o
    gL                 
   @   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 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$Z$ 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! Z.d"d# Z/d$d% Z0G d&d' d'e'Z1G d(d) d)e'Z2G d*d+ d+e'Z3G d,d- d-e'Z4G d.d/ d/e&Z5ej67d0g d1d2d3 Z8G d4d5 d5Z9G d6d7 d7Z:d8d9 Z;G d:d; d;Z<d<d= Z=d>d? Z>d@dA Z?dBdC Z@G dDdE dEZAdFdG ZBdHdI ZCdJdK ZDdLdMgZEdNdOgZFdPZGdQdR ZHG dSdT dTZIdUdV ZJdWdX ZKdYdZ ZLd[d\ ZMG d]d^ d^ZNd_d` ZOG dadb dbZPdcdd ZQG dedf dfZRejSdgdh ZTdidj ZUdkdl ZVdmdn ZWdodp ZXdqdr ZYeY ZZej6[dsej67d0eZdt ej67dueZdu ej67dveZdw ej67dxeZdx ej67dyeZdz d{d| Z\ej67d0eZdt d}d~ Z]dd Z^dd Z_dd Z`dd ZaG dd dZbdd Zcdd Zdd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_SCALAR_METHODS)LINPROG_METHODS)ROOT_METHODS)ROOT_SCALAR_METHODS)QUADRATIC_ASSIGNMENT_METHODS)ScalarFunction
FD_METHODS)
MemoizeJacshow_optionsc               	   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   `/home/ubuntu/cloudmapper/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)r,   r)   r*   皙?Hz>c                 S   s   | t |   S N)r   sinsumr   r   r   r   x_sinx@      ztest_check_grad.<locals>.x_sinxc                 S   s   t | | t |   S r/   r   r0   cosr   r   r   r   
der_x_sinxC      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rr2   r6   r   r   r   test_check_grad!   sL   







rF   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   r;   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)rV   RuntimeErrorr   dotrO   logr1   r   rP   rX   appendcopy)rZ   r   log_pdotlogZfr   r   r   funcj   s   
zCheckOptimize.funcc                 C   sV   |  j d7  _ t| j|}ttt|}t|| }t| j || j S r   )	rW   r   r]   rO   r^   r1   r   	transposerP   rZ   r   ra   rb   pr   r   r   gradt   s
   zCheckOptimize.gradc                 C   s`   t | j|}t tt |}t || }t | jjt t || jt | jj| S r/   )r   r]   rO   r^   r1   r   Tdiagrf   r   r   r   hess{   s   
"zCheckOptimize.hessc                 C   s   t | ||S r/   )r   r]   rk   rZ   r   rg   r   r   r   hessp   r3   zCheckOptimize.hesspN)	__name__
__module____qualname____doc__r[   rd   rh   rk   rm   r   r   r   r   rG   V   s    
rG   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
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 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rU   disp
return_allr   CG)argsmethodjacoptionsr   funnfevnjevstatusT)rU   full_outputrt   retallr+   atol	      r#      )r         rK   )r   g;ӱ.g)`$|;?+=r.   r   rtol)use_wrapperrU   rt   r
   minimizerd   rS   rh   fmin_cgr   rT   rV   rW   rX   )	rZ   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         rK   r#   r   )rE   r   r   r   rc      s   z8CheckOptimizeParameterized.test_cg_cornercase.<locals>.fg      rL   G   rv   rx   rK   h㈵>r   )r   linspacer
   r   successr   r   )rZ   rc   rD   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 )NFrs   BFGSr   ry   rx   rw   rz   r   r{   ry   hess_invr|   r}   r~   Trw   rU   r   rt   r   r+   r   
         )r   g&/LgB__E7?)r   g$g
|3?r   r.   r   )r   rU   rt   r
   r   rd   rS   rh   	fmin_bfgsr   rT   rV   rW   rX   )rZ   r   r   r   r   goptHoptr   r   r   r   r   r   r   	test_bfgs   s<   

z$CheckOptimizeParameterized.test_bfgsc              	      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   <lambda>       z?CheckOptimizeParameterized.test_bfgs_infinite.<locals>.<lambda>c                    s
    |  S r/   r   r   rd   r   r   r         
 r   ignore)overrt   r   r   r   r   rt   )r   errstater   rt   r
   r   r   isfinite)rZ   fprimerD   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 )Ng?ffffff?皙?ffffff?333333?bfgsxrtolMbP?rx   rz   gtol)r
   r   rosennit)rZ   rD   r   refr   r   r   test_bfgs_xrtol   s   

z*CheckOptimizeParameterized.test_bfgs_xrtolc           
   	   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 )NFrs   r   Powellrw   rx   rz   r   r{   direcr   r|   r~   Tr   r+   r   r   h㈵>   r   )r   rU   rt   r
   r   rd   rS   fmin_powellr   rT   rV   rW   
rZ   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 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 )NFrs   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   r.   r   )
r   rU   rt   r
   r   rd   rS   r   r   rX   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	 |d
 |d |d |d f\}}}}}}	|| jksAJ t| || | j	ddd | jdksWJ | j
dks`J d S d S )Nc                 S   s   g | ]	}t j t jfqS r   )r   pi).0_r   r   r   
<listcomp>3  s    zBCheckOptimizeParameterized.test_powell_bounded.<locals>.<listcomp>Frs   r   r   )rw   boundsrx   rz   r   r{   r   r   r|   r~   r+   r   r      r   )rS   r   rU   rt   r
   r   rd   rV   r   rT   rW   )
rZ   r   r   r   r   r   r   r   r   r   r   r   r   test_powell_bounded0  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 )NFrs   r   Nelder-meadr   r   r{   r   r|   r~   Tr   r+   r      r   L   N   )g	dװ?g]fgt䝁?)gә ?g#=^goT?r   r.   r   )r   rU   rt   r
   r   rd   rS   fminr   rT   rV   rW   rX   )	rZ   r   r   r   r   r   r   r   r   r   r   r   test_neldermeadK  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   rL   .rL   r   r-   FTrU   rt   ru   initial_simplexr   r   r   r   r{   r   r|   r~   allvecsr   rw   rU   r   rt   r   r   r+   r   d   2   4   )gIt?g?'ΛTgx8?)gҢ_׆?goMg囎|52?r   r.   r   )r   rQ   rS   ranger   rU   r
   r   rd   r   r   rT   rV   rW   rX   )rZ   simplexjr   r   r   r   r   r   r   r   r   r   r   test_neldermead_initial_simplexj  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)rL   r#   r#   .r   r-   )rL   rL   Fr   r   r   r   Tr   )r   rQ   rS   r   r_   r   rU   r?   r@   r
   r   rd   r   )rZ   bad_simplicesr   r   r   r   r   r   #test_neldermead_initial_simplex_bad  s8   



