I am using LSQR to minimize || L x - b ||_2, where L is a sparse rectangular matrix with 145,253,395 rows, 209,423,775 columns, and around 54 billion non zeros.
The numbers reported below are for a run with 27 compute nodes, each compute node with 4 MPI ranks, so a total of 108 ranks. Throughout the run, I assess the runtime taken by all dot products during the LSQR iterations, and I differentiate between dot products involving vectors of the size of the solution vector "x", and dot products involving vectors of the size of the rhs "b". Here are the numbers I get (we have an implementation of LSQR that performs some extra vector dot products for our needs): 236 VecDotSol take 1.523 seconds 226 VecDotRhs take 326.008 seconds Regarding the partition of rows and columns among the 108 MPI ranks: Rows: min = 838,529 ; avg = 1.34494e+06 ; max = 2,437,206 Columns: min = 1,903,500 ; avg = 1.93911e+06 ; max = 1,946,270 Regarding the partition of rows and columns among the 27 compute nodes: Rows: min = 3,575,584 ; avg = 5.37976e+06 ; max = 8,788,062 Columns: min = 7,637,500 ; avg = 7.75644e+06 ; max = 7,785,080 Questions: 1. Why the average run times are so different between VecDotSol and VecDotRhs? 2. Could the much bigger unbalancing among the number of rows per rank (compared to the very well balanced distribution of columns per rank) be the cause? 3. Have you ever observed such situation? 4. Could it be because of a bad MPI configuration / parametrization with respect to the underlying network? 5. But, if yes, why the VecDotSol dot products are so much faster than VecDotRhs? Thank you in advance, Ernesto. Schlumberger-Private
