[SciPy-user] curve_fit failure when supplying uncertainties
Sat Mar 7 19:20:07 CST 2009
On Sat, Mar 7, 2009 at 7:18 PM, ElMickerino <firstname.lastname@example.org> wrote:
> I think I've identified a problem with curve_fit which occurs when one
> attempts to fit normally distributed data with a gaussian. From the
> documentation of curve_fit, it appears that 'sigma' should be the
> uncertainties on the y-values of the data; however, the following example
> (see attached code) should make it clear that there's a problem with this.
> My best guess is that the sigma are actually weights (=1.0/sigma). Can
> anyone confirm or deny this? Seems like from the name it should be
> uncertainties but from the behavior of the code it appears otherwise.
> Also, I was wondering if there's a way to supply asymmetric errors to
> curve_fit (or for that matter, to leastsqr or any wrapper thereof).
> Thanks very much,
> http://www.nabble.com/file/p22380378/testFit.py testFit.py
> View this message in context: http://www.nabble.com/curve_fit-failure-when-supplying-uncertainties-tp22380378p22380378.html
> Sent from the Scipy-User mailing list archive at Nabble.com.
> SciPy-user mailing list
sigma is the vector of standard deviations for the observations. The
weights in the least squares objective function are 1/sigma.
Essentially it is a heteroscedastic non-linear generalized least
In your case err contains zeros, which means the variance is zero and
the weight 1/sigma for these observations would be infinite. curve_fit
cannot handle zero standard deviation. Infinite standard deviation
works because then the weight becomes zero.
If you force your err to be strictly positive, then this works, e.g.
>>> curve_fit(gaus, centers, data, sigma=1e-6+err)
(array([ 1.91520894e+03, 1.68957830e-01, 6.19128687e-01]),
array([[ 3.03590409e-09, 5.11571694e-18, -6.69243949e-18],
[ 5.11571694e-18, 4.43479563e-16, 6.18126633e-17],
[ -6.69243949e-18, 6.18126633e-17, 3.02641036e-17]]))
I haven't looked closely at the rest of your file, so I'm not sure
about the interpretation of your err
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