o
    Eb]:                     @   s  d Z ddlmZ ddlZddlmZmZ ddlm	Z	m
Z
 ddlm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_dd Zg de_ejejde_dd Zg de_i e_dd Zg de_i e_dd Zddge_ejejejde_dd Z g de _ejejejd e _d!d" Z!d#d$ge!_ejejejd e!_G d%d& d&Z"G d'd( d(Z#G d)d* d*Z$G d+d, d,Z%G d-d. d.Z&dS )/zA Unit tests for nonlinear solvers
Author: Ondrej Certik
May 2007
    )assert_N)_nonlinroot)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?)npZasarrayTr   float)xdcf r   B/usr/lib/python3/dist-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_lucky0   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   g        )r   r(   r   )r   r   r(   )r   r   g      @)r   array)r   Abr   r   r   F38   s   r,   )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_powellB   s   Dr.   r(   )r   r   r   c                 C   s   t | dtg dS )Nr$   )r   r   r   r   )r	   r   r)   r!   r   r   r   F5M   s   r0   )g       @r   r   r   )r   r   r   c              	   C   sd   | \}}t ddgddgg}t |d |d d  d t |t | d	 g}t j|| S )
Ng/$gffffff-@g+,?grD0?r   r%         r   )r   r)   Zsinr-   linalgsolve)r   Zx1Zx2ZJ0vr   r   r   F6W   s   
r6   g      gffffff?c                   @   sL   e Zd ZdZdddZdddZejjdd Z	d	d
 Z
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   s2   |||j |ddd}tt|| |k  d S )N   r   )f_tolmaxiterverbose)xinr   r   absolutemax)selfr   funcr9   r   r   r   r   _check_nonlin_funct   s   zTestNonlin._check_nonlin_funcc                 C   s6   t ||j||dddd}tt|j |k  d S )Nr8   r   )Zftolr:   Zdispmethodoptions)r   r<   r   r   r=   funr>   )r?   r   rC   r9   resr   r   r   _check_rootx   s   

zTestNonlin._check_rootc                 O   s   d S r    r   )r?   akwr   r   r   _check_func_fail}   s   zTestNonlin._check_func_failc                 C   s^   t ttttttfD ]#}t D ]}||j	 v r%|t
 v r$| || q| || qq	d S r    )r   r"   r'   r,   r.   r0   r6   SOLVERSvalues	KNOWN_BAD	MUST_WORKrJ   rA   )r?   r   r@   r   r   r   test_problem_nonlin   s   zTestNonlin.test_problem_nonlinc                    s8   d _  fdd}tjttjddd|d t j  d S )NFc                    s   d _ t|  S )NT)_tol_norm_usedr   r=   r>   r!   r?   r   r   local_norm_func   s   z8TestNonlin.test_tol_norm_called.<locals>.local_norm_funcr   r8   r   )r9   r:   r;   Ztol_norm)rP   nonlinnewton_krylovr   r<   r   )r?   rR   r   rQ   r   test_tol_norm_called   s   zTestNonlin.test_tol_norm_calledc                 C   sR   t ttttttfD ]}tD ]}||jv r|t	v r| 
|| q| || qq	d S r    )r   r"   r'   r,   r.   r0   r6   rK   rM   rN   rJ   rG   )r?   r   Zmethr   r   r   test_problem_root   s   
zTestNonlin.test_problem_rootN)r   )__name__
__module____qualname____doc__rA   rG   pytestZmarkZxfailrJ   rO   rU   rV   r   r   r   r   r7   k   s    


