Energy efficient data flow transformation for Givens Rotation based QR Decomposition

Abstract

QR Decomposition (QRD) is a typical matrix decomposition algorithm that shares many common features with other algorithms such as LU and Cholesky decomposition. The principle can be realized in a large number of valid processing sequences that differ significantly in the number of memory accesses and computations, and hence, the overall implementation energy. With modern low power embedded processors evolving towards register files with wide memory interfaces and vector functional units (FUs), the data flow in matrix decomposition algorithms needs to be carefully devised to achieve energy efficient implementation. In this paper, we present an efficient data flow transformation strategy for the Givens Rotation based QRD that optimizes data memory accesses. We also explore different possible implementations for QRD of multiple matrices using the SIMD feature of the processor. With the proposed data flow transformation, a reduction of up to 36% is achieved in the overall energy over conventional QRD sequences.