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SUBROUTINE PZLASMSUB( A, DESCA, I, L, K, SMLNUM, BUF, LWORK )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* July 31, 2001
*
* .. Scalar Arguments ..
INTEGER I, K, L, LWORK
DOUBLE PRECISION SMLNUM
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
COMPLEX*16 A( * ), BUF( * )
* ..
*
* Purpose
* =======
*
* PZLASMSUB looks for a small subdiagonal element from the bottom
* of the matrix that it can safely set to zero.
*
* 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
* =========
*
* A (global input) COMPLEX*16 array, dimension (DESCA(LLD_),*)
* On entry, the Hessenberg matrix whose tridiagonal part is
* being scanned.
* Unchanged on exit.
*
* DESCA (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix A.
*
* I (global input) INTEGER
* The global location of the bottom of the unreduced
* submatrix of A.
* Unchanged on exit.
*
* L (global input) INTEGER
* The global location of the top of the unreduced submatrix
* of A.
* Unchanged on exit.
*
* K (global output) INTEGER
* On exit, this yields the bottom portion of the unreduced
* submatrix. This will satisfy: L <= M <= I-1.
*
* SMLNUM (global input) DOUBLE PRECISION
* On entry, a "small number" for the given matrix.
* Unchanged on exit.
*
* BUF (local output) COMPLEX*16 array of size LWORK.
*
* LWORK (global input) INTEGER
* On exit, LWORK is the size of the work buffer.
* This must be at least 2*Ceil( Ceil( (I-L)/HBL ) /
* LCM(NPROW,NPCOL) )
* Here LCM is least common multiple, and NPROWxNPCOL is the
* logical grid size.
*
* Notes:
*
* This routine does a global maximum and must be called by all
* processes.
*
* This code is basically a parallelization of the following snip
* of LAPACK code from ZLAHQR:
*
* Look for a single small subdiagonal element.
*
* DO 20 K = I, L + 1, -1
* TST1 = CABS1( H( K-1, K-1 ) ) + CABS1( H( K, K ) )
* IF( TST1.EQ.ZERO )
* $ TST1 = ZLANHS( '1', I-L+1, H( L, L ), LDH, WORK )
* IF( CABS1( H( K, K-1 ) ).LE.MAX( ULP*TST1, SMLNUM ) )
* $ GO TO 30
* 20 CONTINUE
* 30 CONTINUE
*
* Further Details
* ===============
*
* Implemented by: M. Fahey, May 28, 1999
*
* =====================================================================
*
* .. 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 )
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER CONTXT, DOWN, HBL, IBUF1, IBUF2, ICOL1, ICOL2,
$ II, III, IRCV1, IRCV2, IROW1, IROW2, ISRC,
$ ISTR1, ISTR2, ITMP1, ITMP2, JJ, JJJ, JSRC, LDA,
$ LEFT, MODKM1, MYCOL, MYROW, NPCOL, NPROW, NUM,
$ RIGHT, UP
DOUBLE PRECISION TST1, ULP
COMPLEX*16 CDUM, H10, H11, H22
* ..
* .. External Functions ..
INTEGER ILCM, NUMROC
DOUBLE PRECISION PDLAMCH
EXTERNAL ILCM, NUMROC, PDLAMCH
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, IGAMX2D, INFOG1L, INFOG2L,
$ ZGERV2D, ZGESD2D
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DIMAG, MAX, MOD
* ..
* .. Statement Functions ..
DOUBLE PRECISION CABS1
* ..
* .. Statement Function definitions ..
CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
* ..
* .. Executable Statements ..
