9=edZddlZddlZddlmZddlmZddlm Z m Z Gdde Z ddZ ddZddZdZdZdS)z, Spectral Algorithm for Nonlinear Equations N)OptimizeResult)_check_unknown_options)_nonmonotone_line_search_cruz_nonmonotone_line_search_chengceZdZdS)_NoConvergenceN)__name__ __module__ __qualname__8lib/python3.11/site-packages/scipy/optimize/_spectral.pyr r sDrr r :0yE>YnF 绽|=?cruzc 4*+,t|| dvrtd| dd,| *fd} |+,fd},fd}d g}t||||||\}}}+}}d }+*| }||}tj+g| }d }*}d }d } ||}|rt d|||fz| ||||||z|zkrd}d }n t |d| z krd| z tj|z}nt || kr| }| |z}| |||} | dkrt||||| \}!}"}#}$n#| dkrt|||+||| \}!}"}#}$}}n#t$rYnawxYw|"|z }%|$|z }&tj |%|%tj |%|&z }|"}|$}|#+| dkr| |#|dz }Mt|||}'t||}(t|'|||(|d |})|)S)a 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). )chengrzInvalid value z for 'line_search'Ncd|zdzz S)Nrrr )kxFf_0s r eta_strategyz#_root_df_sane..eta_strategyJs!a%!# #rcdz zS)Nrr )rf_knexps rfnormz_root_df_sane..fnormOsT? "rcHtj|zSN)nplinalgnorm)rr"s rfmeritz_root_df_sane..fmeritSsy~~a  $&&rrrFz&too many function evaluations requiredTziter %d: ||F|| = %g, sigma = %gzsuccessful convergencerr)etar)shape)rsuccessmessagefunnfevnit)r ValueError _wrap_func collectionsdequeprintabsr&signrrr vdotappend _wrap_resultr)-funcx0argsftolfatolmaxfevr#callbackdispMr sigma_epssigma_0 line_searchunknown_optionsr)r/fx_kx_shapeF_k is_complexrsigma_kF_0_normprev_fsQC convergedr-F_k_normdr*alphaxpfpFps_ky_krrresultrr!r"s- @@@r _root_df_saner\sBb?++++++K+KKKLLL D $ $ $ $ $ } # # # # # #''''' 3D,6tRvW[,\,\)AsGS#z A CGuSzzHq))G A AI6G05::  N 3q(G6LL M M M   HS#    dXo- - -.GI  w<.wrap_funcs|v%%$&&& aLLLA LLLa  ((22A 44>D>>>**0022Aa  Aq Aa4Krcdkrtdxxdz cc<|}tj|gR}|}||fSr_)r rar&rbrc) rrrHr=r)r;r@rgrhs rriz_wrap_func..wrap_funcs|v%%$&&& aLLLA LLL (##A 44>D>>>**0022Aq Aa4Kr)r&rbr+rc iscomplexobjrd) r;r<r)rgr@r=rrLrirhs ` ```` @rr2r2s#P BBxH 44?T???##))++A$$:(:(:J BIaL          2   !             b(FF1IIq* <r}s))))));;;;;;VVVVVVVV     Y   FJLP