Question

I’d love to reproduce a plot similar to this:

_{(source: brleader.com)}

I mean I have a set of data points and I’d love to have a curve which shows the average trend.

I tried adding random noise to the function y=2x

  from scipy import interpolate

  x=arange(0,1,1e-3)
  noise=np.random.random(len(x))
  y=2*x+noise

And then I used some of the Scipt function to interpolate data

  xnew=arange(0,1,1e-1)
  f=interpolate.UnivariateSpline(x,y)
  g=interpolate.interp1d(x,y)
  plot(x,y,'ro',xnew,f(xnew),'-',xnew,g(xnew),'--')
  show()

But the curve I get hardly resemble y=2*x. I’d love to have a smooth curve which average the data. Which method/function can I use?

Answer 1

One of the reasons why the curve doesn’t look like y=2*x (I think it does, but that’s subject to opinion) is that your noise is large compared to the average change in y. If you try something like:

noise=0.1*np.random.random(len(x))

(i.e make the noise smaller) or

y=5*x**2+noise

(i.e make the change in y larger), you’ll see that the interpolation tracks the data better.

You might also want to check out:

http://www.scipy.org/Cookbook/SignalSmooth