o 4BiJ@s dZddgZddlZddlmZddlmZmZmZm Z m Z m Z m Z m Z mZmZddlmZmZmZmZmZdd lmZdd lmZmZdd lmZmZdd lmZmZd Z e e e!j"Z#ddZ$dddddddddddddde#dfddZ%dddddddde#ddf ddZ&ddZ'ddZ(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_namespace)expinfzrestructuredtext 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)rnp atleast_2d)xfuncepsilonrjacr&X/var/www/html/Trade-python/venv/lib/python3.10/site-packages/scipy/optimize/_slsqp_py.pyr&s  r&dgư>cs|dur|} | | | | dk||d}d}|tfdd|D7}|tfdd|D7}|r9|d||d f7}|rE|d || d f7}t||f|||d |}|rf|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|] }d|dVqdS)eqtypefunrNr&.0crr&r' zfmin_slsqp..c3r/)ineqr1Nr&r4r7r&r'r8r9r0)r2r3r%rr:)r%bounds constraintsr"r3nitstatusmessage)tuple_minimize_slsqp)r#x0eqconsf_eqconsieqcons f_ieqconsr;fprime fprime_eqconsfprime_ieqconsriteraccr+r, full_outputr$r.optsconsresr&r7r'rHs8p  "Fc E sHt| |d}|}| | sd}t|}t|d|d}|j}||jdr(|j}||||d|dustdt)}tdt)}?tdt)}@|d'krt*d2d3|+}At+|,d4}Bt,|}Ct-||||||}D t.g|||%|&|A|C|B|D||.|-|#|$|0|1|2|3|4|5|6|7|8|9|:|;|<|=|>||?|@R|-dkr|+}At,|}C|-dkr*t+|,d4}Bt-||||||}D|.|/krN| dur;| t /|d'krNt*d5|.|*j0|At12|Bft3|-dkrVnt)|.}/q|dkrt*|t)|-d6t4|-d7t*d8|At*d9|.t*d:|*j0t*d;|*j5t6|A|Bddt)|.|*j0|*j5t)|-|t)|-|-dkd< S)=a Minimize a scalar function of one or more variables using Sequential Least Squares Programming (SLSQP). Options ------- ftol : float Precision goal for the value of f in the stopping criterion. eps : float Step size used for numerical approximation of the Jacobian. disp : bool Set to True to print convergence messages. If False, `verbosity` is ignored and set to 0. maxiter : int Maximum number of iterations. finite_diff_rel_step : None or array_like, optional If `jac in ['2-point', '3-point', 'cs']` the relative step size to use for numerical approximation of `jac`. The absolute step size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``, possibly adjusted to fit into the bounds. For ``method='3-point'`` the sign of `h` is ignored. If None (default) then step is selected automatically. rr)ndimxpz real floatingNr&)r0r:r2z"Constraint %d has no type defined.z/Constraints must be defined using a dictionary.z#Constraint's type must be a string.zUnknown constraint type '%s'.r3z&Constraint %d has no function defined.r%csfdd}|S)Ncs:t|}dvrt||dSt|d|dS)N)rz3-pointcs)rrrel_stepr;r)rrrr;)rr)r"r)r$finite_diff_rel_stepr3r% new_boundsr&r'cjac.s  z3_minimize_slsqp..cjac_factory..cjacr&)r3rW)r$rUr%rV)r3r' cjac_factory-s z%_minimize_slsqp..cjac_factoryr)r3r%rz$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) rRrr c(g|]}t|dg|dRqSr3rrr4r"r&r' P z#_minimize_slsqp..r0crarbrcr4rdr&r'reRrfr:rZrY)dtypecSs g|] \}}t|t|fqSr&)r)r5lur&r&r'rekszDSLSQP 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)r5br&r&r'r8vsz"_minimize_slsqp..)r%rr$rUr;z%5s %5s %16s %16s)NITFCOBJFUNGNORMgz%5i %5i % 16.6E % 16.6Ez (Exit mode )z# Current function value:z Iterations:z! Function evaluations:z! Gradient evaluations:) r"r3r%r=nfevnjevr>r?success)7rrrfloat64isdtypergreshapeastypelenr rrclip isinstancedict enumeratelowerKeyError TypeErrorAttributeError ValueErrorgetsummaprmaxremptyfloatfillnanshape IndexErrorerrstateanyjoinr rrr3gradintprintr_eval_constraint_eval_con_normalsrcopyrsrnormabsrlngevr)Er#rBrr%r;r<r)r*r+r,r-r.rUunknown_optionsrJrKrQrgrNicconctypeerWrX exit_modesmeqmieqmlann1mineqlen_wlen_jwwjwxlxubndsbnderrinfbndsf wrapped_fun wrapped_gradmodemajiter majiter_prevalphaf0gsh1h2h3h4tt0toliexactinconsiresetitermxlinen2n3fxgr6ar&)r$rUr%rVr"r'rAs         > " "                            <             rAcsh|drtfdd|dD}ntd}|dr(tfdd|dD}ntd}t||f}|S)Nr0crarbrcr5rrdr&r'rerfz$_eval_constraint..rr:crarbrcrrdr&r'rerf)r r)r"rNc_eqc_ieqr6r&rdr'rs     rc s|drtfdd|dD}nt||f}|dr*tfdd|dD}nt||f}|dkr;t||f} nt||f} t| t|dgfd} | S)Nr0c$g|]}|dg|dRqSr%rr&rrdr&r'rez%_eval_con_normals..r:crrr&rrdr&r'rerrr)r rr ) r"rNrrrrra_eqa_ieqrr&rdr'rs     r))__doc____all__numpyr scipy.optimize._slsqprrrrrr r r r r r _optimizerrrrr_numdiffr _constraintsrrscipy._lib._array_apirrrr __docformat__rr-_epsilonrrrArrr&r&r&r's: 0 "