3 h O@sndZddgZddlZddlmZddlmZmZmZm Z m Z m Z m Z m Z mZmZmZmZmZddlmZmZmZdd lmZdd lmZmZd Ze e ejZd dZ fdfdfdddfd ddddedfddZ!fddfd dddeddf ddZ"ddZ#ddZ$e%dkrjdddddgfddZ&ee gdegdgj'Z(ddge(dddf<d6ddZ)d7d d!Z*d8d#d$Z+d9d%d&Z,d'e)e*d:d(d)e+e,d;d(fZ-e.d*j/d+d,e.d-e!e&eddge)e*e+e,dd.d4dd\Z0Z1e.d0e"e&ed?dgfd5e-id2d.iZ2dS)@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)approx_derivative)old_bound_to_new_arr_to_scalarzrestructuredtext encGst||d||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. z2-point)methodabs_stepargs)rnpZ atleast_2d)xfuncepsilonrjacr!5/tmp/pip-build-riy7u7_k/scipy/scipy/optimize/slsqp.pyr!s dgư>cs|dk r |} | | | | dk||d}f}|tfdd|D7}|tfdd|D7}|rr|d||df7}|r|d || df7}t||f|||d |}|r|d |d |d |d|dfS|d SdS)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)maxiterftoliprintdispepscallbackc3s|]}d|dVqdS)eq)typefunrNr!).0c)rr!r" szfmin_slsqp..c3s|]}d|dVqdS)ineq)r+r,rNr!)r-r.)rr!r"r/sr*)r+r,r rr0)r bounds constraintsrr,nitstatusmessage)tuple_minimize_slsqp)rx0Zeqconsf_eqconsZieqcons f_ieqconsr1Zfprime fprime_eqconsfprime_ieqconsriteraccr&r' full_outputrr)optsconsresr!)rr"rCs,p  "Fc A0 st| |d}|}| | s d}t|tr0|f}ffd}xt|D]\}}y|dj}WnTtk r~td|YnNtk rtdYn4tk rtdYnX|dBkrtd |dd |krtd ||j d }|dkrfdd}||d }|||d ||j dfdf7<qFWdCdddddddddddddddd d!d"d#d$d%i }t |j |dkst |dkrt j t jf}nt|}t j|d|dttt fd&d'|dD}ttt fd(d'|d D}||}td|gj}t }|d}||||}d|||d||d|dd|||||d|||d|dd|d|d|d}|} t|}!t| }"|dkst |dkrt j|td)}#t j|td)}$|#jt j|$jt jntd*d'|Dt}%|%jd|kr:td+t jd,d-&|%dddf|%dddfk}&WdQRX|&jrtd.d/jd0d1|&D|%dddf|%dddf}#}$t|%}'t j|#|'dddf<t j|$|'dddf<t ||| |d2}(tdt!})t|t}t|t!}*d}+tdt},tdt}-tdt}.tdt}/tdt}0tdt}1tdt}2tdt}3tdt}4tdt}5tdt!}6tdt!}7tdt!}8tdt!}9tdt!}:tdt!}tdt!};tdt!}<|dkrt"d3dD|(j#}=ytt j$|=}=Wn"ttfk r0td8YnXt%|(j&d9}>t'|}?t(||||||}@xt)|||#|$|=|?|>|@||*|)|!|"|,|-|.|/|0|1|2|3|4|5|6|7|8|9|:||;|< |)dkr|(j#}=t'|}?|)dEkrt%|(j&d9}>t(||||||}@|*|+kr<| dk r| t j*|dkrft.|)dkrLPt!|*}+qbW|dkrt"|t!|)d;t/|)d<t"d=|=t"d>|*t"d?|(j+t"d@|(j0t1|=|>ddFt!|*|(j+|(j0t!|)|t!|)|)dkdA S)Ga Minimize a scalar function of one or more variables using Sequential Least Squares Programming (SLSQP). Options ------- ftol : float Precision goal for the value of f in the stopping criterion. eps : float Step size used for numerical approximation of the Jacobian. disp : bool Set to True to print convergence messages. If False, `verbosity` is ignored and set to 0. maxiter : int Maximum number of iterations. finite_diff_rel_step : None or array_like, optional If `jac in ['2-point', '3-point', 'cs']` the relative step size to use for numerical approximation of `jac`. The absolute step size is computed as ``h = rel_step * sign(x0) * max(1, abs(x0))``, possibly adjusted to fit into the bounds. For ``method='3-point'`` the sign of `h` is ignored. If