# lsqcurvefit

Find the equation parameters that produce the least squares best fit to a data set.

## 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.

## Examples

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
Modify the previous example to pass an extra parameter to the user function using a function handle.
function y = FittingFunc(p, x, offset)
y = p(1) * exp(-p(2)*x) + offset;
end

handle = @(x, p) FittingFunc(x, p, 2);
[p,res] = lsqcurvefit(handle,p0,x,y+2);

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.

The optimset options and defaults are as follows:
• MaxIter: 400
• MaxFunEvals: 1,000,000
• TolFun: 1.0e-7
• TolX: 1.0e-7
• Jacobian: 'off'
• Display: 'off'