PZLASE2 - initialize 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
- SUBROUTINE PZLASE2(
- UPLO, M, N, ALPHA, BETA, A, IA, JA, DESCA )
CHARACTER UPLO INTEGER IA, JA, M, N COMPLEX*16 ALPHA, BETA INTEGER DESCA( * )
COMPLEX*16 A( * )
PZLASE2 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.
PZLASE2 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
- 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) COMPLEX*16
- The constant to which the offdiagonal elements are to be set.
- BETA (global input) COMPLEX*16
- The constant to which the diagonal elements are to be set.
- A (local output) COMPLEX*16 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.