On Mon, Mar 4, 2013 at 5:23 PM, Jaime Fernández del Río < [email protected]> 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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