biC x d dl Z d dlmZ d dlZd dlmZmZmZmZ d dl Z
d dl m Z m Z m
Z
mZmZmZmZmZ d dlmZ d dlmZmZmZmZ d dlm Z d dl m Z m Z! d e
j e" jF z Z$ e e" jF Z%ejL ejN ejP ejR ejT gZ+ej0 gZ,e+e,z Z-d
Z.d Z/d Z0d
Z1d Z2d Z3d Z4ed Z5 G d d Z6 G d de6 Z7 G d de6 Z8d Z9d Z:d Z; G d d Zd Z?d Z@d! ZAd" ZBej j d#d$ej fd%ej fg d& ZGd' ZHej j d(g d) d* ZIej j d+g d) d, ZJej j d(g d) ej j d-d.d/g d0 ZKd1 ZLej j d(g d) ej j d-d.d/g d2 ZMd3 ZNd4 ZOej j d+e- d5 ZPej j d+ejL ejN ejP ejR g d6 ZQy)7 N) lru_cache)assert_assert_allclose assert_equalassert_array_equal)finfopowernanisclosesqrtexpsincos)optimize) _zeros_pynewton root_scalarOptimizeResult)getfullargspec_no_self) get_tests functions c | dz d| z z
dz
S N xs Z/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/scipy/optimize/tests/test_zeros.pyf1r! " s 6AE>A c d| z dz
S Nr r r s r f1_1r% & s q519r" c dd| z z S N @r r r s r f1_2r) * s Q;r" c B t | t | t | fS N)r! r% r) r s r f1_and_p_and_ppr, . s
a5$q'47 ""r" c 0 t | t | z
S r+ r
r r s r f2r/ 3 q6CF?r" c 0 t | t | z S r+ )r
r r s r f2_1r2 7 r0 r" c 0 t | t | z S r+ r. r s r f2_2r4 ; r0 r" c | S r+ r r s r f_lrucachedr6 @ s Hr" c e Zd Zd ej e j z Zd ej e j z Z ddZ ddZ
ddZ y)TestScalarRootFindersr Nc g }|xs g D ]0 }||vrddddj || }|j || 2 t d
i |}|j ddd |xs g D ]
}|| ||< |j d } |j d d
}
||d |
i|\ } } | | |fS # t $ r1 | t j t d d t
j | |fcY S w xY w) Nx0x1f)abfuncTF full_outputdisprootargsr ) getappenddictupdate Exceptionzeros RootResultsr
_EVALUEERR)
selftcmethod
sig_args_keyssig_kwargs_keyskwargs method_argsk
method_kwargsrC func_argsrrrs
r
_run_one_testz#TestScalarRootFinders._run_one_testK s $" &A{ T37;;AqA r!u % & v
T5 AB &B %A !!uM! % vvf~FF62& VKIiI=IEArR< V**3B8H8H&QSUU U Vs B$ $7C C c < t | }t |j t |j }t |j
|z
}|j
d| } g }
|dv r:|dv r&|
j
d |dv r|
j
d | j |d< n | j |d< | j |d < |D cg c]" } t | j | |f| |
d
| $ } } |xs g }| D
cg c] }
|
d j r|
}}
|D
cg c] }
|
d d
|vs|
}}
|D
cg c]
}
|
d d
}}
t t | |gdg g | j | j d} |j di | |d }|j d|d }| D
cg c] }
|
d j s|
}}
|D
cg c] }
|
d j }}
|D
cg c] }
|
d }}
t! ||| D
cg c]% \ }}}
t# |||| s|
d d
|vr|g|
z ' }}}}
|D cg c]+ \ }}}} | d |g| j dt% - }}}}} t! || D
cg c] \ } }
| dk7 s | g|
z }} }
t |t | gg dg | D cg c] } | d j& } } | D cg c] } | } } t | | yc c} w c c}
w c c}
w c c}
w c c}
w c c}
w c c}
w c c}
}}w c c} }}}w c c}
} w c c} w c c} w )zRun test-cases using the specified method and the supplied signature.
