Fitting to system of equations with 3 variables, but only two variable have data

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Wed, 03/01/2023 - 06:49 am

Hello, I have a fitting problem that I can't figure out how to solve in Igor.

I have a system of 2 equations with 3 variables:

P(a)=...

G(a)=...

It is not possible to analytically eliminate "a" and reduce to a single equation, unfortunately. Papers on the topic mention that this problem is indeed solvable with "numerical methods", but don't elaborate on their implementation.

I have data for P and G, but not "a".  Is there a way to fit the system of equations to the (G,P) data using the Igor fitting capabilities, or perhaps a more specialized XOP?  And if not, but you know where I could find a numerical algorithm to find the solution, I'd appreciate being pointed in the right direction (I looked in "Numerical Recipes" and didn't see an algorithm for fitting). I know the 2nd part of this question is not really the purpose of this forum, but figured I'd ask anyway.

Thanks for reading.

Are you looking for an approximate solution for an over-determined system (fitting), or is there an exact solution to be found by root finding? Some more details about what you're trying to do would be helpful.

March 1, 2023 at 09:06 am - Permalink

To me it sounds like you need curve-fitting to do this. Most likely you can look at File - Example Experiments - Curve Fitting - Batch Curve Fitting Demo since I think this is best suited for your problem... BUT that is a wild guess, there are lots of other options on how to fit in Igor that are simpler than this...

I think what tony said is a good approach, give us some more information and maybe we'll be able to help...

Best,

Johan

March 1, 2023 at 11:59 pm - Permalink

If I understand your situation, you might be able to do an implicit fit (DisplayHelpTopic "Fitting Implicit Functions").

March 2, 2023 at 09:32 am - Permalink

Thank you. This is likely to be helpful, but I still have the problem of an unmeasured variable that I don't want to fit ("a" can't be eliminated and I don't have data for it).  I've been a little slow to respond to the reasonable requests for more information because I've discovered more issues as I dig in deeper to the problem. I will hopefully write back soon with enough information to make the problem clear and concrete.

March 2, 2023 at 09:57 am - Permalink

Let's see- if you have a model that allows you to compute P and G given a, if you have values of P and G, you could use a root finder to get a numerically. But I suppose there are model coefficients that you want to estimate from the data, so you don't actually have a complete model to feed into the root finder...

Sounds like an underdetermined system where you need to solve for both a and the coefficients, with some sort of minimum norm to constrain the a values.

Now I've said everything I'm even a little bit competent to say :)

March 2, 2023 at 03:18 pm - Permalink