SUBROUTINE PZLAPV2( DIREC, ROWCOL, M, N, A, IA, JA, DESCA, IPIV,
$ IP, JP, DESCIP )
*
* -- ScaLAPACK auxiliary routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
CHARACTER DIREC, ROWCOL
INTEGER IA, IP, JA, JP, M, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCIP( * ), IPIV( * )
COMPLEX*16 A( * )
* ..
*
* Purpose
* =======
*
* PZLAPV2 applies either P (permutation matrix indicated by IPIV)
* or inv( P ) to a M-by-N distributed matrix sub( A ) denoting
* A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting. The
* pivot vector should be aligned with the distributed matrix A. For
* pivoting the rows of sub( A ), IPIV should be distributed along a
* process column and replicated over all process rows. Similarly,
* IPIV should be distributed along a process row and replicated over
* all process columns for column pivoting.
*
* 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
* =========
*
* DIREC (global input) CHARACTER
* Specifies in which order the permutation is applied:
* = 'F' (Forward) Applies pivots Forward from top of matrix.
* Computes P * sub( A );
* = 'B' (Backward) Applies pivots Backward from bottom of
* matrix. Computes inv( P ) * sub( A ).
*
* ROWCOL (global input) CHARACTER
* Specifies if the rows or columns are to be permuted:
* = 'R' Rows will be permuted,
* = 'C' Columns will be permuted.
*
* M (global input) INTEGER
* The number of rows to be operated on, i.e. the number of rows
* of the distributed submatrix sub( A ). M >= 0.
*
* N (global input) INTEGER
* The number of columns to be operated on, i.e. the number of
* columns of the distributed submatrix sub( A ). N >= 0.
*
* A (local input/local output) COMPLEX*16 pointer into the
* local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
* On entry, this local array contains the local pieces of the
* distributed matrix sub( A ) to which the row or columns
* interchanges will be applied. On exit, this array contains
* the local pieces of the permuted distributed matrix.
*
* 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.
*
* IPIV (input) INTEGER array, dimension >= LOCr(M_A)+MB_A if
* ROWCOL = 'R', LOCc(N_A)+NB_A otherwise. It contains
* the pivoting information. IPIV(i) is the global row (column),
* local row (column) i was swapped with. The last piece of the
* array of size MB_A (resp. NB_A) is used as workspace. IPIV is
* tied to the distributed matrix A.
*
* IP (global input) INTEGER
* IPIV's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JP (global input) INTEGER
* IPIV's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCIP (global and local input) INTEGER array of dimension 8
* The array descriptor for the distributed matrix IPIV.
*
* =====================================================================
*
* .. 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 )
* ..
* .. Local Scalars ..
LOGICAL FORWRD, ROWPVT
INTEGER I, IB, ICTXT, ICURCOL, ICURROW, IIP, IP1, ITMP,
$ IPVWRK, J, JB, JJP, JP1, K, MA, MBA, MYCOL,
$ MYROW, NBA, NPCOL, NPROW
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, IGEBS2D, IGEBR2D, INFOG2L,
$ PZSWAP
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, NUMROC
EXTERNAL ICEIL, LSAME, NUMROC
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN, MOD
* ..
* .. Executable Statements ..
*
ROWPVT = LSAME( ROWCOL, 'R' )
IF( ROWPVT ) THEN
IF( M.LE.1 .OR. N.LT.1 )
$ RETURN
ELSE
IF( M.LT.1 .OR. N.LE.1 )
$ RETURN
END IF
FORWRD = LSAME( DIREC, 'F' )
*
*
* Get grid and matrix parameters
*
MA = DESCA( M_ )
MBA = DESCA( MB_ )
NBA = DESCA( NB_ )
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* If I'm applying pivots from beginning to end (e.g., repeating
* pivoting done earlier). Thus this section computes P * sub( A ).
