(phSrSSKrSSKrSSKJr SSKJr SSKJ r J r "SS\ 5r SS jr SS jrSS jrS rS rg)z, Spectral Algorithm for Nonlinear Equations N)OptimizeResult)_check_unknown_options)_nonmonotone_line_search_cruz_nonmonotone_line_search_chengc\rSrSrSrg)_NoConvergence N)__name__ __module__ __qualname____firstlineno____static_attributes__r K/var/www/html/venv/lib/python3.13/site-packages/scipy/optimize/_spectral.pyr r srr c ^*^+^,[U5 U S;a[SU <S35eSm,U cU*4Sjn UcU+U,4SjnU,4SjnS/n[XUUXR5unnnm+nnSnT+m*U nU"U5n[R"T+/U 5nS nT*nS nS nU"U5nU(a[ S UUU4-5 Ub U"UU5 UUU-U-:aSnS nO[ U5SU - :aSU - [R"U5-nO[ U5U :aU nU*U-nU "UUU5n U S:Xa[UUUUU S9un!n"n#n$OU S:Xa[UUUT+UUU S9un!n"n#n$nnW"U- n%W$U- n&[R"U%U%5[R"U%U&5- nU"nU$nW#m+U S:XaURU#5 US- nGM![UUUS9n'[UU5n([U'UUU(USUSS9n)U)$![a M8f=f)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). )chengcruzzInvalid value z for 'line_search'c>TSU-S-- $)Nrrr )kxFf_0s r eta_strategy#_root_df_sane..eta_strategyJs!a%!# #rc>TST- -$)N?r )rf_knexps rfnorm_root_df_sane..fnormOsT? "rcH>[RRU5T-$N)nplinalgnorm)rr!s rfmerit_root_df_sane..fmeritSsyy~~a $&&rrrFz&too many function evaluations requiredTziter %d: ||F|| = %g, sigma = %gzsuccessful convergencerr)etar)shapezdf-sane)rsuccessmessagefunnfevnitmethod)r ValueError _wrap_func collectionsdequeprintabsr&signrrr vdotappend _wrap_resultr)-funcx0argsftolfatolmaxfevr"callbackdispMr sigma_epssigma_0 line_searchunknown_optionsr)r0fx_kx_shapeF_k is_complexrsigma_kF_0_normprev_fsQC convergedr.F_k_normdr+alphaxpfpFps_ky_krrresultrr r!s- @@@r _root_df_saner^sb?+++>+8JKLL D $ } #' 3D,6t7;V-K)AsGS#z A CGSzHq)G A AI6G :  3q(G6LL M   S#  dXo- -.GI  wT ST:a [5eT S==S- ss'[U5RT 5n[R"T"U/TQ765R 5n[ U5nT"U5nXC4$Nrr)r _real2complexreshaper&asarrayravel _complex2real) rzvrrJr?r)r=rB nfev_listx0_shapes r wrap_func_wrap_func..wrap_funcst|v%$&& aLA La ((2A 4>D>*002Aa Aq A4Krc>TST:a [5eTS==S- ss'URT5n[R"T"U/TQ765R 5nT"U5nX!4$ra)r rcr&rdre) rrrJr?r)r=rBrirjs rrkrlsc|v%$&& aLA L (#A 4>D>*002Aq A4Kr)r&rdr,re iscomplexobjrf) r=r>r)rirBr?rrNrkrjs ` ```` @rr4r4sP BBxxH 4?T?#))+A$:(:J BIaL  2  !    (F1Iq <gYniNNF Ng|=rr)r r%)__doc__r5numpyr&scipy.optimizerscipy.optimize._optimizer _linesearchrr Exceptionr r^r4r<rbrfr rrrsS);V Y FJLP