
    e!hH                        d Z ddlmZ ddlZddlmZ ddlmZm	Z	 ddl
mZ ddlmZmZ ddlmZ ddlZddlZd	d
lmZ ej*                  ej,                  ej.                  ej0                  ej2                  ej4                  ej6                  dZej*                  ej2                  ej4                  ej6                  dZd Zg de_        i e_         i e_!        i e_"        d Z#g de#_        ej.                  ej0                  de#_         i e#_!        i e#_"        d Z$g de$_        i e$_         i e$_!        i e$_"        d Z%g de%_        i e%_         i e%_!        i e%_"        d Z&ddge&_        ej.                  ej0                  ej,                  de&_         dhe&_!        h de&_"        d Z'g de'_        ej0                  ej.                  ej,                  de'_         ddhe'_!        dhe'_"        d  Z(d!d"ge(_        ej0                  ej.                  ej,                  de(_         i e(_!        i e(_"         G d# d$      Z) G d% d&      Z* G d' d(      Z+ G d) d*      Z, G d+ d,      Z-y)-zA 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                     t        j                  |       j                  } t        g d      }d}| | z  |t	        | j                  | z        z  | z  z
  }|S )N)      g      ?r         ?{Gz?)npasarrayTr   float)xdcfs       h/var/www/html/diagnosisapp-backend/venv/lib/python3.12/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                     | S N r   s    r!   F2r(   /       Hr#   )r   r   r            )r   r   c                     | S r%   r&   r'   s    r!   F2_luckyr.   :   r)   r#   )r   r   r   r   r   r   c                 |    t        j                  g dg dg dg      }t        j                  g d      }|| z  |z
  S )N)r           )r   r0   r   )r   r   r0   )r   r         @)r   arrayr   Abs      r!   F3r7   D   s3    
+z:67A
Aq519r#   )r   r   r   c                     d}|| d   z  | d   z  dz
  t        j                  | d          t        j                  | d          z   dd|z  z   z
  gS )Ng     @r   r   )r   exp)r   r5   s     r!   	F4_powellr:   P   sT    AadF1Q4K!ORVVQqTE]RVVQqTE]:a!A#gFGGr#   r0   )r   r   r   minres>   cgsgmrestfqmrr<   bicgstabc                 F    t        | dt        j                  g d            S )Nr*   )r   r   r   r   )r   r   r3   r'   s    r!   F5rB   `   s    Aq"((+;"<==r#   )       @r   r   r   )r   r   r   r=   c           	      (   | \  }}t        j                  ddgddgg      }t        j                  |dz   |dz  dz
  z  dz   t        j                  |t        j                  |      z  d	z
        g      }t         j                  j                  ||       S )
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                   f   e Zd ZdZddZddZej                  j                  d        Z	ej                  j                  d      d        Zej                  j                  d      ej                  j                  dg d      d	               Zej                  j                  d      d
        Zd Zy)
TestNonlinz
    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           
      |   |t         d   k(  rddD ]_  }||j                  v r |||j                  |d |dd      }t        t	        j
                   ||            j                         |k         a  |||j                  |dd      }t        t	        j
                   ||            j                         |k         y )Nr   r>   r@   r=   r<   r?      r   )methodline_searchf_tolmaxiterverbose)rV   rW   rX   )SOLVERSJAC_KSP_BADxinr   r   absolutemax)selfr    funcrV   rT   r   s         r!   _check_nonlin_funczTestNonlin._check_nonlin_func   s    78$$I 9Q]]*AEE&d$c1>AaD)--/%789 AEEQ?AaD!%%'%/0r#   c                    |dk(  rodD ]j  }||j                   v rt        ||j                  ||ddd|id      }t        t	        j
                  |j                        j                         |k         l t        ||j                  ||ddd      }t        t	        j
                  |j                        j                         |k         y )	Nr   rR   rS   r   rT   )ftolrW   dispjac_optionsrT   options)rb   rW   rc   )ROOT_JAC_KSP_BADr   r[   r   r   r\   funr]   )r^   r    rT   rV   
jac_methodress         r!   _check_rootzTestNonlin._check_root   s    XM <
!3!331aeeF,1c,-4<j3I$KL CGG,002U:;< 1aeeF$)c1EGCGG$((*U23r#   c                      y r%   r&   )r^   akws      r!   _check_func_failzTestNonlin._check_func_fail   s    r#   zignore::DeprecationWarningc                 8   t         t        t        t        t        t
