Abstract. A QR factorization of a tall and skinny matrix with n columns can be represented as a reduction. The operation used along the reduction tree has in input two n-by-n upper triangular matrices and in output an n-by-n upper triangular matrix which is defined as the R factor of the two input matrices stacked the one on top of the other. This operation is binary, associative, and commutative. We can therefore leverage the MPI library capabilities by using user-defined MPI operations and MPI Reduce to perform this reduction. The resulting code is compact and portable. In this context, the user relies on the MPI library to select a reduction tree appropriate for the underlying architecture.
Assuming that the QR factorization of a tall and skinny matrix can be represented as a reduction, Langou REF implemented a methodology to perform the reduction by using user-defined MPI operation and MPI Reduce.
Computing the R of the QR factorization of tall and skinny matrices using MPI_Reduce
arXiv: Numerical Analysis
Mathematics Computer Science