o
    4Bi                 
   @   s0  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l'm(Z(m)Z)m*Z* ddl+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1 dd Z2G dd dZ3G dd de3Z4dd Z5dd Z6dd Z7dd Z8dd Z9d d! Z:d"d# Z;d$d% Z<d&d' Z=d(d) Z>G d*d+ d+e4Z?G d,d- d-e4Z@G d.d/ d/e4ZAG d0d1 d1e4ZBG d2d3 d3e3ZCejDEd4g d5d6d7 ZFG d8d9 d9ZGG d:d; d;ZHG d<d= d=ZId>d? ZJG d@dA dAZKdBdC ZLdDdE ZMdFdG ZNdHdI ZOG dJdK dKZPdLdM ZQdNdO ZRdPdQ ZSdRdSgZTdTdUgZUdVZVdWdX ZWG dYdZ dZZXd[d\ ZYd]d^ ZZd_d` Z[dadb Z\G dcdd ddZ]dedf Z^G dgdh dhZ_didj Z`G dkdl dlZaejbdmdn Zcdodp Zddqdr Zedsdt Zfdudv Zgdwdx Zheh ZiejDjdyejDEd4eidz ejDEd{eid{ ejDEd|eid} ejDEd~eid~ ejDEdeid dd ZkejDEd4eidz dd Zldd Zmdd Zndd Zodd ZpG dd dZqdd Zrdd ZsejDEd4ddgejDEde,e-e.e/e0e1gdd Ztd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OptimizeResult)rosen	rosen_der
rosen_hess)
coo_matrix
csc_matrix
csr_matrix	coo_array	csr_array	csc_arrayc               	   C   sV  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sZJ ttj| ||ddddd }|dksoJ 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 sJ d S )Nc                 S   s   ddt |    S N   npexpx r)   b/var/www/html/Trade-python/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_optimize.pyexpit*      ztest_check_grad.<locals>.expitc                 S   s    t |  dt |   d  S Nr#      r$   r'   r)   r)   r*   	der_expit-       z"test_check_grad.<locals>.der_expit      ?r   random  )	directionseedư>)epsilon)r7   r4   r5   皙?Hz>c                 S   s   | t |   S N)r%   sinsumr'   r)   r)   r*   x_sinxE      ztest_check_grad.<locals>.x_sinxc                 S   s   t | | t |   S r:   r%   r;   cosr'   r)   r)   r*   
der_x_sinxH      z#test_check_grad.<locals>.der_x_sinxr.   皙?random_projectionallgƠ>)r%   arrayr
   
check_gradr   absarangeassert_raises
ValueErrorhimmelblau_gradhimmelblau_hesshimmelblau_x0)r+   r/   x0rr=   rA   r)   r)   r*   test_check_grad&   sL   







rQ   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%   rF   FKzerosfloat64startparamssolutionmaxiter	funccalls	gradcallstraceselfr)   r)   r*   setup_methoda   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)ra   RuntimeErrorr%   dotrZ   logr<   r&   r[   rc   appendcopy)re   r(   log_pdotlogZfr)   r)   r*   funco   s   
zCheckOptimize.funcc                 C   sV   |  j d7  _ t| j|}ttt|}t|| }t| j || j S r"   )	rb   r%   rh   rZ   ri   r<   r&   	transposer[   re   r(   rl   rm   pr)   r)   r*   grady   s
   zCheckOptimize.gradc                 C   s`   t | j|}t tt |}t || }t | jjt t || jt | jj| S r:   )r%   rh   rZ   ri   r<   r&   Tdiagrq   r)   r)   r*   hess   s   
"zCheckOptimize.hessc                 C   s   t | ||S r:   )r%   rh   rv   re   r(   rr   r)   r)   r*   hessp   r>   zCheckOptimize.hesspN)	__name__
__module____qualname____doc__rf   ro   rs   rv   rx   r)   r)   r)   r*   rR   [   s    
rR   c                   @   s  e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Ze	j
ddd Zdd Zdd Zdd Ze	j
ddgddgddgddgg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/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9S ):CheckOptimizeParameterizedc           	   
   C   s   | j r0| j| jdd}tj| j| jdd| j|d}|d |d |d |d	 |d
 f\}}}}}ntj| j| j| jd| jd| jdd}|\}}}}}t	| || | j
dd | jdksaJ | j| jdkskJ | jt	| jdd g dg dgddd d S )NFr`   disp
return_allr)   CG)argsmethodjacoptionsr(   funnfevnjevstatusT)r`   full_outputr   retallr6   atol	      r.      )r         rV   )r   g;ӱ.g)`$|;?+=r9   r   rtol)use_wrapperr`   r   r
   minimizero   r^   rs   fmin_cgr   r_   ra   rb   rc   )	re   optsresparamsfopt
func_calls
grad_callswarnflagretvalr)   r)   r*   test_cg   s6    

z"CheckOptimizeParameterized.test_cgc                 C   sN   dd }t dddD ]}tj||gdd}|jsJ t|jdgd	d
 qd S )Nc                 S   s   ddt d| d   d  S )Ng      @r#         rV   r.   r$   )rP   r)   r)   r*   rn      s   z8CheckOptimizeParameterized.test_cg_cornercase.<locals>.fg      rW   G   r   r   rV   h㈵>r   )r%   linspacer
   r   successr   r(   )re   rn   rO   solr)   r)   r*   test_cg_cornercase   s   
z-CheckOptimizeParameterized.test_cg_cornercasec              
   C   s  | j r8| j| jdd}tj| j| j| jdd|d}|d |d |d |d	 |d
 |d |d f\}}}}}}}	ntj| j| j| jd| jd| jdd}
|
\}}}}}}}	t	| || | j
dd | jdkskJ | j| jdksuJ | jt	| jdd g dg dgddd d S )NFr~   BFGSr)   r   r   r   r   r(   r   r   hess_invr   r   r   Tr   r`   r   r   r   r6   r   
         )r   g&/LgB__E7?)r   g$g
|3?r   r9   r   )r   r`   r   r
   r   ro   r^   rs   	fmin_bfgsr   r_   ra   rb   rc   )re   r   r   r   r   goptHoptr   r   r   r   r)   r)   r*   	test_bfgs   s<   

z$CheckOptimizeParameterized.test_bfgsc                 C   sl   t jtdd% tg d}| jtd d}tjtj	|dd|d W d    d S 1 s/w   Y  d S )	N+'hess_inv0' matrix isn't positive definite.matchg?ffffff?皙?ffffff?333333?   r   	hess_inv0r   r)   rO   r   r   r   )
pytestr	   rK   r%   rF   r   eyer
   r   r   )re   rO   r   r)   r)   r*   test_bfgs_hess_inv0_neg   s   "z2CheckOptimizeParameterized.test_bfgs_hess_inv0_negc                 C   sv   t jtdd* tg d}td}d|d< | j|d}tjtj	|dd	|d
 W d    d S 1 s4w   Y  d S )Nr   r   r   r   r   r   r   r   r   r)   r   )
r   r	   rK   r%   rF   r   r   r
   r   r   )re   rO   r   r   r)   r)   r*   test_bfgs_hess_inv0_semipos   s   
"z6CheckOptimizeParameterized.test_bfgs_hess_inv0_semiposc                 C   sn   t j}tg d}| jdtd d}t j||dd|d}t j||ddd| jid}t|j|jd	d
 d S )Nr   {Gz?r   r   r   r)   r   r   r6   r   )	r
   r   r%   rF   r   r   r   r   r   )re   r   rO   r   r   res_truer)   r)   r*   test_bfgs_hess_inv0_sanity   s   z5CheckOptimizeParameterized.test_bfgs_hess_inv0_sanityignore::UserWarningc              	      s   dd   fdd}dg}t jdd2 | jr*d| ji}tj ||d	d
|dd }n
tj ||| jd}t  |r=J W d    d S 1 sHw   Y  d S )Nc                 S   s   t j|    S r:   )r%   er'   r)   r)   r*   ro         z;CheckOptimizeParameterized.test_bfgs_infinite.<locals>.funcc                    s
    |  S r:   r)   r'   ro   r)   r*   fprime      
z=CheckOptimizeParameterized.test_bfgs_infinite.<locals>.fprimer   ignore)overr   r   r)   r   r(   r   )r%   errstater   r   r
   r   r   isfinite)re   r   rO   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s$J d S )Nr   bfgsxrtolMbP?r   r   gtolr
   r   r   nit)re   rO   r   refr)   r)   r*   test_bfgs_xrtol  s   

z*CheckOptimizeParameterized.test_bfgs_xrtolc                 C   L   g d}t jt j|dddid}t jt j|dddid}|j|jks$J d S )Ng$@g333334@g%@r   333333r   c1:0yE>r   r8   )r
   r   r   r   )re   rO   res_c1_small
res_c1_bigr)   r)   r*   test_bfgs_c1  s   

z'CheckOptimizeParameterized.test_bfgs_c1c                 C   r   )Nr   r   c2?r   r   r   )re   rO   res_defaultres_modr)   r)   r*   test_bfgs_c2  s   