z>CheckOptimizeParameterized.test_neldermead_initial_simplex_badc                 C   s6   ddi}t j| j| jd| jd|d}|jdksJ d S )NrU   	Newton-CGr   rx   ry   rw   rz   r   )r
   r   rd   rS   rh   r~   )rZ   r   resultr   r   r   test_ncg_negative_maxiter  s   z4CheckOptimizeParameterized.test_ncg_negative_maxiterc              
   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 )NFrs   r   r   r   r   r   r+   r   r      rL      (6-H=g?g4u3?r   g_g/N3?r.   r   )r   rU   rt   r
   r   rd   rS   rh   fmin_ncgr   rT   rV   rW   rX   rZ   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 )NFrs   r   r   )rx   ry   rk   rw   rz   r   )fhessrw   rU   r   rt   r   r+   r   r      rL   r   r   r   r.   r   )r   rU   rt   r
   r   rd   rS   rh   rk   r   r   rT   rV   rW   rX   r   r   r   r   test_ncg_hess  :   
z(CheckOptimizeParameterized.test_ncg_hessc                 C   r   )NFrs   r   r   )rx   ry   rm   rw   rz   r   )fhess_prw   rU   r   rt   r   r+   r   r   r   rL   r   r   r   r.   r   )r   rU   rt   r
   r   rd   rS   rh   rm   r   r   rT   rV   rW   rX   r   r   r   r   test_ncg_hessp  r   z)CheckOptimizeParameterized.test_ncg_hesspN)rn   ro   rp   r   r   r   r   r   r   pytestmarkxfailr   r   r   r   r   r   r   r   r  r   r   r   r   rr      s"    "	"
 (!"rr   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   rN   r'   r   rngr   r   cost"     ztest_maxfev_test.<locals>.cost)r   r   r   )r   Nelder-Meadr   maxfevr   r|   )r   r'   default_rngr
   r   )r  imaxfevrx   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 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_2  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
   	_optimize'_wrap_scalar_function_maxfun_validationr   asarrayr   r?   _MaxFuncCallErrorr@   r;   )r  fcallsrd   imsgr   r   r   )test_wrap_scalar_function_with_validation0  s$   "r  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 )Nr  r  c                 S   r  r/   r   r   r   r   r   r   M      z.test_obj_func_returns_scalar.<locals>.<lambda>r   r   r   )r?   r@   r
   r   r   r;   r  r   r   r   test_obj_func_returns_scalarH  s    "r   c                  C   s4   t g d} tjjtj| dd}|jdksJ d S )Nr   :0yE>)xatoliS  )r   r;   r
   	_minimize_minimize_neldermeadr   r   )rD   r   r   r   r   test_neldermead_iteration_numP  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   Z  s    z-test_neldermead_xatol_fatol.<locals>.<lambda>r   r#   r   )rU   r"  fatol)r
   r#  r$  r   r   r   r   test_neldermead_xatol_fatolW  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      t | d S Nr#   r   r1   r   r   r   r   r   a  r   z*test_neldermead_adaptive.<locals>.<lambda>)gM@'?gOC?g~?g -?g?g#j?g ?g~^g?gܠr#?g^cǽ?g)i	?g'?g?g1?g[VΤ?r  r   FadaptiveTr   )r
   r   r   r   )rd   p0r   r   r   r   test_neldermead_adaptive`  s   
r.  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   r   r  r   z3test_bounded_powell_outsidebounds.<locals>.<lambda>)r   r   r/  r/  )rK   gr   r   rx   rM   r+   r   Tr   r   r   r   )r   r   r   )r   r   r   r   )r   rx   rz   )g      r   r   Fr   )r   r
   OptimizeWarningr   r   r   r   r;   lenr   r   r~   )rd   r   rD   r   r   r   r   r   !test_bounded_powell_outsideboundsn  s&    r5  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   r     r   z/test_bounded_powell_vs_powell.<locals>.<lambda>))r   )皙)r   gffffff"@)r0  gffffff@g/)g gr   r   r:  绽|=ftolxtolr   r   rM   r+   r   )rz   r   rx   )r   r8  r   r   r:  )Nr   r8  r   )r0  Nr9  c                 S   sz   t | d  t | d  t | d  | d   t | d  }|t t | d | d  t | d  8 }|d S Nr   r   r#   r4   r   tr   r   r   rd     s   D.z+test_bounded_powell_vs_powell.<locals>.func)r:  r   rL   )r   r   r   r   r1  g8:}?r   )gb4F@g:gW?@)r
   r   r   r   r{   r   r;   infr|   r   r3  )rd   r   rD   rz   
res_powellres_bounded_powellrg   r   r   r   test_bounded_powell_vs_powell  sb   




