Global Optimization Toolbox User's Guide - MathWorks

3 Using GlobalSearch and MultiStart
3-84
Create 200 data points and responses. Use the values a =–3,b =1/4,c =1/2,
and d = 1. Include random noise in the response.
rng default % for reproducibility
N = 200; % number of data points
preal = [-3,1/4,1/2,1]; % real coefficients
xdata = 5*rand(N,2); % data points
ydata = fitfcn(preal,xdata) + 0.1*randn(N,1); % response data with noise
Step 3. Set bounds and initial point.
Set bounds for lsqcurvefit. There is no reason for d to exceed π in absolute
value, because the sine function takes values in its full range over any
interval of width 2π. Assume that the coefficient c must be smaller than 20 in
absolute value, because allowing a very high frequency can cause unstable
responses or spurious convergence.
lb = [-Inf,-Inf,-20,-pi];
ub = [Inf,Inf,20,pi];
Set the initial point arbitrarily to (5,5,5,0).
p0 = 5*ones(1,4); % Arbitrary initial point
p0(4) = 0; % so the initial point satisfies the bounds
Step 4. Find the best local fit.
Fit the parameters to the data, starting at p0.
[xfitted,errorfitted] = lsqcurvefit(fitfcn,p0,xdata,ydata,lb,ub)
Local minimum possible.
lsqcurvefit stopped because the final change in the sum of squares relative
its initial value is less than the default value of the function tolerance.
xfitted =
-2.6149 -0.0238 6.0191 -1.6998
errorfitted =
28.2524