• Support PF! Buy your school textbooks, materials and every day products Here!

Global fitting with shared parameters

  • Thread starter raul_l
  • Start date
  • #1
105
0

Homework Statement



Hi
I'm looking for an algorithm that can perform a fitting procedure on many curves simultaneously. Lets say, for example, that I have 3 exponential decay curves with 3 different decay times but they all share the same initial amplitude. So I have to find a fit for 4 parameters (in reality I'm dealing with much more complicated systems).

Homework Equations



Levenberg-Marquardt:
[tex] \delta a = \frac{1}{\bold{J}^T\bold{J}+\lambda \bold{diag}(\bold{J}^T\bold{J})} \bold{J}^T \boldsymbol{\chi} [/tex]
with the Jacobian
[tex] J_{ij} = \frac{\partial f(x_{i};\bold a)}{\partial a_{j}} [/tex]
where f is the fitting function, x are datapoints and a are the parameters to be fitted.
[tex] \boldsymbol{\chi} [/tex] is defined as
[tex] \chi_i = \frac{y_i - f(x_{i};\bold a)}{\sigma_i} [/tex]

The Attempt at a Solution



So far I've been using the Levenberg-Marquardt algorithm to find fits for single curves. But how to implement global curve fitting when some of the parameters are shared?

I guess a straightforward approach would be to construct a global function that takes the whole data set (constructed from all the curves) as argument. For example, if a single curve consists of 10 000 data points and I'm fitting for 5 parameters, I would need to build Jacobian with dimensions 10 000 x 5 for single-curve-fitting. Now assume I have 10 curves with 2 of those 5 parameters shared. Then I would need a 100 000 x 32 Jacobian which is pretty massive.

My question is this. Are there any algorithms especially designed for multi-curve-fitting or do I have to use the usual single-curve-fitting techniques with a few modifications?
I hope anyone has had experience in that area.
 

Answers and Replies

  • #2
Hi,

I have the same problem and was wondering if you solved it by now. If so, could you please throw some light on what you did.

Thanks,
 

Related Threads on Global fitting with shared parameters

Replies
1
Views
1K
  • Last Post
Replies
4
Views
1K
Replies
3
Views
974
Replies
1
Views
1K
Replies
0
Views
952
  • Last Post
Replies
2
Views
360
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
2
Views
784
Replies
7
Views
2K
  • Last Post
Replies
1
Views
655
Top