z'CheckOptimizeParameterized.test_bfgs_c2r   r   rV   r.   皙r8   rC   c                 C   sV   t jtdd g d}tjtj|d||dd W d    d S 1 s$w   Y  d S )Nz'c1' and 'c2'r   r   cg)r   r   r   )r   r	   rK   r
   r   r   )re   r   r   rO   r)   r)   r*   test_invalid_c1_c2)  s   "z-CheckOptimizeParameterized.test_invalid_c1_c2c           
   	   C   s   | j r2| j| jdd}tj| j| jdd|d}|d |d |d |d	 |d
 |d f\}}}}}}ntj| j| jd| jd| jdd}	|	\}}}}}}t| || | j	dd t|dd  | j	dd  dd | j
dksrJ | j
| jdks|J | jd S )NFr~   r)   Powellr   r   r   r(   r   direcr   r   r   Tr   r6   r   r#   h㈵>   r   )r   r`   r   r
   r   ro   r^   fmin_powellr   r_   ra   rb   
re   r   r   r   r   r   numiterr   r   r   r)   r)   r*   test_powell2  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 r2| j| jdd}tj| j| jdd|d}|d |d |d |d	 |d
 |d f\}}}}}}nt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 )NFr~   r)   r   r   r(   r   r   r   r   r   Tr   "   '   )病~W?f"Bܿg%?)r   r   g:&?)gSϼW?gf"Bg{år?)r   r   {år?)gB?r   r   r   r9   r   )
r   r`   r   r
   r   ro   r^   r   r   rc   r   r)   r)   r*   test_powell_gh14014T  s2   
z.CheckOptimizeParameterized.test_powell_gh14014c                 C   s   dd | j D }| jrM| j| jdd}tj| j| j d|d|d}|d |d	 }}|| jks0J t| || | j	d
dd | jdksFJ | j
dksOJ d S d S )Nc                 S   s   g | ]	}t j t jfqS r)   )r%   pi).0_r)   r)   r*   
<listcomp>z  s    zBCheckOptimizeParameterized.test_powell_bounded.<locals>.<listcomp>Fr~   r)   r   )r   boundsr   r   r(   r   r6   r   r      r   )r^   r   r`   r   r
   r   ro   ra   r   r_   rb   )re   r  r   r   r   r   r)   r)   r*   test_powell_boundedw  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s]J | j
| jdksgJ | jt| jdd g dg dgddd d S )NFr~   r)   Nelder-meadr   r(   r   r   r   r   Tr   r6   r      r   L   N   )g	dװ?g]fgt䝁?)gә ?g#=^goT?r   r9   r   )r   r`   r   r
   r   ro   r^   fminr   r_   ra   rb   rc   )	re   r   r   r   r   r   r   r   r   r)   r)   r*   test_neldermead  s6   
z*CheckOptimizeParameterized.test_neldermeadc              
   C   sH  t d}| j|d< tdD ]}||d |f  d7  < q| jrV| 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sJ | j| jdksJ | jt	| jdd g dg dgddd d S )N)r   rW   .rW   r#   r8   FTr`   r   r   initial_simplexr)   r  r   r(   r   r   r   r   allvecsr   r   r`   r   r   r   r  r6   r   d   2   4   )gIt?g?'ΛTgx8?)gҢ_׆?goMg囎|52?r   r9   r   )r%   r\   r^   ranger   r`   r
   r   ro   r   r	  r_   ra   rb   rc   )re   simplexjr   r   r   r   r   r   r   r   r)   r)   r*   test_neldermead_initial_simplex  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rP| jdd|d}ttt	j
| j| jd	d
|d q4ttt	j| j| jd	| jddd|d
 q4d S )N)rW   r.   r.   .r#   r8   )rW   rW   Fr  r)   r  r   Tr  )r%   r\   r^   r  rj   r   r`   rJ   rK   r
   r   ro   r	  )re   bad_simplicesr  r  r   r)   r)   r*   #test_neldermead_initial_simplex_bad  s8   



z>CheckOptimizeParameterized.test_neldermead_initial_simplex_badc                 C   sZ   dd }t j|dgdgdd}t|jdg t j|ddgdd	gdd}t|jddg d S )
Nc                 S      t | d S Nr.   r%   r<   r'   r)   r)   r*   quad  r   z>CheckOptimizeParameterized.test_neldermead_x0_ub.<locals>.quadr#   )r   rT   nelder-meadr  r   r   r.   )r#         @r
   r   r   r(   )re   r  r   r)   r)   r*   test_neldermead_x0_ub  s   z0CheckOptimizeParameterized.test_neldermead_x0_ubc                 C   s6   ddi}t j| j| jd| jd|d}|jdksJ d S )Nr`   	Newton-CGr)   r   r   r   r   r#   )r
   r   ro   r^   rs   r   )re   r   resultr)   r)   r*   test_ncg_negative_maxiter  s   z4CheckOptimizeParameterized.test_ncg_negative_maxiterc                 C   sX   dd }dd }dg}d}t j|||dt|dd	}|jdks!J t|jd tj d S )
Nc                 S   s   t | d S Nr   )r%   r@   r'   r)   r)   r*   cosine  r   z=CheckOptimizeParameterized.test_ncg_zero_xtol.<locals>.cosinec                 S   s   t | d  S r&  )r%   r;   r'   r)   r)   r*   r        z:CheckOptimizeParameterized.test_ncg_zero_xtol.<locals>.jacr8   r   	newton-cg)xtol)rO   r   r   r   )r
   r   dictr   r   r(   r%   r   )re   r'  r   rO   r*  r$  r)   r)   r*   test_ncg_zero_xtol  s   z-CheckOptimizeParameterized.test_ncg_zero_xtolc              
   C   s   | j r| 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sHJ | j| jdksRJ | jt	| jdd g dg dgddd d S )NFr~   r"  r)   r#  r(   r   r6   r   r      rW   r   (6-H=g?g4u3?r/  g_g/N3?r9   r   )r   r`   r   r
   r   ro   r^   rs   fmin_ncgr   r_   ra   rb   rc   re   r   r   r   r)   r)   r*   test_ncg'  s6   
z#CheckOptimizeParameterized.test_ncgc                 C      | 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sLJ | j| jdksVJ | jt
| jdd g dg dgddd d S )NFr~   r"  r)   )r   r   rv   r   r   r(   )fhessr   r`   r   r   r   r6   r   r      rW   r   r.  r0  r9   r   )r   r`   r   r
   r   ro   r^   rs   rv   r1  r   r_   ra   rb   rc   r2  r)   r)   r*   test_ncg_hessH  :   
z(CheckOptimizeParameterized.test_ncg_hessc                 C   r4  )NFr~   r"  r)   )r   r   rx   r   r   r(   )fhess_pr   r`   r   r   r   r6   r   r   r6  rW   r   r.  r0  r9   r   )r   r`   r   r
   r   ro   r^   rs   rx   r1  r   r_   ra   rb   rc   r2  r)   r)   r*   test_ncg_hesspj  r8  z)CheckOptimizeParameterized.test_ncg_hesspN)ry   rz   r{   r   r   r   r   r   r   r   markfilterwarningsr   r   r   r   parametrizer   r   xfailr   r  r
  r  r  r   r%  r,  r3  r7  r:  r)   r)   r)   r*   r}      s<    "


	

"
 (!"r}   c                     s\   t jd  fdd} dD ]}dD ]}tj|  d|d|id}|d	 |ks*J qqd S )
Nl	   <vgRI*q4 c                         dd S Nr#   rY   r2   r'   rngr)   r*   cost  r   ztest_maxfev_test.<locals>.cost)r#   r   r  )r   Nelder-Meadr   maxfevr   r   )r%   r2   default_rngr
   r   )rD  imaxfevr   r$  r)   rB  r*   test_maxfev_test  s   rI  c                  C   s   dd } t j| tdd\}}tdD ]}|t| |d |d ks(J qd}tt jj|d |t| W d    n1 sEw   Y  t j| tdd\}}d}tt|d |t	ddg W d    d S 1 stw   Y  d S )	Nc                 S      | S r:   r)   r'   r)   r)   r*   func_     z8test_wrap_scalar_function_with_validation.<locals>.func_r#   r   r   zToo many function callsr   @The user-provided objective function must return a scalar value.)
r
   	_optimize'_wrap_scalar_function_maxfun_validationr%   asarrayr  rJ   _MaxFuncCallErrorrK   rF   )rK  fcallsro   imsgr)   r)   r*   )test_wrap_scalar_function_with_validation  s$   "rU  c                  C   sT   d} t t| d tjdd tddgdd W d    d S 1 s#w   Y  d S )NrM  r   c                 S   rJ  r:   r)   r'   r)   r)   r*   <lambda>      z.test_obj_func_returns_scalar.<locals>.<lambda>r#   r   r   )rJ   rK   r
   r   r%   rF   r   r)   r)   r*   test_obj_func_returns_scalar  s    "rX  c                  C   s4   t g d} tjjtj| dd}|jdksJ d S )Nr   r   )xatoliS  )r%   rF   r
   	_minimize_minimize_neldermeadr   r   )rO   r   r)   r)   r*   test_neldermead_iteration_num  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:   )dtyper%   float32r
   r   r'   r)   r)   r*   rosen_  s   
z*test_neldermead_respect_fp.<locals>.rosen_rE  r   )r%   rF   astyper`  r
   r   )rO   ra  r)   r)   r*   test_neldermead_respect_fp  s   rc  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*   ro     rB   z)test_neldermead_xatol_fatol.<locals>.funcr#   r.   r   )r`   rY  fatol)r
   rZ  r[  r   r)   r)   r*   test_neldermead_xatol_fatol  s   
rf  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   r  r  r  r'   r)   r)   r*   ro     r   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?rE  r   FadaptiveTr   )r
   r   r   r   )ro   p0r   r)   r)   r*   test_neldermead_adaptive  s   
ri  c                  C   s  dd } d}g d}t tj tj| ||dd}W d    n1 s#w   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 skw   Y  t|jtg ddd	 t	|j
d t	|jd d S )Nc                 S   r  r  r  r'   r)   r)   r*   ro     r   z/test_bounded_powell_outsidebounds.<locals>.func)r!  r#   rj  rj  )rV   gr   r  rX   r6   r   Tr   r   r   r   )r   r#   r   )r   r   r#   r   )r  r   r   )g      r   r   Fr   )r   r
   OptimizeWarningr   r   r(   r%   rF   lenr   r   r   )ro   r  rO   r   r   r)   r)   r*   !test_bounded_powell_outsidebounds  s&    ro  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 sw   Y  t|jdd
d d S )Nc                 S   r  r  r  r'   r)   r)   r*   ro     r   z+test_bounded_powell_vs_powell.<locals>.func))r!  )r   )r#   gffffff"@)rk  gffffff@g/)g gr   r   rs  绽|=ftolr*  r   r   rX   r6   r   )r   r  r   )r!  r   r#   r   rs  )Nr!  r   r#   )rk  Nrr  c                 S   sz   t | d  t | d  t | d  | d   t | d  }|t t | d | d  t | d  8 }|d S Nr   r#   r.   r?   r(   tr)   r)   r*   ro   -  s   D.)rs  r   rW   )r   r   r   r   r  g8:}?r   )gb4F@g:gW?@)r
   r   r   r(   r   r%   rF   infr   r   rm  )ro   r  rO   r   
res_powellres_bounded_powellrr   r)   r)   r*   test_bounded_powell_vs_powell  sb   




