Curve fitting with a system of equations + convolution

Assuming that your fitting process is optimized (I'm not commenting on that part), you would want your fitting function to execute as fast as possible.  Looking at your code I see many possible optimizations.

1.  At the top of your function you have a bunch of Make commands.  Ideally, you should have one set of Make(s) like this for each running thread and have it called outside the fitting function. 

2.  Inside the function compute w[2]*6 only once and assign to a local variable.

3.  Inside your do loop you the quantity 2*w[2]^2 does not change so you should factor it out of the loop and assign to a local variable.

4.  Similary, 2/(sqrt(2*pi)*w[2] does not change.  In fact, you should also replace the sqrt(2*pi) with something like

  2.50662827463100050241576528481104525300698674060994 (use however many digits you want :).

5. Replace gwave=... with a MatrixOP assignment.

6. Delete the convwave=fwave line.

7. Replace the Convolve and the following line with a single MatrixOP assignment.

I hope this helps.

A.G.

You can use an x-wave with an all-at-once fit function, see DisplayHelpTopic "User-Defined Fitting Function: Detailed Description" Pay attention to the last line.

All-At-Once Fitting Functions

The scheme of calculating one Y value at a time doesn't work well for some fitting functions. This is true of functions that involve a convolution such as might arise if you are trying to fit a theoretical signal convolved with an instrument response. Fitting to a solution to a differential equation might be another example.

For this case, you can create an "all at once" fit function. Such a function provides you with an X and Y wave. The X wave is input to the function; it contains all the X values for which your function must calculate Y values. The Y wave is for output -- you put all your Y values into the Y wave.

Because an all-at-once function is called only once for a given set of fit coefficients, it will be called many fewer times than a basic fit function. Because of the saving in function-call overhead, all-at-once functions can be faster even for problems that don't require an all-at-once function.

Here is the format of an all-at-once fit function:

Function myFitFunc(pw, yw, xw) : FitFunc
    WAVE pw, yw, xw

    yw = <expression involving pw and xw>
End

Note that there is no return statement because the function result is put into the wave yw. Even if you include a return statement the return value is ignored during a curve fit.

The X wave contains all the X values for your fit, whether you provided an X wave to the curve fit or not. If you did not provide an X wave, xw simply contains equally-spaced values derived from your Y wave's X scaling.

A quick comment about gwave = gwave*(2/(sqrt(2*pi)*w[2]))

In addition to calculating the constant beforehand as suggested by Igor you could also use FastOP. It's very fast when you only need to add or multiply with a constant.

First- YES you need an all-at-once fit function. You are integrating over an X range over and over and over...

Since you are using Convolve, your model must have evenly-space X values. But since your data is not evenly spaced, you will need to make an evenly-spaced model as an intermediate step, and then pick out the appropriate Y values based on your xw wave.

If your system has decay constants that vary of orders of magnitude, you may have a "stiff" system. In that case, use IntegrateODE/M=3 to use the BDF method of integration.

Have you run IntegrateODE outside of the fitting function? That is pretty essential to make sure that part of the computation is working correctly. It can be quite difficult to get it right.

Initial conditions go in the first (zero) row of the output wave. The second line here sets the second row (row 1, of course :). If your goal is to initialize the wave to all zeroes, you probably want something like this:

olelytken has quoted a part of the documentation for all-at-once fitting functions. To read all about it, execute this command in Igor: DisplayHelpTopic "All-At-Once Fitting Functions"

It sounds like you have a pretty difficult project. Try to apply what we have suggested here, then come back. I'm sure you will run into further blocks.

The advice Igor is giving you is very good and sound. But I would get the basic implementation doing the right thing first, and then work on the types of optimizations he is suggesting.