B î&]\2ã@sTddlmZmZmZddlmZmZmZmZm Z m Z ddl m Z dgZ ddd„ZdS)é)ÚdivisionÚprint_functionÚabsolute_import)ÚzerosÚasarrayÚeyeÚpoly1dÚhstackÚr_)ÚlinalgÚpadeNc Csxt|ƒ}|dkr0t|ƒd|}|dkr0tdƒ‚|dkr@tdƒ‚||}|t|ƒdkr`tdƒ‚|d|d…}t|d|dƒ}t|d|fdƒ}x:td|dƒD](}|d|…ddd… ||d|…f<q¤WxBt|d|dƒD],}||||…ddd… ||dd…f<qäWt||fƒ}t ||¡}|d|d…} t d ||dd…f} t | ddd…ƒt | ddd…ƒfS) a‘ Return Pade approximation to a polynomial as the ratio of two polynomials. Parameters ---------- an : (N,) array_like Taylor series coefficients. m : int The order of the returned approximating polynomial `q`. n : int, optional The order of the returned approximating polynomial `p`. By default, the order is ``len(an)-m``. Returns ------- p, q : Polynomial class The Pade approximation of the polynomial defined by `an` is ``p(x)/q(x)``. Examples -------- >>> from scipy.interpolate import pade >>> e_exp = [1.0, 1.0, 1.0/2.0, 1.0/6.0, 1.0/24.0, 1.0/120.0] >>> p, q = pade(e_exp, 2) >>> e_exp.reverse() >>> e_poly = np.poly1d(e_exp) Compare ``e_poly(x)`` and the Pade approximation ``p(x)/q(x)`` >>> e_poly(1) 2.7166666666666668 >>> p(1)/q(1) 2.7179487179487181 Nérz.Order of q must be smaller than len(an)-1.z&Order of p must be greater than 0.z0Order of q+p must be smaller than len(an).Údéÿÿÿÿgð?) rÚlenÚ ValueErrorrrÚranger r Zsolver r) ZanÚmÚnÚNZAkjZBkjÚrowÚCZpqÚpÚq©rú6lib/python3.7/site-packages/scipy/interpolate/_pade.pyr s,&(,  )N)Z __future__rrrZnumpyrrrrr r Zscipyr Ú__all__r rrrrÚs