        t        fD ]r  }t        j                         D ]Y  }||j                  j                         v r)|t        j                         v r| j                  ||       H| j                  ||       [ t y r%   )r"   r(   r.   r7   r:   rB   rN   rY   values	KNOWN_BAD	MUST_WORKro   r`   )r^   r    r_   s      r!   test_problem_nonlinzTestNonlin.test_problem_nonlin   s    R2y"b9 	1A( 11;;--//y//11--a6''401	1r#   rT   )lgmresr>   r@   r=   r<   r?   c           	           d _          fd}t        j                  t        t        j                  |ddd|       t         j                          y )NFc                 X    d_         t        j                  |       j                         S )NT)_tol_norm_usedr   r\   r]   )r   r^   s    r!   local_norm_funcz8TestNonlin.test_tol_norm_called.<locals>.local_norm_func   s"    "&D;;q>%%''r#   r   rS   r   )rT   rV   rW   rX   tol_norm)rx   nonlinnewton_krylovr"   r[   r   )r^   rT   ry   s   `  r!   test_tol_norm_calledzTestNonlin.test_tol_norm_called   sF    
 $	( 	QfD%(!&5	7 	##$r#   c                     t         t        t        t        t        t
        t        fD ]H  }t        D ]=  }||j                  v r|t        v r| j                  ||       ,| j                  ||       ? J y r%   )r"   r(   r.   r7   r:   rB   rN   rY   rr   rs   ro   rk   )r^   r    meths      r!   test_problem_rootzTestNonlin.test_problem_root   sf    R2y"b9 	*A *1;;&y(--a6  D)*	*r#   c                     d }t        j                  t        j                  j                        5  t        j                  |dgd       d d d        y # 1 sw Y   y xY w)Nc                     d| z   S )Ng     @@r&   r'   s    r!   wont_convergez5TestNonlin.test_no_convergence.<locals>.wont_converge   s    7Nr#   r   r   )r[   rW   )pytestraisesscipyoptimizeNoConvergencer{   r|   )r^   r   s     r!   test_no_convergencezTestNonlin.test_no_convergence   sL    	 ]]5>>778 	D  QCC	D 	D 	Ds   AAN)r   )__name__
__module____qualname____doc__r`   rk   r   markxfailro   filterwarningsrt   parametrizer}   r   r   r&   r#   r!   rP   rP      s    14" [[  [[ <=1 >1 [[ <=[[X (; <%< >% [[ <=* >*Dr#   rP   c                      e Zd ZdZ ej
                  g d       ej
                  g d       ej
                  g d       ej
                  g d       ej
                  g d       ej
                  g d       ej
                  g d       ej
                  g d	      gZeD  cg c]
  }|d
z  dz
   c}} ZddZd Z	d Z
d Zd Zd Zyc c}} w )
TestSecantzDCheck 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           
      J    |di |}|j                  | j                  d   | j                  d   d       t        t	        | j                  dd | j                  dd             D ];  \  }\  }}|j                  ||       t        t        ||dz               D ]  }| j                  ||z
  dz      | j                  ||z
     z
  }	| j                  ||z
  dz      | j                  ||z
     z
  }
t        t        j                  |	|j                  |
                    ||k\  s| j                  ||z
  dz      | j                  ||z
     z
  }	| j                  ||z
  dz      | j                  ||z
     z
  }
t        t        j                  |	|j                  |
                    > y)z|
        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npointsrn   jacjr   r    kdxdfs              r!   _check_secantzTestSecant._check_secant   sq   
 mm		$''!*dggaj$/"3twwqr{DGGABK#@A 	<IAv1JJq!3w!,- 8WWQqSU^dggacl2WWQqSU^dggacl2B		"678 G|WWQwYq[)DGGAgI,>>WWQwYq[)DGGAgI,>>BKKCIIbM::;	<r#   c                 B    | j                  t        j                         y r%   )r   r{   BroydenFirstr^   s    r!   test_broyden1zTestSecant.test_broyden1   s    6../r#   c                 B    | j                  t        j                         y r%   )r   r{   BroydenSecondr   s    r!   test_broyden2zTestSecant.test_broyden2  s    6//0r#   c           	      Z   t        j                  d      }|j                  | j                  d   | j                  d   d        t        j                  d      dz  }t        t        | j                  dd  | j                  dd              D ]  \  }\  }}|| j                  |   z
  }|| j                  |   z
  }||t        ||      z
  d d d f   |d d d f   z  t        ||      z  z  }|j                  ||       t        t        j                  |j                         |dd	              y )
