U
|
P ±dR ã
|
@ 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$d% d%Z G d&d' d'Z G d(d) d)Z G d*d+ d+Z G d,d- d-Z!G d.d/ d/Z"G d0d1 d1Z#G d2d3 d3Z$G d4d5 d5Z%G d6d7 d7Z&G d8d9 d9Z'dS ):z Tests for chebyshev module.
|
|
é )ÚreduceN©Úpolyval)Úassert_almost_equalÚ assert_raisesÚ assert_equalÚassert_c C s t j| ddS )Ngíµ ÷Æ°>)Ztol)ÚchebÚchebtrim©Úx© r ú\d:\z\workplace\vscode\pyvenv\venv\Lib\site-packages\numpy/polynomial/tests/test_chebyshev.pyÚtrim s r é éÿÿÿÿé éýÿÿÿé iøÿÿÿé é iìÿÿÿé é iÐÿÿÿé iùÿÿÿé8 iÿÿÿé@ iàÿÿÿé i ÿÿÿé é iÿÿÿi° iÀýÿÿé c @ s e Zd Zdd Zdd ZdS )Ú TestPrivatec C sd t dD ]V}t dgdg| tj¡}t dg| dg dg| tj¡}t |¡}t|| qd S )Nr r r ç à?)ÚrangeÚnpÚarrayÚdoubler Z_cseries_to_zseriesr ©ÚselfÚiÚinpÚtgtÚresr r r Útest__cseries_to_zseries! s
|
$
|
z$TestPrivate.test__cseries_to_zseriesc C sd t dD ]V}t dg| dg dg| tj¡}t dgdg| tj¡}t |¡}t|| qd S )Nr r! r r )r" r# r$ r% r Z_zseries_to_cseriesr r& r r r Útest__zseries_to_cseries( s
|
$
|
z$TestPrivate.test__zseries_to_cseriesN)Ú__name__Ú
|
__module__Ú __qualname__r, r- r r r r r s r c @ s, e Zd Zdd Zdd Zdd Zdd Zd S )
|
Ú TestConstantsc C s t tjddg d S )Nr r )r r Z
|
chebdomain©r' r r r Útest_chebdomain2 s z TestConstants.test_chebdomainc C s t tjdg d S )Nr )r r Zchebzeror2 r r r Ú test_chebzero5 s zTestConstants.test_chebzeroc C s t tjdg d S ©Nr )r r Zcheboner2 r r r Ú test_chebone8 s zTestConstants.test_chebonec C s t tjddg d S )Nr r )r r Zchebxr2 r r r Ú
|
test_chebx; s zTestConstants.test_chebxN)r. r/ r0 r3 r4 r6 r7 r r r r r1 0 s r1 c @ s< e Zd Zdd Zdd Zdd Zdd Zd d
|
Zd d Zd S )ÚTestArithmeticc C s t dD ]}t dD ]}d| d| }t t||d ¡}|| d7 < || d7 < t dg| dg dg| dg ¡}tt|t||d qqd S ©Nr úAt i=ú, j=r r ©Úerr_msg)r" r# ÚzerosÚmaxr Úchebaddr r ©r' r( ÚjÚmsgr* r+ r r r Ú test_chebaddA s $zTestArithmetic.test_chebaddc C s t dD ]}t dD ]}d| d| }t t||d ¡}|| d7 < || d8 < t dg| dg dg| dg ¡}tt|t||d qqd S r9 )r" r# r> r? r Zchebsubr r rA r r r Ú test_chebsubK s $zTestArithmetic.test_chebsubc C sv t t dg¡dg t t dg¡ddg tddD ]<}dg| dg }dg|d dddg }t t |¡| q4d S )Nr r r r! )r r Zchebmulxr" )r' r( Zserr* r r r Ú test_chebmulxU s z TestArithmetic.test_chebmulxc C s¨ t dD ]}t dD ]}d| d| }t || d ¡}||| d7 < |t|| d7 < t dg| dg dg| dg ¡}tt|t||d qqd S )Nr r: r; r r! r r< )r" r# r> Úabsr Úchebmulr r rA r r r Ú test_chebmul] s $zTestArithmetic.test_chebmulc
|
C s t dD ]}t dD ]z}d| d| }dg| dg }dg| dg }t ||¡}t ||¡\}}t t ||¡|¡} tt| t||d qqd S )Nr r: r; r r r< )r" r r@ ZchebdivrH r r )
