SUBROUTINE PCUNGR2( M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK,
$ INFO )
*
* -- ScaLAPACK routine (version 1.5) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
INTEGER IA, INFO, JA, K, LWORK, M, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
COMPLEX A( * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PCUNGR2 generates an M-by-N complex distributed matrix Q denoting
* A(IA:IA+M-1,JA:JA+N-1) with orthonormal rows, which is defined as the
* last M rows of a product of K elementary reflectors of order N
*
* Q = H(1)' H(2)' . . . H(k)'
*
* as returned by PCGERQF.
*
* 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
* =========
*
* M (global input) INTEGER
* The number of rows to be operated on i.e the number of rows
* of the distributed submatrix Q. M >= 0.
*
* N (global input) INTEGER
* The number of columns to be operated on i.e the number of
* columns of the distributed submatrix Q. N >= M >= 0.
*
* K (global input) INTEGER
* The number of elementary reflectors whose product defines the
* matrix Q. M >= K >= 0.
*
* A (local input/local output) COMPLEX pointer into the
* local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
* On entry, the i-th row must contain the vector which defines
* the elementary reflector H(i), IA+M-K <= i <= IA+M-1, as
* returned by PCGERQF in the K rows of its distributed
* matrix argument A(IA+M-K:IA+M-1,JA:*). On exit, this array
* contains the local pieces of the M-by-N distributed matrix Q.
*
* 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.
*
* TAU (local input) COMPLEX, array, dimension LOCr(IA+M-1)
* This array contains the scalar factors TAU(i) of the
* elementary reflectors H(i) as returned by PCGERQF.
* TAU is tied to the distributed matrix A.
*
* WORK (local workspace/local output) COMPLEX array,
* dimension (LWORK)
* On exit, WORK(1) returns the minimal and optimal LWORK.
*
* LWORK (local or global input) INTEGER
* The dimension of the array WORK.
* LWORK is local input and must be at least
* LWORK >= NqA0 + MAX( 1, MpA0 ), where
*
* IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
* MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ),
* NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
*
* INDXG2P and NUMROC are ScaLAPACK tool functions;
* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
* the subroutine BLACS_GRIDINFO.
*
* If LWORK = -1, then LWORK is global input and a workspace
* query is assumed; the routine only calculates the minimum
* and optimal size for all work arrays. Each of these
* values is returned in the first entry of the corresponding
* work array, and no error message is issued by PXERBLA.
*
*
* INFO (local output) INTEGER
* = 0: successful exit
* < 0: If the i-th argument is an array and the j-entry had
* an illegal value, then INFO = -(i*100+j), if the i-th
* argument is a scalar and had an illegal value, then
* INFO = -i.
*
* =====================================================================
*
* .. 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 ONE, ZERO
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL LQUERY
CHARACTER COLBTOP, ROWBTOP
INTEGER IACOL, IAROW, I, ICTXT, II, LWMIN, MP, MPA0,
$ MYCOL, MYROW, NPCOL, NPROW, NQA0
COMPLEX TAUI
* ..
* .. External Subroutines ..
EXTERNAL BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT, PCELSET,
$ PCLACGV, PCLARFC, PCLASET, PCSCAL,
$ PTOPGET, PTOPSET, PXERBLA
* ..
* .. External Functions ..
INTEGER INDXG2L, INDXG2P, NUMROC
EXTERNAL INDXG2L, INDXG2P, NUMROC
* ..
* .. Intrinsic Functions ..
INTRINSIC CMPLX, CONJG, MAX, MIN, MOD, REAL
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Test the input parameters
*
INFO = 0
IF( NPROW.EQ.-1 ) THEN
INFO = -(700+CTXT_)
ELSE
CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 7, INFO )
IF( INFO.EQ.0 ) THEN
IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),
$ NPROW )
IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
$ NPCOL )
MPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),
$ MYROW, IAROW, NPROW )
NQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),
$ MYCOL, IACOL, NPCOL )
LWMIN = NQA0 + MAX( 1, MPA0 )
*
WORK( 1 ) = CMPLX( REAL( LWMIN ) )
LQUERY = ( LWORK.EQ.-1 )
IF( N.LT.M ) THEN
INFO = -2
ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
INFO = -3
ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -10
END IF
END IF
END IF
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PCUNGR2', -INFO )
CALL BLACS_ABORT( ICTXT, 1 )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( M.LE.0 )
$ RETURN
*
CALL PTOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
CALL PTOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
CALL PTOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' )
CALL PTOPSET( ICTXT, 'Broadcast', 'Columnwise', 'I-ring' )
*
IF( K.LT.M ) THEN
*
* Initialise rows ia:ia+m-k-1 to rows of the unit matrix
*
CALL PCLASET( 'All', M-K, N-M, ZERO, ZERO, A, IA, JA, DESCA )
CALL PCLASET( 'All', M-K, M, ZERO, ONE, A, IA, JA+N-M, DESCA )
*
END IF
*
TAUI = ZERO
MP = NUMROC( IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW )
*
DO 10 I = IA+M-K, IA+M-1
*
* Apply H(i)' to A(ia:i,ja:ja+n-m+i-ia) from the right
*
CALL PCLACGV( I-IA+N-M, A, I, JA, DESCA, DESCA( M_ ) )
CALL PCELSET( A, I, JA+N-M+I-IA, DESCA, ONE )
CALL PCLARFC( 'Right', I-IA, I-IA+N-M+1, A, I, JA, DESCA,
$ DESCA( M_ ), TAU, A, IA, JA, DESCA, WORK )
II = INDXG2L( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW )
TAUI = TAU( MIN( II, MP ) )
CALL PCSCAL( I-IA+N-M, -TAUI, A, I, JA, DESCA, DESCA( M_ ) )
CALL PCLACGV( I-IA+N-M, A, I, JA, DESCA, DESCA( M_ ) )
CALL PCELSET( A, I, JA+N-M+I-IA, DESCA, ONE-CONJG( TAUI ) )
*
* Set A(i,ja+n-m+i-ia+1:ja+n-1) to zero
*
CALL PCLASET( 'All', 1, IA+M-1-I, ZERO, ZERO, A, I,
$ JA+N-M+I-IA+1, DESCA )
*
10 CONTINUE
*
CALL PTOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
CALL PTOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
*
WORK( 1 ) = CMPLX( REAL( LWMIN ) )
*
RETURN
*
* End of PCUNGR2
*
END