B &]\K@sTdZddlmZmZmZddgZddlZddlm Z ddlm Z m Z m Z m Z mZmZmZmZmZmZmZmZmZdd lmZmZmZd ZeeejZd dZd dd dd dddd d ddddedfddZ d ddd d dddedf ddZ!e"dkrPdddddgfddZ#e e gdegdgj$Z%ddge%dddf<d5ddZ&d6ddZ'd7dd Z(d8d!d"Z)d#e&e'd$d%d&e(e)d'd%fZ*e+d(,d)d*e+d+e e#e d,dge%dd-d.dd\Z-Z.e+d/e!e#e d,dgfd0e%id1d-iZ/e+d2,d)d*e+d+e e#e d,dge&e'e(e)dd-d3dd\Z-Z.e+d/e!e#e d,dgfd4e*id1d-iZ/dS)9a  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|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 rrlenrangeZ transpose) xfuncepsilonargsx0f0jacZdxir#3lib/python3.7/site-packages/scipy/optimize/slsqp.pyrs  r#dgư>cs|dk r |} | | | | dk||d}d}|tfdd|D7}|tfdd|D7}|rr|d||d f7}|r|d || d f7}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)maxiterftoliprintdispepscallbackr#c3s|]}d|dVqdS)eq)typefunrNr#).0c)rr#r$ szfmin_slsqp..c3s|]}d|dVqdS)ineq)r-r.rNr#)r/r0)rr#r$r1sr,)r-r.r!rr2)r!bounds constraintsrr.nitstatusmessage)tuple_minimize_slsqp)rrZeqconsf_eqconsZieqcons f_ieqconsr3fprime fprime_eqconsfprime_ieqconsriteraccr(r) full_outputrr+Zoptsconsresr#)rr$rEs,p  "Fc F! st| |} |}|}| | s d}t|tr0|f}ddd}xt|D]\}}y|d}WnTtk r|td|YnNtk rtdYn4tk rtdYnX|dkrtd|dd |krtd || d }|d kr fd d}||d }|||d || dddf7<qDWdddddddddddd }t ||\}}| rtt | |\}} nt t |f\}} t | tttfdd|dD}tttfd d|d!D}||}td"|g}t}|d"}||||}d#|||d"||d"|d$d$|||||d$|||d"|d$d$|d#|d#|d"} |}!t| }"t|!}#|d kst|dkrtj|td%}$tj|td%}%|$tj|%tjnt|t}&|&jd|krtd&tjd'd(&|&d d df|&d d d"fk}'Wd QRX|'rdtd)d*d+d,|'D|&d d df|&d d d"f}$}%t|&}(tj|$|(d d df<tj|%|(d d d"f<t|$})t|)|$|)tj |)<t|%})t|)tj |%|)|)<tdt!}*t|t}t|t!}+d},tdt}-tdt}.tdt}/tdt}0tdt}1tdt}2tdt}3tdt}4tdt}5tdt}6tdt!}7tdt!}8tdt!}9tdt!}:tdt!};tdt!}tdt!}ytt#|>}>Wn"ttfk rJtd/YnX|drrt$fd0d|dD}?ntd}?|d!rt$fd1d|d!D}@ntd}@t$|?|@f}A|*dks|*d2krtt%| d3}B|drt&fd4d|dD}Cn t||f}C|d!r.t&fd5d|d!D}Dn t||f}D|dkrRt||f}En t&|C|Df}Et$|Et|d"gfd"}Et'|||$|%|>|A|B|E||+|*|"|#|-|.|/|0|1|2|3|4|5|6|7|8|9|:|;||<|= | d k r|+|,kr| t(|d$kr|+|,krt"d6|+|d|>t)*|Bft+|*d"krPt!|+},qW|d"krt"|t!|*d7t,|*d8t"d9|>t"d:|+t"d;|dt"d<|dt-|>|Bd d2t!|+|d|dt!|*|t!