|
r' r( rB rC ÚciÚcjr* ZquoÚremr+ r r r Ú test_chebdivg s zTestArithmetic.test_chebdivc C s| t dD ]n}t dD ]`}d| d| }t |d ¡}ttj|g| t dg¡}t ||¡}tt |t ||d qqd S )Nr r: r; r r< )
|
r" r# Úaranger r rH r$ Zchebpowr r )r' r( rB rC Úcr* r+ r r r Ú test_chebpowr s zTestArithmetic.test_chebpowN) r. r/ r0 rD rE rF rI rM rP r r r r r8 ? s
|
|
|
r8 c @ s e Zd Ze dddg¡Ze dee¡Ze deee¡Zej d¡d d Z
|
e e
|
d dd
|
gZ d d Z d d Zdd Zdd Zdd ZdS )ÚTestEvaluationg @g @ç ø?úi,j->ijú
|
i,j,k->ijk©é r r r ç ð?g @c sè t t g dg¡jd t dd¡ fddtD }tdD ]<}d| }|| }t dg| dg ¡}t|||d q<td D ]`}d
|
g| }t |¡ t t dg¡j
|
| t t ddg¡j
|
| t t dddg¡j
|
| qd S ) Nr r r c s g | ]}t |qS r r ©Ú.0rO r r r Ú
|
<listcomp> s z/TestEvaluation.test_chebval.<locals>.<listcomp>é
|
r: r< rV r ) r r ÚchebvalÚsizer# ÚlinspaceÚTlistr" r r> Úshape)r' Úyr( rC r* r+ Zdimsr r r Ú 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 rV ) r ra r Ú
|
ValueErrorr Ú chebval2dÚc2dr r# Úonesr r` ©
|
r' Úx1Úx2Úx3Úy1Úy2Zy3r* r+ Úzr r r Útest_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 rc ) r ra r re r Ú chebval3dÚc3dr r# rh r r` ri r r r Útest_chebval3d¬ s
|
|
z TestEvaluation.test_chebval3dc
|
C sl | j \}}}| j\}}}t d||¡}t ||| j¡}t|| t d¡} t | | | j¡}t |j
|
dk d S )NrS rd )r rV r rV ) r ra r# Úeinsumr Z
|
chebgrid2drg r rh r r` ri r r r Útest_chebgrid2d½ s
|
|
z TestEvaluation.test_chebgrid2dc
|
C sr | j \}}}| j\}}}t d|||¡}t |||| j¡}t|| t d¡} t | | | | j¡}t |j
|
dk 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 Útest_chebgrid3dË s
|
|
z TestEvaluation.test_chebgrid3dN)r. r/ r0 r# r$ Zc1drt rg rr Úrandomr r ra rb rp rs ru rv r r r r rQ | s rQ c @ s e Zd Zdd Zdd ZdS )Ú 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 qtd D ]n}|d }dg| dg }|gdg| d| g }t |¡}tj|d|gd
|
}t |¡}tt |t | qÈtd 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 | qtd 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
|
}qÆtj|| t t| d
|
}tt |t | qqtd 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 }qÞtj|| t t| dd }tt |t | q¶q¨d S )Nr r! r r )Úlbnd)Úscl©Úaxisr r )ÚmÚk)r} r~ ry )r} r~ rz ©r} ) r Ú TypeErrorr Úchebintre r" r Ú poly2chebÚ cheb2polyr r\ Úlist)
|
r' r( r~ r+ rz Zpolr* Zchebpolr rB r r r Ú test_chebintÜ 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©rV r c S s g | ]}t |¡qS r ©r r rX r r r rZ 3 s z2TestIntegral.test_chebint_axis.<locals>.<listcomp>r r{ c S s g | ]}t |¡qS r r rX r r r rZ 7 s r c S s g | ]}t j|d dqS )rV )r~ r rX r r r rZ ; s rV )r~ r| )r# rw ÚvstackÚTr r r ©r' rg r* r+ r r r Útest_chebint_axis/ s
