# [Numpy-discussion] confused about univaritespline

Charles R Harris charlesr.harris@gmail....
Tue Nov 20 16:29:27 CST 2012

```On Tue, Nov 20, 2012 at 12:30 PM, Neal Becker <ndbecker2@gmail.com> wrote:

> Pauli Virtanen wrote:
>
> > 20.11.2012 21:11, Neal Becker kirjoitti:
> >> import numpy as np
> >> import matplotlib.pyplot as plt
> >>
> >> ibo = np.array ((12, 14, 16, 18, 20, 22, 24, 26, 28, 29, 29.8, 30.2))
> >> gain_deriv = np.array ((0, 0,  0,  0,   0, 0,  .2, .4, .5, .5, 0,
>  -2))
> >>
> >> import scipy.interpolate
> >> s = scipy.interpolate.UnivariateSpline(ibo, gain_deriv, s=0.1)
> >>
> >> xs = linspace(12, 31, 100)
> >> gain = np.vectorize (lambda x: s.integral (12, x)) (xs)
> >>
> >> plot (xs, s(xs))
> >> plot (xs, gain)
> >
> >>From fitpack/splint.f:
> >
> > c           s(x) is considered to be identically zero outside
> > c           the interval (t(k+1),t(n-k)).
> >
> > Not documented in the Python wrapper, though.
> >
>
> Ah, thanks!  Bitten one more by the fact that spline is not meant for
> extrapolation, which here I had done inadvertantly.
>
> IMO, if spline isn't intended to be used to extrapolate, I'd prefer it to
> throw.
>

That can be tricky at the ends due to round off errors. I added a flag to
splev for this back when:

outine splev evaluates in a number of points x(i),i=1,2,...,m
c  a spline s(x) of degree k, given in its b-spline representation.
c
c  calling sequence:
c     call splev(t,n,c,k,x,y,m,e,ier)
c
c  input parameters:
c    t    : array,length n, which contains the position of the knots.
c    n    : integer, giving the total number of knots of s(x).
c    c    : array,length n, which contains the b-spline coefficients.
c    k    : integer, giving the degree of s(x).
c    x    : array,length m, which contains the points where s(x) must
c           be evaluated.
c    m    : integer, giving the number of points where s(x) must be
c           evaluated.
c    e    : integer, if 0 the spline is extrapolated from the end
c           spans for points not in the support, if 1 the spline
c           evaluates to zero for those points, and if 2 ier is set to
c           1 and the subroutine returns.

Chuck
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