a
    Re                 
   @   s  d Z ddlZddlZddlZddlmZmZmZm	Z	m
Z
mZmZ ddlZddlmZ ddlmZ ddlmZmZ ddlmZmZmZ ddlmZ dd	lmZ dd
lmZ ddlmZ ddl m!Z!m"Z" ddl#m$Z$m%Z%m&Z& dd Z'G dd dZ(G dd de(Z)dd Z*dd Z+dd Z,dd Z-dd Z.dd Z/d d! Z0d"d# Z1d$d% Z2d&d' Z3G d(d) d)e)Z4G d*d+ d+e)Z5G d,d- d-e)Z6G d.d/ d/e)Z7G d0d1 d1e(Z8ej9:d2g d3d4d5 Z;G d6d7 d7Z<G d8d9 d9Z=G d:d; d;Z>d<d= Z?G d>d? d?Z@d@dA ZAdBdC ZBdDdE ZCdFdG ZDG dHdI dIZEdJdK ZFdLdM ZGdNdO ZHdPdQgZIdRdSgZJdTZKdUdV ZLG dWdX dXZMdYdZ ZNd[d\ ZOd]d^ ZPd_d` ZQG dadb dbZRdcdd ZSG dedf dfZTdgdh ZUG didj djZVejWdkdl ZXdmdn ZYdodp ZZdqdr Z[dsdt Z\dudv Z]e] Z^ej9_dwej9:d2e^dx ej9:dye^dy ej9:dze^d{ ej9:d|e^d| ej9:d}e^d~ dd Z`ej9:d2e^dx dd Zadd Zbdd Zcdd Zddd ZeG dd dZfdd Zgdd ZhdS )z
Unit tests for optimization routines from optimize.py

Authors:
   Ed Schofield, Nov 2005
   Andrew Straw, April 2008

To run it in its simplest form::
  nosetests test_optimize.py

    N)assert_allcloseassert_equalassert_almost_equalassert_no_warningsassert_warnsassert_array_lesssuppress_warnings)raises)optimize)BoundsNonlinearConstraint)MINIMIZE_METHODSMINIMIZE_METHODS_NEW_CBMINIMIZE_SCALAR_METHODS)LINPROG_METHODS)ROOT_METHODS)ROOT_SCALAR_METHODS)QUADRATIC_ASSIGNMENT_METHODS)ScalarFunction
FD_METHODS)
MemoizeJacshow_optionsOptimizeResultc               	   C   sX  dd } dd }t dg}t| ||}t|d tj| ||ddd	}t|d tj| ||d
d}t|d tj| ||d
ddd}t|d ttj| ||ddd }|dksJ ttj| ||ddddd }|dksJ dd }dd }t ddd}tj|||ddd	}t|d tttj|||ddd	 tjt	t
tddd	}|dk sTJ d S )Nc                 S   s   ddt |    S N   npexpx r    V/var/www/sunrise/env/lib/python3.9/site-packages/scipy/optimize/tests/test_optimize.pyexpit'   s    ztest_check_grad.<locals>.expitc                 S   s    t |  dt |   d  S Nr      r   r   r    r    r!   	der_expit*   s    z"test_check_grad.<locals>.der_expit      ?r   random  )	directionseedư>)epsilon)r,   r)   r*   皙?Hz>c                 S   s   | t |   S N)r   sinsumr   r    r    r!   x_sinxB   s    ztest_check_grad.<locals>.x_sinxc                 S   s   t | | t |   S r/   r   r0   cosr   r    r    r!   
der_x_sinxE   s    z#test_check_grad.<locals>.der_x_sinxr$   皙?Zrandom_projectionallgƠ>)r   arrayr
   Z
check_gradr   absarangeassert_raises
ValueErrorhimmelblau_gradhimmelblau_hesshimmelblau_x0)r"   r%   x0rr2   r5   r    r    r!   test_check_grad#   sL    







rB   c                   @   s8   e Zd ZdZdd Zdd Zdd Zdd	 Zd
d ZdS )CheckOptimizez Base 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   sv   t g dg dg dg dg dg| _t g d| _t dt j| _t g d| _d| _d	| _	d	| _
g | _d S )
Nr   r   r   )r   r   r   )r   r   r   )r   r   r   )      ?333333?      ?   )        g\g)3?  r   )r   r8   FKzerosfloat64startparamssolutionmaxiter	funccalls	gradcallstraceselfr    r    r!   setup_method^   s    
zCheckOptimize.setup_methodc                 C   sj   |  j d7  _ | j dkr tdt| j|}ttt|}|t| j| }| j	
t| |S )Nr   ip  z+too many iterations in optimization routine)rR   RuntimeErrorr   dotrK   logr1   r   rL   rT   appendcopy)rV   r   log_pdotlogZfr    r    r!   funcl   s    
zCheckOptimize.funcc                 C   sV   |  j d7  _ t| j|}ttt|}t|| }t| j || j S r   )	rS   r   rY   rK   rZ   r1   r   Z	transposerL   rV   r   r]   r^   pr    r    r!   gradv   s
    zCheckOptimize.gradc                 C   s`   t | j|}t tt |}t || }t | jjt t || jt | jj| S r/   )r   rY   rK   rZ   r1   r   TZdiagra   r    r    r!   hess}   s    
"zCheckOptimize.hessc                 C   s   t | ||S r/   )r   rY   re   rV   r   rb   r    r    r!   hessp   s    zCheckOptimize.hesspN)	__name__
__module____qualname____doc__rW   r`   rc   re   rg   r    r    r    r!   rC   X   s   
rC   c                   @   s   e Zd Zdd Zdd Zdd Zejddd	 Z	d
d Z
dd Zejjd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 d! Zd"S )#CheckOptimizeParameterizedc           	   
   C   s   | j r`| j| jdd}tj| j| jdd| j|d}|d |d |d |d	 |d
 f\}}}}}n2tj| j| j| jd| jd| jdd}|\}}}}}t	| || | j
dd | jdksJ | j| jdksJ | jt	| jdd g dg dgddd d S )NFrQ   disp
return_allr    CG)argsmethodjacoptionsr   funnfevnjevstatusT)rQ   full_outputrn   retallr+   atol	      r$      )r         rG   )r   g;ӱ.g)`$|;?+=r.   r|   rtol)use_wrapperrQ   rn   r
   minimizer`   rO   rc   fmin_cgr   rP   rR   rS   rT   )	rV   optsresparamsfopt
func_calls
grad_callswarnflagretvalr    r    r!   test_cg   s6     
z"CheckOptimizeParameterized.test_cgc                 C   sN   dd }t dddD ]2}tj||gdd}|js6J t|jdgd	d
 qd S )Nc                 S   s   ddt d| d   d  S )Ng      @r         rG   r$   r   )rA   r    r    r!   r_      s    z8CheckOptimizeParameterized.test_cg_cornercase.<locals>.fg      rH   G   rp   rr   rG   h㈵>r   )r   Zlinspacer
   r   successr   r   )rV   r_   r@   solr    r    r!   test_cg_cornercase   s
    
z-CheckOptimizeParameterized.test_cg_cornercasec              
   C   s  | j rp| j| jdd}tj| j| j| jdd|d}|d |d |d |d	 |d
 |d |d f\}}}}}}}	n6tj| j| j| jd| jd| jdd}
|
\}}}}}}}	t	| || | j
dd | jdksJ | j| jdksJ | jt	| jdd g dg dgddd d S )NFrm   BFGSr    rs   rr   rq   rt   r   ru   rs   Zhess_invrv   rw   rx   Trq   rQ   ry   rn   rz   r+   r{   
         )r   g&/LgB__E7?)r   g$g
|3?r   r.   r   )r   rQ   rn   r
   r   r`   rO   rc   	fmin_bfgsr   rP   rR   rS   rT   )rV   r   r   r   r   ZgoptZHoptr   r   r   r   r    r    r!   	test_bfgs   s<    
z$CheckOptimizeParameterized.test_bfgsignore::UserWarningc              	      s   dd   fdd}dg}t jddb | jrTd| ji}tj ||d	d
|dd }ntj ||| jd}t  |rzJ W d    n1 s0    Y  d S )Nc                 S   s   t j|    S r/   )r   er   r    r    r!   r`      s    z;CheckOptimizeParameterized.test_bfgs_infinite.<locals>.funcc                    s
    |  S r/   r    r   r`   r    r!   fprime   s    z=CheckOptimizeParameterized.test_bfgs_infinite.<locals>.fprimer   ignore)overrn   r   r    r   r   rn   )r   errstater   rn   r
   r   r   isfinite)rV   r   r@   r   r   r    r   r!   test_bfgs_infinite   s    
z-CheckOptimizeParameterized.test_bfgs_infinitec                 C   sL   g d}t jt j|dddid}t jt j|dddid}|j|jksHJ d S )Ng?ffffff?皙?ffffff?333333?bfgsZxrtolMbP?rr   rt   gtol)r
   r   rosennit)rV   r@   r   refr    r    r!   test_bfgs_xrtol   s    

z*CheckOptimizeParameterized.test_bfgs_xrtolc           
   	   C   s   | j rd| j| jdd}tj| j| jdd|d}|d |d |d |d	 |d
 |d f\}}}}}}n0tj| j| jd| jd| jdd}	|	\}}}}}}t| || | j	dd t|dd  | j	dd  dd | j
dksJ | j
| jdksJ | jd S )NFrm   r    Powellrq   rr   rt   r   ru   direcr   rv   rx   Tr   r+   r{   r   h㈵>   r   )r   rQ   rn   r
   r   r`   rO   fmin_powellr   rP   rR   rS   
rV   r   r   r   r   r   numiterr   r   r   r    r    r!   test_powell   s,     z&CheckOptimizeParameterized.test_powellzeThis part of test_powell fails on some platforms, but the solution returned by powell is still valid.reasonc           
   	   C   s   | j rd| j| jdd}tj| j| jdd|d}|d |d |d |d	 |d
 |d f\}}}}}}n0tj| j| jd| jd| jdd}	|	\}}}}}}t| j	dd g dg dg dg dg dgddd d S )NFrm   r    r   r   r   ru   r   r   rv   rx   Tr   "   '   )病~W?f"Bܿg%?)r   r   g:&?)gSϼW?gf"Bg{år?)r   r   {år?)gB?r   r   r   r.   r   )
r   rQ   rn   r
   r   r`   rO   r   r   rT   r   r    r    r!   test_powell_gh14014  s2    z.CheckOptimizeParameterized.test_powell_gh14014c                 C   s   dd | j D }| jr| j| jdd}tj| j| j d|d|d}|d |d	  }}|| jks`J t| || | j	d
dd | jdksJ | j
dksJ d S )Nc                 S   s   g | ]}t j t jfqS r    )r   pi).0_r    r    r!   
<listcomp>8      zBCheckOptimizeParameterized.test_powell_bounded.<locals>.<listcomp>Frm   r    r   )rq   boundsrr   rt   r   rv   r+   r   r      r   )rO   r   rQ   rn   r
   r   r`   rR   r   rP   rS   )rV   r   r   r   r   r   r    r    r!   test_powell_bounded5  s     	z.CheckOptimizeParameterized.test_powell_boundedc           	   	   C   s   | j r\| j| jdd}tj| j| jdd|d}|d |d |d |d	 |d
 f\}}}}}n.tj| j| jd| jd| jdd}|\}}}}}t| || | j	dd | j
dksJ | j
| jdksJ | jt| jdd g dg dgddd d S )NFrm   r    Nelder-meadr   r   ru   r   rv   rx   Tr   r+   r{      r   L   N   )g	dװ?g]fgt䝁?)gә ?g#=^goT?r   r.   r   )r   rQ   rn   r
   r   r`   rO   fminr   rP   rR   rS   rT   )	rV   r   r   r   r   r   r   r   r   r    r    r!   test_neldermeadN  s6    z*CheckOptimizeParameterized.test_neldermeadc              
   C   sL  t d}| j|d< tdD ]}||d |f  d7  < q| jr| jdd|d}tj| j| jd	d
|d}|d |d |d |d |d f\}}}}}	t	|d d |d  n.tj
| j| jd	| jddd|d}
|
\}}}}}	t	| || | jdd | jdksJ | j| jdks"J | jt	| jdd g dg dgddd d S )N)r   rH   .rH   r   r-   FTrQ   rn   ro   initial_simplexr    r   r   r   ru   r   rv   rx   Zallvecsr   rq   rQ   ry   rn   rz   r   r+   r{   d   2   4   )gIt?g?'ΛTgx8?)gҢ_׆?goMg囎|52?r   r.   r   )r   rM   rO   ranger   rQ   r
   r   r`   r   r   rP   rR   rS   rT   )rV   simplexjr   r   r   r   r   r   r   r   r    r    r!   test_neldermead_initial_simplexm  sF    