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    .ArW   r   ru  )r   r  r   rS   c                 S   s   t |  S r:   r  r'   r)   r)   r*   rn   _     z1test_onesided_bounded_powell_stability.<locals>.fg    `F-C6?r   c                 S   .   t t | d  t | dkrd S d S )Nr8   r   r#   r!  r%   rH   r<   rE   r'   r)   r)   r*   rn   e     .gwc                 S   r  )Nr   r   r#   r!  r  r'   r)   r)   r*   rn   l  r  gB+Iar9   r   c                 S   s^   t t | d d d  t t | dd  d  }|t | dkr*d9 }|S d9 }|S )Nr.   r   r8   r   r#   r!  r  rx  r)   r)   r*   rn   s  s
   :g     @@r  g 4&k\)r%   rz  r
   r   r   r   )kwargsrO   rn   r   r)   r)   r*   &test_onesided_bounded_powell_stabilityS  s$   r  c                   @      e Zd ZdZdZdS )TestOptimizeWrapperDispTNry   rz   r{   r   r   r)   r)   r)   r*   r  }      r  c                   @      e Zd ZdZdZdS )TestOptimizeWrapperNoDispTFNr  r)   r)   r)   r*   r    r  r  c                   @   r  )TestOptimizeNoWrapperDispFTNr  r)   r)   r)   r*   r    r  r  c                   @   r  )TestOptimizeNoWrapperNoDispFNr  r)   r)   r)   r*   r    r  r  c                   @   s  e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zejd%ejd&ejd'g d(e d)d* Zejd'g d+d,d- Zd.d/ Zejd'g d0d1d2 Zejd'g d3d4d5 Zd6d7 Zd8d9 Z d:d; Z!d<d= Z"ejd'g d>d?d@ Z#ejd'g dAdBdC Z$ejd&ejd'e%ejdDg dEdFdG Z&dHdI Z'ejd'dJdKdL Z(ejd'g dMdNdO Z)dPS )QTestOptimizeSimplec                 C   sp   dd }dd }t jg}t jddd tj|||dd}t ||s&J W d    d S 1 s1w   Y  d S )	Nc                 S   rJ  r:   r)   r'   r)   r)   r*   ro     rL  z.TestOptimizeSimple.test_bfgs_nan.<locals>.funcc                 S   
   t | S r:   r%   	ones_liker'   r)   r)   r*   r     r   z0TestOptimizeSimple.test_bfgs_nan.<locals>.fprimer   )r   invalidFr   )r%   nanr   r
   r   isnan)re   ro   r   rO   r(   r)   r)   r*   test_bfgs_nan  s   "z TestOptimizeSimple.test_bfgs_nanc                 C   s   dd }t jdd t|d}W d    n1 sw   Y  t |d s)J |d du s1J d	d }d
d }t jdd tj|d|d}W d    n1 sRw   Y  t |d s`J |d du shJ d S )Nc                 S      t jS r:   r%   r  r'   r)   r)   r*   ro        z5TestOptimizeSimple.test_bfgs_nan_return.<locals>.funcr   r  r   r   r   Fc                 S   s   | dkrdS t jS r&  r  r'   r)   r)   r*   ro     r>   c                 S   r  r:   r  r'   r)   r)   r*   r     r   z7TestOptimizeSimple.test_bfgs_nan_return.<locals>.fprime)r   )r%   r   r
   r   r  )re   ro   r$  r   r)   r)   r*   test_bfgs_nan_return  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 )NrT   r)   F)r7   r   r`   r   r6   r   )r%   sqrtspacingr2   randrn  r_   r
   r   ro   r^   r`   r   )re   r7   r   r)   r)   r*   test_bfgs_numerical_jacobian  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   r   TNC2-point3-pointN)r   r   r6   r   )		itertoolsproductr
   r   ro   r^   r   r(   r_   )re   methodsjacsr   r   r$  r)   r)   r*   test_finite_differences_jac  s   z.TestOptimizeSimple.test_finite_differences_jacc              	   C   s   g d}t tjf }t||D ]\}}|tju r| }tj| j| j|| j|d}|j	s.J qg d}|D ]$}t
t tj| j| j|| jd d W d    n1 sTw   Y  q5d S )N)trust-constrr"  	trust-ncgtrust-krylovr   r   rv   )r  r  doglegtrust-exact)r   r
   r   r  r  r   ro   r^   rs   r   r   r	   rK   )re   r  hessesr   rv   r$  r)   r)   r*   test_finite_differences_hess  s(   
z/TestOptimizeSimple.test_finite_differences_hessc                 C   s.   dd }t j|dgdd}t|dddd d S )	Nc                 S   s   | dk rdS | d|   S )Nr   gBrT   r)   r'   r)   r)   r*   rn     s   z/TestOptimizeSimple.test_bfgs_gh_2169.<locals>.f      $@Fr   rT   r  r   r   )r
   r   r   )re   rn   xsr)   r)   r*   test_bfgs_gh_2169  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(   xpseenr)   r*   rn     s   
z:TestOptimizeSimple.test_bfgs_double_evaluations.<locals>.fr   Tr9   )r   r   tol)setr
   r   re   rn   r)   r  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s+J | j| j	dks5J | j	t| j
dd g dg d	gd
dd d S )Nr)   )r   r`   r6   r   r   r   rW   )g><gwT볹gUuAX?)rX   gHg!mʲ3?r   r9   r   )r
   fmin_l_bfgs_bro   r^   rs   r`   r   r_   ra   rb   rc   re   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)approx_gradr`   r6   r   )r
   r  ro   r^   r`   r   r_   r  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:   ro   rs   r'   rd   r)   r*   r     r,   z4TestOptimizeSimple.test_l_bfgs_b_funjac.<locals>.funr`   r6   r   )r
   r  r^   r`   r   ro   r_   )re   r   r   r   r   r  r)   rd   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 s:J t|j
d
 d S )Nc                   @      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   r   r(   rd   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   r   r   re   r(   r)   r)   r*   __call__0  s   zCTestOptimizeSimple.test_l_bfgs_b_maxiter.<locals>.Callback.__call__Nry   rz   r{   r  r  r)   r)   r)   r*   Callback*  s    r  rX   l-bfgs-br`   r   )r   callbackr   r#   Fz+STOP: TOTAL NO. of ITERATIONS REACHED LIMIT)r
   r   r   r   r   r   r(   r   r   r   message)re   r  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s*J d | _| _	tj| j| jd|d}| j|jksCJ t| |j| | jdd d | _| _	tj| j| jd	d|d
}| j|jkslJ t| |j| | jdd d S )NFr   r`   L-BFGS-Br   r   r   r6   r   r   r   r  r   r   r   )r`   r
   r   ro   r^   rs   r   r(   r_   rb   r   ra   r   )re   r   rP   rar)   r)   r*   test_minimize_l_bfgs_bA  s2   
z)TestOptimizeSimple.test_minimize_l_bfgs_bc                 C   sv   d }dD ]4}d| j |d}tj| j| jd| j|d}| |j}|d u r'|}n||k s-J t|| | j|d qd S )N)r8   r  r9   rt  F)r   r`   rv  r  r  r   )	r`   r
   r   ro   r^   rs   r(   r   r_   )re   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rJ d S )Nr   rT   r  Fr#   )r   maxlsr  )r
   r   r   r%   rF   r   r   )re   r   r)   r)   r*   test_minimize_l_bfgs_maxlsn  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   rY   c                    s    | } | |S r:   )rj   )r(   valuern   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   rS  yr)   r)   r*   	<genexpr>  s    zPTestOptimizeSimple.test_minimize_l_bfgs_b_maxfun_interruption.<locals>.<genexpr>)
r
   r   r   r%   fullr  max	enumerateminr   )re   grO   r  lowmediumhighr  kr  targetxminr	  r  r)   r  r*   *test_minimize_l_bfgs_b_maxfun_interruptionu  s   
"z=TestOptimizeSimple.test_minimize_l_bfgs_b_maxfun_interruptionc                 C   sF   		 ddd}g d}t jt j||tddd	}t|jd
ddd d S )Nr)   r8   r  c                 [   s   |}| |}	d}
d}d}d}|rp|sp||k rpd}|d7 }t t|D ]D}|| | || | fD ]!}t|}|||< | |g|R  }|
d7 }
||	k rR|}	|}d}q1|d ur[|| |d urg|
|krgd} nq#|rp|sp||k stj|	|||
|dkdS )Nr#   r   TFr   r(   r   r   r   )r  r%   sizerk   r
   r   )r   rO   r   rF  stepsizer`   r  r   bestxbestyfuncallsniterimprovedstopdimstestxtestyr)   r)   r*   custmin  s<   

