[Numpy-discussion] polyfit with fixed points

[Jaime Fernández del Río]

On Mon, Mar 4, 2013 at 4:53 PM, Aron Ahmadia <aron at ahmadia.net> wrote:

> Interesting, that question would probably have gotten a different response
> on scicomp, it is a pity we are not attracting more questions there!
>
> I know there are two polyfit modules in numpy, one in numpy.polyfit, the
> other in numpy.polynomial, the functionality you are suggesting seems to
> fit in either.
>
> What parameters/functionality are you considering adding?
>

Well, you need two more array-likes, x_fixed and y_fixed, which could
probably be fed to polyfit as an optional tuple parameter:

polyfit(x, y, deg, fixed_points=(x_fixed, y_fixed))

The standard return would still be the deg + 1 coefficients of the fitted
polynomial, so the workings would be perfectly backwards compatible.

An optional return, either when full=True, or by setting an additional
lagrange_mult=True flag, could include the values of the Lagrange
multipliers calculated during the fit.

Jaime



> A
>
>
> On Mon, Mar 4, 2013 at 7:23 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?
>>
>> Thanks,
>>
>> Jaime
>>
>> --
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-- 
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( O.o)
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