Ug3J,dZddgZddlZddlmZddlmZmZmZm Z m Z m Z m Z m Z mZmZddlmZmZmZmZmZdd lmZdd lmZmZdd lmZmZd Ze e ej Z!d Z"dddddddddddddde!dfdZ#dddddddde!ddf 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) zerosarraylinalgappend 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_scalar) atleast_ndarray_namespacezrestructuredtext 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 W/var/www/surfInsights/venv3-11/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$K|] }d|dV dS)ineqr3Nr(r6s r&r9zfmin_slsqp..s-LLq6!T::LLLLLLr'r2)r4r5r%rr;)r%bounds constraintsr"r5nitstatusmessage)tuple_minimize_slsqp)r#x0eqconsf_eqconsieqcons f_ieqconsr<fprime fprime_eqconsfprime_ieqconsriteraccr-r. full_outputr$r0optsconsress ` r&rrEsF` aK  " "D D EIIII&III I IIDELLLLGLLL L LLD# $x   # ## &>  # # $D 4fV&* 4 4.2 4 4C3xUSZXINN3xr'Fc  EFGt| |dz }|}| E| sd}t|}t|d|}|j}||jdr|j}||||dG|t|dkrtj tj fFnt|Ftj GFdFdGt|tr|f}ddd}t|D]\}} |d }|dvrt#d |d zn_#t$$r}t%d |z|d}~wt&$r}t'd |d}~wt($r}t'd |d}~wwxYwd|vrt#d|z|d}|E Ffd}||d}||xx|d||dddfz cc<dddddddddddd }t-t/tGfd |d!D}t-t/tGfd"|d#D}||z}t1d|g}tG}|dz}||z |z|z} d$|z|z|dzz||z dz| d%zzzd%| zz|| z||z zzd%|zz|z|dz|zd%zzd%|zzd$|zzd$|zzdz}!| }"t5|!}#t5|"}$|t|dkrvtj|t8&}%tj|t8&}&|%tj|&tjn#t1d'|Dt8}'|'jd|krtAd(tj!d)*5|'dddf|'dddfk}(dddn #1swxYwY|("r/t#d+d,#d-|(Dz|'dddf|'dddf}&}%tI|'})tj|%|)dddf<tj|&|)dddf<tK|G|| F.}*tM|*j'F}+tM|*j(F},t1dtR}-t1|t8}t1|tR}.d}/t1dt8}0t1dt8}1t1dt8}2t1dt8}3t1dt8}4t1dt8}5t1dt8}6t1dt8}7t1dt8}8t1dt8}9t1dtR}:t1dtR};t1dtR}t1dtR}t1dtR}?t1dtR}@|d%krtUd/d0z|+G}AtW|,Gd1}BtYG|}Ct[G||||||}D t]g||G|%|&|A|C|B|D||.|-|#|$|0|1|2|3|4|5|6|7|8|9|:|;|<|=|>||?|@R|-dkr|+G}AtYG|}C|-dkr.tW|,Gd1}Bt[G||||||}D|.|/krR| | tj/G|d%kr-tUd2|.|*j0|Atcj2|Bfztg|-dkrntS|.}/|dkrtU|tS|-d3zti|-zd4ztUd5|AtUd6|.tUd7|*j0tUd8|*j5tmG|A|BddtS|.|*j0|*j5tS|-|tS|-|-dk9 S):a Minimize a scalar function of one or more variables using Sequential Least Squares Programming (SLSQP). Options ------- ftol : float Precision goal for the value of f in the stopping criterion. eps : float Step size used for numerical approximation of the Jacobian. disp : bool Set to True to print convergence messages. If False, `verbosity` is ignored and set to 0. maxiter : int Maximum number of iterations. finite_diff_rel_step : None or array_like, optional If `jac in ['2-point', '3-point', 'cs']` the relative step size to use for numerical approximation of `jac`. The absolute step size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``, possibly adjusted to fit into the bounds. For ``method='3-point'`` the sign of `h` is ignored. If None (default) then step is selected automatically. rr)ndimxpz real floatingNr()r2r;r4zUnknown constraint type '%s'.z"Constraint %d has no type defined.z/Constraints must be defined using a dictionary.z#Constraint's type must be a string.r5z&Constraint %d has no function defined.r%cfd}|S)Nct|}dvrt||St|d|S)N)rz3-pointcs)rrrel_stepr<r)rrrr<)rr)r"rr$finite_diff_rel_stepr5r% new_boundss r&cjacz3_minimize_slsqp..cjac_factory..cjac+sr%a44A:::0a$:N8B D D DD 1a :A8B D D DDr'r()r5r[r$rYr%rZs` r& cjac_factoryz%_minimize_slsqp..cjac_factory*sA D D D D D D D D D r'r)r5r%rz$Gradient evaluation required (g & a)z$Optimization terminated successfullyz$Function evaluation required (f & c)z4More equality constraints than independent variablesz*More than 3*n iterations in LSQ subproblemz#Inequality constraints incompatiblez#Singular matrix E in LSQ subproblemz#Singular matrix C in LSQ subproblemz2Rank-deficient equality constraint subproblem HFTIz.Positive directional derivative for linesearchzIteration limit reached) rTrr c Tg|]$}t|dg|dR%Sr5rrr7r8r"s r& z#_minimize_slsqp..MsK####81U8A#:& #:#:#:;;###r'r2c Tg|]$}t|dg|dR%Srfrgrhs r&riz#_minimize_slsqp..OsK&&&$HAeHQ$;6$;$;$;<<&&&r'r;r^r])dtypecPg|]#\}}t|t|f$Sr()r)r7lus r&riz#_minimize_slsqp..hsA,,, 1a&a((.*;*;<,,,r'zDSLSQP Error: the length of bounds is not compatible with that of x0.ignore)invalidz"SLSQP Error: lb > ub in bounds %s.z, c34K|]}t|VdS)N)str)r7bs r&r9z"_minimize_slsqp..ss(&>&>!s1vv&>&>&>&>&>&>r')r%rr$rYr<z%5s %5s %16s %16s)NITFCOBJFUNGNORMgz%5i %5i % 16.6E % 16.6Ez (Exit mode )z# Current function value:z Iterations:z! 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