Plapack

Alpatov, P.; Baker, Greg; Edwards, Carter; Gunnels, John A.; Morrow, Greg; Overfelt, James R.; Geijn, Robert van de; Wu, Yuan-Jye Jason

doi:10.1145/509593.509622

Cited by 37 publications

(4 citation statements)

References 5 publications

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“…A similarly broad effort from the same era is the PLAPACK library [18][19][20]. The (self-described) distinction from ScaLAPACK was the adoption of an object-based coding style, yielding improved execution times over ScaLAPACK for certain operations [20].…”

Section: Recent Developments In Parallel Eigenvalue Solversmentioning

confidence: 99%

“…Fortunately, there are now a number of active developments to address parallel eigenvalue solutions for dense matrices and a large number of eigenvalue/eigenvector pairs, including some focused on general-purpose parallel computers [7,[18][19][20][21][22][23][24][25], some geared towards multicore architectures (e.g. the PLASMA project [26]) or towards GPUs ( [27] and references therein; most prominently, the MAGMA project [28]).…”

Section: Introductionmentioning

confidence: 99%

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The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science

Marek

Blüm

Johanni

et al. 2014

J. Phys.: Condens. Matter

250

261

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Abstract. Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic structure theory and many other areas of computational science. The computational effort formally scales as O(N 3 ) with the size of the investigated problem, N (e.g., the electron count in electronic structure theory), and thus often defines the system size limit that practical calculations cannot overcome. In many cases, more than just a small fraction of the possible eigenvalue/eigenvector pairs is needed, so that iterative solution strategies that focus only on few eigenvalues become ineffective. Likewise, it is not always desirable or practical to circumvent the eigenvalue solution entirely. We here review some current developments regarding dense eigenvalue solvers and then focus on the ELPA library, which facilitates the efficient algebraic solution of symmetric and Hermitian eigenvalue problems for dense matrices that have real-valued and complex-valued matrix entries, respectively, on parallel computer platforms. ELPA addresses standard as well as generalized eigenvalue problems, relying on the well documented matrix layout of the ScaLAPACK library but replacing all actual parallel solution steps with subroutines of its own. For these steps, ELPA significantly outperforms the corresponding ScaLAPACK routines and proprietary libraries that implement the ScaLAPACK interface (e.g., Intel's MKL). The most time-critical step is the reduction of the matrix to tridiagonal form and the corresponding backtransformation of the eigenvectors. ELPA offers both a one-step tridiagonalization (successive Householder transformations) and a two-step transformation that is more efficient especially towards larger matrices and larger numbers of CPU cores. ELPA is based on the MPI standard, with an early hybrid MPIOpenMPI implementation available as well. Scalability beyond 10,000 CPU cores for problem sizes arising in the electronic structure theory is demonstrated for current high-performance computer architectures such as Cray or Intel/Infiniband. For a ELPA -Eigenvalue Solutions for Electronic Structure Theory 2 matrix of dimension 260,000, scalability up to 295,000 CPU cores has been shown on BlueGene/P.

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Section: Recent Developments In Parallel Eigenvalue Solversmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science

Marek

Blüm

Johanni

et al. 2014

J. Phys.: Condens. Matter

250

261

View full text Add to dashboard Cite

show abstract

“…The telescoping languages project [29] analyzes MATLAB scripts and optimizes them using procedure specialization, strength reduction, and vectorization. Similarly, Broadway [26] optimizes calls to libraries such as PLA-PACK [4]. Our work differs in that we generate the linear algebra routines instead of making calls to pre-existing libraries.…”

Section: Background and Related Workmentioning

confidence: 99%

Automating the generation of composed linear algebra kernels

Belter

Jessup

Karlin

et al. 2009

Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis

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Memory bandwidth limits the performance of important kernels in many scientific applications. Such applications often use sequences of Basic Linear Algebra Subprograms (BLAS), and highly efficient implementations of those routines enable scientists to achieve high performance at little cost. However, tuning the BLAS in isolation misses opportunities for memory optimization that result from composing multiple subprograms. Because it is not practical to create a library of all BLAS combinations, we have developed a domain-specific compiler that generates them on demand. In this paper, we describe a novel algorithm for compiling linear algebra kernels and searching for the best combination of optimization choices. We also present a new hybrid analytic/empirical method for quickly evaluating the profitability of each optimization. We report experimental results showing speedups of up to 130% relative to the GotoBLAS on an AMD Opteron and up to 137% relative to MKL on an Intel Core 2.

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“…are available in PLAPACK (cf. Alpatov et al, 1997) using MPI and ScaLAPACK (cf. Blackford et al, 1996) using OpenMP or MPI.…”

mentioning

confidence: 99%

Parallel multivariate slice sampling

2010

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Slice sampling provides an easily implemented method for constructing a Markov chain Monte Carlo (MCMC) algorithm. However, slice sampling has two major drawbacks: (i) it requires repeated evaluation of likelihoods for each update, which can make it impractical when evaluations are expensive or as the number of evaluations grows (geometrically) with the dimension of the slice sampler, and (ii) since it can be challenging to construct multivariate updates, the updates are typically univariate, which often results in slow mixing samplers. We propose an approach to multivariate slice sampling that naturally lends itself to a parallel implementation. Our approach takes advantage of recent advances in computer architectures, for instance, the newest generation of graphics cards can execute roughly 30, 000 threads simultaneously. We demonstrate that it is possible to construct a multivariate slice sampler that has good mixing properties and is efficient in terms of computing time. The contributions of this article are therefore twofold. We study approaches for constructing a multivariate slice sampler, and we show how parallel computing can be useful for making MCMC algorithms computationally efficient. We study various implementations of our algorithm in the context of real and simulated data.

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Plapack

Cited by 37 publications

References 5 publications

The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science

The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science

Automating the generation of composed linear algebra kernels

Parallel multivariate slice sampling

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