|
|
z TestIntegral.test_chebint_axisN)r. r/ r0 r
r r r r r rx Ú s Srx c @ s e Zd Zdd Zdd ZdS )ÚTestDerivativec C s t ttjdgd t ttjdgd tdD ]4}dg| dg }tj|dd}tt|t| q,tdD ]N}tddD ]>}dg| dg }tjtj||d|d}t t|t| qxqjtdD ]R}tddD ]B}dg| dg }tjtj||dd|dd}t t|t| qÐqÂd S ) Nr r! r r r r r )r} rz )
|
r r r Úchebderre r" r r r r )r' r( r* r+ rB r r r Ú 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 )Nr c S s g | ]}t |¡qS r ©r r rX r r r rZ _ s z4TestDerivative.test_chebder_axis.<locals>.<listcomp>r r{ c S s g | ]}t |¡qS r r rX r r r rZ c s r )r# rw r r r r r r r r r Útest_chebder_axis[ s
|
z TestDerivative.test_chebder_axisN)r. r/ r0 r r r r r r r @ s r c @ s8 e Zd Zej d¡d d Zdd Zdd Zdd Zd
|
S ) Ú
|
TestVanderrU r r c C sÎ t d¡}t |d¡}t|jdk tdD ].}dg| dg }t|d|f t ||¡ q,t ddgddgdd gg¡}t |d¡}t|jd
|
k tdD ].}dg| dg }t|d|f t ||¡ qd S ) NrV r r r r .r r é )rV r r )
|
r# rN r Ú
|
chebvanderr r` r" r r\ r$ )r' r Úvr( Úcoefr r r Útest_chebvanderl s
|
zTestVander.test_chebvanderc C sx | j \}}}tj d¡}t ||ddg¡}t |||¡}t ||j¡}t|| t |g|gddg¡}t |j
|
dk d S )Nrd r r )r r r ) r r# rw r Z chebvander2drf ÚdotÚflatr r r` ©r' rj rk rl rO Zvanr* r+ r r r Útest_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 rV r r r rV )r r é ) r r# rw r Z chebvander3drq r r r r r` r r r r Útest_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 Zd Zdd ZdS )Ú 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 Úf s z#TestFitting.test_chebfit.<locals>.fc S s | d | d d S )Nr r r r r r r r Úf2 s z$TestFitting.test_chebfit.<locals>.f2r r r r )Úwr rV r r y ð?y ð¿)r re r Zchebfitr r# r^ r Úlenr r\ r$ r Z
|
zeros_likeÚcopy)r' r r r ra Zcoef3Zcoef4Zcoef2dr¡ ZywZwcoef3Zwcoef2dZcoef1Zcoef2r r r Ú test_chebfit sp "
|
|
|
& zTestFitting.test_chebfitN)r. r/ r0 r¤ r r r r r s r c @ s, e Zd Zdd Zdd Zdd Zdd Zd S )
|
ÚTestInterpolatec C s ||d |d S r r )r' r r r r r ç s zTestInterpolate.fc C s( t ttj| jd t ttj| jd d S )Nr g $@)r re r Úchebinterpolater r r2 r r r Ú test_raisesê s zTestInterpolate.test_raisesc C s2 t ddD ]"}tt | j|¡j|d fk q
|
