bx9,
d Z ddlmZ ddlZddlmc mZ ddl m
Z
ddl m Z m
Z
mZmZ ej dg Z ej ddg Z ej g d Z ej g d Z ej g d
Z ej g d Z ej g d Z ej g d
Z ej g d Z ej g d Zeeeeeeeeeeg
Zd Z G d d Z G d d Z G d d Z G d d Z G d d Z! G d d Z" G d d Z# G d d Z$ G d! d" Z% G d# d$ Z&dS )%zTests for hermite module.
)reduceNpolyval)assert_almost_equal
assert_raises assert_equalassert_ )r )r ir ) r ir )r x r i`r )ir i r i r @ )r ipr i
r ir ) i r ir i4 r i r )
r i v r i r i r i r i c . t j | d S )Ngư>)tol)hermhermtrimxs w/builddir/build/BUILD/cloudlinux-venv-1.0.10/venv/lib64/python3.11/site-packages/numpy/polynomial/tests/test_hermite.pytrimr s = % % %% c & e Zd Zd Zd Zd Zd ZdS )
TestConstantsc > t t j ddg d S )Nr
)r r
hermdomainselfs r test_hermdomainz TestConstants.test_hermdomain! s T_r1g.....r c < t t j dg d S )Nr )r r hermzeror$ s r
test_hermzerozTestConstants.test_hermzero$ s T]QC(((((r c < t t j dg d S Nr
)r r hermoner$ s r test_hermonezTestConstants.test_hermone' s T\A3'''''r c > t t j ddg d S )Nr ?)r r hermxr$ s r
test_hermxzTestConstants.test_hermx* s TZ!R)))))r N)__name__
__module__ __qualname__r& r) r- r1 r r r r sP / / /) ) )( ( (* * * * *r r c V e Zd Z ej ddd Zd Zd Zd Zd Z d Z
d Z d
S ) TestArithmetic d c t d D ]}t d D ]}d| d| }t j t || dz }||xx dz
cc< ||xx dz
cc< t j dg|z dgz dg|z dgz }t
t | t | | d S N At i=, j=r
r err_msg)rangenpzerosmaxr hermaddr r r% ijmsgtgtress r test_hermaddzTestArithmetic.test_hermadd1 q @ @A1XX
@
@(a((Q((hs1ayy1}--A! A! lA3q5A3;A << T#YYS 3?????
@ @ @r c t d D ]}t d D ]}d| d| }t j t || dz }||xx dz
cc< ||xx dz cc< t j dg|z dgz dg|z dgz }t
t | t | | d S r< )rB rC rD rE r hermsubr r rG s r test_hermsubzTestArithmetic.test_hermsub; rN r c 4 t t j dg dg t t j dg ddg t dd D ]=}dg|z dgz }dg|dz
z |ddgz }t t j | | >d S )Nr r
r/ r= )r r hermmulxrB )r% rH serrK s r
test_hermmulxz TestArithmetic.test_hermmulxE s T]A3''!---T]A3''!R111q! 2 2A#a%1#+C#q1u+Ar
*C s++S 1 1 1 1 2 2r c t d D ]}dg|z dgz }t j | j | }t d D ]}d| d| }dg|z dgz }t j | j | }t j || }t j | j | } t t
| ||z dz k | t | ||z | d S )Nr= r r
r> r? r@ )rB r hermvalr hermmulr lenr )
r% rH pol1val1rI rJ pol2val2pol3val3s
r test_hermmulzTestArithmetic.test_hermmulM s q
B
BA3q5A3;D<--D1XX
B
B(a((Q((s1us{|DFD11|D$//|DFD11D QUQY.444#D$t)SAAAAA
B
B
Br c t d D ]}t d D ]}d| d| }dg|z dgz }dg|z dgz }t j || }t j || \ }}t j t j || | } t t
| t
| | d S )Nr= r> r? r r
r@ )rB r rF hermdivrX r r )
r% rH rI rJ cicjrK quoremrL s
r test_hermdivzTestArithmetic.test_hermdiv[ s q @ @A1XX
@
@(a((Q((SUaS[SUaS[l2r** <R00Sl4<R#8#8#>> T#YYS 3?????
@ @ @r c r t d D ]}t d D ]}d| d| }t j |dz }t t j |g|z t j dg }t j || }t t | t | | d S )Nr= r> r? r
r@ )
rB rC aranger r rX arrayhermpowr r )r% rH rI rJ crK rL s r test_hermpowzTestArithmetic.test_hermpowf s q @ @A1XX
@
@(a((Q((Ia!e$$ T\A3q5"(A3--@@l1a(( T#YYS 3?????
