
    (phH                        S r SSKJr  SSKrSSKJr  SSKJrJ	r	  SSK
Jr  SSKJrJr  SSKJr  SSKrSSKrS	S
KJr  \R*                  \R,                  \R.                  \R0                  \R2                  \R4                  \R6                  S.r\R*                  \R2                  \R4                  \R6                  S.rS r/ SQ\l        0 \l         0 \l!        0 \l"        S r#/ SQ\#l        \R.                  \R0                  S.\#l         0 \#l!        0 \#l"        S r$/ SQ\$l        0 \$l         0 \$l!        0 \$l"        S r%/ SQ\%l        0 \%l         0 \%l!        0 \%l"        S r&SS/\&l        \R.                  \R0                  \R,                  S.\&l         S1\&l!        1 Sk\&l"        S r'/ SQ\'l        \R0                  \R.                  \R,                  S.\'l         SS1\'l!        S1\'l"        S  r(S!S"/\(l        \R0                  \R.                  \R,                  S.\(l         0 \(l!        0 \(l"         " S# S$5      r) " S% S&5      r* " S' S(5      r+ " S) S*5      r, " S+ S,5      r-g)-z@Unit tests for nonlinear solvers
Author: Ondrej Certik
May 2007
    )assert_N)partial)_nonlinroot)	csr_array)diagdot)inv   )pressure_network)andersondiagbroydenlinearmixingexcitingmixingbroyden1broyden2krylov)r   r   r   r   c                     [         R                  " U 5      R                  n [        / SQ5      nSnU* U -  U[	        U R                  U -  5      -  U -  -
  nU$ )N)      g      ?r         ?{Gz?)npasarrayTr   float)xdcfs       S/var/www/html/venv/lib/python3.13/site-packages/scipy/optimize/tests/test_nonlin.pyFr"   !   sN    


1A !AA	
QU1337^#a''AH    )r   r   r   r   r   c                     U $ N r   s    r!   F2r(   /       Hr#   )r   r   r            )r   r   c                     U $ r%   r&   r'   s    r!   F2_luckyr.   :   r)   r#   )r   r   r   r   r   r   c                 ~    [         R                  " / SQ/ SQ/ SQ/5      n[         R                  " / SQ5      nX-  U-
  $ )N)r           )r   r0   r   )r   r   r0   )r   r         @)r   arrayr   Abs      r!   F3r7   D   s1    
+z:67A
A519r#   )r   r   r   c                     SnXS   -  U S   -  S-
  [         R                  " U S   * 5      [         R                  " U S   * 5      -   SSU-  -   -
  /$ )Ng     @r   r   )r   exp)r   r5   s     r!   	F4_powellr:   P   sR    AdF1Q4K!ORVVQqTE]RVVQqTE]:a!A#gFGGr#   r0   )r   r   r   minres>   cgsgmrestfqmrr<   bicgstabc                 H    [        U S[        R                  " / SQ5      5      $ )Nr*   )r   r   r   r   )r   r   r3   r'   s    r!   F5rB   `   s    Aq"((+;"<==r#   )       @r   r   r   )r   r   r   r=   c           	      ,   U u  p[         R                  " SS/SS//5      n[         R                  " US-   US-  S-
  -  S-   [         R                  " U[         R                  " U5      -  S	-
  5      /5      n[         R                  R                  X45      * $ )
Ng/$gffffff-@g+,?grD0?r   r+         r   )r   r3   sinr9   linalgsolve)r   x1x2J0vs        r!   F6rN   o   s    FB	FD>z*, 
-B
26b!eai(3.&&bffRj1,-/ 	0AIIOOB"""r#   g      gffffff?c                   r   \ rS rSrSrSS jrSS jr\R                  R                  S 5       r
\R                  R                  S5      S 5       r\R                  R                  S5      \R                  R                  S/ S	Q5      S
 5       5       r\R                  R                  S5      S 5       rS rSrg)
TestNonlin   z
Check the Broyden methods for a few test problems.

