psormlq.f

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      SUBROUTINE psormlq( SIDE, TRANS, M, N, K, A, IA, JA, DESCA, TAU,
     $                    C, IC, JC, DESCC, 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 ..
      CHARACTER          SIDE, TRANS
      INTEGER            IA, IC, INFO, JA, JC, K, LWORK, M, N
*     ..
*     .. Array Arguments ..
      INTEGER            DESCA( * ), DESCC( * )
      REAL               A( * ), C( * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  PSORMLQ overwrites the general real M-by-N distributed matrix
*  sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with
*
*                       SIDE = 'L'          SIDE = 'R'
*  TRANS = 'N':      Q * sub( C )         sub( C ) * Q
*  TRANS = 'T':      Q**T * sub( C )      sub( C ) * Q**T
*
*  where Q is a real orthogonal distributed matrix defined as the
*  product of K elementary reflectors
*
*        Q = H(k) . . . H(2) H(1)
*
*  as returned by PSGELQF. Q is of order M if SIDE = 'L' and of order N
*  if SIDE = '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
*  =========
*
*  SIDE    (global input) CHARACTER
*          = 'L': apply Q or Q**T from the Left;
*          = 'R': apply Q or Q**T from the Right.
*
*  TRANS   (global input) CHARACTER
*          = 'N':  No transpose, apply Q;
*          = 'T':  Transpose, apply Q**T.
*
*  M       (global input) INTEGER
*          The number of rows to be operated on i.e the number of rows
*          of the distributed submatrix sub( C ). 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( C ). N >= 0.
*
*  K       (global input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q.  If SIDE = 'L', M >= K >= 0, if SIDE = 'R',
*          N >= K >= 0.
*
*  A       (local input) REAL pointer into the local memory
*          to an array of dimension (LLD_A,LOCc(JA+M-1)) if SIDE='L',
*          and (LLD_A,LOCc(JA+N-1)) if SIDE='R', where
*          LLD_A >= max(1,LOCr(IA+K-1)); On entry, the i-th row must
*          contain the vector which defines the elementary reflector
*          H(i), IA <= i <= IA+K-1, as returned by PSGELQF in the
*          K rows of its distributed matrix argument A(IA:IA+K-1,JA:*).
*          A(IA:IA+K-1,JA:*) is modified by the routine but restored on
*          exit.
*
*  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) REAL, array, dimension LOCc(IA+K-1).
*          This array contains the scalar factors TAU(i) of the
*          elementary reflectors H(i) as returned by PSGELQF.
*          TAU is tied to the distributed matrix A.
*
*  C       (local input/local output) REAL pointer into the
*          local memory to an array of dimension (LLD_C,LOCc(JC+N-1)).
*          On entry, the local pieces of the distributed matrix sub(C).
*          On exit, sub( C ) is overwritten by Q*sub( C ) or Q'*sub( C )
*          or sub( C )*Q' or sub( C )*Q.
*
*  IC      (global input) INTEGER
*          The row index in the global array C indicating the first
*          row of sub( C ).
*
*  JC      (global input) INTEGER
*          The column index in the global array C indicating the
*          first column of sub( C ).
*
*  DESCC   (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix C.
*
*  WORK    (local workspace/local output) REAL 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
*          if SIDE = 'L',
*            LWORK >= MAX( (MB_A*(MB_A-1))/2, ( MpC0 + MAX( MqA0 +
*                     NUMROC( NUMROC( M+IROFFC, MB_A, 0, 0, NPROW ),
*                             MB_A, 0, 0, LCMP ), NqC0 ) )*MB_A ) +
*                     MB_A * MB_A
*          else if SIDE = 'R',
*            LWORK >= MAX( (MB_A*(MB_A-1))/2, (MpC0 + NqC0)*MB_A ) +
*                     MB_A * MB_A
*          end if
*
*          where LCMP = LCM / NPROW with LCM = ICLM( NPROW, NPCOL ),
*
*          IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
*          IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
*          MqA0 = NUMROC( M+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
*
*          IROFFC = MOD( IC-1, MB_C ), ICOFFC = MOD( JC-1, NB_C ),
*          ICROW = INDXG2P( IC, MB_C, MYROW, RSRC_C, NPROW ),
*          ICCOL = INDXG2P( JC, NB_C, MYCOL, CSRC_C, NPCOL ),
*          MpC0 = NUMROC( M+IROFFC, MB_C, MYROW, ICROW, NPROW ),
*          NqC0 = NUMROC( N+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ),
*
*          ILCM, 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    (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.
