
    ^Mh&m                        d dl Zd dlZd dlmZ d dlmZ d dlmZm	Z	m
Z
mZ d dlmZmZmZmZmZmZmZ  G d d          Z G d d	          Z G d
 d          Z G d d          Z G d d          Z G d de          Z G d de          Z G d de          Z G d d          Z G d d          Z G d d          Zd Zd Z d Z!d Z" G d  d!          Z#dS )"    N)
block_diag)
csc_matrix)assert_array_almost_equalassert_array_lessassert_suppress_warnings)NonlinearConstraintLinearConstraintBoundsminimizeBFGSSR1rosenc                   B    e Zd ZdZd	dZd Zd Zd Zed             Z	dS )
MaratosProblem 15.4 from Nocedal and Wright

    The following optimization problem:
        minimize 2*(x[0]**2 + x[1]**2 - 1) - x[0]
        Subject to: x[0]**2 + x[1]**2 - 1 = 0
    <   Nc                     |dz  t           j        z  }t          j        |          t          j        |          g| _        t          j        ddg          | _        || _        || _        d | _	        d S N         ?        
nppicossinx0arrayx_opt
constr_jacconstr_hessboundsselfdegreesr!   r"   radss        n/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/optimize/tests/test_minimize_constrained.py__init__zMaratos.__init__   ]    s{25 6$<<.XsCj))
$&    c                 N    d|d         dz  |d         dz  z   dz
  z  |d         z
  S N   r       r%   xs     r(   funzMaratos.fun!   s0    !A$'AaD!G#a'(1Q4//r+   c                 X    t          j        d|d         z  dz
  d|d         z  g          S N   r   r/   r   r   r1   s     r(   gradzMaratos.grad$   s+    x1Q41QqT6*+++r+   c                 0    dt          j        d          z  S Nr6   r.   r   eyer1   s     r(   hesszMaratos.hess'       {r+   c                 v    d }| j         d }n| j         }| j        d }n| j        }t          |dd||          S )Nc                 0    | d         dz  | d         dz  z   S Nr   r.   r/   r0   r2   s    r(   r3   zMaratos.constr.<locals>.fun,       Q47QqT1W$$r+   c                 0    d| d         z  d| d         z  ggS r-   r0   rB   s    r(   jaczMaratos.constr.<locals>.jac0        1Q41Q4())r+   c                 B    d|d         z  t          j        d          z  S Nr.   r   r;   r2   vs     r(   r=   zMaratos.constr.<locals>.hess6       1vbfQii''r+   r/   r!   r"   r	   r%   r3   rE   r=   s       r(   constrzMaratos.constr*   u    	% 	% 	% ?"* * * * /C#( ( ( ( #D"31c4888r+   r   NN
__name__
__module____qualname____doc__r)   r3   r8   r=   propertyrN   r0   r+   r(   r   r      sz            0 0 0, , ,   9 9 X9 9 9r+   r   c                   H    e Zd ZdZd
dZd Zd Zd Zd Ze	d	             Z
dS )MaratosTestArgsr   r   Nc                     |dz  t           j        z  }t          j        |          t          j        |          g| _        t          j        ddg          | _        || _        || _        || _	        || _
        d | _        d S r   )r   r   r   r   r   r   r    r!   r"   abr#   )r%   rZ   r[   r&   r!   r"   r'   s          r(   r)   zMaratosTestArgs.__init__F   sk    s{25 6$<<.XsCj))
$&r+   c                 N    | j         |k    s| j        |k    rt                      d S N)rZ   r[   
ValueError)r%   rZ   r[   s      r(   
_test_argszMaratosTestArgs._test_argsP   s(    6Q;;$&A++,, &+r+   c                 z    |                      ||           d|d         dz  |d         dz  z   dz
  z  |d         z
  S r-   )r_   r%   r2   rZ   r[   s       r(   r3   zMaratosTestArgs.funT   sD    1!A$'AaD!G#a'(1Q4//r+   c                     |                      ||           t          j        d|d         z  dz
  d|d         z  g          S r5   )r_   r   r   ra   s       r(   r8   zMaratosTestArgs.gradX   s?    1x1Q41QqT6*+++r+   c                 \    |                      ||           dt          j        d          z  S r:   )r_   r   r<   ra   s       r(   r=   zMaratosTestArgs.hess\   s(    1{r+   c                 v    d }| j         d }n| j         }| j        d }n| j        }t          |dd||          S )Nc                 0    | d         dz  | d         dz  z   S rA   r0   rB   s    r(   r3   z#MaratosTestArgs.constr.<locals>.funb   rC   r+   c                 0    d| d         z  d| d         z  ggS r5   r0   rB   s    r(   rE   z#MaratosTestArgs.constr.<locals>.jacf   rF   r+   c                 B    d|d         z  t          j        d          z  S rH   r;   rI   s     r(   r=   z$MaratosTestArgs.constr.<locals>.hessl   rK   r+   r/   rL   rM   s       r(   rN   zMaratosTestArgs.constr`   rO   r+   rP   )rR   rS   rT   rU   r)   r_   r3   r8   r=   rV   rN   r0   r+   r(   rX   rX   >   s              0 0 0, , ,   9 9 X9 9 9r+   rX   c                   R    e Zd ZdZd	dZd Zed             Zd Zed             Z	dS )
MaratosGradInFuncr   r   Nc                     |dz  t           j        z  }t          j        |          t          j        |          g| _        t          j        ddg          | _        || _        || _        d | _	        d S r   r   r$   s        r(   r)   zMaratosGradInFunc.__init__|   r*   r+   c                     d|d         dz  |d         dz  z   dz
  z  |d         z
  t          j        d|d         z  dz
  d|d         z  g          fS )Nr.   r   r/   r6   r7   r1   s     r(   r3   zMaratosGradInFunc.fun   s]    1Q47QqT1W$q()AaD0!AaD&(AadF+,,. 	.r+   c                     dS )NTr0   r%   s    r(   r8   zMaratosGradInFunc.grad   s    tr+   c                 0    dt          j        d          z  S r:   r;   r1   s     r(   r=   zMaratosGradInFunc.hess   r>   r+   c                 v    d }| j         d }n| j         }| j        d }n| j        }t          |dd||          S )Nc                 0    | d         dz  | d         dz  z   S rA   r0   rB   s    r(   r3   z%MaratosGradInFunc.constr.<locals>.fun   rC   r+   c                 0    d| d         z  d| d         z  ggS r5   r0   rB   s    r(   rE   z%MaratosGradInFunc.constr.<locals>.jac   rF   r+   c                 B    d|d         z  t          j        d          z  S rH   r;   rI   s     r(   r=   z&MaratosGradInFunc.constr.<locals>.hess   rK   r+   r/   rL   rM   s       r(   rN   zMaratosGradInFunc.constr   rO   r+   rP   )
rR   rS   rT   rU   r)   r3   rV   r8   r=   rN   r0   r+   r(   ri   ri   t   s            . . .   X   9 9 X9 9 9r+   ri   c                   B    e Zd ZdZddZd Zd Zd Zed             Z	dS )	HyperbolicIneqa  Problem 15.1 from Nocedal and Wright