rE  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    .ArL   r!  r<  )rx   r   rz   rH   c                 S   s   t |  S r/   r+  r   r   r   r   r     s    z8test_onesided_bounded_powell_stability.<locals>.<lambda>g    `F-C6?r   c                 S   .   t t | d  t | dkrd S d S )Nr-   r   r   r   r   r=   r1   r:   r   r   r   r   rc        .z1test_onesided_bounded_powell_stability.<locals>.fgwc                 S   rG  )Nr   r   r   r   rH  r   r   r   r   rc     rI  gB+Iar.   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   r-   r   r   r   rH  r@  r   r   r   rc     s
   :g     @@r   g 4&k\)r   rB  r
   r   r   r{   )kwargsrD   rc   r   r   r   r   &test_onesided_bounded_powell_stability  s$   rK  c                   @      e Zd ZdZdZdS )TestOptimizeWrapperDispTNrn   ro   rp   r   rt   r   r   r   r   rM         rM  c                   @      e Zd ZdZdZdS )TestOptimizeWrapperNoDispTFNrN  r   r   r   r   rQ    rO  rQ  c                   @   rP  )TestOptimizeNoWrapperDispFTNrN  r   r   r   r   rR  
  rO  rR  c                   @   rL  )TestOptimizeNoWrapperNoDispFNrN  r   r   r   r   rS    rO  rS  c                   @   sz  e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zejjd!d"d#d$ Zd%d& Zd'd( Zejd)g d*e d+d, Zejd)g d-d.d/ Zd0d1 Zejd)g d2d3d4 Zejd)g d5d6d7 Zd8d9 Z d:d; Z!d<d= Z"d>d? Z#ejd)g d@dAdB Z$ejd)g dCdDdE Z%dFS )G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   r  r/   r   r   r   r   r   r     r  z2TestOptimizeSimple.test_bfgs_nan.<locals>.<lambda>c                 S   
   t | S r/   r   	ones_liker   r   r   r   r     r   r   )r   invalidFr   )r   nanr   r
   r   isnan)rZ   rd   r   rD   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   rY  r   r   r   r   r   #  s    z9TestOptimizeSimple.test_bfgs_nan_return.<locals>.<lambda>r   rX  r   r{   r   Fc                 S   s   | dkrdS t jS Nr   r]  r   r   r   r   r   +  s    c                 S   rU  r/   rV  r   r   r   r   r   ,  r   )ry   )r   r   r
   r   rZ  )rZ   rd   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 )NrI   r   F)r,   rw   rU   rt   r+   r   )r   sqrtspacingr'   randr4  rT   r
   r   rd   rS   rU   r   )rZ   r,   r   r   r   r   test_bfgs_numerical_jacobian3  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   rv   TNC2-point3-pointN)rx   ry   r+   r   )		itertoolsproductr
   r   rd   rS   r   r   rT   )rZ   methodsjacsrx   ry   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rx   ry   rk   )ro  rp  doglegtrust-exact)r   r
   r   ri  rj  r   rd   rS   rh   r   r  r	   r@   )rZ   rk  hessesrx   rk   r   r   r   r   test_finite_differences_hessH  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rI   r   r   r   r   r   rc   c  s   z/TestOptimizeSimple.test_bfgs_gh_2169.<locals>.f      $@Fr   rI   rF  r   r   )r
   r   r   )rZ   rc   xsr   r   r   test_bfgs_gh_2169b  s   z$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   rc   m  s   
z:TestOptimizeSimple.test_bfgs_double_evaluations.<locals>.fr   Tr.   )rx   ry   tol)setr
   r   rZ   rc   r   r}  r   test_bfgs_double_evaluationsk  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   )rw   rU   r+   r   r   r   rL   )g><gwT볹gUuAX?)rM   gHg!mʲ3?r   r.   r   )r
   fmin_l_bfgs_brd   rS   rh   rU   r   rT   rV   rW   rX   rZ   r   r   r   dr   r   r   test_l_bfgs_bv  s    

z TestOptimizeSimple.test_l_bfgs_bc                 C   sB   t j| j| jd| jd}|\}}}t| || | jdd d S )NT)approx_gradrU   r+   r   )r
   r  rd   rS   rU   r   rT   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/   rd   rh   r   rY   r   r   r{     r!   z4TestOptimizeSimple.test_l_bfgs_b_funjac.<locals>.funrU   r+   r   )r
   r  rS   rU   r   rd   rT   )rZ   r{   r   r   r   r  r   rY   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   rY   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   rZ   r   r   r   r   __call__  s   zCTestOptimizeSimple.test_l_bfgs_b_maxiter.<locals>.Callback.__call__Nrn   ro   rp   r  r  r   r   r   r   Callback  s    r  rM   l-bfgs-brU   r   )rx   callbackrz   r   Fz+STOP: TOTAL NO. of ITERATIONS REACHED LIMIT)r
   r   r   r   r   r   r   r{   r~   r   message)rZ   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)rt   rU   L-BFGS-Brx   ry   rz   r+   r   r   r   rh  ry   rx   rz   )rU   r
   r   rd   rS   rh   r   r   rT   rW   r}   rV   r|   )rZ   r   rE   rar   r   r   test_minimize_l_bfgs_b  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)r-   rF  r.   r;  F)rt   rU   r=  r  r  r   )	rU   r
   r   rd   rS   rh   r   r   rT   )rZ   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 )N333333rI   r  Fr   )rt   maxlsr  )r
   r   r   r   r;   	rosen_derr   )rZ   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   rN   c                    s    | } | |S r/   )r_   )r   valuerc   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>  s    zPTestOptimizeSimple.test_minimize_l_bfgs_b_maxfun_interruption.<locals>.<genexpr>)
r
   r   r  r   fullr  max	enumerateminr   )rZ   grD   r  lowmediumhighr  kr  targetxminr   r  r   r  r   *test_minimize_l_bfgs_b_maxfun_interruption  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   r-   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   sizer`   r
   OptimizeResult)r{   rD   rw   r  stepsizerU   r  rz   bestxbestyfuncallsniterimprovedstopdimstestxtestyr   r   r   custmin  s<   

