Coverage for /home/martinb/.local/share/virtualenvs/camcops/lib/python3.6/site-packages/scipy/interpolate/_pade.py : 15%

Hot-keys on this page
r m x p toggle line displays
j k next/prev highlighted chunk
0 (zero) top of page
1 (one) first highlighted chunk
1from numpy import zeros, asarray, eye, poly1d, hstack, r_
2from scipy import linalg
4__all__ = ["pade"]
6def pade(an, m, n=None):
7 """
8 Return Pade approximation to a polynomial as the ratio of two polynomials.
10 Parameters
11 ----------
12 an : (N,) array_like
13 Taylor series coefficients.
14 m : int
15 The order of the returned approximating polynomial `q`.
16 n : int, optional
17 The order of the returned approximating polynomial `p`. By default,
18 the order is ``len(an)-m``.
20 Returns
21 -------
22 p, q : Polynomial class
23 The Pade approximation of the polynomial defined by `an` is
24 ``p(x)/q(x)``.
26 Examples
27 --------
28 >>> from scipy.interpolate import pade
29 >>> e_exp = [1.0, 1.0, 1.0/2.0, 1.0/6.0, 1.0/24.0, 1.0/120.0]
30 >>> p, q = pade(e_exp, 2)
32 >>> e_exp.reverse()
33 >>> e_poly = np.poly1d(e_exp)
35 Compare ``e_poly(x)`` and the Pade approximation ``p(x)/q(x)``
37 >>> e_poly(1)
38 2.7166666666666668
40 >>> p(1)/q(1)
41 2.7179487179487181
43 """
44 an = asarray(an)
45 if n is None:
46 n = len(an) - 1 - m
47 if n < 0:
48 raise ValueError("Order of q <m> must be smaller than len(an)-1.")
49 if n < 0:
50 raise ValueError("Order of p <n> must be greater than 0.")
51 N = m + n
52 if N > len(an)-1:
53 raise ValueError("Order of q+p <m+n> must be smaller than len(an).")
54 an = an[:N+1]
55 Akj = eye(N+1, n+1, dtype=an.dtype)
56 Bkj = zeros((N+1, m), dtype=an.dtype)
57 for row in range(1, m+1):
58 Bkj[row,:row] = -(an[:row])[::-1]
59 for row in range(m+1, N+1):
60 Bkj[row,:] = -(an[row-m:row])[::-1]
61 C = hstack((Akj, Bkj))
62 pq = linalg.solve(C, an)
63 p = pq[:n+1]
64 q = r_[1.0, pq[n+1:]]
65 return poly1d(p[::-1]), poly1d(q[::-1])