hOI dZddgZddlZddlmZddlmZmZmZm Z m Z m Z m Z m Z mZmZmZddlmZmZmZmZmZdd lmZdd lmZmZd Ze e ejZd Z d dd dd dddd dddddedfdZ!d ddd ddddeddf dZ"dZ#dZ$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 approx_jacobian fmin_slsqpN)slsqp) zerosarraylinalgappendasfarray concatenatefinfosqrtvstackisfinite 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 encRt||d||}tj|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)rnp atleast_2d)xfuncepsilonrjacs T/var/www/html/Sam_Eipo/venv/lib/python3.11/site-packages/scipy/optimize/_slsqp_py.pyrr"s56 D!I!% ' ' 'C =  dgư>cZ ||} | | | | dk||d}d}|t fd|Dz }|t fd|Dz }|r |d|| dfz }|r |d || dfz }t|| f|||d |}|r%|d |d |d |d|dfS|d 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. 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'c3$K|] }d|dV dS)eqtypefunrNr'.0crs r% zfmin_slsqp..s-IIQ4488IIIIIIr&c3$K|] }d|dV dS)ineqr2Nr'r5s r%r8zfmin_slsqp..s-LLq6!T::LLLLLLr&r1)r3r4r$rr:)r$bounds constraintsr!r4nitstatusmessage)tuple_minimize_slsqp)r"x0eqconsf_eqconsieqcons f_ieqconsr;fprime fprime_eqconsfprime_ieqconsriteraccr,r- full_outputr#r/optsconsress ` r%rrDsF` aK  " "D D EIIII&III I IIDELLLLGLLL L LLD# $x   # ## &>  # # $D 4fV&* 4 4.2 4 4C3xUSZXINN3xr&Fc F CDEt| |dz }|}| C| sd}t|E|t|dkrtj tjfDnt |Dt jEDdDdEt|tr|f}ddd}t|D]\}} |d }|dvrtd|dzn_#t$r}td|z|d}~wt$r}td |d}~wt$r}td |d}~wwxYwd |vrtd |z|d }|C Dfd}||d }||xx|d ||dddfz cc<dddddddddddd }t#t%tEfd|dD}t#t%tEfd|d D}||z}t'd|g}tE}|dz}||z |z|z}d!|z|z|dzz||z dz|d"zzzd"|zz||z||z zzd"|zz|z|dz|zd"zzd"|zzd!|zzd!|zzdz}|} t+|}!t+| }"|t|dkrvt j|t.#}#t j|t.#}$|#tj|$tjn#t'd$|Dt.}%|%jd|krt7d%t jd&'5|%dddf|%dddfk}&dddn #1swxYwY|&r/td(d)d*|&Dz|%dddf|%dddf}$}#t?|%}'tj|#|'dddf<tj|$|'dddf<tA|E|| D+}(tC|(j"D})tC|(j#D}*t'dtH}+t'|t.}t'|tH},d}-t'dt.}.t'dt.}/t'dt.}0t'dt.}1t'dt.}2t'dt.}3t'dt.}4t'dt.}5t'dt.}6t'dt.}7t'dtH}8t'dtH}9t'dtH}:t'dtH};t'dtH}|d"krtKd,d-z|)E}?tM|*Ed.}@tOE|}AtQE||||||}B tSg||E|#|$|?|A|@|B||,|+|!|"|.|/|0|1|2|3|4|5|6|7|8|9|:|;|<||=|>R|+dkr|)E}?tOE|}A|+d/kr.tM|*Ed.}@tQE||||||}B|,|-krR| | t j*E|d"kr-tKd0|,|(j+|?tYj-|@fzt]|+dkrntI|,}-|dkrtK|tI|+d1zt_|+zd2ztKd3|?tKd4|,tKd5|(j+tKd6|(j0tcE|?|@dd/tI|,|(j+|(j0tI|+|tI|+|+dk7 S)8a 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. finite_diff_rel_step : None or array_like, optional If `jac in ['2-point', '3-point', 'cs']` the relative step size to use for numerical approximation of `jac`. The absolute step size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``, possibly adjusted to fit into the bounds. For ``method='3-point'`` the sign of `h` is ignored. If None (default) then step is selected automatically. rrNr')r1r:r3zUnknown constraint type '%s'.z"Constraint %d has no type defined.z/Constraints must be defined using a dictionary.z#Constraint's type must be a string.r4z&Constraint %d has no function defined.r$cfd}|S)Nct|}dvrt||St|d|S)N)rz3-pointcs)rrrel_stepr;r)rrrr;)rr)r!rr#finite_diff_rel_stepr4r$ new_boundss r%cjacz3_minimize_slsqp..cjac_factory..cjac%sr%a44A:::0a$:N8B D D DD 1a :A8B D D DDr&r')r4rWr#rUr$rVs` r% cjac_factoryz%_minimize_slsqp..cjac_factory$sA D D D D D D D D D r&r)r4r$rz$Gradient evaluation required (g & a)z$Optimization terminated successfullyz$Function evaluation required (f & c)z4More equality constraints than independent variablesz*More than 3*n iterations in LSQ subproblemz#Inequality constraints incompatiblez#Singular matrix E in LSQ subproblemz#Singular matrix C in LSQ subproblemz2Rank-deficient equality constraint subproblem HFTIz.Positive directional derivative for linesearchzIteration limit reached) rr c Tg|]$}t|dg|dR%Sr4rrr6r7r!s r% z#_minimize_slsqp..GsK####81U8A#:& #:#:#:;;###r&r1c Tg|]$}t|dg|dR%Srcrdres r%rfz#_minimize_slsqp..IsK&&&$HAeHQ$;6$;$;$;<<&&&r&r:r[rZ)dtypecPg|]#\}}t|t|f$Sr')r)r6lus r%rfz#_minimize_slsqp..bsA,,, 1a&a((.*;*;<,,,r&zDSLSQP Error: the length of bounds is not compatible with that of x0.ignore)invalidz"SLSQP Error: lb > ub in bounds %s.z, c34K|]}t|VdS)N)str)r6bs r%r8z"_minimize_slsqp..ms(&>&>!s1vv&>&>&>&>&>&>r&)r$rr#rUr;z%5s %5s %16s %16s)NITFCOBJFUNGNORMgrYz%5i %5i % 16.6E % 16.6Ez (Exit mode )z# Current function value:z Iterations:z! 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