[SciPy-Dev] splev

[Charles R Harris]

On Thu, Jul 8, 2010 at 12:02 AM, Joshua Holbrook <josh.holbrook at gmail.com>wrote:

> On Wed, Jul 7, 2010 at 8:19 PM, Charles R Harris
> <charlesr.harris at gmail.com> wrote:
> >
> >
> > On Wed, Jul 7, 2010 at 10:06 PM, Anne Archibald <
> aarchiba at physics.mcgill.ca>
> > wrote:
> >>
> >> On 7 July 2010 23:45, Charles R Harris <charlesr.harris at gmail.com>
> wrote:
> >> > Hi All,
> >> >
> >> > I opened ticket #1223 because the values returned by splev are not
> zero
> >> > for
> >> > arguments outside of the interval of definition. Because splev
> evaluates
> >> > b-splines, which all have compact support, I think zero is the correct
> >> > value
> >> > for such arguments. However, I also find that some tests assume that
> >> > splev
> >> > extrapolates the interpolating polynomials defined in the first and
> last
> >> > spans, which is what splev currently does.  Consequently I thought it
> >> > worth
> >> > bringing the topic up on the list for discussion before making the
> >> > commit
> >> > that changes the behavior.
> >>
> >> Please do not make this change. The extrapolation you get now is ugly,
> >> as polynomial extrapolation always is, but a discontinuity is
> >> considerably uglier. Remember that the arguments and range are both
> >> floating-point, so that roundoff error can easily move an argument
> >> outside the range; if extrapolation is used this is unimportant, but
> >> if the spline flatly drops to zero this will produce wildly wrong
> >> answers.
> >>
> >
> > Well, for my purposes extrapolation really screws things up. Note that
> the
> > b-splines at the ends are in fact c_{-1}, i.e., discontinuous, and the
> next
> > b-spline in has a discontinuous 1'st derivative, so on and so forth. The
> > discontinuities are mathematically correct, b-splines aren't polynomials.
> > Maybe we can add a keyword?
> >
> > Chuck
> >
> >
> > _______________________________________________
> > SciPy-Dev mailing list
> > SciPy-Dev at scipy.org
> > http://mail.scipy.org/mailman/listinfo/scipy-dev
> >
> >
>
> I personally agree with Anne. While discontinuities may be technically
> correct, I think the current behavior is more forgiving. If this is
> noted in the docs, I say things are g2g.
>
> Chuck: Is checking the interval yourself prohibitive?
>
>
It's inconvenient and time consuming. I'm leaning towards adding a keyword
so that the user can choose one or the other behavior, say
extrapolation=True, which will not impact current usage.

Chuck
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