z/TestOptimizeSimple.test_custom.<locals>.custmin)g?r   r   皙?r   皙?r  r   rT   r  r  r)   Nr8   r  N)r
   r   r   r+  r   r(   )re   r  rO   r   r)   r)   r*   test_custom  s   
zTestOptimizeSimple.test_customc                    s<   ddg d fdd}ddg}t jt j|| d d S )N)rs  r.   )r   rW   constraintsc                    s(   |d  u sJ |d u sJ t  S )Nr  r  r
   r   )r   rO   r   r  r  r)   r*   r    s   z0TestOptimizeSimple.test_gh10771.<locals>.custminr#   )r   r  r  )r
   r   r   )re   r  rO   r)   r  r*   test_gh10771  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 sIJ | d||j d||j q
d S )Nc                 S   s$   | \}}|d |d  |d  d S )Nr.   r   r#   r)   zr(   r  r)   r)   r*   ro     s   z<TestOptimizeSimple.test_minimize_tol_parameter.<locals>.funcc                 S   s:   | \}}t d| |d  d|d   d|d  | gS )Nr.   r   rW   r%   rF   r  r)   r)   r*   dfunc  s   2z=TestOptimizeSimple.test_minimize_tol_parameter.<locals>.dfunc	r  powellr   r   r)  r  tnccobylaslsqpr  r  r  r#   rt  )r   r  r   rT   : z vs. )r
   r   r(   )re   ro   r
  r   r   sol1sol2r)   r)   r*   test_minimize_tol_parameter  s    z.TestOptimizeSimple.test_minimize_tol_parameterr   ignore::RuntimeWarningr   )r	  r   r   r   r1  r  fmin_tnc
fmin_slsqpc           
         sf   dv r	dd }n	t j}t j}t j}td}i } drCtt  } dkr,d|d< n0 d	kr5d
|d< n' dv r>d|d< nd|d< n fdd} dkrUtd
d|d< ntdd|d<  dv re||d< n dv rn||d< n dv rz||d< ||d< g fdd}|||fd|i| t	dksJ t
dd  D sJ td}	td!d  |	D rJ d S )"N)r  r  c                 S   s   t | t | fS r:   )r
   r   r   r'   r)   r)   r*   ro     r,   zDTestOptimizeSimple.test_minimize_callback_copies_array.<locals>.funcr   r	  r  r   iterr  r  r  )r	  r   i  r`   c                     s    |d< t j| i |S )Nr   r
   r   )akwr   r)   r*   routine  s   zGTestOptimizeSimple.test_minimize_callback_copies_array.<locals>.routiner  r  r   r  )r1  r   )r)  r   r  r  r  r  r  rv   c                    s(   t | tjrJ  | t| f d S r:   )
isinstancer
   r   rj   r%   rk   )r(   r   r  )resultsr)   r*   r    s   zHTestOptimizeSimple.test_minimize_callback_copies_array.<locals>.callbackr  r.   c                 s   s"    | ]\}}t ||kV  qd S r:   )r%   rE   r   r(   r  r)   r)   r*   r    s     zITestOptimizeSimple.test_minimize_callback_copies_array.<locals>.<genexpr>c                 s   s(    | ]\}}t |d  |d  V  qdS )r   N)r%   may_share_memoryr!  r)   r)   r*   r    s   & )r
   r   r   r   r%   r\   
startswithgetattrr+  rn  rE   r  combinationsany)
re   r   ro   r   rv   rO   r  r  r  r%  r)   )r   r   r*   #test_minimize_callback_copies_array  sD   










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 r(d }tj|||||d}t||j|j |dkrDt	d ||j|ksMJ d S )Nc                 S      | d d S r-   r)   r'   r)   r)   r*   ro   '  r~  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  r  r  r  r  r  r  zSLSQP returns slightly worse)
r%   rF   r+  r
   r   r   r(   r   r   r>  )	re   r   ro   r)  rO   f0r   r   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)rT   r*  r  r^  r.   )r<   r%   rF   r'   r)   r)   r*   rn   ?  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-  rs  r!  r   r   )r%   rF   concatenaterh   r(   r  r)   r)   r*   consB  s   $z:TestOptimizeSimple.test_slsqp_respect_bounds.<locals>.cons)rV   rT   r1   r*  r  ineqtyper   r   r  )rX   r.   r   r   rW   g-q=r   )r%   rF   r
   r   r   r(   )re   rn   r0  rO   r   r)   r)   r*   test_slsqp_respect_bounds=  s   
"z,TestOptimizeSimple.test_slsqp_respect_bounds)rE  r   r   r   r"  r  SLSQPr  r  r  r  r  c                 C   s   d}t d}ttj|dtjtjd d }|t|dd}|dv r&|j|d< n|dv r4|j|d< |j	|d	< tj
|j|fi |}|j|ksFJ |j|jksNJ t|d
r[|j|jks[J |dkrf|jdkshJ d S d S )Nr   r   r)   r  r   )r"  r   r  rv   r   r6  r   )r%   r\   r   r
   r   r   r   r+  rs   rv   r   r   r   r   hasattrr   ngevr   )re   r   MAXITERrO   sfr  r   r)   r)   r*   test_respect_maxiterK  s(   



z'TestOptimizeSimple.test_respect_maxiter)rE  r   r	  r   c                 C   s   t d}ttj|dtjtjd d }ddd}tjt	dd0 |
dr4tt|}||j|fi | ntj|j|||d	 W d    d S W d    d S 1 sQw   Y  d S )
Nr   r)   r#   T)r`   r   zMaximum number of iterationsr   r	  r   )r%   r\   r   r
   r   r   r   r   warnsRuntimeWarningr#  r$  r   r   )re   r   rO   r:  r   r  r)   r)   r*   test_runtime_warningm  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s0J d S )
Nr   c                 S   s,   t d| d  d| d   d| d   gS )NrC   r   皙?r#   Q?r.   r	  r'   r)   r)   r*   r     s   ,zRTestOptimizeSimple.test_respect_maxiter_trust_constr_ineq_constraints.<locals>.funr1  r2  r   r  r  )r  r   rv   r   r   )	r
   r   r   r   r%   r\   r   r+  r   )	re   r9  rn   r   rv   r   r0  rO   r   r)   r)   r*   2test_respect_maxiter_trust_constr_ineq_constraints|  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sSJ qLt|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      | d S r  r)   r'   r)   r)   r*   rn        z6TestOptimizeSimple.test_minimize_automethod.<locals>.fc                 S   s   | d S r  r)   r'   r)   r)   r*   r0    rC  z9TestOptimizeSimple.test_minimize_automethod.<locals>.consr  r1  r2  )r  )r   r   r  )r  r  r#   r   r   r9   r   r.   r   )r%   rF   r
   r   r   r   r(   )
re   rn   r0  rO   sol_0sol_1sol_2sol_3sol_4r   r)   r)   r*   test_minimize_automethod  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(   r  r)   r)   r*   Y  r>   z=TestOptimizeSimple.test_minimize_coerce_args_param.<locals>.Yc                 S   s   d| |  S r  r)   rL  r)   r)   r*   dY_dx  r~  zATestOptimizeSimple.test_minimize_coerce_args_param.<locals>.dY_dx)rW   r#   r   r#   r   r   r.   r   r   rW   r   r   )r   r   r   r:   )r%   rF   r2   randnrn  r
   r   )re   rM  rN  r  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 ]v\}|dv r,td d	}nt }d
k r8|dv r8qdgd g tj||||d}| d d  d| }|js\J |t|jdg|d |jdksnJ |d
kr|dv rt d d|d q d dkr d dk sJ |q	 qd S )N)gJz5r#   gd~QJ)r   r   r  r"  c                    s`    d d u r| d d krt | d d   d< t |  dkr&td| d d d  S )Nr   g     @zOptimization stepped far away!r#   r.   )rH   r  AssertionErrorr'   first_step_sizescalerO   r)   r*   rn     s
   z7TestOptimizeSimple.test_initial_step_scaling.<locals>.fc                    s   t  | d d  gS Nr   r#   r	  r'   )rU  r)   r*   r    rB   z7TestOptimizeSimple.test_initial_step_scaling.<locals>.g)r   r   r   )r   rt  )r  r"        r   r  rT   err_msgrW   r   g)\(?rV   )	r  r  r+  r
   r   r   r   r(   r   )	re   scalesr  rn   r  r   r   r   rZ  r)   rS  r*   test_initial_step_scaling  s2   "z,TestOptimizeSimple.test_initial_step_scaling)r  r  r   r   r)  r  r  r  r  r  r  r  r  r  c                    sh  t jd dg dd } fdd}dd }d	d
 }t dg}|dv }|dv }||g}	|r2|gn|d g}
|r;|gn|d g}|dkrHtddntdd}t jddW t ;}|td |t	d |t	d t
|	|
|D ]\}}}dg tj||||||d}t|jd qqW d    n1 sw   Y  W d    d S W d    d S 1 sw   Y  d S )Nr3   r   c                 S   r  r:   r  r'   r)   r)   r*   ro     r  z0TestOptimizeSimple.test_nan_values.<locals>.funcc                    s,    d  d7  <  d dkrt jS t j S rw  )r%   r  r2   r  r'   countr)   r*   func2  s   
z1TestOptimizeSimple.test_nan_values.<locals>.func2c                 S   s   t dgS NrT   r	  r'   r)   r)   r*   rs     r~  z0TestOptimizeSimple.test_nan_values.<locals>.gradc                 S      t dggS r`  r	  r'   r)   r)   r*   rv      r   z0TestOptimizeSimple.test_nan_values.<locals>.hessrT   r)  r  r  r  r  r  r  r  r  r  r  r  r  r   r  delta_grad == 0.*.*does not use Hessian.*.*does not use gradient.*)r   rv   r   r   F)r%   r2   r5   rF   r+  r   r   filterUserWarningr=  r  r  r
   r   r   r   )re   r   ro   r_  rs   rv   rO   
needs_grad
needs_hessfuncsgradshesssr   suprn   r  hr   r)   r]  r*   test_nan_values  s2   Pz"TestOptimizeSimple.test_nan_values)r  r   r   r  r  r  r  r  r  r  r  r  c              	   C   s   d  }}|dv r| j }|dv r| j}tjdd- t }|td tj| j	| j
|||d W d    n1 s9w   Y  W d    n1 sHw   Y  tdt| jD ]}t| j|d  | j| rltd| qUd S )	Nrb  rc  r   r  rd  r  r#   zDuplicate evaluations made by )rs   rv   r%   r   r   rg  rh  r
   r   ro   r^   r  rn  rc   array_equalrg   )re   r   r   rv   rn  rS  r)   r)   r*   test_duplicate_evaluations  s(    z-TestOptimizeSimple.test_duplicate_evaluationsnew_cb_interface)r   r#   r.   c           
         sF  fddd_ fdd}fdd}d|d	kr# fd
d}n|dkr5G  fddd}| }n fdd} fdd d _d _ dgd |||d}tjdi |d|i}|dkrgd	 tjdi |ddii}	|j|	jks}J t|j|	j |j|	j  krksJ  J |j|dkrdndksJ d S )Nc                       d _ t| S NF)flagr
   r   r'   rn   r)   r*   rn   ;     
z9TestOptimizeSimple.test_callback_stopiteration.<locals>.fFc                    rt  ru  )rv  r
   r   r'   rw  r)   r*   r  @  rx  z9TestOptimizeSimple.test_callback_stopiteration.<locals>.gc                    rt  ru  )rv  r
   r   r'   rw  r)   r*   ro  D  rx  z9TestOptimizeSimple.test_callback_stopiteration.<locals>.hr   r#   c                    s   | j | jks
J    d S r:   r   r(   )intermediate_resultr  rn   r)   r*   callback_interfaceK     
zJTestOptimizeSimple.test_callback_stopiteration.<locals>.callback_interfacer.   c                       s    e Zd Zdef fddZdS )z@TestOptimizeSimple.test_callback_stopiteration.<locals>.Callbackrz  c                    s   |j |jks
J    d S r:   ry  )re   rz  r{  r)   r*   r  P  r}  zITestOptimizeSimple.test_callback_stopiteration.<locals>.Callback.__call__N)ry   rz   r{   r   r  r)   r{  r)   r*   r  O  s    r  c                    s
      d S r:   r)   )xkr   )r  r)   r*   r|  U  r   c                      s.     j d7  _ d _ j krd _t d S )Nr#   FT)rS  rv  StopIterationr)   )r  r`   r)   r*   r  X  s   
z@TestOptimizeSimple.test_callback_stopiteration.<locals>.callbackr   r  )rO   r   r   r   rv   r  r  r   r`   r  rW   c   r)   )	rv  rS  r
   r   r   r   r(   r   r   )
re   r   rs  r  ro  r|  r  r  r   r   r)   )r  rn   r`   r*   test_callback_stopiteration4  s2   
 z.TestOptimizeSimple.test_callback_stopiterationc                 C   sL   d}t t|d tdd td W d    d S 1 sw   Y  d S )Nz"'x0' must only have one dimension.r   c                 S   rJ  r:   r)   r'   r)   r)   r*   rV  p  rW  z4TestOptimizeSimple.test_ndim_error.<locals>.<lambda>)r.   r#   )rJ   rK   r
   r   r%   onesre   rT  r)   r)   r*   test_ndim_errorm  s   "z"TestOptimizeSimple.test_ndim_error)r  r  r  r  r  r  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 s,w   Y  t g dg d}d}tjt|d tj|g d	||d
 W d    d S 1 sZw   Y  d S )Nc                 S   r  r  r  r'   r)   r)   r*   rn   u  r   z:TestOptimizeSimple.test_minimize_invalid_bounds.<locals>.fr#   r.   rW   r   z?The number of bounds is not compatible with the length of `x0`.r   )r#   r.   rW   rO   r   r  )r#   r   r#   )rW   r   r.   z:An upper bound is less than the corresponding lower bound.)r   r   r	   rK   r
   r   )re   r   rn   r  rT  r)   r)   r*   test_minimize_invalid_boundsr  s   "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 t jdd	 d
d
gf||d| W d    n1 s<w   Y  d|d< t jdd	 d
d
gf||d| d S )Nr  r   Tr   r  Maximum numberr   c                 S   r  r:   r
   r   r'   r)   r)   r*   rV       
 zBTestOptimizeSimple.test_minimize_warnings_gh1953.<locals>.<lambda>r   r   Fr   c                 S   r  r:   r  r'   r)   r)   r*   rV    r  )r
   r   r=  rm  r   r<  r   )re   r   r  warning_typer   r)   r)   r*   test_minimize_warnings_gh1953  s$   

