EXPALS: Least Square Fit of Linear Combination of Exponential Decay Function
Lawrence Livermore Laboratory Livermore, California, USA through the NEADB.
Fortran 4 CDC7600 (C00787C760000).
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)).
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.
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.
Run times vary based on system, on the order of a few seconds.
A legacy Fortran 4 compiler, however, with editing, a Fortran77 compiler should also work.
C. Douglas Gardner, EXPALS-FORTRAN Code for Exponential Approximation by Least Squares, Lawrence Livermore Laboratory report UCRL-14541, Rev. 2 (August 1, 1978) Livermore, California.
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, Oak Ridge National Laboratory report ORNL-455 (February 3, 1950).
Included are the referenced documents, source, data, and sample input and output files in a self-extracting executable on CD.