[SciPy-User] Covariance matrix from curve_fit

Aldcroft, Thomas aldcroft@head.cfa.harvard....
Sun Jun 16 05:57:17 CDT 2013


On Sun, Jun 16, 2013 at 3:24 AM, Thomas Robitaille <
thomas.robitaille@gmail.com> wrote:

> Hi everyone,
>
> I have a question regarding the output from the
> scipy.optimize.curve_fit function - in the following example:
>
> """
>     In [1]: import numpy as np
>
>     In [2]: from scipy.optimize import curve_fit
>
>     In [3]: f = lambda x, a, b: a * x + b
>
>     In [4]: x = np.array([0., 1., 2.])
>
>     In [5]: y = np.array([1.2, 4.6, 7.8])
>
>     In [6]: e = np.array([1., 1., 1.])
>
>     In [7]: curve_fit(f, x, y, sigma=e)
>     Out[7]:
>     (array([ 3.3       ,  1.23333333]),
>      array([[ 0.00333333, -0.00333333],
>            [-0.00333333,  0.00555556]]))
>
>     In [8]: curve_fit(f, x, y, sigma=e * 100)
>     Out[8]:
>     (array([ 3.3       ,  1.23333333]),
>      array([[ 0.00333333, -0.00333333],
>            [-0.00333333,  0.00555556]]))
> """
>
> it's clear that the covariance matrix does not take into account the
> uncertainties on the data points. If I do:
>
> """
> popt, pcov = curve_fit(...)
> """
>
> Then pcov[0,0]**0.5 is therefore not the uncertainty on the parameter,
> so I was wondering how this should be scaled to give the actual
> uncertainty on the parameter?
>

There was a long discussion by email and then github on this:

http://mail.scipy.org/pipermail/scipy-user/2011-August/030412.html
https://github.com/scipy/scipy/pull/448

The open pull request has the code to do the scaling you want.

- Tom


>
> Thanks!
> Tom
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