PCLAQSY(l)

NAME
PCLAQSY - 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 PCLAQSY(
    UPLO, N, A, IA, JA, DESCA, SR, SC, SCOND, AMAX, EQUED )

CHARACTER
    EQUED, UPLO

INTEGER
    IA, JA, N

REAL
    AMAX, SCOND

INTEGER
    DESCA( * )

REAL
    SC( * ), SR( * )

COMPLEX
    A( * )

PURPOSE
PCLAQSY 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 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) REAL 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) REAL 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) REAL
    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) REAL
    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.