MINPACK
Least Squares Minimization

MINPACK is a FORTRAN77 library which solves systems of nonlinear equations, or carries out the least squares minimization of the residual of a set of linear or nonlinear equations, by Jorge More, Danny Sorenson, Burton Garbow, Kenneth Hillstrom.

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.

Given a set of N nonlinear equations in N unknowns, F(X) = 0, Powell's method is used to seek a solution X.

Given a set of M nonlinear functions in N unknowns, F(X), the Levenberg-Marquardt method is used to seek an X which minimizes the L2 norm of the residual ||F(X)||.

The user supplies a subroutine to evaluate the nonlinear function; the jacobian matrix dFi(X)/dXj may also be supplied by the user in a subroutine, or approximated by finite differences.

The original FORTRAN77 version of MINPACK is available through the NETLIB web site.

Licensing:

Minpack Copyright Notice (1999) University of Chicago.  All rights reserved

Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the
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1. Redistributions of source code must retain the above
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redistribution, if any, must include the following
acknowledgment:

   "This product includes software developed by the
   University of Chicago, as Operator of Argonne National
   Laboratory.

Alternately, this acknowledgment may appear in the software
itself, if and wherever such third-party acknowledgments
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Languages:

MINPACK is available in a C++ version and a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

BVLS, a FORTRAN90 library which applies least squares methods to solve a linear system for which lower and upper constraints may have been placed on every variable.

DQED, a FORTRAN77 library which solves constrained least squares problems.

NL2SOL, a FORTRAN77 library which implements an adaptive nonlinear least-squares algorithm.

PRAXIS, a FORTRAN77 library which minimizes a scalar function of several variables.

QR_SOLVE, a FORTRAN77 library which computes the least squares solution of a linear system A*x=b.

SLATEC, a FORTRAN90 library which includes MINPACK.

TEST_LS, a FORTRAN77 library which implements linear least squares test problems of the form A*x=b.

TEST_OPT, a FORTRAN90 library which defines test problems for the minimization of a scalar function of several variables.

TOMS611, a FORTRAN77 library which seeks the minimizer of a scalar functional of multiple variables.

Author:

Original FORTRAN77 version by Jorge More, Danny Sorenson, Burton Garbow, Kenneth Hillstrom.

Reference:

1. Jorge More, Burton Garbow, Kenneth Hillstrom,
   User Guide for MINPACK-1,
   Technical Report ANL-80-74,
   Argonne National Laboratory, 1980.
2. Jorge More, Danny Sorenson, Burton Garbow, Kenneth Hillstrom,
   The MINPACK Project,
   in Sources and Development of Mathematical Software,
   edited by Wayne Cowell,
   Prentice-Hall, 1984,
   ISBN: 0-13-823501-5,
   LC: QA76.95.S68.

Source Code:

• minpack.f, the source code;
• minpack.sh, commands to compile the source code;

Examples and Tests:

• minpack_test.f, sample calling code;
• minpack_test.sh, commands to compile, link and run the sample calling code;
• minpack_test.txt, sample output;

List of Routines:

• CHKDER checks the gradients of M functions of N variables.
• DOGLEG finds the minimizing combination of Gauss-Newton and gradient steps.
• DPMPAR provides double precision machine parameters.
• ENORM computes the Euclidean norm of a vector.
• FDJAC1 estimates an N by N jacobian matrix using forward differences.
• FDJAC2 estimates an M by N jacobian matrix using forward differences.
• HYBRD seeks a zero of N nonlinear equations in N variables.
• HYBRD1 seeks a zero of N nonlinear equations in N variables.
• HYBRJ seeks a zero of N nonlinear equations in N variables.
• HYBRJ1 seeks a zero of N nonlinear equations in N variables by Powell's method.
• LMDER minimizes M functions in N variables by the Levenberg-Marquardt method.
• LMDER1 minimizes M functions in N variables by the Levenberg-Marquardt method.
• LMDIF minimizes M functions in N variables by the Levenberg-Marquardt method.
• LMDIF1 minimizes M functions in N variables using the Levenberg-Marquardt method.
• LMPAR computes a parameter for the Levenberg-Marquardt method.
• LMSTR minimizes M functions in N variables using the Levenberg-Marquardt method.
• LMSTR1 minimizes M functions in N variables using the Levenberg-Marquardt method.
• QFORM produces the explicit QR factorization of a matrix.
• QRFAC computes a QR factorization using Householder transformations.
• QRSOLV solves a rectangular linear system A*x=b in the least squares sense.
• R1MPYQ computes A*Q, where Q is the product of Householder transformations.
• R1UPDT re-triangularizes a matrix after a rank one update.
• RWUPDT computes the decomposition of a triangular matrix augmented by one row.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.