This chapter describes numerical linear algebra, Fourier transforms, random number generation, and other utility software packaged as defined operations that are executed with a function notation similar to standard mathematics. The resulting interface alters the way libraries are presented to the user. Many computations of numerical linear algebra are documented here as operators and generic functions. A notation is developed reminiscent of matrix algebra. This allows the Fortran user to express mathematical formulas in terms of operators. The operators can be used with both dense and sparse matrices.

A comprehensive Fortran module, linear_operators, defines the operators and functions. Its use provides this simplification. Subroutine calls and the use of type-dependent procedure names are largely avoided. This makes a rapid development cycle possible, at least for the purposes of experiments and proof-of-concept. The goal is to provide the Fortran programmer with an interface, operators, and functions that are useful and succinct. The modules can be used with or added to existing Fortran programs, but the operators provide a more readable program whenever they apply. This approach may require more hidden working storage. The size of the executable program may be larger than alternatives using subroutines. There are applications wherein the operator and function interface does not have the functionality that is available using subroutine libraries. To retain greater flexibility, some users will continue to require the techniques of calling subroutines.

A parallel computation for many of the defined operators and functions has been implemented. The type of problem solved is a simple one: several independent problems of the same data type and size. Most of the detailed communication for parallel computation is hidden from the user. Those functions having this data type computed in parallel are designated by the “MPI Capable” logo. The section Dense Matrix Parallelism Using MPI gives an introduction on how users should write their codes to use machines on a network.

A number of examples, in addition to those shown in this document, are supplied in the product examples directory. The name of the example code is shown in parentheses in the example heading, for those examples that are included with the product.