broyden1, broyden2, and newton_krylov must succeed for
all functions. Some of the others don't -- tests in KNOWN_BAD are skipped.

c                 z   U[         S   :X  ae  S H_  nXAR                  ;   a  M  U" XR                  US USSS9n[        [        R
                  " U" U5      5      R                  5       U:  5        Ma     U" XR                  USSS9n[        [        R
                  " U" U5      5      R                  5       U:  5        g )Nr   r>   r@   r=   r<   r?      r   )methodline_searchf_tolmaxiterverbose)rW   rX   rY   )SOLVERSJAC_KSP_BADxinr   r   absolutemax)selfr    funcrW   rU   r   s         r!   _check_nonlin_funcTestNonlin._check_nonlin_func   s    78$$I]]*EE&d$c1>AaD)--/%78 J EEQ?AaD!%%'%/0r#   c                    US:X  ap  S Hj  nXAR                   ;   a  M  [        XR                  UUSSSU0S.S9n[        [        R
                  " UR                  5      R                  5       U:  5        Ml     [        XR                  UUSSS.S9n[        [        R
                  " UR                  5      R                  5       U:  5        g )	Nr   rS   rT   r   rU   )ftolrX   dispjac_optionsrU   options)rd   rX   re   )ROOT_JAC_KSP_BADr   r\   r   r   r]   funr^   )r_   r    rU   rW   
jac_methodress         r!   _check_rootTestNonlin._check_root   s    XM
!3!331eeF,1c,-4<j3I$KL CGG,002U:; N 1eeF$)c1EGCGG$((*U23r#   c                     g r%   r&   )r_   akws      r!   _check_func_failTestNonlin._check_func_fail   s    r#   zignore::DeprecationWarningc                 D   [         [        [        [        [        [
        [        4 Hw  n[        R                  5        H\  nX!R                  R                  5       ;   a+  U[        R                  5       ;   a  U R                  X5        MK  U R                  X5        M^     My     g r%   )r"   r(   r.   r7   r:   rB   rN   rZ   values	KNOWN_BAD	MUST_WORKrr   ra   )r_   r    r`   s      r!   test_problem_nonlinTestNonlin.test_problem_nonlin   so    R2y"b9A(;;--//y//11--a6''0 ) :r#   rU   )lgmresr>   r@   r=   r<   r?   c           
         ^  ST l         U 4S jn[        R                  " [        [        R                  USSSUS9  [        T R                   5        g )NFc                 Z   > STl         [        R                  " U 5      R                  5       $ )NT)_tol_norm_usedr   r]   r^   )r   r_   s    r!   local_norm_func8TestNonlin.test_tol_norm_called.<locals>.local_norm_func   s"    "&D;;q>%%''r#   r   rT   r   )rU   rW   rX   rY   tol_norm)r}   nonlinnewton_krylovr"   r\   r   )r_   rU   r~   s   `  r!   test_tol_norm_calledTestNonlin.test_tol_norm_called   sF    
 $	( 	QfD%(!&5	7 	##$r#   c                     [         [        [        [        [        [
        [        4 HM  n[         H@  nX!R                  ;   a  U[        ;   a  U R                  X5        M/  U R                  X5        MB     MO     g r%   )r"   r(   r.   r7   r:   rB   rN   rZ   rv   rw   rr   rm   )r_   r    meths      r!   test_problem_rootTestNonlin.test_problem_root   sV    R2y"b9A;;&y(--a6  )   :r#   c                     S n[         R                  " [        R                  R                  5         [
        R                  " US/SS9  S S S 5        g ! , (       d  f       g = f)Nc                     SU -   $ )Ng     @@r&   r'   s    r!   wont_converge5TestNonlin.test_no_convergence.<locals>.wont_converge   s    7Nr#   r   r   )r\   rX   )pytestraisesscipyoptimizeNoConvergencer   r   )r_   r   s     r!   test_no_convergenceTestNonlin.test_no_convergence   s?    	 ]]5>>778  QCC 988s   A
