M/Ph>dZddlZddlmZddlmZdZ d d ZdS) a Created on Mon Mar 18 15:48:23 2013 Author: Josef Perktold TODO: - test behavior if nans or infs are encountered during the evaluation. now partially robust to nans, if increasing can be determined or is given. - rewrite core loop to use for...except instead of while. N)optimize)HolderFh㈵>d c ||} } ||}n||dkrtd|}nd}||}n-||dkrtd|}ntd|dz }|t||dz}||| ||ksJ||g|R}||g|R}tjtj||z dkr|dkr|d krd }||g|R}||k}||z }tj|r;d D])}|||zz}||g|R}tj|sn*td tj|r;d D])}|||zz}||g|R}tj|sn*td ||k}|s||}}| | } } d}| 5|dkr/|} || g|Rdkr | } | | z} ||krn|d z }|| g|Rdk | 5|dkr/|} || g|Rdkr | } | | z} ||krn|d z }|| g|Rdk ||krI||g|R}||g|R}tj|r#tj|rtdt j|| | ||| | }| r_|d}t|d j |d j |d j |d j |d j |||f| | f| }||fS|S)a9 find the root of a function in one variable by expanding and brentq Assumes function ``func`` is monotonic. Parameters ---------- func : callable function for which we find the root ``x`` such that ``func(x) = 0`` low : float or None lower bound for brentq upp : float or None upper bound for brentq args : tuple optional additional arguments for ``func`` xtol : float parameter x tolerance given to brentq start_low : float (positive) or None starting bound for expansion with increasing ``x``. It needs to be positive. If None, then it is set to 1. start_upp : float (negative) or None starting bound for expansion with decreasing ``x``. It needs to be negative. If None, then it is set to -1. increasing : bool or None If None, then the function is evaluated at the initial bounds to determine wether the function is increasing or not. If increasing is True (False), then it is assumed that the function is monotonically increasing (decreasing). max_it : int maximum number of expansion steps. maxiter_bq : int maximum number of iterations of brentq. factor : float expansion factor for step of shifting the bounds interval, default is 10. full_output : bool, optional If full_output is False, the root is returned. If full_output is True, the return value is (x, r), where x is the root, and r is a RootResults object. Returns ------- x : float root of the function, value at which ``func(x) = 0``. info : RootResult (optional) returned if ``full_output`` is True. attributes: - start_bounds : starting bounds for expansion stage - brentq_bounds : bounds used with ``brentq`` - iterations_expand : number of iterations in expansion stage - converged : True if brentq converged. - flag : return status, 'converged' if brentq converged - function_calls : number of function calls by ``brentq`` - iterations : number of iterations in ``brentq`` Notes ----- If increasing is None, then whether the function is monotonically increasing or decreasing is inferred from evaluating the function at the initial bounds. This can fail if there is numerically no variation in the data in this range. In this case, using different starting bounds or directly specifying ``increasing`` can make it possible to move the expansion in the right direction. If Nrzstart_upp needs to be positiveg?zstart_low needs to be negativeggV瞯<g:0yE>)g?g?g?z{could not determine whether function is increasing based on starting interval. specify increasing or change starting boundszzcould not determine whether function isincreasing based on starting interval. specify increasing or change starting boundszsmax_it reached the function values at boths bounds are NaN change the starting bounds, set boundsor increase max_it)argsxtolmaxiter full_output) root iterationsfunction_calls convergedflagiterations_expand start_bounds brentq_bounds increasing) ValueErrorminmaxnpabsisnanrbrentqrrrrrr)funclowuppr r start_low start_upprmax_it maxiter_bqfactorrleftrightsuslf_lowf_uppdeltafractionsl_su_n_itresvalinfos ]/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tools/rootfinding.pybrentq_expandingr7sWTs%D     q===>> >       q===>> >  b2g   { R"W   #+J,>BwwwwR$R$ 6"&'' ( (5 0 0R2XX"''BDOdOOOE%-JR 8E?? +. + +8e++S(4(((xE!"*+++ 8E?? +- + +8e++S(4(((xE!"*+++ em "RBTe D |ad4$!##E FNDv~~ AID d4$!## }qd5 4   1$$D VOEv~~ AID d5 4   1$$ v~~R$R$ 8E?? 3rx 3233 3 /$e$#Z&1 3 3 3C!fQ1v(q60!f&Q"b-!   Dy ) NNrrNNNrrrF) __doc__numpyrscipyrstatsmodels.tools.testingrDEBUGr7rr8r6r>sy  ,,,,,, >B@D8:!&HHHHHHr8