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B �5�g*P � @ s� d Z ddlmZ ddlZddlm mZ ddl m Z ddl m Z m Z mZmZ dd� ZdgZddgZd dd gZdd dd gZddd ddgZddddddgZd ddddddgZddddddddgZddddddddd g Zdd dd dd dd dd!g Zeeeeeeeeeeg ZG 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'dS ):z Tests for chebyshev module. � )�reduceN)�polyval)�assert_almost_equal� assert_raises� assert_equal�assert_c C s t j| dd�S )Ng���ư>)Ztol)�cheb�chebtrim)�x� r �[/home/digitalm-up/venv/lib/python3.7/site-packages/numpy/polynomial/tests/test_chebyshev.py�trim s r � ���� ���� i����� � i��� � i���� i�����8 i�����@ i��� i ���� � i����i� i����� c @ s e Zd Zdd� Zdd� ZdS )� TestPrivatec C sh xbt d�D ]V}t�dgdg| tj�}t�dg| dg dg| tj�}t�|�}t||� q W d S )Nr r r g �?)�range�np�array�doubler Z_cseries_to_zseriesr )�self�i�inp�tgt�resr r r �test__cseries_to_zseries! s $ z$TestPrivate.test__cseries_to_zseriesc C sh xbt d�D ]V}t�dg| dg dg| tj�}t�dgdg| tj�}t�|�}t||� q W d S )Nr g �?r r )r r r! r" r Z_zseries_to_cseriesr )r# r$ r% r& r' r r r �test__zseries_to_cseries( s $ z$TestPrivate.test__zseries_to_cseriesN)�__name__� __module__� __qualname__r( r) r r r r r s r c @ s, e Zd Zdd� Zdd� Zdd� Zdd� Zd S ) � TestConstantsc C s t tjddg� d S )Nr r )r r Z chebdomain)r# r r r �test_chebdomain2 s z TestConstants.test_chebdomainc C s t tjdg� d S )Nr )r r Zchebzero)r# r r r � test_chebzero5 s zTestConstants.test_chebzeroc C s t tjdg� d S )Nr )r r Zchebone)r# r r r � test_chebone8 s zTestConstants.test_chebonec C s t tjddg� d S )Nr r )r r Zchebx)r# r r r � test_chebx; s zTestConstants.test_chebxN)r* r+ r, r. r/ r0 r1 r r r r r- 0 s r- c @ s< e Zd Zdd� Zdd� Zdd� Zdd� Zd d � Zd d � Zd S )�TestArithmeticc C s� x�t d�D ]�}x�t d�D ]�}d|� d|� �}t�t||�d �}|| d7 < || d7 < t�dg| dg dg| dg �}tt|�t|�|d� qW q W d S )Nr zAt i=z, j=r r )�err_msg)r r �zeros�maxr �chebaddr r )r# r$ �j�msgr& r' r r r � test_chebaddA s $zTestArithmetic.test_chebaddc C s� x�t d�D ]�}x�t d�D ]�}d|� d|� �}t�t||�d �}|| d7 < || d8 < t�dg| dg dg| dg �}tt|�t|�|d� qW q W d S )Nr zAt i=z, j=r r )r3 )r r r4 r5 r Zchebsubr r )r# r$ r7 r8 r& r' r r r � test_chebsubK s $zTestArithmetic.test_chebsubc C sz t t�dg�dg� t t�dg�ddg� xJtdd�D ]<}dg| dg }dg|d dddg }t t�|�|� q6W d S )Nr r r g �?)r r Zchebmulxr )r# r$ Zserr& r r r � test_chebmulxU s z TestArithmetic.test_chebmulxc C s� x�t d�D ]�}x�t d�D ]�}d|� d|� �}t�|| d �}||| d7 < |t|| � d7 < t�dg| dg dg| dg �}tt|�t|�|d� qW q W d S )Nr zAt i=z, j=r g �?r )r3 )r r r4 �absr �chebmulr r )r# r$ r7 r8 r& r' r r r � test_chebmul] s $zTestArithmetic.test_chebmulc C s� x�t d�D ]�}x�t d�D ]z}d|� d|� �}dg| dg }dg| dg }t�||�}t�||�\}}t�t�||�|�} tt| �t|�|d� qW q W d S )Nr zAt i=z, j=r r )r3 )r r r6 Zchebdivr= r r ) r# r$ r7 r8 �ci�cjr& Zquo�remr' r r r � test_chebdivg s zTestArithmetic.test_chebdivc 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 )r3 ) r r �aranger r r= r! Zchebpowr r )r# r$ r7 r8 �cr& r' r r r � test_chebpowr s zTestArithmetic.test_chebpowN) r* r+ r, r9 r: r; r> rB rE r r r r r2 ? s r2 c @ s� e Zd Ze�dddg�Ze�dee�Ze�deee�Zej � d�d d Z e e d dd g�Z d d � Z d d� Zdd� Zdd� Zdd� ZdS )�TestEvaluationg @g @g �?zi,j->ijz i,j,k->ijk)� 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 )�.0rD )r r r � <listcomp>� s z/TestEvaluation.test_chebval.<locals>.