A!)r}   N)r   )__name__
__module____qualname____firstlineno____doc__ra   rm   r   markxfailrr   filterwarningsrx   parametrizer   r   r   __static_attributes__r&   r#   r!   rP   rP      s    14" [[  [[ <=1 >1 [[ <=[[X (; <%< >% [[ <=* >*Dr#   rP   c                      \ rS rSrSr\R                  " / SQ5      \R                  " / SQ5      \R                  " / SQ5      \R                  " / SQ5      \R                  " / SQ5      \R                  " / SQ5      \R                  " / S	Q5      \R                  " / S
Q5      /r\ V Vs/ s H
  oS-  S-
  PM     snn rSS jr	S r
S rS rS rS rSrgs  snn f )
TestSecant   zDCheck that some Jacobian approximations satisfy the secant condition)      ?rC   r2         @      @)rC   r2   r   r   r   )r2   r   r   r   rC   )r   r   r   rC   r2   )      "@r   r   r   r2   )r1   r   r   r   r2   )r   r         @r   r   )r   rC   r   r   r   r   r   c           
      F   U" S0 UD6nUR                  U R                  S   U R                  S   S5        [        [	        U R                  SS U R                  SS 5      5       GH8  u  nu  pgUR                  Xg5        [        [        X%S-   5      5       H}  nU R                  XX-
  S-      U R                  XX-
     -
  n	U R                  XX-
  S-      U R                  XX-
     -
  n
[        [        R                  " XR                  U
5      5      5        M     XR:  d  M  U R                  XR-
  S-      U R                  XR-
     -
  n	U R                  XR-
  S-      U R                  XR-
     -
  n
[        [        R                  " XR                  U
5      5      (       + 5        GM;     g)zd
Check that the given Jacobian approximation satisfies secant
conditions for last `npoints` points.
r   Nr   r&   )setupxsfs	enumeratezipupdaterangeminr   r   allcloserI   )r_   jac_clsnpointsrq   jacjr   r    kdxdfs              r!   _check_secantTestSecant._check_secant   sL   
 mm		$''!*dggaj$/"3twwqr{DGGABK#@AIAvJJq3w!,-WWQSU^dggacl2WWQSU^dggacl2B		"67 . |WWQYq[)DGGAI,>>WWQYq[)DGGAI,>>BKKIIbM::; Br#   c                 B    U R                  [        R                  5        g r%   )r   r   BroydenFirstr_   s    r!   test_broyden1TestSecant.test_broyden1   s    6../r#   c                 B    U R                  [        R                  5        g r%   )r   r   BroydenSecondr   s    r!   test_broyden2TestSecant.test_broyden2  s    6//0r#   c           
      J   [         R                  " SS9nUR                  U R                  S   U R                  S   S 5        [
        R                  " S5      S-  n[        [        U R                  SS  U R                  SS  5      5       H  u  nu  pEXPR                  U   -
  nX@R                  U   -
  nX&[        X'5      -
  S S 2S 4   US S S 24   -  [        Xw5      -  -  nUR                  XE5        [        [
        R                  " UR                  5       USSS	95        M     g )
N皙?alphar   r+   g      $r   绽|=vIh%<=rtolatol)r   r   r   r   r   r   identityr   r   r	   r   r   r   todense)r_   r   Blast_jr   r    r   r   s           r!   test_broyden1_updateTestSecant.test_broyden1_update  s    !!,		$''!*dggaj$/KKNf%'DGGABK(EFNFFQWWV_$BWWV_$Bs1z/1d7+bqk9CKGGAJJqBKKqu5IJ Gr#   c           
      \   [         R                  " SS9nUR                  U R                  S   U R                  S   S 5        [
        R                  " S5      S-  n[        [        U R                  SS  U R                  SS  5      5       H  u  nu  pEXPR                  U   -
  nX@R                  U   -
