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Topic: Basic Linear Algebra Subprograms

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	GAMS : List of Packages
		A collection of miscellaneous linear algebra files from Netlib by a variety of a...
		Fortran subprograms for evaluating definite integrals of functions of one variab...
		An extension to the Basic Linear Algebra Subroutines (BLAS) for sparse vector op...
	www.numis.northwestern.edu /ftp/pub/list-packages.html (987 words)

	ScaLAPACK
		ScaLAPACK is a library of subroutines/functions which solve linear systems of algebraic equations in parallel.
		BLAS (Basic Linear Algebra Subprograms library) includes subroutines for common linear algebra computations such as dot-product, matrix-vector multiplication, and matrix-matrix multiplication.
		BLACS is a set of Basic Linear Algebra Communication Subprograms that perform the communication tasks that arise frequently in parallel linear algebra computations.
	www.ats.ucla.edu /rct/clustering/software/ScaLAPACK.htm (449 words)

	BLAS1 - Basic Linear Algebra Subprograms - Level 1
		BLAS1 is a library of C++ routines which implement the Level 1 BLAS, or Basic Linear Algebra Subprograms.
		The BLAS are a small core library of linear algebra utilities, which can be highly optimized for various architectures.
		LINPACK is a linear algebra library that uses the BLAS1 routines
	www.csit.fsu.edu /~burkardt/cpp_src/blas1/blas1.html (398 words)

	LAPACK Working Note 100 A Proposal for a Set of Parallel Basic Linear Algebra Subprograms
		The PBLAS are targeted at distributed vector-vector, matrix-vector and matrix-matrix operations with the aim of simplifying the parallelization of linear algebra codes, especially when implemented on top of the sequential BLAS.
		At first glance, because of the apparent simplicity of its sequential counterpart as well as the regularity of the data structures involved in dense linear algebra computations, implementing an equivalent set of parallel routines in terms of portability, efficiency, and ease-of-use seems relatively simple to achieve.
		In view of this fact, it is natural to choose a virtual machine topology that is convenient for dense linear algebra computations and map the virtual machine onto existing topologies.
	www.netlib.org /utk/papers/pblas/pblas.html (275 words)

	Dense Linear Algebra Algorithms
		Objective: The objective of this project is to investigate techniques for basing dense linear algebra algorithms on parallel versions of the Basic Linear Algebra Subprograms (BLAS), thereby allowing parallelism to be hidden within these subprograms.
		Approach: High-performance dense linear algebra libraries like LAPACK are written in terms of a few computational kernels, the Basic Linear Algebra Subprograms, which make it possible to attain high performance in a portable fashion by only tuning those kernels for different platforms.
		The ScaLAPACK project at the University of Tennessee, Oak Ridge National Laboratory, Rice University, UCLA, UC-Berkeley, and the University of Illinois, is an extension of this effort that targets distributed memory parallel supercomputers.
	ct.gsfc.nasa.gov /annual.reports/ess95contents/app.gci.geijn.html (616 words)

	[No title]
		The BLAS (Basic Linear Algebra Subprograms) routines, which make up the bulk of this library, are widely used in dense numerical linear algebra programs.
		Since they are the most useful vector and matrix operations, the availability of versions tuned to the user's machine provides a simple way for speeding up existing programs and writing new numerical programs.
		The Basic Math Library object routines are packaged as a library archive named libkmath.
	www.sandia.gov /ASCI/Red/usage/paragon/man/man3/Kmath.3.html (1181 words)

	Basic Linear Algebra Subprograms - Wikipedia, the free encyclopedia
		Basic Linear Algebra Subprograms (BLAS) are routines which perform basic linear algebra operations such as vector and matrix multiplication.
		Automatically Tuned Linear Algebra Software, an open source implementation of BLAS APIs for C and Fortran 77.
		Society for Industrial and Applied Mathematics, Philadelphia, PA An Overview of the Sparse Basic Linear Algebra Subprograms: The New Standard from the BLAS Technical Forum [10]
	en.wikipedia.org /wiki/Basic_Linear_Algebra_Subprograms (466 words)

	Parallel Math Libraries
		BLAS (Basic Linear Algebra Subprograms) - set of Fortran 77 computational kernels for basic operations commonly used by linear algebra routines, de facto standards.
		In 1973, Hanson, Krogh and Lawson described the advantages of adopting a set of basic routines for problems in linear algebra [1].
		The level 2 BLAS were designed to perform linear algebra operations at a 'higher level' than the level 1 BLAS.
	www.mhpcc.edu /training/workshop/parallel_libs/MAIN.html (2038 words)