<listcomp>� zAt i=)r3 rG r ) r r �chebval�sizer �linspace�Tlistr r r4 �shape)r# �yr$ r8 r& r' Zdimsr )r r � test_chebval� s zTestEvaluation.test_chebvalc C s� | j \}}}| j\}}}tttj||d d� | j� || }t�||| j�}t||� t� d�} t�| | | j�}t |j dk� d S )Nr )r rG ) r rP r � ValueErrorr � chebval2d�c2dr r �onesr rO ) r# �x1�x2�x3�y1�y2�y3r& r' �zr r r �test_chebval2d� s z TestEvaluation.test_chebval2dc C s� | j \}}}| j\}}}tttj|||d d� | j� || | }t�|||| j�}t||� t� d�} t�| | | | j�}t |j dk� d S )Nr )r rG ) r rP r rR r � chebval3d�c3dr r rU r rO ) r# rV rW rX rY rZ r[ r& r' r\ 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 dk� d S )Nzi,j->ij)r rG )r rG r rG ) r rP r �einsumr Z chebgrid2drT r rU r rO ) r# rV rW rX rY rZ r[ r& r' r\ 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 dk� d S )Nz i,j,k->ijk)r rG )r rG r rG r rG ) r rP r ra r Z chebgrid3dr_ r rU r rO ) r# rV rW rX rY rZ r[ r& r' r\ r r r �test_chebgrid3d� s z TestEvaluation.test_chebgrid3dN)r* r+ r, r r! Zc1dra rT r_ �randomr r rP rQ r] r` rb rc r r r r rF | s rF 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$t| �D ]}tj|d|gd �}�q�W tj|| t t| ��d �}tt |�t |�� �q�W �q�W x�td �D ]�}x�tdd �D ]v} dg| dg }|d d � }x&t| �D ]}tj|d|gdd �}�q~W tj|| t t| ��dd �}tt |�t |�� �qTW �qDW x�td �D ]�}x�tdd �D ]v} dg| dg }|d d � }x&t| �D ]}tj|d|gdd �}�qW tj|| t t| ��dd �}tt |�t |�� �q�W �q�W d S )Nr g �?r r )�lbnd)�scl)�axisr r )�m�k)ri rj rf )ri rj rg )ri ) r � TypeErrorr �chebintrR r r � poly2cheb� cheb2polyr rK �list) r# r$ rj r' rg Zpolr& Zchebpolrl r7 r r r � test_chebint� s� zTestIntegral.test_chebintc 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)rG r c S s g | ]}t �|��qS r )r rl )rH rD r r r rI 3 s z2TestIntegral.test_chebint_axis.<locals>.<listcomp>r )rh c S s g | ]}t �|��qS r )r rl )rH rD r r r rI 7 s r c S s g | ]}t j|d d��qS )rG )rj )r rl )rH rD r r r rI ; s rG )rj rh )r rd �vstack�Tr rl r )r# rT r& r' r r r �test_chebint_axis/ s z TestIntegral.test_chebint_axisN)r* r+ r, rp rs r r r r re � s Sre 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 )ri r )ri rg ) r rk r �chebderrR r r r rl r )r# r$ r& r' r7 r r r � test_chebderB s zTestDerivative.test_chebderc C sl t j�d�}t �dd� |jD ��j}tj|dd�}t||� t �dd� |D ��}tj|dd�}t||� d S )N)rG r c S s g | ]}t �|��qS r )r ru )rH rD r r r rI _ s z4TestDerivative.test_chebder_axis.<locals>.<listcomp>r )rh c S s g | ]}t �|��qS r )r ru )rH rD r r r rI c s r )r rd rq rr r ru r )r# rT r& r' r r r �test_chebder_axis[ s z TestDerivative.test_chebder_axisN)r* r+ r, rv rw r r r r rt @ s rt c @ s8 e Zd Zej�d�d d Zdd� Zdd� Zdd � Zd S ) � TestVander)rG 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 ) NrG )rG r r r r .r r � )rG r r ) r rC r � chebvanderr rO r r rK r! )r# r �vr$ �coefr r r �test_chebvanderl s zTestVander.test_chebvanderc C sx | j \}}}tj�d�}t�||ddg�}t�|||�}t�||j�}t||� t�|g|gddg�}t |j dk� d S )N)r rG r r )r r ry ) r r rd r Z chebvander2drS �dot�flatr r rO )r# rV rW rX rD �vanr& r' r r r �test_chebvander2d} s z TestVander.test_chebvander2dc C s� | j \}}}tj�d�}t�|||dddg�}t�||||�}t�||j�}t||� t�|g|g|gdddg�}t |j dk� d S )N)r rG r r r rG )r r � ) r r rd r Z chebvander3dr^ r~ r r r rO )r# rV rW rX rD r� r& r' r r r �test_chebvander3d� s z TestVander.test_chebvander3dN) r* r+ r, r rd r r} r� r� r r r r rx h s rx 