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slsqp.cpython-35.pyc
�B�W?F � @ sk d Z d d l m Z m Z m Z d d g Z d d l Z d d l m Z d d l m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z d d l m Z m Z m Z d Z e e e � j � Z d d � Z f d f d f d d d f d d d d d e d d d � Z! f d d f d d d d e d d d � Z" e# d k rgd d d d d g d d � Z$ e e g d e g d g � j% Z& d d g e& d d � d f <d d d � Z' d d d � Z( d d d � Z) d d d! � Z* d" d# d e' d$ e( d% d6 i d" d& d e) d$ e* d% d7 i f Z+ e, d' j- d( d) � � e, d* � e! e$ e d8 d g � d+ e& d, d d- d. �d d � \ Z. Z/ e, d/ � e" e$ e d9 d g � d+ e& d, d. i �Z0 e, d0 j- d( d) � � e, d* � e! e$ e d: d g � d1 e' d2 e( d3 e) d4 e* d, d d- d. �d d � \ Z. Z/ e, d/ � e" e$ e d; d g � d5 e+ d, d. i �Z0 d S)<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 � )�division�print_function�absolute_import�approx_jacobian� fmin_slsqpN)�slsqp)�zeros�array�linalg�append�asfarray� concatenate�finfo�sqrt�vstack�exp�inf�where�isfinite� atleast_1d� )� wrap_function�OptimizeResult�_check_unknown_optionszrestructuredtext enc G s� t | � } t | | f | � � } t t | � t | � g � } t t | � � } xQ t t | � � D]= } | | | <| | | f | � | | | | <d | | <qh W| 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. g )r r r �len�rangeZ transpose) �x�func�epsilon�args�x0Zf0�jacZdx�i� r# � /slsqp.pyr s #�d g���ư>c sD | d k r | } d | d | d | d | d k d | d | i } f } | t � f d d � | D� � 7} | t � f d d � | D� � 7} | r� | d d d | d | d � i f 7} | r� | d d d | d | d � i f 7} t | | � d | d | d | | �} | r8| d | d | d | d | d f S| d Sd 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. 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 Over-rides 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 exceeded Examples -------- Examples are given :ref:`in the tutorial <tutorial-sqlsp>`. N�maxiter�ftol�iprint�dispr �eps�callbackc 3 s' | ] } d d d | d � i Vq d S)�type�eq�funr Nr# )�.0�c)r r# r$ � <genexpr>� s z fmin_slsqp.<locals>.<genexpr>c 3 s' | ] } d d d | d � i Vq d S)r, �ineqr. r Nr# )r/ r0 )r r# r$ r1 � s r, r- r. r! r r2 �bounds� constraintsr �nit�status�message)�tuple�_minimize_slsqp)r r Zeqcons�f_eqconsZieqcons� f_ieqconsr3 �fprime� fprime_eqcons�fprime_ieqconsr �iter�accr( r) � full_outputr r+ Zopts�cons�resr# )r r$ r E s, p ## 'Fc 4 sr t | � | } | } | } | � | s. d } t | t � rF | f } d f d f i } x9t | � D]+\ } } y | d j � } Wn\ t k r� t d | � � Yn[ t k r� t d � � Yn> t k r� t d � � Yn! X| dE k rt d | d � � d | k r t d | � � | j d � } | d k r]� f d d � } | | d � } | | d | d d | d | j d f � i f 7<qe WdF d d d d d d d d d d d d d d d d d d d! d" d# i } t | | � \ } } | rt | | � \ } } n t t | � f � \ } } t | � j � � t t t � f d$ d% � | d D� � � } t t t � f d& d% � | d D� � � } | | } t d | g � j � } t � � } | d } | | | | } d | | | d | | d | d d | | | | | d | | | d | d d | d | d | d } | }! t | � }" t |! � }# | d k s�t | � d k r�t j | d' t �}$ t j | d' t �}% |$ j t j � |% j t j � n t | t � }& |& j d | k rt d( � � t |& d d � d f |& d d � d f k � d }' |' j � rwt d) d* j d+ d, � |' D� � � � |& d d � d f |& d d � d f }$ }% t |& � }( t j |$ |( d d � d f <t j |% |( d d � d f <t d t � }) t | t � } t | t � }* d }+ | d k r8t d- dG � xh|) d k sS|) d k r�| � � }, | d r�t! � f d2 d% � | d D� � }- n t d � }- | d r�t! � f d3 d% � | d D� � }. n t d � }. t! |- |. f � }/ |) d k s|) dH k r�t" | � � d4 � }0 | d rFt# � f d5 d% � | d D� � }1 n t | | f � }1 | d r�t# � f d6 d% � | d D� � }2 n t | | f � }2 | d k r�t | | f � }3 n t# |1 |2 f � }3 t! |3 t | d g � f d � }3 t$ | | � |$ |% |, |/ |0 |3 | |* |) |" |# � | d k rA|* |+ k rA| � � | d k r�|* |+ k r�t d7 |* | d |, t% j& |0 � f � t' |) � d k r�Pt |* � }+ q;W| d k rt | t |) � d8 t( |) � d9 � t d: |, � t d; |* � t d< | d � t d= | d � t) d> � d |, d |0 d? t |* � d@ | d dA | d dB t |) � dC | t |) � dD |) d k � S)Ia� 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. r r- r2 r, z"Constraint %d has no type defined.z/Constraints must be defined using a dictionary.z#Constraint's type must be a string.z Unknown constraint type '%s'.r. z&Constraint %d has no function defined.r! Nc s � � f d d � } | S)Nc s t | � � | � S)N)r )r r )r r. r# r$ �cjac s z3_minimize_slsqp.