In this session we fit parametrized curves to data and extract the fitted parameters.

Basic example: fit a Gaussian to the resolution

We fit the instrumental resolution file gly180 with a Gaussian function.

Command	Action
? > fl gly180	Load the data file
0 > mr! abs(x)<2	Restrict the frequency range in-place (! means overwrite)
0 > p 7	Plot spectrum 7
0 > cc p0*exp(-(t-p1)^2/2/p2^2)	Create a fit curve (stored as file 1)
1 > a 7	Add curve to plot with default initial values p0=p1=p2=1
1 > cf	Fit (by default, the curve fits data file 0)
1 > 0,1 p 7	Replot data and fit together
0,1 > 1 cp	Print the fitted parameters
1 > oi p2	Create a file of p2 vs z0
2 > g4	Open a new linear-linear plot window
2 > p	Plot p2 vs z0

Tip: Instead of writing out the full Gaussian formula, you can use the shorthand p0*gnn(t-p1, p2), where gnn stands for “Gauss, not normalized”. The expression gauss(t, p2) gives the normalized form exp(-t^2/2/p2^2) / sqrt(2*pi) / p2.

Fixing and setting parameters

Assume file 1 is a curve file.

Command	Action
1 > cx 2	Fix parameter p2 to its current value
1 > op2 1.234	Set p2 to a specific value
1 > op2 pi/z0	Set p2 using an arbitrary expression
1 > cf	Fit with p2 held fixed
1 > cu 2	Unfix p2