σ Κ½χXc @`sαdZddlmZmZmZddlZddlZddlm Z ddl m Z ddl m Z mZdefd „ƒYZdd d d dded ddddd„ Zdd„Zdd„Zd„Zd„ZdS(s, Spectral Algorithm for Nonlinear Equations i(tdivisiontabsolute_importtprint_functionN(tOptimizeResult(t_check_unknown_optionsi(t_nonmonotone_line_search_cruzt_nonmonotone_line_search_chengt_NoConvergencecB`seZRS((t__name__t __module__(((s7/tmp/pip-build-7oUkmx/scipy/scipy/optimize/_spectral.pyR sg:Œ0βŽyE>gYσψΒn₯iθi g»½ΧΩί|Ϋ=gπ?tcruzc* `s:t|ƒ| dkr,td| fƒ‚nd‰| dkrP‡fd†} n|dkrq‡‡fd†}n‡fd†}dg}t||||||ƒ\}}}‰}}d}ˆ‰| }||ƒ}tjˆg| ƒ}d }ˆ}t}d }xέtrΰ||ƒ}|r6td |||fƒn|dk rR|||ƒn||||krvd }t}Pnt |ƒd | kr¦d | t j |ƒ}nt |ƒ| krΑ| }n| |}| |||ƒ} y|| dkrt ||||d| ƒ\}!}"}#}$nB| dkrYt |||ˆ||d| ƒ\}!}"}#}$}}nWntk rnPnX|"|}%|$|}&t j|%|%ƒt j|%|&ƒ}|"}|$}|#‰| dkrΣ|j|#ƒn|d 7}qWt||d|ƒ}'t||ƒ}(td|'d|d|d|(d|dd|ƒ})|)S(s› Solve nonlinear equation with the DF-SANE method Options ------- ftol : float, optional Relative norm tolerance. fatol : float, optional Absolute norm tolerance. Algorithm terminates when ``||func(x)|| < fatol + ftol ||func(x_0)||``. fnorm : callable, optional Norm to use in the convergence check. If None, 2-norm is used. maxfev : int, optional Maximum number of function evaluations. disp : bool, optional Whether to print convergence process to stdout. eta_strategy : callable, optional Choice of the ``eta_k`` parameter, which gives slack for growth of ``||F||**2``. Called as ``eta_k = eta_strategy(k, x, F)`` with `k` the iteration number, `x` the current iterate and `F` the current residual. Should satisfy ``eta_k > 0`` and ``sum(eta, k=0..inf) < inf``. Default: ``||F||**2 / (1 + k)**2``. sigma_eps : float, optional The spectral coefficient is constrained to ``sigma_eps < sigma < 1/sigma_eps``. Default: 1e-10 sigma_0 : float, optional Initial spectral coefficient. Default: 1.0 M : int, optional Number of iterates to include in the nonmonotonic line search. Default: 10 line_search : {'cruz', 'cheng'} Type of line search to employ. 'cruz' is the original one defined in [Martinez & Raydan. Math. Comp. 75, 1429 (2006)], 'cheng' is a modified search defined in [Cheng & Li. IMA J. Numer. Anal. 29, 814 (2009)]. Default: 'cruz' References ---------- .. [1] "Spectral residual method without gradient information for solving large-scale nonlinear systems of equations." W. La Cruz, J.M. Martinez, M. Raydan. Math. Comp. **75**, 1429 (2006). .. [2] W. La Cruz, Opt. Meth. Software, 29, 24 (2014). .. [3] W. Cheng, D.-H. Li. IMA J. Numer. Anal. **29**, 814 (2009). tchengR s"Invalid value %r for 'line_search'ic`sˆd|dS(Nii((tktxtF(tf_0(s7/tmp/pip-build-7oUkmx/scipy/scipy/optimize/_spectral.pyt eta_strategyLsc`s ˆdˆS(Ngπ?((R(tf_ktnexp(s7/tmp/pip-build-7oUkmx/scipy/scipy/optimize/_spectral.pytfnormQsc`stjj|ƒˆS(N(tnptlinalgtnorm(R(R(s7/tmp/pip-build-7oUkmx/scipy/scipy/optimize/_spectral.pytfmeritUsigπ?s&too many function evaluations requiredsiter %d: ||F|| = %g, sigma = %gssuccessful convergenceitetatshapeR tsuccesstmessagetfuntnfevtnit(R R N(Rt ValueErrortNonet _wrap_funct collectionstdequetFalsetTruetprinttabsRtsignRRRtvdottappendt _wrap_resultR(*tfunctx0targstftoltfatoltmaxfevRtcallbacktdisptMRt sigma_epstsigma_0t line_searchtunknown_optionsRRtftx_ktx_shapetF_kt is_complexR tsigma_ktF_0_normtprev_fstQtCt convergedRtF_k_normtdRtalphatxptfptFpts_kty_kR Rtresult((RRRs7/tmp/pip-build-7oUkmx/scipy/scipy/optimize/_spectral.pyt _root_df_sanest1     -       * :   " c `sγtj|ƒ}|j‰tjˆ|ˆŒƒjƒ}tj|ƒpQtj|ƒ}|jƒ}dˆd<|r©‡‡‡‡‡‡fd†}t|ƒ}t|ƒ}n‡‡‡‡‡‡fd†}||ˆˆ|ƒ||fS(s« Wrap a function and an initial value so that (i) complex values are wrapped to reals, and (ii) value for a merit function fmerit(x, f) is computed at the same time, (iii) iteration count is maintained and an exception is raised if it is exceeded. Parameters ---------- func : callable Function to wrap x0 : ndarray Initial value fmerit : callable Merit function fmerit(f) for computing merit value from residual. nfev_list : list List to store number of evaluations in. Should be [0] in the beginning. maxfev : int Maximum number of evaluations before _NoConvergence is raised. args : tuple Extra arguments to func Returns ------- wrap_func : callable Wrapped function, to be called as ``F, fp = wrap_func(x0)`` x0_wrap : ndarray of float Wrapped initial value; raveled to 1D and complex values mapped to reals. x0_shape : tuple Shape of the initial value array f : float Merit function at F F : ndarray of float Residual at x0_wrap is_complex : bool Whether complex values were mapped to reals iic`sˆdˆkrtƒ‚nˆdcd7s   ” J