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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Multi-threaded Sparse Matrix Sparse Matrix Multiplication for Many-Core and GPU Architectures.

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix- matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and data structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A Work-Efficient Parallel Sparse Matrix-Sparse Vector Multiplication Algorithm

We design and develop a work-efficient multithreaded algorithm for sparse matrix-sparse vector multiplication (SpMSpV) where the matrix, the input vector, and the output vector are all sparse. SpMSpV is an important primitive in the emerging GraphBLAS standard and is the workhorse of many graph algorithms including breadth-first search, bipartite graph matching, and maximal independent set. As thread counts increase, existing multithreaded SpMSpV algorithms can spend more time accessing the sparse matrix data structure than doing arithmetic. Our shared-memory parallel SpMSpV algorithm is work efficient in the sense that its total work is proportional to the number of arithmetic operations required. The key insight is to avoid each thread individually scan the list of matrix columns. Our algorithm is simple to implement and operates on existing column-based sparse matrix formats. It performs well on diverse matrices and vectors with heterogeneous sparsity patterns. A high-performance implementation of the algorithm attains up to 15x speedup on a 24-core Intel Ivy Bridge processor and up to 49x speedup on a 64-core Intel KNL manycore processor. In contrast to implementations of existing algorithms, the performance of our algorithm is sustained on a variety of different input types include matrices representing scale-free and high-diameter graphs.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver)

PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix solver. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.

Reddy, C. J.↗
DOE OSTI2018

Massive Asynchronous Parallelization of Sparse Matrix Factorizations

Solving sparse problems is at the core of many DOE computational science applications. We focus on the challenge of developing sparse algorithms that can fully exploit the parallelism in extreme-scale computing systems, in particular systems with massive numbers of cores per node. Our approach is to express a sparse matrix factorization as a large number of bilinear constraint equations, and then solving these equations via an asynchronous iterative method. The unknowns in these equations are the matrix entries of the factorization that is desired.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Solution of the two-dimensional Navier-Stokes equations using sparse matrix solvers

The use of direct sparse matrix solvers in the solution of the Navier-Stokes equations is investigated. The Yale Sparse Matrix Package and its implementation in the solution algorithm is described. The streamfunction-vorticity form of the Navier-Stokes equations are discretized and linearized and the resulting system of equations are solved using this package. Several viscous flow problems are investigated, including flow in a cavity and flow around a NACA0012 airfoil. Massively separated flow around a sine wave airfoil is investigated and high Reynolds number solutions are obtained. A solution of the unsteady flow around a Joukowski airfoil at high angle of attack is presented.

Bender, Erich E.↗
NASA NTRS2001

Crystallization of bFGF-DNA Aptamer Complexes Using a Sparse Matrix Designed for Protein-Nucleic Acid Complexes

The Sparse Matrix approach for obtaining lead crystallization conditions has proven to be very fruitful for the crystallization of proteins and nucleic acids. Here we report a Sparse Matrix developed specifically for the crystallization of protein-DNA complexes. This method is rapid and economical, typically requiring 2.5 mg of complex to test 48 conditions. The method was originally developed to crystallize basic fibroblast growth factor (bFGF) complexed with DNA sequences identified through in vitro selection, or SELEX, methods. Two DNA aptamers that bind with approximately nanomolar affinity and inhibit the angiogenic properties of bFGF were selected for co-crystallization. The Sparse Matrix produced lead crystallization conditions for both bFGF-DNA complexes.

Cannone, Jaime J.↗
DOE OSTI2018

A sparse matrix–vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

Here we present an efficient sparse matrix–vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev–Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix–matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev–Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix–vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

42 ENGINEERING↗
DOE OSTI2018

Exploring Deep Learning and Sparse Matrix Format Selection

We proposed to explore the use of Deep Neural Networks (DNN) for addressing the longstanding barriers. The recent rapid progress of DNN technology has created a large impact in many fields, which has significantly improved the prediction accuracy over traditional machine learning techniques in image classifications, speech recognitions, machine translations, and so on. To some degree, these tasks resemble the decision makings in many HPC tasks, including the aforementioned format selection for SpMV and linear solver selection. For instance, sparse matrix format selection is akin to image classification—such as, to tell whether an image contains a dog or a cat; in both problems, the right decisions are primarily determined by the spatial patterns of the elements in an input. For image classification, the patterns are of pixels, and for sparse matrix format selection, they are of non-zero elements. DNN could be naturally applied if we regard a sparse matrix as an image and the format selection or solver selection as classification problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Graph Partitioning and Sparse Matrix Ordering using Reinforcement Learning and Graph Neural Networks

