a aEQ@sxdZddgZddlZddlZddlmZddlmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZddlmZmZmZmZmZdd lmZdd lmZmZd Zee e j!Z"d dZ#d dd dd dddd ddddde"dfddZ$d ddd dddde"ddf ddZ%ddZ&ddZ'e(dkrtgdfddZ)ee gdegdgj*Z+ddge+dddf<d:dd Z,d;d!d"Z-da  This module implements the Sequential Least Squares Programming optimization algorithm (SLSQP), originally developed by Dieter Kraft. See http://www.netlib.org/toms/733 Functions --------- .. autosummary:: :toctree: generated/ approx_jacobian fmin_slsqp approx_jacobian fmin_slsqpN)slsqp) zerosarraylinalgappendasfarray concatenatefinfosqrtvstackexpinfisfinite atleast_1d)OptimizeResult_check_unknown_options_prepare_scalar_function_clip_x_for_func _check_clip_x)approx_derivative)old_bound_to_new_arr_to_scalarzrestructuredtext encGst||d||d}t|S)a Approximate the Jacobian matrix of a callable function. Parameters ---------- x : array_like The state vector at which to compute the Jacobian matrix. func : callable f(x,*args) The vector-valued function. epsilon : float The perturbation used to determine the partial derivatives. args : sequence Additional arguments passed to func. Returns ------- An array of dimensions ``(lenf, lenx)`` where ``lenf`` is the length of the outputs of `func`, and ``lenx`` is the number of elements in `x`. Notes ----- The approximation is done using forward differences. 2-point)methodabs_stepargs)rnpZ atleast_2d)xfuncepsilonrjacr$d/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/scipy/optimize/slsqp.pyr#s r$dgư>cs|dur |} | | | | 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)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 `. Nr)maxiterftoliprintdispepscallbackr$c3s|]}d|dVqdS)eqtypefunrNr$.0crr$r% zfmin_slsqp..c3s|]}d|dVqdS)ineqr.Nr$r1r4r$r%r5r6r-r/r0r#rr7)r#bounds constraintsr r0nitstatusmessage)tuple_minimize_slsqp)r!x0Zeqconsf_eqconsZieqcons f_ieqconsr9Zfprime fprime_eqconsfprime_ieqconsriteraccr)r* full_outputr"r,optsconsresr$r4r%rEs8p  "Fc C! sDt| |d}|}| | s d}t||dus@t|dkrPtj tjfnt|tddt|t r~|f}ddd}t |D]0\}}z|d }Wnt y}zt d||WYd}~nd}~0t y }zt d|WYd}~nRd}~0ty8}zt d |WYd}~n$d}~00|dvrTtd |dd |vrjtd ||d }|durfdd}||d }|||d ||dddf7<qdddddddddddd }tttfdd|d D}tttfd!d|d"D}||}td|g}t}|d}||||}d#|||d||d|d$d$|||||d$|||d|d$d$|d#|d#|d}|} t|}!t| }"|dust|dkr2tj|td%}#tj|td%}$|#tj|$tjntd&d|Dt}%|%jd|kr^td'tjd(d)0|%dddf|%dddfk}&Wdn1s0Y|&rtd*d+d,d-|&D|%dddf|%dddf}#}$t|%}'tj|#|'dddf<tj|$|'dddf<t ||| d.}(t!|(j"})t!|(j#}*tdt$}+t|t}t|t$},d}-tdt}.tdt}/tdt}0tdt}1tdt}2tdt}3tdt}4tdt}5tdt}6tdt}7tdt$}8tdt$}9tdt$}:tdt$};tdt$}|d$krDt%d/d0|)}?ztt&|?}?Wn4t tfy}ztd1|WYd}~n d}~00t'|*d2}@t(|}At)||||||}Bt*|||#|$|?|A|@|B||,|+|!|"|.|/|0|1|2|3|4|5|6|7|8|9|:|;|<||=|> |+dkr"|)}?t(|}A|+d3krNt'|*d2}@t)||||||}B|,|-kr| durp| t+|d$krt%d4|,|(j,|?t-.|@ft/|+dkrqt$|,}-q|dkr t%|t$|+d5t0|+d6t%d7|?t%d8|,t%d9|(j,t%d:|(j1t2|?