NEA-0732 FATAL.

1. NAME OR DESIGNATION OF PROGRAM:  FATAL 'Fit anything to anything you like'.

3. DESCRIPTION OF PROBLEM OR FUNCTION

A generalized fitting program with a free-format keyword interface to the user. It permits experimental data to be fitted by non-linear regression methods to any function describable by the user. The user requires the minimum  of computer experience but needs to provide a subroutine to define his function. Some statistical output is included as well as 'best'  estimates of the function's parameters.

4. METHOD OF SOLUTION

The regression method used is based on a minimization technique devised by Powell (Harwell Subroutine Library VA05A, 1972) which does not require the use of analytical derivitives. The method employs a quasi-Newton procedure balanced with a steepest descent correction. Experience shows this to be efficient for a very wide range of application.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The current version  of the program permits functions to be defined with up to 20 parameters. The function may be fitted to a maximum of 400 points, preferably with estimated values of weight given.

6. TYPICAL RUNNING TIME

The execution time depends on the complexity  of the function fitted and the number of data points but 'a few seconds' is to be expected for 50 points fitted to a function of 10  parameters.

7. UNUSUAL FEATURES OF THE PROGRAM

The program is suitable for fitting data to both trivial and complex functions provided the user is prepared to offer initial estimates of the parameters to be determined.

8. RELATED AND AUXILIARY PROGRAMS

FATAL has been in general use (with several minimization routines) since 1967. The current version is basically that described in AERE-R7129 (1972) but with some enhancements of the statistical treatment, the ability to 'fix' specified parameters and some additional graphical features.

10. REFERENCES:

- L. Salmon, D.V. Booker:
  "FATAL - A General Purpose Computer Program for Fitting
  Experimental Data to Any Required Function"
  AERE - R 7129 (May 1972).

11. MACHINE REQUIREMENTS:  Standard IBM 360 system or later upgrades.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  MVS (or later upgrades) of IBM.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

HSL subroutines IA01AS, ZA02AS and ZA10AS are written in IBM Assembler code and require an MVS operating system.

IA01AS gets virtual storage at run-time and could be replaced by a COMMON statement. ZA02AS and ZA10AS obtain the CPU time and the date.  They could be omitted or replaced.

The program employs the plotting package 'GHOST'. If this is not locally available, all such calls should be removed or replaced.
(See comments in listing to follow this procedure.)

The user must provide his own routine MYFUN thus:

SUBROUTINE MYFUN (X,Y,P,N)
REAL P(1)
N=               (No. of parameters in function)
                 (Code defining 'Y' for a single value of 'X'
                  using a series of parameters P(1)....P(N)    )
RETURN
END

15. NAME AND ESTABLISHMENT OF AUTHOR

          L. Salmon, T. Budd and M. Marshall
          Environmental and Medical Sciences Division
          Atomic Energy Research Establishment
          Harwell
          Oxfordshire
          United Kingdom

File name	File description	Records
NEA0732_01.003	FATAL INFORMATION FILE	79
NEA0732_01.004	FATAL SOURCE (FORTRAN-4)	742
NEA0732_01.005	HARWELL LIBRARY SUBROUTINES (FORTRAN-4)	1368
NEA0732_01.006	HARWELL LIBRARY SUBROUTINES (ASSEMBLER)	1290
NEA0732_01.007	FATAL INPUT DATA FOR TEST CASE	8
NEA0732_01.008	FATAL OUTPUT OF TEST CASE	212
NEA0732_01.009	FATAL JCL FOR TEST CASE	96