SYNOPSIS

SUBROUTINE PDLASE2(

UPLO, M, N, ALPHA, BETA, A, IA, JA, DESCA )

    

CHARACTER UPLO

    

INTEGER IA, JA, M, N

    

DOUBLE PRECISION ALPHA, BETA

    

INTEGER DESCA( * )

    

DOUBLE PRECISION A( * )

PURPOSE

PDLASE2 initializes an M-by-N distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1) to BETA on the diagonal and ALPHA on the offdiagonals. PDLASE2 requires that only dimension of the matrix operand is distributed.

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 the part of the distributed matrix sub( A ) to be set:
= 'U': Upper triangular part is set; the strictly lower triangular part of sub( A ) is not changed; = 'L': Lower triangular part is set; the strictly upper triangular part of sub( A ) is not changed; Otherwise: All of the matrix sub( A ) is set.

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.

ALPHA (global input) DOUBLE PRECISION

The constant to which the offdiagonal elements are to be set.

BETA (global input) DOUBLE PRECISION

The constant to which the diagonal elements are to be set.

A (local output) DOUBLE PRECISION pointer into the local memory

to an array of dimension (LLD_A,LOCc(JA+N-1)). This array contains the local pieces of the distributed matrix sub( A ) to be set. On exit, the leading M-by-N submatrix sub( A ) is set as follows:

if UPLO = 'U', A(IA+i-1,JA+j-1) = ALPHA, 1<=i<=j-1, 1<=j<=N, if UPLO = 'L', A(IA+i-1,JA+j-1) = ALPHA, j+1<=i<=M, 1<=j<=N, otherwise, A(IA+i-1,JA+j-1) = ALPHA, 1<=i<=M, 1<=j<=N, IA+i.NE.JA+j, and, for all UPLO, A(IA+i-1,JA+i-1) = BETA, 1<=i<=min(M,N).

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.