PZLAQGE - 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
- SUBROUTINE PZLAQGE(
- M, N, A, IA, JA, DESCA, R, C, ROWCND, COLCND, AMAX, EQUED )
CHARACTER EQUED INTEGER IA, JA, M, N DOUBLE PRECISION AMAX, COLCND, ROWCND
INTEGER DESCA( * ) DOUBLE PRECISION C( * ), R( * ) COMPLEX*16 A( * )
PZLAQGE 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 vector. This
vector stores the information required to establish the mapping 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 column.
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
- 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*16 pointer into the
- local memory to an array of dimension (LLD_A,LOCc(JA+N-1)) containing on
entry the M-by-N matrix sub( A ). On exit, the equilibrated 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) DOUBLE PRECISION array, dimension LOCr(M_A)
- The row scale factors for sub( A ). R is aligned with the distributed
matrix A, and replicated across every process column. R is tied to the
distributed matrix A.
- C (local input) DOUBLE PRECISION 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) DOUBLE PRECISION
- The global ratio of the smallest R(i) to the largest R(i), IA <= i
<= IA+M-1.
- COLCND (global input) DOUBLE PRECISION
- The global ratio of the smallest C(i) to the largest C(i), JA <= j
<= JA+N-1.
- AMAX (global input) DOUBLE PRECISION
- 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)).
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 element. If AMAX >
LARGE or AMAX < SMALL, row scaling is done.