*
*  Alignment requirements
*  ======================
*
*  The distributed submatrices A(IA:*, JA:*) and C(IC:IC+M-1,JC:JC+N-1)
*  must verify some alignment properties, namely the following
*  expressions should be true:
*
*  If SIDE = 'L',
*    ( NB_A.EQ.MB_C .AND. ICOFFA.EQ.IROFFC )
*  If SIDE = 'R',
*    ( NB_A.EQ.NB_C .AND. ICOFFA.EQ.ICOFFC .AND. IACOL.EQ.ICCOL )
*
*  =====================================================================
*
*     .. 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            LEFT, LQUERY, NOTRAN
      CHARACTER          COLBTOP, ROWBTOP, TRANST
      INTEGER            I, I1, I2, I3, IACOL, IB, ICC, ICCOL, ICOFFA,
     $                   icoffc, icrow, ictxt, iinfo, ipw, iroffc, jcc,
     $                   lcm, lcmp, lwmin, mi, mpc0, mqa0, mycol, myrow,
     $                   ni, npcol, nprow, nq, nqc0
*     ..
*     .. Local Arrays ..
      INTEGER            IDUM1( 4 ), IDUM2( 4 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           blacs_gridinfo, chk1mat, pchk2mat, pslarfb,
     $                   pslarft, psorml2, pb_topget, pb_topset, pxerbla
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ICEIL, ILCM, INDXG2P, NUMROC
      EXTERNAL           iceil, ilcm, indxg2p, lsame, numroc
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ichar, 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 = -(900+ctxt_)
      ELSE
         left = lsame( side, 'L' )
         notran = lsame( trans, 'n' )
*
*        NQ is the order of Q
*
         IF( LEFT ) THEN
            NQ = M
            CALL CHK1MAT( K, 5, M, 3, IA, JA, DESCA, 9, INFO )
         ELSE
            NQ = N
            CALL CHK1MAT( K, 5, N, 4, IA, JA, DESCA, 9, INFO )
         END IF
         CALL CHK1MAT( M, 3, N, 4, IC, JC, DESCC, 14, INFO )
.EQ.         IF( INFO0 ) THEN
            ICOFFA = MOD( JA-1, DESCA( NB_ ) )
            IROFFC = MOD( IC-1, DESCC( MB_ ) )
            ICOFFC = MOD( JC-1, DESCC( NB_ ) )
            IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
     $                       NPCOL )
            ICROW = INDXG2P( IC, DESCC( MB_ ), MYROW, DESCC( RSRC_ ),
     $                       NPROW )
            ICCOL = INDXG2P( JC, DESCC( NB_ ), MYCOL, DESCC( CSRC_ ),
     $                       NPCOL )
            MPC0 = NUMROC( M+IROFFC, DESCC( MB_ ), MYROW, ICROW, NPROW )
            NQC0 = NUMROC( N+ICOFFC, DESCC( NB_ ), MYCOL, ICCOL, NPCOL )
*
            IF( LEFT ) THEN
               MQA0 = NUMROC( M+ICOFFA, DESCA( NB_ ), MYCOL, IACOL,
     $                        NPCOL )
               LCM = ILCM( NPROW, NPCOL )
               LCMP = LCM / NPROW
               LWMIN =  MAX( ( DESCA( MB_ ) * ( DESCA( MB_ ) - 1 ) )
     $                  / 2, ( MPC0 + MAX( MQA0 + NUMROC( NUMROC(
     $                  M+IROFFC, DESCA( MB_ ), 0, 0, NPROW ),
     $                  DESCA( MB_ ), 0, 0, LCMP ), NQC0 ) ) *
     $                  DESCA( MB_ ) ) + DESCA( MB_ ) * DESCA( MB_ )
            ELSE
               LWMIN = MAX( ( DESCA( MB_ ) * ( DESCA( MB_ ) - 1 ) ) / 2,
     $                      ( MPC0 + NQC0 ) * DESCA( MB_ ) ) +
     $                 DESCA( MB_ ) * DESCA( MB_ )
            END IF
*
            WORK( 1 ) = REAL( LWMIN )
.EQ.            LQUERY = ( LWORK-1 )
.NOT..AND..NOT.            IF( LEFT  LSAME( SIDE, 'r' ) ) THEN
               INFO = -1
.NOT..AND..NOT.            ELSE IF( NOTRAN  LSAME( TRANS, 't' ) ) THEN
               INFO = -2
.LT..OR..GT.            ELSE IF( K0  KNQ ) THEN
               INFO = -5
.AND..NE.            ELSE IF( LEFT  DESCA( NB_ )DESCC( MB_ ) ) THEN
               INFO = -(900+NB_)
.AND..NE.            ELSE IF( LEFT  ICOFFAIROFFC ) THEN
               INFO = -12
.NOT..AND..NE.            ELSE IF( LEFT  ICOFFAICOFFC ) THEN
               INFO = -13
.NOT..AND..NE.            ELSE IF( LEFT  IACOLICCOL ) THEN
               INFO = -13
