lsqcurvefit

Syntax

x = lsqcurvefit(@func,x0,xdata,ydata)

x = lsqcurvefit(@func,x0,xdata,ydata,lb,ub)

x = lsqcurvefit(@func,x0,xdata,ydata,lb,ub,options)

[x,resnorm,residual,exitflag,output] = lsqcurvefit(...)

Inputs

func

The function of system residuals. See the optimset option Jacobian for details.

x0

An estimate of the best fit parameters.

xdata

The domain values for which the best fit is performed.

ydata

The range values for which the best fit is performed.

lb

The fitting parameter lower bounds.

Not currently supported; use [ ] when using options.

ub

The fitting parameter upper bounds.

Not currently supported; use [ ] when using options.

options

A struct containing option settings.

See optimset for details.

Outputs

x

The best fit parameters.

resnorm

The squared length of the residuals vector.

residual

The residuals vector.

info

The convergence status flag.

info = 4

Relative step size converged to within tolX.

info = 3

Relative function value converged to within tolFun.

info = 2

Step size converged to within tolX.

info = 1

Function value converged to within tolFun.

info = 0

Reached maximum number of iterations or function calls, or the algorithm aborted because it was not converging.

info = -3

Trust region became too small to continue.

output

A struct containing iteration details. The members are as follows:

iterations

The number of iterations.

nfev

The number of function evaluations.

xiter

The candidate solution at each iteration.

resnormiter

The objective function value at each iteration.

Example

Fit an exponential curve to the data provided.

function y = FittingFunc(p, x)
    y = p(1) * exp(-p(2)*x);
end

x = [1; 2; 3; 4];
y = [8.025, 3.975, 2.025, 0.975];
p0 = [15; 1];
[p,res] = lsqcurvefit(@FittingFunc,p0,x,y)

p = [Matrix] 2 x 1
16.09848
 0.69669
res = 0.00190995098

Comments

lsqcurvefit uses a modified Gauss-Netwon algorithm with a trust region method.

Options for convergence tolerance controls and analytical derivatives are specified with optimset.

To pass additional parameters to a function argument, use an anonymous function.