z:CheckOptimizeParameterized.test_neldermead_initial_simplexc                 C   s   g }t d}| jd d |d< tdD ]}||d |f  d7  < q(|| t d}|| |D ]\}| jr| jdd|d}ttt	j
| j| jd	d
|d qhttt	j| j| jd	| jddd|d
 qhd S )N)rH   r$   r$   .r   r-   )rH   rH   Fr   r    r   r   Tr   )r   rM   rO   r   r[   r   rQ   r;   r<   r
   r   r`   r   )rV   Zbad_simplicesr   r   r   r    r    r!   #test_neldermead_initial_simplex_bad  s6    



z>CheckOptimizeParameterized.test_neldermead_initial_simplex_badc                 C   s6   ddi}t j| j| jd| jd|d}|jdks2J d S )NrQ   	Newton-CGr    rr   rs   rq   rt   r   )r
   r   r`   rO   rc   rx   )rV   r   resultr    r    r!   test_ncg_negative_maxiter  s    z4CheckOptimizeParameterized.test_ncg_negative_maxiterc              
   C   s   | j r8| j| jdd}tj| j| jd| jd|dd }n$tj| j| j| jd| jd| jdd}|}t	| || | j
dd	 | jd
ksJ | j| jdksJ | jt	| jdd g dg dgddd d S )NFrm   r   r    r   r   r   r+   r{   r~      rH      (6-H=g?g4u3?r   g_g/N3?r.   r   )r   rQ   rn   r
   r   r`   rO   rc   fmin_ncgr   rP   rR   rS   rT   rV   r   r   r   r    r    r!   test_ncg  s6    z#CheckOptimizeParameterized.test_ncgc                 C   s   | j r<| j| jdd}tj| j| jd| j| jd|dd }n(tj	| j| j| j| jd| jd| jdd	}|}t
| || | jdd	 | jd
ksJ | j| jdksJ | jt
| jdd g dg dgddd d S )NFrm   r   r    )rr   rs   re   rq   rt   r   )Zfhessrq   rQ   ry   rn   rz   r+   r{   r~      rH   r   r   r   r.   r   )r   rQ   rn   r
   r   r`   rO   rc   re   r   r   rP   rR   rS   rT   r   r    r    r!   test_ncg_hess  s:    z(CheckOptimizeParameterized.test_ncg_hessc                 C   s   | j r<| j| jdd}tj| j| jd| j| jd|dd }n(tj	| j| j| j| jd| jd| jdd	}|}t
| || | jdd	 | jd
ksJ | j| jdksJ | jt
| jdd g dg dgddd d S )NFrm   r   r    )rr   rs   rg   rq   rt   r   )Zfhess_prq   rQ   ry   rn   rz   r+   r{   r~   r   rH   r   r   r   r.   r   )r   rQ   rn   r
   r   r`   rO   rc   rg   r   r   rP   rR   rS   rT   r   r    r    r!   test_ncg_hessp  s:    z)CheckOptimizeParameterized.test_ncg_hesspN)rh   ri   rj   r   r   r   pytestmarkfilterwarningsr   r   r   xfailr   r   r   r   r   r   r   r   r   r    r    r    r!   rl      s"   "

	"
 (!"rl   c                     s\   t jd  fdd} dD ]:}dD ]0}tj|  d|d|id}|d	 |ks$J q$qd S )
Nl	   <vgRI*q4 c                    s     dd S Nr   rJ   r'   r   rngr    r!   cost%  s    ztest_maxfev_test.<locals>.cost)r   r   r   )r   Nelder-Meadr   maxfevr   rv   )r   r'   default_rngr
   r   )r   Zimaxfevrr   r   r    r   r!   test_maxfev_test"  s    r   c                  C   s   dd } t j| tdd\}}tdD ]&}|t| |d |d ks*J q*d}tt jj|d |t| W d    n1 s0    Y  t j| tdd\}}d}tt|d" |t	ddg W d    n1 s0    Y  d S )	Nc                 S   s   | S r/   r    r   r    r    r!   func_5  s    z8test_wrap_scalar_function_with_validation.<locals>.func_r   r   r   zToo many function callsmatch@The user-provided objective function must return a scalar value.)
r
   	_optimizeZ'_wrap_scalar_function_maxfun_validationr   Zasarrayr   r;   Z_MaxFuncCallErrorr<   r8   )r   Zfcallsr`   imsgr    r    r!   )test_wrap_scalar_function_with_validation3  s     ,r  c                  C   sR   d} t t| d. tjdd tddgdd W d    n1 sD0    Y  d S )Nr  r   c                 S   s   | S r/   r    r   r    r    r!   <lambda>P  r   z.test_obj_func_returns_scalar.<locals>.<lambda>r   r   r   )r;   r<   r
   r   r   r8   r   r    r    r!   test_obj_func_returns_scalarK  s    r  c                  C   s4   t g d} tjjtj| dd}|jdks0J d S )Nr   :0yE>)xatoliS  )r   r8   r
   	_minimize_minimize_neldermeadr   r   )r@   r   r    r    r!   test_neldermead_iteration_numS  s
    r  c                  C   s2   t ddgt j} dd }tj|| dd d S )N      @      @c                 S   s   | j tjksJ t| S r/   )Zdtyper   float32r
   r   r   r    r    r!   rosen_]  s    z*test_neldermead_respect_fp.<locals>.rosen_r   r   )r   r8   Zastyper  r
   r   )r@   r  r    r    r!   test_neldermead_respect_fpZ  s    r  c                  C   s&   dd } t jj| ddgdddd d S )Nc                 S   s   | d d | d d  S Nr   r$   r   r    r   r    r    r!   r`   g  s    z)test_neldermead_xatol_fatol.<locals>.funcr   r$   r   )rQ   r	  Zfatol)r
   r
  r  r   r    r    r!   test_neldermead_xatol_fatold  s    r  c                  C   sR   dd } g d}t j| |dd}t|jd t j| |dddid	}t|jd d S )
Nc                 S   s   t | d S Nr$   r   r1   r   r    r    r!   r`   o  s    z&test_neldermead_adaptive.<locals>.func)gM@'?gOC?g~?g -?g?g#j?g ?g~^g?gܠr#?g^cǽ?g)i	?g'?g?g1?g[VΤ?r   r   FZadaptiveTr   )r
   r   r   r   )r`   p0r   r    r    r!   test_neldermead_adaptiven  s    
r  c                  C   s  dd } d}g d}t tj" tj| ||dd}W d    n1 sF0    Y  t|jtdgt| dd	 t	|j
d
 t	|jd g dg dg dg}t tj( tj| ||dd|id}W d    n1 s0    Y  t|jtg ddd	 t	|j
d t	|jd d S )Nc                 S   s   t | d S r  r  r   r    r    r!   r`     s    z/test_bounded_powell_outsidebounds.<locals>.func)r   r   r  r  )rG   gr   r   rr   rI   r+   r{   Tr   r   r   r   )r   r   r   )r   r   r   r   )r   rr   rt   )g      r   r   Fr   )r   r
   OptimizeWarningr   r   r   r   r8   lenr   r   rx   )r`   r   r@   r   r   r    r    r!   !test_bounded_powell_outsidebounds}  s"    0 $r  c                  C   s  dd } d}g d}ddd}t j| |d|d}t|jd	d
d t|jd	d
d t j| |||dd}tg d}t|j|d
d t|j| |d
d dtj dfdtjfddf}t j| |||dd}tg d}t|j|d
d t|j| |d
d dd } dgd }g d}t j| |dd}t j| ||dd}t|jdd
d t|jdd
d tj tjfgd }t j| ||dd}t|j|jd
d t|j|jd
d t|j|jd
d g d}dgd }t	t j
" t j| ||dd}W d    n1 s0    Y  t|jdd
d d S )Nc                 S   s   t | d S r  r  r   r    r    r!   r`     s    z+test_bounded_powell_vs_powell.<locals>.func))r   )皙)r   gffffff"@)r  gffffff@g/)g gr   r   r#  绽|=ftolZxtolr   r   rI   r+   r{   )rt   r   rr   )r   r!  r   r   r#  )Nr   r!  r   )r  Nr"  c                 S   sz   t | d  t | d  t | d  | d   t | d  }|t t | d | d  t | d  8 }|d S Nr   r   r$   r3   r   tr    r    r!   r`     s    D.)r#  r   rH   )r   r   r   r   r  g8:}?r   )gb4F@g:gW?@)r
   r   r   r   ru   r   r8   infrv   r   r  )r`   r   r@   rt   Z
res_powellZres_bounded_powellrb   r    r    r!   test_bounded_powell_vs_powell  s`    




