B &]\2 @sdZddlmZmZmZddlZddlZddlm Z ddl m Z ddl m Z mZGdd d eZdddZdddZdddZddZddZdS) z, Spectral Algorithm for Nonlinear Equations )divisionabsolute_importprint_functionN)OptimizeResult)_check_unknown_options)_nonmonotone_line_search_cruz_nonmonotone_line_search_chengc@s eZdZdS)_NoConvergenceN)__name__ __module__ __qualname__rr7lib/python3.7/site-packages/scipy/optimize/_spectral.pyr sr r:0yE>YnF 绽|=?cruzc* sBt|| dkrtd| fd| dkr6fdd} |dkrLfdd}fd d }d g}t||||||\}}}}}d }| }||}tg| }d }}d }d}x\||}|rtd|||f|dk r|||||||krd}d}Pt|d| kr"d| t|}nt|| kr4| }| |}| |||} yV| dkrrt ||||| d\}!}"}#}$n,| dkrt |||||| d\}!}"}#}$}}Wnt k rPYnX|"|}%|$|}&t |%|%t |%|&}|"}|$}|#| dkr| |#|d7}qWt|||d}'t||}(t|'|||(|d |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). )chengrz"Invalid value %r for 'line_search'Ncsd|dS)Nrrr)kxF)f_0rr eta_strategyLsz#_root_df_sane..eta_strategycs dS)Ng?r)r)f_knexprrfnormQsz_root_df_sane..fnormcstj|S)N)npZlinalgZnorm)r)rrrfmeritUsz_root_df_sane..fmeritrg?Fz&too many function evaluations requiredziter %d: ||F|| = %g, sigma = %gzsuccessful convergenceTrr)etar)shape)rZsuccessmessageZfunnfevZnit)r ValueError _wrap_func collectionsdequeprintabsr!Zsignrr r Zvdotappend _wrap_resultr)*funcx0argsZftolZfatolmaxfevr callbackZdispMrZ sigma_epsZsigma_0Z line_searchZunknown_optionsr"r&fZx_kZx_shapeZF_k is_complexrZsigma_kZF_0_normZprev_fsQCZ convergedr%ZF_k_normdr#ZalphaZxpfpZFpZs_kZy_krrresultr)rrrr _root_df_sanest1       &    r<c st|}|jt|f}t|p:t|}|}dd<|rxfdd}t|}t|}nfdd}|||||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 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 rrcs`dkrtdd7<t|}t|f}t|}|}||fS)Nrr)r _real2complexreshaper!asarrayravel _complex2real)rzvrr5)r1r"r/r2 nfev_listx0_shaperr wrap_funcs z_wrap_func..wrap_funccsTdkrtdd7<|}t|f}|}||fS)Nrr)r r>r!r?r@)rrr5)r1r"r/r2rDrErrrFs  )r!r?r$r@Z iscomplexobjrA) r/r0r"rDr2r1rr6rFr)r1r"r/r2rDrErr(s(    r(cCs(|rt|}n|}|dk r$||}|S)zA Convert from real to complex and reshape result arrays. N)r=r>)r;r6r$rBrrrr.s   r.cCstj|tdtjS)N)dtype)r!ascontiguousarrayfloatviewZ complex128)rrrrr=sr=cCstj|tdtjS)N)rG)r!rHcomplexrJZfloat64)rBrrrrAsrA) rrrrNNFrNrrr)r)N)__doc__Z __future__rrrr)Znumpyr!Zscipy.optimizerZscipy.optimize.optimizerZ linesearchrr Exceptionr r<r(r.r=rArrrrs    J