Extract the arguments for the method call from the test case
dictionary using the supplied keys for the method's signature.N)secantr halley)r r] fprime)r] fprime2tolxtolrtol)rQ rR r rE IDr ra rb )rb atolr< rD r )_getfullargspecr
kwonlyargslendefaultsrD rG ra rb listrZ convergedr rI rF rC zipr tuplerP )!rN testsrP name
known_failrS sig nDefaults nRequiredrQ rR rO resultseltnotcvgd notcvged_IDStolsrb re cvgdapproxcorrectr= cnotclosearootfulloutfvsfvresultmethod_from_result_expected_methods! r run_testsz TestScalarRootFinders.run_testsb s] f%CNN"# % MI- ),
1 1++ &&x0:%#**95 IIF5M !YYF6N !YYF6N CHI<> *** 7&3 +7/57 8 I I
%2
")B3Q1A1A3BB")M3SWT]*-L3MM189#B
9 9c,' 6B@ 4995 f F|xxtF|, &;#a&*:*:;;)-.##a&++..%)*c3q6**/267D/I 9 9)!Q 14d;B
Z7 C#I 9 9
-56 6(5!Wb r#wu7rvvfeg 67 6 6.1#x.@L72sB!GRD3JLLhH
.Q8=D E6fQi . . E E)01A411' 9?I CM9 <.*96L E1s` 'K 3K!K!K&"K&,K+ K04K0>K5 K:9*K?.0L
2
L L(L Lc L t || } | j |||fd|i| y)zuRun a collection of tests using the specified method.
The name is used to determine some optional arguments.
smoothnessrp N)r r )rN
collectionrP ro r rp rS rn s r run_collectionz$TestScalarRootFinders.run_collection s,
*<ufdLzLVLr" )NNr+ ) __name__
__module__ __qualname__npr floatepsra rb rZ r r r r" r r8 r8 E sZ
xrxx"" "D xrxx"" "D6:&*V.9:v CG"&Mr" r8 c e Zd Zej j de ej j de d Zej j de ej j de d Z ej j de ej j de d Z
ej j de d Z ej j de j e j e j g d Zej j de d Zd Zy
) TestBracketMethodsrP functionc , dt d }}t ||j ||g|| j | j }|j
sJ t
|j d| j | j |j |j k( sJ y N ? )rP bracketr: ra rb ?re rb ) r r r ra rb rk r rC rP rN rP r r= r> rX s r test_basic_root_scalarz)TestBracketMethods.test_basic_root_scalar st 471 1a&Q !YYTYY
8{{{$))$))Dxx6??***r" c dt d }} ||||| j | j d \ }}|j sJ t |d| j | j y )Nr r T)ra rb rA r r )r ra rb rk r )rN rP r r= r> rC rX s r test_basic_individualz(TestBracketMethods.test_basic_individual sX 4711adiidii%)+a {{{c Br" c R dt d }}t ||j t j ||g || j
| j }|j sJ t |j d| j
| j |j |j k( sJ y r ) r r r r arrayra rb rk r rC rP r s r test_bracket_is_arrayz(TestBracketMethods.test_bracket_is_array s 471 "!Q 0QTYY !YY
( {{{$))$))Dxx6??***r" c B | j d||j d y )Napsr r )r r )rN rP s r test_aps_collectionz&TestBracketMethods.test_aps_collection s E66??qIr" c r |t j k( rdhni }| j d||j | y )Nzfun7.4 chandrupatla)rp )rK ridderr r )rN rP rp s r test_chandrupatla_collectionz/TestBracketMethods.test_chandrupatla_collection s8 $*U\\#9hZr
NFFOO'1 3r" c h d\ }} |t ||d \ }}|j sJ t |d y )N)rE r TrA r )r6 rk r )rN rP r= r> rC rX s r test_lru_cached_individualz-TestBracketMethods.test_lru_cached_individual s7 1a=a{{{a r" c t j t d 5 t j d ddd d d d y # 1 sw Y y xY w)Nzmaxiter must be >= 0matchc | dz dz
S r r r s r z2TestBracketMethods.test_gh_22934.. 1a4!8 r" r rE maxiter)pytestraises
ValueErrorrK brentqrN s r
test_gh_22934z TestBracketMethods.test_gh_22934 s=
]]:-C
D @ LL+RB ? @ @ @s A A N)r r r r mark parametrizebracket_methodststutils_functionsr r r r rK bisectr toms748r r r r r" r r r sN [[ X7 [[ Z);<
+ = 8
+ [[ X7 [[ Z);< C = 8 C [[ X7 [[ Z);< + = 8 + [[ X7J 8J [[ X ell(-
(7 8383
[[ X7! 8!@r" r c e Zd Zd Zd Zd Zd Zd Zd Zd Z d Z
d Z d
Z d Z
d Zd
Zd Zd Zd Zd Zej* j- d e ddig d Zej* j- dddg d Zd Zy)
TestNewtonc n dg}|ddgz
}dD ]& }| j |t j dd| ( y )N aps.13.00z aps.12.05 aps.12.17r complexr r r rp r rK r rN rp r s r test_newton_collectionsz"TestNewton.test_newton_collections sL !]