&r+  c                  C   s   dt j dfgd dddd} g d}dd	 }tj||fi | }t|jd
dd dd	 }tj||fi | }t|jd dd	 }tj||fi | }t|jddd dd	 }t j dfgd | d< tj||fi | }t|jddd d S )Nr   g    .ArH   r  r%  )rr   r   rt   rD   c                 S   s   t |  S r/   r  r   r    r    r!   r_     s    z1test_onesided_bounded_powell_stability.<locals>.fg    `F-C6?r{   c                 S   s,   t t | d  t | dkr&dnd S )Nr-   r   r   r   r   r9   r1   r7   r   r    r    r!   r_     s    gwc                 S   s,   t t | d  t | dkr&dnd S )Nr   r   r   r   r-  r   r    r    r!   r_     s    gB+Iar.   r   c                 S   sX   t t | d d d  t t | dd  d  }|t | dkrNdnd9 }|S )Nr$   r   r-   r   r   r   r-  r(  r    r    r!   r_     s    :g     @@r   g 4&k\)r   r*  r
   r   r   ru   )kwargsr@   r_   r   r    r    r!   &test_onesided_bounded_powell_stability  s$    r/  c                   @   s   e Zd ZdZdZdS )TestOptimizeWrapperDispTNrh   ri   rj   r   rn   r    r    r    r!   r0    s   r0  c                   @   s   e Zd ZdZdZdS )TestOptimizeWrapperNoDispTFNr1  r    r    r    r!   r2    s   r2  c                   @   s   e Zd ZdZdZdS )TestOptimizeNoWrapperDispFTNr1  r    r    r    r!   r3    s   r3  c                   @   s   e Zd ZdZdZdS )TestOptimizeNoWrapperNoDispFNr1  r    r    r    r!   r4  !  s   r4  c                   @   s  e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zejjd!d"d#d$ Zd%d& Zd'd( Zejd)ejd*ejd+g d,e d-d. Zejd+g d/d0d1 Zd2d3 Zejd+g d4d5d6 Zejd+g d7d8d9 Z d:d; Z!d<d= Z"d>d? Z#d@dA Z$ejd+g dBdCdD Z%ejd+g dEdFdG Z&ejd*ejd+e'ejdHg dIdJdK Z(dLdM Z)ejd+dNdOdP Z*ejd+g dQdRdS Z+dTS )UTestOptimizeSimplec                 C   sn   dd }dd }t jg}t jddd4 tj|||dd}t ||sLJ W d    n1 s`0    Y  d S )	Nc                 S   s   | S r/   r    r   r    r    r!   r`   *  s    z.TestOptimizeSimple.test_bfgs_nan.<locals>.funcc                 S   s
   t | S r/   r   Z	ones_liker   r    r    r!   r   ,  s    z0TestOptimizeSimple.test_bfgs_nan.<locals>.fprimer   )r   invalidFr   )r   nanr   r
   r   isnan)rV   r`   r   r@   r   r    r    r!   test_bfgs_nan(  s    z TestOptimizeSimple.test_bfgs_nanc                 C   s   dd }t jdd t|d}W d    n1 s60    Y  t |d sRJ |d du sbJ d	d }d
d }t jdd  tj|d|d}W d    n1 s0    Y  t |d sJ |d du sJ d S )Nc                 S   s   t jS r/   r   r8  r   r    r    r!   r`   7  s    z5TestOptimizeSimple.test_bfgs_nan_return.<locals>.funcr   r7  r   ru   r   Fc                 S   s   | dkrdS t jS Nr   r;  r   r    r    r!   r`   @  s    c                 S   s
   t | S r/   r6  r   r    r    r!   r   B  s    z7TestOptimizeSimple.test_bfgs_nan_return.<locals>.fprime)rs   )r   r   r
   r   r9  )rV   r`   r   r   r    r    r!   test_bfgs_nan_return3  s    *.z'TestOptimizeSimple.test_bfgs_nan_returnc                 C   s^   t t dt jt| j }tj| j	| j
|d| jdd}t| 	|| 	| jdd d S )NrE   r    F)r,   rq   rQ   rn   r+   r{   )r   sqrtspacingr'   randr  rP   r
   r   r`   rO   rQ   r   )rV   r,   r   r    r    r!   test_bfgs_numerical_jacobianJ  s    "z/TestOptimizeSimple.test_bfgs_numerical_jacobianc                 C   s^   g d}g d}t ||D ]<\}}tj| j| j||d}t| |j| | jdd qd S )N)r   rp   TNC2-point3-pointN)rr   rs   r+   r{   )		itertoolsproductr
   r   r`   rO   r   r   rP   )rV   methodsjacsrr   rs   r   r    r    r!   test_finite_differences_jacV  s    z.TestOptimizeSimple.test_finite_differences_jacc              	   C   s   g d}t tjf }t||D ]<\}}|tju r8| }tj| j| j|| j|d}|j	s J q g d}|D ]H}t
t* tj| j| j|| jd d W d    qj1 s0    Y  qjd S )N)trust-constrr   	trust-ncgtrust-krylovrr   rs   re   )rM  rN  doglegtrust-exact)r   r
   r   rG  rH  r   r`   rO   rc   r   r   r	   r<   )rV   rI  Zhessesrr   re   r   r    r    r!   test_finite_differences_hess_  s"    
z/TestOptimizeSimple.test_finite_differences_hessc                 C   s.   dd }t j|dgdd}t|dddd d S )	Nc                 S   s   | dk rdS | d|   S d S )Nr   gBrE   r    r   r    r    r!   r_   z  s    z/TestOptimizeSimple.test_bfgs_gh_2169.<locals>.f      $@Fr   rE   r,  r   r|   )r
   r   r   )rV   r_   xsr    r    r!   test_bfgs_gh_2169y  s    z$TestOptimizeSimple.test_bfgs_gh_2169c                    s*    fdd}t   tj|ddddd d S )Nc                    s2   | d }| vsJ   | d| d  d|  fS )Nr   r   r$      )add)r   Zxpseenr    r!   r_     s    
z:TestOptimizeSimple.test_bfgs_double_evaluations.<locals>.fr   Tr.   )rr   rs   tol)setr
   r   rV   r_   r    rY  r!   test_bfgs_double_evaluations  s    z/TestOptimizeSimple.test_bfgs_double_evaluationsc                 C   s   t j| j| j| jd| jd}|\}}}t| || | jdd | jdksVJ | j| j	dksjJ | j	t| j
dd g dg d	gd
dd d S )Nr    )rq   rQ   r+   r{   r~   r   rH   )g><gwT볹gUuAX?)rI   gHg!mʲ3?r   r.   r   )r
   fmin_l_bfgs_br`   rO   rc   rQ   r   rP   rR   rS   rT   rV   r   r   r   dr    r    r!   test_l_bfgs_b  s     
z TestOptimizeSimple.test_l_bfgs_bc                 C   sB   t j| j| jd| jd}|\}}}t| || | jdd d S )NT)Zapprox_gradrQ   r+   r{   )r
   r`  r`   rO   rQ   r   rP   ra  r    r    r!   test_l_bfgs_b_numjac  s    
z'TestOptimizeSimple.test_l_bfgs_b_numjacc                    sJ    fdd}t j| j jd}|\}}}t |  jdd d S )Nc                    s     |  | fS r/   r`   rc   r   rU   r    r!   ru     s    z4TestOptimizeSimple.test_l_bfgs_b_funjac.<locals>.funrQ   r+   r{   )r
   r`  rO   rQ   r   r`   rP   )rV   ru   r   r   r   rb  r    rU   r!   test_l_bfgs_b_funjac  s    

z'TestOptimizeSimple.test_l_bfgs_b_funjacc                 C   s   G dd d}| }t jt jddgd|ddid}t|jd t|j|j t|j|j t|jd |j	d	u stJ t|j
d
 d S )Nc                   @   s   e Zd Zdd Zdd ZdS )z:TestOptimizeSimple.test_l_bfgs_b_maxiter.<locals>.Callbackc                 S   s   d| _ d | _d | _d S r=  )r   ru   r   rU   r    r    r!   __init__  s    zCTestOptimizeSimple.test_l_bfgs_b_maxiter.<locals>.Callback.__init__c                 S   s$   || _ t|| _|  jd7  _d S r   )r   r
   r   ru   r   rV   r   r    r    r!   __call__  s    zCTestOptimizeSimple.test_l_bfgs_b_maxiter.<locals>.Callback.__call__Nrh   ri   rj   rh  rj  r    r    r    r!   Callback  s   rl  rI   l-bfgs-brQ   r   )rr   callbackrt   r   Fz+STOP: TOTAL NO. of ITERATIONS REACHED LIMIT)r
   r   r   r   r   r   r   ru   rx   r   message)rV   rl  cr   r    r    r!   test_l_bfgs_b_maxiter  s    z(TestOptimizeSimple.test_l_bfgs_b_maxiterc                 C   s   d| j d}tj| j| jd| j|d}t| |j| | jdd | j	|j
ksTJ d | _| _	tj| j| jd|d}| j|jksJ t| |j| | jdd d | _| _	tj| j| jd	d|d
}| j|jksJ t| |j| | jdd d S )NFrn   rQ   L-BFGS-Brr   rs   rt   r+   r{   r   r   rF  rs   rr   rt   )rQ   r
   r   r`   rO   rc   r   r   rP   rS   rw   rR   rv   )rV   r   rA   rar    r    r!   test_minimize_l_bfgs_b  s2    z)TestOptimizeSimple.test_minimize_l_bfgs_bc                 C   sv   d }dD ]h}d| j |d}tj| j| jd| j|d}| |j}|d u rN|}n||k sZJ t|| | j|d qd S )N)r-   r,  r.   r$  F)rn   rQ   r&  rs  rt  r   )	rQ   r
   r   r`   rO   rc   r   r   rP   )rV   Zv0r\  r   r   vr    r    r!   test_minimize_l_bfgs_b_ftol  s    z.TestOptimizeSimple.test_minimize_l_bfgs_b_ftolc                 C   s6   t jt jtddgdt jdddd}|jr2J d S )N333333rE   rs  Fr   )rn   Zmaxlsrt  )r
   r   r   r   r8   	rosen_derr   )rV   r   r    r    r!   test_minimize_l_bfgs_maxls  s
    z-TestOptimizeSimple.test_minimize_l_bfgs_maxlsc                    s   t j t j}g tdd} fdd}d\}}}t j||||d tdd t|d  D \}}|| }	td | }
t j |||	d\}}}t	||
 d S )	Nr~   rJ   c                    s    | } | |S r/   )r[   )r   valuer_   valuesr    r!   objfun  s    
zMTestOptimizeSimple.test_minimize_l_bfgs_b_maxfun_interruption.<locals>.objfun)   r   i,  )r   maxfunc                 s   s   | ]\}}||fV  qd S r/   r    )r   r  yr    r    r!   	<genexpr>  r   zPTestOptimizeSimple.test_minimize_l_bfgs_b_maxfun_interruption.<locals>.<genexpr>)
r
   r   r{  r   fullr`  max	enumerateminr   )rV   gr@   r  lowZmediumhighrx  kr  targetZxminr   rb  r    r~  r!   *test_minimize_l_bfgs_b_maxfun_interruption
  s    
"z=TestOptimizeSimple.test_minimize_l_bfgs_b_maxfun_interruptionc                 C   sB   ddd}g d}t jt j||tddd	}t|jd
ddd d S )Nr    r-   r   c                 [   s   |}| |}	d}
d}d}d}|r|s||k rd}|d7 }t t|D ]}|| | || | fD ]B}t|}|||< | |g|R  }|
d7 }
||	k rb|}	|}d}qb|d ur|| |d urF|
|krFd} qqFqtj|	|||
|dkdS )Nr   r   TFru   r   r   rv   r   )r   r   sizer\   r
   r   )ru   r@   rq   r   stepsizerQ   rn  rt   bestxbestyfuncallsniterimprovedstopZdimstestxtestyr    r    r!   custmin&  s6    

z/TestOptimizeSimple.test_custom.<locals>.custmin)g??r   皙?r   皙?r  r   rE   r,  rT  )r    Nr-   r   N)r
   r   r   dictr   r   )rV   r  r@   r   r    r    r!   test_custom$  s      
zTestOptimizeSimple.test_customz$output not reliable on all platformsr   c                 C   s:  t jddgt jdd}t jf i |ddi | \}}d|vrJd|vsNJ t jf i |dd	i | \}}d|v rd|vsJ t jf i |dd
i | \}}d|v rd|v sJ t jf i |d
dd | \}}d|vrd|vsJ t jf i |ddd | \}}d|v r2d|v s6J d S )Nr   rH   )rH   r   r  )r`   r@   r   r   iprintr   rs  z
At iterater   r   F)r  rn   T)r
   r   r{  r`  Z
readouterr)rV   Zcapfdr.  outr   r    r    r!   test_gh13321J  s$    
zTestOptimizeSimple.test_gh13321c                    s<   ddg d fdd}ddg}t jt j|| d d S )N)r#  r$   )r   rH   constraintsc                    s(   |d  u sJ |d u s J t  S )Nr   r  r
   r   )ru   r@   rt   r   r  r    r!   r  r  s    z0TestOptimizeSimple.test_gh10771.<locals>.custminr   )rr   r   r  )r
   r   r   )rV   r  r@   r    r  r!   test_gh10771l  s    zTestOptimizeSimple.test_gh10771c                 C   s   dd }dd }dD ]~}|dv r&d }n|}t j|ddg|d|d	}t j|ddg|d
|d	}||j||jk sJ | d||j d||j qd S )Nc                 S   s$   | \}}|d |d  |d  d S )Nr$   r   r   r    zr   r  r    r    r!   r`   }  s    z<TestOptimizeSimple.test_minimize_tol_parameter.<locals>.funcc                 S   s:   | \}}t d| |d  d|d   d|d  | gS )Nr$   r   rH   r   r8   r  r    r    r!   dfunc  s    z=TestOptimizeSimple.test_minimize_tol_parameter.<locals>.dfunc	nelder-meadpowellcgr   	newton-cgrm  tnccobylaslsqpr  r  r  r   r$  )rs   r\  rr   rE   z: z vs. )r
   r   r   )rV   r`   r  rr   rs   Zsol1Zsol2r    r    r!   test_minimize_tol_parameter{  s    z.TestOptimizeSimple.test_minimize_tol_parameterr   ignore::RuntimeWarningrr   )r   r   r   r   r   r`  fmin_tnc
fmin_slsqpc           	         sh   dv rdd }nt j}t j}t j}td}i } drtt  } dkrXd|d< q d	krjd
|d< q dv r|d|d< qd|d< n2 fdd} dkrtd
d|d< ntdd|d<  dv r||d< n* dv r||d< n dv r||d< ||d< g fdd}|||fd|i| t	dks,J t
dd  D sDJ td!d  tdD rdJ d S )"N)r  r`  c                 S   s   t | t | fS r/   )r
   r   r{  r   r    r    r!   r`     s    zDTestOptimizeSimple.test_minimize_callback_copies_array.<locals>.funcr   r   r  r   iterr  r   r  )r   r   i  rQ   c                     s    |d< t j| i |S )Nrr   r
   r   )akwr   r    r!   routine  s    zGTestOptimizeSimple.test_minimize_callback_copies_array.<locals>.routiner  r  rt   rf  )r   r   )r  rs   rN  rQ  rM  rP  rL  re   c                    s(   t | tjrJ  | t| f d S r/   )
isinstancer
   r   r[   r   r\   )r   rq   r.  )resultsr    r!   rn    s    zHTestOptimizeSimple.test_minimize_callback_copies_array.<locals>.callbackrn  r$   c                 s   s    | ]\}}t ||kV  qd S r/   )r   r7   r   r   r  r    r    r!   r    r   zITestOptimizeSimple.test_minimize_callback_copies_array.<locals>.<genexpr>c                 s   s&   | ]\}}t |d  |d  V  qdS )r   N)r   Zmay_share_memoryr  r    r    r!   r    r   )r
   r   r{  
rosen_hessr   rM   
startswithgetattrr  r  r7   anyrG  combinations)	rV   rr   r`   rs   re   r@   r.  r  rn  r    )rr   r  r!   #test_minimize_callback_copies_array  sB    










