NAME
PZLAQSY - equilibrate a symmetric distributed matrix sub( A ) =
A(IA:IA+N-1,JA:JA+N-1) using the scaling factors in the vectors SR and
SC
SYNOPSIS
SUBROUTINE PZLAQSY( UPLO, N, A, IA, JA, DESCA, SR, SC, SCOND, AMAX,
EQUED )
CHARACTER EQUED, UPLO
INTEGER IA, JA, N
DOUBLE PRECISION AMAX, SCOND
INTEGER DESCA( * )
DOUBLE PRECISION SC( * ), SR( * )
COMPLEX*16 A( * )
PURPOSE
PZLAQSY equilibrates a symmetric distributed matrix sub( A ) =
A(IA:IA+N-1,JA:JA+N-1) using the scaling factors in the vectors SR and
SC.
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
ARGUMENTS
UPLO (global input) CHARACTER
Specifies whether the upper or lower triangular part of the
symmetric distributed matrix sub( A ) is to be referenced:
= ’U’: Upper triangular
= ’L’: Lower triangular
N (global input) INTEGER
The number of rows and columns to be operated on, i.e. the
order of the distributed submatrix sub( A ). N >= 0.
A (input/output) COMPLEX*16 pointer into the local
memory to an array of local dimension (LLD_A,LOCc(JA+N-1)). On
entry, the local pieces of the distributed symmetric matrix
sub( A ). If UPLO = ’U’, the leading N-by-N upper triangular
part of sub( A ) contains the upper triangular part of the
matrix, and the strictly lower triangular part of sub( A ) is
not referenced. If UPLO = ’L’, the leading N-by-N lower
triangular part of sub( A ) contains the lower triangular part
of the matrix, and the strictly upper trian- gular part of sub(
A ) is not referenced. On exit, if EQUED = ’Y’, the
equilibrated matrix:
diag(SR(IA:IA+N-1)) * sub( A ) * diag(SC(JA:JA+N-1)).
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.
SR (local input) DOUBLE PRECISION array, dimension LOCr(M_A)
The scale factors for A(IA:IA+M-1,JA:JA+N-1). SR is aligned
with the distributed matrix A, and replicated across every
process column. SR is tied to the distributed matrix A.
SC (local input) DOUBLE PRECISION array, dimension LOCc(N_A)
The scale factors for sub( A ). SC is aligned with the dis-
tributed matrix A, and replicated down every process row. SC
is tied to the distributed matrix A.
SCOND (global input) DOUBLE PRECISION
Ratio of the smallest SR(i) (respectively SC(j)) to the largest
SR(i) (respectively SC(j)), with IA <= i <= IA+N-1 and JA <= j
<= JA+N-1.
AMAX (global input) DOUBLE PRECISION
Absolute value of the largest distributed submatrix entry.
EQUED (output) CHARACTER*1
Specifies whether or not equilibration was done. = ’N’: No
equilibration.
= ’Y’: Equilibration was done, i.e., sub( A ) has been re-
placed by:
diag(SR(IA:IA+N-1)) * sub( A ) * diag(SC(JA:JA+N-1)).
PARAMETERS
THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors. If SCOND < THRESH, scaling
is done.
LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element. If
AMAX > LARGE or AMAX < SMALL, scaling is done.