a j @s~dZddlZddlZddlmZddlmZddlm Z m Z Gddde Z dddZ dddZdddZddZddZdS)z, Spectral Algorithm for Nonlinear Equations N)OptimizeResult)_check_unknown_options)_nonmonotone_line_search_cruz_nonmonotone_line_search_chengc@s eZdZdS)_NoConvergenceN)__name__ __module__ __qualname__r r >E:\soccer\ml_env\Lib\site-packages\scipy/optimize/_spectral.pyr srr :0yE>YnF 绽|=?cruzc* sDt|| dvr td| dd| dur8fdd} |durNfdd }fd d }d g}t||||||\}}}}}d }| }||}tg| }d }}d}d}||}|rtd|||f|dur|||||||krd}d}qt|d| kr"d| t|}nt|| kr4| }| |}| |||} zV| dkrrt ||||| d\}!}"}#}$n,| dkrt |||||| d\}!}"}#}$}}Wnt yYqYn0|"|}%|$|}&t |%|%t |%|&}|"}|$}|#| dkr| |#|d7}qt|||d}'t||}(t|'|||(|d |dd})|)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'Ncsd|dS)Nrrr )kxF)f_0r r eta_strategyJsz#_root_df_sane..eta_strategycs dS)Nrr r)f_knexpr r fnormOsz_root_df_sane..fnormcstj|S)N)npZlinalgZnormr)rr r fmeritSsz_root_df_sane..fmeritrrFz&too many function evaluations requiredziter %d: ||F|| = %g, sigma = %gzsuccessful convergenceTrr)etar)shapezdf-sane)rsuccessmessageZfunnfevnitmethod)r ValueError _wrap_func collectionsdequeprintabsrsignrrrZvdotappend _wrap_resultr)*funcx0argsZftolZfatolmaxfevrcallbackZdispMrZ sigma_epsZsigma_0Z line_searchZunknown_optionsr r%fZx_kZx_shapeZF_k is_complexrZsigma_kZF_0_normZprev_fsQCZ convergedr$ZF_k_normdr!alphaZxpfpZFpZs_kZy_krrresultr )rrrr _root_df_sanes1               r?c st|}|jt|gR}t|p.wrap_funccsVdkrtdd7<|}t|gR}|}||fSr@)rrBrrCrD)rrr7rHr r rJs  )rrCr"rDZ iscomplexobjrE) r1r2r rIr4r3rr8rJr rHr r)s(    r)cCs(|rt|}n|}|dur$||}|S)zA Convert from real to complex and reshape result arrays. N)rArB)r>r8r"rFr r r r0s   r0cCstj|tdtjSN)Zdtype)rascontiguousarrayfloatviewZ complex128)rr r r rAsrAcCstj|tdtjSrK)rrLcomplexrNZfloat64)rFr r r rEsrE) r r rrNNFrNrrr)r )N)__doc__r*numpyrZscipy.optimizerZscipy.optimize._optimizerZ _linesearchrr Exceptionrr?r)r0rArEr r r r s    J