	University of Houston Computer Science Department
		The Scalable Linear Algebra PACKage, or ScaLAPACK, is a library of linear algebra routines for high-performance computing.
		ScaLAPACK was derived from the Linear Algebra PACKAGE (LAPACK) that was widely used for many years to solve the same types of problems as ScaLAPACK.
		The basic components of ScaLAPACK are two libraries: PBLAS, which stands for "Parallel Basic Linear Algebra Subprograms" and BLACS, which stands for "Basic Linear Algebra Communication Subprograms".
	www.cs.uh.edu /software/scalapack.shtml (172 words)

	Research Computing Technologies
		The BLAS (Basic Linear Algebra Subprograms) are a collection of common linear-algebra computational subprograms which provide basic operations such as dot product, matrix/vector multiplication, and matrix/matrix multiplication.
		These are the Level 1, 2, and 3 BLAS subprograms optimized for single CPU Intel Pentium Pro and Pentium II processors.
		Some of the underlying code in these routines are Unix conversions of subprograms from Intel's Math Kernel Library, part of the Intel Performance Library Suite.
	www.ats.ucla.edu /rct/software/libraries/blas.htm (563 words)

	Center for Parallel Computers - Numerical Libraries at PDC
		BLAS is a set of Basic Linear Algebra Subprograms that provides low-level operations often found in computational kernels.
		The Linear Algebra PACKage is a Fortran 77 library containing subroutines for solving the most common problems in numerical linear algebra.
		BLACS, Basic Linear Algebra Communication Subprograms, is a set of portable communication routines designed for parallel linear algebra computations.
	www.pdc.kth.se /compresc/software/numlib (2491 words)

	NAG Technical Reports - Numerical Analysis
		The aim of this report is to show how the complete range of NAG C DLL routines can be called directly from Visual Basic, and thus allow programmers/package builders maximum flexibility when incorporating calls to NAG library routines into their Visual Basic code.
		A substantial part of the library material being developed is concerned with the solution of PDE problems using parallel sparse linear algebra modules.
		It provides parallel subroutines in some of the areas covered by traditional numerical libraries, such as dense and sparse linear algebra, optimization, quadrature and random number generation, as well as utility routines for data distribution, input/output and process management.
	www.nag.co.uk /doc/TechRep/NP1513.asp (3186 words)

	BLAS - AMD Core Math Library (ACML) (Site not responding. Last check: 2007-10-13)
		The BLAS are a set of well defined basic linear algebra operations ([1], [2], [3]).
		The implementation of higher level linear algebra algorithms on these systems depends critically on the use of the BLAS as building blocks.
		These routines perform operations on a sparse vector x which is stored in compressed form and a vector y in full storage form.
	seldon.it.northwestern.edu /sscc/acmldoc/BLAS.html (128 words)

	Automatically Tuned Linear Algebra Software (Site not responding. Last check: 2007-10-13)
		However much of the technology and approach developed here can be applied to the other Level 3 BLAS and the general strategy can have an impact on basic linear algebra operations in general and may be extended to other important kernel operations.
		While these BLAS are used heavily in linear algebra computations, such as solving dense systems of equations, they have also found their way into the basic computing infrastructure of many applications.
		The BLAS (Basic Linear Algebra Subprograms) are high quality ``building block'' routines for performing basic vector and matrix operations.
	www.cs.utk.edu /~rwhaley/ATL/INDEX.HTM (8542 words)

	3. The BLAS Interface (cvxopt.blas)
		The names and calling sequences of the Python functions in the interface closely match the corresponding Fortran BLAS routines (described in the references below) and their functionality is exactly the same.
		First, some of the functions it includes are not easily implemented using the basic matrix arithmetic.
		Thus they can be viewed as generalizations of the in-place matrix addition and scalar multiplication of section 2.3 to more complicated operations.
	www.ee.ucla.edu /~vandenbe/cvxopt/doc/node14.html (280 words)

	NAG Numerical Analysis Technical Reports with Abstacts only
		The K system provides a compact command language for generalised linear modelling in Genstat and has been designed to be especially suitable for intensive interactive work.
		Linear convergence of the row cyclic Jacobi and Kogbetliantz methods can be guaranteed if certain constraints concerning the angles of rotations are implemented.
		We present an overview of the numerical solution of the linear least-squares problem associated with the general Gauss-Markov linear model y = XBeta + e, e is a product of sets N(0,sigma2 W), where sigma2 W is a symmetric non-negative definite variance-covariance matrix.
	www.nag.co.uk /doc/techrep/TRarchive.asp (3933 words)