z0TestOptimizeSimple.test_minimize_warnings_gh1953N)*ry   rz   r{   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r;  r<  r=  r   r'  r,  r5  r;  r>  rA  rK  rQ  r\  rp  rr  r   r  r  r  r  r)   r)   r)   r*   r    sf    		&

=


2
-

6
r  r   )r  r  r   rE  c                 C   s<   dd }t j|ddg| d}|jsJ t|jdgdd d S )	Nc                 S   r  r  r  r'   r)   r)   r*   rn     r   z$test_minimize_with_scalar.<locals>.f   )r  r  r  rX   r   r   )r
   r   r   r   r(   )r   rn   r   r)   r)   r*   test_minimize_with_scalar  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  r_   rd   r)   r)   r*   rf     rx  zTestLBFGSBBounds.setup_methodr*  c                 C   s    d| |d | |d |   S )NrT   r   r#   r)   rw   r)   r)   r*   r     r0   zTestLBFGSBBounds.func                 C   s   ||d  S r"   r)   rw   r)   r)   r*   r     r~  zTestLBFGSBBounds.jacc                 C   s   |  ||| ||fS r:   r   r   rw   r)   r)   r*   fj  rB   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   taskr6   r   )r
   r  r   r   r  r   r_   re   r(   rn   r  r)   r)   r*   test_l_bfgs_b_bounds  s   z%TestLBFGSBBounds.test_l_bfgs_b_boundsc                 C   sL   t j| jddgd| jd\}}}|d dksJ |d t|| jdd d S )	Nr   r!  r*  )r   r  r   r  r6   r   )r
   r  r  r  r   r_   r  r)   r)   r*   r    s
   z%TestLBFGSBBounds.test_l_bfgs_b_funjacc                 C   sH   t j| jddgd| j| jd}|d sJ |d t|j| jdd d S )	Nr   r!  r  r   r   r  r   r  r6   r   )r
   r   r   r   r  r   r(   r_   )re   r   r)   r)   r*   test_minimize_l_bfgs_b_bounds  s
   z.TestLBFGSBBounds.test_minimize_l_bfgs_b_boundsr  )r   r#   rE  c                 C   sP   t jtdd tj| jddgd| j|d W d    d S 1 s!w   Y  d S )Nz	.*bound.*r   r   r!  r  r  )r   r	   rK   r
   r   r   r   )re   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 ])\}}tj| jddg|d|| jdd id}|d	 s.J |d
 t|j| jdd qd S )Nr  r  r)   r   r!  r  finite_diff_rel_step)r   r   r   r  r   r   r  r6   r   )	r  r  r
   r   r   r  r   r(   r_   )re   r  argssr   r   r   r)   r)   r*    test_minimize_l_bfgs_b_bounds_FD  s   z1TestLBFGSBBounds.test_minimize_l_bfgs_b_bounds_FDNr  )ry   rz   r{   rf   r   r   r  r  r  r  r   r;  r=  r  r  r)   r)   r)   r*   r    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   
   d| _ d S )Nr1   )r_   rd   r)   r)   r*   rf     r   zTestOptimizeScalar.setup_methodr1   c                 C   s   || d d S )zObjective functionr.   r   r)   )re   r(   r  r)   r)   r*   r        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 s\w   Y  d}tjt|d
 t j| jdd W d    d S 1 s~w   Y  d S )Nr6   r   r-  rs  brackTr   r   ir!     /\(f\(xb\) < f\(xa\)\) and \(f\(xb\) < f\(xc\)\)r   r!  r   r#   \(xa < xb\) and \(xb < xc\)r   r!  r#   )r
   brentr   r   r_   r   r	   rK   )re   r(   r  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 ]$}t j| jddd}t j| j|dd}|d |d }}t|| | qTd}tjt|d t j| jdd W d    n1 sw   Y  d}tjt|d t j| jdd W d    d S 1 sw   Y  d S )Nr6   r   r  r  Tr  r   r  r  )r   r#   r   )r`   r   r.   r  r   r  r  r  )	r
   goldenr   r   r_   r   r   r	   rK   )re   r(   maxiter_test_casesr`   rO   nfev0r   r  r)   r)   r*   test_golden  s0   "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   r6   )	r
   	fminboundr   r   r_   r%   rF   rJ   rK   r  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w   Y  t| jdtd}t	|| j
dd d S )Nz.*must be finite scalars.*r   r#   r.   r#   r   r6   r   )r   r	   rK   r
   r  r   r%   r\   rF   r   r_   r  r)   r)   r*   test_fminbound_scalar'  s
   z(TestOptimizeScalar.test_fminbound_scalarc                 C   s   dd }t |dd d S )Nc                 S   rB  r  r)   r'   r)   r)   r*   r   /  rC  z,TestOptimizeScalar.test_gh11207.<locals>.funr   )r
   r  )re   r   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sJ t j| jdtddd}|jr-J 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 )Nr6   r   Brentr   rW   r  r   r  r1   )bracketr   r   )r   r   r  r  )r   r#   Bounded)r  r   r   r#   r  )r#   r   boundedr   r1   )r   r#   r  r   r   r.   r  )r
   minimize_scalarr   r(   r   r_   r   r+  r%   rF   rJ   rK   r\   r  r)   r)   r*   test_minimize_scalar3  s   









