MAGMA Users��� Guide

The International Journal of High Performance Computing Applications, 2020

With the acquisition and widespread use of more resources that rely on accelerator/wide vector–based computing, there has been a strong demand for science and engineering applications to take advantage of these latest assets. This, however, has been extremely challenging due to the diversity of systems to support their extreme concurrency, complex memory hierarchies, costly data movement, and heterogeneous node architectures. To address these challenges, we design a programming model and describe its ease of use in the development of a new MAGMA Templates library that delivers high-performance scalable linear algebra portable on current and emerging architectures. MAGMA Templates derives its performance and portability by (1) building on existing state-of-the-art linear algebra libraries, like MAGMA, SLATE, Trilinos, and vendor-optimized math libraries, and (2) providing access (seamlessly to the users) to the latest algorithms and architecture-specific optimizations through a singl...

Journal of Physics: Conference Series, 2009

The emergence and continuing use of multi-core architectures and graphics processing units require changes in the existing software and sometimes even a redesign of the established algorithms in order to take advantage of now prevailing parallelism. Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) and Matrix Algebra on GPU and Multics Architectures (MAGMA ) are two projects that aims to achieve high performance and portability across a wide range of multi-core architectures and hybrid systems respectively. We present in this document a comparative study of PLASMA's performance against established linear algebra packages and some preliminary results of MAGMA on hybrid multi-core and GPU systems.

Acta Numerica

Many crucial scientific computing applications, ranging from national security to medical advances, rely on high-performance linear algebra algorithms and technologies, underscoring their importance and broad impact. Here we present the state-of-the-art design and implementation practices for the acceleration of the predominant linear algebra algorithms on large-scale accelerated multicore systems. Examples are given with fundamental dense linear algebra algorithms – from the LU, QR, Cholesky, and LDLT factorizations needed for solving linear systems of equations, to eigenvalue and singular value decomposition (SVD) problems. The implementations presented are readily available via the open-source PLASMA and MAGMA libraries, which represent the next generation modernization of the popular LAPACK library for accelerated multicore systems. To generate the extreme level of parallelism needed for the efficient use of these systems, algorithms of interest are redesigned and then split int...

In this chapter, we present a hybridization methodology for the development of linear algebra software for GPUs. The methodology is successfully used in MAGMA -a new generation of linear algebra libraries, similar in functionality to LAPACK, but extended for hybrid, GPU-based systems. Algorithms of interest are split into computational tasks. The tasks' execution is scheduled over the computational components of a hybrid system of multicore CPUs with GPU accelerators using StarPU -a runtime system for accelerator-based multicore architectures. StarPU enables to express parallelism through sequential-like code and schedules the different tasks over the hybrid processing units. The productivity becomes then fast and cheap as the development is high level, using existing software infrastructure. Moreover, the resulting hybrid algorithms are better performance-wise than corresponding homogeneous algorithms designed exclusively for either GPUs or homogeneous multicore CPUs.

2008

We propose two high-level application programming interfaces (APIs) to use a graphics processing unit (GPU) as a coprocessor for dense linear algebra operations. Combined with an extension of the FLAME API and an implementation on top of NVIDIA CUBLAS, the result is an efficient and user-friendly tool to design, implement, and execute dense linear algebra operations on the current generation of NVIDIA graphics processors, of wide-appeal to scientists and engineers. As an application of the developed APIs, we implement and evaluate the performance of three different variants of the Cholesky factorization.

The modern graphics processing unit (GPU) found in many standard personal computers is a highly parallel math processor capable of nearly 1 TFLOPS peak throughput at a cost similar to a high-end CPU and an excellent FLOPS/ watt. ratio There is strong desire to utilize such power, but it can be difficult to harness given the features and limitations of the platform. As such, libraries can be of great utility, allowing novices and experts alike to access high computational performance without knowledge of GPU programming. Some routines such as FFTs are quite common in scientific and numerical computing and it would be wasteful for each user to implement such routines that could instead be provided in a centralized library. Moreover, a library routine that is tuned by an expert will often outperform and be more feature robust, allowing the user to instead focus on their particular area of expertise. In this paper we present CULA, a library of linear algebra routines developed using a hybrid computation model employing both CPU and GPU power.

SIAM review, 1995

This paper discusses the design of linear algebra libraries for high performance computers. Particular emphasis is placed on the development of scalable algorithms for MIMD distributed memory concurrent computers. A brief description of the EISPACK, LINPACK, and LAPACK libraries is given, followed by an outline of ScaLAPACK, which is a distributed memory version of LAPACK currently under development. The importance of block-partitioned algorithms in reducing the frequency of data movement between di erent levels of hierarchical memory is stressed. The use of such algorithms helps reduce the message startup costs on distributed memory concurrent computers. Other key ideas in our approach are the use of distributed versions of the Level 3 Basic Linear Algebra Subprograms (BLAS) as computational building blocks, and the use of Basic Linear Algebra Communication Subprograms (BLACS) as communication building blocks. Together the distributed BLAS and the BLACS can be used to construct higher-level algorithms, and hide many details of the parallelism from the application developer. The block-cyclic data distribution is described, and adopted as a good way of distributing blockpartitioned matrices. Block-partitioned versions of the Cholesky and LU factorizations are presented, and optimization issues associated with the implementation of the LU factorization algorithm on distributed memory concurrent computers are discussed, together with its performance on the Intel Delta system. Finally, approaches to the design of library interfaces are reviewed.

2016

A particularly challenging class of problems arising in many applications, called batched problems, involves linear algebra operations on many small-sized matrices. We proposed and designed batched BLAS (Basic Linear Algebra Subroutines), Level-2 GEMV and Level-3 GEMM, to solve them. We illustrate how to optimize batched GEMV and GEMM to assist batched advance factorization (e.g. bi-diagonalization) and other BLAS routines (e.g. forward/back substitution) to achieve optimal performance on GPUs. Our solutions achieved up to 2.8-3× speedups compared to CUBLAS and MKL solutions, wherever possible. We applied our batched methodology in a real-world Hydrodynamic application by reformulating the tensor operations into batched BLAS GEMV and GEMM operations. A 2.5× speedup and a 1.4× greenup are obtained by changing 10% of the code. We accelerated and scaled it on Titan supercomputer to 4096 nodes.

Scientific Programming, 2015

This paper presents the design and implementation of several fundamental dense linear algebra (DLA) algorithms for multicore with Intel Xeon Phi coprocessors. In particular, we consider algorithms for solving linear systems. Further, we give an overview of the MAGMA MIC library, an open source, high performance library, that incorporates the developments presented here and, more broadly, provides the DLA functionality equivalent to that of the popular LAPACK library while targeting heterogeneous architectures that feature a mix of multicore CPUs and coprocessors. The LAPACK-compliance simplifies the use of the MAGMA MIC library in applications, while providing them with portably performant DLA. High performance is obtained through the use of the high-performance BLAS, hardware-specific tuning, and a hybridization methodology whereby we split the algorithm into computational tasks of various granularities. Execution of those tasks is properly scheduled over the heterogeneous hardware...

Journal of Symbolic Computation, 1997

In the first of two papers on Magma, a new system for computational algebra, we present the Magma language, outline the design principles and theoretical background, and indicate its scope and use. Particular attention is given to the constructors for structures, maps, and sets.