o
    `^hH                     @   s6  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jejejejdZejejejejdZdd Zg de_i e_ i e_!i e_"dd Z#g de#_ejejde#_ i e#_!i e#_"dd Z$g de$_i e$_ i e$_!i e$_"dd Z%g de%_i e%_ i e%_!i e%_"dd Z&ddge&_ejejejde&_ dhe&_!h d e&_"d!d" Z'g d#e'_ejejejd$e'_ d%dhe'_!dhe'_"d&d' Z(d(d)ge(_ejejejd$e(_ i e(_!i e(_"G d*d+ d+Z)G d,d- d-Z*G d.d/ d/Z+G d0d1 d1Z,G d2d3 d3Z-dS )4zA Unit tests for nonlinear solvers
Author: Ondrej Certik
May 2007
    )assert_N)partial)_nonlinroot)	csr_array)diagdot)inv   )pressure_network)andersondiagbroydenlinearmixingexcitingmixingbroyden1broyden2krylov)r   r   r   r   c                 C   s@   t | j} tg d}d}| |  |t| j|   |   }|S )N)      g      ?r
         ?{Gz?)npasarrayTr   float)xdcf r   ^/home/air/shanriGPT/back/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_nonlin.pyF!   s
    r!   )r
   r
   r
   r
   r
   c                 C      | S Nr   r   r   r   r    F2/      r%   )r
   r   r            )r   r   c                 C   r"   r#   r   r$   r   r   r    F2_lucky:   r&   r*   )r   r   r   r   r   r   c                 C   s6   t g dg dg dg}t g d}||  | S )N)r
           )r
   r+   r
   )r   r
   r+   )r
   r         @)r   array)r   Abr   r   r    F3D   s   r1   )r
   r   r   c                 C   sH   d}|| d  | d  d t | d  t | d   dd|   gS )Ng     @r   r
   )r   exp)r   r/   r   r   r    	F4_powellP   s   Dr3   r+   )r   r   r   minres>   cgsgmrestfqmrr5   bicgstabc                 C   s   t | dtg dS )Nr'   )r   r   r   r   )r   r   r.   r$   r   r   r    F5`   s   r:   )       @r   r   r   )r   r   r   r6   c              	   C   sd   | \}}t ddgddgg}t |d |d d  d t |t | d	 g}t j|| S )
Ng/$gffffff-@g+,?grD0?r   r(         r
   )r   r.   sinr2   linalgsolve)r   x1x2J0vr   r   r    F6o   s   
rE   g      gffffff?c                   @   s   e Zd ZdZdddZdddZejjdd Z	ej
d	d
d Zej
d	ejdg ddd Zej
d	dd Zdd ZdS )
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.

    r   c              
   C   s   |t d kr*dD ]!}||jv rq|||j|d |ddd}tt|| |k  q|||j|ddd}tt|| |k  d S )Nr   r7   r9   r6   r5   r8      r   )methodline_searchf_tolmaxiterverbose)rK   rL   rM   )SOLVERSJAC_KSP_BADxinr   r   absolutemax)selfr   funcrK   rI   r   r   r   r    _check_nonlin_func   s   
zTestNonlin._check_nonlin_funcc              
   C   s   |dkr+dD ]$}||j v rqt||j||ddd|idd}tt|j |k  qt||j||dddd}tt|j |k  d S )	Nr   rG   rH   r   rI   )ftolrL   dispjac_optionsrI   options)rV   rL   rW   )ROOT_JAC_KSP_BADr   rP   r   r   rQ   funrR   )rS   r   rI   rK   
jac_methodresr   r   r    _check_root   s   