    The following optimization problem:
        minimize 1/2*(x[0] - 2)**2 + 1/2*(x[1] - 1/2)**2
        Subject to: 1/(x[0] + 1) - x[1] >= 1/4
                                   x[0] >= 0
                                   x[1] >= 0
    Nc                     ddg| _         ddg| _        || _        || _        t	          dt
          j                  | _        d S )Nr   g~T>?g~1[?)r   r    r!   r"   r   r   infr#   )r%   r!   r"   s      r(   r)   zHyperbolicIneq.__init__   s?    a&)
$&Q''r+   c                 H    d|d         dz
  dz  z  d|d         dz
  dz  z  z   S )N      ?r   r.   r/   r0   r1   s     r(   r3   zHyperbolicIneq.fun   s/    AaD1Hq= 3!s
Q#666r+   c                 .    |d         dz
  |d         dz
  gS )Nr   r.   r/   rx   r0   r1   s     r(   r8   zHyperbolicIneq.grad   s    !q!A$*%%r+   c                 *    t          j        d          S Nr.   r;   r1   s     r(   r=   zHyperbolicIneq.hess   s    vayyr+   c                     d }| j         d }n| j         }| j        d }n| j        }t          |dt          j        ||          S )Nc                 0    d| d         dz   z  | d         z
  S )Nr/   r   r0   rB   s    r(   r3   z"HyperbolicIneq.constr.<locals>.fun   s    adQh<!A$&&r+   c                 *    d| d         dz   dz  z  dggS )Nr   r/   r.   r0   rB   s    r(   rE   z"HyperbolicIneq.constr.<locals>.jac   s!    QqTAXM)2.//r+   c                 l    d|d         z  t          j        d| d         dz   dz  z  dgddgg          z  S )Nr.   r   r/      r7   rI   s     r(   r=   z#HyperbolicIneq.constr.<locals>.hess   sH    1vbhAaD1Hq=!(<)*A(0 1 1 1 1r+   g      ?r!   r"   r	   r   rv   rM   s       r(   rN   zHyperbolicIneq.constr   sw    	' 	' 	' ?"0 0 0 0 /C#1 1 1 1 #D"3bfc4@@@r+   )NNrQ   r0   r+   r(   rt   rt      s         ( ( ( (7 7 7& & &   A A XA A Ar+   rt   c                   B    e Zd ZdZd
dZd Zd Zd Zed             Z	d	S )
RosenbrockzRosenbrock function.

