Provided by: scalapack-doc_1.5-11_all 
NAME
PDZSUM1 - return the sum of absolute values of a complex distributed vector sub( X ) in
ASUM,
SYNOPSIS
SUBROUTINE PDZSUM1( N, ASUM, X, IX, JX, DESCX, INCX )
INTEGER IX, INCX, JX, N
DOUBLE PRECISION ASUM
INTEGER DESCX( * )
COMPLEX*16 X( * )
PURPOSE
PDZSUM1 returns the sum of absolute values of a complex distributed vector sub( X ) in
ASUM,
where sub( X ) denotes X(IX:IX+N-1,JX:JX), if INCX = 1,
X(IX:IX,JX:JX+N-1), if INCX = M_X.
Based on PDZASUM from the Level 1 PBLAS. The change is
to use the 'genuine' absolute value.
The serial version of this routine was originally contributed by Nick Higham for use with
ZLACON.
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
Because vectors may be viewed as a subclass of matrices, a distributed vector is
considered to be a distributed matrix.
When the result of a vector-oriented PBLAS call is a scalar, it will be made available
only within the scope which owns the vector(s) being operated on. Let X be a generic term
for the input vector(s). Then, the processes which receive the answer will be (note that
if an operation involves more than one vector, the processes which re- ceive the result
will be the union of the following calculation for each vector):
If N = 1, M_X = 1 and INCX = 1, then one can't determine if a process row or process
column owns the vector operand, therefore only the process of coordinate {RSRC_X, CSRC_X}
receives the result;
If INCX = M_X, then sub( X ) is a vector distributed over a process row. Each process part
of this row receives the result;
If INCX = 1, then sub( X ) is a vector distributed over a process column. Each process
part of this column receives the result;
PARAMETERS
N (global input) pointer to INTEGER
The number of components of the distributed vector sub( X ). N >= 0.
ASUM (local output) pointer to DOUBLE PRECISION
The sum of absolute values of the distributed vector sub( X ) only in its scope.
X (local input) COMPLEX*16 array containing the local
pieces of a distributed matrix of dimension of at least ( (JX-1)*M_X + IX + ( N -
1 )*abs( INCX ) ) This array contains the entries of the distributed vector sub( X
).
IX (global input) pointer to INTEGER
The global row index of the submatrix of the distributed matrix X to operate on.
JX (global input) pointer to INTEGER
The global column index of the submatrix of the distributed matrix X to operate
on.
DESCX (global and local input) INTEGER array of dimension 8.
The array descriptor of the distributed matrix X.
INCX (global input) pointer to INTEGER
The global increment for the elements of X. Only two values of INCX are supported
in this version, namely 1 and M_X.