{K00
, EJ
ELL(+,
E Er" c b g d}dD ]& }| j |t j dd| ( y )N)z aps.12.06z aps.12.07z aps.12.08z aps.12.09z aps.12.10z aps.12.11z aps.12.12z aps.12.13z aps.12.14z aps.12.15z aps.12.16r z aps.12.18r r r] r r r r s r test_halley_collectionsz"TestNewton.test_halley_collections s? 0
- EJ
ELL(+,
E Er" c t t t ft t t
ffD ] \ }}}t
j |dd }t || dd t
j |ddd }t || dd t
j |d|d }t || dd t
j |d||d }t || dd y )
Nr ư>r` r re )r; r` )r^ r` )r^ r_ r` ) r! r% r) r/ r2 r4 rK r r )rN r< f_1f_2r s r test_newtonzTestNewton.test_newton s t ,r4.>? 0KAsC Qt,A AaD!$ / QaT2A AaD!$ / Q#48A AaD!$ / Q#sEA AaD!$ / 0r" c f t t t ft t t
ffD ]4 \ }}}t
|dd|d }t ||j dd 6 t t t ft t t
ffD ]3 \ }}}t
|ddd }t ||j dd 5 y) z#Invoke newton through root_scalar()r r r )rP r: r^ ra r r rP r: ra N r! r% r) r/ r2 r4 r r rC rN r< r r rX s r test_newton_by_namez TestNewton.test_newton_by_name s t ,r4.>? 5KAsCAh1StLA AaffIqt 4 5 t ,r4.>? 5KAsCAh14@A AaffIqt 4 5r" c t t t ft t t
ffD ]b \ }}}t
|dddd }t ||j dd t
|dddd }t ||j dd d t t t ft t t
ffD ]3 \ }}}t
|ddd }t ||j dd 5 y
) z#Invoke secant through root_scalar()r\ r r r rP r: r; ra r r r r Nr r s r test_secant_by_namez TestNewton.test_secant_by_name s t ,r4.>? 5KAsCAh1FA AaffIqt 4Ah1FA AaffIqt 4 5
t ,r4.>? 5KAsCAh14@A AaffIqt 4 5r" c t t t ft t t
ffD ]5 \ }}}t
|dd||d }t ||j dd 7 y)z#Invoke halley through root_scalar()r] r r )rP r: r^ r_ ra r r Nr r s r test_halley_by_namez TestNewton.test_halley_by_name sV t ,r4.>? 5KAsCAh1#&$@A AaffIqt 4 5r" c , d}t j t | 5 t t dt
dd d d d d}t j t | 5 t t dt dd d d d y # 1 sw Y HxY w# 1 sw Y y xY w) Nz$fprime2 must be specified for halleyr r] r r )rP r^ r: ra z#fprime must be specified for halley)rP r_ r: ra )r r r r r! r% r) )rN messages r test_root_scalar_failz TestNewton.test_root_scalar_fail! s 8
]]:W
5 K 8DQT J K7
]]:W
5 L 8Tad K L L K K L Ls A> B
>B
Bc d }d }d }t j g d }t j t d dz dz }||dd dd
f}dgdz }t j
|||| }d } t
|| t j
||||| }t
|| t j
|||
}t
|| y)ztest newton with arrayc |d | |d z z }|d |d t j ||d z dz
z z
||d z z
| z
S )Nr r r r r r r r r
r r= r> s r r! z(TestNewton.test_array_newton..f1, sW !q1Q4xAQ4!A$"&&QqT"2S"899A!HDqH Hr" c |d |d z }|d t j |d |d z | |z z z |z |d |d z z
dz
S )Nr r r r r r r r s r r% z*TestNewton.test_array_newton..f1_10 s] !qt AaD5266!A$1+A"566:QqTAaD[H1L Lr" c z |d |d z }|d t j |d |d z | |z z z |dz z S )Nr r r r r r s r r) z*TestNewton.test_array_newton..f1_24 sK !qt AaD5266!A$1+A"566A= =r" )
g
4O@gNk@g]0J@g]Qݚt@g~EO5@g$J ?g~
5,@gXCڭ@gͮ9@@gӍ@
r g @& .>Mbp?n2d?)
gԩ˰@g9~4b'@gaq(@g0p @gk"z?g4se?gU+F@gwQu%@gd6)@g)i!@)r_ rD N)r r r rangerK r r )
rN r! r% r) a0a1rD r: r
x_expecteds
r test_array_newtonz TestNewton.test_array_newton) s I M > XX
ffU2Y #%
,Bub'2URZ LLRt ,
:& LLRtT ::& LLRd +:&r" c ^ d }d }t j dd }t j ||| }t || d t j
d }t j ||| }t || d t j || }t || d y )Nc | dz dz S )Nr ?r r s r r< z/TestNewton.test_array_newton_complex..fQ s q58Or" c yNr r r s r r^ z4TestNewton.test_array_newton_complex..fprimeT s r" r r )r^ )r fullrK r r ones)rN r< r^ tr s r test_array_newton_complexz$TestNewton.test_array_newton_complexP s
GGArN LLAf -!b!