    The following optimization problem:
        minimize sum(100.0*(x[1:] - x[:-1]**2.0)**2.0 + (1 - x[:-1])**2.0)
    r.   r   c                     t           j                            |          }|                    dd|          | _        t          j        |          | _        d | _        d S )Nr   r/   )r   randomRandomStateuniformr   onesr    r#   )r%   nrandom_staterngs       r(   r)   zRosenbrock.__init__   sH    i##L11++b!Q''WQZZ
r+   c                     t          j        |          }t          j        d|dd          |d d         dz  z
  dz  z  d|d d         z
  dz  z   d          }|S )Ng      Y@r/   r          @r   axis)r   asarraysum)r%   r2   rs      r(   r3   zRosenbrock.fun   sh    JqMMF5AabbEAcrcFCK/#55QssVc8II  r+   c                 z   t          j        |          }|dd         }|d d         }|dd          }t          j        |          }d||dz  z
  z  d||dz  z
  z  |z  z
  dd|z
  z  z
  |dd<   d|d         z  |d         |d         dz  z
  z  dd|d         z
  z  z
  |d<   d|d         |d         dz  z
  z  |d<   |S )	Nr/   r   r.        pr   )r   r   
zeros_like)r%   r2   xmxm_m1xm_p1ders         r(   r8   zRosenbrock.grad   s    JqMMqtW#2#!""mABM*EBEM*R/023q2v,?AbD	!!qtQw/!q1Q4x.@A22)*B
r+   c                    t          j        |          }t          j        d|d d         z  d          t          j        d|d d         z  d          z
  }t          j        t	          |          |j                  }d|d         dz  z  d|d         z  z
  dz   |d<   d	|d<   d
d|dd         dz  z  z   d|dd          z  z
  |dd<   |t          j        |          z   }|S )Nr   r   r/   r   )dtypei  r   r.   r      )r   
atleast_1ddiagzeroslenr   )r%   r2   Hdiagonals       r(   r=   zRosenbrock.hess   s    M!GD1SbS6M1%%afb(A(AA8CFF!'222QqT1WnsQqTz1A5ta"gqj003122;>2!!!r+   c                     dS )Nr0   r0   rm   s    r(   rN   zRosenbrock.constr   s    rr+   N)r.   r   rQ   r0   r+   r(   r   r      sz              
 
 
     X  r+   r   c                   0    e Zd ZdZddZed             ZdS )IneqRosenbrockzRosenbrock subject to inequality constraints.

    The following optimization problem:
        minimize sum(100.0*(x[1] - x[0]**2)**2.0 + (1 - x[0])**2)
        subject to: x[0] + 2 x[1] <= 1

    Taken from matlab ``fmincon`` documentation.
    r   c                 p    t                               | d|           ddg| _        ddg| _        d | _        d S )Nr.   r         gn?g$?r   r)   r   r    r#   r%   r   s     r(   r)   zIneqRosenbrock.__init__  s<    D!\222t*f%
r+   c                 H    ddgg}d}t          |t          j         |          S Nr/   r.   r
   r   rv   )r%   Ar[   s      r(   rN   zIneqRosenbrock.constr  s(    VHBF7A...r+   Nr   rR   rS   rT   rU   r)   rV   rN   r0   r+   r(   r   r      sM             / / X/ / /r+   r   c                       e Zd ZdZddZdS )BoundedRosenbrocka  Rosenbrock subject to inequality constraints.

    The following optimization problem:
        minimize sum(100.0*(x[1] - x[0]**2)**2.0 + (1 - x[0])**2)
        subject to:  -2 <= x[0] <= 0
                      0 <= x[1] <= 2

    Taken from matlab ``fmincon`` documentation.
    r   c                     t                               | d|           ddg| _        d | _        t	          ddgddg          | _        d S )Nr.   gɿg?r   r   )r   r)   r   r    r   r#   r   s     r(   r)   zBoundedRosenbrock.__init__  sI    D!\222+
b!Wq!f--r+   Nr   )rR   rS   rT   rU   r)   r0   r+   r(   r   r     s2         . . . . . .r+   r   c                   0    e Zd ZdZddZed             ZdS )EqIneqRosenbrocka*  Rosenbrock subject to equality and inequality constraints.

    The following optimization problem:
        minimize sum(100.0*(x[1] - x[0]**2)**2.0 + (1 - x[0])**2)
        subject to: x[0] + 2 x[1] <= 1
                    2 x[0] + x[1] = 1

    Taken from matlab ``fimincon`` documentation.
    r   c                 p    t                               | d|           ddg| _        ddg| _        d | _        d S )Nr.   r   r   gWs`?g|\*?r   r   s     r(   r)   zEqIneqRosenbrock.__init__0  s<    D!\222t*w'
r+   c                 x    ddgg}d}ddgg}d}t          |t          j         |          t          |||          fS r   r   )r%   A_ineqb_ineqA_eqb_eqs        r(   rN   zEqIneqRosenbrock.constr6  sN    a&Ax "&&99 tT224 	4r+   Nr   r   r0   r+   r(   r   r   &  sM             4 4 X4 4 4r+   r   c                   R    e Zd ZdZ	 	 ddZd Zd Zd Zd	 Zd
 Z	e
d             ZdS )Eleca  Distribution of electrons on a sphere.

    Problem no 2 from COPS collection [2]_. Find
    the equilibrium state distribution (of minimal
    potential) of the electrons positioned on a
    conducting sphere.

