# [SciPy-User] fitting cosine with curve_fit - problem with frequency

Brian Blais bblais@bryant....
Wed Oct 12 19:23:58 CDT 2011

```Hello,

So I am trying to fit some data that is a mixture of oscillations, so I figured I'd try to do a "toy" problem...and that problem is stumping me (full code at the bottom).  I generate data like:

x=pylab.linspace(0,50,100)
y=cos(x/2)+pylab.randn(len(x))*.1

and fit a model like:

def m1(t,a,b,c):
return a*cos(b*t+c)

with scipy.optimize.curve_fit.  It seems as if the method used in curve_fit doesn't like oscillatory data, especially when estimating the frequency.  Unless my initial guess for the frequency is *very* close to the right answer (i.e. I need the right answer already to get the answer), it doesn't even get close.

Is there a better way to fit this sort of a function?  Should I do an fft, pick off frequencies, and use those as the initial estimates?  Am I doing something wrong?

any ideas, or references to places I can read about it, would be great!

thanks,

Brian Blais

--
Brian Blais
bblais@bryant.edu
http://web.bryant.edu/~bblais
http://bblais.blogspot.com/

#=====================code below====================
import pylab
from scipy import optimize
from numpy import *

def m1(t,a,b,c):
return a*cos(b*t+c)

x=pylab.linspace(0,50,100)
y=cos(x/2)+pylab.randn(len(x))*.1

pylab.figure(1)
pylab.clf()
pylab.plot(x,y,'o-')

func=m1
p0=[5,0.9,2]

popt, pcov = optimize.curve_fit(func, x, y,
p0=p0,  # initial guess
)

xf=linspace(x[0],x[-1],1000)
yf=func(xf,*popt)

pylab.plot(xf,yf,'.-')

pylab.draw()

```