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r r r � test_legx* s zTestConstants.test_legxN)�__name__� __module__� __qualname__r# r$ r& r' r r r r r s r c @ sJ e Zd Ze�ddd�Zdd� Zdd� Zdd � Zd d � Z d d � Z dd� Z dS )�TestArithmeticr r �d c C s� t d�D ]�}t d�D ]�}d|� d|� �}t�t||�d �}|| d7 < || d7 < t�dg| dg dg| dg �}tt|�t|�|d� qqd 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 $zTestArithmetic.test_legaddc C s� t d�D ]�}t d�D ]�}d|� d|� �}t�t||�d �}|| d7 < || d8 < t�dg| dg dg| dg �}tt|�t|�|d� qqd S r- )r2 r3 r4 r5 r Zlegsubr r r7 r r r � test_legsub; s $zTestArithmetic.test_legsubc C s� t t�dg�dg� t t�dg�ddg� tdd�D ]T}d| d }dg| dg }dg|d || d|d | g }t t�|�|� q4d S )Nr r r r )r r Zlegmulxr2 )r" r8 �tmpZserr; r r r � test_legmulxE s $zTestArithmetic.test_legmulxc C s� t d�D ]�}dg| dg }t�| j|�}t d�D ]x}d|� d|� �}dg| dg }t�| j|�}t�||�}t�| j|�} tt|�|| d k|� t| || |d� q2qd S )Nr r r r. r/ r0 )r2 r �legvalr �legmulr �lenr ) r" r8 Zpol1Zval1r9 r: Zpol2Zval2Zpol3Zval3r r r � test_legmulN s zTestArithmetic.test_legmulc C s� t d�D ]�}t d�D ]z}d|� d|� �}dg| dg }dg| dg }t�||�}t�||�\}}t�t�||�|�} tt| �t|�|d� qqd S )Nr r. r/ r r r0 )r2 r r6 ZlegdivrB r r ) r" r8 r9 r: ZciZcjr; ZquoZremr< r r r � test_legdiv\ s zTestArithmetic.test_legdivc C s| t d�D ]n}t d�D ]`}d|� d|� �}t�|d �}ttj|g| t�dg��}t�||�}tt |�t |�|d� qqd S )Nr r. r/ r r0 ) r2 r3 �aranger r rB �arrayZlegpowr r )r" r8 r9 r: �cr; r< r r r � test_legpowg s zTestArithmetic.test_legpowN) r( r) r* r3 �linspacer r= r> r@ rD rE rI r r r r r+ . s r+ c @ s� e Zd Ze�g d��Ze�dee�Ze�deee�Zej � d�d d Z e e g d��Z dd � Z d d � Zd d � Zdd� Zdd� ZdS )�TestEvaluation)� @rL rL �i,j->ij� i,j,k->ijk�r r r r )� �?rL g @c s� t t�g dg�jd� t�dd�� � fdd�tD �}td�D ]<}d|� �}|| }t�� dg| dg �}t|||d� q<td �D ]^}d g| }t� |�� t t�� dg�j |� t t�� ddg�j |� t t�� g d ��j |� q�d S ) Nr r r c s g | ]}t � |��qS r r ��.0rH r r r � <listcomp>� � z.TestEvaluation.test_legval.<locals>.<listcomp>� r. r0 r r )r r r ) r r rA �sizer3 rJ �Llistr2 r r4 �shape)r" �yr8 r: r; r< 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 rY r � ValueErrorr �legval2d�c2dr r3 �onesr rX � r" �x1�x2�x3Zy1Zy2Zy3r; r< �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 r[ ) r rY r r] r �legval3d�c3dr r3 r` r rX ra 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 )NrM r\ )r r r r ) r rY r3 �einsumr Z leggrid2dr_ r r` r rX ra 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 )NrN r\ )r r r r r r ) r rY r3 rj r Z leggrid3drh r r` r rX ra r r r �test_leggrid3d� s z TestEvaluation.test_leggrid3dN)r( r) r* r3 rG Zc1drj r_ rh �randomr r rY rZ rf ri rk rl r r r r rK q s rK c @ s$ e Zd Zdd� Zdd� Zdd� ZdS )� TestIntegralc C s2 t ttjdgd� t ttjdgd� t ttjdgdddg� t ttjdgdgd� t ttjdgdgd� t ttjdgdd� tdd �D ]8}dg|d dg }tjdg||d �}t|ddg� q�td �D ]n}|d }dg| dg }|gdg| d| g }t�|�}tj|d|gd �}t�|�}tt |�t |�� q�td �D ]N}|d }dg| dg }t�|�}tj|d|gdd �}tt� d|�|� �q@td �D ]r}|d }dg| dg }|gdg| d| g }t�|�}tj|d|gdd �}t�|�}tt |�t |�� �q�td �D ]r}tdd �D ]`} dg| dg }|d d � }t| �D ]}tj|dd �}�qJtj|| d �}tt |�t |�� �q"�qtd �D ]�}tdd �D ]n} dg| dg }|d d � }t| �D ]}tj|d|gd �}�q�tj|| t t| ��d �}tt |�t |�� �q��q�td �D ]�}tdd �D ]r} dg| dg }|d d � }t| �D ]}tj|d|gdd �}�qPtj|| t t| ��dd �}tt |�t |�� �q(�qtd �D ]�}tdd �D ]r} dg| dg }|d d � }t| �D ]}tj|d|gdd �}�q�tj|| t t| ��dd �}tt |�t |�� �q��q�d S )Nr � �?r r )�lbnd)�scl��axisr r )�m�k)rt ru rp )rt ru rq �rt ) r � TypeErrorr �legintr] r2 r �poly2leg�leg2polyr rA �list) r" r8 ru r< rq �polr; Zlegpolrx r9 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 rx rQ r r r rS ( rT z1TestIntegral.test_legint_axis.<locals>.<listcomp>r rr c S s g | ]}t �|��qS r r� rQ r r r rS , rT r c S s g | ]}t j|d d��qS )r )ru r� rQ r r r rS 0 rT r )ru rs )r3 rm �vstack�Tr rx r �r" r_ r; r< 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 rx r! r r r �test_legint_zerointord4 s z#TestIntegral.test_legint_zerointordN)r( r) r* r} r� r� r r r r rn � s Srn c @ s$ e Zd Zdd� Zdd� Zdd� ZdS )�TestDerivativec C s t ttjdgd� t ttjdgd� td�D ]4}dg| dg }tj|dd�}tt|�t|�� q,td�D ]N}tdd�D ]>}dg| dg }tjtj||d�|d�}t t|�t|�� qxqjtd�D ]R}tdd�D ]B}dg| dg }tjtj||dd�|dd�}t t|�t|�� q�q�d S ) Nr ro r r r rv r )rt rq ) r rw r �legderr] r2 r r rx r )r" r8 r; r< r9 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 )Nr~ c S s g | ]}t �|��qS r �r r� rQ r r r rS W rT z3TestDerivative.test_legder_axis.<locals>.<listcomp>r rr c S s g | ]}t �|��qS r r� rQ r r r rS [ rT r )r3 rm r� r� r r� r r� 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 r r r )r r r� )r" rH 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 Zd Zej�d�d d Zdd� Zdd� Zdd � Zd d � Z d S ) � TestVanderrO r r c C s� t �d�}t�|d�}t|jdk� td�D ].}dg| dg }t|d|f t�||�� q,t � ddgddgdd gg�}t�|d�}t|jd k� td�D ].}dg| dg }t|d|f t�||�� q�d S ) Nr r~ r r r .r r � )r r r ) r3 rF r � legvanderr rX r2 r rA rG )r" r �vr8 �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 )Nr\ r r )r r r� ) r r3 rm r Z legvander2dr^ �dot�flatr r rX �r" rb rc rd rH Zvanr; r< r r r �test_legvander2dx s zTestVander.test_legvander2dc C s� | j \}}}tj�d�}t�|||g d��}t�||||�}t�||j�}t||� t�|g|g|gg d��}t |j dk� d S )N)r r r r� )r r � ) r r3 rm r Z legvander3drg r� r� r r rX r� r r r �test_legvander3d� s zTestVander.test_legvander3dc C s t ttjdd� d S )Nr� r )r r] r r� r! r r r �test_legvander_negdeg� s z