    References
    ----------
    .. [1] E. D. Dolan, J. J. Mor'{e}, and T. S. Munson,
           "Benchmarking optimization software with COPS 3.0.",
            Argonne National Lab., Argonne, IL (US), 2004.
    r   r   Nc                 `   || _         t          j                            |          | _        | j                            ddt          j        z  | j                   }| j                            t          j         t          j        | j                   }t          j        |          t          j        |          z  }t          j        |          t          j        |          z  }t          j        |          }	t          j	        |||	f          | _
        d | _        || _        || _        d | _        d S )Nr   r.   )n_electronsr   r   r   r   r   r   r   r   hstackr   r    r!   r"   r#   )
r%   r   r   r!   r"   phithetar2   yzs
             r(   r)   zElec.__init__N  s    &9((66hq!be)T-=>>  "%0@AAF5MMBF3KK'F5MMBF3KK'F5MM)Q1I&&
$&r+   c                 |    |d | j                  }|| j         d| j         z           }|d| j         z  d          }|||fS r{   r   )r%   r2   x_coordy_coordz_coords        r(   _get_cordinateszElec._get_cordinates^  sT    %T%%&D$Q)9%99:A(())*((r+   c                     |                      |          \  }}}|d d d f         |z
  }|d d d f         |z
  }|d d d f         |z
  }|||fS r]   r   )r%   r2   r   r   r   dxdydzs           r(   _compute_coordinate_deltaszElec._compute_coordinate_deltasd  sm    $($8$8$;$;!'QQQW'QQQW'QQQW'2rzr+   c                    |                      |          \  }}}t          j        d          5  |dz  |dz  z   |dz  z   dz  }d d d            n# 1 swxY w Y   d|t          j        |          <   dt          j        |          z  S )Nignoredivider.   r   r   rx   )r   r   errstatediag_indices_fromr   )r%   r2   r   r   r   dm1s         r(   r3   zElec.funk  s    44Q77
B[))) 	2 	2q52q5=2q5(T1C	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2)*B %%&RVC[[     AAAc                    |                      |          \  }}}t          j        d          5  |dz  |dz  z   |dz  z   dz  }d d d            n# 1 swxY w Y   d|t          j        |          <   t          j        ||z  d           }t          j        ||z  d           }t          j        ||z  d           }t          j        |||f          S )Nr   r   r.         r   r/   r   )r   r   r   r   r   r   )	r%   r2   r   r   r   dm3grad_xgrad_ygrad_zs	            r(   r8   z	Elec.gradr  s   44Q77
B[))) 	2 	2q52q5=2q5(T1C	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2)*B %%&&c****&c****&c****y&&&1222r   c           	         |                      |          \  }}}|dz  |dz  z   |dz  z   dz  }t          j        d          5  |dz  }|dz  }d d d            n# 1 swxY w Y   t          j        | j                  }d|||f<   d|||f<   |d|dz  z  |z  z
  }	t          j        |	d	
           |	||f<   d|z  |z  |z  }
t          j        |
d	
           |
||f<   d|z  |z  |z  }t          j        |d	
           |||f<   |d|dz  z  |z  z
  }t          j        |d	
           |||f<   d|z  |z  |z  }t          j        |d	
           |||f<   |d|dz  z  |z  z
  }t          j        |d	
           |||f<   t          j        t          j        |	|
|f          t          j        |
||f          t          j        |||f          f          }|S )Nr.   rx   r   r   r   r   r/   r   )r   r   r   aranger   r   vstackr   )r%   r2   r   r   r   dr   dm5iHxxHxyHxzHyyHyzHzzr   s                   r(   r=   z	Elec.hess  sj   44Q77
BURU]RU"s*[))) 	 	r'Cr'C	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 Id&''AqD	AqD	AAIO#VCa((((AqD	2glS VCa((((AqD	2glS VCa((((AqD	AAIO#VCa((((AqD	2glS VCa((((AqD	AAIO#VCa((((AqD	IIsCo&&IsCo&&IsCo&&
   s   AA!Ac                       fd} j          fd}n j         } j        d }n j        }t          |t          j         d||          S )Nc                 ^                         |           \  }}}|dz  |dz  z   |dz  z   dz
  S )Nr.   r/   r   )r2   r   r   r   r%   s       r(   r3   zElec.constr.<locals>.fun  s>    (,(<(<Q(?(?%GWgA:
*WaZ7!;;r+   c                                         |           \  }}}dt          j        |          z  }dt          j        |          z  }dt          j        |          z  }t          t          j        |||f                    S r{   )r   r   r   r   r   )r2   r   r   r   JxJyJzr%   s          r(   rE   zElec.constr.<locals>.jac  sw    ,0,@,@,C,C)')))))))))!")RRL"9"9:::r+   c                 R    dt          j        |          z  }t          |||          S r{   )r   r   r   )r2   rJ   Ds      r(   r=   zElec.constr.<locals>.hess  s%    

