PZLASE2(3) ScaLAPACK routine of NEC Numeric Library Collection PZLASE2(3)
NAME
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 offdi-
agonals
SYNOPSIS
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( * )
PURPOSE
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 offdi-
agonals. PZLASE2 requires that only dimension of the matrix operand is
distributed.
Notes
=====
Each global data object is described by an associated description vec-
tor. This vector stores the information required to establish the map-
ping 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 col-
umn.
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) 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 con-
tains 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, oth-
erwise, 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.
ScaLAPACK routine 31 October 2017 PZLASE2(3)