On Mon, Mar 4, 2013 at 5:23 PM, Jaime Fernández del Río <jaime.frio@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.