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Zpol2Zval2Zpol3Zval3r r r � test_lagmulJ s zTestArithmetic.test_lagmulc 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+ Zlagdivr5 r r ) r r, r- r. �ci�cjr/ Zquo�remr0 r r r � test_lagdivX s zTestArithmetic.test_lagdivc 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 r5 �arrayZlagpowr r )r r, r- r. �cr/ r0 r r r � test_lagpowc s zTestArithmetic.test_lagpowN) r r r r( �linspacer r1 r2 r3 r7 r; r? r r r r r! + s r! c @ s� e Zd Ze�dddg�Ze�dee�Ze�deee�Zej � d�d d Z e e d d d g�Z d d � Z dd� Zdd� Zdd� Zdd� ZdS )�TestEvaluationg "@g ,�g @zi,j->ijz i,j,k->ijk)r# r% r r g �?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 )�.0r> )r r r � <listcomp>} s z.TestEvaluation.test_lagval.<locals>.<listcomp>� zAt i=)r& r# r ) r r r4 �sizer( r@ �Llistr' r r) �shape)r �yr, r. r/ r0 Zdimsr )r r � test_lagvalw s zTestEvaluation.test_lagvalc C s� | j \}}}| j\}}}tttj||d d� | j� || }t�||| j�}t||� t� d�} t�| | | j�}t |j dk� d S )Nr )r r# ) r rH r � ValueErrorr �lagval2d�c2dr r( �onesr rG ) r �x1�x2�x3�y1�y2�y3r/ r0 �zr r r � test_lagval2d� s z TestEvaluation.test_lagval2dc C s� | j \}}}| j\}}}tttj|||d d� | j� || | }t�|||| j�}t||� t� d�} t�| | | | j�}t |j dk� d S )Nr )r r# ) r rH r rJ r �lagval3d�c3dr r( rM r rG ) r rN rO rP rQ rR rS r/ r0 rT r r r � test_lagval3d� s z TestEvaluation.test_lagval3dc 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 rH r( �einsumr Z laggrid2drL r rM r rG ) r rN rO rP rQ rR rS r/ r0 rT r r r �test_laggrid2d� s z TestEvaluation.test_laggrid2dc 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 rH r( rY r Z laggrid3drW r rM r rG ) r rN rO rP rQ rR rS r/ r0 rT r r r �test_laggrid3d� s z TestEvaluation.test_laggrid3dN)r r r r( r= Zc1drY rL rW �randomr r rH rI rU rX rZ r[ r r r r rA m s rA c @ s e Zd 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)ra rb r^ )ra rb r_ )ra ) r � TypeErrorr �lagintrJ r' r �poly2lag�lag2polyr r4 �list) r r, rb r0 r_ �polr/ Zlagpolrd r- r r r � test_lagint� s� zTestIntegral.test_lagintc 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 rd )rB r> r r r rC $ s z1TestIntegral.test_lagint_axis.<locals>.<listcomp>r )r` c S s g | ]}t �|��qS r )r rd )rB r> r r r rC ( s r c S s g | ]}t j|d d��qS )r# )rb )r rd )rB r> r r r rC , s r# )rb r` )r( r\ �vstack�Tr rd r )r rL r/ r0 r r r �test_lagint_axis s z TestIntegral.test_lagint_axisN)r r r ri rm r r r r r] � s Sr] c @ s e Zd 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 )ra r )ra r_ ) r rc r �lagderrJ r' r r rd r )r r, r/ r0 r- r r r � test_lagder3 s zTestDerivative.test_lagderc C sl t j�d�}t �dd� |jD ��j}tj|dd�}t||� t �dd� |D ��}tj|dd�}t||� d S )N)r# rj c S s g | ]}t �|��qS r )r ro )rB r> r r r rC P s z3TestDerivative.test_lagder_axis.<locals>.