inverse prediction order 2 or 3 polynomials

[petergod]

Well this is a very nice implementation indeed. I wish my code would be that nice on the first go.

I use the LM algorithm as it was a simple way to implement a wider solution where the basic regression model we use is the logistic one. I know it is a bit over the top to use it for polynomial or even linear fitting !!

But it works fine.

I like your example very much.

Thanks for your help

[altenbach]

Of course for an arbitrary model, you can no longer use my solution. Here's what I would do:

Lets assume that your function is always increasing in the range you are using it and the desired function value is in the range you just fitted. (This is often a valid assumption, e.g. for a calibration curve). In this case, you would just get an estimate using threshold array from your best fit data, followed by a few Newton Raphson iterations to get the value with near infinite precision.

I think I have an old newton-raphson implementation that calls the model function via reference node, wIth a model type compatible with the nonlinerar fitting (VI model). This way your entire code can be made nearly model-free and will adapt automatically as you change the fitting model. I don't have access to my old code at the moment, maybe I can find it over the weekend.

(I even once fitted a function that required newton-raphson internally for the model calculation, but that's a different story.)

If your data is dense enough, a simple interpolation of the best fit data array would probably be sufficient. LabVIEW has all the tools for that. 🙂

[shoneill]

Altenbach,

if you have a look at the Lev-Mar rroutines shipped with LV 8.2.X you'll see that they're included the option of calling a model by reference in their implementation.  This REALLY improves performance over the old text-based solution only.

To the best of my knowledge, the NI version is also using a Newthon-Raphson optimisation, no?  At least a similar approach if I'm not mistaken (Which I may well be of course).

Shane.

[altenbach]

Shane,

I think you misuderstood my point. I am very aware of the 8.0+ Lev-Mar implementation and even gave a talk and demos about it at the last two NI week meetings in Austin. 🙂

My point was to get the inverse function of the model function once you have the best fitting parameters. This is a seperate task.

The model function calculates y=f(x). We now want to calculate x for any given f(x).

The model function calculates y= f( x, [Ai] ), where [Ai] are given model paramters.

Lev-Mar finds the best set of [Ai] such that [y(fit)] best matches [y(experimetal)].

Newton-raphson calculates x=f'( y, [Ai] ) where [Ai] are the same given model paramters, e.g. obtained via Lev-Mar.

This can be done using newton-raphson and for convenience, we can make a VI with the following connectors:

• Inputs
1. a function VI reference to the model y=f(x) (using the same connector pattern as the Lev_Mar model function).
2. y1
3. An estimate for x1
• outputs
1. x1 such that x1=f(y1), (using newtwon-raphson)

 This way we can change the model but don't need to change the rest of the code. 🙂

[shoneill]

Altenbach,

it truly would have surprised me if you HADN'T known about the new features, so the fact that you're implying something else than I understand doesn't surprise me really.

Having never been in Austin, I wouldn't know about anything you're presented.

I get what you're saying now.

Shane.