Multilevel communication optimal least squares

Using a recently proposed communication optimal variant of TSQR, weak scalability of the least squares solver (LS) with multiple right hand sides is studied. The communication for TSQR based LS solver for multiple right hand sides remains optimal in the sense that no additional messages are necessary compared to TSQR. However, LS has additional communication volume and flops compared to that for TSQR. Additional flops and words sent for LS is derived. A PGAS model, namely, global address space programming framework (GPI) is used for inter- nodal one sided communication. Within NUMA sockets, C++-11 threading model is used. Scalability results of the proposed method up to a few thousand cores are shown.