<locals>.cjac_factory.<locals>.cjacr# )r. rD )r )r. r$ � cjac_factory s z%_minimize_slsqp.<locals>.cjac_factoryr r z$Gradient evaluation required (g & a)z%Optimization terminated successfully.z$Function evaluation required (f & c)� z4More equality constraints than independent variables� z*More than 3*n iterations in LSQ subproblem� z#Inequality constraints incompatible� z#Singular matrix E in LSQ subproblem� z#Singular matrix C in LSQ subproblem� z2Rank-deficient equality constraint subproblem HFTI� z.Positive directional derivative for linesearch� zIteration limit exceededc s- g | ]# } t | d � | d � � � q S)r. r )r )r/ r0 )r r# r$ � <listcomp>7 s z#_minimize_slsqp.<locals>.<listcomp>c s- g | ]# } t | d � | d � � � q S)r. r )r )r/ r0 )r r# r$ rN 8 s ZdtypezDSLSQP Error: the length of bounds is not compatible with that of x0.z"SLSQP Error: lb > ub in bounds %s.z, c s s | ] } t | � Vq d S)N)�str)r/ �br# r# r$ r1 X s z"_minimize_slsqp.<locals>.<genexpr>z%5s %5s %16s %16s�NIT�FC�OBJFUN�GNORMc s- g | ]# } t | d � | d � � � q S)r. r )r )r/ �con)r r# r$ rN r s c s- g | ]# } t | d � | d � � � q S)r. r )r )r/ rU )r r# r$ rN w s g c s' g | ] } | d � | d � � q S)r! r r# )r/ rU )r r# r$ rN � s c s' g | ] } | d � | d � � q S)r! r r# )r/ rU )r r# r$ rN � s z%5i %5i % 16.6E % 16.6Ez (Exit mode �)z# Current function value:z Iterations:z! Function evaluations:z! Gradient evaluations:r r5 ZnfevZnjevr6 r7 �success)r- r2 ���)rQ rR rS rT rX )*r � isinstance�dict� enumerate�lower�KeyError� TypeError�AttributeError� ValueError�getr r r Zflatten�sum�mapr r �maxr �np�empty�floatZfill�nan�shape� IndexErrorr �any�joinr �int�printr r r r r Znorm�absrO r )4r r r r! r3 r4 r& r' r( r) r* r+ Zunknown_optionsr< r? r@ rB ZicrU ZctyperD rE Z exit_modesZfevalZgevalZmeqZmieq�mZla�nZn1ZmineqZlen_wZlen_jw�wZjwZxlZxu�bndsZbnderrZinfbnd�modeZmajiterZ majiter_prevZfxZc_eqZc_ieqr0 �gZa_eqZa_ieq�ar# )r r r$ r9 � s� ,, z 6 - !1 & .r9 �__main__rH rF c C sf t | d � | d | d d | d | d d | d | d | d | d | d | d S)z Objective function r rF r rG rH )r )r �rr# r# r$ r. � s Or. g�������?g�������?c C s! t | d d | d | g � S)z Equality constraint r rF r )r )r rP r# r# r$ �feqcon� s ry c C s t d | d d g g � S)z! Jacobian of equality constraint rF r r )r )r rP r# r# r$ �jeqcon� s rz � c C s t | d | d | g � S)z Inequality constraint r r )r )r r0 r# r# r$ �fieqcon� s r| c C s t d d g g � S)z# Jacobian of Inequality constraint r )r )r r0 r# r# r$ �jieqcon� s r} r, r- r! r r2 z Bounds constraints �H �-z * fmin_slsqpr3 r) rA Tz * _minimize_slsqpz% Equality and inequality constraints r: r= r; r> r4 )r )r{ rX rX rX rX )1�__doc__Z __future__r r r �__all__Znumpyre Zscipy.optimize._slsqpr r r r r r r r r r r r r r r �optimizer r r Z __docformat__rg r* Z_epsilonr r r9 �__name__r. �Trs ry rz r| r} rB rn �centerr �frC r# r# r# r$ �<module> sX ^ & � � $ ! $
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__init__.cpython-35.opt-1.pyc
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__init__.cpython-35.pyc
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_basinhopping.cpython-35.opt-1.pyc
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_basinhopping.cpython-35.pyc
