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REAL FUNCTION PSLATRA( N, A, IA, JA, DESCA )
*
* -- ScaLAPACK auxiliary routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
INTEGER IA, JA, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
REAL A( * )
* ..
*
* Purpose
* =======
*
* PSLATRA 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 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
*
* 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) REAL 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.
*
* ====================================================================
*
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
$ LLD_, MB_, M_, NB_, N_, RSRC_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
REAL ZERO
PARAMETER ( ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER ICURCOL, ICURROW, II, IOFFA, J, JB, JJ, JN,
$ LDA, LL, MYCOL, MYROW, NPCOL, NPROW
REAL TRACE
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, INFOG2L, SGSUM2D
* ..
* .. External Functions ..
INTEGER ICEIL
EXTERNAL ICEIL
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN, MOD
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL )
*
TRACE = ZERO
IF( N.EQ.0 ) THEN
PSLATRA = TRACE
RETURN
END IF
*
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, II, JJ,
$ ICURROW, ICURCOL )
*
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
JB = JN-JA+1
LDA = DESCA( LLD_ )
IOFFA = II + ( JJ - 1 ) * LDA
*
* Handle first diagonal block separately
*
IF( MYROW.EQ.ICURROW .AND. MYCOL.EQ.ICURCOL ) THEN
DO 10 LL = IOFFA, IOFFA + (JB-1)*(LDA+1), LDA+1
TRACE = TRACE + A( LL )
10 CONTINUE
END IF
IF( MYROW.EQ.ICURROW )
$ IOFFA = IOFFA + JB
IF( MYCOL.EQ.ICURCOL )
$ IOFFA = IOFFA + JB*LDA
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
* Loop over the remaining block of columns
*
DO 30 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYROW.EQ.ICURROW .AND. MYCOL.EQ.ICURCOL ) THEN
DO 20 LL = IOFFA, IOFFA + (JB-1)*(LDA+1), LDA+1
TRACE = TRACE + A( LL )
20 CONTINUE
END IF
IF( MYROW.EQ.ICURROW )
$ IOFFA = IOFFA + JB
IF( MYCOL.EQ.ICURCOL )
$ IOFFA = IOFFA + JB*LDA
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
30 CONTINUE
*
CALL SGSUM2D( DESCA( CTXT_ ), 'All', ' ', 1, 1, TRACE, 1, -1,
$ MYCOL )
*
PSLATRA = TRACE
*
RETURN
*
* End of PSLATRA
*
END
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