|@dd3t$|,|(j,|(j1t$|+|t$|+|+dkd; S)t|}dvr&t||dSt|d|dSdS)N)rz3-pointcs)rrZrel_stepr9r)rrrr9)rr)r r)r"finite_diff_rel_stepr0r# new_boundsr$r%cjac&s  z3_minimize_slsqp..cjac_factory..cjacr$)r0rN)r"rLr#rM)r0r% cjac_factory%s z%_minimize_slsqp..cjac_factoryr)r0r#rz$Gradient evaluation required (g & a)z$Optimization terminated successfullyz$Function evaluation required (f & c)z4More equality constraints than independent variablesz*More than 3*n iterations in LSQ subproblemz#Inequality constraints incompatiblez#Singular matrix E in LSQ subproblemz#Singular matrix C in LSQ subproblemz2Rank-deficient equality constraint subproblem HFTIz.Positive directional derivative for linesearchzIteration limit reached) rr cs(g|] }t|dg|dRqSr0rrr1r r$r% Hsz#_minimize_slsqp..r-cs(g|] }t|dg|dRqSrYrZr1r[r$r%r\Jsr7rRrQ)ZdtypecSs g|]\}}t|t|fqSr$)r)r2lur$r$r%r\cszDSLSQP 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)r2br$r$r%r5nr6z"_minimize_slsqp..)r#rr"rLr9z%5s %5s %16s %16s)ZNITZFCZOBJFUNZGNORMz'Objective function must return a scalargrPz%5i %5i % 16.6E % 16.6Ez (Exit mode )z# Current function value:z Iterations:z! Function evaluations:z! Gradient evaluations:) r r0r#r;nfevZnjevr<r=success)3rr flattenlenrrrZclip isinstancedict enumeratelowerKeyError TypeErrorAttributeError ValueErrorgetsummaprmaxremptyfloatfillnanshape IndexErrorZerrstateanyjoinrrrr0ZgradintprintZasarrayr_eval_constraint_eval_con_normalsrcopyrdrZnormabsraZngevr)Cr!r@rr#r9r:r'r(r)r*r+r,rLZunknown_optionsrErFrIZicconctypeerNrOZ exit_modesmeqmieqmlanZn1ZmineqZlen_wZlen_jwwZjwZxlZxubndsZbnderrZinfbndZsfZ wrapped_funZ wrapped_gradmodeZmajiterZ majiter_prevalphaZf0Zgsh1h2h3h4tt0ZtolZiexactZinconsZiresetZitermxlineZn2Zn3Zfxgr3ar$)r"rLr#rMr r%r?sR   "          > @ "                                             r?csh|dr$tfdd|dD}ntd}|drPtfdd|dD}ntd}t||f}|S)Nr-cs(g|] }t|dg|dRqSrYrZr2rr[r$r%r\sz$_eval_constraint..rr7cs(g|] }t|dg|dRqSrYrZrr[r$r%r\s)r r)r rIZc_eqZc_ieqr3r$r[r%r~s     r~c s|dr$tfdd|dD}n t||f}|drTtfdd|dD}n t||f}|dkrvt||f} n t||f} t| t|dgfd} | S)Nr-cs$g|]}|dg|dRqSr#rr$rr[r$r%r\sz%_eval_con_normals..r7cs$g|]}|dg|dRqSrr$rr[r$r%r\srr)r rr ) r rIrrrrrZa_eqZa_ieqrr$r[r%rs       r__main__)rSrQrSrQrcCsdt|d|d|dd|d|dd|d|d|d|d|d|dS)z Objective function rrQrrRrS)r)r rr$r$r%r0s0r0rQg?g?cCst|dd|d|gS)z Equality constraint rrQrrr rbr$r$r%feqconsrcCstd|ddggS)z! Jacobian of equality constraint rQrrrrr$r$r%jeqconsr cCst|d|d|gS)z Inequality constraint rrrr r3r$r$r%fieqconsrcCstddggS)z# Jacobian of inequality constraint rrrr$r$r%jieqconsrr-)rr8r7)rz Bounds constraints H-z * fmin_slsqprPT)r9r*rGz * _minimize_slsqpr9r*z% Equality and inequality constraints )rArCrBrDr*rGr:)r)r)r)r)6__doc____all__warningsZnumpyrZscipy.optimize._slsqprrrrrr r r r r rrrroptimizerrrrrZ_numdiffr _constraintsrrZ __docformat__rur+Z_epsilonrrr?r~r__name__r0TrrrrrrIr}centerr frJr$r$r$r%s| < "