Hi,
I'm a little bit desperated. I googled for days to find an appropriate way
to calculate the absolute errors of parameters of non-linear fits. I found
different sites which suggest different, sometimes more or less similar
ways. But the results don't make sense. Here is a simple example:
from pylab import *
from scipy.optimize import curve_fit
def f(x,a,b):
return a*x+b
def fit(n=1000):
x,y=array([0,1,1]),array([1,2,4])
xf=[(min(x)+i*(max(x)-min(x))/float(n)) for i in range(0,int(n)+1)]
a,acov=curve_fit(f,x,y)
yf=[f(*tuple([i]+list(a))) for i in xf]
meansq=sum([pow(y[i]-f(x[i],a[0],a[1]),2)/(len(x)) for i in
range(0,len(x))])
redchi2=sum([pow(y[i]-f(x[i],a[0],a[1]),2)/(len(x)-len(a)) for i in
range(0,len(x))])
print 'standard dev:',sqrt(diag(acov))
print 'abs. meansq err.:',[acov[i][i]*sqrt(meansq) for i in
range(0,len(a))]
print 'abs. reduced meansq err.:',[acov[i][i]*sqrt(redchi2) for i in
range(0,len(a))]
fit()
I included 3 ways I found. The used arrays have 3 points, where for x=1 I
give 2 different y values. I would say,
a=2+/-1, b=1+/-0,
but no way yields to a similar result! How can I trust this function on more
complicated, really non-linear functions? Or is simply this example wrong?
Or are the methods not right?
I'm very thankful for any help!
Best regards,
André
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