N!!Q***r+   r   r   rM   s   `   r(   rN   zElec.constr  s    	< 	< 	< 	< 	< ?"; ; ; ; ; ; /C#+ + + + #D"3C>>>r+   )r   r   NN)rR   rS   rT   rU   r)   r   r   r3   r8   r=   rV   rN   r0   r+   r(   r   r   @  s          67.2    ) ) )  ! ! !3 3 3$ $ $L ? ? X? ? ?r+   r   c                   :   e Zd Z e             ed           e e                       ed e                       e             e             ed           e e                       ed e                       e             e	             e
             e             ed           edd           ed e                       edd e                      gZej        j        ej                            d	e          ej                            d
d          ej                            ddd e             ed           ed          f          d                                                 Zd Zd Zd Zd Zd Zd Zd Zd ZdS )TestTrustRegionConstr2-point)r"   )r!   r"   3-pointr.   r   )r   r"   )r   r!   r"   probr8   )	prob.gradr   Fr=   	prob.hessdamp_update)exception_strategyskip_updatec           
      `   |dk    r|j         n|}|dk    r|j        n|}|dv r|dv rt          j        d           |j         du r|dv rt          j        d           t	          |t
                    o|d	k    ot	          |t                    }|rt          j        d
           t                      5 }|	                    t          d           t          |j        |j        d|||j        |j                  }d d d            n# 1 swxY w Y   |j        <t#          |j        |j        d           |j        dk    rt)          |j        d           |j        dk    r5t)          |j        d           |j        dk    rt)          |j        d           d|j         d}|j        dvs
J |            d S )Nr   r   >   Fcsr   r   >   r  r   r   z+Numerical Hessian needs analytical gradientT>   Fr   z6prob.grad incompatible with grad in {'3-point', False}r   z3Seems sensitive to initial conditions w/ Acceleratedelta_grad == 0.0trust-constrmethodrE   r=   r#   constraints   decimalr/   :0yE>r.   tr_interior_pointzInvalid termination condition: .>   r   r   )r8   r=   pytestskip
isinstancer   r   xfailr   filterUserWarningr   r3   r   r#   rN   r    r   r2   statusr   
optimality	tr_radiusr  barrier_parameter)r%   r   r8   r=   	sensitivesupresultmessages           r(   test_list_of_problemsz+TestTrustRegionConstr.test_list_of_problems  s1    !K//tyyT K//tyyT777444KEFFF9);!;!;KPQQQ&788 0TY=N 0#D$// 	 	PLNOOO   	7CJJ{$7888dh%3"&T%)[*.+	7 7 7F	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 :!%fh
./1 1 1 1 }!!!&"3T:::=Af.555} 333!&":DAAA EFMDDD}F***G*****s   0ADD	Dc                 h    d }dg}t          |dg|d          }t          |j        dd           d S )	Nc                     | dz
  dz  S r   r0   rB   s    r(   r3   z<TestTrustRegionConstr.test_default_jac_and_hess.<locals>.fun      Ea<r+   r   r.   r   r  )r   r#   r  r/   r	  r
  r   r   r2   r%   r3   r#   ress       r(   test_default_jac_and_hessz/TestTrustRegionConstr.test_default_jac_and_hess  sM    	  	  	 svf^LLL!#%A666666r+   c                 j    d }dg}t          |dg|dd          }t          |j        dd	           d S )
Nc                     | dz
  dz  S r   r0   rB   s    r(   r3   z4TestTrustRegionConstr.test_default_hess.<locals>.fun	  r   r+   r!  r   r  r   )r   r#   r  rE   r/   r	  r
  r"  r#  s       r(   test_default_hessz'TestTrustRegionConstr.test_default_hess  sV    	  	  	 svf^$& & &!#%A666666r+   c                    t                      }t          |j        |j        d|j        |j                  }t          |j        |j        dd          }t          |j        |j        dd          }t          |j        |j        d           t          |j        |j        d           t          |j        |j        d           d S )	Nr  )r  rE   r=   zL-BFGS-Br   )r  rE   r   r	  r
  )	r   r   r3   r   r8   r=   r   r2   r    )r%   r   r  result1result2s        r(   test_no_constraintsz)TestTrustRegionConstr.test_no_constraints  s    ||$(DG!/"idi9 9 9 48TW",(* * * 48TW",(* * * 	"&(DJBBBB!')TZCCCC!')TZCCCCCCr+   c           	         t                      fd}t          j        j        dj        |j        j                  }j        t          |j	        j        d           |j
        dk    rt          |j        d           |j
        dk    r5t          |j        d           |j        dk    rt          |j        d           |j
        d	v rt!          d
          d S )Nc                 X                         |           }|                    |          S r]   )r=   dot)r2   pr   r   s      r(   hesspz/TestTrustRegionConstr.test_hessp.<locals>.hessp#  s!    		!A5588Or+   r  )r  rE   r1  r#   r  r.   r
  r/   r  r  r   r   Invalid termination condition.)r   r   r3   r   r8   r#   rN   r    r   r2   r  r   r  r  r  r  RuntimeError)r%   r1  r  r   s      @r(   
test_hesspz TestTrustRegionConstr.test_hessp   s   yy	 	 	 	 	 $(DG!/"iu!%&*k	3 3 3 :!%fh
AFFFF =Af/666=Af.555} 333!&":DAAA=F""?@@@ #"r+   c           
         t          dd          }t          |j        |j        dd|j        |j        |j        |j                  }|j        t          |j
        |j        d           |j        dk    rt          |j        d	           |j        dk    r5t          |j        d	           |j        d
k    rt          |j        d	           |j        dv rt#          d          d S )NrZ      )rZ   r7  r  r  r.   r
  r/   r  r  r2  r3  )rX   r   r3   r   r8   r=   r#   rN   r    r   r2   r  r   r  r  r  r  r4  )r%   r   r  s      r(   	test_argszTestTrustRegionConstr.test_args=  s    sC(($(DGZ!/"idi!%&*k	3 3 3 :!%fh
AFFFF =Af/666=Af.555} 333!&":DAAA=F""?@@@ #"r+   c           	          t                      }d}t          j        t          |          5  t	          |j        |j        ddd|j                   d d d            d S # 1 swxY w Y   d S )Nz9Whenever the gradient is estimated via finite-differencesmatchr  r   )r  rE   r=   r  )r   r  raisesr^   r   r3   r   rN   )r%   r   r  s      r(   test_raise_exceptionz*TestTrustRegionConstr.test_raise_exceptionU  s    yyM]:W555 	> 	>TXtw~9#> > > >	> 	> 	> 	> 	> 	> 	> 	> 	> 	> 	> 	> 	> 	> 	> 	> 	> 	>s   %AA"%A"c                    d }t          d dgd d |d          }t          |                    d                     t          |                    d	d
          dk               t          |                    dd
          dk               d S )Nc                 J    t          d|v            t          d|v            d S )Nnitniter)r   )r2   infos     r(   callbackz7TestTrustRegionConstr.test_issue_9044.<locals>.callbacka  s,    ETM"""GtO$$$$$r+   c                     | dz  S r{   r0   rB   s    r(   <lambda>z7TestTrustRegionConstr.test_issue_9044.<locals>.<lambda>e  s
    AqD r+   r   c                     d| z  S r{   r0   rB   s    r(   rE  z7TestTrustRegionConstr.test_issue_9044.<locals>.<lambda>e  s
    QqS r+   c                     dS r{   r0   rB   s    r(   rE  z7TestTrustRegionConstr.test_issue_9044.<locals>.<lambda>f  s     r+   r  )rE   r=   rC  r  successr@  r   r/   rA  )r   r   get)r%   rC  r  s      r(   test_issue_9044z%TestTrustRegionConstr.test_issue_9044\  s    
	% 	% 	% ..1#==*{X!/1 1 1 	

