
    gelg                         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mZmZ d dl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e          Z G d de          Zd Z ej!        "                    dd          d              Z# G d! d"          Z$dS )#    N)
block_diag)
csc_matrix)TestCaseassert_array_almost_equalassert_array_lessassert_assert_allclosesuppress_warnings)NonlinearConstraintLinearConstraintBoundsminimizeBFGSSR1c                   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        Nlib/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$'AaD!G#a'(1Q4//r,   c                 X    t          j        d|d         z  dz
  d|d         z  g          S N   r   r0   r   r    r2   s     r)   gradzMaratos.grad#   s+    x1Q41QqT6*+++r,   c                 0    dt          j        d          z  S Nr7   r/   r   eyer2   s     r)   hesszMaratos.hess&       {r,   c                 v    d }| j         d }n| j         }| j        d }n| j        }t          |dd||          S )Nc                 0    | d         dz  | d         dz  z   S Nr   r/   r0   r1   r3   s    r)   r4   zMaratos.constr.<locals>.fun+       Q47QqT1W$$r,   c                 0    d| d         z  d| d         z  ggS r.   r1   rC   s    r)   jaczMaratos.constr.<locals>.jac/        1Q41Q4())r,   c                 B    d|d         z  t          j        d          z  S Nr/   r   r<   r3   vs     r)   r>   zMaratos.constr.<locals>.hess5       1vbfQii''r,   r0   r"   r#   r   r&   r4   rF   r>   s       r)   constrzMaratos.constr)   u    	% 	% 	% ?"* * * * /C#( ( ( ( #D"31c4888r,   r   NN
__name__
__module____qualname____doc__r*   r4   r9   r>   propertyrO   r1   r,   r)   r   r      sz            0 0 0, , ,   9 9 X9 9 9r,   r   c                   H    e Zd ZdZd
dZd Zd Zd Zd Ze	d	             Z
dS )MaratosTestArgsr   r   Nc                     |dz  t           j        z  }t          j        |          t          j        |          g| _        t          j        ddg          | _        || _        || _        || _	        || _
        d | _        d S r   )r   r   r   r   r   r    r!   r"   r#   abr$   )r&   r[   r\   r'   r"   r#   r(   s          r)   r*   zMaratosTestArgs.__init__E   sk    s{25 6$<<.XsCj))
$&r,   c                 N    | j         |k    s| j        |k    rt                      d S N)r[   r\   
ValueError)r&   r[   r\   s      r)   
_test_argszMaratosTestArgs._test_argsO   s(    6Q;;$&A++,, &+r,   c                 z    |                      ||           d|d         dz  |d         dz  z   dz
  z  |d         z
  S r.   )r`   r&   r3   r[   r\   s       r)   r4   zMaratosTestArgs.funS   sD    1!A$'AaD!G#a'(1Q4//r,   c                     |                      ||           t          j        d|d         z  dz
  d|d         z  g          S r6   )r`   r   r    rb   s       r)   r9   zMaratosTestArgs.gradW   s?    1x1Q41QqT6*+++r,   c                 \    |                      ||           dt          j        d          z  S r;   )r`   r   r=   rb   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 rB   r1   rC   s    r)   r4   z#MaratosTestArgs.constr.<locals>.funa   rD   r,   c                 0    d| d         z  d| d         z  ggS r6   r1   rC   s    r)   rF   z#MaratosTestArgs.constr.<locals>.jace   rG   r,   c                 B    d|d         z  t          j        d          z  S rI   r<   rJ   s     r)   r>   z$MaratosTestArgs.constr.<locals>.hessk   rL   r,   r0   rM   rN   s       r)   rO   zMaratosTestArgs.constr_   rP   r,   rQ   )rS   rT   rU   rV   r*   r`   r4   r9   r>   rW   rO   r1   r,   r)   rY   rY   =   s              0 0 0, , ,   9 9 X9 9 9r,   rY   c                   R    e Zd ZdZd	dZd Zed             Zd Zed             Z	dS )
MaratosGradInFuncr   r   Nc                     |dz  t           j        z  }t          j        |          t          j        |          g| _        t          j        ddg          | _        || _        || _        d | _	        d S r   r   r%   s        r)   r*   zMaratosGradInFunc.__init__{   r+   r,   c                     d|d         dz  |d         dz  z   dz
