Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set using multiatom blocks

Chandra Saravanan; Yihan Shao; Roi Baer; Philip N Ross; Martin Head-Gordon

doi:10.1002/jcc.10224

Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set using multiatom blocks

J Comput Chem. 2003 Apr 15;24(5):618-22. doi: 10.1002/jcc.10224.

Authors

Chandra Saravanan¹, Yihan Shao, Roi Baer, Philip N Ross, Martin Head-Gordon

Affiliation

¹ Department of Chemistry, University of California, Berkeley, California 94720, USA.

PMID: 12632476
DOI: 10.1002/jcc.10224

Abstract

A sparse matrix multiplication scheme with multiatom blocks is reported, a tool that can be very useful for developing linear-scaling methods with atom-centered basis functions. Compared to conventional element-by-element sparse matrix multiplication schemes, efficiency is gained by the use of the highly optimized basic linear algebra subroutines (BLAS). However, some sparsity is lost in the multiatom blocking scheme because these matrix blocks will in general contain negligible elements. As a result, an optimal block size that minimizes the CPU time by balancing these two effects is recovered. In calculations on linear alkanes, polyglycines, estane polymers, and water clusters the optimal block size is found to be between 40 and 100 basis functions, where about 55-75% of the machine peak performance was achieved on an IBM RS6000 workstation. In these calculations, the blocked sparse matrix multiplications can be 10 times faster than a standard element-by-element sparse matrix package.