z/TestOptimizeSimple.test_custom.<locals>.custmin)g??r   g?r   皙?r  r   rI   rF  rw  r   Nr-   r   N)r
   r   r   dictr   r   )rZ   r  rD   r   r   r   r   test_custom  s   
zTestOptimizeSimple.test_customz$output not reliable on all platformsr   c                 C   s6  t jddgt jdd}t jdi |ddi | \}}d|vr%d|vs'J t jdi |dd	i | \}}d|v rAd|vsCJ t jdi |dd
i | \}}d|v r]d|v s_J t jdi |d
dd | \}}d|vrzd|vs|J t jdi |ddd | \}}d|v rd|v sJ d S )Nr   rL   )rL   r   r  )rd   rD   r   r   iprintr   r  z
At iterater   r   F)r  rt   Tr   )r
   r   r  r  
readouterr)rZ   capfdrJ  outr   r   r   r   test_gh133213  s$   
zTestOptimizeSimple.test_gh13321c                    s<   ddg d fdd}ddg}t jt j|| d d S )N)r:  r#   )r   rL   constraintsc                    s(   |d  u sJ |d u sJ t  S )Nr   r  r
   r  )r{   rD   rz   r   r  r   r   r  [  s   z0TestOptimizeSimple.test_gh10771.<locals>.custminr   )rx   r   r  )r
   r   r   )rZ   r  rD   r   r  r   test_gh10771U  s   
zTestOptimizeSimple.test_gh10771c                 C   s   dd }dd }dD ]<}|dv rd }n|}t j|ddg|d|d	}t j|ddg|d
|d	}||j||jk sFJ d|||j||jf q
d S )Nc                 S   s$   | \}}|d |d  |d  d S )Nr#   r   r   r   zr   r  r   r   r   rd   f  s   z<TestOptimizeSimple.test_minimize_tol_parameter.<locals>.funcc                 S   s:   | \}}t d| |d  d|d   d|d  | gS )Nr#   r   rL   r   r;   r  r   r   r   dfuncj  s   2z=TestOptimizeSimple.test_minimize_tol_parameter.<locals>.dfunc	nelder-meadpowellcgr   	newton-cgr  tnccobylaslsqpr  r  r  r   r;  )ry   r  rx   rI   z%s: %s vs. %s)r
   r   r   )rZ   rd   r  rx   ry   sol1sol2r   r   r   test_minimize_tol_parameterd  s   4z.TestOptimizeSimple.test_minimize_tol_parameterrx   )r   r   r   r   r   r  fmin_tnc
fmin_slsqpc           	         sb   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!d  tdD rJ d S )"N)r  r  c                 S   s   t | t | fS r/   )r
   r   r  r   r   r   r   r         zHTestOptimizeSimple.test_minimize_callback_copies_array.<locals>.<lambda>r   r   r  r   iterr  r   r  )r   r   i  rU   c                     s    |d< t j| i |S )Nrx   r
   r   )akwr   r   r   routine  s   zGTestOptimizeSimple.test_minimize_callback_copies_array.<locals>.routiner  r  rz   r  )r   r   )r  ry   rp  rs  ro  rr  rn  rk   c                    s     | t| f d S r/   )r_   r   r`   )r   rw   rJ  )resultsr   r   r    r7   zHTestOptimizeSimple.test_minimize_callback_copies_array.<locals>.callbackr  r#   c                 s   s"    | ]\}}t ||kV  qd S r/   )r   r:   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  
rosen_hessr   rQ   
startswithgetattrr  r4  r:   anyri  combinations)	rZ   rx   rd   ry   rk   rD   rJ  r  r  r   )rx   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 r(d }tj|||||d}t||j|j |dkrDt	d ||j|ksMJ d S )Nc                 S   s   | d d S r"   r   r   r   r   r   rd        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  rz  r  r  r  r  r  zSLSQP returns slightly worse)
r   r;   r  r
   r   r   r   r{   r  r  )	rZ   rx   rd   r  rD   f0ry   rz   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)rI   r        @g      @r#   )r1   r   r;   r   r   r   r   rc     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   r;   concatenater]   r   r  r   r   r   cons  s   $z:TestOptimizeSimple.test_slsqp_respect_bounds.<locals>.cons)rK   rI   r&   r  r  ineqtyper{   rx   r  )rM   r#   r   r   rL   g-q=r   )r   r;   r
   r   r   r   )rZ   rc   r  rD   r   r   r   r   test_slsqp_respect_bounds  s   
"z,TestOptimizeSimple.test_slsqp_respect_bounds)r  r   rv   r   r   r  SLSQPrn  rr  ro  rs  rp  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   ry   r  rk   r}   r	  r   )r   rQ   r   r
   r   r  r  r  rh   rk   r   r{   r   r|   hasattrr}   ngevr~   )rZ   rx   MAXITERrD   sfrJ  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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)rU   rt   zMaximum number of iterationsr  r   r   )r   rQ   r   r
   r   r  r  r  warnsRuntimeWarningr  r  r{   r   )rZ   rx   rD   r  rz   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s0J d S )
Nr   c                 S   s,   t d| d  d| d   d| d   gS )Nr8   r   皙?r   Q?r#   r  r   r   r   r   r     s   , zWTestOptimizeSimple.test_respect_maxiter_trust_constr_ineq_constraints.<locals>.<lambda>r  r  r   rn  r  )r  ry   rk   rx   rz   )	r
   r   r  r  r   rQ   r   r  r   )	rZ   r  rc   ry   rk   r{   r  rD   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   rc   *     z6TestOptimizeSimple.test_minimize_automethod.<locals>.fc                 S   s   | d S r*  r   r   r   r   r   r  -  r  z9TestOptimizeSimple.test_minimize_automethod.<locals>.consrv  r  r  )r  )r   r   r   )r  r   r   r   r   r.   r   r#   r   )r   r;   r
   r   r   r   r   )
rZ   rc   r  rD   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   YE  r3   z=TestOptimizeSimple.test_minimize_coerce_args_param.<locals>.Yc                 S   s   d| |  S r*  r   r  r   r   r   dY_dxH  r  zATestOptimizeSimple.test_minimize_coerce_args_param.<locals>.dY_dx)rL   r   r   r   r   r   r#   r   r   rL   r   r   )ry   rw   rx   r/   )r   r;   r'   randnr4  r
   r   )rZ   r   r!  r  xinitr   r   r   test_minimize_coerce_args_paramC  s
   
