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Z
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 dd	lmZ dd
lmZmZ dZ e ee      j<                        Zd Z ddddddddddddddedfdZ!ddddddddeddfdZ"d Z#d Z$y)a  
This module implements the Sequential Least Squares Programming optimization
algorithm (SLSQP), originally developed by Dieter Kraft.
See http://www.netlib.org/toms/733

Functions
---------
.. autosummary::
   :toctree: generated/

    approx_jacobian
    fmin_slsqp

approx_jacobian
fmin_slsqp    N)slsqp)zerosarraylinalgappendasfarrayconcatenatefinfosqrtvstackisfinite
atleast_1d   )OptimizeResult_check_unknown_options_prepare_scalar_function_clip_x_for_func_check_clip_x)approx_derivative)old_bound_to_new_arr_to_scalarzrestructuredtext enc                 L    t        || d||      }t        j                  |      S )a  
    Approximate the Jacobian matrix of a callable function.

    Parameters
    ----------
    x : array_like
        The state vector at which to compute the Jacobian matrix.
    func : callable f(x,*args)
        The vector-valued function.
    epsilon : float
        The perturbation used to determine the partial derivatives.
    args : sequence
        Additional arguments passed to func.

    Returns
    -------
    An array of dimensions ``(lenf, lenx)`` where ``lenf`` is the length
    of the outputs of `func`, and ``lenx`` is the number of elements in
    `x`.

    Notes
    -----
    The approximation is done using forward differences.

    2-point)methodabs_stepargs)r   np
atleast_2d)xfuncepsilonr   jacs        :/usr/lib/python3/dist-packages/scipy/optimize/_slsqp_py.pyr   r   "   s*    6 D!I!%'C ==     d   gư>c                   
 ||}||||dk7  ||d}d}|t        
fd|D              z  }|t        
fd|D              z  }|r|d||
dfz  }|r|d||	
dfz  }t        | |
f|||d	|}|r|d
   |d   |d   |d   |d   fS |d
   S )a/  
    Minimize a function using Sequential Least Squares Programming

    Python interface function for the SLSQP Optimization subroutine
    originally implemented by Dieter Kraft.

    Parameters
    ----------
    func : callable f(x,*args)
        Objective function.  Must return a scalar.
    x0 : 1-D ndarray of float
        Initial guess for the independent variable(s).
    eqcons : list, optional
        A list of functions of length n such that
        eqcons[j](x,*args) == 0.0 in a successfully optimized
        problem.
    f_eqcons : callable f(x,*args), optional
        Returns a 1-D array in which each element must equal 0.0 in a
        successfully optimized problem. If f_eqcons is specified,
        eqcons is ignored.
    ieqcons : list, optional
        A list of functions of length n such that
        ieqcons[j](x,*args) >= 0.0 in a successfully optimized
        problem.
    f_ieqcons : callable f(x,*args), optional
        Returns a 1-D ndarray in which each element must be greater or
        equal to 0.0 in a successfully optimized problem. If
        f_ieqcons is specified, ieqcons is ignored.
    bounds : list, optional
        A list of tuples specifying the lower and upper bound
        for each independent variable [(xl0, xu0),(xl1, xu1),...]
        Infinite values will be interpreted as large floating values.
    fprime : callable `f(x,*args)`, optional
        A function that evaluates the partial derivatives of func.
    fprime_eqcons : callable `f(x,*args)`, optional
        A function of the form `f(x, *args)` that returns the m by n
        array of equality constraint normals. If not provided,
        the normals will be approximated. The array returned by
        fprime_eqcons should be sized as ( len(eqcons), len(x0) ).
    fprime_ieqcons : callable `f(x,*args)`, optional
        A function of the form `f(x, *args)` that returns the m by n
        array of inequality constraint normals. If not provided,
        the normals will be approximated. The array returned by
        fprime_ieqcons should be sized as ( len(ieqcons), len(x0) ).
    args : sequence, optional
        Additional arguments passed to func and fprime.
    iter : int, optional
        The maximum number of iterations.
    acc : float, optional
        Requested accuracy.
    iprint : int, optional
        The verbosity of fmin_slsqp :

        * iprint <= 0 : Silent operation
        * iprint == 1 : Print summary upon completion (default)
        * iprint >= 2 : Print status of each iterate and summary
    disp : int, optional
        Overrides the iprint interface (preferred).
    full_output : bool, optional
        If False, return only the minimizer of func (default).
        Otherwise, output final objective function and summary
        information.
    epsilon : float, optional
        The step size for finite-difference derivative estimates.
    callback : callable, optional
        Called after each iteration, as ``callback(x)``, where ``x`` is the
        current parameter vector.

