PZMAX1(3) ScaLAPACK routine of NEC Numeric Library Collection PZMAX1(3)
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 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
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 opera-
tion 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 pro-
cess 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 col-
umn. 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 vec-
tor 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.
ScaLAPACK routine 31 October 2017 PZMAX1(3)