Abstract
The QR decomposition with column pivoting (QRP) of a matrix is widely used for rank revealing. The performance of LAPACK implementation (DGEQP3) of the Householder QRP algorithm is limited by Level 2 BLAS operations required for updating the column norms. In this paper, we propose an implementation of the QRP algorithm using a distribution of the matrix columns in a round-robin fashion for better data locality and parallel memory bus utilization on multicore architectures. Our performance results show a 60% improvement over the routine DGEQP3 of Intel MKL (version 10.3) on a 12 core Intel Xeon X5670 machine. In addition, we show that the same data distribution is also suitable for general purpose GPU processors, where our implementation obtains up to 90 GFlops on a NVIDIA GeForce GTX480. This is about 2 times faster than the QRP implementation of MAGMA (version 1.2.1).
Topics. Parallel and Distributed Computing.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bischof, C.H.: A parallel QR factorization algorithm with controlled local pivoting. SIAM J. Sci. Stat. Comput. 12, 36–57 (1991)
Chandrasekaran, S., Ipsen, I.C.F.: On rank-revealing factorisations. SIAM J. Matrix Anal. Appl. 15, 592–622 (1994)
Castaldo, A.M., Whaley, R.C.: Scaling LAPACK panel operations using parallel cache assignment. In: 15th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming, pp. 223–231 (2010)
Drmač, Z., Bujanović, Z.: On the failure of rank-revealing QR factorization software – a case study. ACM Trans. Math. Softw. 35, 12:1–12:28 (2008)
Drmač, Z., Veselić, K.: New fast and accurate Jacobi SVD algorithm I. SIAM J. Matrix Anal. Appl. 29, 1322–1342 (2008)
Drmač, Z., Veselić, K.: New fast and accurate Jacobi SVD algorithm II. SIAM J. Matrix Anal. Appl. 29, 1343–1362 (2008)
Golub, G.H.: Numerical methods for solving linear least squares problems. Numer. Math. 7, 206–216 (1965)
Gu, M., Eisenstat, S.: Efficient algorithms for computing a strong rank-revealing QR factorization. SIAM J. Sci. Comput. 17, 848–869 (1996)
Quintana-Orti, G., Sun, X., Bischof, C.H.: A BLAS-3 version of the QR factorization with column pivoting. SIAM J. Sci. Comput. 19, 1486–1494 (1998)
Schreiber, R., van Loan, C.: A storage-efficient WY representation for products of Householder transformations. SIAM J. Sci. Stat. Comput. 10, 53–57 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tomás, A., Bai, Z., Hernández, V. (2013). Parallelization of the QR Decomposition with Column Pivoting Using Column Cyclic Distribution on Multicore and GPU Processors. In: Daydé, M., Marques, O., Nakajima, K. (eds) High Performance Computing for Computational Science - VECPAR 2012. VECPAR 2012. Lecture Notes in Computer Science, vol 7851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38718-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-38718-0_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38717-3
Online ISBN: 978-3-642-38718-0
eBook Packages: Computer ScienceComputer Science (R0)