### Example: Surface plot for rational approximation (2D_INTRL)

Background:
The example serves to illustrate surface fitting, in this case by a rational function depending on fourteen unknown parameters a1, ..., a14 and two independent variables x1 and x2.

The Mathematical Model:
The fitting criterion is given in the form

a = a1/x13 + a2 + a3/x12 + a4/x1 + a5*x1 + a6 x12 + a7*x13 + a8*x22 + a9*x2 + a10/x22 + a11*x12*x2 + a12*x1*x22 + a13/(x12*x2) + a14*x23

The parameters x1 and x2 are scaled.

Implementation:
The complete solution of a data fitting problem is described in six steps:

1. Define model type and document the experiment
... set some informative strings, define the mathematical structure and the variables
2. Specify details of the model structure
... set number of measurement sets, constraints, concentration values
3. Use editor for declaring variables and for defining functions
... the essential part, you have to know the mathematical equations and how to relate them to the format required by
EASY-FITModelDesign
4. Insert measurement data
... the dirty job, can become boring (but you may import data from text files and EXCEL spreadsheets!)
5. Select termination tolerances and start a data fitting run
... only a few mouse clicks
6. A separate process is started and all computed data are displayed
... MODFIT estimates parameters and performs a statistical analysis

Results:
Then you would like to take a look at reports and graphs:
- parameter values
- experimental data versus fitting criterion

Documentation and parameters:

Model structure:

Model equations (or use your own favorite editor):

Measurement data (or use import function for text file or Excel):

Parameters, tolerances and start of a data fitting run:

Numerical results (computed by the least squares code DFNLP):

Report on parameter values, residuals, performance, etc. (or export to Word):

Experimental data versus fitting criterion (also available for Gnuplot):