zTestNonlin._check_rootc                 O   s   d S r#   r   )rS   akwr   r   r    _check_func_fail   s   zTestNonlin._check_func_failzignore::DeprecationWarningc                 C   s^   t ttttttfD ]#}t D ]}||j	 v r%|t
 v r$| || q| || qq	d S r#   )r!   r%   r*   r1   r3   r:   rE   rN   values	KNOWN_BAD	MUST_WORKrb   rU   )rS   r   rT   r   r   r    test_problem_nonlin   s   zTestNonlin.test_problem_nonlinrI   )lgmresr7   r9   r6   r5   r8   c              	      s:   d _  fdd}tjttj|ddd|d t j  d S )NFc                    s   d _ t|  S )NT)_tol_norm_usedr   rQ   rR   r$   rS   r   r    local_norm_func   s   z8TestNonlin.test_tol_norm_called.<locals>.local_norm_funcr   rH   r   )rI   rK   rL   rM   tol_norm)rh   nonlinnewton_krylovr!   rP   r   )rS   rI   rj   r   ri   r    test_tol_norm_called   s   zTestNonlin.test_tol_norm_calledc                 C   sR   t ttttttfD ]}tD ]}||jv r|t	v r| 
|| q| || qq	d S r#   )r!   r%   r*   r1   r3   r:   rE   rN   rd   re   rb   r_   )rS   r   methr   r   r    test_problem_root   s   
zTestNonlin.test_problem_rootc                 C   sN   dd }t tjj tj|dgdd W d    d S 1 s w   Y  d S )Nc                 S   s   d|  S )Ng     @@r   r$   r   r   r    wont_converge   s   z5TestNonlin.test_no_convergence.<locals>.wont_converger   r
   )rP   rL   )pytestraisesscipyoptimizeNoConvergencerl   rm   )rS   rq   r   r   r    test_no_convergence   s   "zTestNonlin.test_no_convergenceN)r   )__name__
__module____qualname____doc__rU   r_   rr   markxfailrb   filterwarningsrf   parametrizern   rp   rw   r   r   r   r    rF      s    





	