TestVander.test_legvander_negdegN) r( r) r* r3 rm r r� r� r� r� r r r r r� c s r� 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 ttjdgdgg d �� t ttjdgdgg � t�dd�}||�}t�||d �}tt|�d � t t� ||�|� t�||g d ��}tt|�d � t t� ||�|� t�||d �}tt|�d� t t� ||�|� t�||g d��}tt|�d� t t� ||�|� t�||g d��}tt|�d� t t� ||�|� t�|t� ||g�j d �}t |t� ||g�j � t�|t� ||g�j g d ��}t |t� ||g�j � t� |�}|�� } d|dd d�< d|dd d�< tj|| d |d �} t | |� tj|| g d �|d �} t | |� tj|t� | | g�j d |d �} t | t� ||g�j � tj|t� | | g�j g d �|d �} t | t� ||g�j � g d�}t t�||d�ddg� t t�||ddg�ddg� t�dd�}||�}t�||d �} t t� || �|� t�||g d��} 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 )�w)r r r� r r )r r r r r )r r r r r )r r r r r )r y �?r y � �)r r r )r r] r Zlegfitrw r3 rJ r rC r rA rG r� Z zeros_like�copy)r" r� r� r rY 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 r% )r r] r � legcompanionr! r r r � test_raises� s zTestCompanion.test_raisesc C s< t dd�D ],}dg| dg }tt�|�j||fk� q d S )Nr r r )r2 r r r� rX )r" r8 r� r r r �test_dimensions� s z TestCompanion.test_dimensionsc C s t t�ddg�d dk� 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 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 rL ) r Zleggaussr� r3 r� r� ZsqrtZdiagonalr Zeye�sum)r" r r� r� ZvvZvdr; 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� tdd�D ]z}t�t�tj dd| d �dd d� �}t �|�}t � ||�}d}t t |�|d k� tt � |�d d� t||� q$d S )Nr r r r r ) r � legfromrootsr r r2 r3 ZcosrJ ZpirA r rC rz )r" r< r8 �rootsr| r; r r r �test_legfromroots s * zTestMisc.test_legfromrootsc C sl t t�dg�g � t t�ddg�dg� tdd�D ]4}t�dd|�}t�t�|��}t t|�t|�� q2d S )Nr r r� r r )r r Zlegrootsr2 r3 rJ r� r )r" r8 r; r< r r r � test_legroots s zTestMisc.test_legrootsc C sb g d�}t ttj|d� tt�|�|d d� � tt�|d�|d d� � tt�|d�dg� d S )N)r r r r r r r r r )r r] r r r )r" r� r r r � test_legtrim s zTestMisc.test_legtrimc C s t t�dd�ddg� d S )Nr r �r r Zlegliner! r r r � test_legline& s zTestMisc.test_leglinec C s t t�dd�dg� d S )Nr r r� r! r r r �test_legline_zeroscl) s z TestMisc.test_legline_zerosclc C s2 t d�D ]$}tt�dg| dg �t| � qd S �NrU r r )r2 r r rz rW �r" r8 r r r � test_leg2poly, s zTestMisc.test_leg2polyc C s2 t d�D ]$}tt�t| �dg| dg � qd S r� )r2 r r ry rW r� r r r � test_poly2leg0 s zTestMisc.test_poly2legc C s* t �ddd�}d}t�|�}t||� d S )Nr r � rP )r3 rJ r Z legweightr )r" r r; r< 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 Znumpyr3 Znumpy.polynomial.legendreZ polynomialZlegendrer Znumpy.polynomial.polynomialr Z numpy.testingr r r r rG ZL0ZL1ZL2ZL3ZL4ZL5ZL6ZL7ZL8ZL9rW r r r+ rK rn r� r� r� r� r� r� r r r r �<module> s6 C^i+3M
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