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LAPACK is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008). The routines handle both real and complex matrices in both single and double precision. LAPACK relies on an underlying BLAS implementation to provide efficient and portable computational building blocks for its routines.
ASCI Red was the first computer built under the Accelerated Strategic Computing Initiative (ASCI), the supercomputing initiative of the United States government created to help the maintenance of the United States nuclear arsenal after the 1992 moratorium on nuclear testing.
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication. They are the de facto standard low-level routines for linear algebra libraries; the routines have bindings for both C and Fortran. Although the BLAS specification is general, BLAS implementations are often optimized for speed on a particular machine, so using them can bring substantial performance benefits. BLAS implementations will take advantage of special floating point hardware such as vector registers or SIMD instructions.
Kazushige Gotō is a software engineer specializing in high performance, hand-written, machine code.
Red Storm is a supercomputer architecture designed for the US Department of Energy’s National Nuclear Security Administration Advanced Simulation and Computing Program. Cray, Inc developed it based on the contracted architectural specifications provided by Sandia National Laboratories. The architecture was later commercially produced as the Cray XT3.
The Texas Advanced Computing Center (TACC) at the University of Texas at Austin, United States, is an advanced computing research center that is based on comprehensive advanced computing resources and supports services to researchers in Texas and across the U.S. The mission of TACC is to enable discoveries that advance science and society through the application of advanced computing technologies. Specializing in high performance computing, scientific visualization, data analysis & storage systems, software, research & development and portal interfaces, TACC deploys and operates advanced computational infrastructure to enable the research activities of faculty, staff, and students of UT Austin. TACC also provides consulting, technical documentation, and training to support researchers who use these resources. TACC staff members conduct research and development in applications and algorithms, computing systems design/architecture, and programming tools and environments.
Automatically Tuned Linear Algebra Software (ATLAS) is a software library for linear algebra. It provides a mature open source implementation of BLAS APIs for C and Fortran77.
Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms efficient. Applications of matrix multiplication in computational problems are found in many fields including scientific computing and pattern recognition and in seemingly unrelated problems such as counting the paths through a graph. Many different algorithms have been designed for multiplying matrices on different types of hardware, including parallel and distributed systems, where the computational work is spread over multiple processors.
Intel oneAPI Math Kernel Library is a library of optimized math routines for science, engineering, and financial applications. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math. That is besides the math.h standard C library, that is also more accurate compared to glibc.
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OpenBLAS is an open-source implementation of the BLAS and LAPACK APIs with many hand-crafted optimizations for specific processor types. It is developed at the Lab of Parallel Software and Computational Science, ISCAS.
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The Roofline model is an intuitive visual performance model used to provide performance estimates of a given compute kernel or application running on multi-core, many-core, or accelerator processor architectures, by showing inherent hardware limitations, and potential benefit and priority of optimizations. By combining locality, bandwidth, and different parallelization paradigms into a single performance figure, the model can be an effective alternative to assess the quality of attained performance instead of using simple percent-of-peak estimates, as it provides insights on both the implementation and inherent performance limitations.
Richard Vuduc is a tenured professor of computer science at the Georgia Institute of Technology. His research lab, The HPC Garage, studies high-performance computing, scientific computing, parallel algorithms, modeling, and engineering. He is a member of the Association for Computing Machinery (ACM). As of 2022, Vuduc serves as Vice President of the SIAM Activity Group on Supercomputing. He has co-authored over 200 articles in peer-reviewed journals and conferences.
ROCm is an Advanced Micro Devices (AMD) software stack for graphics processing unit (GPU) programming. ROCm spans several domains: general-purpose computing on graphics processing units (GPGPU), high performance computing (HPC), heterogeneous computing. It offers several programming models: HIP, OpenMP/Message Passing Interface (MPI), OpenCL.
In scientific computing, BLIS is an open-source framework for implementing a superset of BLAS functionality for specific processor types that was recently awarded the J. H. Wilkinson Prize for Numerical Software. It exposes that functionality through two traditional Application Programming Interfaces (APIs): the BLAS interface and the CBLAS interface. BLIS also includes two APIs native to the framework: a typed (BLAS-like) API and an object API. These native interfaces provide access to BLAS-like functionality that is not supported by, but closely related to, operations found in the BLAS . The framework is developed and supported by the Science of High-Performance Computing (SHPC) group of the Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin and the Matthews Research Group at Southern Methodist University.
GraphBLAS is an API specification that defines standard building blocks for graph algorithms in the language of linear algebra. GraphBLAS is built upon the notion that a sparse matrix can be used to represent graphs as either an adjacency matrix or an incidence matrix. The GraphBLAS specification describes how graph operations can be efficiently implemented via linear algebraic methods over different semirings.
References
- 1 2 3 Markoff, John Gregory (2005-11-28). "Writing the Fastest Code, by Hand, for Fun: A Human Computer Keeps Speeding Up Chips". New York Times . Seattle, Washington, USA. Archived from the original on 2020-03-23. Retrieved 2010-03-04.
- ↑ Milfeld, Kent. "GotoBLAS2". Texas Advanced Computing Center. Archived from the original on 2020-03-23. Retrieved 2013-08-28.
- 1 2 3 Goto, Kazushige; van de Geijn, Robert A. (2008). "Anatomy of High-Performance Matrix Multiplication". ACM Transactions on Mathematical Software . 34 (3): 12:1–12:25. CiteSeerX 10.1.1.111.3873 . doi:10.1145/1356052.1356053. ISSN 0098-3500. (25 pages)
- 1 2 Goto, Kazushige; van de Geijn, Robert A. (2008). "High-performance implementation of the level-3 BLAS" (PDF). ACM Transactions on Mathematical Software . 35 (1): 1–14. doi:10.1145/1377603.1377607.
- ↑ "BLAS-LAPACK at TACC". Texas Advanced Computing Center.
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