9%%&&&

5"%%*+++ 	

7B''1,-----r+   c                 h   t          j        ddg          }d }t          t          j        ddg          t          j        ddg          d          }t                      5 }|                    t
          d           t          d|||	          }d d d            n# 1 swxY w Y   |d
         sJ d S )Nr   rx   c                 8    | d         }| d         }|dz  |dz  z   S )Nr   r/   r.   r0   )r2   x1x2s      r(   objz3TestTrustRegionConstr.test_issue_15093.<locals>.objw  s'    1B1B7R1W$$r+   r   T)keep_feasibler  r  )r  r3   r   r#   rH  )r   r   r   r   r  r  r   )r%   r   rO  r#   r  r  s         r(   test_issue_15093z&TestTrustRegionConstr.test_issue_15093o  s    Xr3i  	% 	% 	%
 "b**BHb"X,>,>&*, , ,    	CJJ{$7888%	  F	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 i      s   "/BB!$B!N)rR   rS   rT   r   r   ri   rt   r   r   r   r   r   r   list_of_problemsr  markthread_unsafeparametrizer  r%  r(  r,  r5  r8  r=  rJ  rQ  r0   r+   r(   r   r     s}       		I666CCEE2229##%%HHH))++&((&9===&4466:::&)37466; ; ;"
&((((**))+++++	BBB>>>y),0 0 0#1( [[V%566[V%DEE[Vk9ccee&*dm&L&L&L&*dm&L&L&L&N O O$4 $4O O FE 76 $4N7 7 77 7 7D D D A A A:A A A0> > >. . .&! ! ! ! !r+   r   c                       e Zd ZdZd ZdS )TestEmptyConstrainta  
    Here we minimize x^2+y^2 subject to x^2-y^2>1.
    The actual minimum is at (0, 0) which fails the constraint.
    Therefore we will find a minimum on the boundary at (+/-1, 0).

    When minimizing on the boundary, optimize uses a set of
    constraints that removes the constraint that sets that
    boundary.  In our case, there's only one constraint, so
    the result is an empty constraint.

    This tests that the empty constraint works.
    c           	         d }d }d }d }d }d }t          |dt          j        ||          }ddg}t          t          j         t          j         gt          j        t          j        g          }t	          ||d	|||g|
          }	t          t          |	j                  t          j        ddg          d           d S )Nc                 0    | d         dz  | d         dz  z   S rA   r0   rB   s    r(   functionz;TestEmptyConstraint.test_empty_constraint.<locals>.function  rC   r+   c                 R    t          j        d| d         z  d| d         z  g          S )Nr   r   r/   r7   rB   s    r(   functionjacobianzCTestEmptyConstraint.test_empty_constraint.<locals>.functionjacobian  s'    8R!Wb1g.///r+   c                     d|z  S )Nr   r0   rI   s     r(   functionhvpz>TestEmptyConstraint.test_empty_constraint.<locals>.functionhvp  s    a4Kr+   c                 V    t          j        | d         dz  | d         dz  z
  g          S rA   r7   rB   s    r(   
constraintz=TestEmptyConstraint.test_empty_constraint.<locals>.constraint  s*    8QqT1WqtQw./000r+   c                 T    t          j        d| d         z  d| d         z  gg          S )Nr.   r   r   r/   r7   rB   s    r(   constraintjacobianzETestEmptyConstraint.test_empty_constraint.<locals>.constraintjacobian  s*    8a!fb1g./000r+   c                 H    t          j        ddgddgg          |d         z  S )Nr   r   g       r   r7   rI   s     r(   constraintlcohzATestEmptyConstraint.test_empty_constraint.<locals>.constraintlcoh  s(    8b"XCy122QqT99r+   r   r   r  )r  rE   r1  r  r#   r/   r   r6   r
  )	r	   r   rv   r   r   r   absr2   r   )
r%   rZ  r\  r^  r`  rb  rd  
startpointr#   r  s
             r(   test_empty_constraintz)TestEmptyConstraint.test_empty_constraint  s
   	% 	% 	%	0 	0 	0	 	 		1 	1 	1	1 	1 	1	: 	: 	: )R);^M M
 "X
"&26'*RVRV,<==