  z  |d         z
  t          j        d|d         z  dz
  d|d         z  g          fS )Nr/   r   r0   r7   r8   r2   s     r)   r4   zMaratosGradInFunc.fun   s]    1Q47QqT1W$q()AaD0!AaD&(AadF+,,. 	.r,   c                     dS )NTr1   r&   s    r)   r9   zMaratosGradInFunc.grad   s    tr,   c                 0    dt          j        d          z  S r;   r<   r2   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 rB   r1   rC   s    r)   r4   z%MaratosGradInFunc.constr.<locals>.fun   rD   r,   c                 0    d| d         z  d| d         z  ggS r6   r1   rC   s    r)   rF   z%MaratosGradInFunc.constr.<locals>.jac   rG   r,   c                 B    d|d         z  t          j        d          z  S rI   r<   rJ   s     r)   r>   z&MaratosGradInFunc.constr.<locals>.hess   rL   r,   r0   rM   rN   s       r)   rO   zMaratosGradInFunc.constr   rP   r,   rQ   )
rS   rT   rU   rV   r*   r4   rW   r9   r>   rO   r1   r,   r)   rj   rj   s   s            . . .   X   9 9 X9 9 9r,   rj   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/   r0   r1   r2   s     r)   r4   zHyperbolicIneq.fun   s/    AaD1Hq= 3!s
Q#666r,   c                 .    |d         dz
  |d         dz
  gS )Nr   r/   r0   ry   r1   r2   s     r)   r9   zHyperbolicIneq.grad   s    !q!A$*%%r,   c                 *    t          j        d          S Nr/   r<   r2   s     r)   r>   zHyperbolicIneq.hess   s    vayyr,   c                     d }| j         d }n| j         }| j        d }n| j        }t          |dt          j        ||          S )Nc                 0    d| d         dz   z  | d         z
  S )Nr0   r   r1   rC   s    r)   r4   z"HyperbolicIneq.constr.<locals>.fun   s    adQh<!A$&&r,   c                 *    d| d         dz   dz  z  dggS )Nr   r0   r/   r1   rC   s    r)   rF   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   r0      r8   rJ   s     r)   r>   z#HyperbolicIneq.constr.<locals>.hess   sH    1vbhAaD1Hq=!(<)*A(0 1 1 1 1r,   g      ?r"   r#   r   r   rw   rN   s       r)   rO   zHyperbolicIneq.constr   sw    	' 	' 	' ?"0 0 0 0 /C#1 1 1 1 #D"3bfc4@@@r,   )NNrR   r1   r,   r)   ru   ru      s         ( ( ( (7 7 7& & &   A A XA A Ar,   ru   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   r0   )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@r0   r          @r   axis)r   asarraysum)r&   r3   rs      r)   r4   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 )	Nr0   r   r/        pr   )r   r   
zeros_like)r&   r3   xmxm_m1xm_p1ders         r)   r9   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   r0   r   )dtypei  r   r/   r      )r   
atleast_1ddiagzeroslenr   )r&   r3   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 )Nr1   r1   rn   s    r)   rO   zRosenbrock.constr   s    rr,   N)r/   r   rR   r1   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 Nr0   r/   r   r   rw   )r&   Ar\   s      r)   rO   zIneqRosenbrock.constr  s(    VHBF7A...r,   Nr   rS   rT   rU   rV   r*   rW   rO   r1   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   )rS   rT   rU   rV   r*   r1   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__/  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)   rO   zEqIneqRosenbrock.constr5  sN    a&Ax "&&99 tT224 	4r,   Nr   r   r1   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$   )
r&   r   r   r"   r#   phithetar3   yzs
             r)   r*   zElec.__init__M  s    &9((66hq!be)T-=>>  "%0@AAF5MMBF3KK'F5MMBF3KK'F5MM)Q1I&&
$&r,   c                 |    |d | j                  }|| j         d| j         z           }|d| j         z  d          }|||fS r|   r   )r&   r3   x_coordy_coordz_coords        r)   _get_cordinateszElec._get_cordinates]  sT    %T%%&D$Q)9%99:A(())*((r,   c                     |                      |          \  }}}|d d d f         |z
  }|d d d f         |z
  }|d d d f         |z