z2TestOptimizeSimple.test_minimize_coerce_args_paramc           	         s   g d}g d} fdd}fdd}t ||D ]q\}|dv r,td d	}nt }d
k r8|dv r8qdgd g tj||||d}d| |}|jsWJ |t|jdg|d |j	dksiJ |d
kr|dv r{t d d|d q d dkr d dk sJ |q	 qd S )N)gJz5r   gd~QJ)rv   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#   )r=   r  AssertionErrorr   first_step_sizescalerD   r   r   rc   V  s
   z7TestOptimizeSimple.test_initial_step_scaling.<locals>.fc                    s   t  | d d  gS Nr   r   r  r   )r(  r   r   r  ]  r7   z7TestOptimizeSimple.test_initial_step_scaling.<locals>.g)rv   r   r!  )r   r;  )r  r         r  z{0} {1}: {2}: {3}rI   err_msgrL   r   g)\(?rK   )
ri  rj  r  r
   r   formatr   r   r   r   )	rZ   scalesrk  rc   r  rx   rz   r   r,  r   r&  r   test_initial_step_scalingO  s8   "z,TestOptimizeSimple.test_initial_step_scaling)r  r  r  r   r  r  r  r  r  rn  rr  ro  rs  rp  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 )Nr(   r   c                 S   r\  r/   r]  r   r   r   r   rd     s   z0TestOptimizeSimple.test_nan_values.<locals>.funcc                    s,    d  d7  <  d dkrt jS t j S r?  )r   rY  r'   rc  r   countr   r   func2  s   
z1TestOptimizeSimple.test_nan_values.<locals>.func2c                 S   s   t dgS NrI   r  r   r   r   r   rh     r  z0TestOptimizeSimple.test_nan_values.<locals>.gradc                 S      t dggS r3  r  r   r   r   r   rk     r  z0TestOptimizeSimple.test_nan_values.<locals>.hessrI   r  rp  rs  ro  rr  rp  rs  ro  rr  r  rz  r  r  r   r^  delta_grad == 0.*.*does not use Hessian.*.*does not use gradient.*)ry   rk   rx   rz   F)r   r'   r*   r;   r  r   r   filterUserWarningr  ri  rj  r
   r   r   r   )rZ   rx   rd   r2  rh   rk   rD   
needs_grad
needs_hessfuncsgradshesssrz   suprc   r  hr   r   r0  r   test_nan_values  s2   Pz"TestOptimizeSimple.test_nan_values)r  r  r   r  r  r  r  rn  rr  ro  rs  rp  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 )	Nr5  r6  r   r^  r7  rq  r   z Duplicate evaluations made by {})rh   rk   r   r   r   r:  r;  r
   r   rd   rS   r   r4  rX   array_equalr\   r-  )rZ   rx   ry   rk   rA  r  r   r   r   test_duplicate_evaluations  s(    z-TestOptimizeSimple.test_duplicate_evaluationsN)&rn   ro   rp   r[  r`  rd  rm  ru  ry  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  parametrizer   r  r  r  r  r  r  r  r$  r/  rC  rE  r   r   r   r   rT    sT    			&
!
:


4
-rT  rx   )r  r  r   r  c                 C   s<   dd }t j|ddg| d}|jsJ t|jdgdd d S )	Nc                 S   r)  r*  r+  r   r   r   r   rc     r  z$test_minimize_with_scalar.<locals>.f   )r  r   r1  rM   r   r   )r
   r   r   r   r   )rx   rc   r   r   r   r   test_minimize_with_scalar  s   
rH  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   rT   rY   r   r   r   r[     s   
zTestLBFGSBBounds.setup_methodr  c                 C   s    d| |d | |d |   S )NrI   r   r   r   rl   r   r   r   r{     r%   zTestLBFGSBBounds.func                 C   s   ||d  S r   r   rl   r   r   r   ry     r  zTestLBFGSBBounds.jacc                 C   s   |  ||| ||fS r/   r{   ry   rl   r   r   r   fj  r7   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  r{   ry   r   r   rT   rZ   r   rc   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  )rw   r   r   rM  r+   r   )r
   r  rL  r   r   rT   rN  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  rx   ry   r   r   r  r+   r   )r
   r   r{   ry   r   r   r   rT   )rZ   r   r   r   r   test_minimize_l_bfgs_b_bounds  s
   z.TestLBFGSBBounds.test_minimize_l_bfgs_b_boundsr   )r   r   r  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
.*bounds.*r  r   r   r  rQ  )r  r	   r@   r
   r   r{   ry   )rZ   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 )Nrf  rP  r   r   r   r  finite_diff_rel_step)rw   rx   ry   r   rz   r   r  r+   r   )	ri  rj  r
   r   r{   r   r   r   rT   )rZ   rl  argssry   rw   r   r   r   r    test_minimize_l_bfgs_b_bounds_FD  s   z1TestLBFGSBBounds.test_minimize_l_bfgs_b_bounds_FDNrP  )rn   ro   rp   r[   r{   ry   rL  rO  r  rR  r  r  rF  rS  rV  r   r   r   r   rI    s    



