12.8 Freely Available Software for Linear Algebra on the Web

Tables 12.1-12.5 present a list of freely available software for the solution of linear algebra problems. The interest is in software for high-performance computers that is available in "open source" form on the web for solving problems in numerical linear algebra, specifically dense, sparse direct and iterative systems and sparse iterative eigenvalue problems.

Additional pointers to software can be found at: www.nhse.org/rib/repositories/nhse/catalog/\hyper@hash{}Numerical_Programs_and_Routines. A survey of Iterative Linear System Solver Packages can be found at: www.netlib.org/utk/papers/iterative-survey.

Notes for Tables 12.1-12.5:

Type: Real for Real arithmetic and Complex for Complex arithmetic
Support: An email address where you can send questions and bug reports.
Language: f77(may also mean Fortran 95), C, C++
Mode: Seq for Sequential, vector and/or SMP/multithreaded versions

Dist for distributed memory message passing (M = MPI, P = PVM)
Dense: Dense, triangular, banded, tridiagonal matrices
Sparse: A sparse matrix representation is used to contain the data.
Direct: A direct approach is used to factor and solve the system.
SPD: The matrix is symmetric and positive definite
Gen: The matrix is general
Iterative: An iterative method is used to solve the system.
P: when used in a column labeled "Sparse Iterative," indicates preconditioners
Sparse eigenvalue: An iterative method is used to find some of the eigenvalues
Sym: The matrix is symmetric (Hermitian in the complex case)

Table 12.1: Support routines for numerical linear algebra. LINALG is a collection of software that is available but too varied to describe.
Package	Support	Type		Language			Mode		Dense	Sparse Direct		Sparse Iterative
		Real	Complex	f77	c	c++	Seq	Dist		SPD	Gen	SPD	Gen
ATLAS	yes	X	X	X	X		X		X
BLAS	yes	X	X	X	X		X		X
FLAME	yes	X	X	X	X		X		X
LINALG *	?
MTL	yes	X				X	X		X
NETMAT	yes	X				X	X		X
NIST S-BLAS	yes	X	X	X	X		X			X	X	X	X
PSBLAS	yes	X	X	X	X		X	M		X	X	X	X
SparseLib++	yes	X	X		X	X	X			X	X	X	X

Table 12.2: Direct solvers for systems of linear equations.
Package	Support	Type		Language			Mode		Dense	Sparse Iterative		Sparse Eigenvalue
		Real	Complex	f77	c	c++	Seq	Dist		SPD	Gen	Sym	Gen
LAPACK	yes	X	X	X	X		X		X
LAPACK95	yes	X	X	95			X		X
NAPACK	yes	X		X			X		X	X		X
PLAPACK	yes	X	X	X	X			M	X
PRISM	yes	X		X			X	M	X
ScaLAPACK	yes	X	X	X	X			M/P	X

Table 12.3: Sparse direct solvers.
Package	Support	Type		Language			Mode		Sparse Direct		Sparse Iterative
		Real	Complex	f77	c	c++	Seq	Dist	SPD	Gen	SPD	Gen
HSL	yes	X	X	X			X		X	X
MFACT	yes	X			X		X		X
MP_SOLVE	yes	X	X		X			M		X
MUMPS	yes	X	X	X	X		X	M	X	X
PSPASES	yes	X		X	X			M	X
SPARSE	yes	X	X		X		X		X	X
SPARSEQR	yes	X			X	X	X		X	X
SPOOLES	yes	X	X		X		X	M	X	X	X	X
SuperLU	yes	X	X	X	X		X	M	X	X
TAUCS	yes	X	X		X		X		X	X	X	X
UMFPACK	yes	X	X	X			X		X	X
Y12M	?	X		X			X		X	X

Table 12.4: Sparse eigenvalue solvers.
Package	Support	Type		Language			Mode		Sparse Eigenvalue
Package	Support	Real	Complex	f77	c	c++	Seq	Dist	Sym	Gen
LZPACK	yes	X	X	X			X	M/P	X
LASO	?	X		X			X		X
P_ARPACK	yes	X	X	X	X	X	X	M/P	X	X
PLANSO	yes	X		X			X	M	X
TRLAN	yes	X		X			X	M	X

Table 12.5: Sparse iterative solvers.
Package	Support	Type		Language			Mode		Sparse Direct		Sparse Iterative		Sparse Eigenvalue
		Real	Complex	f77	c	c++	Seq	Dist	SPD	Gen	SPD	Gen	Sym	Gen
AZTEC	yes	X			X		X	M			X	X
BILUM	yes	X		X			X				X	X
BlockSolve95	?	X		X	X	X		M			X	X
BPKIT	yes	X		X	X	X					P	P
CERFACS	yes	X	X	X			X				X	X
HYPRE	yes	X		X	X		X	M			P	P
IML++	?	X		X	X	X	X				X	X
ISIS++	yes	X				X		M			X	X
ITL	yes	X				X	X				X	X
ITPACK	?	X		X			X				X	X
LASPack	yes	X			X		X				X	X
LSQR	yes	X		X	X		X					X
pARMS	yes	X		X	X		X	M			X	X
PARPRE	yes	X			X			M			P	P
PCG	yes	X		X	X	X		P			X
PETSc	yes	X	X	X	X		X	M			X	X
P-SparsLIB	yes	X		X				M				X
PSPASES	yes	X		X	X		X	M	X
QMRPACK	?	X	X	X			X				X	X	X	X
SLAP	?	X		X							X	X
SPAI	yes	X			X		X	M			X	X
SPLIB	?	X		X			X				X	X
SPOOLES	?	X	X		X		X	M	X	X	X	X
SYMMLQ	yes	X		X			X				X	X
Templates	yes	X		X	X		X				X	X

Reading List

Linear systems. The literature on linear system solving, like the research in this topic, is mostly split along the lines of direct versus iterative solvers. An introduction that covers both (as well as eigenvalue methods) is the book by Dongarra et al. [35]. A very practical book about linear system solving by iterative methods is the Templates book [12], which in addition to the mathematical details contains sections on sparse data storage and other practical matters. More in depth and less software oriented is the book by Saad [98].
Eigensystems. Along the lines of the Templates book for linear systems is a similar book for eigenvalues problems [7].