[SciPy-User] help interpreting univariate spline

[David Warde-Farley]

Elliot Hallmark wrote:
> Hi there,
>
> I am wanting to use a scipy interpolation routine to generate
> polynomials approximating function I have sampled.  these polynomials
> will be solved in c (cython), so I need to extract the coefficencts
> from the interpolation method and pass them to a c function for root
> finding.
>
> using UnivariateSpline I ran this code:
>
> import numpy as np
> from scipy.interpolate import splrep, UnivariateSpline
>
> x = np.linspace(1, 10, 100)
> y = 1/x     #approximate a hyperbola
> g = UnivariateSpline(x, y, w=None, k=3, s=.0005)
> print g.get_knots()
> print g.get_coeffs()
>
> import matplotlib.pyplot as plt
> plt.clf()
> ax = plt.subplot(121)
> l1, = ax.plot(x, y, "rs", ms=10)
> l2, = ax.plot(x, g(x), "bo")
> plt.show()
>
>
>
>
> and the output was:
> [  1.           2.18181818   3.27272727   5.54545455  10.        ]
>
> [ 0.98462432  0.66575572  0.423       0.25461626  0.13929847  0.11763985
>   0.09929961]
>
> That is 5 knots and 7 coefficients for a degree=3 spline.  naively, I
> was expecting 4 coefficents for each interval between knots.
>
> how can I construct a piecewise polynomial from this output? or can I?
>   
You might do well to look through the original documentation for Paul 
Dierckx's FITPACK, which scipy.interpolate wraps.

A textbook he wrote that describes some of the routines is available on 
Google Books: http://tinyurl.com/2djtlnl

David