The design and implementation of SOLAR, a portable library for scalable out-of-core linear algebra computations. SOLAR is a portable high-performance library for out-of-core dense matrix computations. It combines portability with high performance by using existing high-performance in-core subroutine libraries and by using an optimized matrix input-output library. SOLAR works on parallel computers, workstations, and personal computers. It supports in-core computations on both shared-memory and distributed-memory machines, and its matrix input-output library supports both conventional I/O interfaces and parallel I/O interfaces. This paper discusses the overall design of SOLAR, its interfaces, and the design of several important subroutines. Experimental results show that SOLAR can factor on a single workstation an out-of-core positive-definite symmetric matrix at a rate exceeding 215 Mflops, and an out-of-core general matrix at a rate exceeding 195 Mflops. Less than 16 % of the running time is spent on I/O in these computations. These results indicate that SOLAR’s portability does not compromise its performance. We expect that the combination of portability, modularity, and the use of a high-level I/O interface will make the library an important platform for research on out-of-core algorithms and on parallel I/O.

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  1. D’Azevedo, Eduardo; Hu, Zhiang; Su, Shi-Quan; Wong, Kwai: Solving a large scale radiosity problem on GPU-based parallel computers (2014)
  2. D’Azevedo, E.F.; Nintcheu Fata, S.: On the effective implementation of a boundary element code on graphics processing units using an out-of-core LU algorithm (2012)
  3. Badia, J.M.; Movilla, J.L.; Climente, J.I.; Castillo, M.; Marqués, M.; Mayo, R.; Quintana-Ortí, E.S.; Planelles, J.: Large-scale linear system solver using secondary storage: self-energy in hybrid nanostructures (2011)
  4. Kot, Andriy; Chernikov, Andrey N.; Chrisochoides, Nikos P.: Effective out-of-core parallel Delaunay mesh refinement using off-the-shelf software (2011)
  5. Castillo, Maribel; Igual, Francisco D.; Marqués, Mercedes; Mayo, Rafael; Quintana-Ortí, Enrique S.; Quintana-Ortí, Gregorio; Rubio, Rafael; van de Geijn, Robert: Out-of-core solution of linear systems on graphics processors (2009)
  6. Béreux, Natacha: Out-of-core implementations of Cholesky factorization: loop-based versus recursive algorithms (2008)
  7. Vilayannur, Murali; Sivasubramaniam, Anand; Kandemir, Mahmut; Thakur, Rajeev; Ross, Robert: Discretionary caching for I/O on clusters (2006) ioport
  8. Gunter, Brian C.; van de Geijn, Robert A.: Parallel out-of-core computation and updating of the QR factorization (2005)
  9. Rotkin, Vladimir; Toledo, Sivan: The design and implementation of a new out-of-core sparse Cholesky factorization method (2004)
  10. Strazdins, Peter E.: Issues in the design of scalable out-of-core dense symmetric indefinite factorization algorithms (2003)
  11. Kandemir, Mahmut; Choudhary, Alok; Ramanujam, J.: An I/O-conscious tiling strategy for disk-resident data sets (2002)
  12. Toledo, Sivan; Rabani, Eran: Very large electronic structure calculations using an out-of-core filter-diagonalization method (2002)
  13. D’Azevedo, Eduardo; Dongarra, Jack: The design and implementation of the parallel out-of-core scaLAPACK LU, QR, and Cholesky factorization routines (2001)
  14. Toledo, Sivan: A survey of out-of-core algorithms in numerical linear algebra (1999)
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