!l
 
 
 	"#fh--1a&1A1A1MMMMMMr+   N)rR   rS   rT   rU   rg  r0   r+   r(   rW  rW    s2         %N %N %N %N %Nr+   rW  c                  ^   d } t           j                                        5 }|                    t                     t          j        t          j        ddg                    }d d d            n# 1 swxY w Y   t          |dt           j                  }t          | ddgz  |           d S )Nc                 0    | d         dz  | d         dz  z   S rA   r0   rB   s    r(   optztest_bug_11886.<locals>.opt  s    tQwqtQwr+   r/   r   r.   )r  )
r   testingr   r  PendingDeprecationWarningmatrixr   r
   rv   r   )rj  r  r   lin_conss       r(   test_bug_11886ro    s       
	%	%	'	' '3

,---Ibgq!foo&&' ' ' ' ' ' ' ' ' ' ' ' ' ' '  2rv..HS!QC%x000000s   AA11A58A5c                     t          ddgddgd          fdfd} fd}d }fd	}t          j        d
          }t          |dt          j                  t          |dd|          g}t          | |d|          } |j                   |d         j        |d                             |j                  cxk     r|d         j	        k     sn J d S )Nr   r/   T)lbubrP  c                     t          j        | j        k              sJ t          j        | j        k              sJ d S r]   )r   allrq  rr  )r2   bndss    r(   assert_inboundsz%test_gh11649.<locals>.assert_inbounds  sA    va47l#####va47l#######r+   c                      |            t          j        | d                   d| d         dz  z  d| d         dz  z  z   d| d         z  | d         z  z   d| d         z  z   dz   z  S )Nr   r6   r.   r/   )r   expr2   rv  s    r(   rO  ztest_gh11649.<locals>.obj  sn    vad||QqtQwY1Q472QqtVAaD[@1QqT6IAMNNr+   c                 B     |            | d         dz  | d         z   S rA   r0   ry  s    r(   nceztest_gh11649.<locals>.nce  s)    tQw1~r+   c                 @    t          j        d| d         z  dg          S r-   r7   rB   s    r(   nce_jacztest_gh11649.<locals>.nce_jac  s    x1Q4$$$r+   c                 <     |            | d         | d         z  S )Nr   r/   r0   ry  s    r(   nciztest_gh11649.<locals>.nci  s%    tAaDyr+   )gGz?gGz)rE   r  )r3   r   r  r#   r  r   )
r   r   r   r	   rv   r   r2   rq  r3   rr  )	rO  r{  r}  r  r   nlcsr$  rv  ru  s	          @@r(   test_gh11649r    sS    b"X1a&===D$ $ $ $ $O O O O O    % % %     
-	 	 BS"&11Qw7779D sr.D2 2 2COCE7:QCE**7777T!WZ77777777r+   c            	      H   d} t          j        t          |           5  t          j        d          }t          j        d                              d          t          j        d          c}t          fd||          }t          t          |d	|g
           d d d            n# 1 swxY w Y   t          j
                                        5 }|                    t                     t          t          |d	|gddi           d d d            d S # 1 swxY w Y   d S )Nz:...more equality constraints than independent variables...r:  )r.      )r   r.   )r   c                     | z  S r]   r0   )r2   r   s    r(   rE  z3test_gh20665_too_many_constraints.<locals>.<lambda>  s    4!8 r+   )rq  rr  r  r  r  factorization_methodSVDFactorization)r  r  options)r  r<  r^   r   r   r   reshaper	   r   r   rk  r   r  r  )r  r   r   gr  r   s        @r(   !test_gh20665_too_many_constraintsr    s    KG	z	1	1	1 D DWT]]Yq\\))&11274==
d 3 3 3 3FFF>sCCCC	D D D D D D D D D D D D D D D 
	%	%	'	' G3

;>s02DE	G 	G 	G 	GG G G G G G G G G G G G G G G G G Gs$   A?B**B.1B.7DDDc                  :   d } d }t                      5 }|                    t          d           |                    t          d           t          |ddgdt	          | dd                    }d d d            n# 1 swxY w Y   |j        s|j        d	k    sJ d S )
Nc                 N    | \  }}ddg\  }}d|dz  |dz  z  z   |dz  |dz  z  z
  S )N      @      @r   r.   r0   )uu1u2rZ   r[   s        r(   lsfztest_issue_18882.<locals>.lsf  s@    BSz1RUQT\!BEAqDL00r+   c                 0    t          j        | dz            S r{   )r   r   )r  s    r(   ofztest_issue_18882.<locals>.of  s    vad||r+   r  zSingular Jacobian matrix.r   r  r   r  r  )r   r  r  r   r	   rH  constr_violation)r  r  r  r$  s       r(   test_issue_18882r    s    1 1 1
   