  nX'[        X&5      -
  S S 2S 4   US S S 24   -  [        Xf5      -  -  nUR                  XE5        [        [
        R                  " UR                  5       [        U5      SSS	95        M     g )
Nr   r   r   r+   gr   r   r   r   )r   r   r   r   r   r   r   r   r   r	   r   r   r   r   r
   )r_   r   Hr   r   r    r   r   s           r!   test_broyden2_updateTestSecant.test_broyden2_update  s    ""-		$''!*dggaj$/KKNd#'DGGABK(EFNFFQWWV_$BWWV_$Bs1z/1d7+bqk9CKGGAJJqBKKs1vENO Gr#   c                 D    U R                  [        R                  SSSS9  g )Nr   r   )Mw0r   )r   r   Andersonr   s    r!   test_andersonTestSecant.test_anderson!  s    
 	6??aAqAr#   r&   N)r   )r   r   r   r   r   r   r3   r   r   r   r   r   r   r   r   r   ).0r   s   00r!   r   r      s    N
(('
(
(('
(
(('
(
(('
(
(('
(
(('
(
(('
(
(('
(
+B 	BqQ$(B	B<*01KPBs 
 s   (Cr   c                   L    \ rS rSrSrSS jrS rS rS rS r	S r
S	 rS
 rSrg)
TestLineari)  zYSolve a linear equation;
some methods find the exact solution in a finite number of stepsc           
      ,  ^^	 [         R                  R                  S5        [         R                  R                  X"5      mU(       a%  TS[         R                  R                  X"5      -  -   m[         R                  R                  U5      m	U(       a%  T	S[         R                  R                  U5      -  -   m	UU	4S jn[        R
                  " U[         R                  " U5      XSS SS9n[        [         R                  " [        TU5      T	SS95        g )N{                 ?c                 "   > [        TU 5      T-
  $ r%   r	   r4   s    r!   r`   TestLinear._check.<locals>.func7  s    q!9q= r#   ư>r   rX   rW   rV   rY   r   )
r   randomseedrandnr   nonlin_solvezerosr   r   r	   )
r_   r   NrX   complexrq   r`   solr5   r6   s
           @@r!   _checkTestLinear._check-  s    
		sIIOOA!Bryyq,,,AIIOOABryyq)))A	! !!$S(,$KC3K67r#   c                     U R                  [        R                  " SS9SSS5        U R                  [        R                  " SS9SSS5        g Nr   r      )   FT)r   r   r   r   s    r!   r   TestLinear.test_broyden1>  s<    F''c2BEBF''c2BDAr#   c                     U R                  [        R                  " SS9SSS5        U R                  [        R                  " SS9SSS5        g r   )r   r   r   r   s    r!   r   TestLinear.test_broyden2C  s<    F((s3RUCF((s3RTBr#   c                     U R                  [        R                  " SSS9SSS5        U R                  [        R                  " SSS9SSS5        g )N2   r   )r   r   r      FT)r   r   r   r   s    r!   r   TestLinear.test_andersonH  s<    FOOb4b"eDFOOb4b"dCr#   c                     U R                  [        R                  SSSSS9  U R                  [        R                  SSSSS9  g )Nr   r   F
   )inner_mT)r   r   KrylovJacobianr   s    r!   test_krylovTestLinear.test_krylovM  s:    F))2q%DF))2q$Cr#   c           
        ^^ UU4S jnU4S jn[         R                  " U[        R                  " TR                  S   5      USSS SS9n[        R
                  R                  TU-  TSS9  [         R                  " U[        R                  " TR                  S   5      TSSS SS9n[        R
                  R                  TU-  TSS9  g )Nc                 ,   > TR                  U 5      T-
