Modernized 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.

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

• Conversion from fixed (.f) to free-form (.f90) source.
• Modified the tests so they can be automatically run in the CI
• Implementation of C API for all procedures
• Python bindings to the minpack C API

Further updates are planned...

To build this project from the source code in this repository you need to have a Fortran compiler supporting Fortran 2008 and one of the supported build systems:

• fpm version 0.3.0 or newer
• meson version 0.55 or newer, with a build-system backend, i.e. ninja version 1.7 or newer

The project is hosted on GitHub and can be obtained by cloning it with

git clone https://github.com/fortran-lang/minpack
cd minpack

Invoke fpm in the project root with

fpm build

To run the testsuite use

fpm test

You can access the minpack program programs using the run subcommand

fpm run --example --list

To use minpack in your project include it as dependency in your package manifest

[dependencies]
minpack.git = "https://github.com/fortran-lang/minpack"

Optional dependencies are

Setup a build with

meson setup _build

The following build options can be adjusted:

• the Fortran compiler can be selected by setting the FC environment variable.

• the installation location can be set with the --prefix=/path/to/install option

• with the -Dpython=true option the Python bindings can be built

  • Python 3.6 or newer is required with the CFFI package installed
  • the actual Python version can be selected using -Dpython_version=/path/to/python

To compile and run the projects testsuite use

meson test -C _build --print-errorlogs

If the testsuite passes you can install with

meson install -C _build

This might require administrator access depending on the chosen install prefix. Minpack should now be available on your system, you can check by using the pkg-config tool

pkg-config --modversion minpack

To include minpack in your project add the following wrap file to your subprojects directory:

[wrap-git]
directory = minpack
url = https://github.com/fortran-lang/minpack
revision = head

You can retrieve the dependency from the wrap fallback with

minpack_dep = dependency('minpack', fallback: ['minpack', 'minpack_dep'])

and add it as dependency to your targets.

The following compilers are known to work with minpack.

The combinations annotated with latest are tested continuously for this project, for all other results the last commit or tag where this behavior was verified is linked. A list of tested compilers which are currently not working or only partially working and the respective issue are listed below.

Please share your experience with successful and failing builds for compiler/platform/architecture combinations not covered above.

Minpack provides a series of solves for systems of nonlinear equations and nonlinear least squares problems. To select the approriate solver for your problem checkout the diagrams below.

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>]

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/>]

In Fortran projects the above procedures can be made available by including the minpack_module. Examples can be found in the example directory.

To use minpack in non-Fortran projects which are compatible with C checkout the minpack.h header for the available symbols and callback function signatures. Python bindings are available and documented in the python subdirectory of this project.

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

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

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 #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.

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

• nlesolver-fortran

• 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