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)   r8   r  c                 [   s   |d |d  d }| |}	d}
d}d}d}|r`|s`||k r`d}|d7 }|| || fD ]}| |g|R  }|
d7 }
||	k rD|}	|}d}q,|d urM|| |d urX|
|krXd}n|r`|s`||k st j|	|||
|dkdS )Nr#   r   r*  TFr  r  )r   r  r   rF  r  r`   r  r   r  r  r  r  r  r  r  r  r)   r)   r*   r  q  s4   
z?TestOptimizeScalar.test_minimize_scalar_custom.<locals>.custmin)r   r   r  r   )r  r   r   r6   r   r  )r
   r  r   r+  r   r(   r_   )re   r  r   r)   r)   r*   test_minimize_scalar_customo  s   

z.TestOptimizeScalar.test_minimize_scalar_customc                 C   s   t j| jdd d S )Nr1   r   r
   r  r   rd   r)   r)   r*   &test_minimize_scalar_coerce_args_param  s   z9TestOptimizeScalar.test_minimize_scalar_coerce_args_paramr   )r  r  r  c                 C   s"   dD ]}t j| jd|id qd S )N)r   r#   r.   rW   r   )r   r  )re   r   r   r)   r)   r*   	test_disp  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s&J t|ds-J t|d	s4J t|d
s;J t|dsBJ d S )Nr  r  rq  r   r   r(   r   r  r   r   r   )r
   r  r   r7  )re   r   r  r$  r)   r)   r*   test_result_attributes  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r;d|ini }tj	|fd|i||t
ddd}t|jd W d    n1 s`w   Y  W d    d S W d    d S 1 sxw   Y  d S )Nr3   r   c                    s8    d  d7  <  d dkrt jS | d dt |   S )Nr   r#   r   r.   r8   )r%   r  r;   r'   r]  r)   r*   ro     s   z0TestOptimizeScalar.test_nan_values.<locals>.funcr  rj  r   r  rd  re  rf  r  r  r  r  r  r   F)r%   r2   r5   r   r   rg  rh  r=  r
   r  r+  r   r   )re   r   ro   r  r  rn  r  r   r)   r]  r*   rp    s&   
Pz"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   rB  r  r)   r'   r)   r)   r*   rn     rC  zCTestOptimizeScalar.test_minimize_scalar_defaults_gh10911.<locals>.fr   r   r   )r#   r  rY  rt  )r  r   r#   )r
   r  r   r(   )re   rn   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w   Y  t jt|d tjtjtjdfd W d    d S 1 sBw   Y  d S )Nz+Optimization bounds must be finite scalars.r   r#   rD  )	r   r	   rK   r
   r  r%   r;   rz  r  r  r)   r)   r*   'test_minimize_non_finite_bounds_gh10911  s   "z:TestOptimizeScalar.test_minimize_non_finite_bounds_gh10911r  r  c                 C   sJ   d}t jt|d tjtj|dd W d    d S 1 sw   Y  d S )Nz'Use of `bounds` is incompatible with...r   r  r   r  )r   r	   rK   r
   r  r%   r;   )re   r   rT  r)   r)   r*   2test_minimize_unbounded_method_with_bounds_gh10911  s   "zETestOptimizeScalar.test_minimize_unbounded_method_with_bounds_gh10911r  r  r#   r6   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rF||jj  krF ksIJ  J d S )Nc                    s   t | d  S Nr   )r%   rF   reshaper'   r  r)   r*   rn     r,   zITestOptimizeScalar.test_minimize_scalar_dimensionality_gh16196.<locals>.f)r   rC   r  )r  rD  )r   r  )r+  updater
   r  r(   shaper   )	re   r   r  r  rn   r  br  r   r)   r  r*   +test_minimize_scalar_dimensionality_gh16196  s   :z>TestOptimizeScalar.test_minimize_scalar_dimensionality_gh16196)r  r  r  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 s8w   Y  d|d< tj|f||d| d S )Nc                 S   r(  r-   r)   r'   r)   r)   r*   rn     r~  zBTestOptimizeScalar.test_minimize_scalar_warnings_gh1953.<locals>.fr  r  r  rs  r   TrW   r  r  r   r   Fr   )r   r<  r
   rm  r  )re   r   rn   r  kwdr   r)   r)   r*   $test_minimize_scalar_warnings_gh1953  s   
z7TestOptimizeScalar.test_minimize_scalar_warnings_gh1953Nr  )ry   rz   r{   rf   r   r  r   r;  r<  r  r  r  r  r  r  r  r=  r  r  rp  r  r  r  r   r  r  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w   Y  t jt|d t|dtj W d    n1 s>w   Y  t jt|d tj|dd W d    n1 s\w   Y  t jt|d tj|dd W d    n1 szw   Y  d	d }d
}t jt|d tj|dddd W d    d S 1 sw   Y  d S )Nc                 S      d| k | dk @ r| d S dS Nr!  r#   r.   g      Y@r)   r'   r)   r)   r*   rn        z3TestBracket.test_errors_and_status_false.<locals>.f9The algorithm terminated without finding a valid bracket.r   r!  r#   rj  r  c                 S   s<   d| d  d| d   d| d   d| d   d|   d S )	Nrp  r   r      rW      r.   r#   r)   r'   r)   r)   r*   rn     s   <z8No valid bracket was found before the iteration limit...r   rV   r   r  )	r   r	   rg   r
   r  r%   rz  r  r  )re   rn   r  r)   r)   r*   test_errors_and_status_false  s&   "z(TestBracket.test_errors_and_status_falser   )r  r  c                 C   sb   dd }d}t j|d|d}|jrJ ||jv sJ |jdks!J |jdks(J |jdks/J d S )	Nc                 S   r  r  r)   r'   r)   r)   r*   rn   '  r  z9TestBracket.test_minimize_scalar_success_false.<locals>.fr  rj  )r  r   rW   r   r  )r
   r  r   r  r   r   r   )re   r   rn   r  r   r)   r)   r*   "test_minimize_scalar_success_false$  s   
z.TestBracket.test_minimize_scalar_success_falseN)	ry   rz   r{   r   r;  r<  r  r=  r  r)   r)   r)   r*   r    s
    

r  c                   C   s   t ttjtjdd d S )Ng{Gzr  )rJ   rK   r
   r  r%   r@   r)   r)   r)   r*   test_brent_negative_tolerance4  rB   r  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 	Nr   rT   r   r"  r   rv   r  r   r#   r  r   )r%   rF   r
   r   r   r   r   r   r  r   r(   re   rO   r   r)   r)   r*   test_rosenbrock9  s   
zTestNewtonCg.test_rosenbrockc                 C   sT   t t}tjt|ttddd}|jsJ |j	t
|jtdd t
|jtdd d S )Nr"  r6   )r   rv   r   r  r  r   r   )r%   rF   rN   r
   r   
himmelblaurL   rM   r   r  r   r(   himmelblau_xoptr   himmelblau_minr  r)   r)   r*   test_himmelblauC  s   
zTestNewtonCg.test_himmelblauc                 C   sV   t ddg}tjtj|tjdddd}|jsJ |jt|j	t ddgdd	 d S )
Nr   rT   r  r   r"  r  r#   r  r   )
r%   rF   r
   r   r   r   r   r  r   r(   r  r)   r)   r*   test_finite_differenceO  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%   rF   r
   r   r   r   r   r   r  r   r(   r  r)   r)   r*   test_hessian_update_strategyY  s   
z)TestNewtonCg.test_hessian_update_strategyN)ry   rz   r{   r  r  r  r  r)   r)   r)   r*   r  8  s
    

