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NAME

       PDORMTR - 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 PDORMTR( SIDE, UPLO, TRANS, M, N, A, IA, JA, DESCA, TAU,  C,
                           IC, JC, DESCC, WORK, LWORK, INFO )

           CHARACTER       SIDE, TRANS, UPLO

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

           INTEGER         DESCA( * ), DESCC( * )

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

PURPOSE

       PDORMTR  overwrites the general real M-by-N distributed matrix sub( C )
       = C(IC:IC+M-1,JC:JC+N-1) with  TRANS  =  ’T’:       Q**T  *  sub(  C  )
       sub( C ) * Q**T

       where  Q is a real orthogonal distributed matrix of order nq, with nq =
       m if SIDE = ’L’ and nq = n if SIDE = ’R’. Q is defined as  the  product
       of nq-1 elementary reflectors, as returned by PDSYTRD:

       if UPLO = ’U’, Q = H(nq-1) . . . H(2) H(1);

       if UPLO = ’L’, Q = H(1) H(2) . . . H(nq-1).

       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.

       UPLO    (global input) CHARACTER
               = ’U’:  Upper  triangle  of  A(IA:*,JA:*)  contains  elementary
               reflectors  from PDSYTRD; = ’L’: Lower triangle of A(IA:*,JA:*)
               contains elementary reflectors from PDSYTRD.

       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.

       A       (local input) DOUBLE PRECISION pointer into the local memory
               to an array of dimension (LLD_A,LOCc(JA+M-1)) if  SIDE=’L’,  or
               (LLD_A,LOCc(JA+N-1))  if  SIDE  = ’R’. The vectors which define
               the elementary reflectors, as returned by PDSYTRD.  If  SIDE  =
               ’L’,  LLD_A  >=  max(1,LOCr(IA+M-1));  if  SIDE = ’R’, LLD_A >=
               max(1,LOCr(IA+N-1)).

       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 LTAU, where
               if SIDE = ’L’ and UPLO = ’U’, LTAU = LOCc(M_A), if SIDE  =  ’L’
               and  UPLO  = ’L’, LTAU = LOCc(JA+M-2), if SIDE = ’R’ and UPLO =
               ’U’, LTAU = LOCc(N_A), if SIDE = ’R’ and UPLO  =  ’L’,  LTAU  =
               LOCc(JA+N-2).   TAU(i)  must  contain  the scalar factor of the
               elementary reflector H(i), as returned by PDSYTRD. 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 UPLO = ’U’, IAA = IA, JAA = JA+1, ICC = IC, JCC =  JC;  else
               UPLO  =  ’L’,  IAA = IA+1, JAA = JA; if SIDE = ’L’, ICC = IC+1;
               JCC = JC; else ICC = IC; JCC = JC+1; end if end if

               If  SIDE  =  ’L’,  MI  =  M-1;  NI   =   N;   LWORK   >=   MAX(
               (NB_A*(NB_A-1))/2,  (NqC0  + MpC0)*NB_A ) + NB_A * NB_A else if
               SIDE = ’R’, MI = M; MI = N-1; LWORK >= MAX(  (NB_A*(NB_A-1))/2,
               (  NqC0  +  MAX(  NpA0 + NUMROC( NUMROC( NI+ICOFFC, NB_A, 0, 0,
               NPCOL ), NB_A, 0, 0, LCMQ ), MpC0 ) )*NB_A ) + NB_A * NB_A  end
               if

               where LCMQ = LCM / NPCOL with LCM = ICLM( NPROW, NPCOL ),

               IROFFA = MOD( IAA-1, MB_A ), ICOFFA = MOD( JAA-1, NB_A ), IAROW
               = INDXG2P( IAA, MB_A, MYROW, RSRC_A, NPROW ),  NpA0  =  NUMROC(
               NI+IROFFA, MB_A, MYROW, IAROW, NPROW ),

               IROFFC = MOD( ICC-1, MB_C ), ICOFFC = MOD( JCC-1, NB_C ), ICROW
               = INDXG2P( ICC, MB_C, MYROW, RSRC_C, NPROW ), ICCOL =  INDXG2P(
               JCC,  NB_C,  MYCOL,  CSRC_C, NPCOL ), MpC0 = NUMROC( MI+IROFFC,
               MB_C, MYROW, ICROW, NPROW ), NqC0 =  NUMROC(  NI+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’,  (  MB_A.EQ.MB_C .AND. IROFFA.EQ.IROFFC .AND.
               IAROW.EQ.ICROW  )  If  SIDE  =  ’R’,   (   MB_A.EQ.NB_C   .AND.
               IROFFA.EQ.ICOFFC )