*
IF( FORWRD ) THEN
CALL INFOG2L( IP, JP, DESCIP, NPROW, NPCOL, MYROW, MYCOL,
$ IIP, JJP, ICURROW, ICURCOL )
*
* If I'm pivoting the rows of sub( A )
*
IF( ROWPVT ) THEN
IPVWRK = NUMROC( DESCIP( M_ ), DESCIP( MB_ ), MYROW,
$ DESCIP( RSRC_ ), NPROW ) + 1 -
$ DESCIP( MB_ )
*
* Loop over rows of sub( A )
*
I = IA
IB = MIN( M, ICEIL( IA, MBA ) * MBA - IA + 1 )
10 CONTINUE
*
* Find local pointer into IPIV, and broadcast this block's
* pivot information to everyone in process column
*
IF( MYROW.EQ.ICURROW ) THEN
CALL IGEBS2D( ICTXT, 'Columnwise', ' ', IB, 1,
$ IPIV( IIP ), IB )
ITMP = IIP
IIP = IIP + IB
ELSE
ITMP = IPVWRK
CALL IGEBR2D( ICTXT, 'Columnwise', ' ', IB, 1,
$ IPIV( ITMP ), IB, ICURROW, MYCOL )
END IF
*
* Pivot the block of rows
*
DO 20 K = I, I+IB-1
IP1 = IPIV( ITMP ) - IP + IA
IF( IP1.NE.K )
$ CALL PZSWAP( N, A, K, JA, DESCA, MA, A, IP1, JA,
$ DESCA, MA )
ITMP = ITMP + 1
20 CONTINUE
*
* Go on to next row of processes, increment row counter,
* and figure number of rows to pivot next
*
ICURROW = MOD( ICURROW+1, NPROW )
I = I + IB
IB = MIN( MBA, M-I+IA )
IF( IB .GT. 0 ) GOTO 10
*
* If I am pivoting the columns of sub( A )
*
ELSE
IPVWRK = NUMROC( DESCIP( N_ ), DESCIP( NB_ ), MYCOL,
$ DESCIP( CSRC_ ), NPCOL ) + 1 -
$ DESCIP( NB_ )
*
* Loop over columns of sub( A )
*
J = JA
JB = MIN( N, ICEIL( JA, NBA ) * NBA - JA + 1 )
30 CONTINUE
*
* Find local pointer into IPIV, and broadcast this block's
* pivot information to everyone in process row
*
IF( MYCOL.EQ.ICURCOL ) THEN
CALL IGEBS2D( ICTXT, 'Rowwise', ' ', JB, 1,
$ IPIV( JJP ), JB )
ITMP = JJP
JJP = JJP + JB
ELSE
ITMP = IPVWRK
CALL IGEBR2D( ICTXT, 'Rowwise', ' ', JB, 1,
$ IPIV( ITMP ), JB, MYROW, ICURCOL )
END IF
*
* Pivot the block of columns
*
DO 40 K = J, J+JB-1
JP1 = IPIV( ITMP ) - JP + JA
IF( JP1.NE.K )
$ CALL PZSWAP( M, A, IA, K, DESCA, 1, A, IA, JP1,
$ DESCA, 1 )
ITMP = ITMP + 1
40 CONTINUE
*
* Go on to next column of processes, increment column
* counter, and figure number of columns to pivot next
*
ICURCOL = MOD( ICURCOL+1, NPCOL )
J = J + JB
JB = MIN( NBA, N-J+JA )
IF( JB .GT. 0 ) GOTO 30
END IF
*
* If I want to apply pivots in reverse order, i.e. reversing
* pivoting done earlier. Thus this section computes
* inv( P ) * sub( A ).
*
ELSE
*
* If I'm pivoting the rows of sub( A )
*
IF( ROWPVT ) THEN
CALL INFOG2L( IP+M-1, JP, DESCIP, NPROW, NPCOL, MYROW,
$ MYCOL, IIP, JJP, ICURROW, ICURCOL )
*
IPVWRK = NUMROC( DESCIP( M_ ), DESCIP( MB_ ), MYROW,
$ DESCIP( RSRC_ ), NPROW ) + 1 -
$ DESCIP( MB_ )
*
* If I'm not in the current process row, my IIP points out
* past end of pivot vector (since I don't own a piece of the
* last row). Adjust IIP so it points at last pivot entry.