r  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 qt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 qfd S )N)333333r!  r   r-  )r   r#   ffffff@rW   rX   r   r   r   )rX   r.   r-  r   rT   r   r   r   r  r   rX   r#   r   r   r!  r#   rX   r   r#   r   r   r  rX   r   r   r#   r-  rW   )rT   r#   r   r   )rT   r   r!  r.   r1   )r*  r   r!  r.   gffffff?g333333@)rT   r   r!  r   r6   r   g333333)r
   rN  _line_for_searchr%   rF   r   rz  )line_for_searchlower_boundupper_boundrO   x1	all_testsr(   alphalminlmaxmimar)   r)   r*   test_line_for_searchd  sV   r  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 ]X\}}| ||||dd\}	}
}t|	||| dd t|
|| dd t||| dd | |||d|||d\}	}
}t|	||| dd t|
|| dd t||| dd qbd S )Nc                 S      t | t g d d S N)rW  r*  r1   皙ٿr.   r%   r<   rF   r'   r)   r)   r*   ro     r  z$test_linesearch_powell.<locals>.funcr  r   r  r!  r  r.   r  r1   r  r  rW  r   r#   r         ?rX   r   r#   r#   皙?r*  r   r!  r#   r   )fvalr  r6   r   r  r  r  r  )r
   rN  _linesearch_powellr%   rF   rz  r   linesearch_powellro   rh  r  r  r  r  xilrn   rr   r4   r)   r)   r*   test_linesearch_powell  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 q_t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 ]4\}}| |||d|||d\}	}
}t|	||||  dd t|
|||  dd t||| dd q@t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 ]0\}}| |||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 ]4\}}| |||d|||d\}	}
}t|	||||  dd t|
|||  dd t||| dd q4d S )"Nc                 S   r  r  r  r'   r)   r)   r*   ro     r  z,test_linesearch_powell_bounded.<locals>.funcr  g       r   r*  r  r!  r  r.   r  r1   r  r  r  r   r  r  r  r  r   r  r6   r   g333333ӿrW   g?r   rU   g333333ÿ)rW  r   r   r.   r   g333333)r
   rN  r  r%   rF   r   rz  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?r  c                    s8   | \}}|  j k r|  jk sJ |d |d  S r  )lbrE   ub)r(   r  r  rD  r)   r*   r   J	  s    ztest_powell_limits.<locals>.funr   r  r#   T)r  r  keep_feasiblec                 S   s   | dkr| dks
J t | S rV  r$   r'   r)   r)   r*   ro   T	  r}  z test_powell_limits.<locals>.funcrV   r  )r   rO   r   r  )r
   r   r   )r   ro   r)   rD  r*   test_powell_limitsF	  s   r  c                   @      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)rW   r   r   )r.   r.   r.   )r%   rF   r
   rosen_hess_prodrh   r   r   )re   r(   rr   hpdothpr)   r)   r*   	test_hess]	  s
   zTestRosen.test_hessN)ry   rz   r{   r  r)   r)   r)   r*   r  [	      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.
    r  r   r)   )rr   r(   r  r  r  r)   r)   r*   r  f	  s   r  c                 C   sn   | \}}t d|d  d| |  d|  d|d   d d|d  d| |  d|d   d|  d gS )Nr   rW   *   r.         r-  r	  rr   r(   r  r)   r)   r*   rL   q	  s   2.rL   c                 C   s^   | \}}t d|d  d|  d d| d|  gd| d|  d| d|d   d ggS )Nr  r.   r   r  r  r	  r  r)   r)   r*   rM   w	  s   *&rM   gHzGѿgrW   r.   rX   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   rC   r   r?  r#   r@  r.   r	  r'   r)   r)   r*   ro   	     0z0test_minimize_multiple_constraints.<locals>.funcc                 S      t | d gS r"   r	  r'   r)   r)   r*   func1	  r(  z1test_minimize_multiple_constraints.<locals>.func1c                 S   r  r  r	  r'   r)   r)   r*   r_  	  r(  z1test_minimize_multiple_constraints.<locals>.func2r1  r2  c                 S   s   d| d | d  | d   S )Nr!  r   r#   r.   r)   r'   r)   r)   r*   rn   	  r  z-test_minimize_multiple_constraints.<locals>.frl  r6  r4  )}   r   r   rt  r   r  )ro   r   r_  r0  rn   r   r)   r)   r*   "test_minimize_multiple_constraints	  s   r"  c                   @   r  )TestOptimizeResultAttributesc                 C   s8   ddg| _ tj| _tj| _tj| _tj| _	ddg| _
d S )Nr   )rX   r  )rO   r
   r   ro   r   r   r   rv   r  rx   r  rd   r)   r)   r*   rf   	  s   
z)TestOptimizeResultAttributes.setup_methodc              
   C   s   g d}ddgi}t D ]R}t }|td tj| j| j|| j| j	| j
d}W d    n1 s1w   Y  |D ]}||v rE||| v rEq8t||sLJ |t|v sTJ q8t|jts]J qd S )N)r   r   r(   r   r   r   r  r  r   z7Method .+ does not use (gradient|Hessian.*) information)r   r   rv   rx   )r   r   rg  r=  r
   r   ro   rO   r   rv   rx   r7  dirr  r  str)re   
attributesskipr   rn  r   	attributer)   r)   r*   test_attributes_present	  s&   
z4TestOptimizeResultAttributes.test_attributes_presentN)ry   rz   r{   rf   r)  r)   r)   r)   r*   r#  	  s    r#  c                 G   s^   | \}}|\}}}}}}	}
}}}}}}||d  || |  ||d   ||  ||  |	 S r  r)   r  r   r(   r  r  r  r  r  r   rn   r  ro  rS  r  r  r  rU  r)   r)   r*   f1	  s   8r+  c                 G   sP   | \}}|\}}}}}}	}
}}}}}}|
 t || d || d   |  S r  r$   r*  r)   r)   r*   f2	     *r,  c                 G   sP   | \}}|\}}}}}}	}
}}}}}}| t || d || d   |  S r  r$   r*  r)   r)   r*   f3	  r-  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	  r  r0  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.   rW   r   r   r   r   ,   r!  r.   r  r#   rs  rV   rk  r         ?g_}gi?)r   slicerrangesr%   rF   r_   rd   r)   r)   r*   rf   	  s   zTestBrute.setup_methodc                 G   s   t |g|R  S r:   )r0  )re   r  r   r)   r)   r*   r0  	  r  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r   r   finishr   r   r   r#   )	r
   bruter0  r5  r   r	  r   r_   r   )re   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.   )rn  r  r'   r)   r)   r*   rn   	  s   zTestBrute.test_1D.<locals>.frj  rW   )Nsr7  )r
   r8  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 )NTr6  r.   )r   r   r7  workersr!  r   )r
   r8  r0  r5  r   r   )re   r9  	resbrute1r)   r)   r*   test_workers	  s   zTestBrute.test_workersc                    sf   t jd  fdd}d}tjt|d tj|| j| j	dd W d    d S 1 s,w   Y  d S )Nr3   c                    r?  r@  rA  r/  rB  r)   r*   ro   

  r   z,TestBrute.test_runtime_warning.<locals>.funczFfinal optimization did not succeed.*|Maximum number of function eval.*r   T)r   r   )
r%   r2   rG  r   r<  r=  r
   r8  r5  r   )re   capsysro   rT  r)   rB  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(   r   r)   r)   r*   rn   
  r~  z+TestBrute.test_coerce_args_param.<locals>.frk  r   r3  r.   r  r   )r
   r8  r4  r   )re   rn   r9  r)   r)   r*   test_coerce_args_param
  s   z TestBrute.test_coerce_args_paramN)
ry   rz   r{   rf   r0  r:  r<  r?  r>  rB  r)   r)   r)   r*   r1  	  s    

r1  c                     s   dd l } dd lfddfddd  fdd} fd	d
}| j $}g }||| ||| |D ]}|  q>W d    d S 1 sPw   Y  d S )Nr   c                    s     d | d d S )Nr8   r   r.   sleepr'   timer)   r*   
objective1!
  s   
z*test_cobyla_threadsafe.<locals>.objective1c                    s     d | d d d S )Nr8   r   r#   r.   rC  r'   rE  r)   r*   
objective2%
  s   
z*test_cobyla_threadsafe.<locals>.objective2COBYLAc                         t jdg dS NrX   r   r  r)   )
min_methodrG  r)   r*   
minimizer1+
     z*test_cobyla_threadsafe.<locals>.minimizer1c                      rJ  rK  r  r)   )rL  rH  r)   r*   
minimizer20
  rN  z*test_cobyla_threadsafe.<locals>.minimizer2)concurrent.futuresrF  futuresThreadPoolExecutorrj   submitr$  )
concurrentrM  rO  pooltasksry  r)   )rL  rG  rH  rF  r*   test_cobyla_threadsafe
  s   
"rW  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   r  r&  )r  rd   r)   r)   r*   rf   A
  r   z TestIterationLimits.setup_methodc                 C   s\   |  j d7  _ t|d d |d d  t|d |d }}t|d | |d  S )Nr#   r   r.   r  rV   )r  r%   r  arctan2r;   )re   r  rP   ry  r)   r)   r*   	slow_funcD
  s   4zTestIterationLimits.slow_funcc                 C      |  dd d S )NrE     check_limitsrd   r)   r)   r*   test_neldermead_limitI
  r(  z)TestIterationLimits.test_neldermead_limitc                 C   r[  )Nr  rY   r]  rd   r)   r)   r*   test_powell_limitL
  r(  z%TestIterationLimits.test_powell_limitc              	   C   s  ddgddgddgfD ]}dD ]/}d| _ tj| j||d|id}| j |d ks)J |d	 r6|d |k s5J q|d |ks>J qdD ]#}tj| j||d
|id}|d	 r\|d |ks[J qA|d |ksdJ qAddgddgdtjgfD ]>\}}d| _ tj| j||||dd}| j |d ksJ |d	 r|d |k r|d |ksJ qq|d |ks|d |ksJ qqtjd gd tjgfD ]O\}}d| _ tj| j||||dd}| j |d ksJ |d	 r|d u r|d |d k sJ q|d |d ksJ q|d |d ks	|d |d ks	J qqd S )Nr8   r#   r.   )r  i    r   rF  r   r   r   r`   r   r  ra  )r`   rF  )r  r
   r   rZ  r%   rz  )re   r   default_itersstart_vmfevr   mitr)   r)   r*   r^  O
  sd   

 

z TestIterationLimits.check_limitsN)ry   rz   r{   rf   rZ  r_  r`  r^  r)   r)   r)   r*   rX  =
  s    rX  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 ]}t j| tdg|||d}|jjd
ksGJ q/d S )Nc                 S   s   | |  S r:   r)   r'   r)   r)   r*   r   
  rC  z2test_result_x_shape_when_len_x_is_one.<locals>.func                 S   s   d|  S Nr*  r)   r'   r)   r)   r*   r   
  rC  z2test_result_x_shape_when_len_x_is_one.<locals>.jacc                 S   ra  rf  r	  r'   r)   r)   r*   rv   
  r   z3test_result_x_shape_when_len_x_is_one.<locals>.hess)rE  r   r   r   r  r  rI  r6  r8   r   r  )r  r  r  r  r  r"  r  )r
   r   r%   rF   r(   r  )r   r   rv   r  r   r   r)   r)   r*   %test_result_x_shape_when_len_x_is_one
  s   rg  c                   @   r  )FunctionWithGradientc                 C   r  r&  )number_of_callsrd   r)   r)   r*   r  
  r   zFunctionWithGradient.__init__c                 C   s$   |  j d7  _ t|d d| fS r-   )ri  r%   r<   r  r)   r)   r*   r  
  s   zFunctionWithGradient.__call__Nr  r)   r)   r)   r*   rh  
  s    rh  c                   C   s   t  S r:   )rh  r)   r)   r)   r*   function_with_gradient
  s   rj  c                 C   s   t | }tddg}t||d | jdksJ t||d|  | jdks,J dt|d| ddd	 | jdks@J dd S )
NrT   r*  r]  r#   r.   zHfunction is not recomputed if gradient is requested after function valueg      4@(different input triggers new computationrY  )r   r%   rF   r   ri  
derivativerj  memoized_functionrO   r)   r)   r*   )test_memoize_jac_function_before_gradient
  s   ro  c                 C   s   t | }tddg}t||d|  | jdksJ t||d | jdks,J dt|d| d| dd	 | jdksCJ dd S )
NrT   r*  r.   r#   r]  zHfunction is not recomputed if function value is requested after gradientr   rk  rY  )r   r%   rF   r   rl  ri  rm  r)   r)   r*   )test_memoize_jac_gradient_before_function
  s   rp  c                 C   s   t | }|j}t }tddg}t||d||dd}| jdks#J ||d  | jdks1J ||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.
    rT   rV   r)   Nr#   r8   r.   rC   rW   )	r   rl  r
   r   r%   rF   r   ri  r   )rj  rn  r   rv   rO   scalar_functionr)   r)   r*   test_memoize_jac_with_bfgs
  s   rr  c                   C   sH   t   tjdd tj tjdd W d    d S 1 sw   Y  d S )Nc                 S   s   t | d gS r  r	  r'   r)   r)   r*   rV  
      ztest_gh12696.<locals>.<lambda>Fr   )r   r
   r  r%   r   r)   r)   r)   r*   test_gh12696
  s
   "rt  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!  rW  )rW   r.   r.   rW  Tc                    s0   |r	| j dks	J |rt|      d S d S r  )r  r   )r(   
check_sizecheck_values)i_ebr  r)   r*   check_x
  s
   z(setup_test_equal_bounds.<locals>.check_xc                        |  t | S r:   r  r'   rx  r)   r*   ro   
     