	rF   c                   @   s   e Zd ZdZeg deg deg deg deg deg deg deg d	gZd
d eD ZdddZdd Z	dd Z
dd Zdd Zdd ZdS )
TestSecantzDCheck that some Jacobian approximations satisfy the secant condition)      ?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   r-   )r   r         @r   r   )r   r;   r   r   r   c                 C   s   g | ]}|d  d qS )r   r
   r   ).0r   r   r   r    
<listcomp>   s    zTestSecant.<listcomp>r
   c              	   K   s6  |di |}| | jd | jd d tt| jdd | jdd D ]s\}\}}||| tt||d D ]-}| j|| d  | j||   }	| j|| d  | j||   }
tt	
|	||
 q:||kr| j|| d  | j||   }	| j|| d  | j||   }
tt	
|	||
  q%dS )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   allcloser@   )rS   jac_clsnpointsra   jacjr   r   kdxdfr   r   r    _check_secant   s   .    zTestSecant._check_secantc                 C      |  tj d S r#   )r   rl   BroydenFirstri   r   r   r    test_broyden1      zTestSecant.test_broyden1c                 C   r   r#   )r   rl   BroydenSecondri   r   r   r    test_broyden2  r   zTestSecant.test_broyden2c                 C   s   t jdd}|| jd | jd d  tdd }tt| jdd  | jdd  D ]C\}\}}|| j|  }|| j|  }||t	|| d d d f |d d d f  t	|| 7 }|
|| ttj| |ddd	 q+d S )
N皙?alphar   r(   g      $r
   绽|=vIh%<=rtolatol)rl   r   r   r   r   r   identityr   r   r   r   r   r   todense)rS   r   Blast_jr   r   r   r   r   r   r    test_broyden1_update  s   .8zTestSecant.test_broyden1_updatec                 C   s   t jdd}|| jd | jd d  tdd }tt| jdd  | jdd  D ]E\}\}}|| j|  }|| j|  }||t	|| d d d f |d d d f  t	|| 7 }|
|| ttj| t|ddd	 q+d S )
Nr   r   r   r(   gr
   r   r   r   )rl   r   r   r   r   r   r   r   r   r   r   r   r   r   r	   )rS   r   Hr   r   r   r   r   r   r   r    test_broyden2_update  s   .8 zTestSecant.test_broyden2_updatec                 C   s   | j tjdddd d S )Nr   r   )Mw0r   )r   rl   Andersonri   r   r   r    test_anderson!  s   zTestSecant.test_andersonN)r
   )rx   ry   rz   r{   r   r.   r   r   r   r   r   r   r   r   r   r   r   r    r      s$    
r   c                   @   sR   e Zd ZdZdddZdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd ZdS )
TestLinearz]Solve a linear equation;
    some methods find the exact solution in a finite number of stepsFc              	      s   t jd t j|| |r dt j||   t j||r,dt j|   fdd}tj|t |||dd dd}tt jt	 |dd d S )	N{                 ?c                    s   t  |  S r#   r   r$   r/   r0   r   r    rT   7     zTestLinear._check.<locals>.funcư>r   rL   rK   rJ   rM   r   )
r   randomseedrandnrl   nonlin_solvezerosr   r   r   )rS   r   NrL   complexra   rT   solr   r   r    _check-  s   zTestLinear._checkc                 C   4   |  tjddddd |  tjddddd d S Nr   r      )   FT)r   rl   r   ri   r   r   r    r   >     zTestLinear.test_broyden1c                 C   r   r   )r   rl   r   ri   r   r   r    r   C  r   zTestLinear.test_broyden2c                 C   s8   |  tjdddddd |  tjdddddd d S )N2   r   )r   r   r      FT)r   rl   r   ri   r   r   r    r   H  s   zTestLinear.test_andersonc                 C   s0   | j tjddddd | j tjddddd d S )Nr   r   F
   )inner_mT)r   rl   KrylovJacobianri   r   r   r    test_krylovM  s   zTestLinear.test_krylovc              	      s    fdd} fdd}t j|tjd |ddd dd}tjj | dd	 t j|tjd  ddd dd}tjj | dd	 d S )
Nc                    s     |  S r#   r   r$   r   r   r    rT   S  r   z'TestLinear._check_autojac.<locals>.funcc                    s    S r#   r   )rD   r/   r   r    r   V  r&   z&TestLinear._check_autojac.<locals>.jacr   r   r   r   r   )rl   r   r   r   shapetestingassert_allclose)rS   r/   r0   rT   r   r   r   r   r    _check_autojacR  s   zTestLinear._check_autojacc                 C   sF   t ddgddgg}tddg}| || | d| d|  d S Nr
   r   r4   y      ?       @y       @       @)r   r   r.   r   rS   r/   r0   r   r   r    test_jac_sparsea  s   zTestLinear.test_jac_sparsec                 C   sH   t ddgddgg}t ddg}| || | d| d|  d S r   )r   r.   r   r   r   r   r    test_jac_ndarrayg  s   zTestLinear.test_jac_ndarrayN)F)rx   ry   rz   r{   r   r   r   r   r   r   r   r   r   r   r   r    r   )  s    
r   c                   @   sd   e Zd ZdZdddZdddZd	d
 Zdd Zdd Zdd Z	dd Z
dd Zejjdd ZdS )TestJacobianDotSolvezP
    Check that solve/dot methods in Jacobian approximations are consistent
    Nc                 C   s   |d d t || S )Nr   r
   )r   r   )rS   r   r/   r   r   r    _funcs  s   zTestJacobianDotSolve._funcFr   c                    s  t jdd} fdd}fdd}|||}|}	|di |}
|
|	| |	|t| j|d td| D ]}||}t|
d	rt 	|
}t|
d
rc|

|}t j
||}|||d t|
dr}|
|}t j
|j |}|||d t|
dr|
|}t ||}|||d t|
dr|
|}t |j |}|||d t|
drt|
d
r|
|}|

|
|}|||d t|
drt|
dr|
|}|
|
|}|||d ||}|
|| || q<d S )Nr   r<   c                     s$   j |  } r|dj |    }|S )Nr   )rand)r`   q)r   rngr   r    r   {  s   
z-TestJacobianDotSolve._check_dot.<locals>.randc                    sD   t | |  } t |    }||kr t| d|dd S )Nz: err g)absrR   AssertionError)r`   r0   msgr   r   )tolr   r    assert_close  s
   z5TestJacobianDotSolve._check_dot.<locals>.assert_closer   r   	__array__r@   zsolve vs arrayrsolvezrsolve vs arraymatveczdot vs arrayrmatveczrmatvec vs arrayzdot vs solvezrmatvec vs rsolver   )r   r   RandomStater   r   r   r   r   hasattrr.   r@   r?   r   r   conjr   r   r   r   )rS   r   r   r   ra   r   r   r   r/   x0r   r   rD   JdGvGv2JvJv2r   r   )r   r   r   r    
_check_dotv  sN   

