Re: proposal for new m-file function

[Martin Helm]

Am 22.03.2012 13:17, schrieb Ben Abbott:
> On Mar 22, 2012, at 6:31 AM, Martin Helm wrote:
>
>> Am 22.03.2012 10:43, schrieb Carlo de Falco:
>>>
>>> 2012/3/22 <address@hidden
>>> <mailto:address@hidden>>
>>>
>>>    Message: 2
>>>    Date: Wed, 21 Mar 2012 20:33:01 -0400
>>>    From: Ben Abbott <address@hidden <mailto:address@hidden>>
>>>    To: octave maintainers mailing list <address@hidden
>>>    <mailto:address@hidden>>
>>>    Subject: proposal for new m-file function
>>>    Message-ID: <address@hidden
>>>    <mailto:address@hidden>>
>>>    Content-Type: text/plain; charset="us-ascii"
>>>
>>>    A user's question about fixed points piecewise-linear fitting led
>>>    to the development of a function looks to be a good fit for
>>>    Octave's core.
>>>
>>>
>>>     
>>> https://mailman.cae.wisc.edu/pipermail/help-octave/2012-March/050900.html
>>>
>>>    The idea was to fit a piece-wise polynomial to a set of data.
>>>    After some discussion between myself and Martin Helm, the attached
>>>    ppfit.m was produced. The name was chosen to match the existing
>>>    ppval().
>>>
>>>    The function provides a least-squares fit of a 1D interpolation
>>>    with specified break positions to a set of data.
>>>
>>>    Demos and tests are included.
>>>
>>>    Any concern about adding this to Octave's core ?
>>>
>>>    Ben
>>>
>>>
>>> googling for the name 'ppfit' I found this function:
>>>
>>> https://www.assembla.com/code/zaxxon_scripts/subversion/nodes/trunk/project/scripts/ppfit.m
>>>
>>> which seems to do the same as yours with the additional option of
>>> returning a spline with N continuous derivatives
>>> Would it be possible to add that option to your code?
>>> The license of the linked function looks like BSD so it should be no
>>> problem to get the code from there.
>>> c.
>> Wouldn't it be much cleaner to add that additional fitting options
>> (quadratics and higher order splines) to interp1 (without breaking
>> matlab compatibility of course)?
>> I think that is the place where such functionality should naturally
>> live. I could look at it over the weekend and propose a patch for it.
> Ok. I'll wait on your changeset.
>
> Is it possible for interp1 to return the available methods and whether the 
> underlying interpolants are linear functions ?
>
> Ben
>
>
What do you have in mind, is something like interp1("methods") which
returns some cellarray for example with the method names and a flag
indicating linear/nonlinear an option?
For the linearity there is of course the question in which way linearity
is seen:
(1) The interpolation being a linear operator as a function of the node
values for every given set of nodes or (2) the calculated interpolant
(in a piecewise sense)?
The first one is what I referred to when we talked about why for
pchip/cubic the simple linear system for calculating the least squares
solution fails and the nonlinear solver is essential, the second would
only be true for option "linear" anyway. The first one is what makes
most sense IMHO as an additional information.
I hope I did now not misunderstand your suggestion.

In any case if enhancing interp1 with additional features not existing
in the corresponding matlab function is not what is wanted it is of
course also a possibility to write an extra wrapper function (interp1e =
interp1 enhanced?) which provides the additional features if that is the
preferred way to handle that in octave.

I am not too familiar with the precise philosophy in octave here if ML
compatibility also means = restricted to what ML provides for that
function or if a generalization to provide a superset of features is ok.