nonlinear least squares in matlab

Nonlinear least squares is a common method used for curve fitting and data analysis. MATLAB provides several options for nonlinear least squares optimization. One of the most commonly used functions is "lsqcurvefit".

Here is an example of how to use "lsqcurvefit" for nonlinear least squares optimization in MATLAB:

main.m
% Define the function to fit
function y = myfun(x, xdata)
    y = x(1) * exp(-x(2)*xdata) + x(3);

% Define the initial guess
x0 = [1 1 1];

% Define the independent variable data
xdata = [0:0.1:1];

% Define the dependent variable data with some noise
ydata = 1.2 * exp(-0.5*xdata) + 0.8 + 0.1*randn(size(xdata));

% Call lsqcurvefit to perform the optimization
x = lsqcurvefit(@myfun, x0, xdata, ydata);

% Plot the data and fitted curve
plot(xdata, ydata, 'ro')
hold on
plot(xdata, myfun(x, xdata), 'b-')
xlabel('xdata')
ylabel('ydata')
legend('Data', 'Fitted curve')
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In the above example, we define the function we want to fit (myfun), the initial guess (x0), and the independent and dependent variable data. We then call lsqcurvefit to perform the optimization and obtain the optimal parameters (x). Finally, we plot the data and the fitted curve.