PLAPACK

PLAPACK (Parallel Linear Algebra PACKage) is a software library designed to perform dense linear algebra computations on distributed-memory parallel machines. It provides portable, high-level interfaces for a broad set of linear algebra operations, abstracting away the details of data distribution and communication. The library is intended to complement vendor-tuned BLAS/LAPACK by offering scalable parallel algorithms that operate on distributed matrices and vectors.

Implementation and architecture: PLAPACK represents matrices using a block cyclic distribution across a process grid. Computations are organized into a sequence of tasks that operate on blocks, with data movement driven by the dependencies among tasks. The design aims to minimize communication and balance load across processors. PLAPACK interfaces (primarily Fortran, with C wrappers in some versions) call into local BLAS/LAPACK kernels for dense computations and leverage MPI for inter-process communication. It is designed to be portable across MPI implementations and hardware architectures.

Supported operations: The library provides parallel versions of common dense linear algebra routines, including LU, QR, Cholesky factorizations, matrix factorizations, solving linear systems, eigenvalue and singular value problems, and various iterative methods for linear systems and eigenproblems. Higher-level routines facilitate operations such as matrix-matrix multiplications, least squares, and solving generalized problems.

History and availability: PLAPACK originated as a research and development project in the 1990s to provide scalable parallel linear algebra on distributed memory systems. It has been distributed as an open-source package and used in academic and research settings to study parallel algorithms and performance. It competes with other parallel libraries such as ScaLAPACK and Elemental, offering a different interface and design philosophy.