Step 3. Specify the parameters that will be adjusted

We don't just specify the parameters--we also test the Generator, and constrain the parameters.


A. Parameter specification

The function is

  A*(exp(-k1*$1) - exp(-k2*$1))
and its parameters are A, k1, and k2. We want the optimizer to be able to adjust all of these in order to fit the function to the data.

In the MRF, clicking on Parameters / Add Parameter

brings up a tool for specifying the name of a parameter.
We click in edit field, type A, and then click on the Accept button.

The left panel of the MRF now contains "A".

We epeat the same sequence for k1 and k2.
The MRF finally looks like this, with A, k1, and k2 appearing in its left panel.

Save to a session file!


B. Testing the Generator

Let's see if things are working properly.

In the Generator, we click on the Error Value button.
This makes the Generator evaluate and plot the function. The Generator also computes the sum of squared error between the function and the experimental data for every value of the independent variable in the interval bracketed by the blue lines.

The Error Value field shows a nonzero value, suggesting that the Generator is working OK.

But where is the black trace that shows the trajectory of the parameterized function?

Ah, we completely forgot about the values of the parameters.


C. Viewing (and changing) parameter values

In the MRF, we click on Parameters / Parameter Panel

A = 1 (good), but k1 = k2 = 1, so our function is 1 times the difference between two identical exponentials, i.e. 0.

In the Generator you can click on the the x axis and confirm that a trace is there (crosshairs will appear, and you can run the crosshairs along the length of the x axis).

Let's change a parameter so we can see this trace.
In the Parameter panel, we change k2 to 10.

Now we go back to the Generator and click on Error Value again.

A small black curve appears--we're on the right track.

You don't absolutely have to save a session file now, but what harm could it do?


D. Constraining parameters

We're almost ready to start optimizing. But first, let's do something that may make the optimizer's job easier :
   constrain the values that the parameters may assume.

In the MRF, we click on Parameters / Domain Panel

The MulRunFitter Domain window shows that all parameters are unbounded, i.e. they are free to vary from -1e9 to 1e9.
But we know that A, k1, and k2 must be > 0. We know that, but the optimizer doesn't. We may be able to save a lot of time just by fencing off parts of parameter space that we aren't interested in.

So in the MulRunFitter Domain window we click on
   group attributes / postive definite limits

Now the parameters are constrained to lie between 1e-9 and 1e9.

It's OK to close the MulRunFitter Domain window; we can always bring it up again if we need it.


Save to a session file before proceeding any further!


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Copyright © 2003 by N.T. Carnevale and M.L. Hines, All Rights Reserved.