3 6^K@sTdZddlmZmZmZddgZddlZddlm Z ddlm Z m Z m Z m Z mZmZmZmZmZmZmZmZmZdd lmZmZmZd ZeeejZd dZfdfdfdddfd d dddedfddZ fddfd d ddedf ddZ!e"dkrPdddddgfddZ#e e gdegdgj$Z%ddge%dddf<d1ddZ&d2ddZ'd3ddZ(d4d d!Z)d"e&e'd5d#d$e(e)d6d#fZ*e+d%j,d&d'e+d(e e#e d7dge%dd)d*dd\Z-Z.e+d+e!e#e d8dgfd,e%id-d)iZ/e+d.j,d&d'e+d(e e#e d9dge&e'e(e)dd)d/dd\Z-Z.e+d+e!e#e d:dgfd0e*id-d)iZ/dS);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 )divisionprint_functionabsolute_importapprox_jacobian fmin_slsqpN)slsqp) zerosarraylinalgappendasfarray concatenatefinfosqrtvstackexpinfisfinite atleast_1d) wrap_functionOptimizeResult_check_unknown_optionszrestructuredtext enc Gst|}t||f|}tt|t|g}tt|}xBtt|D]2}|||<|||f|||||<d||<qHW|jS)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 rrlenrangeZ transpose) xfuncepsilonargsx0f0jacZdxir#5/tmp/pip-build-vw4w4j08/scipy/scipy/optimize/slsqp.pyrs  dgư>cs|dk r |} | | | | dk||d}f}|tfdd|D7}|tfdd|D7}|rr|d||df7}|r|d || df7}t||f|||d |}|r|d |d |d |d|dfS|d SdS)a6 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 `. Nr)maxiterftoliprintdispepscallbackc3s|]}d|dVqdS)eq)typefunrNr#).0c)rr#r$ szfmin_slsqp..c3s|]}d|dVqdS)ineq)r-r.rNr#)r/r0)rr#r$r1sr,)r-r.r!rr2)r!bounds constraintsrr.nitstatusmessage)tuple_minimize_slsqp)rrZeqconsf_eqconsZieqcons f_ieqconsr3fprime fprime_eqconsfprime_ieqconsriteraccr(r) full_outputrr+optsconsresr#)rr$rEs,p  "Fc F0 st| |} |}|}| | s d}t|tr0|f}ffd}xt|D]\}}y|dj}WnTtk r|td|YnNtk rtdYn4tk rtdYnX|dDkrtd |dd |krtd ||j d }|d kr fdd}||d }|||d ||j dfdf7<qDWdEdddddddddddddddd d!d"d#d$d%i }t ||\}}| rt | |\}} nt t |f\}} t |j tttfd&d'|dD}tttfd(d'|dD}||}td|gj}t}|d}||||}d|||d||d|dd|||||d|||d|dd|d|d|d} |}!t| }"t|!}#|d kst|dkrtj|td)}$tj|td)}%|$jtj|%jtjnt|t}&|&jd|krtd*tjd+d,&|&d d df|&d d dfk}'Wd QRX|'jrxtd-d.jd/d0|'D|&d d df|&d d df}$}%t|&}(tj|$|(d d df<tj|%|(d d df<tj|$})tj|)|$|)tj |)<tj|%})tj|)tj |%|)|)<tdt!}*t|t}t|t!}+d},tdt}-tdt}.tdt}/tdt}0tdt}1tdt}2tdt}3tdt}4tdt}5tdt}6tdt!}7tdt!}8tdt!}9tdt!}:tdt!};tdt!}tdt!}yttj#|>}>Wn"ttfk r^td6YnX|drt$fd7d'|dD}?ntd}?|drt$fd8d'|dD}@ntd}@t$|?|@f}A|*dks|*dGkrt%| d9}B|drt&fd:d'|dD}Cn t||f}C|drBt&fd;d'|dD}Dn t||f}D|dkrft||f}En t&|C|Df}Et$|Et|dgfd}Et'|||$|%|>|A|B|E||+|*|"|#|-|.|/|0|1|2|3|4|5|6|7|8|9|:|;||<|= | d k r|+|,kr| tj(|dkr"|+|,kr"t"d<|+|d|>t)j*|Bft+|*dkr2Pt!|+},qW|dkrt"|t!|*d=t,|*d>t"d?|>t"d@|+t"dA|dt"dB|dt-|>|Bd dHt!|+|d|dt!|*|t!