GGAJ LLAf -!b! LLA !b!r" c ~ t j d ddgt j ddg g }t |d y) z8test secant doesn't continue to iterate zero derivativesc | | z |d z
S )Nr r r r= s r r z>TestNewton.test_array_secant_active_zero_der..e s qsQqTz r" gˡE}@r r: rD )f~@g @N)rK r r r r rN r s r !test_array_secant_active_zero_derz,TestNewton.test_array_secant_active_zero_derc s7 LL1uaj !xxR 1 2
434r" c t j d dgdz ddgf }t |d t j d d gdz d
d gf }t |d y ) Nc || dz z
S r$ r yzs r r z7TestNewton.test_array_newton_integers..k a!q&j r" @r g .@g 1@r )gNO@r c || dz z
S r$ r r s r r z7TestNewton.test_array_newton_integers..o r r" r r )rK r r r s r test_array_newton_integersz%TestNewton.test_array_newton_integersi sY LL03%!) $d|o
/AB LL01#'"b LABr" c t j t 5 t j d ddgd d d d t j t 5 t j d ddgd d }t |j d |j j sJ |j j rJ d d d y # 1 sw Y xY w# 1 sw Y y xY w) Nc | dz dz
S r$ r r
s r r z@TestNewton.test_array_newton_zero_der_failures..u r r" r c d| z S r$ r r s r r z@TestNewton.test_array_newton_zero_der_failures..u s
Q r" c | dz dz
S r$ r r s r r z@TestNewton.test_array_newton_zero_der_failures..x s QTAX r" c d| z S r$ r r s r r z@TestNewton.test_array_newton_zero_der_failures..y s
QqS r" Tr r ) r warnsRuntimeWarningrK r r rC zero_derallrk any)rN rt s r #test_array_newton_zero_der_failuresz.TestNewton.test_array_newton_zero_der_failuresr s
\\.
) H LL+b"X G H \\.
) /ll#5Bx#0dDG GLL! ,##'') )) ((,,. ... / / H H / /s C
A,C
CC"c d }d }d }d }t |dd| }t |ddd }t |j |j d
t d |j z |j t |d d||
}t |d dd }t |j |j d
t d|j z |j y )Nc | dz d| z z
dz
S r r r s r r! z+TestNewton.test_newton_combined..f1 s 6AE>A% %r" c d| z dz
S r$ r r s r r% z-TestNewton.test_newton_combined..f1_1 s q519 r" c dd| z z S r' r r s r r) z-TestNewton.test_newton_combined..f1_2 s Q; r" c 0 | dz d| z z
dz
d| z dz
dfS )Nr r r( r r s r r, z8TestNewton.test_newton_combined..f1_and_p_and_pp s' a4!A#:a<1Q+ +r" r r )rP r: r^ T:0yE>r r r] )rP r: r^ r_ )rP r: r_ )r r rC r function_calls)rN r! r% r) r, sol0sols r test_newton_combinedz TestNewton.test_newton_combined~ s & , 2h1TB/(qN 388$7Qs)))4+>+>?2h1T4P/(q$O 388$7Qs)))4+>+>?r" c d}g d}t d D ] }ddd}dt gdt ggd | D ]
\ }}|||< t j t
|fdd i|\ }} t
| j t || j t | j | j f|| |d
k( r | j | j d z k s(J t | j |d z | j z | j d z
}
t j t
|f|
d d |\ }} t
| j t || j t | j |
|d k( s[d
|
d} t j t | 5 t j t
|f|
dd |\ }} d d d y # 1 sw Y xY w)Nr )) )r r )r r T)r` rA r^ r_ rB Fr r )r rB zFailed to converge after z iterations, value is .*r )r r% r) rK r r! r rk r rC
iterationsr# r r RuntimeError) rN capsysr: expected_countsderivsrS rU vr rX itersmsgs r test_newton_full_outputz"TestNewton.test_newton_full_output s
3Ah TF !$9F"D)It+<=gvF
1 q
<<B=U=f=DAq AKK AFF # !,,(8(89?6;R S{''1<.func s 6C< r" c d| z S r$ r r s r dfuncz1TestNewton.test_deriv_zero_warning..dfunc s q5Lr" r FrB zDerivative was zeror )r r r rK r r r, )rN r? r7 s r test_deriv_zero_warningz"TestNewton.test_deriv_zero_warning sx
\\.
