ivan-pi / minpack

Library for solving nonlinear equations and nonlinear least squares problems

Minpack

Information

This repository contains the original double precision Minpack from netlib.org, together with CMake makefiles and examples.

About Minpack

Minpack includes software for solving nonlinear equations and nonlinear least squares problems. Five algorithmic paths each include a core subroutine and an easy-to-use driver. The algorithms proceed either from an analytic specification of the Jacobian matrix or directly from the problem functions. The paths include facilities for systems of equations with a banded Jacobian matrix, for least squares problems with a large amount of data, and for checking the consistency of the Jacobian matrix with the functions.

Jorge Moré, Burt Garbow, and Ken Hillstrom at Argonne National Laboratory.

Documentation

Minpack contains 4 subroutines for solution of systems of nonlinear equations:

• hybrd, hybrd1: Jacobian matrix is calculated by a forward difference approximation
• hybrj, hybrj1: Jacobian matrix is provided by the user

and 6 subroutines for nonlinear least squares problems:

• lmdif, lmdif1: Jacobian matrix is calculated by a forward difference approximation
• lmder, lmder1: Jacobian matrix is provided by the user
• lmstr, lmstr1: Jacobian matrix is provided by the user, one row per call (uses less memory)

The routines without 1 in the name expose all parameters to the user (core subroutines), routines with 1 only expose the essential parameters and set default values for the rest (easy-to-use driver). Finally:

• chkder: checks the consistency of the Jacobian matrix with the functions

More general documentation is given in the 1980 Argonne technical report written by the authors of Minpack, Chapters 1-3. The Chapter 4 (also available in the file ex/file06) contains detailed documentation for all these routines together with an example of usage. Ready to use examples of usage are in the examples directory.

Other files in the ex directory are original examples of usage of various routines (single and double precision), but are not compiled by default.