    Returns
    -------
    out : ndarray of float
        The final minimizer of func.
    fx : ndarray of float, if full_output is true
        The final value of the objective function.
    its : int, if full_output is true
        The number of iterations.
    imode : int, if full_output is true
        The exit mode from the optimizer (see below).
    smode : string, if full_output is true
        Message describing the exit mode from the optimizer.

    See also
    --------
    minimize: Interface to minimization algorithms for multivariate
        functions. See the 'SLSQP' `method` in particular.

    Notes
    -----
    Exit modes are defined as follows ::

        -1 : Gradient evaluation required (g & a)
         0 : Optimization terminated successfully
         1 : Function evaluation required (f & c)
         2 : More equality constraints than independent variables
         3 : More than 3*n iterations in LSQ subproblem
         4 : Inequality constraints incompatible
         5 : Singular matrix E in LSQ subproblem
         6 : Singular matrix C in LSQ subproblem
         7 : Rank-deficient equality constraint subproblem HFTI
         8 : Positive directional derivative for linesearch
         9 : Iteration limit reached

    Examples
    --------
    Examples are given :ref:`in the tutorial <tutorial-sqlsp>`.

    r   )maxiterftoliprintdispepscallbackr'   c              3   *   K   | ]
  }d |d  yw)eqtypefunr   Nr'   .0cr   s     r%   	<genexpr>zfmin_slsqp.<locals>.<genexpr>   s     IQ448I   c              3   *   K   | ]
  }d |d  yw)ineqr2   Nr'   r5   s     r%   r8   zfmin_slsqp.<locals>.<genexpr>   s     Lq6!T:Lr9   r1   )r3   r4   r$   r   r;   )r$   boundsconstraintsr!   r4   nitstatusmessage)tuple_minimize_slsqp)r"   x0eqconsf_eqconsieqcons	f_ieqconsr<   fprimefprime_eqconsfprime_ieqconsr   iteraccr,   r-   full_outputr#   r/   optsconsress             `          r%   r   r   D   s    ` aK "D D 	EI&IIIDELGLLLD $x  # 	#&>  # 	# $D 4fV&*4.24C3xUSZXINN3xr&   Fc                   FG t        |       |dz
  }|}|
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                   t        j
                  fGnt        |      Gt	        j                  |Gd   Gd         }t        |t              r|f}ddd}t        |      D ]  \  }}	 |d   j                         }|dvrt        d|d   z        d|vrt        d|z        |j!                  d      }|FGfd} ||d         }||xx   |d   ||j!                  dd      dfz  cc<    dddddddddddd}t#        t%        t        |d   D cg c]  }t'         |d   |g|d           c}            }t#        t%        t        |d   D cg c]  }t'         |d   |g|d           c}            }||z   }t)        d|g      j+                         }t        |      }|dz   }||z
  |z   |z   } d|z  |z   |dz   z  ||z
  dz   | d z   z  z   d | z  z   || z   ||z
  z  z   d |z  z   |z   |dz   |z  d z  z   d |z  z   d|z  z   d|z  z   dz   }!| }"t-        |!      }#t-        |"      }$|t        |      dk(  rvt	        j.                  |t0        !      }%t	        j.                  |t0        !      }&|%j3                  t        j4                         |&j3                  t        j4                         nt)        |D '(cg c]  \  }'}(t7        |'      t7        |(      f c}(}'t0              })|)j8                  d   |k7  rt;        d"      t	        j<                  d#$      5  |)dddf   |)dddf   kD  }*ddd       *j?                         r$t        d%d&jA                  d' |*D              z        |)dddf   |)dddf   }&}%tC        |)       }+t        j4                  |%|+dddf   <   t        j4                  |&|+dddf   <   tE        | |||
G(      },tG        |,jH                  G      }-tG        |,jJ                  G      }.t)        dtL              }/t)        |t0              }t)        |tL              }0d}1t)        dt0              }2t)        dt0              }3t)        dt0              }4t)        dt0              }5t)        dt0              }6t)        dt0              }7t)        dt0              }8t)        dt0              }9t)        dt0              }:t)        dt0              };t)        dtL              }<t)        dtL              }=t)        dtL              }>t)        dtL              }?t)        dtL              }@t)        dtL              }t)        dtL              }At)        dtL              }B|d k\  rtO        d)d*z          |-|      }CtQ         |.|      d+      }DtS        ||      }tU        |||||||      }E	 tW        g ||||%|&C|DE||0|/|#|$|2|3|4|5|6|7|8|9|:|;|<|=|>|?@|AB  |/dk(  r |-|      }CtS        ||      }|/d,k(  r#tQ         |.|      d+      }DtU        |||||||      }E|0|1kD  rQ| |t	        jX                  |             |d k\  r/tO        d-|0|,jZ                  Ct]        j^                  D      fz         ta        |/      dk7  rntM        |0      }1|dk\  rmtO        |tM        |/         d.z   tc        |/      z   d/z          tO        d0C       tO        d1|0       tO        d2|,jZ                         tO        d3|,jd                         tg        |CDdd, tM        |0      |,jZ                  |,jd                  tM        |/      |tM        |/         |/dk(  4	      S # t        $ r}t        d|z        |d}~wt        $ r}t        d	      |d}~wt        $ r}t        d
      |d}~ww xY wc c}w c c}w c c}(}'w # 1 sw Y   xY w)5a  
    Minimize a scalar function of one or more variables using Sequential
    Least Squares Programming (SLSQP).