rI  c                   @   s   e Zd Zdd Zd'ddZdd Zdd	 Zd
d Zdd Zdd Z	dd Z
dd Zdd Zejdg ddd Zejdg ddd Zejdg ddd Zdd Zd d! Zejdd"d#gd$d% Zd&S )(TestOptimizeScalarc                 C   
   d| _ d S )Nr&   )rT   rY   r   r   r   r[        
zTestOptimizeScalar.setup_methodr&   c                 C   s   || d d S )zObjective functionr#   r   r   )rZ   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 )Nr+   r   r   r:  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   rT   r  r	   r@   )rZ   r   r  r   r   r   
test_brent#  s    "zTestOptimizeScalar.test_brentc                 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 )Nr+   r   r[  r\  Tr^  r   r_  r  )r   r   r   )rU   r   r#   ra  r  rb  rc  rd  )	r
   goldenr{   r   rT   r   r  r	   r@   )rZ   r   maxiter_test_casesrU   rD   nfev0r|   r  r   r   r   test_golden8  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   rF  r   r   r+   )	r
   	fminboundr{   r   rT   r   r;   r?   r@   r  r   r   r   test_fminboundW  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   r+   r   )r  r	   r@   r
   rl  r{   r   rQ   r;   r   rT   r  r   r   r   test_fminbound_scalarb  s
   z(TestOptimizeScalar.test_fminbound_scalarc                 C   s   dd }t |dd d S )Nc                 S   r  r*  r   r   r   r   r   r{   j  r  z,TestOptimizeScalar.test_gh11207.<locals>.funr   )r
   rl  )rZ   r{   r   r   r   test_gh11207i  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 )Nr+   r   Brentr   rL   r  r   r[  r&   )bracketrw   rx   )rx   rw   r_  rh  )r   r   Bounded)r   rw   rx   r   rF  )r   r   boundedr   r&   )r   r   r   rx   rw   r#   r1  )r
   minimize_scalarr{   r   r   rT   r   r  r   r;   r?   r@   rQ   r  r   r   r   test_minimize_scalarn  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   r-   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{   rs  rw   r  r  rU   r  rz   r  r  r  r  r  r  r  r  r   r   r   r    s4   
z?TestOptimizeScalar.test_minimize_scalar_custom.<locals>.custmin)r   r   r  r  )rs  rx   rz   r+   r   r  )r
   rw  r{   r  r   r   rT   )rZ   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&   rw   r
   rw  r{   rY   r   r   r   &test_minimize_scalar_coerce_args_param  s   z9TestOptimizeScalar.test_minimize_scalar_coerce_args_paramrx   )re  ru  rh  c                 C   s"   dD ]}t j| jd|id qd S )N)r   r   r#   rL   rt   )rz   r{  )rZ   rx   rt   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 )Nru  r   r7  r   rx   r   r   r  r{   r|   r   )r
   rw  r{   r
  )rZ   rx   rJ  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 )Nr(   r   c                    s8    d  d7  <  d dkrt jS | d dt |   S )Nr   r   r   r#   r-   )r   rY  r0   r   r0  r   r   rd     s   z0TestOptimizeScalar.test_nan_values.<locals>.funcrb  r/  r   r^  r7  r8  r9  ru  r   rs  rz  r  r   F)r   r'   r*   r   r   r:  r;  r  r
   rw  r  r   r   )rZ   rx   rd   rs  r   rA  rJ  r   r   r0  r   rC    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   r  r*  r   r   r   r   r   rc     r  zCTestOptimizeScalar.test_minimize_scalar_defaults_gh10911.<locals>.fr   r!  r   )r   r   r"  r;  )r   rz   r   )r
   rw  r   r   )rZ   rc   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   r  )	r  r	   r@   r
   rw  r   r0   rB  rY  )rZ   r  r   r   r   'test_minimize_non_finite_bounds_gh10911  s   "z:TestOptimizeScalar.test_minimize_non_finite_bounds_gh10911re  rh  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  rn  rx   r   )r  r	   r@   r
   rw  r   r0   )rZ   rx   r  r   r   r   2test_minimize_unbounded_method_with_bounds_gh10911  s   "zETestOptimizeScalar.test_minimize_unbounded_method_with_bounds_gh10911Nrr  )rn   ro   rp   r[   r{   rf  rk  rm  ro  rp  rx  ry  r|  r  r  rF  r}  r~  rC  r  r  r  r   r   r   r   rW    s*    
<#



