PDORMRQ(3)    ScaLAPACK routine of NEC Numeric Library Collection   PDORMRQ(3)



NAME
       PDORMRQ - overwrite 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'

SYNOPSIS
       SUBROUTINE PDORMRQ( SIDE, TRANS, M, N, K, A, IA, JA, DESCA, TAU, C, IC,
                           JC, DESCC, WORK, LWORK, INFO )

           CHARACTER       SIDE, TRANS

           INTEGER         IA, IC, INFO, JA, JC, K, LWORK, M, N

           INTEGER         DESCA( * ), DESCC( * )

           DOUBLE          PRECISION A( * ), C( * ), TAU( * ), WORK( * )

PURPOSE
       PDORMRQ  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(1) H(2) . . . H(k)

       as returned by PDGERQF. 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  vec-
       tor.  This vector stores the information required to establish the map-
       ping 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 col-
       umn.
       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) DOUBLE PRECISION 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 PDGERQF 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) DOUBLE PRECISION array, dimension LOCc(IA+K-1).
               This array contains the scalar factors TAU(i) of the elementary
               reflectors  H(i)  as  returned  by PDGERQF.  TAU is tied to the
               distributed matrix A.

       C       (local input/local output) DOUBLE PRECISION 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) DOUBLE PRECISION 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 subrou-
               tine 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 )



ScaLAPACK routine               31 October 2017                     PDORMRQ(3)