.TH PCMAX1 l "12 May 1997" "LAPACK version 1.5" "LAPACK auxiliary routine (version 1.5)"
.SH NAME
PCMAX1 - compute the global index of the maximum element in absolute value of a distributed vector sub( X )
.SH SYNOPSIS
.TP 19
SUBROUTINE PCMAX1(
N, AMAX, INDX, X, IX, JX, DESCX, INCX )
.TP 19
.ti +4
INTEGER
INDX, INCX, IX, JX, N
.TP 19
.ti +4
COMPLEX
AMAX
.TP 19
.ti +4
INTEGER
DESCX( * )
.TP 19
.ti +4
COMPLEX
X( * )
.SH PURPOSE
PCMAX1 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,
.br

where sub( X ) denotes X(IX:IX+N-1,JX) if INCX = 1,
.br
                       X(IX,JX:JX+N-1) if INCX = M_X.
.br

Notes
.br
=====
.br

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.
.br

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".
.br

NOTATION        STORED IN      EXPLANATION
.br
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
                               DTYPE_A = 1.
.br
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.
.br
M_A    (global) DESCA( M_ )    The number of rows in the global
                               array A.
.br
N_A    (global) DESCA( N_ )    The number of columns in the global
                               array A.
.br
MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
                               the rows of the array.
.br
NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
                               the columns of the array.
.br
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.
.br
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.
.br
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.
.br
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.
.br
The values of LOCr() and LOCc() may be determined via a call to the
ScaLAPACK tool function, NUMROC:
.br
        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:
.br
        LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
.br
        LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
.br

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):
.br

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;
.br

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 PCAMAX from Level 1 PBLAS. The change is to use the
'genuine' absolute value.
.br

The serial version was contributed to LAPACK by Nick Higham for use
with CLACON.
.br

.SH ARGUMENTS
.TP 8
N       (global input) pointer to INTEGER
The number of components of the distributed vector sub( X ).
N >= 0.
.TP 8
AMAX    (global output) pointer to REAL
The absolute value of the largest entry of the distributed
vector sub( X ) only in the scope of sub( X ).
.TP 8
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.
.TP 8
X       (local input) COMPLEX 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 ).
.TP 8
IX      (global input) INTEGER
The row index in the global array X indicating the first
row of sub( X ).
.TP 8
JX      (global input) INTEGER
The column index in the global array X indicating the
first column of sub( X ).
.TP 8
DESCX   (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix X.
.TP 8
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.