*
IF( MYROW.NE.ICURROW ) IIP = IIP - 1
*
* Loop over rows in reverse order, starting at last row
*
I = IA + M - 1
IB = MOD( I, MBA )
IF( IB .EQ. 0 ) IB = MBA
IB = MIN( IB, M )
50 CONTINUE
*
* Find local pointer into IPIV, and broadcast this block's
* pivot information to everyone in process column
*
IF( MYROW.EQ.ICURROW ) THEN
ITMP = IIP
IIP = IIP - IB
CALL IGEBS2D( ICTXT, 'Columnwise', ' ', IB, 1,
$ IPIV( IIP+1 ), IB )
ELSE
CALL IGEBR2D( ICTXT, 'Columnwise', ' ', IB, 1,
$ IPIV( IPVWRK ), IB, ICURROW, MYCOL )
ITMP = IPVWRK + IB - 1
END IF
*
* Pivot the block of rows
*
DO 60 K = I, I-IB+1, -1
IP1 = IPIV( ITMP ) - IP + IA
IF( IP1.NE.K )
$ CALL PZSWAP( N, A, K, JA, DESCA, MA, A, IP1, JA,
$ DESCA, MA )
ITMP = ITMP - 1
60 CONTINUE
*
* Go to previous row of processes, decrement row counter,
* and figure number of rows to be pivoted next
*
ICURROW = MOD( NPROW+ICURROW-1, NPROW )
I = I - IB
IB = MIN( MBA, I-IA+1 )
IF( IB .GT. 0 ) GOTO 50
*
* Otherwise, I'm pivoting the columns of sub( A )
*
ELSE
CALL INFOG2L( IP, JP+N-1, DESCIP, NPROW, NPCOL, MYROW,
$ MYCOL, IIP, JJP, ICURROW, ICURCOL )
IPVWRK = NUMROC( DESCIP( N_ ), DESCIP( NB_ ), MYCOL,
$ DESCIP( CSRC_ ), NPCOL ) + 1 -
$ DESCIP( NB_ )
*
* If I'm not in the current process column, my JJP points out
* past end of pivot vector (since I don't own a piece of the
* last column). Adjust JJP so it points at last pivot entry.
*
IF( MYCOL.NE.ICURCOL ) JJP = JJP - 1
*
* Loop over columns in reverse order starting at last column
*
J = JA + N - 1
JB = MOD( J, NBA )
IF( JB .EQ. 0 ) JB = NBA
JB = MIN( JB, N )
70 CONTINUE
*
* Find local pointer into IPIV, and broadcast this block's
* pivot information to everyone in process row
*
IF( MYCOL.EQ.ICURCOL ) THEN
ITMP = JJP
JJP = JJP - JB
CALL IGEBS2D( ICTXT, 'Rowwise', ' ', JB, 1,
$ IPIV( JJP+1 ), JB )
ELSE
CALL IGEBR2D( ICTXT, 'Rowwise', ' ', JB, 1,
$ IPIV( IPVWRK ), JB, MYROW, ICURCOL )
ITMP = IPVWRK + JB - 1
END IF
*
* Pivot a block of columns
*
DO 80 K = J, J-JB+1, -1
JP1 = IPIV( ITMP ) - JP + JA
IF( JP1.NE.K )
$ CALL PZSWAP( M, A, IA, K, DESCA, 1, A, IA, JP1,
$ DESCA, 1 )
ITMP = ITMP - 1
80 CONTINUE
*
* Go to previous row of processes, decrement row counter,
* and figure number of rows to be pivoted next
*
ICURCOL = MOD( NPCOL+ICURCOL-1, NPCOL )
J = J - JB
JB = MIN( NBA, J-JA+1 )
IF( JB .GT. 0 ) GOTO 70
END IF
*
END IF
*
RETURN
*
* End PZLAPV2
*
END