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_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 )�wry rG r r y �?y � �)r rR r Zchebfitrk r rM r �lenr rK r! rr Z zeros_like�copy)r# r� r� r rP Zcoef3Zcoef4Zcoef2dr� ZywZwcoef3Zwcoef2dZcoef1Zcoef2r r r � test_chebfit� sp " & zTestFitting.test_chebfitN)r* r+ r, r� r r r r r� � s r� c @ s, e Zd Zdd� Zdd� Zdd� Zdd� Zd S ) �TestInterpolatec C s ||d |d S )Nr r r )r# r r r r r� � s zTestInterpolate.fc C s( t ttj| jd� t ttj| jd� d S )Nr g $@)r rR r �chebinterpolater� rk )r# r r r � test_raises� s zTestInterpolate.test_raisesc C s6 x0t dd�D ]"}tt�| j|�j|d fk� q W d S )Nr r )r r r r� r� rO )r# �degr r r �test_dimensions� s z TestInterpolate.test_dimensionsc C sr dd� }t �ddd�}xVtdd�D ]H}xBtd|d �D ]0}t�|||f�}tt�||�|||�dd� q6W q"W d S ) Nc S s | | S )Nr )r �pr r r �powx� s z0TestInterpolate.test_approximation.<locals>.powxr r rJ r � )�decimal)r rM r r r� r rK )r# r� r r� r� rD r r r �test_approximation� s z"TestInterpolate.test_approximationN)r* r+ r, r� r� r� r� r r r r r� � s r� c @ s$ e Zd Zdd� Zdd� Zdd� ZdS )� TestCompanionc C s" t ttjg � t ttjdg� d S )Nr )r rR r � chebcompanion)r# r r r r� 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� rO )r# r$ r| r r r r� 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�� tj }t|� � |� d S )N�d �c r ) r Z chebgaussrz r r~ rr �sqrtZdiagonalr �eye�pi�sum)r# r r� r{ �vvZvdr& r r r �test_100 s zTestGauss.test_100N)r* r+ r, r� r r r r r� s r� c @ sT e Zd Zdd� Zdd� Zdd� Zdd� Zd d � Zd d � Zd d� Z dd� Z dd� Z dS )�TestMiscc C s� t �g �}tt|�dg� xttdd�D ]f}t�t�tj dd| d �dd d� �}dg| dg }t �|�d|d }tt|�t|�� q&W d S )Nr r r r ) r � chebfromrootsr r r r �cosrM r� )r# r' r$ �rootsr& r r r �test_chebfromroots" s *zTestMisc.test_chebfromrootsc 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 Z chebrootsr r rM r� r )r# r$ r& r' r r r �test_chebroots+ s zTestMisc.test_chebrootsc C sf ddddg}t ttj|d� tt�|�|d d� � tt�|d�|d d� � tt�|d�dg� d S )Nr r r r r )r rR r r r )r# r| r r r � test_chebtrim3 s zTestMisc.test_chebtrimc C s t t�dd�ddg� d S )NrG r )r r Zchebline)r# r r r � test_chebline> s zTestMisc.test_cheblinec C s6 x0t d�D ]$}tt�dg| dg �t| � q W d S )NrJ r r )r r r rn rN )r# r$ r r r �test_cheb2polyA s zTestMisc.test_cheb2polyc C s6 x0t d�D ]$}tt�t| �dg| dg � q W d S )NrJ r r )r r r rm rN )r# r$ r r r �test_poly2chebE s zTestMisc.test_poly2chebc C sN t �ddd�dd� }dt �d| �t �d| � }t�|�}t||� d S )Nr r � g �?)r rM r� r Z chebweightr )r# r r& r' r r r � test_weightI s zTestMisc.test_weightc C s� t ttjd� t ttjd� dg}tt�d�|� ddg}tt�d�|� dddg}tt�d �|� d d d d g}tt�d�|� d S )Ng �?r r g�;f���g�;f���?r g�LX�z��g�LX�z��?rG g( 1�k��gŜ��}ؿgŜ��}�?g( 1�k��?r )r rR r Zchebpts1r )r# r& r r r � test_chebpts1O s zTestMisc.test_chebpts1c C s� t ttjd� t ttjd� ddg}tt�d�|� dddg}tt�d�|� ddddg}tt�d �|� d d dd d g}tt�d�|� d S )Ng �?r r r r rG g �g �?r g �g�Kf���g�Kf���?g �?r )r rR r Zchebpts2r )r# r& r r r � test_chebpts2^ s zTestMisc.test_chebpts2N) r* r+ r, r� r� r� r� r� r� r� r� r� r r r r r� s r� )(�__doc__� functoolsr �numpyr Znumpy.polynomial.chebyshevZ polynomialZ chebyshevr Znumpy.polynomial.polynomialr Z numpy.testingr r r r r ZT0ZT1ZT2ZT3ZT4ZT5ZT6ZT7ZT8ZT9rN r r- r2 rF re rt rx r� r� r� r� r� r r r r �<module> s: =^f(0M
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