[SciPy-User] Global Curve Fitting of 2 functions to 2 sets of data-curves

josef.pktd@gmai... josef.pktd@gmai...
Thu Jun 10 13:27:13 CDT 2010

On Thu, Jun 10, 2010 at 4:05 AM, Sebastian Haase <seb.haase@gmail.com> wrote:
> Hi,
> so far I have been using scipy.optimize.leastsq to satisfy all my
> curve fitting needs.
> But now I am thinking about "global fitting" - i.e. fitting multiple
> dataset with shared parameters
> (e.g. ref here:
> http://www.originlab.com/index.aspx?go=Products/Origin/DataAnalysis/CurveFitting/GlobalFitting)
> I have looked here (http://www.scipy.org/Cookbook/FittingData) and here
> (http://docs.scipy.org/doc/scipy/reference/optimize.html)
> Can someone provide an example  ? Which of the routines of
> scipy.optimize are "easiest" to use ?
> Finally, I'm thinking about a "much more" complicated fitting task:
> fitting two sets of datasets with two types of functions.
> In total I have 10 datasets to be fit with a function f1, and 10 more
> to be fit with function f2. Each function depends on 6 parameters
> A1,A2,A3, r1,r2,r3.
> A1,A2,A3 should be identical ("shared") between all 20 sets, while
> r1,r2,r3 should be shared between the i-th set of type f1 and the i-th
> set of f2.
> Last but not least it would be nice if one could specify constrains
> such that r1,r2,r3 >0 and A1+A2+A3 == 1 and 0<=Ai<=1.
> ;-)  Is this too much ?
> Thanks for any help or hints,

Assuming your noise or error terms are uncorrelated, I would still use
optimize.leastsq or optimize.curve_fit using a function that stacks
all the errors in one 1-d array. If there are differences in the noise
variance, then weights/sigma per function as in curve_fit can be used.

common parameter restrictions across functions can be encoded by using
the same parameter in several (sub-)functions.

In this case, I would impose the constraints through reparameterization, e.g
r1 = exp(r1_), ...
A1 = exp(A1_)/(exp(A1_) + exp(A2_) + 1)
A1 = exp(A2_)/(exp(A1_) + exp(A2_) + 1)
A1 = 1/(exp(A1_) + exp(A2_) + 1)

(maybe it's more tricky to get the standard deviation of the original
parameter estimate)

or as an alternative, calculate the total weighted sum of squared
errors and use one of the constraint fmin in optimize.


> Sebastian Haase
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