SUBROUTINE PZGERQ2( M, N, 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, LWORK, M, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
COMPLEX*16 A( * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PZGERQ2 computes a RQ factorization of a complex distributed M-by-N
* matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * Q.
*
* 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 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, the local pieces of the M-by-N distributed matrix
* sub( A ) which is to be factored. On exit, if M <= N, the
* upper triangle of A( IA:IA+M-1, JA+N-M:JA+N-1 ) contains the
* M by M upper triangular matrix R; if M >= N, the elements on
* and above the (M-N)-th subdiagonal contain the M by N upper
* trapezoidal matrix R; the remaining elements, with the array
* TAU, represent the unitary matrix Q as a product of
* elementary reflectors (see Further Details).
*
* 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 output) COMPLEX*16, array, dimension LOCr(IA+M-1)
* This array contains the scalar factors of the elementary
* reflectors. TAU is tied to the distributed matrix A.
*
* WORK (local workspace/local output) COMPLEX*16 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 >= Nq0 + MAX( 1, Mp0 ), where
*
* IROFF = MOD( IA-1, MB_A ), ICOFF = MOD( JA-1, NB_A ),
* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
* Mp0 = NUMROC( M+IROFF, MB_A, MYROW, IAROW, NPROW ),
* Nq0 = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ),
*
* and NUMROC, INDXG2P 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.
*
* Further Details
* ===============
*
* The matrix Q is represented as a product of elementary reflectors
*
* Q = H(ia)' H(ia+1)' . . . H(ia+k-1)', where k = min(m,n).
*
* Each H(i) has the form
*
* H(i) = I - tau * v * v'
*
* where tau is a complex scalar, and v is a complex vector with
* v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
* exit in A(ia+m-k+i-1,ja:ja+n-k+i-2), and tau in TAU(ia+m-k+i-1).
*
* =====================================================================
*
* .. 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*16 ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL LQUERY
CHARACTER COLBTOP, ROWBTOP
INTEGER IACOL, IAROW, I, ICTXT, J, K, LWMIN, MP, MYCOL,
$ MYROW, NPCOL, NPROW, NQ
COMPLEX*16 AII
* ..
* .. External Subroutines ..
EXTERNAL BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT,
$ PTOPGET, PTOPSET, PXERBLA, PZELSET, PZLACGV,
$ PZLARF, PZLARFG
* ..
* .. External Functions ..
INTEGER INDXG2P, NUMROC
EXTERNAL INDXG2P, NUMROC
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, MAX, MIN, MOD
* ..
* .. 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 = -(600+CTXT_)
ELSE
CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, INFO )
IF( INFO.EQ.0 ) THEN
IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),
$ NPROW )
IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
$ NPCOL )
MP = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),
$ MYROW, IAROW, NPROW )
NQ = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),
$ MYCOL, IACOL, NPCOL )
LWMIN = NQ + MAX( 1, MP )
*
WORK( 1 ) = DCMPLX( DBLE( LWMIN ) )
LQUERY = ( LWORK.EQ.-1 )
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
$ INFO = -9
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PZGERQ2', -INFO )
CALL BLACS_ABORT( ICTXT, 1 )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 )
$ RETURN
*
CALL PTOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
CALL PTOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
CALL PTOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' )
CALL PTOPSET( ICTXT, 'Broadcast', 'Columnwise', 'D-ring' )
*
K = MIN( M, N )
DO 10 I = IA+K-1, IA, -1
J = JA + I - IA
*
* Generate elementary reflector H(i) to annihilate
* A(i+m-k,ja:j+n-k-1)
*
CALL PZLACGV( N-K+J-JA+1, A, I+M-K, JA, DESCA, DESCA( M_ ) )
CALL PZLARFG( N-K+J-JA+1, AII, I+M-K, J+N-K, A, I+M-K, JA,
$ DESCA, DESCA( M_ ), TAU )
*
* Apply H(i) to A(ia:i+m-k-1,ja:j+n-k) from the right
*
CALL PZELSET( A, I+M-K, J+N-K, DESCA, ONE )
CALL PZLARF( 'Right', M-K+I-IA, N-K+J-JA+1, A, M-K+I, JA,
$ DESCA, DESCA( M_ ), TAU, A, IA, JA, DESCA, WORK )
CALL PZELSET( A, I+M-K, J+N-K, DESCA, AII )
CALL PZLACGV( N-K+J-JA+1, A, I+M-K, JA, DESCA, DESCA( M_ ) )
*
10 CONTINUE
*
CALL PTOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
CALL PTOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
*
WORK( 1 ) = DCMPLX( DBLE( LWMIN ) )
*
RETURN
*
* End of PZGERQ2
*
END