## Le Roy Fitting Routines

I am pleased to provide copies of my computer subroutines LLSQF, LLSQFVL and
NLLSSRR for performing linear or non-linear least-squares fits. These
routines are very efficient, robust and accurate. Subroutine LLSQF is
appropriate for linear least-squares (or a single cycle on a non-linear fit)
cases in which the data set being treated is of modest size, so that
calculating and storing the entire partial derivative array presents no
problem. LLSQFVL is essentially identical to LLSQF except that the partial
derivatives for each datum are generated and used as they are needed, one at
a time, and there is no need to store the entire array. The latter is often
more convenient when one is performing many-parameter fits to very large data
sets. Supplementary documentation is provided by University of
Waterloo Chemical Physics Research Report CP-628, a set of notes about
linear and non-linear least-squares fitting which describes the use of
subroutines LLSQF and LLSQFVL.
For most practical purposes, routines LLSQF and LLSQFVL have been
superceded by a more general linear or non-linear fitting routine called
NLLSSRR, which implements iterative convergence for non-linear fits
internally, and automatically performs (if desired) the sequential rounding
and refitting (SRR) procedure described in the paper *"Uncertainty,
Precision, Convergence and Rounding in Performing and Reporting Least-Squares
Fits"*, by R.J. Le Roy [J.Mol.Spectrosc. 191, 223-231 (1998)]. This SRR
method yields a final set of fitted parameters with minimum numbers of
significant digits with no loss of accuracy. Note, however, that while there
are detailed comments in the NLLSSRR code which describe its use, report
CP-628 have not yet been updated to incorporate a description of NLLSSRR.

The Fortran source code for these routines are automatically distributed
(by e-mail) to those who fill in the form: Download
Fitting Subroutines . There are no charges associated with distribution
or use of this software, but its use should be acknowledged by reference as a
private communication from the author and by reference to the above CP
Report. Users are also requested NOT to distribute the programs further
themselves, but to refer interested parties to this source. I will be
pleased to receive information regarding apparent or real malfunctions, but
can not promise immediate response.

Queries regarding these notes or use of any of the associated subroutines
should be addressed to R.J. Le Roy (519) 888-4051: leroy @ uwaterloo.ca.

**Site owned by R.J. Le Roy: leroy @ UWaterloo.ca
**
This page was last updated on