Ei^SrSS/rSSKrSSKJr SSKJr SSK J r J r J r J r JrJr SS KJr SS KJrJr SS KJr SS KJr SS KJr SSKJr Sr\R>"\R@"\RB5RD5r#Sr$SSSSSSSSSSSSSS\#S4Sjr%SSSSSSSS\#SSS4 Sjr&S\S\S\'S\(S\(4 Sjr)S\S\S\'S\(S\(4 Sjr*g)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_wrap_callback)approx_derivative)old_bound_to_new_arr_to_scalar)array_namespace)array_api_extra)_call_callback_maybe_halt)NDArrayzrestructuredtext encF[XSUUS9n[R"U5$)aC Approximate the Jacobian matrix of a callable function. Parameters ---------- x : array_like The state vector at which to compute the Jacobian matrix. func : callable f(x,*args) The vector-valued function. epsilon : float The perturbation used to determine the partial derivatives. args : sequence Additional arguments passed to func. Returns ------- An array of dimensions ``(lenf, lenx)`` where ``lenf`` is the length of the outputs of `func`, and ``lenx`` is the number of elements in `x`. Notes ----- The approximation is done using forward differences. 2-point)methodabs_stepargs)rnp atleast_2d)xfuncepsilonrjacs U/home/mande/repo/quber/.venv/lib/python3.13/site-packages/scipy/optimize/_slsqp_py.pyrr$s(6 DI!% 'C == dgư>cJ^ UbUn [US5nU U U U S:gUUS.nSnU[U 4SjU55- nU[U 4SjU55- nU(a USX8T S.4- nU(a US XYT S.4- n[XT 4XvUS .UD6nU(aUS US US USUS4$US $)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 `. rr)maxiterftoliprintdispepscallbackr"c30># UH nSUTS.v M g7f)eqtypefunrNr".0crs r fmin_slsqp..sI&Q448&c30># UH nSUTS.v M g7f)ineqr-Nr"r0s r r3r4sLGq6!T:Gr5r,)r.r/rrr7)rbounds constraintsrr/nitstatusmessage)r tuple_minimize_slsqp)rx0eqconsf_eqconsieqcons f_ieqconsr8fprime fprime_eqconsfprime_ieqconsriteraccr'r( full_outputrr*optsconsress ` r rrFs` h0HaK  "D D EI&I IIDELGL LLD $x # # & # # $D 4f&* 4.2 4C3xUSZXINN3xr!Fc ^^ ^5^6[U5 UnU m5U (dSn[U5n[R"UR U5SUS9nUR nUR URS5(a URnURURUU5S5nUb[U5S:Xa"[R*[R4m6O [U5m6[R"UT6ST6S5n[U[ 5(aU4nSSS.n[#U5HunnUS R%5nUS;a['S US S 35eSU;a['S US35eUR/S5nUcU5U UU64SjnU"US5nUU==USUUR/SS5S.4- ss'M SSSSSSSSSSS S!. n[1[3[US"Vs/sH&n[R4"US"U/USQ765PM( sn55n[1[3[US#Vs/sH&n[R4"US"U/USQ765PM( sn55nUU-n[U5nUb[U5S:Xar[R6"U[8S$9n [R6"U[8S$9n!U R;[R<5 U!R;[R<5 GOF[R>"UV"V#s/sHun"n#[AU"5[AU#54PM sn#n"[85n$U$RBSU:wa [ES%5e[RF"S&S'9 U$SS2S4U$SS2S4:n%SSS5 W%RI5(a%['S(S)RKS*U%55S+35eU$SS2S4RM5U$SS2S4RM5n!n [RN"U$5)n&[R<U U&SS2S4'[R<U!U&SS2S4'[QUUTX*T T6U S,9n'[SU'RTT65n([SU'RVT65n)0S-U_S.S/_S0S/_S1S/_S2S/_S3S/_S4S/_S5S/_S6S/_S7S/_S8S9U-_S:S_S;S_S[YU5_S?S_UUSUS@.En*USA:a[[SBSCSDSESCSDSFSGSDSHSG35 [R\"[_USAU--SA-S5/[R`S$9n+UUS--SA-SIU-U--USJU--SK-U-- SLU--SMU-U--SNU--UU--SO-n,US:XaU,SAU-US--- n,[R\"[_U,S5[R S$9n-U("U5n.U)"U5n/[R\"[_SUSAU--SA-5/[R S$9n0[R\"[_SU5U/[R SPSQ9n1[R\"[_SU5/[R S$9n2[cU1UUUU5 [eU2UUUU5 Sn3[gU*U.U/U1U2UU0U U!U-U+5 U*SRS:Xa U'RUU5n.[eU2UUUU5 U*SRS:Xa U'RWU5n/[cU1UUUU5 U*S=U3:aiU b0[i[RL"U5U.SS9n4[kU U45(aOPUSA:a0[[U*S=STSDU'RlSTSDU.SUSD[oU/5SU35 [qU*SR5S:waOU*S=n3MUS:ab[[UU*SRSVU*SRSW3-5 [[SXU.5 [[SYU*S=5 [[SZU'Rl5 [[S[U'Rr5 [iUU.U/U*S=U'RlU'RrU*SRUU*SRU*SRS:HU0SUS\9 $![(an[)S US 35UeSnAf[*an[+S5UeSnAf[,an[+S5UeSnAff=fs snfs snfs sn#n"f!,(df  GN=f)]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, optional Maximum number of iterations. Default value is 100. 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. Hanson, 1995, "Solving Least Squares Problems", SIAM, Philadelphia, PA. rr)ndimxpz real floatingNr")r,r7r.zUnknown constraint type 'z'.z Constraint z has no type defined.z/Constraints must be defined using a dictionary.z#Constraint's type must be a string.r/z has no function defined.rc>^UUUUU4SjnU$)Nc `>[UT5nTS;a[TUTUTTS9$[TUSTUTS9$)N)rz3-pointcs)rrrel_stepr8r)rrrr8)r r)rrrfinite_diff_rel_stepr/r new_boundss r cjac3_minimize_slsqp..cjac_factory..cjacasT%a4A::0a$:N8B DD 1a :A8B DDr!r")r/rWrrUrrVs` r cjac_factory%_minimize_slsqp..cjac_factory`s D D r!r)r/rrz$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) rPrr r,r7)dtypezDSLSQP Error: the length of bounds is not compatible with that of x0.ignore)invalidzSLSQP Error: lb > ub in bounds z, c38# UHn[U5v M g7f)N)str)r1bs r r3"_minimize_slsqp..s)A&Q#a&&&s.)rrrrUr8workersrHalphagf0gsh1h2h3h4tt0tolg$@exact inconsistentresetrGitermaxline)mmeqmodenr[NITz>5 FCOBJFUNz>16GNORMr\r^r`rbra#F)rcorderr})rr/5dz16.6Ez (Exit mode )z# Current function value:z Iterations:z! 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