z6TestOptimizeSimple.test_minimize_callback_copies_arrayr  c           	      C   s   dd }dd }t dg}||}|}|dkr:tddntdd	}|d
v rPd }tj|||||d}t||j|j |dkrt	d ||j|ksJ d S )Nc                 S   s   | d d S r#   r    r   r    r    r!   r`     s    z1TestOptimizeSimple.test_no_increase.<locals>.funcc                 S   s   d| d  d d S )Nr$   r   r   r    r   r    r    r!   bad_grad  s    z5TestOptimizeSimple.test_no_increase.<locals>.bad_grad       @r  rW  r  rf  r  ru  r  zSLSQP returns slightly worse)
r   r8   r  r
   r   r   r   ru   r   r   )	rV   rr   r`   r  r@   Zf0rs   rt   r   r    r    r!   test_no_increase  s    
z#TestOptimizeSimple.test_no_increasec                 C   sX   dd }dd }t g d}tj||dd|dd	}t|jt g d
d dd d S )Nc                 S   s   t | tg d d S )N)rE   r        @r  r$   )r1   r   r8   r   r    r    r!   r_     s    z7TestOptimizeSimple.test_slsqp_respect_bounds.<locals>.fc                 S   s:   t g dg dg}t t || t ddg | gS )N)r   r   r   r   )r  r#  r   r   r   )r   r8   ZconcatenaterY   r   r  r    r    r!   cons  s    z:TestOptimizeSimple.test_slsqp_respect_bounds.<locals>.cons)rG   rE   r&   r  r  ineqtyperu   rr   r  )rI   r$   r   r   rH   g-q=r{   )r   r8   r
   r   r   r   )rV   r_   r  r@   r   r    r    r!   test_slsqp_respect_bounds  s    
z,TestOptimizeSimple.test_slsqp_respect_bounds)r   r   rp   r   r   rs  SLSQPrL  rP  rM  rQ  rN  c                 C   s   d}t d}ttj|dtjtjd d }|t|dd}|dv rL|j|d< n|dv rh|j|d< |j	|d	< tj
|j|fi |}|j|ksJ |j|jksJ t|d
r|j|jksJ |dkr|jdksJ d S )Nr   r   r    rf  r   )r   rs   r  re   rw   r  r}   )r   rM   r   r
   r   r{  r  r  rc   re   r   ru   r   rv   hasattrrw   Zngevrx   )rV   rr   MAXITERr@   sfr.  r   r    r    r!   test_respect_maxiter   s$    



z'TestOptimizeSimple.test_respect_maxiter)r   r   r   r   c                 C   s   t d}ttj|dtjtjd d }ddd}tjt	ddN |
drhtt|}||j|fi | ntj|j|||d	 W d    n1 s0    Y  d S )
Nr   r    r   T)rQ   rn   zMaximum number of iterationsr   r   r   )r   rM   r   r
   r   r{  r  r   warnsRuntimeWarningr  r  ru   r   )rV   rr   r@   r  rt   r  r    r    r!   test_runtime_warning"  s    



z'TestOptimizeSimple.test_runtime_warningc           	   
   C   sd   d}t j}t j}t j}dd }d|df}td}t j|||||dt|dd	}|j|ks`J d S )
Nr   c                 S   s,   t d| d  d| d   d| d   gS )Nr6   r   皙?r   Q?r$   r  r   r    r    r!   ru   :  s    zRTestOptimizeSimple.test_respect_maxiter_trust_constr_ineq_constraints.<locals>.funr  r  r   rL  rf  )r  rs   re   rr   rt   )	r
   r   r{  r  r   rM   r   r  r   )	rV   r  r_   rs   re   ru   r  r@   r   r    r    r!   2test_respect_maxiter_trust_constr_ineq_constraints1  s    
zETestOptimizeSimple.test_respect_maxiter_trust_constr_ineq_constraintsc           
      C   s   dd }dd }t dg}t||}tj||d|dgd}tj||d	gd
}tj||d|dgd	gd}tj||d|dgdgd}|||||fD ]}	|	jsJ qt|jddd t|jddd t|jddd t|jddd t|jddd d S )Nc                 S   s   | d S r  r    r   r    r    r!   r_   F  s    z6TestOptimizeSimple.test_minimize_automethod.<locals>.fc                 S   s   | d S r  r    r   r    r    r!   r  I  s    z9TestOptimizeSimple.test_minimize_automethod.<locals>.consrS  r  r  )r  )r   r   r   )r  r   r   r   r   r.   r{   r$   r   )r   r8   r
   r   r   r   r   )
rV   r_   r  r@   Zsol_0Zsol_1Zsol_2Zsol_3Zsol_4r   r    r    r!   test_minimize_automethodE  s.    


z+TestOptimizeSimple.test_minimize_automethodc                 C   sH   dd }ddd}t g d}t jt|}tj||||dd d S )	Nc                 S   s   t | | d S r  r  r   rp  r    r    r!   Ya  s    z=TestOptimizeSimple.test_minimize_coerce_args_param.<locals>.Yc                 S   s   d| |  S r  r    r  r    r    r!   dY_dxd  s    zATestOptimizeSimple.test_minimize_coerce_args_param.<locals>.dY_dx)rH   r   r   r   r   r}   r$   r   r   rH   r   r   )rs   rq   rr   )N)r   r8   r'   Zrandnr  r
   r   )rV   r  r  rp  Zxinitr    r    r!   test_minimize_coerce_args_param_  s
    
z2TestOptimizeSimple.test_minimize_coerce_args_paramc           	         s"  g d}g d} fdd}fdd}t ||D ]\}|dv rXtd d	}nt }d
k rp|dv rpq8dgd g tj||||d}d| |}|jsJ |t|jdg|d |j	dksJ |d
kr8|dv rt d d|d n$ d dkr d dk sJ |q8q8d S )N)gJz5r   gd~QJ)rp   r   rs  r   c                    s`    d d u r4| d d kr4t | d d   d< t |  dkrLtd| d d d  S )Nr   g     @zOptimization stepped far away!r   r$   )r9   r  AssertionErrorr   Zfirst_step_sizescaler@   r    r!   r_   r  s
    z7TestOptimizeSimple.test_initial_step_scaling.<locals>.fc                    s   t  | d d  gS Nr   r   r  r   )r  r    r!   r  y  s    z7TestOptimizeSimple.test_initial_step_scaling.<locals>.g)rp   r   r  )r   r$  )rs  r         ru  z{} {}: {}: {}rE   err_msgrH   r   g)\(?rG   )
rG  rH  r  r
   r   formatr   r   r   r   )	rV   ZscalesrI  r_   r  rr   rt   r   r  r    r  r!   test_initial_step_scalingk  s6    &z,TestOptimizeSimple.test_initial_step_scaling)r  r  r  r   r  rm  r  r  r  rL  rP  rM  rQ  rN  c                    sZ  t jd dg dd } fdd}dd }d	d
 }t dg}|dv }|dv }||g}	|rd|gn|d g}
|rv|gn|d g}|dkrtddntdd}t jdd t v}|td |t	d |t	d t
|	|
|D ]2\}}}dg tj||||||d}t|jd qW d    n1 s,0    Y  W d    n1 sL0    Y  d S )Nr(   r   c                 S   s   t jS r/   r;  r   r    r    r!   r`     s    z0TestOptimizeSimple.test_nan_values.<locals>.funcc                    s0    d  d7  <  d dkr"t jS t j S d S r'  )r   r8  r'   rA  r   countr    r!   func2  s    z1TestOptimizeSimple.test_nan_values.<locals>.func2c                 S   s   t dgS NrE   r  r   r    r    r!   rc     s    z0TestOptimizeSimple.test_nan_values.<locals>.gradc                 S   s   t dggS r  r  r   r    r    r!   re     s    z0TestOptimizeSimple.test_nan_values.<locals>.hessrE   r  rN  rQ  rM  rP  rN  rQ  rM  rP  r  rW  r  rf  r   r<  delta_grad == 0.*.*does not use Hessian.*.*does not use gradient.*)rs   re   rr   rt   F)r   r'   r*   r8   r  r   r   filterUserWarningr  rG  rH  r
   r   r   r   )rV   rr   r`   r  rc   re   r@   Z
needs_gradZ
needs_hessfuncsZgradsZhesssrt   supr_   r  hr   r    r  r!   test_nan_values  s.    z"TestOptimizeSimple.test_nan_values)r  r  r   rm  r  r  r  rL  rP  rM  rQ  rN  c              	   C   s   d  }}|dv r| j }|dv r$| j}tjddZ t 4}|td tj| j	| j
|||d W d    n1 sr0    Y  W d    n1 s0    Y  tdt| jD ].}t| j|d  | j| rtd| qd S )	Nr  r  r   r<  r  rO  r   zDuplicate evaluations made by )rc   re   r   r   r   r  r  r
   r   r`   rO   r   r  rT   Zarray_equalrX   )rV   rr   rs   re   r  r  r    r    r!   test_duplicate_evaluations  s    Bz-TestOptimizeSimple.test_duplicate_evaluationsnew_cb_interface)r   r   r$   c           
         sL  fddd_ fdd}fdd}d|d	krF fd
d}n0|dkrjG  fddd}| }n fdd} fdd d _d _ dgd |||d}tjf i |d|i}|dkrΈd	 tjf i |ddii}	|j|	jksJ t|j|	j |j|	j  kr$ks*n J |j|dkr<dndksHJ d S )Nc                    s   d _ t| S NF)flagr
   r   r   r_   r    r!   r_     s    z9TestOptimizeSimple.test_callback_stopiteration.<locals>.fFc                    s   d _ t| S r  )r  r
   r{  r   r  r    r!   r    s    z9TestOptimizeSimple.test_callback_stopiteration.<locals>.gc                    s   d _ t| S r  )r  r
   r  r   r  r    r!   r    s    z9TestOptimizeSimple.test_callback_stopiteration.<locals>.hr   r   c                    s   | j | jksJ    d S r/   ru   r   intermediate_resultrn  r_   r    r!   callback_interface  s    zJTestOptimizeSimple.test_callback_stopiteration.<locals>.callback_interfacer$   c                       s    e Zd Zed fddZdS )z@TestOptimizeSimple.test_callback_stopiteration.<locals>.Callbackr  c                    s   |j |jksJ    d S r/   r  )rV   r  r	  r    r!   rj    s    zITestOptimizeSimple.test_callback_stopiteration.<locals>.Callback.__call__N)rh   ri   rj   r   rj  r    r	  r    r!   rl    s   rl  c                    s
      d S r/   r    )Zxkrq   )rn  r    r!   r
    s    c                      s.     j d7  _ d _ j kr*d _t d S )Nr   FT)r  r  StopIterationr    )rn  rQ   r    r!   rn    s
    