    Options
    -------
    ftol : float
        Precision goal for the value of f in the stopping criterion.
    eps : float
        Step size used for numerical approximation of the Jacobian.
    disp : bool
        Set to True to print convergence messages. If False,
        `verbosity` is ignored and set to 0.
    maxiter : int
        Maximum number of iterations.
    finite_diff_rel_step : None or array_like, optional
        If `jac in ['2-point', '3-point', 'cs']` the relative step size to
        use for numerical approximation of `jac`. The absolute step
        size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``,
        possibly adjusted to fit into the bounds. For ``method='3-point'``
        the sign of `h` is ignored. If None (default) then step is selected
        automatically.
    r   r   Nr'   )r1   r;   r3   zUnknown constraint type '%s'.z"Constraint %d has no type defined.z/Constraints must be defined using a dictionary.z#Constraint's type must be a string.r4   z&Constraint %d has no function defined.r$   c                       fd}|S )Nc                 h    t        |       } dv rt        | |      S t        | d|      S )N)r   z3-pointcs)r   r   rel_stepr<   r   )r   r   r   r<   )r   r   )r!   r   r#   finite_diff_rel_stepr4   r$   
new_boundss     r%   cjacz3_minimize_slsqp.<locals>.cjac_factory.<locals>.cjac%  sT    %a4A::0a$:N8B D D  1a	:A8B D Dr&   r'   )r4   rX   r#   rV   r$   rW   s   ` r%   cjac_factoryz%_minimize_slsqp.<locals>.cjac_factory$  s    
D 
D r&   r   )r4   r$   r   z$Gradient evaluation required (g & a)z$Optimization terminated successfullyz$Function evaluation required (f & c)z4More equality constraints than independent variablesz*More than 3*n iterations in LSQ subproblemz#Inequality constraints incompatiblez#Singular matrix E in LSQ subproblemz#Singular matrix C in LSQ subproblemz2Rank-deficient equality constraint subproblem HFTIz.Positive directional derivative for linesearchzIteration limit reached)r   r                        	   r1   r;   r\   r[   )dtypezDSLSQP Error: the length of bounds is not compatible with that of x0.ignore)invalidz"SLSQP Error: lb > ub in bounds %s.z, c              3   2   K   | ]  }t        |        y w)N)str)r6   bs     r%   r8   z"_minimize_slsqp.<locals>.<genexpr>m  s     &>!s1v&>s   )r$   r   r#   rV   r<   z%5s %5s %16s %16s)NITFCOBJFUNGNORMg        rZ   z%5i %5i % 16.6E % 16.6Ez    (Exit mode )z#            Current function value:z            Iterations:z!            Function evaluations:z!            Gradient evaluations:)	r!   r4   r$   r>   nfevnjevr?   r@   success)4r   r
   flattenlenr   infr   clip
isinstancedict	enumeratelower
ValueErrorKeyError	TypeErrorAttributeErrorgetsummapr   r   maxr   emptyfloatfillnanr   shape
IndexErrorerrstateanyjoinr   r   r   r4   gradintprintr	   _eval_constraint_eval_con_normalsr   copyrn   r   normabsrg   ngevr   )Hr"   rC   r   r$   r<   r=   r*   r+   r,   r-   r.   r/   rV   unknown_optionsrK   rL   r!   rO   icconctypeerX   rY   
exit_modesr7   meqmieqmlann1mineqlen_wlen_jwwjwxlxulubndsbnderrinfbndsfwrapped_funwrapped_gradmodemajitermajiter_prevalphaf0gsh1h2h3h4tt0toliexactinconsiresetitermxlinen2n3fxgar#   rW   sH      `        `                                                         @@r%   rB   rB      s   8 ?+Q;D
CG 	A ~V)vvgrvv&
%f-
 	:a=*Q-0A +t$"ob!D[) +9C	PK%%'E N* !@3v;!NOO EJKK wwu~<  E
+D 	UE
 $!$!46 9 	9S+9Z =<<LB;;;JF/
1J c#Dz# #81U8A#:&	#:; # $ %Cs3V& $HAeHQ$;6$;< & ' (D 	d
A	1v			BAA 
QBGbL2ErT!VbdORVAXa001U7:BuHr#v;NNeqS!Ga<(*+A#.01!467d;=>?EFeA	vB ~V)XXau%XXau%

