Tjaz Brelih Tjaz Brelih - 10 months ago 32
Python Question

Most accurate way to interpolate data and find the peak?

The data I have is always on a second degree polynomial (quadratic function). I want to find the peak of the interpolated function as accurately as possible.

Data sample points

So far I've been using

and then extract the peak value using
and a simple
loop. Although you can use a large number of newly generated samples in
you can still be more precise using the derivative of the fitted polynomial.
I haven't found a way to do that using

Now the only function I've found that returns the fitted polynomial coefficients is
, but this fitted function is quite inaccurate (most of the time the function doesn't even go through the data points).

<code>interp1d</code> and <code>polyfit</code> functions

I've tried using
and the fitted function seems to be quite accurate and it's very simple to get the derivative spline and its root.

Other polynomial fitting functions (
, ...) state that they are not computing polynomial coefficients for reasons of numerical stability.

How accurate is
and its derivatives, or are there any better options out there?


In the end I went with polyfit. Although the fitted function didn't go exactly through the data points the end result was still good. From the returned coefficients I got the desired x and y coordinates of the peak.