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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). |