	Matrix Multiplication on the Sun Platform
		If the variables a and b are scalars and if the array A is an m by p matrix and B is p by n, then C must be m by n and the Expression (1) represents an m by n matrix.
		As the name implies, the Basic Linear Algebra Subprograms (BLAS) are a package of computational tools for numerical linear algebra.
		A subprogram written in C provided the interface to the system routine that returns information about the platform on which the program is running.
	people.ee.ethz.ch /~ballisti/computer_topics/matrix_multiply.html (5598 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		master netlib.bell-labs.com file c/meschach/meschach1.shar (plus dependencies) for basic dense linear algebra lib linalg for various functions complementing the bigger linear algebra libraries editor Jack Dongarra master ornl.gov file slatec/chk/blachk.f (plus dependencies) for Quick check for Basic Linear Algebra Subprograms.
		K., (LLNL) file slatec/chk/dlapqc.f (plus dependencies) for Quick check for testing Sparse Linear Algebra Package gams D2A4, D2B4 by Mark K. Seager (LLNL) file slatec/chk/slapqc.f (plus dependencies) for Quick check for testing Sparse Linear Algebra Package gams D2A4, D2B4 by Mark K. Seager (LLNL) lib sparse-blas for sparse extension to Basic Linear Algebra Subprograms.
		9(1976)279-307 file pppack/slvblktext.f (plus dependencies) for almost block diagonal linear system lib lapack for the most common problems in numerical linear algebra, linear equations, linear least squares problems, eigenvalue problems,, and singular value problems.
	www.cs.purdue.edu /homes/jrr/CS501-97/material/linalg (449 words)

	Bibliography
		Basic Linear Algebra Subprograms for Fortran Usage, ACM Transactions on Mathematical Software, Vol.5, No.3 (September 1979) 308-325.
		An Extended Set of Fortran Basic Linear Algebra Subprograms, ACM Transactions on Mathematical Software, Vol.14, No.1 (March 1988) 1-32.
		A Set of Level 3 Basic Linear Algebra Subprograms, ACM Transactions on Mathematical Software (December 1989).
	www.intel.com /software/products/mkl/docs/WebHelp/mklbiblio.html (1172 words)

	NPACI All-Hands: ScaLAPACK (Site not responding. Last check: 2007-10-13)
		ScaLAPACK is a library of high-performance linear algebra routines for distributed-memory message-passing MIMD computers and networks of workstations supporting PVM and/or MPI.
		It is a continuation of the LAPACK project, which designed and produced analogous software for workstations, vector supercomputers, and shared-memory parallel computers.
		The library is currently written in Fortran 77 (with the exception of a few symmetric eigenproblem auxiliary routines written in C to exploit IEEE arithmetic) in a Single Program Multiple Data (SPMD) style using explicit message passing for interprocessor communication.
	legion.virginia.edu /workshops/all-hands/scalapack.html (193 words)

	Clint Whaley's Papers and Publications
		"An Updated Set of Basic Linear Algebra Subprograms (BLAS)", by L. Susan Blackford, James Demmel, Jack Dongarra, Iain Duff, Sven Hammarling, Greg Henry, Micheal Heroux, Linda Kaufman, Andrew Lumsdain, Antoine Petitet, Roldan Pozo, Karin Remington, and R. Clint Whaley.
		"A Proposal for a Set of Parallel Basic Linear Algebra Subprograms", by Jaeyoung Choi, J. Dongarra, S. Ostrouchov, A. Petitet, D. Walker and R. Whaley.
		"Basic Linear Algebra Communication Subprograms: Analysis and Implementation Across Multiple Parallel Architectures" by R. Clint Whaley.
	www.cs.utsa.edu /~whaley/papers.html (640 words)

	The Object-Oriented Numerics Page
		Seldon, C++ library for linear algebra with BLAS interface.
		LAPACK++ (Linear Algebra PACKage in C++), solves systems of linear equations and eigenvalue problems on high performance computer architectures.
		The Template Numerical Toolkit (TNT) for linear algebra is a successor to the Lapack++, Sparselib++, IML++, and MV++ packages.
	oonumerics.org /oon (1872 words)

	Jerzy Wisniewski: Linear Algebra With Recursive Algorithms
		Recursion provides a new, easy and very successful way of programming numerical linear algebra algorithms.
		Recursion has also been successfully applied to the BLAS (Basic Linear Algebra Subprograms).
		Several recursive numerical dense linear algebra algorithms will be explained, and a comparison of the performance of these new algorithms with that of the traditional algorithms will be shown.
	www.ewh.ieee.org /r7/st_maurice/html/20000929.htm (212 words)

	Information Bridge: DOE Scientific and Technical Information - - Document #78703
		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.
		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.
	www.osti.gov /bridge/product.biblio.jsp?osti_id=78703 (402 words)

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