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

NAME

       PDLATRA - compute the trace of an N-by-N distributed matrix sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 )

SYNOPSIS

       DOUBLE PRECISION FUNCTION PDLATRA( N, A, IA, JA, DESCA )

	   INTEGER	IA, JA, N

	   INTEGER	DESCA( * )

	   DOUBLE	PRECISION A( * )

PURPOSE

       PDLATRA computes the trace of an N-by-N distributed matrix sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 ). The result is left on every process
       of the grid.

       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

ARGUMENTS

       N       (global input) INTEGER
	       The number of rows and columns to be operated on i.e the order of the distributed submatrix sub( A ).  N >= 0.

       A       (local input) DOUBLE PRECISION pointer into the local memory
	       to an array of dimension ( LLD_A, LOCc(JA+N-1) ). This array contains the local pieces of the distributed matrix the trace is to be
	       computed.

       IA      (global input) INTEGER
	       The row index in the global array A indicating the first row of sub( A ).

       JA      (global input) INTEGER
	       The column index in the global array A indicating the first column of sub( A ).

       DESCA   (global and local input) INTEGER array of dimension DLEN_.
	       The array descriptor for the distributed matrix A.

LAPACK version 1.5						    12 May 1997 							PDLATRA(l)