ó î&]\c@`sTdZddlmZmZmZddgZddlZddlm Z ddlm Z m Z m Z m Z mZmZmZmZmZmZmZmZmZdd lmZmZmZd ZeeeƒjƒZd „Zfe fe fe e e fd d de dee d„Z!fe e fd d de"ee d„ Z#e$dkrPdddddgd„Z%e e gdegdgƒj&Z'ddge'dd…dfc `sU|dk r|} ni| d6| d6| d6| dkd6|d6|d6}d}|t‡fd†|Dƒƒ7}|t‡fd †|Dƒƒ7}|rÃ|id d 6|d 6|d 6ˆd6f7}n|rõ|idd 6|d 6| d 6ˆd6f7}nt||ˆd |d|d||}|rI|d|d |d|d|dfS|dSdS(s6 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 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 `. tmaxitertftoltiprintitdisptepstcallbackc3`s*|] }idd6|d6ˆd6VqdS(teqttypetfunRN((t.0tc(R(s3lib/python2.7/site-packages/scipy/optimize/slsqp.pys Ãsc3`s*|] }idd6|d6ˆd6VqdS(tineqR)R*RN((R+R,(R(s3lib/python2.7/site-packages/scipy/optimize/slsqp.pys ÄsR(R)R*RRR-tboundst constraintsRtnittstatustmessageN((tNonettuplet_minimize_slsqp(RRteqconstf_eqconstieqconst f_ieqconsR.tfprimet fprime_eqconstfprime_ieqconsRtitertaccR$R%t full_outputRR'toptstconstres((Rs3lib/python2.7/site-packages/scipy/optimize/slsqp.pyREs,p        'c G" `s) t| ƒ|} |}|}| ‰| s1d}nt|tƒrL|f}nid@d6dAd6}xAt|ƒD]3\}}y|djƒ}WnYtk r°td|ƒ‚n\tk rÌtdƒ‚n@tk rètdƒ‚n$X|dBkr td|dƒ‚nd |kr+td |ƒ‚n|j d ƒ}|d'krh‡fd †}||d ƒ}n||ci|d d 6|d 6|j d dCƒd 6f7tdt#ƒ}?|dkr t$d+dDƒnxE|,dks&|,dkr,||ƒ}@yttj%|@ƒƒ}@Wn#ttfk rptd0ƒ‚nX|dr¸t&g|dD]#}t|d ||d Œƒ^q‰ƒ}An tdƒ}A|dr t&g|dD]#}t|d ||d Œƒ^q܃}Bn tdƒ}Bt&|A|Bfƒ}n|,dksD|,dkrV t'| |ƒd1ƒ}C|dršt(g|dD]}|d ||d Œ^qqƒ}Dnt||fƒ}D|drít(g|dD]}|d ||d Œ^qă}Ent||fƒ}E|dkr t||fƒ}Fnt(|D|Efƒ}Ft&|Ft|dgƒfdƒ}Fnt)||||&|'|@||C|F||-|,|$|%|/|0|1|2|3|4|5|6|7|8|9|:|;|<|=| |>|?ƒ | d'k rë |-|.krë | tj*|ƒƒn|dkr- |-|.kr- t$d2|-|d|@t+j,|Cƒfƒnt-|,ƒdkrC Pnt#|-ƒ}.qW|dkrÄ t$|t#|,ƒd3t.|,ƒd4ƒt$d5|@ƒt$d6|-ƒt$d7|dƒt$d8|dƒnt/d9|d |@d |Cd d:t#|-ƒd;|dd<|dd=t#|,ƒd>|t#|,ƒd?|,dkƒ S(Esë Minimize a scalar function of one or more variables using Sequential Least SQuares Programming (SLSQP). Options ------- ftol : float Precision goal for the value of f in the stopping criterion. eps : float Step size used for numerical approximation of the Jacobian. disp : bool Set to True to print convergence messages. If False, `verbosity` is ignored and set to 0. maxiter : int Maximum number of iterations. iR(R-R)s"Constraint %d has no type defined.s/Constraints must be defined using a dictionary.s#Constraint's type must be a string.sUnknown constraint type '%s'.R*s&Constraint %d has no function defined.Rc`s‡‡fd†}|S(Nc`st|ˆˆ|ŒS(N(R(RR(RR*(s3lib/python2.7/site-packages/scipy/optimize/slsqp.pytcjacs((R*RC(R(R*s3lib/python2.7/site-packages/scipy/optimize/slsqp.pyt cjac_factorysRs$Gradient evaluation required (g & a)iÿÿÿÿs%Optimization