*
HBL = DESCA( MB_ )
CONTXT = DESCA( CTXT_ )
LDA = DESCA( LLD_ )
ULP = PDLAMCH( CONTXT, 'PRECISION' )
CALL BLACS_GRIDINFO( CONTXT, NPROW, NPCOL, MYROW, MYCOL )
LEFT = MOD( MYCOL+NPCOL-1, NPCOL )
RIGHT = MOD( MYCOL+1, NPCOL )
UP = MOD( MYROW+NPROW-1, NPROW )
DOWN = MOD( MYROW+1, NPROW )
NUM = NPROW*NPCOL
*
* BUFFER1 STARTS AT BUF(ISTR1+1) AND WILL CONTAINS IBUF1 ELEMENTS
* BUFFER2 STARTS AT BUF(ISTR2+1) AND WILL CONTAINS IBUF2 ELEMENTS
*
ISTR1 = 0
ISTR2 = ( ( I-L ) / HBL )
IF( ISTR2*HBL.LT.( I-L ) )
$ ISTR2 = ISTR2 + 1
II = ISTR2 / ILCM( NPROW, NPCOL )
IF( II*ILCM( NPROW, NPCOL ).LT.ISTR2 ) THEN
ISTR2 = II + 1
ELSE
ISTR2 = II
END IF
IF( LWORK.LT.2*ISTR2 ) THEN
*
* Error!
*
RETURN
END IF
CALL INFOG2L( I, I, DESCA, NPROW, NPCOL, MYROW, MYCOL, IROW1,
$ ICOL1, II, JJ )
MODKM1 = MOD( I-1+HBL, HBL )
*
* COPY OUR RELEVANT PIECES OF TRIADIAGONAL THAT WE OWE INTO
* 2 BUFFERS TO SEND TO WHOMEVER OWNS H(K,K) AS K MOVES DIAGONALLY
* UP THE TRIDIAGONAL
*
IBUF1 = 0
IBUF2 = 0
IRCV1 = 0
IRCV2 = 0
DO 10 K = I, L + 1, -1
IF( ( MODKM1.EQ.0 ) .AND. ( DOWN.EQ.II ) .AND.
$ ( RIGHT.EQ.JJ ) ) THEN
*
* WE MUST PACK H(K-1,K-1) AND SEND IT DIAGONAL DOWN
*
IF( ( DOWN.NE.MYROW ) .OR. ( RIGHT.NE.MYCOL ) ) THEN
CALL INFOG2L( K-1, K-1, DESCA, NPROW, NPCOL, MYROW,
$ MYCOL, IROW1, ICOL1, ISRC, JSRC )
IBUF1 = IBUF1 + 1
BUF( ISTR1+IBUF1 ) = A( ( ICOL1-1 )*LDA+IROW1 )
END IF
END IF
IF( ( MODKM1.EQ.0 ) .AND. ( MYROW.EQ.II ) .AND.
$ ( RIGHT.EQ.JJ ) ) THEN
*
* WE MUST PACK H(K ,K-1) AND SEND IT RIGHT
*
IF( NPCOL.GT.1 ) THEN
CALL INFOG2L( K, K-1, DESCA, NPROW, NPCOL, MYROW, MYCOL,
$ IROW1, ICOL1, ISRC, JSRC )
IBUF2 = IBUF2 + 1
BUF( ISTR2+IBUF2 ) = A( ( ICOL1-1 )*LDA+IROW1 )
END IF
END IF
*
* ADD UP THE RECEIVES
*
IF( ( MYROW.EQ.II ) .AND. ( MYCOL.EQ.JJ ) ) THEN
IF( ( MODKM1.EQ.0 ) .AND. ( ( NPROW.GT.1 ) .OR. ( NPCOL.GT.
