PCLAQGE(3) ScaLAPACK routine of NEC Numeric Library Collection PCLAQGE(3)
NAME
PCLAQGE - equilibrate a general M-by-N distributed matrix sub( A ) =
A(IA:IA+M-1,JA:JA+N-1) using the row and scaling factors in the vectors
R and C
SYNOPSIS
SUBROUTINE PCLAQGE( M, N, A, IA, JA, DESCA, R, C, ROWCND, COLCND, AMAX,
EQUED )
CHARACTER EQUED
INTEGER IA, JA, M, N
REAL AMAX, COLCND, ROWCND
INTEGER DESCA( * )
REAL C( * ), R( * )
COMPLEX A( * )
PURPOSE
PCLAQGE equilibrates a general M-by-N distributed matrix sub( A ) =
A(IA:IA+M-1,JA:JA+N-1) using the row and scaling factors in the vectors
R and C.
Notes
=====
Each global data object is described by an associated description vec-
tor. This vector stores the information required to establish the map-
ping between an object element and its corresponding process and memory
location.
Let A be a generic term for any 2D block cyclicly distributed array.
Such a global array has an associated description vector DESCA. In the
following comments, the character _ should be read as "of the global
array".
NOTATION STORED IN EXPLANATION
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
M_A (global) DESCA( M_ ) The number of rows in the global
array A.
N_A (global) DESCA( N_ ) The number of columns in the global
array A.
MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
the rows of the array.
NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
row of the array A is distributed.
CSRC_A (global) DESCA( CSRC_ ) The process column over which the
first column of the array A is
distributed.
LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
array. LLD_A >= MAX(1,LOCr(M_A)).
Let K be the number of rows or columns of a distributed matrix, and
assume that its process grid has dimension p x q.
LOCr( K ) denotes the number of elements of K that a process would
receive if K were distributed over the p processes of its process col-
umn.
Similarly, LOCc( K ) denotes the number of elements of K that a process
would receive if K were distributed over the q processes of its process
row.
The values of LOCr() and LOCc() may be determined via a call to the
ScaLAPACK tool function, NUMROC:
LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). An upper
bound for these quantities may be computed by:
LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
ARGUMENTS
M (global input) INTEGER
The number of rows to be operated on i.e the number of rows of
the distributed submatrix sub( A ). M >= 0.
N (global input) INTEGER
The number of columns to be operated on i.e the number of
columns of the distributed submatrix sub( A ). N >= 0.
A (local input/local output) COMPLEX pointer into the
local memory to an array of dimension (LLD_A,LOCc(JA+N-1)) con-
taining on entry the M-by-N matrix sub( A ). On exit, the equi-
librated distributed matrix. See EQUED for the form of the
equilibrated distributed submatrix.
IA (global input) INTEGER
The row index in the global array A indicating the first row of
sub( A ).
JA (global input) INTEGER
The column index in the global array A indicating the first
column of sub( A ).
DESCA (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix A.
R (local input) REAL array, dimension LOCr(M_A)
The row scale factors for sub( A ). R is aligned with the dis-
tributed matrix A, and replicated across every process column.
R is tied to the distributed matrix A.
C (local input) REAL array, dimension LOCc(N_A)
The column scale factors of sub( A ). C is aligned with the
distributed matrix A, and replicated down every process row. C
is tied to the distributed matrix A.
ROWCND (global input) REAL
The global ratio of the smallest R(i) to the largest R(i), IA
<= i <= IA+M-1.
COLCND (global input) REAL
The global ratio of the smallest C(i) to the largest C(i), JA
<= j <= JA+N-1.
AMAX (global input) REAL
Absolute value of largest distributed submatrix entry.
EQUED (global output) CHARACTER
Specifies the form of equilibration that was done. = 'N': No
equilibration
= 'R': Row equilibration, i.e., sub( A ) has been pre-
multiplied by diag(R(IA:IA+M-1)),
= 'C': Column equilibration, i.e., sub( A ) has been post-
multiplied by diag(C(JA:JA+N-1)),
= 'B': Both row and column equilibration, i.e., sub( A ) has
been replaced by diag(R(IA:IA+M-1)) * sub( A ) *
diag(C(JA:JA+N-1)).
PARAMETERS
THRESH is a threshold value used to decide if row or column scaling
should be done based on the ratio of the row or column scaling factors.
If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column
scaling is done.
LARGE and SMALL are threshold values used to decide if row scaling
should be done based on the absolute size of the largest matrix ele-
ment. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
ScaLAPACK routine 31 October 2017 PCLAQGE(3)