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_updatezTestSecant.test_broyden1_update  s   !!,		$''!*dggaj$/KKNf%'DGGABK(EF 	KNFFQTWWV_$BTWWV_$B"s1bz/1d7+bqk9CBKGGAJJq!BKKqu5IJ	Kr#   c           	      l   t        j                  d      }|j                  | j                  d   | j                  d   d        t        j                  d      dz  }t        t        | j                  dd  | j                  dd              D ]  \  }\  }}|| j                  |   z
  }|| j                  |   z
  }||t        ||      z
  d d d f   |d d d f   z  t        ||      z  z  }|j                  ||       t        t        j                  |j                         t        |      dd	              y )
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_updatezTestSecant.test_broyden2_update  s   ""-		$''!*dggaj$/KKNd#'DGGABK(EF 	PNFFQTWWV_$BTWWV_$B"s1bz/1d7+bqk9CBKGGAJJq!BKKs1vENO	Pr#   c                 J    | j                  t        j                  ddd       y )Nr   r   )Mw0r   )r   r{   Andersonr   s    r!   test_andersonzTestSecant.test_anderson!  s    
 	6??aAqAr#   N)r   )r   r   r   r   r   r3   r   r   r   r   r   r   r   r   ).0r   s   00r!   r   r      s    N
"(('
(
"(('
(
"(('
(
"(('
(
"(('
(
"(('
(
"(('
(
"(('
(
+B 	q!Q$(	B<*01KPBs 
 s   &Cr   c                   B    e Zd ZdZddZd Zd Zd Zd Zd Z	d Z
d	 Zy
)
TestLinearz]Solve a linear equation;
    some methods find the exact solution in a finite number of stepsc           	      "  	 t         j                  j                  d       t         j                  j                  ||      |r&dt         j                  j                  ||      z  z   t         j                  j                  |      	|r%	dt         j                  j                  |      z  z   		fd}t	        j
                  |t        j                  |      ||dd d      }t        t        j                  t        |      	d             y )N{                 ?c                 "    t        |       z
  S r%   r	   r4   s    r!   r_   zTestLinear._check.<locals>.func7  s    q!9q= r#   ư>r   rW   rV   rU   rX   r   )
r   randomseedrandnr{   nonlin_solvezerosr   r   r	   )
r^   r   NrW   complexrn   r_   solr5   r6   s
           @@r!   _checkzTestLinear._check-  s    
		sIIOOAq!Bryyq!,,,AIIOOABryyq)))A	! !!$S'(,$KC3K67r#   c                     | j                  t        j                  d      ddd       | j                  t        j                  d      ddd       y Nr   r      )   FT)r   r{   r   r   s    r!   r   zTestLinear.test_broyden1>  s<    F''c2BEBF''c2BDAr#   c                     | j                  t        j                  d      ddd       | j                  t        j                  d      ddd       y r   )r   r{   r   r   s    r!   r   zTestLinear.test_broyden2C  s<    F((s3RUCF((s3RTBr#   c                     | j                  t        j                  dd      ddd       | j                  t        j                  dd      ddd       y )N2   r   )r   r   r      FT)r   r{   r   r   s    r!   r   zTestLinear.test_andersonH  s<    FOOb4b"eDFOOb4b"dCr#   c                     | j                  t        j                  dddd       | j                  t        j                  dddd       y )Nr   r   F
   )inner_mT)r   r{   KrylovJacobianr   s    r!   test_krylovzTestLinear.test_krylovM  s:    F))2q%DF))2q$Cr#   c           	         fd}fd}t        j                  |t        j                  j                  d         |ddd d      }t        j
                  j                  |z  d       t        j                  |t        j                  j                  d         ddd d      }t        j
                  j                  |z  d       y )Nc                 ,    j                  |       z
  S r%   r   r4   s    r!   r_   z'TestLinear._check_autojac.<locals>.funcS  s    558a<r#   c                     S r%   r&   )rM   r5   s    r!   r   z&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_autojaczTestLinear._check_autojacR  s    	 	 !!$(<c1(,$K


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


""1s7AD"9r#   c                     t        ddgddgg      }t        j                  ddg      }| j                  ||       | j                  d|z  d|z         y Nr   r   r;   y      ?       @y       @       @)r   r   r3   r   r^   r5   r6   s      r!   test_jac_sparsezTestLinear.test_jac_sparsea  sS    1v1v&'HHaWAq!VqL6Q,7r#   c                     t        j                  ddgddgg      }t        j                  ddg      }| j                  ||       | j                  d|z  d|z         y r   )r   r3   r   r   s      r!   test_jac_ndarrayzTestLinear.test_jac_ndarrayg  sW    HHq!fq!f%&HHaWAq!VqL6Q,7r#   N)F)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                   |    e Zd ZdZddZddZd Zd Zd Zd Z	d	 Z
