Linear System Analyzer Computational Components

The "meat" of the LSA is its linear system codes, which comprise its "components". This should be distinguished from the LSA subsystems, the reusable software infrastructure parts that can be applied to form PSEs in other problem domains.

The general categories in which the linear system components have been grouped are

I/O components for getting systems into and solutions out of the LSA
Filter components for manipulating the systems with re-orderings, scalings, or dropping of entries based on their relative sizes
Solver components for actually solving the systems
Information components for providing some analysis of the systems.

Components currently available are listed below. Please note that the hyperlinks below are to the original library source of the codes, which in most cases have been modified to constitute stand-alone components.

NewSystem (I/O) uses some local and some Sparskit routines to read a system in a Harwell-Boeing or Matrix Market formatted file into the LSA. Later this will be extended to accept input from a running process.
ExtractVector (I/O) outputs a vector to a file or another component. It is used to retrieve the solution vector, or some auxiliary information such as permutation or scaling vectors.
BasicInfo (Information) uses primarily Sparskit routines to provide analysis of the system for symmetry, density, diagonal dominance, etc. It also creates a GIF image of the sparsity (nonzero) structure of the coefficient matrix.
Reorder (Filter) applies some standard re-orderings: reverse Cuthill-McKee, nested dissection, and minimum degree. These are modifications of Sparspak routines.
Scale (Filter) applies row and/or column scaling, and equilibration.
Squeeze (Filter) removes entries based on their relative absolute value.
Banded (Solver) is based on Linpack routines, and converts the system to banded data structure and then solves the system.
Dense (Solver) uses LAPACK routines to solve the system after first converting it to a dense 2D array data structure.
SuperLU (Solver) is a sparse direct solver based on supernodal methods, and is a code developed at UC Berkeley.
SPLIB (Solver) is a package of preconditioned iterative solvers developed at Indiana University. SPLIB includes thirteen iterative methods and seven preconditioners.

These are not an exhaustive compendium of numerical software available for large sparse linear systems, but they span enough of the common operations to demonstrate the application of the LSA.

Next page: the target audience for the LSA.

bramley@cs.indiana.edu

Last updated: Tue Jan 26 12:29:15 1999