Linear algebra on high performance computers

OpenCL is an open standard to write parallel applications for heterogeneous computing systems. Since its usage is restricted to a single operating system instance, programmers need to use a mix of OpenCL and MPI to program a heterogeneous cluster. In this paper, we introduce an MPI-OpenCL implementation of the LINPACK benchmark for a cluster with multi-GPU nodes. The LINPACK benchmark is one of the most widely used benchmark applications for evaluating high performance computing systems. Our implementation is based on High Performance LINPACK (HPL) and uses the blocked LU decomposition algorithm. We address that optimizations aimed at reducing the overhead of CPUs are necessary to overcome the performance gap between the CPUs and the multiple GPUs. Our LINPACK implementation achieves 93.69 Tflops (46 percent of the theoretical peak) on the target cluster with 49 nodes, each node containing two eight-core CPUs and four GPUs.

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“…HPL uses the right-looking blocked LU decomposition algorithm [15]. It adopts the block-cyclic data distribution scheme [16].…”

Section: Hpl Algorithmmentioning

confidence: 99%

Accelerating LINPACK with MPI-OpenCL on Clusters of Multi-GPU Nodes

Nah

Lee

et al. 2015

IEEE Trans. Parallel Distrib. Syst.

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“…Several algorithms which improve the data locality for dense linear algebra problems have been suggested for shiuvd memoty systems (e.g.see [2], [4]). These algorithms are based on BLAS3 (Basic Linear Algebra level 3) modules consisting matrix times matrix operations.…”

Section: Introductionmentioning

confidence: 99%

Towards efficient parallel implementation of the CG method applied to a class of block tridiagonal linear systems

Chronopoulos

1991

Proceedings of the 1991 ACM/IEEE Conference on Supercomputing - Supercomputing '91

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An efficient implementation of Conjugate Gradient (CG) methods on vector and parallel machines is presented. The two different architecture models considered are the shared memory machines with memory hierarchy and the message passing private memory machines. For a parametrized vector architecture similu to CRAY-2 we present (theoretically) an implementation of the s-step CG used to solve an elliptic partiaJ differential-equation fast as that of the standard parallel computem we show of s-step CG can be up to mance of the standatd CG.

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“…experience on a variety of computers led Dongarra and Sorensen [7] to conclude that nearly optimal performance of numerical linear algebra code can be achieved if the subroutines for simple matrix and vector operations, such as BLAS [12], are written to perform on the computer at hand. We have written these subroutines so that they run efficiently on an IBM 3090 VF vector computer when the compiler VS FORTRAN 2.3.0 with parameter vlev = 2 is used.…”

Section: Much Computationalmentioning

confidence: 99%

Algorithm 686: FORTRAN subroutines for updating the QR decomposition

Reichel

Gragg

1990

ACM Trans. Math. Softw.

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Let the matrix A E R""", m 2 n, have a QR decomposition A = QR, where Q E R""" has orthonormal columns, and R E R""" is upper triangular. Assume that Q and R are explicitly known. We present FORTRAN subroutines that update the QR decomposition in a numerically stable manner when A is modified by a matrix of rank one, or when a row or a column is inserted or deleted. These subroutines are modifications of the Algol procedures in Daniel et al. [5]. We also present a subroutine that permutes the columns of A and updates the QR decomposition so that the elements in the lower right corner of R will generally be small if the columns of A are nearly linearly dependent. This subroutine is an implementation of the rank-revealing QR decomposition scheme recently proposed by Chan [3].

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Linear algebra on high performance computers

Cited by 32 publications

References 22 publications

Accelerating LINPACK with MPI-OpenCL on Clusters of Multi-GPU Nodes

Accelerating LINPACK with MPI-OpenCL on Clusters of Multi-GPU Nodes

Towards efficient parallel implementation of the CG method applied to a class of block tridiagonal linear systems

Algorithm 686: FORTRAN subroutines for updating the QR decomposition

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