d
 Zej                  j                  d        Zy)TestJacobianDotSolvezP
    Check that solve/dot methods in Jacobian approximations are consistent
    Nc                 @    |dz  dz
  t        j                  ||      z   S )Nr   r   )r   r	   )r^   r   r5   s      r!   _funczTestJacobianDotSolve._funcs  s    !tax"&&A,&&r#   c                    t         j                  j                  d      d}fd}fd} |||      }j                  |      }	 |di |}
|
j	                  |	| j                  |	|      t        | j
                  |             t        d|z        D ]5  } ||      }t        |
d      rMt        j                  |
      }t        |
d      r;|
j                  |      }t         j                  j                  ||      } |||d	       t        |
d
      rS|
j                  |      }t         j                  j                  |j                  j                         |      } |||d       t        |
d      r1|
j                  |      }t        j                   ||      } |||d       t        |
d      rI|
j#                  |      }t        j                   |j                  j                         |      } |||d       t        |
d      rGt        |
d      r;|
j                  |      }|
j                  |
j                  |            } |||d       t        |
d      rGt        |
d
      r;|
j#                  |      }|
j#                  |
j                  |            } |||d        ||      }|
j%                  || j                  ||             8 y )Nr   rE   c                  T     j                   |  }r|d j                   |  z  z   }|S )Nr   )rand)rm   qr   rngs     r!   r   z-TestJacobianDotSolve._check_dot.<locals>.rand{  s2    !A8388Q<'Hr#   c                     t        | |z
        j                         }t        |      j                         z  z   }||kD  rt        | d|d      y )Nz: err g)absr]   AssertionError)rm   r6   msgr   r    tols        r!   assert_closez5TestJacobianDotSolve._check_dot.<locals>.assert_close  sT    AE
 Ac!fjjl3&&A1u$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  rn   r   r   r  r5   x0r   r   rM   JdGvGv2JvJv2r   r   s     ``               @r!   
_check_dotzTestJacobianDotSolve._check_dotv  s>   ii##C(		: AJ XXa[mm		"djjQ'q)AB qs !	,AQAsK(XXc]3(1B))//"a0C S*:;3)AB))//"$$))+q9C S*;<3)AB&&Q-C S.93	*QB&&a0C S*<=sH%'#w*?ZZ]ii

2/Rn5sI&73+A[[^kk#**R.1R&9:QAJJq$**Q*+C!	,r#   c                     | j                  t        j                  d       | j                  t        j                  d       y NF)r   T)r  r{   r   r   s    r!   r   z"TestJacobianDotSolve.test_broyden1  .    ++U;++T:r#   c                     | j                  t        j                  d       | j                  t        j                  d       y r  )r  r{   r   r   s    r!   r   z"TestJacobianDotSolve.test_broyden2  s.    ,,e<,,d;r#   c                     | j                  t        j                  d       | j                  t        j                  d       y r  )r  r{   r   r   s    r!   r   z"TestJacobianDotSolve.test_anderson  s*    76r#   c                     | j                  t        j                  d       | j                  t        j                  d       y r  )r  r{   DiagBroydenr   s    r!   test_diagbroydenz%TestJacobianDotSolve.test_diagbroyden  s.    **E:**D9r#   c                     | j                  t        j                  d       | j                  t        j                  d       y r  )r  r{   LinearMixingr   s    r!   test_linearmixingz&TestJacobianDotSolve.test_linearmixing  r  r#   c                     | j                  t        j                  d       | j                  t        j                  d       y r  )r  r{   ExcitingMixingr   s    r!   test_excitingmixingz(TestJacobianDotSolve.test_excitingmixing  s.    --u=--t<r#   c                     | j                  t        j                  dd       | j                  t        j                  dd       y )NFgMbP?)r   r  T)r  r{   r   r   s    r!   r   z TestJacobianDotSolve.test_krylov  s2    --u$G--tFr#   r%   )Fr   )r   r   r   r   r   r  r   r   r   r  r  r!  r   r   thread_unsafer   r&   r#   r!   r   r   n  sP    ':,x;<7:;= [[G Gr#   r   c                   X    e Zd ZdZd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd Zd Zy)TestNonlinOldTestsz Test 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                     t        j                  t        t        j                  dd      }t	        t        j
