PZMAX1 - compute the global index of the maximum element in absolute value of a
distributed vector sub( X )

- SUBROUTINE PZMAX1(
- N, AMAX, INDX, X, IX, JX, DESCX, INCX )

INTEGER INDX, INCX, IX, JX, N COMPLEX*16 AMAX INTEGER DESCX( * ) COMPLEX*16 X( *
)

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.

- 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.