	r7   c                   @   s   e Zd ZdZeg deeg deeg deeg deeg deeg deeg deeg d	egZd
d eD ZdddZ	dd Z
dd Zdd Zdd Zdd ZdS )
TestSecantzDCheck that some Jacobian approximations satisfy the secant condition)r   r   r   r$   r%   )r   r   r$   r%   r   )r   r$   r%   r   r   )r$   r%   r   r   r   )	   r   r]   r   r   )r   r   r]   r   r   )r%   r%   r1   r   r   )r   r   r1   r%   r   c                 C   s   g | ]}|d  d qS )r   r   r   ).0r   r   r   r   
<listcomp>   s    zTestSecant.<listcomp>r   c              	   K   s6  |di |}| | jd | jd d tt| jdd | jdd D ]s\}\}}||| tt||d D ]-}| j|| d  | j||   }	| j|| d  | j||   }
tt	
|	||
 q:||kr| j|| d  | j||   }	| j|| d  | j||   }
tt	
|	||
  q%dS )z|
        Check that the given Jacobian approximation satisfies secant
        conditions for last `npoints` points.
        r   Nr   r   )setupxsfs	enumeratezipupdaterangeminr   r   allcloser4   )r?   jac_clsnpointsrI   jacjr   r   kdxdfr   r   r   _check_secant   s   .    zTestSecant._check_secantc                 C      |  tj d S r    )rp   rS   BroydenFirstrQ   r   r   r   test_broyden1      zTestSecant.test_broyden1c                 C   rq   r    )rp   rS   BroydenSecondrQ   r   r   r   test_broyden2   rt   zTestSecant.test_broyden2c                 C   s   t jdd}|| jd | jd d  tdd }tt| jdd  | jdd  D ]C\}\}}|| j|  }|| j|  }||t	|| d d d f |d d d f  t	|| 7 }|
|| ttj| |ddd	 q+d S )
N皙?alphar   r%   g      $r   绽|=vIh%<=Zrtolatol)rS   rr   r`   ra   rb   r   identityrc   rd   r   re   r   rh   todense)r?   rk   Blast_jr   r   ro   rn   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 )
Nrw   rx   r   r%   gr   rz   r{   r|   )rS   ru   r`   ra   rb   r   r~   rc   rd   r   re   r   rh   r   r   )r?   rk   Hr   r   r   ro   rn   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   )MZw0rj   )rp   rS   AndersonrQ   r   r   r   test_anderson   s   zTestSecant.test_andersonN)r   )rW   rX   rY   rZ   r   r)   r   ra   rb   rp   rs   rv   r   r   r   r   r   r   r   r\      s$    
r\   c                   @   s:   e Zd ZdZd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*   r+   r   r   r@      s   zTestLinear._check.<locals>.funcư>r   )r:   r9   Zline_searchr;   )r}   )
r   randomseedZrandnrS   Znonlin_solveZzerosr   rh   r   )r?   rk   Nr:   complexrI   r@   Z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 N      ?rx      )   FT)r   rS   rr   rQ   r   r   r   rs        zTestLinear.test_broyden1c                 C   r   r   )r   rS   ru   rQ   r   r   r   rv     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   ry   r      FT)r   rS   r   rQ   r   r   r   r     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
   )Zinner_mT)r   rS   KrylovJacobianrQ   r   r   r   test_krylov  s   zTestLinear.test_krylovN)F)	rW   rX   rY   rZ   r   rs   rv   r   r   r   r   r   r   r      s    
r   c                   @   sZ   e Zd ZdZ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dd ZdS )TestJacobianDotSolvezFCheck that solve/dot methods in Jacobian approximations are consistentc                 C   s   |d d t | j| S )Nr   r   )r   r   r*   r?   r   r   r   r   _func  s   zTestJacobianDotSolve._funcFr   c                    s  t jd d} fdd}fdd}|||| _t j|}|di |}	|	|| || j td| D ]}
||}t|	drt 	|	}t|	d	r_|	
|}t j
||}|||d
 t|	dry|	|}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 ||}|	|| | q8d S )Nr   r1   c                     s(   t jj|  } r|dt jj|    }|S )Nr   )r   r   rand)rH   qr   r   r   r   !  s   z-TestJacobianDotSolve._check_dot.<locals>.randc                    s@   t | |  } t |    }||krtd||f d S )Nz
%s: err %g)absr>   AssertionError)rH   r+   msgr   r   )tolr   r   assert_close'  s
   z5TestJacobianDotSolve._check_dot.<locals>.assert_closer   Z	__array__r4   zsolve vs arrayrsolvezrsolve vs arraymatveczdot vs arrayrmatveczrmatvec vs arrayzdot vs solvezrmatvec vs rsolver   )r   r   r   r*   r   r`   r   rf   hasattrr)   r4   r3   r   r   Zconjr   r   r   re   )r?   ri   r   r   rI   r   r   r   Zx0rk   rm   r5   ZJdZGvZGv2ZJvZJv2r   r   r   r   r   
_check_dot  sN   