                  |      dk         t	        t        j
                  t        |            dk         y N   r   iterr   &.>)r{   r   r"   r[   r   normr^   r   s     r!   r   z TestNonlinOldTests.test_broyden1  I    OOAquu2Q7A%&AaD!D()r#   c                     t        j                  t        t        j                  dd      }t	        t        j
                  |      dk         t	        t        j
                  t        |            dk         y r'  )r{   r   r"   r[   r   r,  r-  s     r!   r   z TestNonlinOldTests.test_broyden2  r.  r#   c                     t        j                  t        t        j                  ddd      }t	        t        j
                  |      dk         y )Nr(  Q?r+   )r*  r   r   Q?)r{   r   r"   r[   r   r,  r-  s     r!   r   z TestNonlinOldTests.test_anderson  s1    OOAquu2TQ?A%&r#   c                     t        j                  t        t        j                  dd      }t	        t        j
                  |      dk         t	        t        j
                  t        |            dk         y )N<   r   r)  Hz>)r{   r   r"   r[   r   r,  r-  s     r!   r  z$TestNonlinOldTests.test_linearmixing  sK    155r=A%&AaD!D()r#   c                     t        j                  t        t        j                  dd      }t	        t        j
                  |      dk         t	        t        j
                  t        |            dk         y )Nr   r   r)  h㈵>)r{   r   r"   r[   r   r,  r-  s     r!   test_excitingz TestNonlinOldTests.test_exciting  sK    !!!QUU3?A%&AaD!D()r#   c                     t        j                  t        t        j                  dd      }t	        t        j
                  |      dk         t	        t        j
                  t        |            dk         y )N   r   r)  :0yE>)r{   r   r"   r[   r   r,  r-  s     r!   r  z#TestNonlinOldTests.test_diagbroyden  sK    q!%%b:A%&AaD!D()r#   c                     t        t        t        j                  ddddid      }t        t	        j
                  |j                        dk         t        t	        j
                  |j                        dk         y )Nr   r(  r   r   nitrd   re   r+  r   r"   r[   r   r{   r,  r   rh   r^   rj   s     r!   test_root_broyden1z%TestNonlinOldTests.test_root_broyden1  W    1aeeJ#%wlCECEE"T)*CGG$t+,r#   c                     t        t        t        j                  ddddid      }t        t	        j
                  |j                        dk         t        t	        j
                  |j                        dk         y )Nr   r(  r   r   r=  re   r+  r?  r@  s     r!   test_root_broyden2z%TestNonlinOldTests.test_root_broyden2  rB  r#   c           	          t        t        t        j                  dddddd      }t        t	        j
                  |j                        dk         y )	Nr   r(  r1  r+   )r   r   r=  re   r2  )r   r"   r[   r   r{   r,  r   r@  s     r!   test_root_andersonz%TestNonlinOldTests.test_root_anderson  sD    1aeeJ#%59+BDE 	CEE"T)*r#   c                     t        t        t        j                  ddddid      }t        t	        j
                  |j                        dk         t        t	        j
                  |j                        dk         y )Nr   r4  r   r   r=  re   r5  r?  r@  s     r!   test_root_linearmixingz)TestNonlinOldTests.test_root_linearmixing  s[    1aeeN#%,3S>;< 	CEE"T)*CGG$t+,r#   c                     t        t        t        j                  ddddid      }t        t	        j
                  |j                        dk         t        t	        j
                  |j                        dk         y )Nr   r   r   r   r=  re   r7  r?  r@  s     r!   test_root_excitingmixingz+TestNonlinOldTests.test_root_excitingmixing  s\    1aee$4#%,3S>;< 	CEE"T)*CGG$t+,r#   c                     t        t        t        j                  ddddid      }t        t	        j
                  |j                        dk         t        t	        j
                  |j                        dk         y )Nr   r:  r   r   r=  re   r;  r?  r@  s     r!   test_root_diagbroydenz(TestNonlinOldTests.test_root_diagbroyden  s[    1aeeM#%,3Q<9: 	CEE"T)*CGG$t+,r#   N)r   r   r   r   r   r   r   r  r8  r  rA  rD  rF  rH  rJ  rL  r&   r#   r!   r%  r%    sC    
*
*
'*
*
*
--+---r#   r%  ).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|   rY   rs   r"   r[   rr   rZ   rg   r(   r.   r7   r:   rB   rN   rP   r   r   r   r%  r&   r#   r!   <module>rT     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#   