pcgeqrf.f

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      SUBROUTINE pcgeqrf( M, N, A, IA, JA, DESCA, TAU, WORK, LWORK,
     $                    INFO )
*
*  -- ScaLAPACK routine (version 1.7) --
*     University of Tennessee, Knoxville, Oak Ridge National Laboratory,
*     and University of California, Berkeley.
*     May 25, 2001
*
*     .. Scalar Arguments ..
      INTEGER            IA, INFO, JA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      INTEGER            DESCA( * )
      COMPLEX            A( * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  PCGEQRF computes a QR factorization of a complex distributed M-by-N
*  matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * R.
*
*  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 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, the elements on
*          and above the diagonal of sub( A ) contain the min(M,N) by N
*          upper trapezoidal matrix R (R is upper triangular if M >= N);
*          the elements below the diagonal, 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, array, dimension
*          LOCc(JA+MIN(M,N)-1). This array contains the scalar factors
*          TAU of the elementary reflectors. 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 >= NB_A * ( Mp0 + Nq0 + NB_A ), 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    (global 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(ja) H(ja+1) . . . H(ja+k-1), where k = min(m,n).
*
*  Each H(i) has the form
*
*     H(j) = I - tau * v * v'
*
*  where tau is a complex scalar, and v is a complex vector with
*  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
*  A(ia+i:ia+m-1,ja+i-1), and tau in TAU(ja+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 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      CHARACTER          COLBTOP, ROWBTOP
      INTEGER            I, IACOL, IAROW, ICOFF, ICTXT, IINFO, IPW, J,
     $                   jb, jn, k, lwmin, mp0, mycol, myrow, npcol,
     $                   nprow, nq0
*     ..
*     .. Local Arrays ..
      INTEGER            IDUM1( 1 ), IDUM2( 1 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           blacs_gridinfo, chk1mat, pchk1mat, pcgeqr2,
     $                   pclarfb, pclarft, pb_topget, pb_topset, pxerbla
*     ..
*     .. External Functions ..
      INTEGER            ICEIL, INDXG2P, NUMROC
      EXTERNAL           iceil, indxg2p, numroc
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          cmplx, 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 = -(600+ctxt_)
      ELSE
         CALL chk1mat( m, 1, n, 2, ia, ja, desca, 6, info )
         IF( info.EQ.0 ) THEN
            icoff = mod( ja-1, desca( nb_ ) )
            iarow = indxg2p( ia, desca( mb_ ), myrow, desca( rsrc_ ),
     $                       nprow )
            iacol = indxg2p( ja, desca( nb_ ), mycol, desca( csrc_ ),
     $                       npcol )
            mp0 = numroc( m+mod( ia-1, desca( mb_ ) ), desca( mb_ ),
     $                    myrow, iarow, nprow )
            nq0 = numroc( n+icoff, desca( nb_ ), mycol, iacol, npcol )
            lwmin = desca( nb_ ) * ( mp0 + nq0 + desca( nb_ ) )
*
            work( 1 ) = cmplx( real( lwmin ) )
            lquery = ( lwork.EQ.-1 )
            IF( lwork.LT.lwmin .AND. .NOT.lquery )
     $         info = -9
         END IF
         IF( lwork.EQ.-1 ) THEN
            idum1( 1 ) = -1
         ELSE
            idum1( 1 ) = 1
         END IF
         idum2( 1 ) = 9
         CALL pchk1mat( m, 1, n, 2, ia, ja, desca, 6, 1, idum1, idum2,
     $                  info )
      END IF
*
      IF( info.NE.0 ) THEN
         CALL pxerbla( ictxt, 'PCGEQRF', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 )
     $   RETURN
*
      k = min( m, n )
      ipw = desca( nb_ ) * desca( nb_ ) + 1
      CALL pb_topget( ictxt, 'Broadcast', 'Rowwise', rowbtop )
      CALL pb_topget( ictxt, 'Broadcast', 'Columnwise', colbtop )
      CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', 'I-ring' )
      CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', ' ' )
*
*     Handle the first block of columns separately
*
      jn = min( iceil( ja, desca( nb_ ) ) * desca( nb_ ), ja+k-1 )
      jb = jn - ja + 1
*
*     Compute the QR factorization of the first block A(ia:ia+m-1,ja:jn)
*
      CALL pcgeqr2( m, jb, a, ia, ja, desca, tau, work, lwork, iinfo )
*
      IF( ja+jb.LE.ja+n-1 ) THEN
*
*        Form the triangular factor of the block reflector
*        H = H(ja) H(ja+1) . . . H(jn)
*
         CALL pclarft( 'Forward', 'Columnwise', m, jb, a, ia, ja, desca,
     $                 tau, work, work( ipw ) )
*
*        Apply H' to A(ia:ia+m-1,ja+jb:ja+n-1) from the left
*
         CALL pclarfb( 'Left', 'conjugate transpose', 'forward',
     $                 'columnwise', M, N-JB, JB, A, IA, JA, DESCA,
     $                 WORK, A, IA, JA+JB, DESCA, WORK( IPW ) )
      END IF
*
*     Loop over the remaining blocks of columns
*
      DO 10 J = JN+1, JA+K-1, DESCA( NB_ )
         JB = MIN( K-J+JA, DESCA( NB_ ) )
         I = IA + J - JA
*
*        Compute the QR factorization of the current block
*        A(i:ia+m-1,j:j+jb-1)
*
         CALL PCGEQR2( M-J+JA, JB, A, I, J, DESCA, TAU, WORK, LWORK,
     $                 IINFO )
*
.LE.         IF( J+JBJA+N-1 ) THEN
*
*           Form the triangular factor of the block reflector
*           H = H(j) H(j+1) . . . H(j+jb-1)
*
            CALL PCLARFT( 'forward', 'columnwise', M-J+JA, JB, A, I, J,
     $                    DESCA, TAU, WORK, WORK( IPW ) )
*
*           Apply H' to A(i:ia+m-1,j+jb:ja+n-1) from the left
*
            CALL PCLARFB( 'left', 'conjugate transpose', 'forward',
     $                     'columnwise', M-J+JA, N-J-JB+JA, JB, A, I, J,
     $                     DESCA, WORK, A, I, J+JB, DESCA, WORK( IPW ) )
         END IF
*
   10 CONTINUE
*
      CALL PB_TOPSET( ICTXT, 'broadcast', 'rowwise', ROWBTOP )
      CALL PB_TOPSET( ICTXT, 'broadcast', 'columnwise', colbtop )
*
      work( 1 ) = cmplx( real( lwmin ) )
*
      RETURN
*
*     End of PCGEQRF
*
      END