Fitting of Data

This chapter deals with the modelling and the analysis of image and table data by fitting non-linear functions, using least squares approximation. The different non-linear least squares methods implemented in MIDAS are first shortly described and discussed. The MIDAS commands dealing with functions or linear combination of functions and with the modelling process are then presented.

The basic scheme under these commands is to provide the necessary tools to define the functions entering in the fit, to give initial guesses for the parameters and, in iterations controlled by the user, find the optimal parameters of the functions. These parameters can be used to generate fitted data either as images or as columns in tabular form.

Due to the nature of the methods, it is recommended to use these commands in
fitting problems involving small amounts of data. For analysis involving large
amounts of data, like full CCD images, there are algorithms, in the context of
2D-photometry, optimized for special purpose analyses. A tutorial command
(`TUTORIAL/FIT`) has been introduced in order to show the capabilities of
the package.

A brief description of the implemented methods is included in
section 8.1.
Section 8.2 describes how to specify functions in the
fit.
Section 8.3 describes how to include external functions.
The usage of the commands is illustrated in
section 8.4. The output of the programs and their
possible interpretation
are discussed in section 8.5.
An example is presented in
section 8.6, it may be convenient for first time users to run the
command `TUTORIAL/FIT` while reading this section.
Section 8.7 contains a summary of the commands.
Finally, the functions supported in the current version are listed in
section 8.8. References can be found in
section 8.9.

- Outline of the Available Methods
- Function Specification
- External Functions
- The Fitting Process.
- Outputs
- Tutorial
- Command Summary
- Basic Functions
- References