  }|||fS r^   r   )r&   r3   r   r   r   dxdydzs           r)   _compute_coordinate_deltaszElec._compute_coordinate_deltasc  sm    $($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   ry   )r   r   errstatediag_indices_fromr   )r&   r3   r   r   r   dm1s         r)   r4   zElec.funj  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   r0   r   )r   r   r   r   r   r   )	r&   r3   r   r   r   dm3grad_xgrad_ygrad_zs	            r)   r9   z	Elec.gradq  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/   ry   r   r   r   r   r0   r   )r   r   r   aranger   r   vstackr   )r&   r3   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/   r0   r   )r3   r   r   r   r&   s       r)   r4   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   )r3   r   r   r   JxJyJzr&   s          r)   rF   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   )r3   rK   Ds      r)   r>   zElec.constr.<locals>.hess  s%    

N!!Q***r,   r   r   rN   s   `   r)   rO   zElec.constr  s    	< 	< 	< 	< 	< ?"; ; ; ; ; ; /C#+ + + + #D"3C>>>r,   )r   r   NN)rS   rT   rU   rV   r*   r   r   r4   r9   r>   rW   rO   r1   r,   r)   r   r   ?  s          67.2    ) ) )  ! ! !3 3 3$ $ $L ? ? X? ? ?r,   r   c                   h    e Zd Zej        j        d             Zd Zd Zd Z	d Z
d Zd Zd Zd	 Zd
S )TestTrustRegionConstrc                 `   t                      t          d          t          t                                t          dt                                t                      t                      t          d          t          t	                                t          dt	                                t                      t                      t                      t                      t          d          t          dd          t          dt                                t          ddt                                g}|D ]h}|j
        dd	fD ]Y}|j        dt                      t	          d
          t	          d          fD ] }|dv r|dv r|j
        du r|dv rt                      5 }|                    t          d           t          |j        |j        d|||j        |j                  }d d d            n# 1 swxY w Y   |j        <t+          |j        |j        d           |j        dk    rt1          |j        d           |j        dk    r5t1          |j        d           |j        dk    rt1          |j        d           |j        dv rt;          d          "[jd S )N2-point)r#   )r"   r#   3-pointr/   r   )r   r#   )r   r"   r#   Fdamp_update)exception_strategyskip_update)r   r   csF)r   r   r  T)r   Fdelta_grad == 0.0trust-constrmethodrF   r>   r$   constraints   decimalr0   :0yE>tr_interior_pointr   r   Invalid termination condition.)r   r   rj   ru   r   r   r   r   r   r   r9   r>   r
   filterUserWarningr   r4   r   r$   rO   r!   r   r3   statusr   
optimality	tr_radiusr  barrier_parameterRuntimeError)r&   list_of_problemsprobr9   r>   supresults          r)   test_list_of_problemsz+TestTrustRegionConstr.test_list_of_problems  s$   #II#	:::#666#yceeLLL-//*,,*yAAA*tvv>>>*i7;vv? ? ?&LL*,,,..-// Q/// QIFFF QCEEBBB Q9-0UU4 4 4#5( % $	M $	MDIu5 #M #M!Y& UU!]CCC!]CCC	E "M "MD BBB;;; yD((T5G-G-G *,, C

;0CDDD!)$(DG1?.2156:k	"C "C "CC C C C C C C C C C C C C C C z-1&(DJ:;= = = = "=A---f.?FFF})))&*:DAAA!=,???-f.FMMM}..*+KLLL /C"M#M$	M $	Ms   0AH	H	Hc                 h    d }dg}t          |dg|d          }t          |j        dd           d S )	Nc                     | dz
  dz  S r   r1   rC   s    r)   r4   z<TestTrustRegionConstr.test_default_jac_and_hess.<locals>.fun      Ea<r,   r   r/   r   r  )r   r$   r  r0   r  r  r   r   r3   r&   r4   r$   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   r1   rC   s    r)   r4   z4TestTrustRegionConstr.test_default_hess.<locals>.fun  r  r,   r  r   r  r   )r   r$   r  rF   r0   r  r  r  r  s       r)   test_default_hessz'TestTrustRegionConstr.test_default_hess  sV    	  	  	 svf^$& & &!#%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  rF   r>   zL-BFGS-Br   )r  rF   r   r  r  )	r   r   r4   r   r9   r>   r   r3   r!   )r&   r  r  result1result2s        r)   test_no_constraintsz)TestTrustRegionConstr.test_no_constraints  s    ||$(DG!/"idi9 9 9 48TW",(* * * 48TW",(* * * 	"&(DJBBBB!')TZCCCC!')TZCCCCCCr,   c           	         t                      fd}t          j        j        dj        |j        j                  }j        t          |j	        j        d           |j
