtrim s zTestMisc.test_legtrimc C s t t�dd�ddg� d S )Nr rm )r r �legline)r r r r � test_legline& s zTestMisc.test_leglinec C s t t�dd�dg� d S )Nr r )r r r� )r r r r �test_legline_zeroscl) s z TestMisc.test_legline_zerosclc C s6 x0t d�D ]$}tt�dg| dg �t| � q W d S )NrG r r )r) r r ri rI )r r. r r r � test_leg2poly, s zTestMisc.test_leg2polyc C s6 x0t d�D ]$}tt�t| �dg| dg � q W d S )NrG r r )r) r r rh rI )r r. r r r � test_poly2leg0 s zTestMisc.test_poly2legc C s* t �ddd�}d}t�|�}t||� d S )Nr r � g �?)r* rC r Z legweightr )r r r1 r2 r r r � test_weight4 s zTestMisc.test_weightN) r# r$ r% r� r� r� r� r� r� r� r� r r r r r� s r� )'�__doc__� functoolsr �numpyr* Znumpy.polynomial.legendreZ polynomialZlegendrer Znumpy.polynomial.polynomialr Z numpy.testingr r r r r@ ZL0ZL1ZL2ZL3ZL4ZL5ZL6ZL7ZL8ZL9rI r r r& rD r` rr rw r� r� r� r� r r r r �<module> s6 "C^i+3M
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