ScaLAPACK - Content

 

The ScaLAPACK library includes routines for the solution of linear systems of equations, symmetric positive definite banded linear systems of equations, condition estimation and iterative refinement, for LU and Cholesky factorization, matrix inversion, full-rank linear least squares problems, orthogonal and generalized orthogonal factorizations, orthogonal transformation routines, reductions to upper Hessenberg, bidiagonal and tridiagonal form, reduction of a symmetric-definite generalized eigenproblem to standard form, the symmetric, generalized symmetric and the nonsymmetric eigenproblem. Software is available in single precision real, double precision real, single precision complex, and double precision complex.

The subroutines in ScaLAPACK are classified as follows:

• driver routines, each of which solves a complete problem, for example solving a system of linear equations, or computing the eigenvalues of a real symmetric matrix. Users are recommended to use a driver routine if there is one that meets their requirements. Global and local input error-checking are performed for these routines.
• computational routines, each of which performs a distinct computational task, for example an LU factorization, or the reduction of a real symmetric matrix to tridiagonal form. Each driver routine calls a sequence of computational routines. Users (especially software developers) may need to call computational routines directly to perform tasks, or sequences of tasks, that cannot conveniently be performed by the driver routines. Global and local input error-checking are performed for these routines.
• auxiliary routines, which in turn can be classified as follows:
  • routines that perform subtasks of block-partitioned algorithms -- in particular, routines that implement unblocked versions of the algorithms;
  • routines that perform some commonly required low-level computations, for example scaling a matrix, computing a matrix-norm, or generating an elementary Householder matrix; some of these may be of interest to numerical analysts or software developers and could be considered for future additions to the PBLAS;
  • a few extensions to the PBLAS, such as routines for matrix-vector operations involving complex symmetric matrices (the PBLAS themselves are not strictly speaking part of ScaLAPACK).

A draft ScaLAPACK Users' Guide [32] and a comprehensive Installation Guide is provided, as well as test suites for all ScaLAPACK, PBLAS, and BLACS routines.

• Linear Equations
• Band Decomposition
• Orthogonal Factorizations and Linear Least Squares Problems
• Generalized Orthogonal Factorizations and Linear Least Squares Problems
• Symmetric Eigenproblems
• Nonsymmetric Eigenproblem and Schur Factorization
• Singular Value Decomposition
• Generalized Symmetric Definite Eigenproblems