Sparse Matrix Multiplication Cost

962 Sparse Matrix Vector Multiplication. On all real-valued matrices from the Sparse Matrix Collection we obtain a maximum speedup of 261 times and average speedup of 106 times over double precision while maintaining higher accuracy compared to single precision.

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The computational complexity of sparse operations is proportional to nnz the number of nonzero elements in the matrixComputational complexity also depends linearly on the row size m and column size n of the matrix but is independent of the product mn the total number of zero and nonzero elements.

Sparse matrix multiplication cost. In this work we propose MatRaptor a novel SpGEMM accelerator that is high performance and highly resource efficient. For example the time cost of calculating the multiplication of a 8000 8000 sparse matrix with sparsity of 09 ie 90 of elements are zeros to a dense matrix with single precision requires 780 m s by using cuSPARSE on an Nvidia Tesla P100 GPU while the corresponding dense algorithm by cuBLAS only requires 121 m s. Kreutzer Hager Wellein Fehske and Bishop A unified sparse matrix data format for modern processors with wide SIMD units 2014.

Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid. Sparse matrixvector multiplication SpMV is a crucial operation used for solving many engineering and scientific problems. Sparse matrix-matrix multiplication or SpGEMM is a key primitive for many high-performance graph algorithms as well as for some linear solvers such as algebraic multigrid.

Thus sparse matrix multiplication algorithms must mini-mize communication costs in order to scale to large processor counts. Liu Smelyanskiy Chow and Dubey Efficient sparse matrix-vector multiplication on x86-based many-core processors 2013. 1 Introduction 15 Sparse -Spar se SS matrix multiplication forms the computational backbone of scientific computation in many fields.

Further reduce the cost of sparse matrix multiplication by yielding only upper triangular andor dense matrices. Fast sparse matrix multiplication Raphael Yuster y Uri Zwick z Abstract Let A and B two n n matrices over a ring R eg the reals or the integers each containing at most m non-zero elements. The following code fragment performs the matrix-vector multiplication when the matrix is stored using the Compressed Sparse Row method.

I ELLPACK Sparse Block ESB format. I want to express the computational complexity fo two algorithms. Matrix-vector multiplication in the Compressed Sparse Row method.

Given two sparse matrices Sparse Matrix and its representations Set 1 Using Arrays and Linked Lists perform operations such as add multiply or transpose of the matrices in their sparse form itselfThe result should consist of three sparse matrices one obtained by adding the two input matrices one by multiplying the two matrices and one obtained by transpose of the first matrix. Web of Science You must be logged in with an active subscription to view this. I distilled the problem down to the matrix multiplication cost Tsum x Tlog z.

Note that changing this cost function in the sparse case cell 3 to the squared error cost Tsum. In this paper we consider multiplying sparse matrices cor-responding to Erdos-R enyi random graphs on distributed-memory parallel machines. AbstractSparse-sparse matrix multiplication SpGEMM is a computation kernel widely used in numerous application domains such as data analytics graph processing and scientific comput-ing.

1 1 1 Both cuSPARSE and cuBLAS are from the library of. The sparse-matrix sparse-vector multiplication and the sparse-matrix sparse-matrix multiplication as implemented in Eigen or Cusparse using CSR representation. Parallel algorithms designed around halo exchange frequently show up not just in mesh-based solvers as seen in Section 961 but also in sparse linear algebra operations such as the sparse matrix vector multiplication used in the high performance conjugate gradients HPCG benchmark presented in.

This preprocessing phase is inexpensive enough for the associated cost to be compensated in just a few repetitions of. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. This works in the dense case see cell 2 but gives an error in the sparse case see cell 3.

Parallel sparse gpu matrix-matrix 1 Introduction Operations on sparse data structures abound in all areas of information and physical science. In general there is no single SpMV method that gives high performance for all sparse matrices. We prove a new lower bound on the expected communication cost for a wide class.

Sparse Matrix Operations Efficiency of Operations Computational Complexity. Nnz Number of Non-Zero values N dimension of matrix Row access is easy but column access difficult. In particular the sparse matrix-matrix multiplication SpMM is a fundamental operation that arises in many practical contexts including.

I know that it depends on several parameters especially the number of non-zero values in each elements. MpSpMVs decision to lower to single precision is data driven based on individual nonzero values of the sparse matrix. We present a new algorithm that multiplies A and B using Om07n12 n2o1 alge- braic operations ie multiplications additions and subtractions over RThe naive matrix multiplication.

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