z%setup_test_equal_bounds.<locals>.funcc                    ry  r:   )r
   r   r'   rz  r)   r*   rs   
  r{  z%setup_test_equal_bounds.<locals>.gradc                    s    |  d S r:   r)   rA  rz  r)   r*   r     r~  z)setup_test_equal_bounds.<locals>.callbackc                    s    | dd | dd d S )NFrv  r   r#   r)   r'   rz  r)   r*   constraint1     z,setup_test_equal_bounds.<locals>.constraint1c                    "    | dd t | }d|d< |S )NFr|  r#   r   r%   
zeros_liker(   dcrz  r)   r*   	jacobian1     
z*setup_test_equal_bounds.<locals>.jacobian1c                    s    | dd | dd d S )NFr|  r.   rW   rV   r)   r'   rz  r)   r*   constraint2  r~  z,setup_test_equal_bounds.<locals>.constraint2c                    r  )NFr|  r#   r.   r  r  rz  r)   r*   	jacobian2  r  z*setup_test_equal_bounds.<locals>.jacobian2)r  r6  r  Fr  c                    s    | | fS r:   r)   r'   r  r)   r*   rV  #  rs  z)setup_test_equal_bounds.<locals>.<lambda>c                 S   s   t t| |S r:   )listzipr  r  r)   r)   r*   rV  '  s    r  )	r  kwdsbound_typesr  	callbacksr  r  rO   rw  )TT)r%   r2   r5   r  rF   r   rz  r   )rO   r  r  r}  r  r  r  c1ac1bc2ac2br  r  r  r  r  datar)   )rx  ro   rs   rw  r  r*   setup_test_equal_bounds
  sP   r  z0Failures due to floating point issues, not logicr  r  
bound_typer  r  r  r  c                 C   s  t  dkr| dkr|d du r|durtd td td }}td	 td
 }}|\}	}
|	r:| dks:td |	|
k}|||}||| ||	|d tjdi |}tjtj|| tj	||
d}|j
shJ t|j|jdd t|j|jdd |s|d du rtj|j|< |jjd dksJ 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 dS dS 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
    aarch64r  r   FNzTolerance violation on aarchr  r  rO   rw  r6  z)Only SLSQP supports nonlinear constraints)rO   r   r  r  r  )r   r   r  r  gTqs*>r   gMb@?r   r   r6   c                 S   s,   t t jdt jdg}| |ddg< t|S )Nr.   r!  r   )r%   rF   r  r
   r   )r(   new_xr)   r)   r*   r   t  s   
ztest_equal_bounds.<locals>.funr.   r  g>r)   )platformmachiner   r'  eb_datar  r
   r   r   r   r   r   r   r(   r%   r  r   r  r  r   )r   r  r  r  r  r  r  rO   rw  test_constraintsreference_constraints	fd_neededr  r   expectedr   fd_resr)   r)   r*   test_equal_boundsB  sF   





r  c           	      C   s  ddd}ddg}d}t j|||| d}|jsJ t|j|dd	g |jdks*J |jd
ks1J d}t j|||| |d}|jsBJ t|j|dd	gd |  dkrdd }t|t	j
 d}t j|||| |gd}|jdu sqJ t|j|dd	g |jdksJ d}|j|sJ t|t	j
 d}t j|||| |gd}|jdu sJ t|j|dd	g |jdksJ d}|j|sJ d S d S )Nr#   c                 S   s   t j| | S r:   )r%   linalgnorm)r(   p1r)   r)   r*   rn     r(  z test_all_bounds_equal.<locals>.fr  )r.   r.   )rT   r  r  rT   r*  z/All independent variables were fixed by bounds.)r.   r  r.   r6  c                 S   r  r:   r  r'   r)   r)   r*   con  r   z"test_all_bounds_equal.<locals>.conrX   )r  r   r  Fz3All independent variables were fixed by bounds, butr   Tz8All independent variables were fixed by bounds at valuesr  )r
   r   r   r   r   r   r  upperr   r%   rz  r#  )	r   rn   r  rO   r   r   r  nlcr  r)   r)   r*   test_all_bounds_equal  sD   


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s-J d S )Nc                 S   s(   | d d | d d  | d | d   S )Nr   rW   r#   r.   r)   r'   r)   r)   r*   rn     s   (ztest_eb_constraints.<locals>.fc                 S   s$   | d | d  | d  | d  d S )Nr   r#   r.   rW   (   r)   r'   r)   r)   r*   cfun  s   $z!test_eb_constraints.<locals>.cfunr1  r2  )r   r  r   )r   r   r#   )r#   r.   rW   r   r6  )rO   r   r  r  r   r   r  )rn   r  r  r  r)   r)   r*   test_eb_constraints  s   
r  c                  C   sh   t tttttd} |  D ]\}}|D ]}t|| qqdddd}| D ]\}}tt	t|| q&d S )N)r   r  rootroot_scalarlinprogquadratic_assignmentekkir   )r   maximizemaximize_scalar)
r   r   r   r   r   r   itemsr   rJ   rK   )solver_methodssolverr  r   unknown_solver_methodr)   r)   r*   test_show_options  s$   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]  r  r  r   r   r  )r
   r   r   r   r%   rF   rD  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 ]*}d }d }||v r)|}||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%   rI   r  r<   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%   rI   r  r/  r)   r)   r*   	fquad_jac  s   z3test_x_overwritten_user_function.<locals>.fquad_jacc                 S   s   t t | d S rf  )r%   r   r  r'   r)   r)   r*   
fquad_hess  r,   z4test_x_overwritten_user_function.<locals>.fquad_hess)r)  r  r  r  r  r  )r  r  r  r  r  r   r1   r  g-C6*?r   )	r%   r  r   r
   r   r   r(   rI   r  )
r  r  r  meth_jac	meth_hessrO   methr   rv   r   r)   r)   r*    test_x_overwritten_user_function  s    r  c                   @   r  )TestGlobalOptimizationc                 C   s   dd }t j|ddt |dgt |dgt |dgt |dgg}|D ]4}t|t js0J t|ds7J t|ds>J t|dsEJ t|d	sLJ t|d
sSJ t|dsZJ q&d S )Nc                 S   rB  r  r)   r'   r)   r)   r*   ro     rC  zDTestGlobalOptimization.test_optimize_result_attributes.<locals>.funcr#   )rO   )rk  r   r(   r   r  r   r   r   )	r
   basinhoppingdifferential_evolutionshgodual_annealingdirectr  r   r7  )re   ro   r   r$  r)   r)   r*   test_optimize_result_attributes  s    z6TestGlobalOptimization.test_optimize_result_attributesN)ry   rz   r{   r  r)   r)   r)   r*   r    r  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
   approx_fprimerN   r  r   rL   rM   )r  ro  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 rd  r)   r'   r)   r)   r*   rn   8  r  ztest_gh12594.<locals>.frq  r   r  r   r   r  )r   r
   r   r%   rF   r   r   r(   )rn   r  r   r   r)   r)   r*   test_gh125943  s    r  r"  r  sparse_typec                    s    fdd}ddg}t jt|| t|d}t jt|| ttd}t|j|j t|j|j |j|jks4J |j	|j	ks<J |j
|j
ksDJ d S )Nc                    s    t | S r:   )r   r'   r  r)   r*   sparse_rosen_hessM  r~  z.test_sparse_hessian.<locals>.sparse_rosen_hessr*  r  )r
   r   r   r   r   r   r   r(   r   r   nhev)r   r  r  rO   
res_sparse	res_denser)   r  r*   test_sparse_hessianD  s   	

r  )ur|   r  r  numpyr%   numpy.testingr   r   r   r   r   r   r   r   r	   rJ   scipyr
   scipy.optimize._minimizer   r   r   r   r   scipy.optimize._linprogr   scipy.optimize._rootr   scipy.optimize._root_scalarr   scipy.optimize._qapr   (scipy.optimize._differentiable_functionsr   r   scipy.optimize._optimizer   r   r   scipy.optimizer   r   r   scipy.sparser   r   r   r   r    r!   rQ   rR   r}   rI  rU  rX  r\  rc  rf  ri  ro  r}  r  r  r  r  r  r  r;  r=  r  r  r  r  r  r  r  r  r  r  r  r  rL   rM   rN   r  r  r"  r#  r+  r,  r.  r0  r1  rW  rX  rg  rh  fixturerj  ro  rp  rr  rt  r  r  xfail_on_32bitr  r  r  r  r  r  r  r  r  r  r)   r)   r)   r*   <module>   s    $ 50    

L*      	

=  .),?&}"J#B	
	T
>
+(