None (default) then step is selected automatically. rr)r*r0r+z"Constraint %d has no type defined.z/Constraints must be defined using a dictionary.z#Constraint's type must be a string.r*r0zUnknown constraint type '%s'.r,z&Constraint %d has no function defined.r Ncsfdd}|S)Ncs0dkrt||dSt|d|dSdS)N2-point3-pointcs)rrZrel_step)rrr)rCrDrE)r)rr)rfinite_diff_rel_stepr,r r!r"cjacs  z3_minimize_slsqp..cjac_factory..cjacr!)r,rG)rrFr )r,r" cjac_factorysz%_minimize_slsqp..cjac_factoryr)r,r rz$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 linesearch zIteration limit reachedcs&g|]}t|df|dqS)r,r)r)r-r.)rr!r" Bsz#_minimize_slsqp..cs&g|]}t|df|dqS)r,r)r)r-r.)rr!r"rQDs)ZdtypecSs g|]\}}t|t|fqSr!)r)r-lur!r!r"rQ]szDSLSQP 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)r-br!r!r"r/hsz"_minimize_slsqp..)r rrrFr1z%5s %5s %16s %16sNITFCOBJFUNGNORMz'Objective function must return a scalargz%5i %5i % 16.6E % 16.6Ez (Exit mode )z# Current function value:z Iterations:z! 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Gradient evaluations:) rr,r r3nfevZnjevr4r5success)r*r0)rXrYrZr[r_r_)2r isinstancedict enumeratelowerKeyError TypeErrorAttributeError ValueErrorgetr flattenlenrrrZclipsummaprmaxremptyfloatfillnanshape IndexErrorZerrstateanyjoinrrintprintr,ZasarrayrZgrad_eval_constraint_eval_con_normalsrcopyr]rZnormabsrVZngevr)Arr8rr r1r2r$r%r&r'r(r)rFZunknown_optionsr=r>rAZicconctyperGrHZ exit_modesZ new_boundsmeqmieqmlanZn1ZmineqZlen_wZlen_jwwZjwZxlZxubndsZbnderrZinfbndZsfmodeZmajiterZ majiter_prevalphaZf0Zgsh1h2h3h4tt0ZtolZiexactZinconsZiresetZitermxlineZn2Zn3Zfxgr.ar!)rrFr rr"r7s        x  * "                                           r7csh|dr$tfdd|dD}ntd}|drPtfdd|dD}ntd}t||f}|S)Nr*cs&g|]}t|df|dqS)r,r)r)r-r|)rr!r"rQsz$_eval_constraint..rr0cs&g|]}t|df|dqS)r,r)r)r-r|)rr!r"rQs)r r)rrAZc_eqZc_ieqr.r!)rr"rxs   rxc s|dr$tfdd|dD}n t||f}|drTtfdd|dD}n t||f}|dkrvt||f} n t||f} t| t|dgfd} | S)Nr*cs"g|]}|df|dqS)r rr!)r-r|)rr!r"rQsz%_eval_con_normals..r0cs"g|]}|df|dqS)r rr!)r-r|)rr!r"rQsrr)r rr ) rrArrrr~rZa_eqZa_ieqrr!)rr"rys     ry__main__rKrIcCsdt|d|d|dd|d|dd|d|d|d|d|d|dS)z Objective function rrIrrJrK)r)rrr!r!r"r,s Nr,g?g?cCst|dd|d|gS)z Equality constraint rrIr)r)rrWr!r!r"feqconsrcCstd|ddggS)z! Jacobian of equality constraint rIrr)r)rrWr!r!r"jeqconsr cCst|d|d|gS)z Inequality constraint rr)r)rr.r!r!r"fieqcon srcCstddggS)z# Jacobian of inequality constraint r)r)rr.r!r!r"jieqconsrr*)r+r,r rr0z Bounds constraints H-z * fmin_slsqpT)r1r'r?z * _minimize_slsqpr1r'z% Equality and inequality constraints )r9r;r:r<r'r?r2)r)r)r)r)r)rr_r_r_r_)3__doc____all__ZnumpyrZscipy.optimize._slsqprrrrrr r r r r rrrroptimizerrrZ_numdiffrZ _constraintsrrZ __docformat__ror(Z_epsilonrrr7rxry__name__r,TrrrrrrArwcenterrfrBr!r!r!r"sb < " t