Question

I have a 1000×2 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.