U |e#@s@ddlmZmZmZmZmZmZddlmZdgZ dddZ dS))zerosasarrayeyepoly1dhstackr_)linalgpadeNc Cszt|}|dkr0t|d|}|dkr0td|dkr@td||}|t|dkr`td|d|d}t|d|d|jd}t|d|f|jd}td|dD](}|d|ddd ||d|f<qt|d|dD],}||||ddd ||ddf<qt||f}t ||}|d|d} t d ||ddf} t | dddt | dddfS) 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)-1-m``. Returns ------- p, q : Polynomial class The Pade approximation of the polynomial defined by `an` is ``p(x)/q(x)``. Examples -------- >>> import numpy as np >>> 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 Nrz.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).)dtypeg?) rlen ValueErrorrr rrangerrsolverr) anmnNZAkjZBkjrowCZpqpqrT/var/www/website-v5/atlas_env/lib/python3.8/site-packages/scipy/interpolate/_pade.pyr s,'&*  )N) numpyrrrrrrscipyr__all__r rrrrs