) 7 LLsE 6 7
]] B
>B
Bc t j ddg }|j }t t j |t j
t
|| y )N皙?r )r r copyr r r r )rN r: x0_copys r test_newton_does_not_modify_x0z)TestNewton.test_newton_does_not_modify_x0 s=
XXsAh
'')rvvr266"2w'r" c d }t |ddd }t |dddd }t |dddd
d }t ||j d d
|j j t k( sJ t ||j d d
|j j t k( sJ t ||j d d
|j j t k( sJ |j |j cxk( r|j k7 sJ J |j |j d z
cxk( r3|j cxk( r#|j cxk7 r|j dz k( sJ J y )Nc F t j | sJ t | S r+ )r isscalarr! r s r r< z+TestNewton.test_gh17570_defaults..f s ;;q> !>a5Lr" r r r r r\ r r T)r: r; r` rA r r r )r r r rC shaperm r+ r# )rN r< res_newton_defaultres_secant_default
res_secants r test_gh17570_defaultsz TestNewton.test_gh17570_defaults s )8 M (8a.2 4 A!tFqI
,112ADA!&&,,777,112ADA!&&,,777*//*AD9$$/// #'' ??1%001 2 1 2 1 #--%44q87 ((7 &007 &44Q6 7 8 7 8 7r" rS rP r c d }t j |fddd|}|j sJ t |j d y )Nc . |dk( sJ |dk( sJ | |z |z
S )Nr r r r s r r< z'TestNewton.test_args_gh19090..f s& 6M66M6FQJ r" r )r r r r )r r rk r rC )rN rS r< ress r test_args_gh19090z TestNewton.test_args_gh19090 s?
""1BB6B}} }!$r" r\ c d }t j |d| }|j sJ t t |j
d |j
j t j t j k( sJ y )Nc | dz dz
S )Nr r r r s r r< z)TestNewton.test_int_x0_gh19280..f s b519 r" r )r: rP g;f?) r r rk r absrC dtyper float64)rN rP r< rI s r test_int_x0_gh19280z TestNewton.test_int_x0_gh19280 s^
""16:}} }CHH
w/xx~~"**!5555r" c t j t d 5 t j t
dd d d d t j t d 5 t j t
ddd d d d t j t d
5 t j t
dd d d d y # 1 sw Y xY w# 1 sw Y VxY w# 1 sw Y y xY w) Nz
tol too smallr r ưr z maxiter must be greater than 0r i)r` r zx1 and x0 must be different)r; )r r r rK r r! r s r test_newton_special_parametersz)TestNewton.test_newton_special_parameters s ]]:_
= + LLQE * + ]]:-M
N 7 LLQD# 6 7 ]]:-J
L & LLQ1 % & &
+ + 7 7 & &s# C C CC CC$N)r r r r r r r r r r r r r r r r& r3 r9 r> rF r r r rH rJ rP rS r r" r r r s EE 05 55L%'N"&5 C
/@*"TH+( 8D [[ X80D'EF% G% [[ X(';< 6 = 6
&r" r c dfd} t j t j g}t x}}|D ], } || dd|| }t |||d|j
. y )Nr; c | z
S r+ r r rC s r r< ztest_gh_5555..f 4xr" ח cArd zmethod )re rb err_msg)rK r r TOLr r )r< methodsra rb rP rI rC s @r test_gh_5555r] sk D ||U\\*GD4 =Qc48c4")&//): ; ==r" c d } d}dt z }t j t j g}|D ] } || dd|| }t d||| y ) Nc | dk ry| dz
S )Nr g333333?r r s r r< ztest_gh_5557..f( s s7s7Nr" gR Q?r r r rd r` r )
_FLOAT_EPSrK r brenthr )r< re rb r\ rP rI s r test_gh_5557rc sX D z>D||U\\*G 8Q14d3St$78r" c d} d}| |fD ]Y \ }}}t j | t j t j fD ] } |fd|| }t || [ y )N)g |g ug y)g u@g |@g y@c 4 t j | z
S r+ r )r r| s r r z9test_brent_underflow_in_root_bracketing..A s 266!9Q; r" )r r
rK rb r r )underflow_scenariooverflow_scenarior= r> rC rP rI r| s @r 'test_brent_underflow_in_root_bracketingrh 6 sn
2-)+<= '
1d FF4L ||U\\2 'F.15C D# & ''r" c F e Zd Z ej ddddd Zd Zd Zy )
