Sparse matrix-vector multiplication (SpMV) is a fundamental building block for numerous applications. In this paper, we propose CSR5 (Compressed Sparse Row 5), a new storage format, which offers high-throughput SpMV on various platforms including CPUs, GPUs and Xeon Phi. First, the CSR5 format is insensitive to the sparsity structure of the input matrix. Thus the […]

March 20, 2015 by hgpu

Sparse matrix multiplication is an important algorithm in a wide variety of problems, including graph algorithms, simulations and linear solving to name a few. Yet, there are but a few works related to acceleration of sparse matrix multiplication on a GPU. We present a fast, novel algorithm for sparse matrix multiplication, outperforming the previous algorithm […]

March 18, 2015 by hgpu

Fast sorting is an important step in many parallel algorithms, which require data ranking, ordering or partitioning. Parallel sorting is a widely researched subject, and many algorithms were developed in the past. In this paper, the focus is on implementing highly efficient sorting routines for the sparse linear algebra operations, such as parallel sparse matrix […]

March 18, 2015 by hgpu

ViennaCL is a free open-source linear algebra library for computations on many-core architectures (GPUs, MIC) and multi-core CPUs. The library is written in C++ and supports CUDA, OpenCL, and OpenMP. In addition to core functionality and many other features including BLAS level 1-3 support and iterative solvers, the latest release family ViennaCL 1.6.x provides fast […]

February 22, 2015 by hgpu

Sparse Matrix-Vector multiplication (SpMV) is one of the key operations in linear algebra. Overcoming thread divergence, load imbalance and un-coalesced and indirect memory access due to sparsity and irregularity are challenges to optimizing SpMV on GPUs. This dissertation develops solutions that address these challenges effectively. The first part of this dissertation focuses on a new […]

February 9, 2015 by hgpu

This technical report provides performance numbers for several benchmark problems running on several different hardware platforms. The goal of this report is twofold. First, it helps us better understand how the performance of OpenCL changes on different platforms. Second, it provides a OpenCL-OpenMP comparison for a sparse matrix-vector multiplication operation. The VexCL library will be […]

February 6, 2015 by hgpu

We present a library for parallel block-sparse matrix-matrix multiplication on distributed memory clusters. The library is based on the Chunks and Tasks programming model [Parallel Comput. 40, 328 (2014)]. Acting as matrix library developers, using this model we do not have to explicitly deal with distribution of work and data or communication between computational nodes […]

February 2, 2015 by hgpu

Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage of GPU hardware. As sparse matrix vector multiplication (SPMV) operations are commonly used in finite element analysis, a new SPMV algorithm and several variations are […]

January 5, 2015 by hgpu

We present an interpretation of subdivision surface evaluation in the language of linear algebra. Specifically, the vector of surface points can be computed by left-multiplying the vector of control points by a sparse subdivision matrix. This "matrix-driven" interpretation applies to any level of subdivision, holds for many common subdivision schemes (including Catmull-Clark and Loop), supports […]

January 5, 2015 by hgpu

This paper presents a sparse matrix partitioning strategy to improve the performance of SpMV on GPUs and multicore CPUs. This method has wide adaptability for different types of sparse matrices, and is different from existing methods which only adapt to some particular sparse matrices. In addition, our partitioning method can obtain dense blocks by analyzing […]

November 3, 2014 by hgpu

A multi-dimensional data model provides a good conceptual view of the data in data warehousing and On-Line Analytical Processing (OLAP). A typical representation of such a data model is as a multi-dimensional array which is well suited when the array is dense. If the array is sparse, i.e., has a few number of non-zero elements […]

September 8, 2014 by hgpu

The runtime of a Lattice QCD simulation is dominated by a small kernel, which calculates the product of a vector by a sparse matrix known as the "Dslash" operator. Therefore, this kernel is frequently optimized for various HPC architectures. In this contribution we compare the performance of the Intel Xeon Phi to current Kepler-based NVIDIA […]

September 5, 2014 by hgpu