  $ r%   r   r4   s    r!   r`   'TestLinear._check_autojac.<locals>.funcS  s    558a<r#   c                    > T$ r%   r&   )rM   r5   s    r!   r   &TestLinear._check_autojac.<locals>.jacV  s    Hr#   r   r   r   r   r   )r   r   r   r   shapetestingassert_allclose)r_   r5   r6   r`   r   r   s    ``   r!   _check_autojacTestLinear._check_autojacR  s    	 	 !!$(<c1(,$K


""1s7AD"9!!$(<a(,$K


""1s7AD"9r#   c                     [        SS/SS//5      n[        R                  " SS/5      nU R                  X5        U R                  SU-  SU-  5        g Nr   r   r;   y      ?       @y       @       @)r   r   r3   r
  r_   r5   r6   s      r!   test_jac_sparseTestLinear.test_jac_sparsea  sQ    1v1v&'HHaWA!VqL6Q,7r#   c                     [         R                  " SS/SS//5      n[         R                  " SS/5      nU R                  X5        U R                  SU-  SU-  5        g r  )r   r3   r
  r  s      r!   test_jac_ndarrayTestLinear.test_jac_ndarrayg  sU    HHq!fq!f%&HHaWA!VqL6Q,7r#   r&   N)F)r   r   r   r   r   r   r   r   r   r   r
  r  r  r   r&   r#   r!   r   r   )  s4    H8"B
C
D
D
:88r#   r   c                       \ rS rSrSrSS jrSS jrS rS rS r	S	 r
S
 rS r\R                  R                  S 5       rSrg)TestJacobianDotSolvein  zH
Check that solve/dot methods in Jacobian approximations are consistent
Nc                 @    US-  S-
  [         R                  " X!5      -   $ )Nr   r   )r   r	   )r_   r   r5   s      r!   _funcTestJacobianDotSolve._funcs  s    !tax"&&,&&r#   c           	        ^^^ [         R                  R                  S5      mSnUU4S jnU4S jnU" XU5      nTR                  U5      n	U" S0 UD6n
U
R	                  XR                  X5      [        U R
                  US95        [        SU-  5       GHb  nU" U5      n[        U
S5      (       Ga`  [         R                  " U
5      n[        U
S5      (       a9  U
R                  U5      n[         R                  R                  X5      nU" XS	5        [        U
S
5      (       aR  U
R                  U5      n[         R                  R                  UR                  R                  5       U5      nU" XS5        [        U
S5      (       a1  U
R                  U5      n[         R                   " X5      nU" UUS5        [        U
S5      (       aJ  U
R#                  U5      n[         R                   " UR                  R                  5       U5      nU" UUS5        [        U
S5      (       aL  [        U
S5      (       a;  U
R                  U5      nU
R                  U
R                  U5      5      nU" UUS5        [        U
S5      (       aL  [        U
S
5      (       a;  U
R#                  U5      nU
R#                  U
R                  U5      5      nU" UUS5        U" U5      nU
R%                  UU R                  UU5      5        GMe     g )Nr   rE   c                  ^   > TR                   " U 6 nT(       a  USTR                   " U 6 -  -   nU$ )Nr   )rand)rp   qr   rngs     r!   r  -TestJacobianDotSolve._check_dot.<locals>.rand{  s.    !A388Q<'Hr#   c                    > [        X-
  5      R                  5       nT[        U5      R                  5       T-  -   nX4:  a  [        U SUS 35      eg )Nz: err g)absr^   AssertionError)rp   r6   msgr   r    tols        r!   assert_close5TestJacobianDotSolve._check_dot.<locals>.assert_close  sP    AE
 Ac!fjjl3&&Au$uF1Q%%899 r#   )r5   r   	__array__rI   zsolve vs arrayrsolvezrsolve vs arraymatveczdot vs arrayrmatveczrmatvec vs arrayzdot vs solvezrmatvec vs rsolver&   )r   r   RandomStater  r   r  r   r   hasattrr3   rI   rH   r(  r   conjr)  r	   r*  r   )r_   r   r   r$  rq   r   r  r%  r5   x0r   r   rM   JdGvGv2JvJv2r   r  s     ``               @r!   