<listcomp>r )r` c S s g | ]}t �|��qS r )r ro )rB r> r r r rC T s r )r( r\ rk rl r ro r )r rL r/ r0 r r r �test_lagder_axisL s z TestDerivative.test_lagder_axisN)r r r rp rq r r r r rn 1 s rn c @ s8 e Zd Zej�d�d d Zdd� Zdd� Zdd � Zd 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# rj rj r r .r r% r )r# r rj ) r( r< r � lagvanderr rG r' r r4 r= )r r �vr, �coefr r r �test_lagvander] s zTestVander.test_lagvanderc 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% r ) r r( r\ r Z lagvander2drK �dot�flatr r rG )r rN rO rP r> �vanr/ r0 r r r �test_lagvander2dn s zTestVander.test_lagvander2dc C s� | j \}}}tj�d�}t�|||dddg�}t�||||�}t�||j�}t||� t�|g|g|gdddg�}t |j dk� d S )N)r r# rj r r r# )r r% r ) r r( r\ r Z lagvander3drV rw rx r r rG )r rN rO rP r> ry r/ r0 r r r �test_lagvander3d{ s zTestVander.test_lagvander3dN) r r r r( r\ r rv rz r{ r r r r rr Y s rr c @ s e Zd Zdd� ZdS )� TestFittingc C s� dd� }t ttjdgdgd� t ttjdggdgd� t ttjg dgd� t ttjdgdgggd� t ttjddgdgd� t ttjdgddgd� t ttjdgdgddggd� t ttjdgdgdddgd� t ttjdgdgdg� t ttjdgdgdddg� 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�|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 � dd dd g}t t�||d�ddg� t t�||ddg�ddg� d S )Nc S s | | d | d S )Nr r r )r r r r �f� s z"TestFitting.test_lagfit.<locals>.fr r r r )�wr r# rj r% y �?y � �)r rJ r Zlagfitrc r( r@ r r6 r r4 r= rl Z zeros_like�copy) r r} r rH Zcoef3Zcoef4Zcoef2dr~ ZywZwcoef3Zwcoef2dr r r � test_lagfit� sZ " & zTestFitting.test_lagfitN)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 rJ r � lagcompanion)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� rG )r r, ru 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 Zlaggaussrs r( rw rl �sqrtZdiagonalr �eye�sum)r r r~ rt �vvZvdr/ r r r �test_100� s zTestGauss.test_100N)r r r r� r r r r r� � s r� c @ sD e Zd Zdd� Zdd� Zdd� Zdd� Zd d � Zd d � Zd d� 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 � lagfromrootsr r r' r( �cosr@ �pir4 r r6 rf )r r0 r, �rootsrh r/ r r r �test_lagfromroots� s * zTestMisc.test_lagfromrootsc 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 r r% r# )r r Zlagrootsr' r( r@ r� r )r r, r/ r0 r r r � test_lagroots� s zTestMisc.test_lagrootsc C sf ddddg}t ttj|d� tt�|�|d d� � tt�|d�|d d� � tt�|d�dg� d S )Nr r r r r" )r rJ r r r )r ru r r r � test_lagtrim� s zTestMisc.test_lagtrimc C s t t�dd�ddg� d S )Nr# rj rD r )r r Zlagline)r r r r � test_lagline s zTestMisc.test_laglinec C s6 x0t d�D ]$}tt�dg| dg �t| � q W d S )NrD r r )r' r r rf rF )r r, r r r � test_lag2poly s zTestMisc.test_lag2polyc C s6 x0t d�D ]$}tt�t| �dg| dg � q W d S )NrD r r )r' r r re rF )r r, r r r � test_poly2lag s zTestMisc.test_poly2lagc C s2 t �ddd�}t �| �}t�|�}t||� d S )Nr � � )r( r@ �expr Z lagweightr )r r r/ r0 r r r � test_weight s zTestMisc.test_weightN) r r r r� r� r� r� r� r� r� r r r r r� � s r� )$�__doc__� functoolsr �numpyr( Znumpy.polynomial.laguerreZ polynomialZlaguerrer Znumpy.polynomial.polynomialr 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