List of Notation

  

 
1D 		 One-dimensional (as in 1D data distribution)

 		 Bandwidth (or throughput) for the network

2D 		 Two-dimensional (as in 2D data distribution)

 		 Total number of floating-point operations 

 		 Total number of messages 

CSRC_ Entry in DESC_ indicating the process column over which

        		 the first column of the array is distributed 

CTXT_ Entry in DESC_ indicating the BLACS context associated with the

        		 global array  

 		 Total number of data items communicated 

DESC_ Array descriptor for a global array 

DESCA  		 Array descriptor for global array A

DESCB  		 Array descriptor for global array B

DLEN_ Length of the descriptor DESC_ 

DTYPE_ First entry of the descriptor DESC_, identifying

        		 the descriptor type  

E()   		 Estimated parallel efficiency 

 		 Time per floating point operation in matrix-matrix multiply 

Gflop/s 		 Gigaflops ( floating point operations) per second

IA     		 Global row index in the global array A indicating the

       		 first row of  

ICTXT 		 BLACS context associated with a process grid 

INFO 		 Output integer argument of driver and computational routines

     		 indicating the success or failure of the routine

JA     		 Global column index in the global array A indicating the

       		 first column of  

 		 Least common multiple of () 

LLD_ Entry in DESC_ indicating the local leading dimension of the

      		 local array 

 		 Local leading dimension of the local array A

 		 Local leading dimension of the local array B

(K_) 		 Number of columns that a process receives if  columns

               		 of a matrix are distributed over c columns of its process row. 

(K_) 		 Number of rows that a process would receive if  rows

               		 of a matrix are distributed over r rows of its process column. 

M     		 Global number of rows of the distributed submatrix 

M_ Entry of DESC_ indicating the number of rows in the global

      		 array 

MB    		 Global row block size for partitioning the global matrix

MB_ Entry in DESC_ indicating the block size used to distribute

      		 the rows of the global array 

MB/s 		 Megabyte per second

Mflop/s 		 Megaflops ( floating point operations) per second

MYCOL  		 The calling process's column coordinate in the process grid. 

MYROW  		 The calling process's row coordinate in the process grid 

N     		 Global number of columns of the distributed submatrix 

N_ Entry of DESC_ indicating the number of columns in the

      		 global array 

NB    		 Global column block size for partitioning the global matrix

NB_ Entry in DESC_ indicating the block size used to distribute

      		 the columns of the global array 

NBRHS 		 Global column block size for the solution matrix 

NPCOL  		 Number of process columns in the process grid (equivalent to ) 

NPROCS 		 Total number of processes in the process grid (equivalent to P) 

NPROW  		 Number of process rows in the process grid (equivalent to ) 

NRHS  		 Global number of columns in the global solution matrix B 

NUMROC 		 TOOLS routine used to calculate the number of rows or columns

       		 in a local array 

P     		 Total number of processes in the process grid, i.e.,  

 		 Number of process columns in the process grid 

 		 Number of process rows in the process grid 

RSRC_ Entry in DESC_ indicating the process row over which the

        		 first row of the array is distributed 

 		 Distributed submatrix A(IA:IA+M-1,JA:JA+N-1)

T()   		 Estimated parallel execution time 

() 		 Estimated serial execution time 

 		 Time per floating-point operation (typically ) 

 		 Time per message (latency) 

 		 Time required to solve a problem of size N on P processors 

 		 Time required to solve a problem of size N/2 on P processors 

 		 Time per data item communicated