_check_dotTestJacobianDotSolve._check_dotv  sF   ii##C(		: J XXa[mm		"jj'q)AB qsAQAsK((XXc]3((1B))//"0C *:;3))AB))//"$$))+q9C *;<3))AB&&-C S.93	**QB&&a0C S*<=sH%%'#w*?*?ZZ]ii

2/Rn5sI&&73+A+A[[^kk#**R.1R&9:QAJJq$**Q*+C r#   c                 |    U R                  [        R                  SS9  U R                  [        R                  SS9  g NF)r   T)r4  r   r   r   s    r!   r   "TestJacobianDotSolve.test_broyden1  .    ++U;++T:r#   c                 |    U R                  [        R                  SS9  U R                  [        R                  SS9  g r7  )r4  r   r   r   s    r!   r   "TestJacobianDotSolve.test_broyden2  s.    ,,e<,,d;r#   c                 |    U R                  [        R                  SS9  U R                  [        R                  SS9  g r7  )r4  r   r   r   s    r!   r   "TestJacobianDotSolve.test_anderson  s*    76r#   c                 |    U R                  [        R                  SS9  U R                  [        R                  SS9  g r7  )r4  r   DiagBroydenr   s    r!   test_diagbroyden%TestJacobianDotSolve.test_diagbroyden  s.    **E:**D9r#   c                 |    U R                  [        R                  SS9  U R                  [        R                  SS9  g r7  )r4  r   LinearMixingr   s    r!   test_linearmixing&TestJacobianDotSolve.test_linearmixing  r9  r#   c                 |    U R                  [        R                  SS9  U R                  [        R                  SS9  g r7  )r4  r   ExcitingMixingr   s    r!   test_excitingmixing(TestJacobianDotSolve.test_excitingmixing  s.    --u=--t<r#   c                     U R                  [        R                  SSS9  U R                  [        R                  SSS9  g )NFgMbP?)r   r$  T)r4  r   r   r   s    r!   r    TestJacobianDotSolve.test_krylov  s2    --u$G--tFr#   r&   r%   )Fr   )r   r   r   r   r   r  r4  r   r   r   r@  rD  rH  r   r   thread_unsafer   r   r&   r#   r!   r  r  n  sP    ':,x;<7:;= [[G Gr#   r  c                   `    \ rS rSrSrS rS rS rS rS r	S r
S	 rS
 rS rS rS rS rSrg)TestNonlinOldTestsi  zTest case for a simple constrained entropy maximization problem
(the machine translation example of Berger et al in
Computational Linguistics, vol 22, num 1, pp 39--72, 1996.)
c                     [         R                  " [        [        R                  SSS9n[	        [         R
                  " U5      S:  5        [	        [         R
                  " [        U5      5      S:  5        g N   r   iterr   &.>)r   r   r"   r\   r   normr_   r   s     r!   r    TestNonlinOldTests.test_broyden1  I    OOAquu2Q7A%&AaD!D()r#   c                     [         R                  " [        [        R                  SSS9n[	        [         R
                  " U5      S:  5        [	        [         R
                  " [        U5      5      S:  5        g rP  )r   r   r"   r\   r   rU  rV  s     r!   r    TestNonlinOldTests.test_broyden2  rX  r#   c                     [         R                  " [        [        R                  SSSS9n[	        [         R
                  " U5      S:  5        g )NrQ  Q?r+   )rS  r   r   Q?)r   r   r"   r\   r   rU  rV  s     r!   r    TestNonlinOldTests.test_anderson  s1    OOAquu2TQ?A%&r#   c                     [         R                  " [        [        R                  SSS9n[	        [         R
                  " U5      S:  5        [	        [         R
                  " [        U5      5      S:  5        g )N<   r   rR  Hz>)r   r   r"   r\   r   rU  rV  s     r!   rD  $TestNonlinOldTests.test_linearmixing  sK    155r=A%&AaD!D()r#   c                     [         R                  " [        [        R                  SSS9n[	        [         R
