Fitting a sin function to a sparse dataset with a known parameter.

Question #4 in the last few days... Thank you all for the help so far!

I have a sparse dataset (4 points, soon 5) of an environmental variable whose concentration changes as a function of time of year, and whose shape I know approximates a sin wave, i.e.

var(t) = a1 * (sin(2*pi/365days)*t+b1)+c1

I know the frequency of the function, but I don't know the amplitude (a1), phase offset (b1) or offset in y (c1), so I'd like to fit a sin function to it.

Question: Is there a function that will allow me to specify a given known parameter (frequency) and that will solve for the remaining unknowns (amp, phase, y offset)? I've tried using cftool, but as far as I can tell, it doesn't allow me to specify frequency. And I've started to try to use the fit function, but I'm having a hard time sorting out how to format my input variables.

TIA, Jonathan

Answer 1

[Dr. Seis]

Having only a few data points to work with is a little worrisome, but something like this may work:

function estimates = fitsinewave(xdata, ydata, start_point)
% Call fminsearch with a starting point.

model = @sinefun;
options = optimset('MaxFunEvals',3000);
estimates = fminsearch(model, start_point, options);

% sinefun accepts curve parameters as inputs, and outputs sse,
% the sum of squares error for A*sin(2*pi/365*xdata-B)+C-ydata.
  function sse = sinefun(params)
      A = params(1);
      B = params(2);
      C = params(3);
      ErrorVector = A*sin(2*pi/365*xdata-B)+C - ydata;
      sse = sum(ErrorVector .^ 2);
  return
  end
return
end

Here is an example to test it out:

A = 3;
B = 3*pi/4;
C = -1.5;
xdata = sort(rand(1,5)*365);
ydata = A*sin(2*pi/365*xdata-B)+C;
start_point = [0, 0, 0]; % Zeros unless you have a good guess for A, B, and C
ABCestimates = fitsinewave(xdata, ydata, starting_point)

ABCestimates =

    3.0001    2.3562   -1.5000

[Jonathan]

Thank you Elige for putting this together for me, and sorry that I didn't thank you earlier. My first shot at using it vastly overestimated the amplitude, but I think I can work with a few things and improve it.

Thanks,

Jonathan

[Dr. Seis]

That stinks!

Can you share a set of your points so I can look into it as well?