How can I fit a cosine function? - matlab

Question

I wrote a python function to get the parameters of the following cosine function:
param = Parameters()
param.add( 'amp', value = amp_guess, min = 0.1 * amp_guess, max = amp_guess )
param.add( 'off', value = off_guess, min = -10, max = 10 )
param.add( 'shift', value = shift_guess[0], min = 0, max = 2 * np.pi, )
fit_values = minimize( self.residual, param, args = ( azi_unique, los_unique ) )
def residual( self, param, azi, data ):
"""
Parameters
----------
Returns
-------
"""
amp = param['amp'].value
off = param['off'].value
shift = param['shift'].value
model = off + amp * np.cos( azi - shift )
return model - data
In Matlab how can get the amplitude, offset and shift of the cosine function?

Answer 1

My experience tells me that it's always good to depend as little as possible on toolboxes. For your particular case, the model is simple and doing it manually is pretty straightforward.
Assuming that you have the following model:
y = B + A*cos(w*x + phi)
and that your data is equally-spaced, then:
%// Create some bogus data
A = 8;
B = -4;
w = 0.2;
phi = 1.8;
x = 0 : 0.1 : 8.4*pi;
y = B + A*cos(w*x + phi) + 0.5*randn(size(x));
%// Find kick-ass initial estimates
L = length(y);
N = 2^nextpow2(L);
B0 = (max(y(:))+min(y(:)))/2;
Y = fft(y-B0, N)/L;
f = 5/(x(2)-x(1)) * linspace(0,1,N/2+1);
[A0,I] = max( 2*abs(Y(1:N/2+1)) );
w0 = f(I);
phi0 = 2*imag(Y(I));
%// Refine the fit
sol = fminsearch(#(t) sum( (y(:)-t(1)-t(2)*cos(t(3)*x(:)+t(4))).^2 ), [B0 A0 w0 phi0])
Results:
 
sol = %// B was -4 A was 8 w was 0.2 phi was 1.8
-4.0097e+000 7.9913e+000 1.9998e-001 1.7961e+000

Answer 2

MATLAB has a function called lsqcurvefit in the optimisation toolbox:
lsqcurvefit(fun,X0,xdata,ydata,lbound,ubound);
where fun is the function to fit, x0 is the initial parameter guess, xdata and ydata are self-explanatory, and lbound and ubound are the lower and upper bounds to the parameters. So, for instance, you might have a function:
% x(1) = amp
% x(2) = shift
% x(3) = offset
% note cosd instead of cos, because your data appears to be in degrees
cosfit = #(x,xdata) x(1) .* cosd(xdata - x(2)) + x(3);
You would then call the lsqcurvefit function as follows:
guess = [7,150,0.5];
lbound = [-10,0,-10]
ubound = [10,360,10]
fit_values = lsqcurvefit(cosfit,guess,azi_unique,los_unique,lbound,ubound);