MATLAB CURVE FITTING TOOLBOX - RELEASE NOTES Guide de l'utilisateur télécharger pdf (Page 188)

fitoptions

4-112

The fit results are shown below.

gfit

gfit =

General model Gauss2:

gfit(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2)

Coefficients (with 95% confidence bounds):

a1 = 43.59 (-411.9, 499.1)

b1 = 7.803 (0.7442, 14.86)

c1 = 4.371 (-3.065, 11.81)

a2 = -10.86 (-373.4, 351.7)

b2 = 11.05 (-190.4, 212.5)

c2 = 6.985 (-124.6, 138.5)

As you can see by examining the fitted coefficients, it is clear that the algorithm

has difficulty fitting the narrow peak, and does a good job fitting the broad

peak. In particular, note that the fitted value of the

a2 coefficient is negative.

To help the fitting procedure converge, specify that the lower bounds of the

amplitude and width parameters for both peaks must be greater than zero. To

do this, create a fit options object for the

gauss2 model and configure the Lower

property to zero for

a1, c1, a2, and c2, but leave b1 and b2 unconstrained.

opts = fitoptions('gauss2');

opts.Lower = [0 -Inf 0 0 -Inf 0];

Fit the data using the new constraints.

gfit = fit(x,gdata,ftype,opts)

gfit =

General model Gauss2:

gfit(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2)

Coefficients (with 95% confidence bounds):

a1 = 35 (34.82, 35.17)

b1 = 7.48 (7.455, 7.504)

c1 = 3.993 (3.955, 4.03)

a2 = 4.824 (2.964, 6.684)

b2 = 3 (2.99, 3.01)

c2 = 0.03209 (0.01774, 0.04643)

This is a much better fit, although you can still improve the a2 value.

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MATLAB CURVE FITTING TOOLBOX - RELEASE NOTES Guide de l'utilisateur Page 188