z@TestOptimizeSimple.test_callback_stopiteration.<locals>.callbackr   r  )r@   rr   ru   rs   re   rn  r  rt   rQ   rL  rH   c   )	r  r  r
   r   ru   r   r   r   rx   )
rV   rr   r  r  r  r
  rl  r.  r   r   r    )rn  r_   rQ   r!   test_callback_stopiteration  s2    
"z.TestOptimizeSimple.test_callback_stopiterationc                 C   sJ   d}t t|d& tdd td W d    n1 s<0    Y  d S )Nz"'x0' must only have one dimension.r   c                 S   s   | S r/   r    r   r    r    r!   r  '  r   z4TestOptimizeSimple.test_ndim_error.<locals>.<lambda>)r$   r   )r;   r<   r
   r   r   onesrV   r  r    r    r!   test_ndim_error$  s    z"TestOptimizeSimple.test_ndim_error)r  rm  r  r  r  rL  c                 C   s   dd }t ddgddg}d}tjt|d& tj|g d	||d
 W d    n1 sX0    Y  t g dg d}d}tjt|d& tj|g d	||d
 W d    n1 s0    Y  d S )Nc                 S   s   t | d S r  r  r   r    r    r!   r_   ,  s    z:TestOptimizeSimple.test_minimize_invalid_bounds.<locals>.fr   r$   rH   r   z?The number of bounds is not compatible with the length of `x0`.r   )r   r$   rH   r@   rr   r   )r   r   r   )rH   r   r$   z:An upper bound is less than the corresponding lower bound.)r   r   r	   r<   r
   r   )rV   rr   r_   r   r  r    r    r!   test_minimize_invalid_bounds)  s    4z/TestOptimizeSimple.test_minimize_invalid_bounds)r   r  r  r  c                 C   s   |dkri ndt ji}|dkr"tnt j}ddd}tj|dd2 t jdd	 d
d
gf||d| W d    n1 sx0    Y  d|d< t jdd	 d
d
gf||d| d S )Nr  rs   Tr   rr  Maximum numberr   c                 S   s
   t | S r/   r
   r   r   r    r    r!   r  C  r   zBTestOptimizeSimple.test_minimize_warnings_gh1953.<locals>.<lambda>r   r   Frn   c                 S   s
   t | S r/   r  r   r    r    r!   r  G  r   )r
   r{  r  r  r   r  r   )rV   rr   r.  Zwarning_typert   r    r    r!   test_minimize_warnings_gh19539  s"    
$z0TestOptimizeSimple.test_minimize_warnings_gh1953N),rh   ri   rj   r:  r>  rB  rK  rR  rV  r_  rc  rd  rg  rq  rw  ry  r|  r  r  r   r   r   r  r  r  r   parametrizer   r  r  r  r  r  r  r  r  r  r   r  r   r  r  r  r  r    r    r    r!   r5  &  sh   		&
!

<


4
-

6
r5  rr   )rm  r  r   r   c                 C   s<   dd }t j|ddg| d}|js&J t|jdgdd d S )	Nc                 S   s   t | d S r  r  r   r    r    r!   r_   Q  s    z$test_minimize_with_scalar.<locals>.f   )r[  r   r  rI   r   r{   )r
   r   r   r   r   )rr   r_   r   r    r    r!   test_minimize_with_scalarK  s    
r  c                   @   sz   e Zd Zdd ZdddZdddZddd	Zd
d Zdd Zdd Z	e
jdddgddgddggdd Zdd ZdS )TestLBFGSBBoundsc                 C   s   d| _ d| _d S )N))r   NNN)r   r   )r   rP   rU   r    r    r!   rW   Z  s    zTestLBFGSBBounds.setup_methodr  c                 C   s    d| |d | |d |   S )NrE   r   r   r    rf   r    r    r!   ru   ^  s    zTestLBFGSBBounds.func                 C   s   ||d  S r   r    rf   r    r    r!   rs   a  s    zTestLBFGSBBounds.jacc                 C   s   |  ||| ||fS r/   ru   rs   rf   r    r    r!   fjd  s    zTestLBFGSBBounds.fjc                 C   sN   t j| jddg| j| jd\}}}|d dks:J |d t|| jdd d S )Nr   r   )r   r   r   taskr+   r{   )r
   r`  ru   rs   r   r   rP   rV   r   r_   rb  r    r    r!   test_l_bfgs_b_boundsg  s    z%TestLBFGSBBounds.test_l_bfgs_b_boundsc                 C   sL   t j| jddgd| jd\}}}|d dks8J |d t|| jdd d S )	Nr   r   r  )rq   r   r   r  r+   r{   )r
   r`  r  r   r   rP   r  r    r    r!   rg  n  s
    z%TestLBFGSBBounds.test_l_bfgs_b_funjacc                 C   sH   t j| jddgd| j| jd}|d s2J |d t|j| jdd d S )	Nr   r   rs  rr   rs   r   r   ro  r+   r{   )r
   r   ru   rs   r   r   r   rP   )rV   r   r    r    r!   test_minimize_l_bfgs_b_boundsu  s
    z.TestLBFGSBBounds.test_minimize_l_bfgs_b_boundsr   )r   r   r  c                 C   sN   t jtdd, tj| jddgd| j|d W d    n1 s@0    Y  d S )Nz	.*bound.*r   r   r   rs  r!  )r   r	   r<   r
   r   ru   rs   )rV   r   r    r    r!   'test_minimize_l_bfgs_b_incorrect_bounds|  s    z8TestLBFGSBBounds.test_minimize_l_bfgs_b_incorrect_boundsc              
   C   st   g d}ddg}t ||D ]R\}}tj| jddg|d|| jdd id}|d	 s\J |d
 t|j| jdd qd S )NrD  r   r    r   r   rs  Zfinite_diff_rel_step)rq   rr   rs   r   rt   r   ro  r+   r{   )	rG  rH  r
   r   ru   r   r   r   rP   )rV   rJ  Zargssrs   rq   r   r    r    r!    test_minimize_l_bfgs_b_bounds_FD  s    z1TestLBFGSBBounds.test_minimize_l_bfgs_b_bounds_FDN)r  )r  )r  )rh   ri   rj   rW   ru   rs   r  r  rg  r"  r   r   r  r#  r$  r    r    r    r!   r  Y  s   



r  c                   @   sN  e Zd Zdd Zd3ddZdd Zejdd	d
 Z	dd Z
dd Zdd Zdd Zdd Zdd Zejdg ddd Zejdg ddd Zejdejdg ddd Zdd  Zd!d" Zejdd#d$gd%d& Zejd'ejdeejd(d)d*gejd+g d,d-d. Zejdg d/d0d1 Zd2S )4TestOptimizeScalarc                 C   s
   d| _ d S )Nr&   )rP   rU   r    r    r!   rW     s    zTestOptimizeScalar.setup_methodr&   c                 C   s   || d d S )zObjective functionr$   r   r    )rV   r   r  r    r    r!   ru     s    zTestOptimizeScalar.func                 C   s  t | j}t|| jdd t j| jdd}t|| jdd t j| jdd}t|d | jdd t j| jdd}t|| jdd d	}tjt|d
  t j| jdd W d    n1 s0    Y  d}tjt|d
  t j| jdd W d    n1 s0    Y  d S )Nr+   r{   r  r#  ZbrackTry   r   ir      /\(f\(xb\) < f\(xa\)\) and \(f\(xb\) < f\(xc\)\)r   r   r   r   \(xa < xb\) and \(xb < xc\)r   r   r   )r
   brentru   r   rP   r   r	   r<   )rV   r   ro  r    r    r!   
test_brent  s    .zTestOptimizeScalar.test_brentr   c                 C   s~  t | j}t|| jdd t j| jdd}t|| jdd t j| jdd}t|d | jdd t j| jdd}t|| jdd t j| jdd	}t|| j g d
}|D ]H}t j| jddd}t j| j|dd}|d |d  }}t|| | qd}tjt|d  t j| jdd W d    n1 s,0    Y  d}tjt|d  t j| jdd W d    n1 sp0    Y  d S )Nr+   r{   r&  r'  Tr(  r   r)  r\  )r   r   r   )rQ   ry   r$   r+  r   r,  r-  r.  )	r
   goldenru   r   rP   r   r   r	   r<   )rV   r   Zmaxiter_test_casesrQ   r@   Znfev0rv   ro  r    r    r!   test_golden  s,    0zTestOptimizeScalar.test_goldenc                 C   s   t | jdd}t|ddd t | jdd}t|| jdd t | jtdgtdg}t|| jdd ttt j| jdd d S )Nr   r   r,  r{   r   r+   )	r
   	fminboundru   r   rP   r   r8   r;   r<   ri  r    r    r!   test_fminbound  s     z!TestOptimizeScalar.test_fminboundc                 C   sn   t jtdd& t| jtdd W d    n1 s:0    Y  t| jdtd}t	|| j
dd d S )Nz.*must be finite scalars.*r   r   r$   r   r   r+   r{   )r   r	   r<   r
   r4  ru   r   rM   r8   r   rP   ri  r    r    r!   test_fminbound_scalar  s    4z(TestOptimizeScalar.test_fminbound_scalarc                 C   s   dd }t |dd d S )Nc                 S   s   | d S r  r    r   r    r    r!   ru     s    z,TestOptimizeScalar.test_gh11207.<locals>.funr   )r
   r4  )rV   ru   r    r    r!   test_gh11207  s    zTestOptimizeScalar.test_gh11207c                 C   s4  t | jj}t|| jdd t j| jdd}|js8J t j| jdtddd}|jrZJ t j| jdd	dd
j}t|| jdd t j| jdd	dj}t|| jdd t j| jdd	dd
j}t|| jdd t j| jdd	dd
j}t|| jdd t j| jdd	dj}t|| jdd t j| jdd	dd
j}t|| jdd t j| jdd	ddj}t|ddd t j| jdd	ddj}t|| jdd t j| jt	dgt	dgft	dgfddj}t|| jdd t
tt j| jddd	d t
tt j| jtddfdd	d t j| jdt	dfddj}t|| jdd d S )Nr+   r{   ZBrentr   rH   rf  r   r&  )r&   )bracketrq   rr   )rr   rq   r)  r2  )r   r   ZBounded)r   rq   rr   r   r,  )r   r   boundedr   r&   )r   r   r   rr   rq   r$   r  )r
   minimize_scalarru   r   r   rP   r   r  r   r8   r;   r<   rM   ri  r    r    r!   test_minimize_scalar  sr    









z'TestOptimizeScalar.test_minimize_scalarc                 C   s:   ddd}t j| jd|tddd	}t|j| jd
d d S )Nr    r-   r   c                 [   s   |d |d  d }| |}	d}
d}d}d}|r|s||k rd}|d7 }|| || fD ]0}| |g|R  }|
d7 }
||	k rX|}	|}d}qX|d ur|| |d ur,|
|kr,d}qq,t j|	|||
|dkdS )Nr   r   r  TFr  r  )ru   r9  rq   r   r  rQ   rn  rt   r  r  r  r  r  r  r  r  r    r    r!   r  (  s0    
z?TestOptimizeScalar.test_minimize_scalar_custom.<locals>.custmin)r   r   r  r  )r9  rr   rt   r+   r{   )r    Nr-   r   N)r
   r<  ru   r  r   r   rP   )rV   r  r   r    r    r!   test_minimize_scalar_custom&  s      