@ @ @r N) r2 r3 r4 rC linspacer rM rQ rU r` rg rm r5 r r r7 r7 . s B3 A@ @ @@ @ @2 2 2 B B B @ @ @@ @ @ @ @r r7 c e Zd Z ej g d Z ej dee Z ej deee Zej d dz dz
Z
e e
g d Z d Z
d Zd
Zd Zd Zd
S )TestEvaluation)g @ ?g ?i,j->ij
i,j,k->ijkr9 r= r r
)rq g @g @c t t j g dg j d t j dd fdt D }t d D ]>}d| }|| }t j dg|z dgz }t ||| ?t d D ]}d g|z }t j | t t j dg j
| t t j ddg j
| t t j g d
j
| d S ) Nr
r r" c 0 g | ]}t | S r5 r ).0rl r s r
z/TestEvaluation.test_hermval.. s! * * *qWQ]] * * *r
r> r@ r9 r )r
r r ) r r rW sizerC rn HlistrB r rD shape)r% yrH rJ rK rL dimsr s @r test_hermvalzTestEvaluation.test_hermvalz sU T\"qc**/333
KA * * * *E * * *r 7 7A !++CA$C,q1#a%1#+..C S# 6 6 6 6 6 q A AA3q5DA a!--3T : : : a!Q006 = = = a3394 @ @ @ @ A Ar c ~ | j \ }}}| j \ }}}t t t j ||d d | j ||z }t j ||| j }t || t j d } t j | | | j }t |j dk d S Nr r r9 ) r r} r
ValueErrorr hermval2dc2dr rC onesr r|
r% x1x2x3y1y2y3rK rL zs
r test_hermval2dz TestEvaluation.test_hermval2d s V
BV
B j$."b!fdhGGG enRTX..C%%%
GFOOnQ48,, V#$$$$$r c | j \ }}}| j \ }}}t t t j |||d d | j ||z |z }t j |||| j }t || t j d } t j | | | | j }t |j dk d S r ) r r} r r r hermval3dc3dr rC r r r| r s
r test_hermval3dz TestEvaluation.test_hermval3d s V
BV
B j$."b"RaR&$(KKK eBhnRR22C%%%
GFOOnQ1dh// V#$$$$$r c B | j \ }}}| j \ }}}t j d|| }t j ||| j }t || t j d } t j | | | j }t |j
dk d S )Nrr r )r r9 r r9 ) r r} rC einsumr
hermgrid2dr r r r r| r s
r test_hermgrid2dz TestEvaluation.test_hermgrid2d s V
BV
B i 2r**ob"dh//C%%%
GFOOoaDH-- X%&&&&&r c H | j \ }}}| j \ }}}t j d||| }t j |||| j }t || t j d } t j | | | | j }t |j
dk d S )Nrs r )r r9 r r9 r r9 ) r r} rC r r
hermgrid3dr r r r r| r s
r test_hermgrid3dz TestEvaluation.test_hermgrid3d s V
BV
B i b"b11ob"b$(33C%%%
GFOOoaAtx00 X%&&&&&r N)r2 r3 r4 rC rj c1dr r r randomr r r} r r r r r r5 r r rp rp p s
"(>>>
"
"C
")IsC
(
(C
")L#sC
0
0C "Q&A<<< AA A A*% % %"% % %" ' ' ' ' ' ' ' 'r rp c e Zd Zd Zd ZdS ) TestIntegralc T t t t j dgd t t t j dgd t t t j dgdddg t t t j dgdg t t t j dgdg t t t j dgd t dd D ]9}dg|dz
z dgz }t j dg||
}t
|ddg :t d D ]}|dz }dg|z dgz }|gdg|z z d|z gz }t j | }t j |d|g
}t j | }t
t | t | t d D ]a}|dz }dg|z dgz }t j | }t j |d|gd }t
t j
d| | bt d D ]}|dz }dg|z dgz }|gdg|z z d|z gz }t j | }t j |d|gd }t j | }t
t | t | t d D ]}t dd D ]~} dg|z dgz }|d d }t | D ]}t j |d
}t j ||
}t
t | t | t d D ]}t dd D ]} dg|z dgz }|d d }t | D ]}t j |d|g
