Lots of ways I guess. To make it all explicit, here is an example of one way:
% a fixed parameter:
E = 1.25;
% some data
x = rand(50,1);
y = 1 + 2*sin(x - E) + randn(size(x))/1000;
% establish the model:
mdl = fittype(@(a,b,x) a + b*sin(x - E),'independent','x','coefficients', {'a','b'})
mdl =
General model:
mdl(a,b,x) = a+b*sin(x-E)
% Do the fit. Here, only a and b will be estimated.
ab = fit(x,y,mdl)
Warning: Start point not provided, choosing random start point.
> In curvefit.attention.Warning/throw (line 30)
In fit>iFit (line 299)
In fit (line 108)
ab =
General model:
ab(x) = a+b*sin(x-E)
Coefficients (with 95% confidence bounds):
a = 0.9992 (0.9982, 1)
b = 1.999 (1.997, 2)
As you can see, fit can "see" that E is a parameter, held at a fixed value. I could have gotten rid of the warning by providing starting values for a and b.
The general idea is that I encapsulated the parameter E into the function handle. It is now fixed at the value held by E at the time I created the function handle. Be careful though. Even were you to later change the value of E while that function handle still exists, the function handle will still retain the original value of E.