TestRootResultsr , . r r )rC r+ r# flagrP c F d}t t | j | y )Nz converged: True
flag: converged
function_calls: 46
iterations: 44
root: 1.0
method: newton)r reprrX )rN
expected_reprs r test_reprzTestRootResults.test_reprI s I
T$&&\=1r" c < t | j t sJ y r+ )
isinstancerX r r s r test_typezTestRootResults.test_typeO s $&&.111r" N)r r r rK rL rX rq rt r r" r rj rj E s) sr"1!) +A2 2r" rj c d } d }d }t dd }d}t j | ||||d }t | |g| d d
|gd z }d}t j | ||||d }t | |g| d d
y )
z&Test Halley's works with complex rootsc 6 |d | dz z |d | z z |d z S )Nr r r r r s r r< z test_complex_halley..fU s* tad{QqTAX%!,,r" c $ d|d z | z |d z S )Nr r r r r s r r z test_complex_halley..f_1X s 1Q4x!|ad""r" c X d|d z } t | }|g|z S # t $ r |cY S w xY w)Nr r )rh TypeError)r r= retvalsizes r r z test_complex_halley..f_2[ sA QqT #q6D 8d? " M s ))r r( )r( g @r
r )rD r^ r_ r` r r r N)r rK r r )r< r r r coeffsr
s r test_complex_halleyr} S s -## SA
F
QsCTJAAaM&M140
bA
F
QsCTJAAaM&M140r" c t j t j dz }d|z
d|z z }t j
5 t j ddt t j d |gdz }d d d t d
gdz d }t j
5 t j dd t t j d
|d }d d d t |d t j t d 5 t j d |d }d d d d}t j
5 t j dd t t j d |d }d d d t |d t j t d 5 t j d |d }d d d y # 1 sw Y SxY w# 1 sw Y xY w# 1 sw Y xY w# 1 sw Y xxY w# 1 sw Y y xY w)zBTest secant method with a non-zero dp, but an infinite newton stepg Q ?g i@r( ignorezRMS ofc | dz
dz S )Ng Y@r r r s r r z%test_zero_der_nz_dp..| s AI> r" r r: Nd g.ЗK.? Tolerance ofc | dz
dz S Nr r r r s r r z%test_zero_der_nz_dp.. AG> r" F)r: rB r r c | dz
dz S r r r s r r z%test_zero_der_nz_dp.. r r" Tg.ЗK.c | dz dz S r r r s r r z%test_zero_der_nz_dp.. r r" rE c | dz dz S r r r s r r z%test_zero_der_nz_dp.. r r" )r r r r warningscatch_warningsfilterwarningsr rK r r r r r, )r- dxp0r s r test_zero_der_nz_dpr o s
% $B "*r "B " A (NC LL1rdRi @A Aurz" $B " F ..I LL1bu EF Aq |> : E LL1bt DE %B " F ..I LL1bu EF Ar |> : E LL1bt DE E#A A F FE EF FE Es< 8G,5G G(5G4,H G G%(G14G= H c d} dd}d}d}||z | z |z }fd}t j t 5 t j |g dd|| gd
}|j
j
rJ d d d t j t 5 t j |d gdz d|| gd
}d d d y # 1 sw Y LxY w# 1 sw Y y xY w)
z(Test that array newton fails as expectedr; ga2U0*#?g@g\mJ A?gCl@c dt j | z dt j dz |z d|z t j | z z z z S )Nr r g
@gGz@)r r log10)darcy_frictionredia roughnesss r
colebrook_eqnz1test_array_newton_failures..colebrook_eqn s[ BGGN++BHHY_s 2 !BY )@ @ A B BB Cr" ){Gz?g?g vÖ?g333333?r T)r: r rD rA Nr ) r r r rK r rk r r r, )diameterrhomuureynolds_numberr r r s @r test_array_newton_failuresr s
HI
C B
AAg(2-OC
n % * 7!8,$
##'')))) *
| $
tfqj!!8,$
* *
s ;B<!C<CCc f d } t j | d }t |dt j t j t j | dgdz }t |dt j t j d }d }t j | d| }t |dt j t j t j | d|| }t |dt j t j t j | dgdz | }t |dt j t j t j | dgdz || }t |dt j t j t j | d
| }t |dt j t j t j | d