|*|*dkd= S)>a Minimize a scalar function of one or more variables using Sequential Least SQuares Programming (SLSQP). Options ------- ftol : float Precision goal for the value of f in the stopping criterion. eps : float Step size used for numerical approximation of the Jacobian. disp : bool Set to True to print convergence messages. If False, `verbosity` is ignored and set to 0. maxiter : int Maximum number of iterations. rr#)r,r2r-z"Constraint %d has no type defined.z/Constraints must be defined using a dictionary.z#Constraint's type must be a string.zUnknown constraint type '%s'.r.z&Constraint %d has no function defined.r!Ncsfdd}|S)Ncst|f|S)N)r)rr)rr.r#r$cjacsz3_minimize_slsqp..cjac_factory..cjacr#)r.rD)r)r.r$ cjac_factorysz%_minimize_slsqp..cjac_factoryr)r.r!rz$Gradient evaluation required (g & a)z%Optimization terminated successfully.z$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 linesearchzIteration limit exceeded) rr cs&g|]}t|df|dqS)r.r)r)r/r0)rr#r$ 8sz#_minimize_slsqp..r,cs&g|]}t|df|dqS)r.r)r)r/r0)rr#r$rO:sr2rrHrG)ZdtypezDSLSQP Error: the length of bounds is not compatible with that of x0.ignore)Zinvalidz"SLSQP Error: lb > ub in bounds %s.z, css|]}t|VqdS)N)str)r/br#r#r$r1]sz"_minimize_slsqp..z%5s %5s %16s %16s)ZNITZFCZOBJFUNZGNORMz'Objective function must return a scalarcs&g|]}t|df|dqS)r.r)r)r/con)rr#r$rOscs&g|]}t|df|dqS)r.r)r)r/rS)rr#r$rOsrFgcs"g|]}|df|dqS)r!rr#)r/rS)rr#r$rOscs"g|]}|df|dqS)r!rr#)r/rS)rr#r$rOsz%5i %5i % 16.6E % 16.6Ez (Exit mode )z# Current function value:z Iterations:z! Function evaluations:z! Gradient evaluations:) rr.r!r5ZnfevZnjevr6r7Zsuccess).r isinstancedict enumeratelowerKeyError TypeErrorAttributeError ValueErrorgetrrr Zflattensummaprr maxrnpemptyfloatZfillnanshape IndexErrorZerrstateanyjoinrZcliprintprintZasarrayr r rrcopyr ZnormabsrQr)Frrrr!r3r4r&r'r(r)r*r+Zunknown_optionsr<r?r@rBZicrSZctyperDrEZ exit_modesZfevalZgevalZmeqZmieqmZlanZn1ZmineqZlen_wZlen_jwwZjwZxlZxubndsZbnderrZinfbndZ have_boundmodeZmajiterZ majiter_prevZalphar ZgsZh1Zh2Zh3Zh4tZt0ZtolZiexactZinconsZiresetZitermxlineZn2Zn3ZfxZc_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 )rrRr#r#r$feqconsrxcCstd|ddggS)z! Jacobian of equality constraint rGrr)r )rrRr#r#r$jeqconsry cCst|d|d|gS)z Inequality constraint rr)r )rr0r#r#r$fieqconsr{cCstddggS)z# Jacobian of Inequality constraint r)r )rr0r#r#r$jieqconsr|r,)r)r-r.r!rr2)rzz Bounds constraints H-z * fmin_slsqprFT)r3r)rAz * _minimize_slsqpr3r)z% Equality and inequality constraints )r:r=r;r>r)rAr4)r)r)rz)rz)0__doc__Z __future__rrr__all__ZnumpyraZscipy.optimize._slsqprrr r r r r rrrrrrroptimizerrrZ __docformat__rcr*Z_epsilonrrr9__name__r.Trprxryr{r|rBrjcenterrfrCr#r#r#r$s^ <&