Modernized Minpack

Description

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.

This version is a modernization of the original Fortran 77 code. This is a work in progress. Modifications include:

• Conversion from fixed (.f) to free-form (.f90) source.
• Modified the tests so they can be automatically run in the CI

Further updates are planned...

Decision trees

Decision tree for systems of nonlinear equations

flowchart TB
	start[Is the Jacobian matrix available?]
	start--Yes-->middle1[Is flexibility required?]
	start--No-->middle2[Is flexibility required?]
	middle1--Yes-->b1[<a href='https://fortran-lang.github.io/minpack/proc/hybrj.html'>hybrj</a>]
	middle1--No-->b2[<a href='https://fortran-lang.github.io/minpack/proc/hybrj1.html'>hybrj1</a>]
	middle2--Yes-->b3[<a href='https://fortran-lang.github.io/minpack/proc/hybrd.html'>hybrd</a>]
	middle2--No-->b4[<a href='https://fortran-lang.github.io/minpack/proc/hybrd1.html'>hybrd1</a>]

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Decision tree for nonlinear least squares problems

flowchart TB
	start[Is the Jacobian matrix available?]
	start--Yes-->m1[Is storage limited?]
	start--No-->m2[Is flexibility required?]
	m1--Yes-->ml1[Is flexibility required?]
	m1--No-->ml2[Is flexibility required?]
	ml1--Yes-->b1[<a href='https://fortran-lang.github.io/minpack/proc/lmstr.html'>lmstr</a/>]
	ml1--No-->b2[<a href='https://fortran-lang.github.io/minpack/proc/lmstr1.html'>lmstr1</a/>]
	ml2--Yes-->b3[<a href='https://fortran-lang.github.io/minpack/proc/lmder.html'>lmder</a/>]
	ml2--No-->b4[<a href='https://fortran-lang.github.io/minpack/proc/lmder1.html'>lmder1</a/>]
	m2--Yes-->mr1[<a href='https://fortran-lang.github.io/minpack/proc/lmdif.html'>lmdif</a/>]
	m2--No-->mr2[<a href='https://fortran-lang.github.io/minpack/proc/lmdif1.html'>lmdif1</a/>]

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Documentation

• The API documentation for the latest default branch can be found here. This is generated by processing the source files with FORD.

License

The Minpack source code and related files and documentation are distributed under a permissive free software license (BSD-style).

History

Minpack has been developed in 1980 by Jorge J. Moré, Burton S. Garbow, Kenneth E. Hillstrom and other contributors as listed on page 8 of the User Guide for MINPACK-1.

Since 2012 Ondřej Čertík has maintained a GitHub repository for minpack with many contributions from Carlos Une and Zuo Zhihua.

In 2021 Jacob Williams started a new minpack repository at GitHub and translated all files from fixed form to free form and other modernizations.

We have discussed at fortran-lang#8 which version to use as the community maintained fortran-lang version and decided to use the latter repository, which became the fortran-lang version. We have been porting improvements from the former repository over to the new fortran-lang repository.

Contributors

Many people have contributed to Minpack over the years:

• Jorge J. Moré, Burton S. Garbow, Kenneth E. Hillstrom and other contributors as listed on page 8 of the User Guide for MINPACK-1.
• Ondřej Čertík
• Carlos Une
• Zuo Zhihua
• Jacob Williams
• Sebastian Ehlert

See also

• nlesolver-fortran

References

• Original sourcecode from: Netlib
• J. J. Moré, B. S. Garbow, and K. E. Hillstrom, User Guide for MINPACK-1, Argonne National Laboratory Report ANL-80-74, Argonne, Ill., 1980.
• J. J. Moré, D. C. Sorensen, K. E. Hillstrom, and B. S. Garbow, The MINPACK Project, in Sources and Development of Mathematical Software, W. J. Cowell, ed., Prentice-Hall, pages 88-111, 1984.
• M. J. D. Powell, A Hybrid Method for Nonlinear Equations. Numerical Methods for Nonlinear Algebraic Equations, P. Rabinowitz, editor. Gordon and Breach, 1970.
• Jorge J. More, The Levenberg-Marquardt Algorithm, Implementation and Theory. Numerical Analysis, G. A. Watson, editor. Lecture Notes in Mathematics 630, Springer-Verlag, 1977.
• MINPACK-2