gdz | }t |dt j t j y ) z@Test that Newton or Halley don't warn if zero derivative at rootc | dz | dz z
S Nr r r r s r f_zeroder_rootz9test_gh8904_zeroder_at_root_fails..f_zeroder_root s !tad{r" r r r r c d| dz z d| z z
S r r r s r fderz/test_gh8904_zeroder_at_root_fails..fder s 1a4x!a% r" c d| z dz
S )Nr( r r r s r fder2z0test_gh8904_zeroder_at_root_fails..fder2 sQwr" )r: r^ )r: r^ r_ r N)rK r r _xtol_rtol)r rX r r s r !test_gh8904_zeroder_at_root_failsr su ^*AAqu{{=
^B/AAqu{{= ^$7AAqu{{=
^$ " $AAqu{{=
^BtAAqu{{=r" c dfd} fd}fd}d}t | ||d \ }}|j sJ t | |||d \ }}|j sJ y )
zzTest that Halley's method realizes that the 2nd order adjustment
is too big and drops off to the 1st order adjustment.r* c B t | dz t dz z
S r r r ns r r< ztest_gh_8881..f s" QAq#a% 00r" c . t | dz
z z S r r r s r fpztest_gh_8881..fp s QQ "1$$r" c L t | ddz z
z dz z dz
z z S r r r s r fppztest_gh_8881..fpp s3 QQqS! $A.#a%8::r" r; T)r^ rA r^ r_ rA N)r rk )r< r r r: rtrX r s @r test_gh_8881r sf
A1%;
B
1b 6EB ;;;
1bSd CEB ;;;r" c d } d }d }t j dgt j }t | |||d \ }}|j sJ t j ddgt j }t j t 5 t j | |||d }d d d d
}t j | |||d }|j j sJ y # 1 sw Y CxY w) z_
Test that shape is preserved for array inputs even if fprime or fprime2 is
scalar
c | dz S r$ r r s r r< z,test_gh_9608_preserve_array_shape..f s !t r" c d| z S r$ r r s r r z-test_gh_9608_preserve_array_shape..fp 1u r" c yr$ r r s r r z.test_gh_9608_preserve_array_shape..fpp s r" r rN Tr Nc t t j t j | dt j S )Nr r )r r rB float32r s r fpp_arrayz4test_gh_9608_preserve_array_shape..fpp_array s! wwrxx{ARZZ88r" )
r r r r rk r r
IndexErrorrK r ) r< r r r: r rX x0_arrayr r s r !test_gh_9608_preserve_array_shaper s
2$bjj )B 1bSd CEB ;;;xxR
3H z "
xCT
9 \\ 8B tF !! !
s C..C7z maximum_iterations,flag_expectedr r c
t j d ddddd| dd }|d j |k( sJ |t j k( r|d j | k( sJ y
|t j
k( r|d j | k sJ y
y
) z]
Test that if the maximum iterations is exceeded that the flag is not
converged.
c * d| z dz
| z dz | z dz
S )Ng333333?gffffff@g333333 @g @r r s r r z6test_gh9254_flag_if_maxiter_exceeded..& s! CECK?S(!+c1 r" i r r TFr@ r N)rK r rm CONVERRr+ CONVERGED)maximum_iterations
flag_expectedr s r $test_gh9254_flag_if_maxiter_exceededr s \\1 RT4!3u&F !9>>] ** *
%ay##'9999 %// )ay##&8888
*r" c d } d }t j t 5 t j | d|d ddd t j
t d 5 t j | d| ddd t j | t d d | }t |t d
d y# 1 sw Y |xY w# 1 sw Y MxY w) zBTest that if disp is true then zero derivative raises RuntimeErrorc | | z dz S Nr r r s r r< z/test_gh9551_raise_error_if_disp_true..f5 r r" c d| z S r$ r r s r f_pz1test_gh9551_raise_error_if_disp_true..f_p8 s s
r" r Fr8 NzY^Derivative was zero\. Failed to converge after \d+ iterations, value is [+-]?\d*\.\d+\.$r g $@r ) r r r rK r r r, r r )r< r rC s r $test_gh9551_raise_error_if_disp_truer 2 s
n % .