z.TestOptimizeScalar.test_minimize_scalar_customc                 C   s   t j| jdd d S )Nr&   rq   r
   r<  ru   rU   r    r    r!   &test_minimize_scalar_coerce_args_paramI  s    z9TestOptimizeScalar.test_minimize_scalar_coerce_args_paramrr   )r/  r:  r2  c                 C   s"   dD ]}t j| jd|id qd S )N)r   r   r$   rH   rn   )rt   r@  )rV   rr   rn   r    r    r!   	test_dispM  s    zTestOptimizeScalar.test_dispc                 C   s   |dkrdddgini }t j| jfd|i|}t|ds>J t|dsLJ t|dsZJ t|d	shJ t|d
svJ t|dsJ d S )Nr:  r   r   r   rr   r   r   ro  ru   rv   r   )r
   r<  ru   r  )rV   rr   r.  r   r    r    r!   test_result_attributesS  s    z)TestOptimizeScalar.test_result_attributesc              	      s   t jd dg  fdd}d}d}t jdd t }|td	 |td
 |td dg |dkrvd|ini }tj	|fd|i||t
ddd}t|jd W d    n1 s0    Y  W d    n1 s0    Y  d S )Nr(   r   c                    s<    d  d7  <  d dkr"t jS | d dt |   S d S )Nr   r   r   r$   r-   )r   r8  r0   r   r  r    r!   r`   f  s    z0TestOptimizeScalar.test_nan_values.<locals>.funcr,  r  r   r<  r  r  r  r:  r   r9  rW  rf  r   F)r   r'   r*   r   r   r  r  r  r
   r<  r  r   r   )rV   rr   r`   r9  r   r  r.  r   r    r  r!   r   ^  s$    
z"TestOptimizeScalar.test_nan_valuesc                 C   sF   dd }t |}t|jddd t j|dddid	}t|jd
 d S )Nc                 S   s   | d S r  r    r   r    r    r!   r_     s    zCTestOptimizeScalar.test_minimize_scalar_defaults_gh10911.<locals>.fr   r  r{   )r   r   r	  r$  )r   rt   r   )r
   r<  r   r   )rV   r_   r   r    r    r!   %test_minimize_scalar_defaults_gh10911}  s    
z8TestOptimizeScalar.test_minimize_scalar_defaults_gh10911c                 C   s   d}t jt|d& tjtjdtjfd W d    n1 s>0    Y  t jt|d& tjtjtjdfd W d    n1 s0    Y  d S )Nz+Optimization bounds must be finite scalars.r   r   r  )	r   r	   r<   r
   r<  r   r0   r*  r8  r  r    r    r!   'test_minimize_non_finite_bounds_gh10911  s
    4z:TestOptimizeScalar.test_minimize_non_finite_bounds_gh10911r/  r2  c                 C   sH   d}t jt|d" tjtj|dd W d    n1 s:0    Y  d S )Nz'Use of `bounds` is incompatible with...r   r6  rr   r   )r   r	   r<   r
   r<  r   r0   )rV   rr   r  r    r    r!   2test_minimize_unbounded_method_with_bounds_gh10911  s    zETestOptimizeScalar.test_minimize_unbounded_method_with_bounds_gh10911r  r\  r   r+   fshape)r    r   r   r   c           	         s    fdd}d\}}|dkr*t ||fdnt ||fd}|t ||d tj|fi |}|jj|jj  kr||jj  kr ksn J d S )Nc                    s   t | d  S Nr   )r   r8   Zreshaper   rH  r    r!   r_     s    zITestOptimizeScalar.test_minimize_scalar_dimensionality_gh16196.<locals>.f)r!  r6   r:  )r9  r  )rr   r\  )r  updater
   r<  r   shaperu   )	rV   rr   r\  rH  r_   r  br.  r   r    rL  r!   +test_minimize_scalar_dimensionality_gh16196  s    z>TestOptimizeScalar.test_minimize_scalar_dimensionality_gh16196)r:  r/  r2  c                 C   s   dd }i }|dkrdnd}ddg||< dd	d
}t jtjdd( tj|f||d| W d    n1 sp0    Y  d|d< tj|f||d| d S )Nc                 S   s   | d d S r#   r    r   r    r    r!   r_     s    zBTestOptimizeScalar.test_minimize_scalar_warnings_gh1953.<locals>.fr:  r   r9  r#  r   TrH   rr  r  r   r   Frn   )r   r  r
   r  r<  )rV   rr   r_   r.  Zkwdrt   r    r    r!   $test_minimize_scalar_warnings_gh1953  s    
$z7TestOptimizeScalar.test_minimize_scalar_warnings_gh1953N)r&   )rh   ri   rj   rW   ru   r0  r   r   r   r3  r5  r7  r8  r=  r>  rA  r  rB  rC  r   rD  rE  rG  r   rP  rQ  r    r    r    r!   r%    s:   


<#



	

r%  c                   @   s6   e Zd Zejddd Zejdddd ZdS )	TestBracketr  c                 C   sP  dd }d}t jt|d t|dd W d    n1 s>0    Y  t jt|d  t|dtj W d    n1 s|0    Y  t jt|d tj|dd W d    n1 s0    Y  t jt|d tj|dd W d    n1 s0    Y  d	d }d
}t jt|d" tj|dddd W d    n1 sB0    Y  d S )Nc                 S   s   d| k | dk @ r| d S dS Nr   r   r$   g      Y@r    r   r    r    r!   r_     s    z3TestBracket.test_errors_and_status_false.<locals>.f9The algorithm terminated without finding a valid bracket.r   r   r   r  r'  c                 S   s<   d| d  d| d   d| d   d| d   d|   d S )	Nr  r   r      rH      r$   r   r    r   r    r    r!   r_     s    z8No valid bracket was found before the iteration limit...r   rG   r   rf  )	r   r	   rX   r
   r9  r   r*  r/  r2  )rV   r_   ro  r    r    r!   test_errors_and_status_false  s    ,.,,z(TestBracket.test_errors_and_status_falserr   )r/  r2  c                 C   sb   dd }d}t j|d|d}|jr&J ||jv s4J |jdksBJ |jdksPJ |jdks^J d S )	Nc                 S   s   d| k | dk @ r| d S dS rS  r    r   r    r    r!   r_     s    z9TestBracket.test_minimize_scalar_success_false.<locals>.frT  r  )r9  rr   rH   r   r   )r
   r<  r   ro  rv   r   ru   )rV   rr   r_   ro  r   r    r    r!   "test_minimize_scalar_success_false  s    
z.TestBracket.test_minimize_scalar_success_falseN)	rh   ri   rj   r   r   r   rW  r  rX  r    r    r    r!   rR    s   

rR  c                   C   s   t ttjtjdd d S )Ng{Gzr1  )r;   r<   r
   r/  r   r4   r    r    r    r!   test_brent_negative_tolerance  s    rY  c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestNewtonCgc                 C   sX   t ddg}tjtj|tjtjddd}|js:J |jt	|j
t ddgdd d S 	Nrz  rE   r   r   rs   re   r\  rr   r   r,  r   )r   r8   r
   r   r   r{  r  r   ro  r   r   rV   r@   r   r    r    r!   test_rosenbrock  s    
zTestNewtonCg.test_rosenbrockc                 C   sT   t t}tjt|ttddd}|js0J |j	t
|jtdd t
|jtdd d S )Nr   r+   )rs   re   rr   r\  r,  r   r{   )r   r8   r?   r
   r   
himmelblaur=   r>   r   ro  r   r   himmelblau_xoptru   himmelblau_minr]  r    r    r!   test_himmelblau  s    
zTestNewtonCg.test_himmelblauc                 C   sV   t ddg}tjtj|tjdddd}|js8J |jt|j	t ddgdd	 d S )
Nrz  rE   rE  r   r   r\  r   r,  r   )
r   r8   r
   r   r   r{  r   ro  r   r   r]  r    r    r!   test_finite_difference  s    
z#TestNewtonCg.test_finite_differencec                 C   sZ   t ddg}tjtj|tjt ddd}|js<J |jt	|j
t ddgdd d S r[  )r   r8   r
   r   r   r{  r   r   ro  r   r   r]  r    r    r!   test_hessian_update_strategy  s    
z)TestNewtonCg.test_hessian_update_strategyN)rh   ri   rj   r^  rb  rc  rd  r    r    r    r!   rZ    s   

rZ  c                  C   s  t jj} tg d}tg d}tg d}tg d}|tg dddf|tg dd	d
f|tg dddf|tg dddf|tg dd	d
f|tg dddf|tg dddf|tg dddf|tg ddd	f|tg dddf|tg dddf|tg ddd	f|tg dddff}|D ]<\}}}}	| ||||\}
}t|
|dd t||	dd qLttj d	tj dg}ttjd
dtjg}|tg dtj tjf|tg dd	d
f|tg dtj df|tg ddtjf|tg dd	d
f|tg ddtjf|tg dtj tjf|tg ddd	f|tg dtj df|tg ddtjf|tg ddd	f|tg ddtjff}|D ]<\}}}}	| ||||\}
}t|
|dd t||	dd qd S )N)333333r   r   r  )r   r   ffffff@rH   rI   r   r   r   )rI   r$   r  r   rE   r   r   r   re  r   rI   r   r   r   r   r   rI   r   r   r   r   rf  rI   r   r   r   r  rH   )rE   r   r   r   )rE   r   r   r$   r&   )r  r   r   r$   gffffff?g333333@)rE   r   r   r   r+   r{   g333333)r
   r  Z_line_for_searchr   r8   r   r*  )Zline_for_searchlower_boundupper_boundr@   x1	all_testsr   alphaZlminZlmaxmimar    r    r!   test_line_for_search  sT    rs  c               
   C   sz  t jj} dd }tg d}||}ttj gd }ttjgd }tg ddftg ddftg d	d
ftg ddftg ddftg ddftg ddff}|D ]\}}| ||||dd\}	}
}t|	||| dd t|
|| dd t||| dd | |||d|||d\}	}
}t|	||| dd t|
|| dd t||| dd qd S )Nc                 S   s   t | t g d d S N)r  r  r&   皙ٿr$   r   r1   r8   r   r    r    r!   r`   _  s    z$test_linesearch_powell.<locals>.funcrg  r   rh  r   ri  r$   rj  r&   rk  ru  r  r   r   r         ?rI   r   r   r   皙?r  r   r   r   r   )fvalr\  r+   r{   r\  rl  rm  r}  )r
   r  _linesearch_powellr   r8   r*  r   Zlinesearch_powellr`   r  r}  rl  rm  ro  xilr_   rb   r)   r    r    r!   test_linesearch_powellZ  s:    

r  c               
   C   s  t jj} dd }tg d}||}tdgd }tdgd }tg ddftg d	d
ftg ddftg ddftg ddftg ddftg ddff}|D ]^\}}| |||d|||d\}	}
}t|	||| dd t|
|| dd t||| dd qtdgd dg }tdgd dg }tg ddftg d	dftg ddftg ddftg ddftg ddftg ddff}|D ]`\}}| |||d|||d\}	}
}t|	||| dd t|
|| dd t||| dd qtg d}||}tg dd ftg d	dftg ddftg dd!ff}|D ]h\}}| |||d|||d\}	}
}t|	||||  dd t|
|||  dd t||| dd qtg d}||}tdtj tj dg}ttjdtjdg}tg ddftg d	dftg ddftg ddftg ddftg ddftg ddff}|D ]`\}}| |||d|||d\}	}
}t|	||| dd t|
|| dd t||| dd qtg d}||}tg dd ftg d	dftg ddftg dd!ff}|D ]h\}}| |||d|||d\}	}
}t|	||||  dd t|
|||  dd t||| dd qjd S )"Nc                 S   s   t | t g d d S rt  rv  r   r    r    r!   r`     s    z,test_linesearch_powell_bounded.<locals>.funcrg  g       r   r  rh  r   ri  r$   rj  r&   rk  ru  rw  rx  ry  rz  r{  r|  r   r~  r+   r{   g333333ӿrH   g?r  rF   g333333ÿ)r  r   r   r$   r   g333333)r
   r  r  r   r8   r   r*  r  r    r    r!   test_linesearch_powell_bounded  s    







