COMPLEX FUNCTION PCLATRA( 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( * ) COMPLEX A( * ) * .. * * Purpose * ======= * * PCLATRA 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) COMPLEX 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 ) COMPLEX ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER ICURCOL, ICURROW, II, IOFFA, J, JB, JJ, JN, $ LDA, LL, MYCOL, MYROW, NPCOL, NPROW COMPLEX TRACE * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CGSUM2D, INFOG2L * .. * .. 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 PCLATRA = 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 CGSUM2D( DESCA( CTXT_ ), 'All', ' ', 1, 1, TRACE, 1, -1, $ MYCOL ) * PCLATRA = TRACE * RETURN * * End of PCLATRA * END