o EbP@stdZddgZddlZddlmZddlmZmZmZm Z m Z m Z m Z m Z mZmZmZmZmZddlmZmZmZmZmZdd lmZdd lmZmZd Ze e ej Z!d dZ"d dd dd dddd ddddde!dfddZ#d ddd dddde!ddf ddZ$ddZ%ddZ&e'dkr8gdfddZ(ee gdegdgj)Z*ddge*dddf<d)dd Z+d)d!d"Z,d,d$d%Z-d,d&d'Z.d(e+e,d)d*d+e-e.d,d*fZ/e0d-1d.d/e0d0e#e(ed1dge*dd2d3dd\Z2Z3e0d4e$e(ed1dgfd5e*id6d2iZ4e0d71d.d/e0d0e#e(ed1dge+e,e-e.dd2d8dd\Z2Z3e0d4e$e(ed1dgfd9e/id6d2iZ4dSdS):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 concatenatefinfosqrtvstackexpinfisfinite 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 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)rnpZ atleast_2d)xfuncepsilonrjacr$:/usr/lib/python3/dist-packages/scipy/optimize/_slsqp_py.pyr"s  r$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$r% zfmin_slsqp..c3r-)ineqr/Nr$r2r5r$r%r6r7r.r0r1r#rr8)r#bounds constraintsr r1nitstatusmessage)tuple_minimize_slsqp)r!x0Zeqconsf_eqconsZieqcons f_ieqconsr:Zfprime fprime_eqconsfprime_ieqconsriteraccr)r* full_outputr"r,Zoptsconsresr$r5r%rDs8p  "Fc C st| |d}|}| | sd}t||dus t|dkr(tj tjfnt|tddt|t r?|f}ddd}t |D]\}}z|d }Wn3t yg}zt d||d}~wt yw}zt d|d}~wty}zt d |d}~ww|dvrtd |dd |vrtd ||d }|durfdd}||d }|||d ||dddf7<qHdddddddddddd }tttfdd|d D}tttfd!d|d"D}||}td|g}t}|d}||||}d#|||d||d|d$d$|||||d$|||d|d$d$|d#|d#|d}|} t|}!t| }"|dusft|dkrtj|td%}#tj|td%}$|#tj|$tjn|td&d|Dt}%|%jd|krtd'tjd(d)|%dddf|%dddfk}&Wdn 1swY|&rtd*d+d,d-|&D|%dddf|%dddf}#}$t|%}'tj|#|'dddf<tj|$|'dddf<t ||| d.}(t!|(j"})t!|(j#}*tdt$}+t|t}t|t$},d}-tdt}.tdt}/tdt}0tdt}1tdt}2tdt}3tdt}4tdt}5tdt}6tdt}7tdt$}8tdt$}9tdt$}:tdt$};tdt$}|d$krt%d/d0|)}?t&|*d1}@t'|}At(||||||}B t)g|||#|$|?|A|@|B||,|+|!|"|.|/|0|1|2|3|4|5|6|7|8|9|:|;|<||=|>R|+dkr|)}?t'|}A|+d2krt&|*d1}@t(||||||}B|,|-kr2| dur| t*|d$kr2t%d3|,|(j+|?t,-|@ft.|+dkr:nt$|,}-q|dkrkt%|t$|+d4t/|+d5t%d6|?t%d7|,t%d8|(j+t%d9|(j0t1|?|@dd2t$|,|(j+|(j0t$|+|t$|+|+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(x0) * max(1, abs(x0))``, 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$)r.r8r0z"Constraint %d has no type defined.z/Constraints must be defined using a dictionary.z#Constraint's type must be a string.zUnknown constraint type '%s'.r1z&Constraint %d has no function defined.r#csfdd}|S)Ncs:t|}dvrt||dSt|d|dS)N)rz3-pointcs)rrZrel_stepr:r)rrrr:)rr)r r)r"finite_diff_rel_stepr1r# new_boundsr$r%cjac%s  z3_minimize_slsqp..cjac_factory..cjacr$)r1rN)r"rLr#rM)r1r% cjac_factory$s z%_minimize_slsqp..cjac_factoryr)r1r#rz$Gradient evaluation required (g & a)z$Optimization terminated successfullyz$Function evaluation required (f & c)z4More equality constraints than independent variablesz*More than 3*n iterations in LSQ subproblemz#Inequality constraints incompatiblez#Singular matrix E in LSQ subproblemz#Singular matrix C in LSQ subproblemz2Rank-deficient equality constraint subproblem HFTIz.Positive directional derivative for linesearchzIteration limit reached) rr c(g|]}t|dg|dRqSr1rrr2r r$r% G z#_minimize_slsqp..r.crYrZr[r2r\r$r%r]Ir^r8rRrQ)ZdtypecSs g|] \}}t|t|fqSr$)r)r3lur$r$r%r]bszDSLSQP Error: the length of bounds is not compatible with that of x0.ignore)Zinvalidz"SLSQP Error: lb > ub in bounds %s.z, css|]}t|VqdS)N)str)r3br$r$r%r6msz"_minimize_slsqp..)r#rr"rLr:z%5s %5s %16s %16s)ZNITZFCZOBJFUNZGNORMgrPz%5i %5i % 16.6E % 16.6Ez (Exit mode )z# Current function value:z Iterations:z! 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Jacobian of equality constraint rQrrrrr$r$r%jeqcon sr cCst|d|d|gS)z Inequality constraint rrrr r4r$r$r%fieqconsrcCstddggS)z# Jacobian of inequality constraint rrrr$r$r%jieqconsrr.)rr9r8)rz Bounds constraints H-z * fmin_slsqprPT)r:r*rHz * _minimize_slsqpr:r*z% Equality and inequality constraints )rBrDrCrEr*rHr;)5__doc____all__ZnumpyrZscipy.optimize._slsqprrrrrr r r r r rrrr _optimizerrrrrZ_numdiffrZ _constraintsrrZ __docformat__rtr+Z_epsilonrrr@r}r~__name__r1TrrrrrrIr|centerr frJr$r$r$r%s| < "  {