        dk    rt          |j        d           |j
        dk    r5t          |j        d           |j        dk    rt          |j        d           |j
        d	v rt!          d
          d S )Nc                 X                         |           }|                    |          S r^   )r>   dot)r3   pr   r  s      r)   hesspz/TestTrustRegionConstr.test_hessp.<locals>.hessp  s!    		!A5588Or,   r  )r  rF   r-  r$   r  r/   r  r0   r
  r  r  r  )r   r   r4   r   r9   r$   rO   r!   r   r3   r  r   r  r  r  r  r  )r&   r-  r  r  s      @r)   
test_hesspz TestTrustRegionConstr.test_hessp  s   yy	 	 	 	 	 $(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 )Nr[      )r[   r0  r  r  r/   r  r0   r
  r  r  r  )rY   r   r4   r   r9   r>   r$   rO   r!   r   r3   r  r   r  r  r  r  r  )r&   r  r  s      r)   	test_argszTestTrustRegionConstr.test_args8  s    sC(($(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  rF   r>   r  )r   pytestraisesr_   r   r4   r   rO   )r&   r  messages      r)   test_raise_exceptionz*TestTrustRegionConstr.test_raise_exceptionP  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   )r3   infos     r)   callbackz7TestTrustRegionConstr.test_issue_9044.<locals>.callback\  s,    ETM"""GtO$$$$$r,   c                     | dz  S r|   r1   rC   s    r)   <lambda>z7TestTrustRegionConstr.test_issue_9044.<locals>.<lambda>`  s
    AqD r,   r   c                     d| z  S r|   r1   rC   s    r)   r@  z7TestTrustRegionConstr.test_issue_9044.<locals>.<lambda>`  s
    QqS r,   c                     dS r|   r1   rC   s    r)   r@  z7TestTrustRegionConstr.test_issue_9044.<locals>.<lambda>a  s     r,   r  )rF   r>   r>  r  successr;  r   r0   r<  )r   r   get)r&   r>  r  s      r)   test_issue_9044z%TestTrustRegionConstr.test_issue_9044W  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   ry   c                 8    | d         }| d         }|dz  |dz  z   S )Nr   r0   r/   r1   )r3   x1x2s      r)   objz3TestTrustRegionConstr.test_issue_15093.<locals>.objr  s'    1B1B7R1W$$r,   r   T)keep_feasibler  r  )r  r4   r   r$   rC  )r   r    r   r
   r  r  r   )r&   r   rJ  r$   r  r  s         r)   test_issue_15093z&TestTrustRegionConstr.test_issue_15093j  s    Xr3i  	% 	% 	%
 "b**BHb"X,>,>&*, , ,    	CJJ{$7888%	  F	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 i      s   "/BB!$B!N)rS   rT   rU   r5  markslowr  r!  r$  r(  r.  r1  r8  rE  rL  r1   r,   r)   r   r     s        [9M 9M 9Mv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 rB   r1   rC   s    r)   functionz;TestEmptyConstraint.test_empty_constraint.<locals>.function  rD   r,   c                 R    t          j        d| d         z  d| d         z  g          S )Nr   r   r0   r8   rC   s    r)   functionjacobianzCTestEmptyConstraint.test_empty_constraint.<locals>.functionjacobian  s'    8R!Wb1g.///r,   c                     d|z  S )Nr   r1   rJ   s     r)   functionhvpz>TestEmptyConstraint.test_empty_constraint.<locals>.functionhvp  s    a4Kr,   c                 V    t          j        | d         dz  | d         dz  z
  g          S rB   r8   rC   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   r0   r8   rC   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   r8   rJ   s     r)   constraintlcohzATestEmptyConstraint.test_empty_constraint.<locals>.constraintlcoh  s(    8b"XCy122QqT99r,   r   r   r  )r  rF   r-  r  r$   r0   r   r7   r  )	r   r   rw   r   r   r   absr3   r    )
r&   rS  rU  rW  rY  r[  r]  
startpointr$   r  s
             r)   test_empty_constraintz)TestEmptyConstraint.test_empty_constraint  s   	% 	% 	%	0 	0 	0	 	 		1 	1 	1	1 	1 	1	: 	: 	: )RASUcdd
"X
"&26'*RVRV,<==

!l
 
 