QSu-. /
0 " QS! "
<<74. 4DD'#s+,. ." "s B5 C5B>C
solver_name)r rb r r r c d }t t | }t j t d 5 ||dd d d d y # 1 sw Y y xY w)Nc " t j S r+ )r r
r s r r< ztest_gh3089_8394..fK s vv
r" zThe function value at x...r r r )getattrrK r r r )r r< solvers r test_gh3089_8394r F sD
UK
(F z)E F q!Q s AA rP c fdd_ t d| }|j du sJ |j j d sJ |j
j k( sJ t
|j |j v sJ y )Nc N xj dz
c_ t j S r )_countr r
r r< s r r< ztest_gh18171..fY s A
vv
r" r )r r )r rP FzThe function value at x)r r rk rm
startswithr# strrC )rP rI r< s @r test_gh18171r S s| AH
a
7C ==E !! ! 88 8 99 9 )) ) sxx=CHH $$ $r" rs_interfaceTFc |rd nt t | }fdd_ |ddd }|r |j j k( sJ y |d j j k( sJ y )Nc t | ||f S N)r r r< r= r> rS s r r z%test_function_calls..k QA)G r" c > xj dz
c_ | dz dz
S )Nr r )callsr s r r< z test_function_calls..fn s 1 !taxr" r r Tr r )r rK r r# )r r r rI r< s @r test_function_callsr e sr H#*5+#> AG
Art
,C!!QWW,,,1v$$///r" c d } t j t d 5 t | ddd }ddd j rJ |j
d k( sJ t j t d 5 t
| ddd
d d
}ddd |j rJ |j
d k( sJ y# 1 sw Y xY w# 1 sw Y 5xY w)zDTest that zero slope with secant method results in a converged=Falsec @ | t j | | z z dz
S )NgQ ?r r s r lhsz*test_gh_14486_converged_false..lhs} s 2661"Q$< $&&r" r r r\ g333333ÿr )rP r: r; Nzconvergence errorFT)r: r; rB rA r )r r r r rk rm r )r rI s r test_gh_14486_converged_falser { s '
nN ; B#h5SAB}} 88* ** * nN ; MSUsDI!LM}} 88* ** *B B
M Ms B-1B9-B69Cc |rd nt t | }d }t j t d 5 ||ddd d d d ||dd d }|r|n|d
}|j
sJ t
|j d d
||dt d d }|r|n|d
}|j
sJ t
|j d d
y # 1 sw Y xY w)Nc t | ||f S r r r s r r z test_gh5584.. r r" c d| z S )NgN~hr r s r r< ztest_gh5584..f s axr" z ...must have different signsr g gٿTr g?r r r" r z-0.0) r rK r r r rk r rC r )r r r r< rI s r test_gh5584r s H#*5+#>
z)G H 0q$$/0 D#4
0C #3q6C ===CHHad+ D%-T
:C #3q6C ===CHHad+0 0s
C Cc d } d}t j t j }t j
| dd|d|z } | | }t j
| dd|d|z } | | }||k sJ d|d z d
d |d
d }t
j t |
5 t j
| dd||d z d d d y # 1 sw Y y xY w)Nc | dz d| z z
dz
S )Nr r r r r s r r< ztest_gh13407..f s !taczA~ r" gY ng|=g _Br rd r zrtol too small \(r gz < z\)r ) r r r r rK r r r r )r< ra r r; r! x4f4r s r test_gh13407r s D
((5/
C q%Dqu =B
2B q%Dqu =B
2B
7N7 #3q5)3s1gR8G z 1 =
a4c!e<= = =s # C
Cc d } t | d }t |dd t | ddd }t |j dd y ) Nc | dz
S r r )r s r r< z&test_newton_complex_gh10103..f r r" y ? ?r g-q=r y @ ?r\ )r: r; rP )r r r rC )r< rI s r test_newton_complex_gh10103r s>
D/CC'
aDVH
=CCHHae,r" c d}t j t | 5 | t ddd d d d y # 1 sw Y y xY w)Nz2'float' object cannot be interpreted as an integerr r r g R@r )r r ry r! )rP r s r test_maxiter_int_check_gh10236r s; CG y 0 ,r3U+, , ,s 8Ac j dd}dt j t j z dz }fd}t j
t d 5 | |dd |d
t d d d t j
t d 5 | |dd |d
| d d d y # 1 sw Y .f rW r" zxtol too smallr rX rY rR )rD ra rb zrtol too smallr )r r r r r r r r[ )rP rD rtolbadr< rC s @r test_bisect_special_parameterr s
D &D"((5/%%%)G
z)9 : =
asE<= z)9 : @
asDw?@ @= =@ @s B B) B&)B2)Rr functoolsr r
numpy.testingr r r r numpyr r r r
r r r
r r scipyr scipy.optimizer rK r r r scipy._lib._utilr rf scipy.optimize._tstutilsr r r r r r[ ra r r r rb r r gradient_methods all_methodsr! r% r) r, r/ r2 r4 r6 r8 r r r] rc rh rj r} r r r r r r r r r r r r r r r r r r r r r r" r r s
/ / A A A , , G P
5\
<< u||U\\=="LL> 00 #
^M ^MBA@. A@Hc&& c&L = 80 ' 2 2 18 E@
D,>`4 "D &%--3013939$-( LNN LN
%N
% LN $ 70 8N0&
+ LN $ 7, 8N,4=.
- ;/, 0, ELL%,,$)LL%,,$@ A
@A
@r"