NESC0321 EXPALS

EXPALS, Least Square Fit of Linear Combination of Exponential Decay Function

NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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1. NAME OR DESIGNATION OF PROGRAM: EXPALS.

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2. COMPUTERS

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Program name	Package id	Status	Status date
EXPALS	NESC0321/01	Tested	23-DEC-1980

Machines used:

Package ID	Orig. computer	Test computer
NESC0321/01	CDC 7600	CDC 7600

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3. DESCRIPTION OF PROBLEM OR FUNCTION

This program fits by least squares a function which is a linear combination of real exponential decay functions. The function is y(k) = summation over j of a(j) * exp(-lambda(j) * k). Values of the independent variable (k) and the dependent variable y(k) are specified as input data. Weights may be specified as input information or set by the program (w(k) = 1/y(k)).

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4. METHOD OF SOLUTION

The Prony-Householder iteration method is used. For unequally-spaced data, a number of interpolation options are provided. This revision includes an option to call a differential correction subroutine REFINE to improve the approximation to unequally-spaced data when equal-interval interpolation is faulty. If convergence is achieved, the probable errors in the computed parameters are calculated also.

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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Generally, it is desirable to have at least 10n observations where n equals the number of terms and to input k+n significant figures if k significant figures are expected.

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6. TYPICAL RUNNING TIME:

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7. UNUSUAL FEATURES OF THE PROGRAM:

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8. RELATED AND AUXILIARY PROGRAMS:

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9. STATUS

Package ID	Status date	Status
NESC0321/01	23-DEC-1980	Tested at NEADB

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10. REFERENCES

- C. Douglas Gardner, EXPALS-FORTRAN Code for Exponential Approximation by Least Squares, UCRL-14541, Rev. 2, August 1, 1978.
- R. E. von Holdt, Minimize Linear Residuals, LLL Computer Information Center Report F3-001, March 1969.
- J. D. Lawrence, Polynomial Root Finder, LLL Computer Information Center Report C2.2-001, December 16, 1966.
- A. S. Householder, On Prony's Method of Fitting Exponential Decay Curves and Multiple-Hit Survival Curves, ORNL-455, February 3, 1950.

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11. MACHINE REQUIREMENTS

EXPALS requires about 74,062 (octal) words with the maximum number of observations or interpolated values (MMX) set at 200 and the maximum number of values for the lambda calculation (NMX) set at 25.

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12. PROGRAMMING LANGUAGE(S) USED

Package ID	Computer language
NESC0321/01	FORTRAN-IV

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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED: SCOPE 2.1.

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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:

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15. NAME AND ESTABLISHMENT OF AUTHOR

Contributed by: Radiation Safety Information Computational Center
                Oak Ridge National Laboratory
                Oak Ridge, Tennessee, USA
Develped by:    C. Douglas Gardner
                Computation Department
                Lawrence Livermore Laboratory
                P. O. Box 808
                Livermore, California 94550, USA

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16. MATERIAL AVAILABLE

NESC0321/01

File name	File description	Records
NESC0321_01.001	INFORMATION FILE	3
NESC0321_01.002	SOURCE	1035
NESC0321_01.003	S.P. INPUT	52
NESC0321_01.004	S.P. OUTPUT	859
NESC0321_01.005	JCL	18

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17. CATEGORIES

P. General Mathematical and Computing System Routines

Keywords: decay, least square fit, radioactivity.