}t j || t t |
}t
t | t | t d D ]}t dd D ]} dg|z dgz }|d d }t | D ]}t j |d|gd } t j || t t | d }t
t | t | t d D ]}t dd D ]} dg|z dgz }|d d }t | D ]}t j |d|gd } t j || t t | d }t
t | t | d S )Nr r/ r" r
)lbnd)sclaxisr r= )mk)r r r )r r r r ) r TypeErrorr hermintr rB r poly2herm herm2polyr rW list)
r% rH r rL r polrK hermpolr rI s
r test_hermintzTestIntegral.test_hermint s i sB777j$,R888j$,QA???j$,1#>>>>j$,!====i s<<<< q! . .AQU qc!A,sa1---C aW - - - - q 6 6Aa%C#a%1#+C#A+3'CnS))Gl7aA3777G.))C S 499 5 5 5 5 q > >Aa%C#a%1#+CnS))Gl7aA3R@@@G R 9 91 = = = = q 6 6Aa%C#a%1#+C#A+3'CnS))Gl7aA3A>>>G.))C S 499 5 5 5 5 q : :A1a[[
:
:c!eqck!!!f q 1 1A ,sa000CCl3!,,,#DIItCyy9999
: q : :A1a[[
:
:c!eqck!!!f q 8 8A ,saA3777CCl3!tE!HH~~>>>#DIItCyy9999
: q : :A1a[[
:
:c!eqck!!!f q A AA ,saA3R@@@CCl3!tE!HH~~BGGG#DIItCyy9999
: q : :A1a[[
:
:c!eqck!!!f q ? ?A ,saA3A>>>CCl3!tE!HH~~1EEE#DIItCyy9999
: : :r c t j d }t j d |j D j }t j |d }t
|| t j d |D }t j |d }t
|| t j d |D }t j |dd }t
|| d S )
Nr9 r
c 6 g | ]}t j | S r5 r r rw rl s r rx z2TestIntegral.test_hermint_axis..' 888Q a 888r r r c 6 g | ]}t j | S r5 r r s r rx z2TestIntegral.test_hermint_axis..+ 666Q a 666r r
c : g | ]}t j |d S )r9 )r r r s r rx z2TestIntegral.test_hermint_axis../ s' ;;;! a1---;;;r r9 )r r )rC r vstackTr r r r% r rK rL s r test_hermint_axisz TestIntegral.test_hermint_axis# s i v&&i88#%88899;l3Q'''C%%%i66#66677l3Q'''C%%%i;;s;;;<<l3!!,,,C%%%%%r N)r2 r3 r4 r r r5 r r r r s6 Q: Q: Q:f& & & & &r r c e Zd Zd Zd ZdS )TestDerivativec V t t t j dgd t t t j dgd t d D ]L}dg|z dgz }t j |d }t
t | t | Mt d D ]s}t dd D ]`}dg|z dgz }t j t j || | }t t | t | att d D ]u}t dd D ]b}dg|z dgz }t j t j ||d |d }t t | t | cvd S ) Nr r/ r" r= r
r r )r r )
r r r hermderr rB r r r r )r% rH rK rL rI s r test_hermderzTestDerivative.test_hermder6 s i sB777j$,R888 q / /A#a%1#+C,sa(((C cDII . . . . q : :A1a[[
:
:c!eqckl4<q#9#9#9Q???#DIItCyy9999
: q : :A1a[[
:
:c!eqckl4<qa#@#@#@A2NNN#DIItCyy9999
: : :r c h t j d }t j d |j D j }t j |d }t
|| t j d |D }t j |d }t
|| d S )Nr c 6 g | ]}t j | S r5 r r r s r rx z4TestDerivative.test_hermder_axis..S r r r r c 6 g | ]}t j | S r5 r r s r rx z4TestDerivative.test_hermder_axis..W r r r
)rC r r r r r r r s r test_hermder_axisz TestDerivative.test_hermder_axisO s i v&&i88#%88899;l3Q'''C%%%i66#66677l3Q'''C%%%%%r N)r2 r3 r4 r r r5 r r r r 4 s2 : : :2
&
&
&
&
&r r c ` e Zd Zej d dz dz