.NOT..AND..NE.            ELSE IF( LEFT  DESCA( NB_ )DESCC( NB_ ) ) THEN
               INFO = -(1400+NB_)
.NE.            ELSE IF( ICTXTDESCC( CTXT_ ) ) THEN
               INFO = -(1400+CTXT_)
.LT..AND..NOT.            ELSE IF( LWORKLWMIN  LQUERY ) THEN
               INFO = -16
            END IF
         END IF
         IF( LEFT ) THEN
            IDUM1( 1 ) = ICHAR( 'l' )
         ELSE
            IDUM1( 1 ) = ICHAR( 'r' )
         END IF
         IDUM2( 1 ) = 1
         IF( NOTRAN ) THEN
            IDUM1( 2 ) = ICHAR( 'n' )
         ELSE
            IDUM1( 2 ) = ICHAR( 't' )
         END IF
         IDUM2( 2 ) = 2
         IDUM1( 3 ) = K
         IDUM2( 3 ) = 5
.EQ.         IF( LWORK-1 ) THEN
            IDUM1( 4 ) = -1
         ELSE
            IDUM1( 4 ) = 1
         END IF
         IDUM2( 4 ) = 16
         IF( LEFT ) THEN
            CALL PCHK2MAT( K, 5, M, 3, IA, JA, DESCA, 9, M, 3, N, 4, IC,
     $                     JC, DESCC, 14, 4, IDUM1, IDUM2, INFO )
         ELSE
            CALL PCHK2MAT( K, 5, N, 4, IA, JA, DESCA, 9, M, 3, N, 4, IC,
     $                     JC, DESCC, 14, 4, IDUM1, IDUM2, INFO )
         END IF
      END IF
*
.NE.      IF( INFO0 ) THEN
         CALL PXERBLA( ICTXT, 'psormlq', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
.EQ..OR..EQ..OR..EQ.      IF( M0  N0  K0 )
     $   RETURN
*
      CALL PB_TOPGET( ICTXT, 'broadcast', 'rowwise', ROWBTOP )
      CALL PB_TOPGET( ICTXT, 'broadcast', 'columnwise', COLBTOP )
*
.AND..OR.      IF( ( LEFT  NOTRAN ) 
.NOT..AND..NOT.     $    ( LEFT  NOTRAN ) ) THEN
         I1 = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+K-1 )
     $             + 1
         I2 = IA + K - 1
         I3 = DESCA( MB_ )
      ELSE
         I1 = MAX( ( (IA+K-2) / DESCA( MB_ ) ) * DESCA( MB_ ) + 1, IA )
         I2 = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+K-1 )
     $                    + 1
         I3 = -DESCA( MB_ )
      END IF
*
      IF( LEFT ) THEN
         NI  = N
         JCC = JC
      ELSE
         MI  = M
         ICC = IC
         CALL PB_TOPSET( ICTXT, 'broadcast', 'rowwise', ' ' )
         IF( notran ) THEN
            CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', 'D-ring' )
         ELSE
            CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', 'I-ring' )
         END IF
      END IF
*
      IF( notran ) THEN
         transt = 'T'
      ELSE
         transt = 'N'
      END IF
*
      IF( ( left .AND. notran ) .OR. ( .NOT.left .AND. .NOT.notran ) )
     $   CALL psorml2( side, trans, m, n, i1-ia, a, ia, ja, desca, tau,
     $                 c, ic, jc, descc, work, lwork, iinfo )
*
      ipw = desca( mb_ ) * desca( mb_ ) + 1
      DO 10 i = i1, i2, i3
         ib = min( desca( mb_ ), k-i+ia )
*
*        Form the triangular factor of the block reflector
*        H = H(i) H(i+1) . . . H(i+ib-1)
*
         CALL pslarft( 'Forward', 'Rowwise', nq-i+ia, ib, a, i, ja+i-ia,
     $                 desca, tau, work, work( ipw ) )
         IF( left ) THEN
*
*           H or H' is applied to C(ic+i-ia:ic+m-1,jc:jc+n-1)
*
            mi  = m - i + ia
            icc = ic + i - ia
         ELSE
*
*           H or H' is applied to C(ic:ic+m-1,jc+i-ia:jc+n-1)
*
            ni = n - i + ia
            jcc = jc + i - ia
         END IF
*
*        Apply H or H'
*
         CALL pslarfb( side, transt, 'Forward', 'Rowwise', mi, ni, ib,
     $                 a, i, ja+i-ia, desca, work, c, icc, jcc, descc,
     $                 work( ipw ) )
   10 CONTINUE
*
      IF( ( left .AND. .NOT.notran ) .OR. ( .NOT.left .AND. notran ) )
     $   CALL psorml2( side, trans, m, n, i2-ia, a, ia, ja, desca, tau,
     $                 c, ic, jc, descc, work, lwork, iinfo )
*
      CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', rowbtop )
      CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', colbtop )
*
      work( 1 ) = real( lwmin )
*
      RETURN
*
*     End of PSORMLQ
*
      END