Basic linear algebra subprograms for FORTRAN usage

A package of 38 low level subprograms for many of the basic operations of numerical linear algebra is presented. The package is intended to be used with FORTRAN. The operations in the package are dot products, elementary vector operations, Givens transformations, vector copy and swap, vector norms, vector scaling, and the indices of components of largest magnitude. The subprograms and a test driver are available in portable FORTRAN. Versions of the subprograms are also provided in assembly language for the IBM 360/67, the CDC 6600 and CDC 7600, and the Univac 1108

Library for advanced functions in algorithms, data structures and AI implemented in C/C++ - Olib

Developers of one of most popular languages used for scientific computations which is C, have a lot of libraries at their disposal. Many of those allows usage of modern platforms equipped with advanced multicore processors. Among them is BLAS (Basic Linear Algebra Subprograms) and LAPACK (Linear Algebra PACKage). They contain mainly high performance procedures operating on matrix and vectors

PB-BLAS: A set of parallel block basic linear algebra subprograms

We propose a new library of routines for performing dense linear algebra computations on block-partitioned matrices. The routines are referred to as the Block Basic Linear Algebra Subprograms, and their use is restricted to computations in which one or more of the matrices involved consists of a single row or column of blocks, and in which no more than one of the matrices consists of an unrestricted two-dimensional array of blocks. The functionality of the block BLAS routines can also be provided by Level 2 and 3 BLAS routines. However, for Non-Uniform Memory Access machines the use of the block BLAS permit certain optimizations in memory access to be taken advantage of. This is particularly true for distributed memory machines, for which the block BLAS are referred to as the Parallel Block Basic Linear Algebra Subprograms (PB-BLAS). The PB-BLAS are the main focus of this paper, and for a block-cyclic data distribution, a single row or column of blocks lies in a single row or column of the processor template. The PB-BLAS consist of calls to the sequential BLAS for local computations, and calls to the BLACS for communication. The PB-BLAS are the building blocks for implementing ScaLAPACK, the distributed-memory version of LAPACK, and provide the same ease-of-use and portability for ScaLAPACK that the BLAS provide for LAPACK. The PB-BLAS consists of all nine Level 3 BLAS routines, four of the Level-2 BLAS routines, and 2 auxiliary transpose routines. The PB-BLAS are currently available for all numeric data types, i.e., single and double precision real and complex

libNMF -- A Library for Nonnegative Matrix Factorization

We present libNMF -- a computationally efficient high performance library for computing nonnegative matrix factorizations (NMF) written in C. Various algorithms and algorithmic variants for computing NMF are supported. libNMF is based on external routines from BLAS (Basic Linear Algebra Subprograms), LAPack (Linear Algebra package) and ARPack, which provide efficient building blocks for performing central vector and matrix operations. Since modern BLAS implementations support multi-threading, libNMF can exploit the potential of multi-core architectures. In this paper, the basic NMF algorithms contained in libNMF and existing implementations found in the literature are briefly reviewed. Then, libNMF is evaluated in terms of computational efficiency and numerical accuracy and compared with the best existing codes available. libNMF is publicly available at http://rlcta.univie.ac.at/software

Una introducción al uso de Lapack

LAPACK (Linear Algebra Package) is a collection of FORTRAN 77 subroutines that are useful in the solution of the mathematical problems related to mathematical modeling and belonging to the field of numerical linear algebra. The LAPACK subroutines are based on simpler subroutines called BLAS (Basic Linear Algebra Subprograms). In these notes, we introduce LAPACK and numerical linear algebra, explain in detail the more common LAPACK subroutines, illustrate their use by selected examples and all the time we encourage the readers to use quality software available in the public domain.El software LAPACK (Linear Algebra Package) es una colección de subrutinas escritas en FORTRAN 77 que sirve para resolver los problemas matemáticos más comunes que surgen a partir del modelamiento matemático y que se enmarcan en el campo de álgebra lineal numérica. Las subrutinas de LAPACK se basan en unas subrutinas más sencillas que se conocen por la sigla BLAS (Basic Linear Algebra Subprograms). En estas notas, presentamos a LAPACK y al álgebra lineal numérica, destacamos las rutinas más comunes de LAPACK, ilustramos el uso de las rutinas con ejemplos seleccionados y todo lo hacemos en un tono motivador hacia el uso de software de calidad disponible en el dominio público