What is the blocking factor used to distribute the array?

Question

In the documentation for example of descinit we find the following attributes in the descriptor of a distributed array (arguments 4 and 5):

 *  MB      (global input) INTEGER
 *          The blocking factor used to distribute the rows of the
 *          matrix. MB >= 1.
 *
 *  NB      (global input) INTEGER
 *          The blocking factor used to distribute the columns of the
 *          matrix. NB >= 1.

What is the blocking factor described here ?

Answer 1

Blocking factors determine the memory layout of a 2D block-cyclic array. For example, a 6x5 array with a 2x2 BLACS process grid and a blocking factor of 2 across rows and columns could be distributed like this:

0 0 1 1 0
0 0 1 1 0
2 2 3 3 2
2 2 3 3 2
0 0 1 1 0
0 0 1 1 0

Here process 0 holds two full blocks and two half blocks, meaning the global dimensions of the array don't have to be multiples of the blocking factors.

Increasing the block size leads to less MPI communication overhead whereas a smaller block size, depending on the array dimensions, can lead to better load balancing.