$*, 1a &a(.*;< ,-24::a=A ; < < [[* 	-!Q$Z$q!t*,F	- ::<A!YY&>v&>>? @ @adT!Q$ZB 4.666!Q$<666!Q$< 
"$ss7K)3
5B
 #266:6K#BGGZ8L C=D
U
CD#GL !UOE	q%B	q%B	q%B	q%B	q%B	q%BaA	q%B
5/C1c]F1c]F1c]F1c]FC=D	q#B	q#B	q#B {!$DDE
 
QB|A$AD!A!T2q!S$7A
 	a 	 	a 	 	R 	 	Q 	 	1 	c 	7 	D 	! 	R 					!#	%'	)+	-.	02	47			$	&,	.2	 	 	 	
 19QB D)A2:|A,A!!T2q!S$?A\!#$ {/7BGG35v{{1~3G G H t9>7|; @ {jT#&77#d)CcIJ3R8'11277;1277;A21Sb6s7|!wwRWWSY",SY"7$!)N Nw  	M?"DE1L 	2 * +012 	JABI	Jd#&2,	- 	-sN   :^!%_1%_6 _;
+`!	_.*^99_.__._))_.`c                 @   |d   r3t        |d   D cg c]  }t         |d   | g|d           c}      }nt        d      }|d   r3t        |d   D cg c]  }t         |d   | g|d           c}      }nt        d      }t        ||f      }|S c c}w c c}w )Nr1   r4   r   r   r;   )r   r   r   )r!   rO   r   c_eqc_ieqr7   s         r%   r   r     s    Dz'+Dz3 # 'zs5z!'Bc&k'BC 3 4 QxF|(,V6!$ (
E
1(Cs6{(CD 6 7 a 	T5M"AH36s   BBc           
      |   |d   r*t        |d   D cg c]  } |d   | g|d     c}      }nt        ||f      }|d   r*t        |d   D cg c]  } |d   | g|d     c}      }	nt        ||f      }	|dk(  rt        ||f      }
nt        ||	f      }
t        |
t        |dg      fd      }
|
S c c}w c c}w )Nr1   r$   r   r;   r   r   )r   r   r   )r!   rO   r   r   r   r   r   r   a_eqa_ieqr   s              r%   r   r     s    Dz"&t*. "s5z!2c&k2 . / c1XF|#'<1 #E
13s6{3 1 2 tQi  	Av2q'ND%=!Qr1g'+AH%.1s   B4B9)%__doc____all__numpyr   scipy.optimize._slsqpr   r   r   r   r	   r
   r   r   r   r   r   r   	_optimizer   r   r   r   r   _numdiffr   _constraintsr   r   __docformat__r   r.   _epsilonr   r   rB   r   r   r'   r&   r%   <module>r      s    l
+  '7 7 7 7' ' ( : &e  !D !#T2T"#6d8	Od $&4 "fQU 4dwNt&r&   