|*|*dkdC 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,r2r-z"Constraint %d has no type defined.z/Constraints must be defined using a dictionary.z#Constraint's type must be a string.r,r2zUnknown constraint type '%s'.r.z&Constraint %d has no function defined.r!Ncsfdd}|S)Ncst|f|S)N)r)rr)rr.r#r$cjacsz3_minimize_slsqp..cjac_factory..cjacr#)r.rE)r)r.r$ cjac_factorysz%_minimize_slsqp..cjac_factoryr)r.r!rrz$Gradient evaluation required (g & a)z%Optimization terminated successfully.z$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 linesearch zIteration limit exceededcs&g|]}t|df|dqS)r.r)r)r/r0)rr#r$ 8sz#_minimize_slsqp..cs&g|]}t|df|dqS)r.r)r)r/r0)rr#r$rO:s)ZdtypezDSLSQP Error: the length of bounds is not compatible with that of x0.ignore)invalidz"SLSQP Error: lb > ub in bounds %s.z, css|]}t|VqdS)N)str)r/br#r#r$r1]sz"_minimize_slsqp..z%5s %5s %16s %16sNITFCOBJFUNGNORMz'Objective function must return a scalarcs&g|]}t|df|dqS)r.r)r)r/con)rr#r$rOscs&g|]}t|df|dqS)r.r)r)r/rX)rr#r$rOsgcs"g|]}|df|dqS)r!rr#)r/rX)rr#r$rOscs"g|]}|df|dqS)r!rr#)r/rX)rr#r$rOsz%5i %5i % 16.6E % 16.6Ez (Exit mode )z# Current function value:z Iterations:z! Function evaluations:z! Gradient evaluations:) rr.r!r5ZnfevZnjevr6r7success)r,r2)rTrUrVrWr[r[).r isinstancedict enumeratelowerKeyError TypeErrorAttributeError ValueErrorgetrrr flattensummaprr maxrnpemptyfloatfillnanshape IndexErrorZerrstateanyjoinrZcliprintprintZasarrayr r rrcopyr ZnormabsrRr)Frrrr!r3r4r&r'r(r)r*r+Zunknown_optionsr<r?r@rCZicrXctyperErFZ exit_modesZfevalZgevalZmeqZmieqmZlanZn1ZmineqZlen_wZlen_jwwZjwZxlZxubndsZbnderrZinfbndZ have_boundmodeZmajiterZ majiter_prevalphar Zgsh1h2h3h4tt0ZtolZiexactZinconsZiresetZitermxlineZn2Zn3ZfxZc_eqZc_ieqr0gZa_eqZa_ieqar#)rrr$r9s6         x  * "                                              r9__main__rIrGcCsdt|d|d|dd|d|dd|d|d|d|d|d|dS)z Objective function rrGrrHrI)r)rrr#r#r$r.s Nr.g?g?cCst|dd|d|gS)z Equality constraint rrGr)r )rrSr#r#r$feqconsrcCstd|ddggS)z! Jacobian of equality constraint rGrr)r )rrSr#r#r$jeqconsr cCst|d|d|gS)z Inequality constraint rr)r )rr0r#r#r$fieqconsrcCstddggS)z# Jacobian of Inequality constraint r)r )rr0r#r#r$jieqconsrr,)r-r.r!rr2z Bounds constraints H-z * fmin_slsqpT)r3r)rAz * _minimize_slsqpr3r)z% Equality and inequality constraints )r:r=r;r>r)rAr4)r)r)r)r)r)rr[r[r[r[)0__doc__ __future__rrr__all__ZnumpyriZscipy.optimize._slsqprrr r r r r rrrrrrroptimizerrrZ __docformat__rkr*Z_epsilonrrr9__name__r.TrzrrrrrCrscenterrfrDr#r#r#r$s^ <&