 











zTestJacobianDotSolve._check_dotc                 C   $   | j tjdd | j tjdd d S NF)r   T)r   rl   r   ri   r   r   r    r        z"TestJacobianDotSolve.test_broyden1c                 C   r   r   )r   rl   r   ri   r   r   r    r     r   z"TestJacobianDotSolve.test_broyden2c                 C   r   r   )r   rl   r   ri   r   r   r    r     r   z"TestJacobianDotSolve.test_andersonc                 C   r   r   )r   rl   DiagBroydenri   r   r   r    test_diagbroyden  r   z%TestJacobianDotSolve.test_diagbroydenc                 C   r   r   )r   rl   LinearMixingri   r   r   r    test_linearmixing  r   z&TestJacobianDotSolve.test_linearmixingc                 C   r   r   )r   rl   ExcitingMixingri   r   r   r    test_excitingmixing  r   z(TestJacobianDotSolve.test_excitingmixingc                 C   s(   | j tjddd | j tjddd d S )NFgMbP?)r   r   T)r   rl   r   ri   r   r   r    r     s   z TestJacobianDotSolve.test_krylovr#   )Fr   )rx   ry   rz   r{   r   r   r   r   r   r   r   r   rr   r|   thread_unsafer   r   r   r   r    r   n  s    

<r   c                   @   sp   e Zd ZdZdd Zdd Zdd Zdd	 Zd
d Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd ZdS )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                 C   @   t jttjddd}tt |dk  tt t|dk  d S N   r
   iterr   &.>)rl   r   r!   rP   r   normrS   r   r   r   r    r        z TestNonlinOldTests.test_broyden1c                 C   r   r   )rl   r   r!   rP   r   r  r  r   r   r    r     r  z TestNonlinOldTests.test_broyden2c                 C   s,   t jttjdddd}tt |dk  d S )Nr   Q?r(   )r   r   r   Q?)rl   r   r!   rP   r   r  r  r   r   r    r     s   z TestNonlinOldTests.test_andersonc                 C   r   )N<   r   r   Hz>)rl   r   r!   rP   r   r  r  r   r   r    r     r  z$TestNonlinOldTests.test_linearmixingc                 C   r   )Nr   r   r   h㈵>)rl   r   r!   rP   r   r  r  r   r   r    test_exciting  r  z TestNonlinOldTests.test_excitingc                 C   r   )N   r
   r   :0yE>)rl   r   r!   rP   r   r  r  r   r   r    r     r  z#TestNonlinOldTests.test_diagbroydenc                 C   H   t ttjddddidd}tt|jdk  tt|jdk  d S )Nr   r   r   r
   nitrX   rY   r  r   r!   rP   r   rl   r  r   r\   rS   r^   r   r   r    test_root_broyden1  
   
z%TestNonlinOldTests.test_root_broyden1c                 C   r  )Nr   r   r   r
   r  rY   r  r  r  r   r   r    test_root_broyden2  r  z%TestNonlinOldTests.test_root_broyden2c                 C   s6   t ttjddddddd}tt|jdk  d S )	Nr   r   r  r(   )r   r   r  rY   r  )r   r!   rP   r   rl   r  r   r  r   r   r    test_root_anderson  s   
z%TestNonlinOldTests.test_root_andersonc                 C   r  )Nr   r  r   r   r  rY   r  r  r  r   r   r    test_root_linearmixing     
z)TestNonlinOldTests.test_root_linearmixingc                 C   r  )Nr   r   r   r   r  rY   r	  r  r  r   r   r    test_root_excitingmixing  r  z+TestNonlinOldTests.test_root_excitingmixingc                 C   r  )Nr   r  r   r
   r  rY   r  r  r  r   r   r    test_root_diagbroyden  r  z(TestNonlinOldTests.test_root_diagbroydenN)rx   ry   rz   r{   r   r   r   r   r
  r   r  r  r  r  r  r  r   r   r   r    r     s    r   ).r{   numpy.testingr   rr   	functoolsr   scipy.optimizer   rl   r   scipy.sparser   numpyr   r   numpy.linalgr	   r   rt   test_minpackr   r   r   r   r   r   r   rm   rN   re   r!   rP   rd   rO   r[   r%   r*   r1   r3   r:   rE   rF   r   r   r   r   r   r   r   r    <module>   s    








	XLEb