Parallel Engineering and Scientific Subroutine Library for AIX Version 2 Release 3: Guide and Reference

NUMROC--Compute the Number of Rows or Columns of a Block-Cyclically Distributed Matrix Contained in a Process

This function computes the local number of rows or columns of a block-cyclically distributed matrix contained in a process row or process column, respectively, indicated by the calling sequence argument iproc.

See references [14] and [15].

Syntax

On Entry

n

is the number of rows M_ or columns N_ in a global matrix that has been block-cyclically distributed.

Scope: global

Specified as: a fullword integer; n >= 0.

nb

is the row block size MB_ or the column block size NB_.

Scope: global

Specified as: a fullword integer; nb > 0.

iproc

is process row index myrow or the process column index mycol.

Scope: local

Specified as: a fullword integer; 0 <= iproc < nprocs.

isrcproc

is the process row RSRC_ or the process column CSRC_ over which the first row or column, respectively, of the global matrix is distributed.

Scope: global

Specified as: a fullword integer; 0 <= isrcproc < nprocs.

nprocs

is the number of rows nprow or the number of columns npcol in the process grid.

Scope: global

Specified as: a fullword integer; nprocs > 0.

On Return

Function value

is the local number of rows or columns of a block-cyclically distributed matrix contained in a process row or process column, respectively, indicated by the calling sequence argument iproc.

Scope: local

Returned as: a fullword integer.

Note

The variables p and nprow are used interchangeably to indicate the number of rows in a process grid. The variables q and npcol are used interchangeably to indicate the number of columns in a process grid.

Error Conditions

Computational Errors

None

Resource Errors

None

Input-Argument and Miscellaneous Errors

Stage 1:  

1. nb <= 0
2. nprocs <= 0

Example

This example shows the local invocations of NUMROC from four processes in a 2 × 2 process grid, using a global symmetric matrix of order 9.

Call Statements and Input

ORDER = 'R'
NPROW = 2
NPCOL = 2
CALL BLACS_GET(0, 0, ICONTXT)
CALL BLACS_GRIDINIT(ICONTXT, ORDER, NPROW, NPCOL)
CALL BLACS_GRIDINFO(ICONTXT, NPROW, NPCOL, MYROW, MYCOL)

The NUMROC function invocations and associated data on each process are shown in "Local Invocations of NUMROC."

The pertinent array descriptor values for global matrix C are shown below:

Global symmetric matrix C of order 9 is stored in upper storage mode with block sizes 4 × 4:

B,D             0                       1                2
     *                                                       *
     | -6.0  0.0  0.0  0.0  |   0.0 -2.0 -2.0  0.0  |   -2.0 |
     |   .  -6.0 -2.0  0.0  |  -2.0 -4.0  0.0 -4.0  |   -2.0 |
 0   |   .    .  -6.0 -2.0  |  -2.0  0.0  2.0  0.0  |    6.0 |
     |   .    .    .  -6.0  |   2.0  0.0  2.0  0.0  |    2.0 |
     | ---------------------|-----------------------|------- |
     |   .    .    .    .   |  -8.0 -4.0  0.0 -2.0  |    0.0 |
     |   .    .    .    .   |    .  -6.0  0.0 -4.0  |   -6.0 |
 1   |   .    .    .    .   |    .    .  -4.0  0.0  |    0.0 |
     |   .    .    .    .   |    .    .    .  -4.0  |   -4.0 |
     | ---------------------|-----------------------|------- |
 2   |   .    .    .    .   |    .    .    .    .   |  -16.0 |
     *                                                       *

The following is the 2 × 2 process grid:

B,D  |   0 2   |  1  
-----| ------- |-----
0    |   P00   |  P01
2    |         |
-----| ------- |-----
1    |   P10   |  P11

Local arrays for C:

p,q  |             0              |           1
-----|----------------------------|----------------------
     | -6.0  0.0  0.0  0.0  -2.0  |   0.0 -2.0 -2.0  0.0
     |   .  -6.0 -2.0  0.0  -2.0  |  -2.0 -4.0  0.0 -4.0
 0   |   .    .  -6.0 -2.0   6.0  |  -2.0  0.0  2.0  0.0
     |   .    .    .  -6.0   2.0  |   2.0  0.0  2.0  0.0
     |   .    .    .    .  -16.0  |    .    .    .    .
-----|----------------------------|----------------------
     |   .    .    .    .   0.0   |  -8.0 -4.0  0.0 -2.0
     |   .    .    .    .  -6.0   |    .  -6.0  0.0 -4.0
 1   |   .    .    .    .   0.0   |    .    .  -4.0  0.0
     |   .    .    .    .  -4.0   |    .    .    .  -4.0

Local Invocations of NUMROC:

p,q  |                      0                       |                       1
-----|----------------------------------------------|----------------------------------------------
     |             M_C  MB_C  MYROW  RSRC_C  NPROW  |              M_C  MB_C  MYROW  RSRC_C  NPROW
     |              |    |     |       |      |     |               |    |     |       |      |
     | MP = NUMROC( 9,   4,    0,      0,     2)    |  MP = NUMROC( 9,   4,    0,      0,     2)
 0   |                                              |
     |             N_C  NB_C  MYCOL  CSRC_C  NPCOL  |              N_C  NB_C  MYCOL  CSRC_C  NPCOL
     |              |    |     |       |      |     |               |    |     |       |      |
     | NQ = NUMROC( 9,   4,    0,      0,     2)    |  NQ = NUMROC( 9,   4,    1,      0,     2)
-----|----------------------------------------------|----------------------------------------------
     |             M_C  MB_C  MYROW  RSRC_C  NPROW  |              M_C  MB_C  MYROW  RSRC_C  NPROW
     |              |    |     |       |      |     |               |    |     |       |      |
     | MP = NUMROC( 9,   4,    1,      0,     2)    |  MP = NUMROC( 9,   4,    1,      0,     2)
 1   |                                              |
     |             N_C  NB_C  MYCOL  CSRC_C  NPCOL  |              N_C  NB_C  MYCOL  CSRC_C  NPCOL
     |              |    |     |       |      |     |               |    |     |       |      |
     | NQ = NUMROC( 9,   4,    0,      0,     2)    |  NQ = NUMROC( 9,   4,    1,      0,     2)

Output:

The local number of rows MP and columns NQ of the block-cyclically distributed matrix returned by NUMROC on each process:

p,q  |   0    |    1
-----|--------|--------
 0   |  MP=5  |   MP=5
     |  NQ=5  |   NQ=4
-----|--------|--------
 1   |  MP=4  |   MP=4
     |  NQ=5  |   NQ=4