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307. STEPT: Direct Search Optimization Solution of
Least-Squares Problems
by J. P. Chandler, Computer Science Department,
Oklahoma State University, Stillwater, Oklahoma 74074
This is a package of compatible routines for finding
local minima of an objective function by any of several
methods. These include direct search methods due to
Hooke & Jeeves; Nelder & Mead; Powell; Zangwill;
Davies, Swann & Campey; and the Gauss-Newton, Hartley,
and Marquardt methods for solving nonlinear least-
squares problems. These routines may be used, among
other applications, to solve systems of nonlinear
equations or to fit models to data by the criterion of
least-squares (or other criteria). Statistical errors
and correlations of the fitted parameters may be
computed in fitting problems.
This package includes current versions of STEPIT
(formerly QCPE 66) and SIMPLEX (formerly QCPE 67). The
new versions are somewhat longer than the originals.
The package also contains a few other miscellaneous
routines for fitting, smoothing, and plotting.
Included are the following items:
1. Routines for finding local minima of a smooth
function (FOBJ) of several parameters (X(J), J=1,
..., NV), using any one of several direct search
methods (methods which do not use derivatives).
These include the following routines and associated
methods:
STEPIT -- an original method
STP -- shorter version of STEPIT
SIMPLEX -- method of Nelder & Mead
KAUPE -- pattern search method of Hooke & Jeeves
MINF -- choice of the method of Powell, or of one
of two methods of Zangwill; or of a modification
of the method of Davies, Swann & Campey
2. UNICY, a simple version of STEPIT for functions of
a single variable
3. MARQ, a routine to solve nonlinear least-squares
problems using Marquardt's method, the Gauss-Newton
method, or Hartley's modification of the Gauss-Newton
method
4. FIDO, which is used in conjunction with STEPIT,
STP, SIMPLEX, KAUPE, MINF, or MARQ to find
statistical errors in the fitted values of parameters
in problems which involve the fitting of a model to
data
5. CURVFIT, a main program which reads data in a
simple format and calls STEPIT (or...) to fit models
of a simple form
6. Miscellaneous routines:
SMOTH -- smooths data using least-squares spline
functions (method by Reinsch)
LSQS -- smooths data with equispaced abscissae,
using least-squares polynomials
ORTHL -- routine of Conte & deBoor for a least-
squares fit of a polynomial to data
RPLOT -- plots data, fit, and residuals on a line
printer
PLOT 6 -- routine by Andrews & Tukey to give
fast six-line plots on a teletype-writer
7. Test programs and test data for the above
FORTRAN IV (ANSI Standard)
Lines of Code: 8260
Recommended Citation: J. P. Chandler, QCPE 11, 307
(1976).
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