We build two high-performance implementations of the QR factorization optimized for the long vector units in the accelerator developed as part of the European Processor Initiative. Both realizations, based on the Householder and Gram-Schmidt (GS) methods respectively, are optimized via linear algebra kernels that can be reused for other applications. The experimental evaluation on an early test-chip of this accelerator shows significant gains over the LAPACK code running on a scalar RISC-V core. It also shows the superiority of the Householder-based solution for square matrices and the advantages of GS for tall-and-skinny matrices when both the triangular and orthogonal factors are needed.

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QR Factorization on a Long-Vector Processor

  • Andrés E. Tomás,
  • Pablo Vizcaino,
  • Enrique S. Quintana-Ortí,
  • Filippo Mantovani

摘要

We build two high-performance implementations of the QR factorization optimized for the long vector units in the accelerator developed as part of the European Processor Initiative. Both realizations, based on the Householder and Gram-Schmidt (GS) methods respectively, are optimized via linear algebra kernels that can be reused for other applications. The experimental evaluation on an early test-chip of this accelerator shows significant gains over the LAPACK code running on a scalar RISC-V core. It also shows the superiority of the Householder-based solution for square matrices and the advantages of GS for tall-and-skinny matrices when both the triangular and orthogonal factors are needed.