$ 1 ) ) ) THEN
*
* WE MUST RECEIVE H(K-1,K-1) FROM DIAGONAL UP
*
IRCV1 = IRCV1 + 1
END IF
IF( ( MODKM1.EQ.0 ) .AND. ( NPCOL.GT.1 ) ) THEN
*
* WE MUST RECEIVE H(K ,K-1) FROM LEFT
*
IRCV2 = IRCV2 + 1
END IF
END IF
*
* POSSIBLY CHANGE OWNERS (OCCURS ONLY WHEN MOD(K-1,HBL) = 0)
*
IF( MODKM1.EQ.0 ) THEN
II = II - 1
JJ = JJ - 1
IF( II.LT.0 )
$ II = NPROW - 1
IF( JJ.LT.0 )
$ JJ = NPCOL - 1
END IF
MODKM1 = MODKM1 - 1
IF( MODKM1.LT.0 )
$ MODKM1 = HBL - 1
10 CONTINUE
*
* SEND DATA ON TO THE APPROPRIATE NODE IF THERE IS ANY DATA TO SEND
*
IF( IBUF1.GT.0 ) THEN
CALL ZGESD2D( CONTXT, IBUF1, 1, BUF( ISTR1+1 ), IBUF1, DOWN,
$ RIGHT )
END IF
IF( IBUF2.GT.0 ) THEN
CALL ZGESD2D( CONTXT, IBUF2, 1, BUF( ISTR2+1 ), IBUF2, MYROW,
$ RIGHT )
END IF
*
* RECEIVE APPROPRIATE DATA IF THERE IS ANY
*
IF( IRCV1.GT.0 ) THEN
CALL ZGERV2D( CONTXT, IRCV1, 1, BUF( ISTR1+1 ), IRCV1, UP,
$ LEFT )
END IF
IF( IRCV2.GT.0 ) THEN
CALL ZGERV2D( CONTXT, IRCV2, 1, BUF( ISTR2+1 ), IRCV2, MYROW,
$ LEFT )
END IF
*
* START MAIN LOOP
*
IBUF1 = 0
IBUF2 = 0
CALL INFOG2L( I, I, DESCA, NPROW, NPCOL, MYROW, MYCOL, IROW1,
$ ICOL1, II, JJ )
MODKM1 = MOD( I-1+HBL, HBL )
*
* LOOK FOR A SINGLE SMALL SUBDIAGONAL ELEMENT.
*
* Start loop for subdiagonal search
*
DO 40 K = I, L + 1, -1
IF( ( MYROW.EQ.II ) .AND. ( MYCOL.EQ.JJ ) ) THEN
IF( MODKM1.EQ.0 ) THEN
*
* Grab information from WORK array
*
IF( NUM.GT.1 ) THEN
IBUF1 = IBUF1 + 1
H11 = BUF( ISTR1+IBUF1 )
ELSE
H11 = A( ( ICOL1-2 )*LDA+IROW1-1 )
END IF
IF( NPCOL.GT.1 ) THEN
IBUF2 = IBUF2 + 1
H10 = BUF( ISTR2+IBUF2 )
ELSE
H10 = A( ( ICOL1-2 )*LDA+IROW1 )
END IF
ELSE
*
* Information is local
*
H11 = A( ( ICOL1-2 )*LDA+IROW1-1 )
H10 = A( ( ICOL1-2 )*LDA+IROW1 )
END IF
H22 = A( ( ICOL1-1 )*LDA+IROW1 )
TST1 = CABS1( H11 ) + CABS1( H22 )
IF( TST1.EQ.ZERO ) THEN
*
* FIND SOME NORM OF THE LOCAL H(L:I,L:I)
*
CALL INFOG1L( L, HBL, NPROW, MYROW, 0, IROW1, III )
IROW2 = NUMROC( I, HBL, MYROW, 0, NPROW )
CALL INFOG1L( L, HBL, NPCOL, MYCOL, 0, ICOL1, III )
ICOL2 = NUMROC( I, HBL, MYCOL, 0, NPCOL )
DO 30 III = IROW1, IROW2
DO 20 JJJ = ICOL1, ICOL2
TST1 = TST1 + CABS1( A( ( JJJ-1 )*LDA+III ) )
20 CONTINUE
30 CONTINUE
END IF
IF( CABS1( H10 ).LE.MAX( ULP*TST1, SMLNUM ) )
$ GO TO 50
IROW1 = IROW1 - 1
ICOL1 = ICOL1 - 1
END IF
MODKM1 = MODKM1 - 1
IF( MODKM1.LT.0 )
$ MODKM1 = HBL - 1
IF( ( MODKM1.EQ.HBL-1 ) .AND. ( K.GT.2 ) ) THEN
II = MOD( II+NPROW-1, NPROW )
JJ = MOD( JJ+NPCOL-1, NPCOL )
CALL INFOG2L( K-1, K-1, DESCA, NPROW, NPCOL, MYROW, MYCOL,
$ IROW1, ICOL1, ITMP1, ITMP2 )
END IF
40 CONTINUE
50 CONTINUE
CALL IGAMX2D( CONTXT, 'ALL', ' ', 1, 1, K, 1, ITMP1, ITMP2, -1,
$ -1, -1 )
RETURN
*
* End of PZLASMSUB
*
END
|
