[Numpy-discussion] polyfit with fixed points

[Charles R Harris]

On Mon, Mar 4, 2013 at 5:23 PM, Jaime Fernández del Río <
jaime.frio at gmail.com> wrote:

> A couple of days back, answering a question in StackExchange (
> http://stackoverflow.com/a/15196628/110026), I found myself using
> Lagrange multipliers to fit a polynomial with least squares to data, making
> sure it went through some fixed points. This time it was relatively easy,
> because some 5 years ago I came across the same problem in real life, and
> spent the better part of a week banging my head against it. Even knowing
> what you are doing, it is far from simple, and in my own experience very
> useful: I think the only time ever I have fitted a polynomial to data with
> a definite purpose, it required that some points were fixed.
>
> Seeing that polyfit is entirely coded in python, it would be relatively
> straightforward to add support for fixed points. It is also something I
> feel capable, and willing, of doing.
>
>  * Is such an additional feature something worthy of investigating, or
> will it never find its way into numpy.polyfit?
>  * Any ideas on the best syntax for the extra parameters?
>
>
There are actually seven versions of polynomial fit, two for the usual
polynomial basis, and one each for Legendre, Chebyshev, Hermite, Hermite_e,
and Laguerre ;)

How do you propose to implement it? I think Lagrange multipliers is
overkill, I'd rather see using the weights (approximate) or change of
variable -- a permutation in this case -- followed by qr and lstsq.

Chuck
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