PSCSUM1(l)					      LAPACK auxiliary routine (version 1.5)						PSCSUM1(l)

NAME

       PSCSUM1 - return the sum of absolute values of a complex distributed vector sub( X ) in ASUM,

SYNOPSIS

       SUBROUTINE PSCSUM1( N, ASUM, X, IX, JX, DESCX, INCX )

	   INTEGER	   IX, INCX, JX, N

	   REAL 	   ASUM

	   INTEGER	   DESCX( * )

	   COMPLEX	   X( * )

PURPOSE

       PSCSUM1 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 PSCASUM 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 CLACON.

       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 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 oper-
       ation  involves more than one vector, the processes which re- ceive the result will be the union of the following calculation for each vec-
       tor):

       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 REAL
	       The sum of absolute values of the distributed vector sub( X ) only in its scope.

       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 ).

       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.

LAPACK version 1.5						    12 May 1997 							PSCSUM1(l)