hompack

Description

hompack is a package for finding zeros or fixed points of nonlinear systems using globally convergent probability-one homotopy algorithms.

History

The first version of the library, named HOMPACK, was originally released in 1987 ¹, and the last "official" update, named HOMPACK90, dates from 1997 ².

hompack is (will be) a modernization of the HOMPACK90 code ³, intended to make the library easier to use and maintain. The main changes include:

• Conversion from fixed-form (.f) to free-form (.f90).
• Conversion from upper case to lower case.
• Modularization.
• Removal of DATA statements, labeled do loops, and (most) gotos.
• Addition of intent(in/out) to all procedures.
• Addition of explicit interfaces to BLAS/LAPACK routines.
• Implementation of a C API.
• Automatic code documentation with FORD.
• Python bindings, available in the companion repo hompack-python.

Version	Year	Standard
hompack	202x	Fortran 2018
HOMPACK90	1997	FORTRAN 90
HOMPACK	1987	FORTRAN 77

Build instructions

Dependencies

hompack depends on a number of functions from BLAS and LAPACK.

The build configuration files provided with the code (see further below) assume a suitable BLAS/LAPACK library is locally installed. Alternatively, the subset of required functions is available in ./external.

With fpm

The easiest way to build/test the code and run the examples is by means of fpm.

To build the library, do:

fpm build --profile release

To run the tests, do:

fpm test --profile release

To run the provided examples, do:

fpm run --example "example_name" --profile release

With meson

First, setup the build:

meson setup builddir -Dbuild_tests=true

To build the libraries, do:

meson compile -C builddir

To run the tests, do:

meson test -C builddir

Licence

• The original hompack code is public domain.
• Modifications introduced in this project are covered under the MIT license.

References

Footnotes

1. Layne T. Watson, Stephen C. Billups, and Alexander P. Morgan. 1987. Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms. ACM Trans. Math. Softw. 13, 3 (Sept. 1987), 281–310. https://doi.org/10.1145/29380.214343 ↩

2. Layne T. Watson, Maria Sosonkina, Robert C. Melville, Alexander P. Morgan, and Homer F. Walker. 1997. Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms. ACM Trans. Math. Softw. 23, 4 (Dec. 1997), 514–549. https://doi.org/10.1145/279232.279235 ↩

3. Original source code from Netlib. ↩