	rW  c                   C   s   t ttjtjdd d S )Ng{Gzrg  )r?   r@   r
   re  r   r5   r   r   r   r   test_brent_negative_tolerance  r7   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  rI   r   r   ry   rk   r  rx   r   rF  r   )r   r;   r
   r   r   r  r  r   r  r   r   rZ   rD   r   r   r   r   test_rosenbrock$  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   r+   )ry   rk   rx   r  rF  r   r   )r   r;   rC   r
   r   
himmelblaurA   rB   r   r  r   r   himmelblau_xoptr{   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sJ |jt|j	t ddgdd	 d S )
Nr  rI   rg  r   r   r  r   rF  r   )
r   r;   r
   r   r   r  r   r  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   r;   r
   r   r   r  r   r   r  r   r   r  r   r   r   test_hessian_update_strategyD  s   
z)TestNewtonCg.test_hessian_update_strategyN)rn   ro   rp   r  r  r  r  r   r   r   r   r  #  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@rL   rM   r   r   r   )rM   r#   r   r   rI   r   r   r   r  r   rM   r   r   r   r   r   rM   r   r   r   r   r  rM   r   r   r   r   rL   )rI   r   r   r   )rI   r   r   r#   r&   )r  r   r   r#   gffffff?g333333@)rI   r   r   r   r+   r   g333333)r
   r  _line_for_searchr   r;   r   rB  )line_for_searchlower_boundupper_boundrD   x1	all_testsr   alphalminlmaxmimar   r   r   test_line_for_searchO  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)r*  r  r&   皙ٿr#   r   r1   r;   r   r   r   r   r         z(test_linesearch_powell.<locals>.<lambda>r  r   r  r   r  r#   r  r&   r  r  r*  r   r   r         ?rM   r   r   r   皙?r  r   r   r   r   )fvalr  r+   r   r  r  r  r  )r
   r  _linesearch_powellr   r;   rB  r   linesearch_powellrd   r-  r  r  r  r  xilrc   rg   r)   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   r     r  z0test_linesearch_powell_bounded.<locals>.<lambda>r  g       r   r  r  r   r  r#   r  r&   r  r  r  r  r  r  r  r  r   r  r+   r   g333333ӿrL   g?r  rJ   g333333ÿ)r*  r   r   r#   r   g333333)r
   r  r  r   r;   r   rB  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?rz  c                    s8   | \}}|  j k r|  jk sJ |d |d  S r*  )lbr:   ub)r   r  br  r   r   r{   3  s    ztest_powell_limits.<locals>.funr   rD   rx   r   r   T)r  r  keep_feasiblec                 S   s   | dkr| dks
J t | S r)  r   r   r   r   r   rd   =  s   
z test_powell_limits.<locals>.funcrK   r  )r{   rD   rx   r   )r
   r   r   )r{   rd   r   r  r   test_powell_limits/  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)rL   r   r   )r#   r#   r#   )r   r;   r
   rosen_hess_prodr]   r  r   )rZ   r   rg   hpdothpr   r   r   	test_hessF  s
   zTestRosen.test_hessN)rn   ro   rp   r  r   r   r   r   r  D      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   )rg   r   r  r  r  r   r   r   r  O  s   r  c                 C   sn   | \}}t d|d  d| |  d|  d|d   d d|d  d| |  d|d   d|  d gS )Nr   rL   *   r#         r   r  rg   r   r  r   r   r   rA   Z  s   2.rA   c                 C   s^   | \}}t d|d  d|  d d| d|  gd| d|  d| d|d   d ggS )N   r#   r   r  r  r  r  r   r   r   rB   `  s   *&rB   gHzGѿgrL   r#   rM   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   r8   r   r  r   r  r#   r  r   r   r   r   rd   m     0z0test_minimize_multiple_constraints.<locals>.funcc                 S      t | d gS r   r  r   r   r   r   func1p     z1test_minimize_multiple_constraints.<locals>.func1c                 S   r  r*  r  r   r   r   r   r2  s  r  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   z  r  z4test_minimize_multiple_constraints.<locals>.<lambda>r2  r	  r  )}   r   r   r;  r   )r
   r   r   r   )rd   r  r2  r  rc   r   r   r   r   "test_minimize_multiple_constraintsk  s   r  c                   @   r  )TestOptimizeResultAttributesc                 C   s8   ddg| _ tj| _tj| _tj| _tj| _	ddg| _
d S )Nr   )rM   rv  )rD   r
   r   rd   r  ry   r  rk   r  rm   r   rY   r   r   r   r[     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)rx   ry   rk   rm   )r   r   r:  r  r
   r   rd   rD   ry   rk   rm   r
  dir
isinstancer  str)rZ   
attributesskiprx   rA  r   	attributer   r   r   test_attributes_present  s&   
z4TestOptimizeResultAttributes.test_attributes_presentN)rn   ro   rp   r[   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   rc   r  rB  r  r   r  r  r(  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  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#   rL   r   r   r   r   ,   r   r#   r  r   r:  rK   r0  r         ?g_}gi?)r   slicerrangesr   r;   rT   rY   r   r   r   r[     s   zTestBrute.setup_methodc                 G   s   t |g|R  S r/   )r  )rZ   r  r   r   r   r   r    rZ  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rw   r   finishr   r   r   r   )	r
   bruter  r  r   r   r   rT   r   )rZ   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#   )r4  shaper   r   r   r   rc     s   zTestBrute.test_1D.<locals>.fr/  rL   )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#   )rw   r   r  workersr   r   )r
   r  r  r  r   r   )rZ   r  	resbrute1r   r   r   test_workers  s   zTestBrute.test_workersc                    sb   t jd  fdd}tjtdd tj|| j| j	dd W d    d S 1 s*w   Y  d S )Nr(   c                    r  r  r  r  r	  r   r   rd     r  z,TestBrute.test_runtime_warning.<locals>.funcz)Either final optimization did not succeedr  T)rw   rt   )
r   r'   r  r  r  r  r
   r  r  r   )rZ   rd   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   rw   r   r   r   rc     r  z+TestBrute.test_coerce_args_param.<locals>.fr0  r   r  r#   rz  r   )r
   r  r  r   )rZ   rc   r  r   r   r   test_coerce_args_param  s   z TestBrute.test_coerce_args_paramN)
rn   ro   rp   r[   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 $}g }||| ||| |D ]}| }q>W d    d S 1 sPw   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                         t jdg dS NrM   r   r  r   )
min_methodr  r   r   
minimizer1	     z*test_cobyla_threadsafe.<locals>.minimizer1c                      r  r  r  r   )r  r  r   r   
minimizer2	  r  z*test_cobyla_threadsafe.<locals>.minimizer2)concurrent.futuresr  futuresThreadPoolExecutorr_   submitr   )
concurrentr  r  pooltasksrA  r   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   rX  r_  )r  rY   r   r   r   r[   )	  rY  z TestIterationLimits.setup_methodc                 C   s\   |  j d7  _ t|d d |d d  t|d |d }}t|d | |d  S )Nr   r   r#   rz  rK   )r  r   ra  arctan2r0   )rZ   r  rE   rA  r   r   r   	slow_func,	  s   4zTestIterationLimits.slow_funcc                 C      |  dd d S )Nr     check_limitsrY   r   r   r   test_neldermead_limit1	  r  z)TestIterationLimits.test_neldermead_limitc                 C   r	  )Nr  rN   r  rY   r   r   r   test_powell_limit4	  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 )Nr-   r   r#   )r   i    r   r  r   r|   r   rU   r   r   r  )rU   r  )r  r
   r   r  r   rB  )rZ   rx   default_itersstart_vmfevr   mitr   r   r   r  7	  sb   

 

