MATLAB Mathematics - SERC - Index of

Minimizing Functions and Finding Zeros
model = @expfun;
estimates = fminsearch(model, start_point);
% expfun accepts curve parameters as inputs, and outputs sse,
% the sum of squares error for A * exp(-lambda * xdata) - ydata,
% and the FittedCurve. FMINSEARCH only needs sse, but we want to
% plot the FittedCurve at the end.
function [sse, FittedCurve] = expfun(params)
A = params(1);
lambda = params(2);
FittedCurve = A .* exp(-lambda * xdata);
ErrorVector = FittedCurve - ydata;
sse = sum(ErrorVector .^ 2);
end
end
The M-file calls the function fminsearch, which find parameters A and lambda
that minimize the sum of squares of the differences between the data and the
exponential function A*exp(-lambda*t). The nested function expfun computes
the sum of squares.
Running the Example
To run the example, first create some random data to fit. The following
commands create random data that is approximately exponential with
parameters A = 40 and lambda = .5.
xdata = (0:.1:10)';
ydata = 40 * exp(-.5 * xdata) + randn(size(xdata));
To fit an exponential function to the data, enter
[estimates, model] = fitcurvedemo(xdata,ydata)
This returns estimates for the parameters A and lambda,
estimates =
40.1334 0.5025
and a function handle, model, to the function that computes the exponential
function A*exp(-lambda*t).
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