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_differentialevolution.cpython-35.opt-1.pyc
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_differentialevolution.cpython-35.pyc
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_hungarian.cpython-35.opt-1.pyc
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_hungarian.cpython-35.pyc
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_linprog.cpython-35.opt-1.pyc
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_linprog.cpython-35.pyc
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_minimize.cpython-35.opt-1.pyc
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_minimize.cpython-35.pyc
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_numdiff.cpython-35.opt-1.pyc
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_numdiff.cpython-35.pyc
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_root.cpython-35.opt-1.pyc
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_root.cpython-35.pyc
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_spectral.cpython-35.opt-1.pyc
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_spectral.cpython-35.pyc
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_trustregion.cpython-35.opt-1.pyc
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_trustregion.cpython-35.pyc
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_trustregion_dogleg.cpython-35.opt-1.pyc
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_trustregion_dogleg.cpython-35.pyc
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_trustregion_ncg.cpython-35.opt-1.pyc
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_trustregion_ncg.cpython-35.pyc
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_tstutils.cpython-35.opt-1.pyc
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_tstutils.cpython-35.pyc
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cobyla.cpython-35.opt-1.pyc
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cobyla.cpython-35.pyc
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lbfgsb.cpython-35.opt-1.pyc
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lbfgsb.cpython-35.pyc
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linesearch.cpython-35.opt-1.pyc
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linesearch.cpython-35.pyc
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minpack.cpython-35.opt-1.pyc
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minpack.cpython-35.pyc
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nnls.cpython-35.opt-1.pyc
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nnls.cpython-35.pyc
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nonlin.cpython-35.opt-1.pyc
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nonlin.cpython-35.pyc
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optimize.cpython-35.opt-1.pyc
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optimize.cpython-35.pyc
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setup.cpython-35.opt-1.pyc
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setup.cpython-35.pyc
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slsqp.cpython-35.opt-1.pyc
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slsqp.cpython-35.pyc
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tnc.cpython-35.opt-1.pyc
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tnc.cpython-35.pyc
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zeros.cpython-35.opt-1.pyc
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zeros.cpython-35.pyc
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