Tutorial

A tutorial procedure (`TUTORIAL/FIT`) shows how to use the fitting package
in the simple case of a 1D-image consisting of two overlapping gaussians on
top of a non-linear background with additional noise. It is recommended to
run the tutorial while reading this section and if possible,
on a graphic terminal.

Two functions are copied into your area if you run the example: `TEST` to
generate the artificial data, and `FUNCTION` with the ``model'' to be
fitted.

The artificial image, to be used in the example, is created as follows:
First it creates a reference image, called `REF`, to provide the
definition interval of the independent variable.
Then the command `COMPUTE/FUNCTION` creates the 1D frame with the gaussian
profiles on top of the background.
Finally, some noise is added to the data. The resulting frame, `PROFILE`
is displayed on the graphic screen.

Now the `model' `FUNCTION` will be fitted to the frame `PROFILE`,
using the command `FIT/IMAGE`. The 'model' was copied into your area
already, but you could define it using the editor as:

EDIT/FIT FUNCTION

This command allows you to create or modify `FIT`-files
(ref Volume C of the MIDAS User guide and
Appendix C
for use of the EDIT command on your terminal).
In our example, the user will edit the three basic
functions e.g. as follows:

where two of the parameters of the second gaussian, height and FWHM, are related to the parameters of the first Gaussian.1 GAUSS(X;A1,A2,A3) A1=50. A2=95. A3=45.

2 GAUSS(X;A4,A5,A6) A4=A1 A5=135. A6=A3

3 POLY(X;A,B,C) A=0. B=0. C=0.

The different fitting methods are then successively applied, changing
regularly the options through the `SET/FIT`. The exact sequence of
instructions is:

SHOW/FIT

FIT/IMAGE 11,1.,0.5 PROFILE FUNCTION

SET/FIT METHOD=CGNND

SET/FIT PRINT=0

FIT/IMAGE 30,.5 PROFILE FUNCTION

SET/FIT METHOD=QN

SET/FIT PRINT=-4

FIT/IMAGE 30,.5 PROFILE FUNCTION

SHOW/FIT

SET/FIT METHOD=MGN

FIT/IMAGE 30,.5 PROFILE FUNCTION

It is possible to compare efficiency, precision and effects.

Finally, the fitted result is computed as:

and the fitted frame is plotted on top of the original data.COMPUTE/FIT FITTED = FUNCTION

Individual components of the fit can be selected with the command
`SELECT/FUNCTION`. In the example, the sequence of commands

is used to compute the two gaussian components on top of the background. The results are also plotted.SELECT/FUNCTION FUNCTION 1,3

COMPUTE/FIT FIT1 = FUNCTION

SELECT/FUNCTION FUNCTION 2,3

COMPUTE/FIT FIT2 = FUNCTION

SELECT/FUNCTION FUNCTION ALL

The full compatibility between image and tabular formats for input and output
means that, in our example, the fitted parameters can be used to compute fitted
values in a table, using the `COMPUTE/FIT` command as follows:

whereCOMPUTE/FIT table :outcol = fitname(:incol)

To begin with, it is advised to consult the appendix or use the MIDAS
interactive `HELP` about `EDIT/FIT,
SET/FIT,
CREATE/FUNCTION,
REPLACE/FUNCTION,
FIT,
FIT/IMAGE,
FIT/TABLE,
COMPUTE/FIT`.