Sparse Matrix-Vector Multiplication (SpMV) kernel dominates the computing cost in numerous scientific applications. Many implementations based on different sparse formats were proposed recently for this kernel on the GPU side. Since the performance of these sparse formats varies significantly according to the sparsity characteristics of the input matrix and the hardware specifications, no one of them can be considered as the best one to use for every sparse matrix. In this paper, we address the problem of selecting the best representation for a given sparse matrix on GPU by using a machine learning approach. First, we present some interesting and easy to compute features for characterizing the sparse matrices on GPU. Second, we use a multiclass Support Vector Machine (SVM) classifier to select the best format for each input matrix. We consider in this paper four popular formats (COO, CSR, ELL, and HYB), but our work can be extended to support more sparse representations. Experimental results on two different GPUs (Fermi GTX 580 and Maxwell GTX 980 Ti) show that we achieved more than 98% of the performance possible with a perfect selection.

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The Sparse Matrix-Vector Multiplication (SpMV) kernel dominates the computing cost in numerous scientific applications. Many implementations based on different sparse formats were proposed to improve this kernel on the recent GPU architectures. However, it has been widely observed that there is no "best-for-all" sparse format for the SpMV kernel on GPU. Indeed, serious performance degradation of an order of magnitude can be observed without a careful selection of the sparse format to use. To address this problem, we propose in this article BestSF (Best Sparse Format), a new learning-based sparse meta-format that automatically selects the most appropriate sparse format for a given input matrix. To do so, BestSF relies on a cost-sensitive classification system trained using Weighted Support Vector Machines (WSVMs) to predict the best sparse format for each input sparse matrix. Our experimental results on two different NVIDIA GPU architectures using a large number of real-world sparse matrices show that BestSF achieved a noticeable overall performance improvement over using a single sparse format. While BestSF is trained to select the best sparse format in terms of performance (GFLOPS), our further experimental investigations revealed that using BestSF also led, in most of the test cases, to the best energy efficiency (MFLOPS/W). To prove its practical effectiveness, we also evaluate the performance and energy efficiency improvement achieved when using BestSF as a building block in a GPU-based Preconditioned Conjugate Gradient (PCG) iterative solver.

Sparse matrix–vector multiplication (SpMV) kernel dominates the computing cost in numerous applications. Most of the existing studies dedicated to improving this kernel have been targeting just one type of processing units, mainly multicore CPUs or graphics processing units (GPUs), and have not explored the potential of the recent, rapidly emerging, CPU-GPU heterogeneous platforms. To take full advantage of these heterogeneous systems, the input sparse matrix has to be partitioned on different available processing units. The partitioning problem is more challenging with the existence of many sparse formats whose performances depend both on the sparsity of the input matrix and the used hardware. Thus, the best performance does not only depend on how to partition the input sparse matrix but also on which sparse format to use for each partition. To address this challenge, we propose in this article a new CPU-GPU heterogeneous method for computing the SpMV kernel that combines between different sparse formats to achieve better performance and better utilization of CPU-GPU heterogeneous platforms. The proposed solution horizontally partitions the input matrix into multiple block-rows and predicts their best sparse formats using machine learning-based performance models. A mapping algorithm is then used to assign the block-rows to the CPU and GPU(s) available in the system. Our experimental results using real-world large unstructured sparse matrices on two different machines show a noticeable performance improvement.

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