 	"#fh--1a&1A1A1MMMMMMr,   N)rS   rT   rU   rV   r`  r1   r,   r)   rP  rP    s2         $N $N $N $N $Nr,   rP  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 rB   r1   rC   s    r)   optztest_bug_11886.<locals>.opt  s    tQwqtQwr,   r0   r   r/   )r  )
r   testingr
   r  PendingDeprecationWarningmatrixr   r   rw   r   )rc  r  r   lin_conss       r)   test_bug_11886rh    s       
	%	%	'	' '3

,---Ibgq!foo&&' ' ' ' ' ' ' ' ' ' ' ' ' ' '  2rv..HS!QC%x000000s   AA11A58A5z(Known bug in trust-constr; see gh-11649.T)reasonstrictc                  p   t          ddgddgd          fdfd} fd}fd}t          j        d	          }t          |d
t          j                  t          |dd          g}t          | |d|          }|j        sJ  |j                   |d         j        |d         	                    |j                  cxk     r|d         j
        k     sn J t           ||j                  |d         j
                   t          | |d|          }t          |j	        |j	                   d S )Nr   r0   T)lbubrK  c                     t          j        | j        k              sJ t          j        | j        k              sJ d S r^   )r   allrl  rm  )r3   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   r7   r/   r0   )r   expr3   rq  s    r)   rJ  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 rB   r1   rt  s    r)   nceztest_gh11649.<locals>.nce  s)    tQw1~r,   c                 <     |            | d         | d         z  S )Nr   r0   r1   rt  s    r)   nciztest_gh11649.<locals>.nci  s%    tAaDyr,   )gGz?gGzr  )r4   r   r  r$   r  r   slsqp)r   r   r    r   rw   r   rC  r3   rl  r4   rm  r	   )	rJ  rv  rx  r   nlcsr   refrq  rp  s	          @@r)   test_gh11649r}    s    b"X1a&===D$ $ $ $ $O O O O O         
-	 	 BS"&11Q**,D sr.D2 2 2C;OCE7:QCE**7777T!WZ777777CCJJQ
+++
sr'D2 2 2CCGSW%%%%%r,   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_optgg      @g      "@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 boundsry  Nelder-Meadr  r$   gMbP?)atol)r   r
   r  r  r   r4   r   
less_equalrl  r3   ro  rm  allclose)r&   r$   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  ry     r  r  
r   r   r
   r  r  r   r4   r   r  r3   r&   r  r$   r  r  s        r)   test_equal_all_boundsz+TestBoundedNelderMead.test_equal_all_bounds  s    ||c
S#J//   	5CJJ{ %; < < <dha%2%+- - -F ;vx#s444444	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5   ABBBc                 @   t                      }t          ddgddg          }t                      5 }|                    t          d           t          |j        ddgd|          }t          j        |j	        dd	g          sJ 	 d d d            d S # 1 swxY w Y   d S )
Nr  r  g      4@r  ry  r  r  r  g      0@r  r  s        r)   test_equal_one_boundsz+TestBoundedNelderMead.test_equal_one_bounds	  s    ||c
S$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.r3  r   r  g      ry  r   r  r  )	r   r5  r6  r_   r   r   rw   r   r4   r&   r  r7  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)ri  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 )
Nr  r3  r   r  r  ry  r  r  r  )	r   r5  warnsr  r   r   rw   r   r4   r  s       r)   test_outside_bounds_warningz1TestBoundedNelderMead.test_outside_bounds_warning  s     ||D\+W555 	$ 	$bfWcNS#J77FTXQx)"$ $ $ $	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$r  N)rS   rT   rU   r5  rM  parametrizer   r   rw   r   r!   r  r  r  r  xfailr  r1   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   r5  scipy.linalgr   scipy.sparser   numpy.testingr   r   r   r   r	   r
   scipy.optimizer   r   r   r   r   r   r   rY   rj   ru   r   r   r   r   r   r   rP  rh  rM  r  r}  r  r1   r,   r)   <module>r     sE        # # # # # # # # # # # #. . . . . . . . . . . . . . . .! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !*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|? |? |? |? |? |? |? |?~D! D! D! D! D!H D! D! D!L1N 1N 1N 1N 1N( 1N 1N 1Nh1 1 1 D      &  &    &F=$ =$ =$ =$ =$ =$ =$ =$ =$ =$r,   