How to use multiple parameters with fittype in Matlab - matlab

Question

I have a 1000x2 data file that I'm using for this problem.
I am supposed to fit the data with Acos(wt + phi). t is time, which is the first column in the data file, i.e. the independent variable. I need to find the fit parameters (A, f, and phi) and their uncertainties.
My code is as follows:
%load initial data file
data = load('hw_fit_cos_problem.dat');
t = data(:,1); %1st column is t (time)
x = t;
y = data(:,2); %2nd column is y (signal strength)
%define fitting function
f = fittype('A*cos(w*x + p)','coefficients','A','problem',{'w','p'});
% check fit parameters
coeffs = coeffnames(f);
%fit data
[A] = fit(x,y,f)
disp('confidence interval/errorbars');
ci = confint(A)
which yields 4 different error messages that I don't understand.
Error Messages:
Error using fit>iAssertNumProblemParameters (line 1113)
Missing problem parameters. Specify the values as a cell array with one element for each problem parameter
in the fittype.
Error in fit>iFit (line 198)
iAssertNumProblemParameters( probparams, probnames( model ) );
Error in fit (line 109)
[fitobj, goodness, output, convmsg] = iFit( xdatain, ydatain, fittypeobj, ...
Error in problem2 (line 14)
[A] = fit(x,y,f)

Answer 1

The line of code
f = fittype('A*cos(w*x + p)','coefficients','A','problem',{'w','p'});
specifies A as a "coefficient" in the model, and the values w and p as "problem" parameters.
Thus, the fitting toolbox expects that you will provide some more information about w and p, and then it will vary A. When no further information about w and p was provided to the fitting tool, that resulted in an error.
I am not sure of the goal of this project, or why w and p were designated as problem parameters. However, one simple solution is to allow the toolbox to treat A, w, and p as "coefficients", as follows:
f = fittype('A*cos(w*x + p)','coefficients', {'A', 'w', 'p'});
In this case, the code will not throw an error, and will return 95% confidence intervals on A, w, and p.
I hope that helps.

Answer 2

The straightforward answer to your question is that the error "Missing problem parameters" is generated because you have identified w and p as problem-specific fixed parameters,
but you have not told the fit function what these fixed values are.
You can do this by changing the line
[A] = fit(x,y,f)
to
[A]=fit(x,y,f,'problem',{100,0.1})
which supplies the values w=100 and p=0.1 in the fit. This should resolve the errors you specified (all 4 error messages result from this error)
In general specifying some of the quantities in your fit equation as problem-specific fixed parameters might be a valid thing to do - for example if you have determined them independently and have good reason to believe the values you obtained to be reliable. In this case, you might know the frequency w in this way, but you most probably won't know the phase p, so that should be a fit coefficient.
Hope that helps.