Yh;]hdZddgZddlZddlmZddlmZddl m Z m Z m Z m Z mZdd lmZdd lmZmZdd lmZdd lmZdd lmZdZejejejjZ dZ!dddddddddddddde dfdZ"dddddddde dddf dZ#dedede$de%de%f dZ&dedede$de%de%f 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)norm)OptimizeResult_check_unknown_options_prepare_scalar_function_clip_x_for_func _check_clip_x)approx_derivative)old_bound_to_new_arr_to_scalar)array_namespace)array_api_extra)NDArrayzrestructuredtext 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)r np atleast_2d)xfuncepsilonrjacs j/var/www/tools.fuzzalab.pt/emblema-extractor/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)aC 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$K|] }d|dV dS)eqtypefunrNr .0crs r zfmin_slsqp..s-IIQ4488IIIIIIrc3$K|] }d|dV dS)ineqr+Nr r.s rr1zfmin_slsqp..s-LLq6!T::LLLLLLrr*)r,r-rrr3)rbounds constraintsrr-nitstatusmessage)tuple_minimize_slsqp)rx0eqconsf_eqconsieqcons f_ieqconsr4fprime fprime_eqconsfprime_ieqconsriteraccr%r& full_outputrr(optsconsress ` rrrEsF` aK  " "D D EIIII&III I IIDELLLLGLLL L LLD# $x   # ## &>  # # $D 4fV&* 4 4.2 4 4C3xUSZXINN3xrFc  012t||}| 0| sd}t|}tj||d|}|j}||jdr|j}|| ||d2|t|dkrtj tj f1nt|1tj21d1d2t|t r|f}ddd}t#|D]\}} |d }|dvrt'd |d d n`#t($r}t)d |d |d}~wt*$r}t+d|d}~wt,$r}t+d|d}~wwxYwd|vrt'd |d|d}|0 1fd}||d}||xx|d||dddfz cc<ddddddddddd d! }t1t3t2fd"|d#D}t1t3t2fd$|d%D}||z}t2}|t|dkrvtj|t6&}tj|t6&}|tj|tjnRtjd'|Dt6} | jd|krtAd(tj!d)*5| dddf| dddfk}!dddn #1swxYwY|!"r0t'd+d,#d-|!Dd.| dddf$| dddf$}}tj%| }"tj||"dddf<tj||"dddf<tM|2|| 1| /}#tO|#j(1}$tO|#j)1}%id0|d1d2d3d2d4d2d5d2d6d2d7d2d8d2d9d2d:d2d;d<|zd=dd>dd?dd@ddA|dBd||d|dC}&|dDkrtUdEdFdGdHdFdGdIdJdGdKdJtj+tY|dD|zzdDzdgtj-&}'||dzzdDzdL|z|zz|dM|zzdNz|zz dO|zzdP|z|zzdQ|zz||zzdRz}(|dkr|(dD|z|dzzz }(tj+tY|(dtj&})|$2}*|%2}+tj+tYd|dD|zzdDzgtj&},tj+tYd||gtjdST}-tj+tYd|gtj&}.t]|-2|||t_|.2|||d}/ ta|&|*|+|-|.2|,|||)|' |&dVdkr(|#(2}*t_|.2||||&dVdkr(|#)2}+t]|-2||||&d@|/kr[| | tj$2|dDkr6tU|&d@dWdG|#j1dWdG|*dXdGte|+dXtg|&dVdkrn |&d@}/ |dkrxtU||&dVdY|&dVdZztUd[|*tUd\|&d@tUd]|#j1tUd^|#j4tk2|*|+|&d@|#j1|#j4|&dV||&dV|&dVdk|,d|_ S)`a Minimize a scalar function of one or more variables using Sequential Least Squares Programming (SLSQP). Parameters ---------- ftol : float Precision target for the value of f in the stopping criterion. This value controls the final accuracy for checking various optimality conditions; gradient of the lagrangian and absolute sum of the constraint violations should be lower than ``ftol``. Similarly, computed step size and the objective function changes are checked against this value. Default is 1e-6. 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. workers : int, map-like callable, optional A map-like callable, such as `multiprocessing.Pool.map` for evaluating any numerical differentiation in parallel. This evaluation is carried out as ``workers(fun, iterable)``. .. versionadded:: 1.16.0 Returns ------- res : OptimizeResult The optimization result represented as an `OptimizeResult` object. In this dict-like object the following fields are of particular importance: ``x`` the solution array, ``success`` a Boolean flag indicating if the optimizer exited successfully, ``message`` which describes the reason for termination, and ``multipliers`` which contains the Karush-Kuhn-Tucker (KKT) multipliers for the QP approximation used in solving the original nonlinear problem. See ``Notes`` below. See also `OptimizeResult` for a description of other attributes. Notes ----- The KKT multipliers are returned in the ``OptimizeResult.multipliers`` attribute as a NumPy array. Denoting the dimension of the equality constraints with ``meq``, and of inequality constraints with ``mineq``, then the returned array slice ``m[:meq]`` contains the multipliers for the equality constraints, and the remaining ``m[meq:meq + mineq]`` contains the multipliers for the inequality constraints. The multipliers corresponding to bound inequalities are not returned. See [1]_ pp. 321 or [2]_ for an explanation of how to interpret these multipliers. The internal QP problem is solved using the methods given in [3]_ Chapter 25. Note that if new-style `NonlinearConstraint` or `LinearConstraint` were used, then ``minimize`` converts them first to old-style constraint dicts. It is possible for a single new-style constraint to simultaneously contain both inequality and equality constraints. This means that if there is mixing within a single constraint, then the returned list of multipliers will have a different length than the original new-style constraints. References ---------- .. [1] Nocedal, J., and S J Wright, 2006, "Numerical Optimization", Springer, New York. .. [2] Kraft, D., "A software package for sequential quadratic programming", 1988, Tech. Rep. DFVLR-FB 88-28, DLR German Aerospace Center, Germany. .. [3] Lawson, C. L., and R. J. 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