We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. Our approach is to recursively partition coarser representations of a given graph. The neural network is implemented using SAGE graph convolution layers, and trained using an advantage actor critic (A2C) agent. We present two variants, one for finding an edge separator that minimizes the normalized cut or quotient cut, and one that finds a small vertex separator. The vertex separators are then used to construct a nested dissection ordering to permute a sparse matrix so that its triangular factorization will incur less fill-in. The partitioning quality is compared with partitions obtained using METIS and SCOTCH, and the nested dissection ordering is evaluated in the sparse solver SuperLU. Our results show that the proposed method achieves similar partitioning quality as METIS and SCOTCH. Furthermore, the method generalizes across different classes of graphs, and works well on a variety of graphs from the SuiteSparse sparse matrix collection.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Sparse matrix‐vector and matrix‐multivector products for the truncated SVD on graphics processors

Summary Many practical algorithms for numerical rank computations implement an iterative procedure that involves repeated multiplications of a vector, or a collection of vectors, with both a sparse matrix and its transpose. Unfortunately, the realization of these sparse products on current high performance libraries often deliver much lower arithmetic throughput when the matrix involved in the product is transposed. In this work, we propose a hybrid sparse matrix layout, named CSRC, that combines the flexibility of some well‐known sparse formats to offer a number of appealing properties: (1) CSRC can be obtained at low cost from the popular CSR (compressed sparse row) format; (2) CSRC has similar storage requirements as CSR; and especially, (3) the implementation of the sparse product kernels delivers high performance for both the direct product and its transposed variant on modern graphics accelerators thanks to a significant reduction of atomic operations compared to a conventional implementation based on CSR. This solution thus renders considerably higher performance when integrated into an iterative algorithm for the truncated singular value decomposition (SVD), such as the randomized SVD or, as demonstrated in the experimental results, the block Golub–Kahan–Lanczos algorithm.

Aliaga, José I.↗
DOE OSTI2018

Design Principles for Sparse Matrix Multiplication on the GPU

We implement two novel algorithms for sparse-matrix dense-matrix multiplication (SpMM) on the GPU. Our algorithms expect the sparse input in the popular compressed-sparse-row (CSR) format and thus do not require expensive format conversion. While previous SpMM work concentrates on thread-level parallelism, we additionally focus on latency hiding with instruction-level parallelism and load-balancing. We show, both theoretically and experimentally, that the proposed SpMM is a better fit for the GPU than previous approaches. We identify a key memory access pattern that allows efficient access into both input and output matrices that is crucial to getting excellent performance on SpMM. By combining these two ingredients---(i) merge-based load-balancing and (ii) row-major coalesced memory access---we demonstrate a 4.1x peak speedup and a 31.7% geomean speedup over state-of-the-art SpMM implementations on real-world datasets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Performance analysis of distributed symmetric sparse matrix vector multiplication algorithm for multi-core architectures

In this article, sparse matrix vector multiply (SpMVM) is an important kernel that frequently arises in high performance computing applications. Due to its low arithmetic intensity, several approaches have been proposed in literature to improve its scalability and efficiency in large scale computations. In this paper, our target systems are high end multi-core architectures and we use messaging passing interface + open multiprocessing hybrid programming model for parallelism. We analyze the performance of recently proposed implementation of the distributed symmetric SpMVM, originally developed for large sparse symmetric matrices arising in ab initio nuclear structure calculations. We also study important features of this implementation and compare with previously reported implementations that do not exploit underlying symmetry. Our SpMVM implementations leverage the hybrid paradigm to efficiently overlap expensive communications with computations. Our main comparison criterion is the "CPU core hours" metric, which is the main measure of resource usage on supercomputers. We analyze the effects of topology-aware mapping heuristic using simplified network load model. Furthermore, we have tested the different SpMVM implementations on two large clusters with 3D Torus and Dragonfly topology. Our results show that the distributed SpMVM implementation that exploits matrix symmetry and hides communication yields the best value for the "CPU core hours" metric and significantly reduces data movement overheads.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Sparse matrix methods research using the CSM testbed software system

Research is described on sparse matrix techniques for the Computational Structural Mechanics (CSM) Testbed. The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the CSM Testbed. Thus, one of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A suite of subroutines to extract from the data base the relevant structural and numerical information about the matrix equations was written, and all the demonstration problems distributed with the testbed were successfully solved. These codes were documented, and performance studies comparing the SPARSPAK technology to the methods currently in the testbed were completed. In addition, some preliminary studies were done comparing some recently developed out-of-core techniques with the performance of the testbed processor INV.

Chu, Eleanor↗
NASA NTRS1976

An algorithm for reducing the bandwidth and profile of a sparse matrix

A new algorithm for reducing the bandwidth and profile of a sparse matrix is described. Extensive testing on finite element matrices indicates that the algorithm typically produces bandwidth and profile which are comparable to those of the commonly-used reverse Cuthill-McKee algorithm, yet requires significantly less computation time.

Gibbs, N. E.↗
NASA NTRS1990

SPARSKIT: A basic tool kit for sparse matrix computations

Presented here are the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate the exchange of software and data between researchers in sparse matrix computations. The starting point is the Harwell/Boeing collection of matrices for which the authors provide a number of tools. Among other things, the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, and performing linear algebra operations with sparse matrices.

Saad, Youcef↗