(z TestIterationLimits.check_limitsN)rn   ro   rp   r[   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 ]}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{   g	  r  z2test_result_x_shape_when_len_x_is_one.<locals>.func                 S   s   d|  S Nr  r   r   r   r   r   ry   j	  r  z2test_result_x_shape_when_len_x_is_one.<locals>.jacc                 S   r4  r  r  r   r   r   r   rk   m	  r  z3test_result_x_shape_when_len_x_is_one.<locals>.hess)r  r   rv   r   r  re  r  r	  r-   r   r   )rn  rr  ro  rs  rp  r   rq  )r
   r   r   r;   r   r  )r{   ry   rk   rk  rx   r   r   r   r   %test_result_x_shape_when_len_x_is_onef	  s   r  c                   @   r  )FunctionWithGradientc                 C   rX  r_  )number_of_callsrY   r   r   r   r  	  rY  zFunctionWithGradient.__init__c                 C   s$   |  j d7  _ t|d d| fS r"   )r  r   r1   r  r   r   r   r  	  s   zFunctionWithGradient.__call__Nr  r   r   r   r   r  	  s    r  c                   C   s   t  S r/   )r  r   r   r   r   function_with_gradient	  s   r  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 )
NrI   r        @r   r#   zHfunction is not recomputed if gradient is requested after function valueg      4@(different input triggers new computationr+  )r   r   r;   r   r  
derivativer  memoized_functionrD   r   r   r   )test_memoize_jac_function_before_gradient	  s   r  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 )
NrI   r  r#   r   r  zHfunction is not recomputed if function value is requested after gradientr   r  r+  )r   r   r;   r   r  r  r  r   r   r   )test_memoize_jac_gradient_before_function	  s   r   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.
    rI   rK   r   Nr   r-   r#   r8   rL   )	r   r  r
   r   r   r;   r   r  r{   )r  r  ry   rk   rD   scalar_functionr   r   r   test_memoize_jac_with_bfgs	  s   r"  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   r   	      ztest_gh12696.<locals>.<lambda>Fr   )r   r
   rl  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*  )rL   r#   r#   r*  Tc                    s0   |r	| j dks	J |rt|      d S d S )Nr   )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   r   r(  r   r   rd   	     
z%setup_test_equal_bounds.<locals>.funcc                    r)  r/   )r
   r  r   r*  r   r   rh   	  r+  z%setup_test_equal_bounds.<locals>.gradc                    s    |  d S r/   r   r  r*  r   r   r  	  r  z)setup_test_equal_bounds.<locals>.callbackc                    s    | dd | dd d S )NFr&  r   r   r   r   r*  r   r   constraint1	     z,setup_test_equal_bounds.<locals>.constraint1c                    "    | dd t | }d|d< |S )NFr,  r   r   r   
zeros_liker   dcr*  r   r   	jacobian1	     
z*setup_test_equal_bounds.<locals>.jacobian1c                    s    | dd | dd d S )NFr,  r#   rL   rK   r   r   r*  r   r   constraint2	  r.  z,setup_test_equal_bounds.<locals>.constraint2c                    r/  )NFr,  r   r#   r0  r2  r*  r   r   	jacobian2	  r5  z*setup_test_equal_bounds.<locals>.jacobian2)r  r	  re  FrK  c                    s    | | fS r/   r   r   r  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   rJ  )	rk  kwdsbound_typesr  	callbacksr  r  rD   r'  )TT)r   r'   r*   rc  r;   r   rB  r   )rD   r  r  r-  r4  r6  r7  c1ac1bc2ac2brk  r;  r<  r  r=  datar   )r(  rd   rh   r'  r  r   setup_test_equal_bounds	  sP   rC  z0Failures due to floating point issues, not logicrk  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
    aarch64re  ry   FNzTolerance violation on aarchr  r  rD   r'  r	  z)Only SLSQP supports nonlinear constraints)rD   rx   r   r  r  )rx   ry   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   r;   rY  r
   r   )r   new_xr   r   r   r{   [
  s   
ztest_equal_bounds.<locals>.funr#   r  g>r   )platformmachiner  r  eb_dataupdater
   r   r   r  r   r   r{   r   r   rY  ry   r  r  r   )rx   r;  rD  r  r  r  r  rD   r'  test_constraintsreference_constraints	fd_neededr   r   expectedr{   fd_resr   r   r   test_equal_bounds)
  sF   





rP  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   rc   q
  r  z test_all_bounds_equal.<locals>.f)r   r   )r#   r#   )rI   r  r1  rI   r  z/All independent variables were fixed by bounds.)r#   rv  r#   r	  c                 S   rU  r/   r+  r   r   r   r   con
  rY  z"test_all_bounds_equal.<locals>.conrM   )r   rx   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   rB  r  )	rx   rc   r   rD   r   rw   rT  nlcr  r   r   r   test_all_bounds_equalm
  sD   


rW  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   rL   r   r#   r   r   r   r   r   rc   
  s   (ztest_eb_constraints.<locals>.fc                 S   s$   | d | d  | d  | d  d S )Nr   r   r#   rL   (   r   r   r   r   r   cfun
  s   $z!test_eb_constraints.<locals>.cfunr  r  )r   rz  r   )r   r   r   )r   r#   rL   r   r	  )rD   rx   r   r  r   r{   r  )rc   rY  r  r   r   r   r   test_eb_constraints
  s   
rZ  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   rw  rootroot_scalarlinprogquadratic_assignmentekkir  )r   maximizemaximize_scalar)
r   r   r   r   r   r   itemsr   r?   r@   )solver_methodssolverrk  rx   unknown_solver_methodr   r   r   test_show_options
  s$   rf  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  rv  r:  r   r   r  )r
   r   r   r   r   r;   r  r   r   r   test_bounds_with_list
  s   
rg  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   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   eyer  r   r   r   r   r   
  r  z2test_x_overwritten_user_function.<locals>.<lambda>)r  rr  ro  rs  rp  rn  )rr  ro  rs  rp  rn  r   r&   rq  g-C6*?r   )	r   onesr   r
   r   r   r   r>   r  )
rh  ri  
fquad_hessmeth_jac	meth_hessrD   methry   rk   r   r   r   r    test_x_overwritten_user_function
  s    rp  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   r  r*  r   r   r   r   r   rd   
  r  zDTestGlobalOptimization.test_optimize_result_attributes.<locals>.funcr   )rD   )r0  r   r   r   r  r{   r|   r   )	r
   basinhoppingdifferential_evolutionshgodual_annealingdirectr  r  r
  )rZ   rd   r  r   r   r   r   test_optimize_result_attributes
  s    z6TestGlobalOptimization.test_optimize_result_attributesN)rn   ro   rp   rw  r   r   r   r   rq  
  r  rq  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_fprimerC   r  r   rA   rB   )r  rB  r   r   r   test_approx_fprime  s   ry  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   rc     s   ztest_gh12594.<locals>.fr7  r   r:  )r   r   r   r  )r   r
   r   r   r;   r   r{   r   )rc   r   r   r   r   r   r   test_gh12594  s    rz  )erq   ri  rG  numpyr   numpy.testingr   r   r   r   r   r   r   r  r	   r?   scipyr
   scipy.optimize._minimizer   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   rF   rG   rr   r  r  r   r%  r(  r.  r5  rE  rK  rM  rQ  rR  rS  rT  r  rF  rH  rI  rW  r  r  r  r  r  r  r  r  rA   rB   rC   r  r  r  r  r  r  r  r  r  r  r  r  r  fixturer  r  r   r"  r$  rC  rI  xfail_on_32bitrP  rW  rZ  rf  rg  rp  rq  ry  rz  r   r   r   r   <module>   s    $50   	K)     A

=  ,?%|"J#A	
	T
>
+'