terminated successfully.s$Function evaluation required (f & c)is4More equality constraints than independent variablesis*More than 3*n iterations in LSQ subproblemis#Inequality constraints incompatibleis#Singular matrix E in LSQ subproblemis#Singular matrix C in LSQ subproblemis2Rank-deficient equality constraint subproblem HFTIis.Positive directional derivative for linesearchisIteration limit exceededi tdtypesDSLSQP Error: the length of bounds is not compatible with that of x0.tinvalidtignoreNs"SLSQP Error: lb > ub in bounds %s.s, cs`s|]}t|ƒVqdS(N(tstr(R+tb((s3lib/python2.7/site-packages/scipy/optimize/slsqp.pys ]ss%5s %5s %16s %16stNITtFCtOBJFUNtGNORMs'Objective function must return a scalargs%5i %5i % 16.6E % 16.6Es (Exit mode t)s# Current function value:s Iterations:s! Function evaluations:s! Gradient evaluations:RR0tnfevtnjevR1R2tsuccess(((R(R-((RJRKRLRM(0Rt isinstancetdictt enumeratetlowertKeyErrort TypeErrortAttributeErrort ValueErrortgetR3RRR tflattentsumtmapRRRtmaxRtnptemptytfloattfilltnantshapet IndexErrorterrstatetanytjoinRtclipRtinttprinttasarrayR R RRtcopyRtnormtabsRHR(GRRRRR.R/R"R#R$R%R&R'tunknown_optionsR:R=R>RAtictcontctypeRCRDt exit_modestfevaltgevalRR,tmeqtmieqtmtlatntn1tmineqtlen_wtlen_jwtwtjwtxltxutbndstbnderrtinfbndt have_boundtmodetmajitert majiter_prevtalphaRtgsth1th2th3th4tttt0ttoltiexacttinconstiresettitermxtlinetn2tn3tfxtc_eqtc_ieqtgta_eqta_ieqta((Rs3lib/python2.7/site-packages/scipy/optimize/slsqp.pyR5×s6            7 7   z  2  - $%   7  7  1 1 $-  &  ( t__main__iicC`sft|dƒ|d|dd|d|dd|d|d|d|d|d|dS(s Objective function iiiii(R(Rtr((s3lib/python2.7/site-packages/scipy/optimize/slsqp.pyR*ãs Ogš™™™™™¹?gš™™™™™É?cC`s!t|dd|d|gƒS(s Equality constraint iii(R(RRI((s3lib/python2.7/site-packages/scipy/optimize/slsqp.pytfeqconîscC`std|ddggƒS(s! Jacobian of equality constraint iii(R(RRI((s3lib/python2.7/site-packages/scipy/optimize/slsqp.pytjeqconòsi cC`st|d|d|gƒS(s Inequality constraint ii(R(RR,((s3lib/python2.7/site-packages/scipy/optimize/slsqp.pytfieqconöscC`stddggƒS(s# Jacobian of Inequality constraint i(R(RR,((s3lib/python2.7/site-packages/scipy/optimize/slsqp.pytjieqconúsR(R)R*RRR-s Bounds constraints iHt-s * fmin_slsqpiÿÿÿÿR.R%R?s * _minimize_slsqps% Equality and inequality constraints R7R;R9R<R/(3t__doc__t __future__RRRt__all__tnumpyR_tscipy.optimize._slsqpRRRRR R R R R RRRRRtoptimizeRRRt __docformat__RaR&t_epsilonRR3RtFalseR5t__name__R*tTR„R¤R¥R¦R§RARktcentertTrueRtfRB(((s3lib/python2.7/site-packages/scipy/optimize/slsqp.pytsZ  X &     Ž  ÿ $    "( $