d S )Nr r )r" r r r¦ r r` )r' Údegr r r Útest_dimensionsî s z TestInterpolate.test_dimensionsc C sj dd }t ddd¡}tddD ]D}td|d D ]0}t |||f¡}tt ||¡|||dd q2q d S ) Nc S s | | S )Nr )r Úpr r r Úpowxô s z0TestInterpolate.test_approximation.<locals>.powxr r r[ r é )Údecimal)r# r^ r" r r¦ r r\ )r' r« r r¨ rª rO r r r Útest_approximationò s z"TestInterpolate.test_approximationN)r. r/ r0 r r§ r© r® r r r r r¥ å s r¥ c @ s$ e Zd Zdd Zdd Zdd ZdS )Ú TestCompanionc C s" t ttjg t ttjdg d S r5 )r re r Ú chebcompanionr2 r r r r§ s zTestCompanion.test_raisesc C s< t ddD ],}dg| dg }tt |¡j||fk 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 ddg¡d dk d S )Nr r )r r ç à¿)r r r° r2 r r r Útest_linear_root s z TestCompanion.test_linear_rootN)r. r/ r0 r§ r© r² r r r r r¯ þ s r¯ c @ s e Zd Zdd ZdS )Ú TestGaussc C s~ t d¡\}}t |d¡}t |j| |¡}dt | ¡ ¡ }|d d
d f | | }t|t d¡ tj
|
}t| ¡ | d S )Néd éc r ) r Z chebgaussr r# r r ÚsqrtZdiagonalr ZeyeÚpiÚsum)r' r r¡ r ÚvvZvdr* r r r Útest_100 s zTestGauss.test_100N)r. r/ r0 rº r r r r r³ s r³ c @ sT e Zd Zdd Zdd Zdd Zdd Zd d
|
Zd d Zd d Z dd Z
|
dd Z dS )ÚTestMiscc C s t g ¡}tt|dg tddD ]f}t t tj dd| d ¡dd d
¡}dg| dg }t |¡d|d }tt|t| q$d S )Nr r r r ) r Ú chebfromrootsr r r" r# Úcosr^ r· )r' r+ r( Úrootsr* r r r Útest_chebfromroots" s
|
*zTestMisc.test_chebfromrootsc C sl t t dg¡g t t ddg¡dg tddD ]4}t dd|¡}t t |¡¡}t t|t| q2d S )Nr r r± r r )r r Z chebrootsr" r# r^ r¼ r )r' r( r* r+ r r r Útest_chebroots+ s zTestMisc.test_chebrootsc C sf ddddg}t ttj|d tt |¡|d d
tt |d¡|d d
tt |d¡dg d S )Nr r r r r )r re r r
|
r )r' r r r r Ú test_chebtrim3 s
|
zTestMisc.test_chebtrimc C s t t dd¡ddg d S )NrV r )r r Zchebliner2 r r r Ú test_chebline> s zTestMisc.test_cheblinec C s2 t dD ]$}tt dg| dg ¡t| qd S ©Nr[ r r )r" r r r r_ ©r' r( r r r Útest_cheb2polyA s zTestMisc.test_cheb2polyc C s2 t dD ]$}tt t| ¡dg| dg qd S rà )r" r r r r_ rÄ r r r Útest_poly2chebE s zTestMisc.test_poly2chebc C sN t ddd¡dd
}dt d| ¡t d| ¡ }t |¡}t|| d S )Nr r é rW )r# r^ r¶ r Z
|
chebweightr )r' r r* r+ r r r Ú 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 )NrR r r gÌ;f æ¿gÌ;f æ?r g«LXèz¶ë¿g«LXèz¶ë?rV g( 1Ïkí¿gŦâ}Ø¿gŦâ}Ø?g( 1Ïkí?r )r re r Zchebpts1r ©r' r* r r r Ú 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 )NrR r r r r rV r± r! r g ð¿g¸Kf æ¿g¸Kf æ?rW r )r re r Zchebpts2r rÉ r r r Ú test_chebpts2^ s
|
zTestMisc.test_chebpts2N) r. r/ r0 r¿ rÀ rÁ r rÅ rÆ rÈ rÊ rË r r r r r» s r» )(Ú__doc__Ú functoolsr Únumpyr# Znumpy.polynomial.chebyshevZ
|
polynomialZ chebyshevr Znumpy.polynomial.polynomialr Z numpy.testingr r r r r ZT0ZT1ZT2ZT3ZT4ZT5ZT6ZT7ZT8ZT9r_ r r1 r8 rQ rx r r r r¥ r¯ r³ r» r r r r Ú<module> s:
|
=^f(0M
|