r  c                     sl   t ddgddg  fdd} t j| ddgd d t jdgdgd	gd
 dd }t j|dgd d d S )Nr   g333333?rW  c                    s8   | \}}|  j k r$|  jk s(J |d |d  S r  )lbr7   ub)r   r  rO  r  r    r!   ru   	  s     ztest_powell_limits.<locals>.funr   r  r   T)r  r  Zkeep_feasiblec                 S   s   | dkr| dksJ t | S r  r   r   r    r    r!   r`   	  s    z test_powell_limits.<locals>.funcrG   r  )ru   r@   rr   r   )r
   r   r   )ru   r`   r    r  r!   test_powell_limits  s    r  c                   @   s   e Zd Zdd ZdS )	TestRosenc                 C   sH   t g d}t g d}t||}t t||}t|| d S )N)rH   r   r   )r$   r$   r$   )r   r8   r
   rosen_hess_prodrY   r  r   )rV   r   rb   hpZdothpr    r    r!   	test_hess	  s
    zTestRosen.test_hessN)rh   ri   rj   r  r    r    r    r!   r  	  s   r  c                 C   s8   | \}}|| | d }|||  d }|| ||  S )zx
    R^2 -> R^1 test function for optimization. The function has four local
    minima where himmelblau(xopt) == 0.
    rV  r~   r    )rb   r   r  r  rO  r    r    r!   r_  	  s    r_  c                 C   sn   | \}}t d|d  d| |  d|  d|d   d d|d  d| |  d|d   d|  d gS )Nr   rH   *   r$         r   r  rb   r   r  r    r    r!   r=   (	  s    2.r=   c                 C   s^   | \}}t d|d  d|  d d| d|  gd| d|  d| d|d   d ggS )NrU  r$   r   r  r  r  r  r    r    r!   r>   .	  s    *&r>   gHzGѿgrH   r$   rI   c                  C   sj   dd } dd }dd }d| dd|dd|df}d	d
 }t j|g dd|d}t|jg ddd d S )Nc                 S   s0   t dd| d   d| d   d| d   gS )N   r6   r   r  r   r  r$   r  r   r    r    r!   r`   ;	  s    z0test_minimize_multiple_constraints.<locals>.funcc                 S   s   t | d gS r   r  r   r    r    r!   func1>	  s    z1test_minimize_multiple_constraints.<locals>.func1c                 S   s   t | d gS r  r  r   r    r    r!   r  A	  s    z1test_minimize_multiple_constraints.<locals>.func2r  r  c                 S   s   d| d | d  | d   S )Nr   r   r   r$   r    r   r    r    r!   r_   H	  s    z-test_minimize_multiple_constraints.<locals>.fr  r  r  )}   r   r   r$  r{   )r
   r   r   r   )r`   r  r  r  r_   r   r    r    r!   "test_minimize_multiple_constraints9	  s    r  c                   @   s   e Zd Zdd Zdd ZdS )TestOptimizeResultAttributesc                 C   s8   ddg| _ tj| _tj| _tj| _tj| _	ddg| _
d S )Nr   )rI   rS  )r@   r
   r   r`   r{  rs   r  re   r  rg   r   rU   r    r    r!   rW   R	  s    
z)TestOptimizeResultAttributes.setup_methodc              
   C   s   g d}ddgi}t D ]}t <}|td tj| j| j|| j| j	| j
d}W d    n1 sb0    Y  |D ]8}||v r||| v rqpt||sJ |t|v spJ qpt|jtsJ qd S )N)r   rv   r   r   rx   ru   ro  r  r   z7Method .+ does not use (gradient|Hessian.*) information)rr   rs   re   rg   )r   r   r  r  r
   r   r`   r@   rs   re   rg   r  dirr  ro  str)rV   
attributesskiprr   r  r   	attributer    r    r!   test_attributes_presentZ	  s"    
$z4TestOptimizeResultAttributes.test_attributes_presentN)rh   ri   rj   rW   r  r    r    r    r!   r  O	  s   r  c                 G   s^   | \}}|\}}}}}}	}
}}}}}}||d  || |  ||d   ||  ||  |	 S r  r    r  r   r   r  r  rO  rp  rb  r   r_   r  r  r  r   r  r  r  r    r    r!   f1q	  s    r  c                 G   sP   | \}}|\}}}}}}	}
}}}}}}|
 t || d || d   |  S r  r   r  r    r    r!   f2w	  s    r  c                 G   sP   | \}}|\}}}}}}	}
}}}}}}| t || d || d   |  S r  r   r  r    r    r!   f3}	  s    r  c                 G   s0   t | g|R  t| g|R   t| g|R   S r/   )r  r  r  r  r   r    r    r!   
brute_func	  s    r  c                   @   sD   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dS )	TestBrutec                 C   s4   d| _ tdddtdddf| _tddg| _d S )N)r$   rH   r~   r   r}   r   ,   r   r$   r  r   r#  rG   r  r         ?g_}gi?)r   slicerrangesr   r8   rP   rU   r    r    r!   rW   	  s    zTestBrute.setup_methodc                 G   s   t |g|R  S r/   )r  )rV   r  r   r    r    r!   r  	  s    zTestBrute.brute_funcc                 C   s   t jt| j| jdt jd}t|d | jdd t|d t| jg| jR  dd t jt| j| jdt jd}t|d | jdd t|d t| jg| jR  dd t j| j| j| jdt jd}t|d | jdd d S )NTrq   ry   finishr   r   r{   r   )	r
   bruter  r  r   r   r   rP   r   )rV   resbruter    r    r!   
test_brute	  s(    zTestBrute.test_brutec                 C   s    dd }t j|dgdd d d S )Nc                 S   s,   t | jdksJ | jd dks$J | d S )Nr   r   r$   )r  rN  r   r    r    r!   r_   	  s    zTestBrute.test_1D.<locals>.fr  rH   )ZNsr  )r
   r  r^  r    r    r!   test_1D	  s    zTestBrute.test_1Dc                 C   sZ   t jt| j| jdd d}t jt| j| jdd dd}t|d |d  t|d |d  d S )NTr  r$   )rq   ry   r  workersr   r   )r
   r  r  r  r   r   )rV   r  Z	resbrute1r    r    r!   test_workers	  s    zTestBrute.test_workersc                    s`   t jd  fdd}tjtdd& tj|| j| j	dd W d    n1 sR0    Y  d S )Nr(   c                    s     dd S r   r   r  r   r    r!   r`   	  s    z,TestBrute.test_runtime_warning.<locals>.funcz)Either final optimization did not succeedr   T)rq   rn   )
r   r'   r   r   r  r  r
   r  r  r   )rV   r`   r    r   r!   r  	  s    zTestBrute.test_runtime_warningc                 C   s0   dd }t j|tdddfdd}t|d d S )	Nc                 W   s   | |d  S r=  r    r   rq   r    r    r!   r_   	  s    z+TestBrute.test_coerce_args_param.<locals>.fr  r   r  r$   r?  r   )r
   r  r  r   )rV   r_   r  r    r    r!   test_coerce_args_param	  s    z TestBrute.test_coerce_args_paramN)
rh   ri   rj   rW   r  r  r  r  r  r  r    r    r    r!   r  	  s   

r  c                     s   dd l } dd lfddfddd  fdd} fd	d
}| j F}g }||| ||| |D ]}|  q|W d    n1 s0    Y  d S )Nr   c                    s     d | d d S )Nr-   r   r$   sleepr   timer    r!   
objective1	  s    
z*test_cobyla_threadsafe.<locals>.objective1c                    s     d | d d d S )Nr-   r   r   r$   r  r   r  r    r!   
objective2	  s    
z*test_cobyla_threadsafe.<locals>.objective2COBYLAc                      s   t jdg dS NrI   r   r  r    )
min_methodr  r    r!   
minimizer1	  s    z*test_cobyla_threadsafe.<locals>.minimizer1c                      s   t jdg dS r  r  r    )r  r  r    r!   
minimizer2	  s    z*test_cobyla_threadsafe.<locals>.minimizer2)concurrent.futuresr  ZfuturesZThreadPoolExecutorr[   Zsubmitr   )Z
concurrentr  r  poolZtasksr)  r    )r  r  r  r  r!   test_cobyla_threadsafe	  s    r  c                   @   s4   e Zd Zdd Zdd Zdd Zdd Zd	d
 ZdS )TestIterationLimitsc                 C   s
   d| _ d S r=  )r  rU   r    r    r!   rW   	  s    z TestIterationLimits.setup_methodc                 C   s\   |  j d7  _ t|d d |d d  t|d |d  }}t|d | |d  S )Nr   r   r$   rW  rG   )r  r   r?  Zarctan2r0   )rV   rx  rA   r)  r    r    r!   	slow_func	  s    4zTestIterationLimits.slow_funcc                 C   s   |  dd d S )Nr      check_limitsrU   r    r    r!   test_neldermead_limit 
  s    z)TestIterationLimits.test_neldermead_limitc                 C   s   |  dd d S )Nr  rJ   r  rU   r    r    r!   test_powell_limit
  s    z%TestIterationLimits.test_powell_limitc              	   C   s0  ddgddgddgfD ]}dD ]^}d| _ tj| j||d|id}| j |d ksTJ |d	 rn|d |k s~J q |d |ks J q dD ]F}tj| j||d
|id}|d	 r|d |ksJ q|d |ksJ qddgddgdtjgfD ]\}}d| _ tj| j||||dd}| j |d ks J |d	 rL|d |k rF|d |kshJ q|d |ks|d |ksJ qtjd gd tjgfD ]\}}d| _ tj| j||||dd}| j |d ksJ |d	 r|d u r|d |d k sJ n|d |d ks&J n(|d |d ks~|d |d ks~J q~qd S )Nr-   r   r$   )r   i    r   r   r   rv   r   rQ   r   r   r  )rQ   r   )r  r
   r   r  r   r*  )rV   rr   Zdefault_itersZstart_vZmfevr   Zmitr    r    r!   r  
  sZ    

 