Zd Zd Zd ZdS )
TestVanderrt r r
c 8 t j d }t j |d }t |j dk t
d D ]7}dg|z dgz }t |d|f t j || 8t j ddgddgdd gg }t j |d }t |j d
k t
d D ]7}dg|z dgz }t |d|f t j || 8d S ) Nr9 r r
r r
.r r= )r9 r r
)
rC ri r
hermvanderr r| rB r rW rj )r% r vrH coefs r test_hermvanderzTestVander.test_hermvander` s) IaLL OAq ! !6!"""q B BA3q5A3;D #q& 4<4+@+@ A A A A
Hq!fq!fq!f- . . OAq ! !9$%%%q B BA3q5A3;D #q& 4<4+@+@ A A A A B Br c n | j \ }}}t j d }t j ||ddg }t j ||| }t j ||j }t || t j |g|gddg }t |j
dk d S )Nr r
r )r
r= r ) r rC r r hermvander2dr dotflatr r r| r% r r r rl vanrK rL s r test_hermvander2dz TestVander.test_hermvander2dq s V
B I V $ $ BA//nRQ''fS!&!!C%%% rdQF33 Y&'''''r c v | j \ }}}t j d }t j |||g d }t j |||| }t j ||j }t || t j |g|g|gg d }t |j
dk d S )N)r r9 r
)r
r r9 )r
r= ) r rC r r hermvander3dr r r r r r| r s r test_hermvander3dz TestVander.test_hermvander3d~ s V
B I Y ' ' BIII66nRR++fS!&!!C%%% rdRD)))<< Z'(((((r N) r2 r3 r4 rC r r r r r r5 r r r r \ sc
"Q&AB B B" ( ( ( ) ) ) ) )r r c e Zd Zd ZdS ) TestFittingc d }d }t t t j dgdgd t t t j dggdgd t t t j g dgd t t t j dgdgggd t t t j ddgdgd t t t j dgddgd t t t j dgdgddgg t t t j dgdgdddg t t t j dgdgdg t t t j dgdgg d t t t j dgdgg t j dd } || }t j ||d }t t | d
t t j
|| | t j ||g d }t t | d
t t j
|| | t j ||d
}t t | d t t j
|| | t j ||g d
}t t | d t t j
|| | t j ||g d }t t | d t t j
|| | t j |t j ||g j d }t |t j ||g j t j |t j ||g j g d }t |t j ||g j t j
| }| } d|dd d< d|dd d< t j || d | }
t |
| t j || g d | }
t |
| t j |t j | | g j d | } t | t j ||g j t j |t j | | g j g d | } t | t j ||g j g d}t t j ||d ddg t t j ||ddg ddg t j dd } || }t j ||d
} t t j
|| | t j ||g d }
t t j
||
| t | |
d S )Nc | | dz
z | dz
z S )Nr
r r5 r s r fz#TestFitting.test_hermfit..f s a!e9a!e$ $r c | dz | dz z dz S )Nr
r r
r5 r s r f2z$TestFitting.test_hermfit..f2 s a4!Q$;? "r r
r" r r )w)r r" r r9 r
)r r
r r9 r= )r r
r r9 r
)r r9 r
r
r )r
y ?r" y r/ )r r r
)r r r hermfitr rC rn r rY r rW rj r
zeros_likecopy)r% r r r r} coef3coef4coef2dr ywwcoef3wcoef2dcoef1coef2s r test_hermfitzTestFitting.test_hermfit s % % % # # # j$,aS"===i uqc1===i rA3:::i sqcUGQ???i 1vsA>>>i sQFA>>>i sQCseDDDDi sQCq!fEEEEj$,aS2%@@@j$,aS***EEEi sQC<<<
K1
AaDD Q1%%SZZ###DLE 2 2A666 Q<<<00SZZ###DLE 2 2A666 Q1%%SZZ###DLE 2 2A666 Q???33SZZ###DLE 2 2A666 Q???33SZZ###DLE 2 2A666 a1a&!1!1!3Q77FBHeU^$<$<$>??? a1a&!1!1!3\\\BBFBHeU^$<$<$>??? M!
