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NESC0321 EXPALS

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

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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.