                  " U5      S:  5        [	        [         R
                  " [        U5      5      S:  5        g )Nr   r   rR  h㈵>)r   r   r"   r\   r   rU  rV  s     r!   test_exciting TestNonlinOldTests.test_exciting  sK    !!!QUU3?A%&AaD!D()r#   c                     [         R                  " [        [        R                  SSS9n[	        [         R
                  " U5      S:  5        [	        [         R
                  " [        U5      5      S:  5        g )N   r   rR  :0yE>)r   r   r"   r\   r   rU  rV  s     r!   r@  #TestNonlinOldTests.test_diagbroyden  sK    q!%%b:A%&AaD!D()r#   c                     [        [        [        R                  SSSS0S.S9n[        [        R
                  " UR                  5      S:  5        [        [        R
                  " UR                  5      S:  5        g )Nr   rQ  r   r   nitrf   rg   rT  r   r"   r\   r   r   rU  r   rj   r_   rl   s     r!   test_root_broyden1%TestNonlinOldTests.test_root_broyden1  W    1aeeJ#%wlCECEE"T)*CGG$t+,r#   c                     [        [        [        R                  SSSS0S.S9n[        [        R
                  " UR                  5      S:  5        [        [        R
                  " UR                  5      S:  5        g )Nr   rQ  r   r   rl  rg   rT  rn  ro  s     r!   test_root_broyden2%TestNonlinOldTests.test_root_broyden2  rr  r#   c           	          [        [        [        R                  SSSSS.S.S9n[        [        R
                  " UR                  5      S:  5        g )	Nr   rQ  r\  r+   )r   r   rl  rg   r]  )r   r"   r\   r   r   rU  r   ro  s     r!   test_root_anderson%TestNonlinOldTests.test_root_anderson  sD    1aeeJ#%59+BDE 	CEE"T)*r#   c                     [        [        [        R                  SSSS0S.S9n[        [        R
                  " UR                  5      S:  5        [        [        R
                  " UR                  5      S:  5        g )Nr   r`  r   r   rl  rg   ra  rn  ro  s     r!   test_root_linearmixing)TestNonlinOldTests.test_root_linearmixing  s[    1aeeN#%,3S>;< 	CEE"T)*CGG$t+,r#   c                     [        [        [        R                  SSSS0S.S9n[        [        R
                  " UR                  5      S:  5        [        [        R
                  " UR                  5      S:  5        g )Nr   r   r   r   rl  rg   rd  rn  ro  s     r!   test_root_excitingmixing+TestNonlinOldTests.test_root_excitingmixing  s\    1aee$4#%,3S>;< 	CEE"T)*CGG$t+,r#   c                     [        [        [        R                  SSSS0S.S9n[        [        R
                  " UR                  5      S:  5        [        [        R
                  " UR                  5      S:  5        g )Nr   rh  r   r   rl  rg   ri  rn  ro  s     r!   test_root_diagbroyden(TestNonlinOldTests.test_root_diagbroyden  s[    1aeeM#%,3Q<9: 	CEE"T)*CGG$t+,r#   r&   N)r   r   r   r   r   r   r   r   rD  re  r@  rp  rt  rw  rz  r}  r  r   r&   r#   r!   rN  rN    sC    
*
*
'*
*
*
--+---r#   rN  ).r   numpy.testingr   r   	functoolsr   scipy.optimizer   r   r   scipy.sparser   numpyr   r	   numpy.linalgr
   r   r   test_minpackr   r   r   r   r   r   r   r   rZ   rw   r"   r\   rv   r[   ri   r(   r.   r7   r:   rB   rN   rP   r   r   r  rN  r&   r#   r!   <module>r     sY   "   2 "     * ,,!..#22))+  fooF4H4HJ	 	  
 & 3 3"("7"79  "    
 H
 R	'-':':)/)>)>&,&8&8:	  "
	 L	 > 
"("7"7 & 3 3%113 "j # "("7"7 & 3 3%113  UD UDpIB IBXB8 B8J_G _GDH- H-r#   