o Th@sdZddlZddlZddlmZddlmZddlm 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 X/home/air/segue/gpt/backup/venv/lib/python3.10/site-packages/scipy/optimize/_spectral.pyr srr :0yE>YnF 绽|=?cruzc* s2t|| dvrtd| dd| durfdd} |dur'fdd }fd d }d g}t||||||\}}}}}d }| }||}tg| }d }}d}d} ||}|rhtd|||f|durq|||||||kr~d}d}nt|d| krd| t|}nt|| kr| }| |}| |||} z)| dkrt ||||| d\}!}"}#}$n| dkrt |||||| d\}!}"}#}$}}Wn t yYn)w|"|}%|$|}&t |%|%t |%|&}|"}|$}|#| dkr| |#|d7}qYt|||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 fnormOs z_root_df_sane..fnormcstj|SN)nplinalgnormr)rr r fmeritSsz_root_df_sane..fmeritrrFz&too many function evaluations requiredTziter %d: ||F|| = %g, sigma = %gzsuccessful convergencerr)etar)shapezdf-sane)rsuccessmessagefunnfevnitmethod)r ValueError _wrap_func collectionsdequeprintabsr signrrrvdotappend _wrap_resultr)*funcx0argsftolfatolmaxfevrcallbackdispMr sigma_epssigma_0 line_searchunknown_optionsr#r)fx_kx_shapeF_k is_complexrsigma_kF_0_normprev_fsQC convergedr'F_k_normdr$alphaxpfpFps_ky_krrresultr )rrrr _root_df_sanes1          4  rWc st|}|jt|gR}t|pt|}|}dd<|r=fdd}t|}t|}n fdd}|||||fS)a 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 1-D 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 rrcsbdkr tdd7<t|}t|gR}t|}|}||fSNrr)r _real2complexreshaper asarrayravel _complex2real)rzvrrCr8r#r6r; nfev_listx0_shaper r wrap_funcs z_wrap_func..wrap_funccsVdkr tdd7<|}t|gR}|}||fSrX)rrZr r[r\)rrrCr`r r rcs  )r r[r%r\ iscomplexobjr]) r6r7r#rar;r8rrGrcr r`r r-s (  r-cCs(|rt|}n|}|dur||}|S)zA Convert from real to complex and reshape result arrays. N)rYrZ)rVrGr%r^r r r r5s   r5cCtj|tdtjSN)dtype)r ascontiguousarrayfloatview complex128)rr r r rYrYcCrerf)r rhcomplexrjfloat64)r^r r r r]rlr]) r r rrNNFrNrrr)r r)__doc__r.numpyr scipy.optimizerscipy.optimize._optimizer _linesearchrr ExceptionrrWr-r5rYr]r r r r s      J