		 


; 3444

; ;<<<#J!+CA66	
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 >#"6"="="="="="=s   AA<<B B c                   r   e Zd Zej                            d eej         ej                   e	            j
        f eej         d          ddgf edej                  ddgf eddgddg          ddgfg          d             Zd	 Zd
 Zd Zej                            d          d             ZdS )TestBoundedNelderMeadzbounds, x_optgr  g      "@r   r        @c                 L   t                      }t                      5 }|                    t          d           t	          |j        ddgd|          }t          j        |j        |j	                  
                                sJ t          j        |j	        |j                  
                                sJ t          j        |                    |j	                  |j                  sJ t          j        |j	        |d          sJ 	 d d d            d S # 1 swxY w Y   d S )N0Initial guess is not within the specified boundsr  Nelder-Meadr  r#   gMbP?)atol)r   r   r  r  r   r3   r   
less_equalrq  r2   rt  rr  allclose)r%   r#   r    r   r  r  s         r(   test_rosen_brock_with_boundsz2TestBoundedNelderMead.test_rosen_brock_with_bounds  sW    ||   		<CJJ{ %; < < <dhc
%2%+- - -F =FH5599;;;;;=695599;;;;;;txx116:>>>>>;vxU;;;;;;;		< 		< 		< 		< 		< 		< 		< 		< 		< 		< 		< 		< 		< 		< 		< 		< 		< 		<s   C.DD Dc                 @   t                      }t          ddgddg          }t                      5 }|                    t          d           t          |j        ddgd|          }t          j        |j	        ddg          sJ 	 d d d            d S # 1 swxY w Y   d S )Nr  r  r  r     r  r  
r   r   r   r  r  r   r3   r   r  r2   r%   r   r#   r  r  s        r(   test_equal_all_boundsz+TestBoundedNelderMead.test_equal_all_bounds%  s    ||c
S#J//   	5CJJ{ %; < < <dha%2%+- - -F ;vx#s444444	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5   ABBBc                 @   t                      }t          ddgddg          }t                      5 }|                    t          d           t          |j        ddgd|          }t          j        |j	        dd	g          sJ 	 d d d            d S # 1 swxY w Y   d S )
Nr  r  g      4@r  r  r  r  r  g      0@r  r  s        r(   test_equal_one_boundsz+TestBoundedNelderMead.test_equal_one_bounds0  s    ||c
S$K00   	6CJJ{ %; < < <dha%2%+- - -F ;vx#t555555	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6r  c                     t                      }d}t          j        t          |          5  t	          t
          j         dgddg          }t          |j        ddgd|	           d d d            d S # 1 swxY w Y   d S )
Nz:An upper bound is less than the corresponding lower bound.r:  r   r  g      r  r   r  r  )	r   r  r<  r^   r   r   rv   r   r3   r%   r   r  r#   s       r(   test_invalid_boundsz)TestBoundedNelderMead.test_invalid_bounds;  s    ||N]:W555 	$ 	$bfWcNS$K88FTXQx)"$ $ $ $	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$   :A33A7:A7z5Failing on Azure Linux and macOS builds, see gh-13846)reasonc                     t                      }d}t          j        t          |          5  t	          t
          j         dgddg          }t          |j        ddgd|	           d d d            d S # 1 swxY w Y   d S )
Nr  r:  r   r  r  r  r  r  r  )	r   r  warnsr  r   r   rv   r   r3   r  s       r(   test_outside_bounds_warningz1TestBoundedNelderMead.test_outside_bounds_warningD  s     ||D\+W555 	$ 	$bfWcNS#J77FTXQx)"$ $ $ $	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$r  N)rR   rS   rT   r  rS  rU  r   r   rv   r   r    r  r  r  r  r  r  r0   r+   r(   r  r    s'       [_%vrvgrv66

8JK%vrvgt44tTlC%vc2622S#J?%vsCj3*==BxH ! !< <! !<	5 	5 	5	6 	6 	6$ $ $ [ - . .$ $. .$ $ $r+   r  )$numpyr   r  scipy.linalgr   scipy.sparser   numpy.testingr   r   r   r   scipy.optimizer	   r
   r   r   r   r   r   r   rX   ri   rt   r   r   r   r   r   r   rW  ro  r  r  r  r  r0   r+   r(   <module>r     s,        # # # # # # # # # # # #. . . . . . . . . . . .# # # # # # # # # # # # # # # # # #*9 *9 *9 *9 *9 *9 *9 *9Z39 39 39 39 39 39 39 39l,9 ,9 ,9 ,9 ,9 ,9 ,9 ,9^+A +A +A +A +A +A +A +A\+ + + + + + + +\/ / / / /Z / / /,. . . . .
 . . ."4 4 4 4 4z 4 4 44|? |? |? |? |? |? |? |?~H! H! H! H! H! H! H! H!T2N 2N 2N 2N 2N 2N 2N 2Nj	1 	1 	1 8  8  8FG G G? ? ?(=$ =$ =$ =$ =$ =$ =$ =$ =$ =$r+   