VVXX!$Q$!$Q$ aQ!,,,FE*** a\\\Q777FE***,q"(B8"4"4"6Q???GRXuen%=%=%?@@@,q"(B8"4"4"6 JJJGRXuen%=%=%?@@@
DLAq 1 1Ar7;;;DLA1v 6 6B@@@ KA BqEE Q1%%DLE 2 2A666 Q999--DLE 2 2A666E5)))))r N)r2 r3 r4 r r5 r r r r s( H* H* H* H* H*r r c e Zd Zd Zd Zd ZdS )
TestCompanionc t t t j g t t t j dg d S r+ )r r r
hermcompanionr$ s r test_raiseszTestCompanion.test_raises s4 j$"4b999j$"4qc:::::r c t dd D ]8}dg|z dgz }t t j | j ||fk 9d S )Nr
r= r )rB r r r r| )r% rH r s r test_dimensionsz TestCompanion.test_dimensions s\ q! > >A3q5A3;D D&t,,2q!f< = = = = > >r c ` t t j ddg d dk d S )Nr
r )r r g п)r r r r$ s r test_linear_rootz TestCompanion.test_linear_root s/ "Aq6**40D899999r N)r2 r3 r4 r r r r5 r r r r sA ; ; ;> > >
: : : : :r r c e Zd Zd ZdS ) TestGaussc t j d \ }}t j |d }t j |j |z | }dt j | z }|d d d f |z |z }t |t j d t j t j
}t | | d S )Nr: c r
) r hermgaussr rC r r sqrtdiagonalr eyepisum)r% r r r vvvdrK s r test_100zTestGauss.test_100 s ~c""1
OAr " "
VAC!GQ
rwr{{}}%%
%
4[2
"Bs ,,, gbennAEEGGS)))))r N)r2 r3 r4 r r5 r r r r s# * * * * *r r c 8 e Zd Zd Zd Zd Zd Zd Zd Zd Z dS ) TestMiscc t j g }t t | dg t dd D ]}t j t j t
j dd|z dz dd d }t j | }t j || }d}t t | |dz k t t j | d d t || d S )Nr
r= r r r" )
r
hermfromrootsr r rB rC cosrn r rW r rY r )r% rL rH rootsr rK s r test_hermfromrootszTestMisc.test_hermfromroots s $$DIIs+++q! * *AF2;vq!A#'::14a4@AAE$U++C,uc**CC CHHA% & & & s 3 3B 7 ; ; ; S ) ) ) ) * *r c t t j dg g t t j ddg dg t dd D ]h}t j dd| }t j t j | }t t | t | id S )Nr
g r r= r" )r r hermrootsrB rC rn r r )r% rH rK rL s r test_hermrootszTestMisc.test_hermroots s DNA3 / /444DNAq6 2 2SE:::q! 6 6A+b!Q''C.!3C!8!899C S 499 5 5 5 5 6 6r c B g d}t t t j |d t t j | |d d t t j |d |d d t t j |d dg d S )N)r r" r
r r" r
r8 r r )r r r r r )r% r s r
test_hermtrimzTestMisc.test_hermtrim s }} j$-r::: T]4(($ss)444T]4++T#2#Y777T]4++aS11111r c P t t j dd ddg d S )Nr9 r
r )r r hermliner$ s r
test_hermlinezTestMisc.test_hermline s( T]1a((1a&11111r c t d D ]7}t t j dg|z dgz t | 8d S Nry r r
)rB r r r r{ r% rH s r test_herm2polyzTestMisc.test_herm2poly sR r G GA s1us{ ; ;U1X F F F F G Gr c t d D ]7}t t j t | dg|z dgz 8d S r )rB r r r r{ r s r test_poly2hermzTestMisc.test_poly2herm# sR r G GA uQx 8 81#a%1#+ F F F F G Gr c t j ddd }t j |dz }t j | }t || d S )Nr= r )rC rn expr
hermweightr )r% r rK rL s r test_weightzTestMisc.test_weight' sM KAr " "fadUmmoa C%%%%%r N)
r2 r3 r4 r r r r r r r r5 r r r r s
*
*
*6 6 6 2 2 22 2 2G G GG G G& & & & &r r )'__doc__ functoolsr numpyrC numpy.polynomial.hermite
polynomialhermiter numpy.polynomial.polynomialr
numpy.testingr r r r rj H0H1H2H3H4H5H6H7H8H9r{ r r r7 rp r r r r r r r r5 r r r0 sc ' ' ' ' ' ' ' ' ' / / / / / / RXqc]]
RXq!f
RXjjj
RXnnn
RX!!!""
RX&&&''
RX,,,--
RX33344
RX;;;<<
RX???@@ RRRRR0& & & * * * * * * * * ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@D[' [' [' [' [' [' [' ['|c& c& c& c& c& c& c& c&L%& %& %& %& %& %& %& %&P-) -) -) -) -) -) -) -)`J* J* J* J* J* J* J* J*Z : : : : : : : : * * * * * * * *&0& 0& 0& 0& 0& 0& 0& 0& 0& 0&r