The model of the computing environment for PBLAS is represented as a one-dimensional array of processes or also a two-dimensional process grid. To use PBLAS, all global matrices or vectors must be distributed on this array or grid prior to calling the PBLAS routines.

PBLAS uses the two-dimensional block-cyclic data distribution as a layout for dense matrix computations. This distribution provides good work balance between available processors, as well as gives the opportunity to use PBLAS Level 3 routines for optimal local computations. Information about the data distribution that is required to establish the mapping between each global array and its corresponding process and memory location is contained in the so called array descriptor associated with each global array. Table

"Content of the array descriptor for dense matrices"

gives an example of an array descriptor structure.

The number of rows and columns of a global dense matrix that a particular process in a grid receives after data distributing is denoted by

LOCr

()

and

LOCc

()

, respectively. To compute these numbers, you can use the ScaLAPACK tool routine

numroc

.

After the block-cyclic distribution of global data is done, you may choose to perform an operation on a submatrix of the global matrix

A

, which is contained in the global subarray

sub(

A

)

, defined by the following 6 values (for dense matrices):

Intel® oneAPI Math Kernel Library

provides the PBLAS routines with interface similar to the interface used in the Netlib PBLAS (see http://www.netlib.org/scalapack/html/pblas_qref.html).