Provided by: scalapack-doc_1.5-11_all 
NAME
PZMAX1 - compute the global index of the maximum element in absolute value of a distributed vector sub( X
)
SYNOPSIS
SUBROUTINE PZMAX1( N, AMAX, INDX, X, IX, JX, DESCX, INCX )
INTEGER INDX, INCX, IX, JX, N
COMPLEX*16 AMAX
INTEGER DESCX( * )
COMPLEX*16 X( * )
PURPOSE
PZMAX1 computes the global index of the maximum element in absolute value of a distributed vector sub( X
). The global index is returned in INDX and the value is returned in AMAX,
where sub( X ) denotes X(IX:IX+N-1,JX) if INCX = 1,
X(IX,JX:JX+N-1) if INCX = M_X.
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;
Based on PZAMAX from Level 1 PBLAS. The change is to use the
The serial version was contributed to LAPACK by Nick Higham for use with ZLACON.
ARGUMENTS
N (global input) pointer to INTEGER
The number of components of the distributed vector sub( X ). N >= 0.
AMAX (global output) pointer to DOUBLE PRECISION
The absolute value of the largest entry of the distributed vector sub( X ) only in the scope of
sub( X ).
INDX (global output) pointer to INTEGER
The global index of the element of the distributed vector sub( X ) whose real part has maximum
absolute value.
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) INTEGER
The row index in the global array X indicating the first row of sub( X ).
JX (global input) INTEGER
The column index in the global array X indicating the first column of sub( X ).
DESCX (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix X.
INCX (global input) INTEGER
The global increment for the elements of X. Only two values of INCX are supported in this
version, namely 1 and M_X. INCX must not be zero.
LAPACK version 1.5 12 May 1997 PZMAX1(l)