zTestJacobianDotSolve._check_dotc                 C   $   | j tjdd | j tjdd d S NFr   T)r   rS   rr   rQ   r   r   r   rs   X     z"TestJacobianDotSolve.test_broyden1c                 C   r   r   )r   rS   ru   rQ   r   r   r   rv   \  r   z"TestJacobianDotSolve.test_broyden2c                 C   r   r   )r   rS   r   rQ   r   r   r   r   `  r   z"TestJacobianDotSolve.test_andersonc                 C   r   r   )r   rS   ZDiagBroydenrQ   r   r   r   test_diagbroydend  r   z%TestJacobianDotSolve.test_diagbroydenc                 C   r   r   )r   rS   ZLinearMixingrQ   r   r   r   test_linearmixingh  r   z&TestJacobianDotSolve.test_linearmixingc                 C   r   r   )r   rS   ZExcitingMixingrQ   r   r   r   test_excitingmixingl  r   z(TestJacobianDotSolve.test_excitingmixingc                 C   s(   | j tjddd | j tjddd d S )NFgMbP?r   T)r   rS   r   rQ   r   r   r   r   p  s   z TestJacobianDotSolve.test_krylovN)Fr   )rW   rX   rY   rZ   r   r   rs   rv   r   r   r   r   r   r   r   r   r   r     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   iterry   &.>)rS   r   r   r<   r   normr   r   r   r   rs   {     z TestNonlinOldTests.test_broyden1c                 C   r   r   )rS   r   r   r<   r   r   r   r   r   r   rv     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   ry   r   Q?)rS   r
   r   r<   r   r   r   r   r   r   r     s   z TestNonlinOldTests.test_andersonc                 C   r   )N<   r   r   Hz>)rS   r   r   r<   r   r   r   r   r   r   r     r   z$TestNonlinOldTests.test_linearmixingc                 C   r   )Nr   r   r   h㈵>)rS   r   r   r<   r   r   r   r   r   r   test_exciting  r   z TestNonlinOldTests.test_excitingc                 C   r   )N   r   r   :0yE>)rS   r   r   r<   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   ry   r   ZnitZjac_optionsrB   r   r   r   r<   r   rS   r   r   rE   r?   rF   r   r   r   test_root_broyden1  
   
z%TestNonlinOldTests.test_root_broyden1c                 C   r   )Nr   r   ry   r   r   rB   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%   )ry   r   r   rB   r   )r   r   r<   r   rS   r   r   r   r   r   r   test_root_anderson  s   
z%TestNonlinOldTests.test_root_andersonc                 C   r   )Nr   r   ry   r   r   rB   r   r   r   r   r   r   test_root_linearmixing     
z)TestNonlinOldTests.test_root_linearmixingc                 C   r   )Nr   r   ry   r   r   rB   r   r   r   r   r   r   test_root_excitingmixing  r   z+TestNonlinOldTests.test_root_excitingmixingc                 C   r   )Nr   r   ry   r   r   rB   r   r   r   r   r   r   test_root_diagbroyden  r   z(TestNonlinOldTests.test_root_diagbroydenN)rW   rX   rY   rZ   rs   rv   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   u  s    r   )'rZ   Znumpy.testingr   r[   Zscipy.optimizer   rS   r   Znumpyr   r   Znumpy.linalgr   r   Ztest_minpackr	   r
   r   r   r   r   r   rT   rK   rN   r   r<   rM   r"   r'   r,   r.   r0   r6   r7   r\   r   r   r   r   r   r   r   <module>   sj    






	
5L*_