[SciPy-Dev] splev

[Anne Archibald]

On 8 July 2010 08:59, Charles R Harris <charlesr.harris at gmail.com> wrote:
>
>
> 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
>> >
>> >
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>> >
>> >
>>
>> 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.

If you're going to do this it may make sense to offer a third option
that raises an exception when outside the interval. There are again
floating-point issues, but there are certainly times when it would be
useful to find out right away that one had supplied bogus values.

Anne

> Chuck
>
>
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