"


z TestIterationLimits.check_limitsN)rh   ri   rj   rW   r  r  r  r  r    r    r    r!   r  	  s
   r  c                  C   s   dd } dd }dd }g d}|D ],}t j| tdg|d	}|jjd
ks$J q$g d}|D ]0}t j| tdg|||d}|jjd
ks^J q^d S )Nc                 S   s   | |  S r/   r    r   r    r    r!   ru   6
  s    z2test_result_x_shape_when_len_x_is_one.<locals>.func                 S   s   d|  S Nr  r    r   r    r    r!   rs   9
  s    z2test_result_x_shape_when_len_x_is_one.<locals>.jacc                 S   s   t dggS r  r  r   r    r    r!   re   <
  s    z3test_result_x_shape_when_len_x_is_one.<locals>.hess)r   r   rp   r   rs  rC  r  r  r-   r   rI  )rL  rP  rM  rQ  rN  r   rO  )r
   r   r   r8   r   rN  )ru   rs   re   rI  rr   r   r    r    r!   %test_result_x_shape_when_len_x_is_one5
  s    r  c                   @   s   e Zd Zdd Zdd ZdS )FunctionWithGradientc                 C   s
   d| _ d S r=  )number_of_callsrU   r    r    r!   rh  O
  s    zFunctionWithGradient.__init__c                 C   s$   |  j d7  _ t|d d| fS r#   )r  r   r1   ri  r    r    r!   rj  R
  s    zFunctionWithGradient.__call__Nrk  r    r    r    r!   r  N
  s   r  c                   C   s   t  S r/   )r  r    r    r    r!   function_with_gradientW
  s    r  c                 C   s   t | }tddg}t||d | jdks2J t||d|  | jdksXJ dt|d| ddd	 | jdksJ dd S )
NrE   r  r  r   r$   zHfunction is not recomputed if gradient is requested after function valueg      4@(different input triggers new computationr  )r   r   r8   r   r  
derivativer  memoized_functionr@   r    r    r!   )test_memoize_jac_function_before_gradient\
  s    r  c                 C   s   t | }tddg}t||d|  | jdks8J t||d | jdksXJ dt|d| d| dd	 | jdksJ dd S )
NrE   r  r$   r   r  zHfunction is not recomputed if function value is requested after gradientr   r  r  )r   r   r8   r   r  r  r  r    r    r!   )test_memoize_jac_gradient_before_functiono
  s    r  c                 C   s   t | }|j}t }tddg}t||d||dd}| jdksFJ ||d  | jdksbJ ||d  | jd	ks~J dS )
z Tests that using MemoizedJac in combination with ScalarFunction
        and BFGS does not lead to repeated function evaluations.
        Tests changes made in response to GH11868.
    rE   rG   r    Nr   r-   r$   r6   rH   )	r   r  r
   r   r   r8   r   r  ru   )r  r  rs   re   r@   Zscalar_functionr    r    r!   test_memoize_jac_with_bfgs
  s    r  c                   C   sF   t  , tjdd tj tjdd W d    n1 s80    Y  d S )Nc                 S   s   t | d gS r  r  r   r    r    r!   r  
  r   ztest_gh12696.<locals>.<lambda>Fr   )r   r
   r4  r   r   r    r    r    r!   test_gh12696
  s    r  c                     s  t jd t jd} t g dt g d}|kdfdd	  fdd	 fd
d fdd} fdd} fdd} fdd} fdd}t|t j d}t|t j d|}t|t j d}	t|t j d|}
d}dddfddddf}dd tf}dg g f||f|
|
f|g|gf|	g|
gf||	g||
gf||
g||
gf||
g||
gff	}d |f}||||||| d	}|S )Nr   r   )r   r$   r   r  )rH   r$   r$   r  Tc                    s,   |r| j dksJ |r(t|      d S rK  )r  r   )r   Z
check_sizecheck_values)i_ebr  r    r!   check_x
  s    z(setup_test_equal_bounds.<locals>.check_xc                    s    |  t | S r/   r  r   r  r    r!   r`   
  s    z%setup_test_equal_bounds.<locals>.funcc                    s    |  t | S r/   )r
   r{  r   r  r    r!   rc   
  s    z%setup_test_equal_bounds.<locals>.gradc                    s    |  d S r/   r    r  r  r    r!   rn  
  s    z)setup_test_equal_bounds.<locals>.callbackc                    s    | dd | dd d S )NFr  r   r   r    r   r  r    r!   constraint1
  s    z,setup_test_equal_bounds.<locals>.constraint1c                    s"    | dd t | }d|d< |S )NFr  r   r   r   Z
zeros_liker   dcr  r    r!   	jacobian1
  s    
z*setup_test_equal_bounds.<locals>.jacobian1c                    s    | dd | dd d S )NFr  r$   rH   rG   r    r   r  r    r!   constraint2
  s    z,setup_test_equal_bounds.<locals>.constraint2c                    s"    | dd t | }d|d< |S )NFr  r   r$   r  r  r  r    r!   	jacobian2
  s    
z*setup_test_equal_bounds.<locals>.jacobian2)rs  r  rC  Fr  c                    s    | | fS r/   r    r   re  r    r!   r  
  r   z)setup_test_equal_bounds.<locals>.<lambda>c                 S   s   t t| |S r/   )listzipr  r  r    r    r!   r  
  r   r  )	rI  kwdsbound_typesr  	callbacksr  r  r@   r  )TT)r   r'   r*   rA  r8   r   r*  r   )r@   r  rn  r  r  r  r  Zc1aZc1bZc2aZc2brI  r  r  r  r  datar    )r  r`   rc   r  r  r!   setup_test_equal_bounds
  sP    r  z0Failures due to floating point issues, not logicrI  r  
bound_typer  r  rn  r  c                 C   s  t  dkr2| dkr2|d du r2|dur2td td td  }}td	 td
  }}|\}	}
|	rt| dksttd |	|
k}|||}||| ||	|d tjf i |}tjtj|| tj	||
d}|j
sJ t|j|jdd t|j|jdd |s|d du rtj|j|< |jjd dks*J t|j| |j| dd |d s|	st|tsdd }tj||ddg | |ddd d}t|j|j t|jddg |jdd dS )z
    Tests that minimizers still work if (bounds.lb == bounds.ub).any()
    gh12502 - Divide by zero in Jacobian numerical differentiation when
    equality bounds constraints are used
    aarch64rC  rs   FNzTolerance violation on aarchr  r  r@   r  r  z)Only SLSQP supports nonlinear constraints)r@   rr   r   r  rn  )rr   rs   r   r  r+   r   gMb@?r   r   c                 S   s,   t t jdt jdg}| |ddg< t|S )Nr$   r   r   )r   r8   r8  r
   r   )r   Znew_xr    r    r!   ru   *  s    ztest_equal_bounds.<locals>.funr$   rF  g>)platformmachiner   r  eb_datarM  r
   r   r   r{  r   r   ru   r   r   r8  rs   rN  r  r   )rr   r  r  r  rn  r  r  r@   r  Ztest_constraintsZreference_constraintsZ	fd_neededr   r   expectedru   Zfd_resr    r    r!   test_equal_bounds
  sJ    






r  c           	      C   s  ddd}ddg}d}t j|||| d}|js2J t|j|dd	g |jdksTJ |jd
ksbJ d}t j|||| |d}|jsJ t|j|dd	gd |  dkrdd }t|t	j
 d}t j|||| |gd}|jdu sJ t|j|dd	g |jdksJ d}|j|sJ t|t	j
 d}t j|||| |gd}|jdu sTJ t|j|dd	g |jdksxJ d}|j|sJ d S )Nr   c                 S   s   t j| | S r/   )r   ZlinalgZnorm)r   p1r    r    r!   r_   @  s    z test_all_bounds_equal.<locals>.frJ  )r$   r$   )rE   r  r  rE   r  z/All independent variables were fixed by bounds.)r$   r;  r$   r  c                 S   s
   t | S r/   r  r   r    r    r!   conQ  s    z"test_all_bounds_equal.<locals>.conrI   )r   rr   r  Fz3All independent variables were fixed by bounds, butr   Tz8All independent variables were fixed by bounds at values)r   )r
   r   r   r   ru   rv   ro  upperr   r   r*  r  )	rr   r_   r   r@   r   rq   r  Znlcro  r    r    r!   test_all_bounds_equal<  s@    


r  c                  C   s^   dd } dd }d|dg}dgd }d	|d
< t j| g dd||d |d d |ksZJ d S )Nc                 S   s(   | d d | d d  | d | d   S )Nr   rH   r   r$   r    r   r    r    r!   r_   k  s    ztest_eb_constraints.<locals>.fc                 S   s$   | d | d  | d  | d  d S )Nr   r   r$   rH   (   r    r   r    r    r!   cfunn  s    z!test_eb_constraints.<locals>.cfunr  r  )r   rW  r   )r   r   r   )r   r$   rH   r   r  )r@   rr   r   r  r   ru   r  )r_   r  r  r   r    r    r!   test_eb_constraintsh  s    
r  c                  C   sh   t tttttd} |  D ]\}}|D ]}t|| q&qdddd}| D ]\}}tt	t|| qLd S )N)r   r<  rootZroot_scalarZlinprogZquadratic_assignmentZekkir  )r   ZmaximizeZmaximize_scalar)
r   r   r   r   r   r   itemsr   r;   r<   )Zsolver_methodsZsolverrI  rr   Zunknown_solver_methodr    r    r!   test_show_options  s     r  c                  C   s8   t jddgddgd} t jt jtddgd| d d S )Nr  rS  r  r}   r   r  )r
   r   r   r   r   r8   r  r    r    r!   test_bounds_with_list  s    r  c            
      C   s   dd } dd }dd }g d}g d}t d	d
 }tD ]T}d }d }||v rR|}||v r^|}tj| ||||d}	t|	jt t |dd q:d S )Nc                 S   s*   t t | }| |8 } | | 9 } t | S r/   )r   r:   r  r1   r  r    r    r!   fquad  s    z/test_x_overwritten_user_function.<locals>.fquadc                 S   s(   t t | }| d9 } | d| 8 } | S r  )r   r:   r  r  r    r    r!   	fquad_jac  s    z3test_x_overwritten_user_function.<locals>.fquad_jacc                 S   s   t t | d S r  )r   Zeyer  r   r    r    r!   
fquad_hess  s    z4test_x_overwritten_user_function.<locals>.fquad_hess)r  rP  rM  rQ  rN  rL  )rP  rM  rQ  rN  rL  r   r&   rO  g-C6*?r{   )	r   r  r   r
   r   r   r   r:   r  )
r  r  r  Zmeth_jacZ	meth_hessr@   methrs   re   r   r    r    r!    test_x_overwritten_user_function  s    r  c                   @   s   e Zd Zdd ZdS )TestGlobalOptimizationc                 C   s   dd }t j|ddt |dgt |dgt |dgt |dgg}|D ]h}t|t js`J t|dsnJ t|ds|J t|dsJ t|d	sJ t|d
sJ t|dsLJ qLd S )Nc                 S   s   | d S r  r    r   r    r    r!   r`     s    zDTestGlobalOptimization.test_optimize_result_attributes.<locals>.funcr   )r@   )r  r   r   r   ro  ru   rv   r   )	r
   ZbasinhoppingZdifferential_evolutionZshgoZdual_annealingdirectr  r   r  )rV   r`   r  r   r    r    r!   test_optimize_result_attributes  s    z6TestGlobalOptimization.test_optimize_result_attributesN)rh   ri   rj   r   r    r    r    r!   r    s   r  c                  C   s@   t tt} t| ttdd t tt}t|ttdd d S )Nr   r   )r
   Zapprox_fprimer?   r_  r   r=   r>   )r  r  r    r    r!   test_approx_fprime  s    r  c                  C   s   dd } t ddgddgd}tj| dd|d}t tddgtddgd}tj| dd|d}t|j|j t|j|j d S )	Nc                 S   s   | d d | d d d  S r  r    r   r    r    r!   r_     s    ztest_gh12594.<locals>.fr   r   r  )r   r   r   r  )r   r
   r   r   r8   r   ru   r   )r_   r   r   r   r    r    r!   test_gh12594  s     r  )irk   rG  r  numpyr   Znumpy.testingr   r   r   r   r   r   r   r   r	   r;   Zscipyr
   Zscipy.optimize._minimizer   r   r   r   r   Zscipy.optimize._linprogr   Zscipy.optimize._rootr   Zscipy.optimize._root_scalarr   Zscipy.optimize._qapr   Z(scipy.optimize._differentiable_functionsr   r   Zscipy.optimize._optimizer   r   r   rB   rC   rl   r   r  r  r  r  r  r  r  r+  r/  r0  r2  r3  r4  r5  r   r  r  r  r%  rR  rY  rZ  rs  r  r  r  r  r_  r=   r>   r?   r`  ra  r  r  r  r  r  r  r  r  r  r  r  Zfixturer  r  r  r  r  r  r  Zxfail_on_32bitr  r  r  r  r  r  r  r  r  r    r    r    r!   <module>   s   $50   

L*      +

=  .),?&}"J#A	
	T
>
+(
