I am currently using numpy.polyfit(x,y,deg) to fit a polynomial to experimental data. I would however like to fit a polynomial that uses weighting based on the errors of the points.
I have found scipy.curve_fit which makes use of weights and I suppose I could just set the function, 'f', to the form a polynomial of my desired order, and put my weights in 'sigma', which should achieve my goal.
I was wondering is there another, better way of doing this?
Many Thanks.
For weighted polynomial fitting you can use:
numpy.polynomial.polynomial.polyfit(x, y, deg, rcond=None, full=False, w=weights)
see http://docs.scipy.org/doc/numpy/reference/generated/numpy.polynomial.polynomial.polyfit.html
Important to note that in this function the weights should not be supplied as 1/variance
(which is the usual form in many weighted applications), but as 1/sigma
Although curve_fit
and leastsq
are much more general and powerful optimization tools than polyfit
(in that they can fit just any function), polyfit
has the advantage that it yields an (exact) analytical solution and is therefore probably much faster than iterative approximation methods like curve_fit
and leastsq
- especially in the case of fitting polynomials to multiple sets of y-data (obtained at the same x-vector)
Update: As of numpy version 1.7, numpy.polyfit
also takes weights as an input (which ideally should be supplied as 1/sigma
, not 1/variance
)
Take a look at http://scipy-cookbook.readthedocs.io/items/FittingData.html in particular the section 'Fitting a power-law to data with errors'. It shows how to use scipy.optimize.leastsq with a function that includes error weighting.
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