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NAME

       PSORMBR  -  VECT = ’Q’, PSORMBR overwrites the general real distributed
       M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with   SIDE = ’L’  SIDE
       = ’R’ TRANS = ’N’

SYNOPSIS

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

           CHARACTER       SIDE, TRANS, VECT

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

           INTEGER         DESCA( * ), DESCC( * )

           REAL            A( * ), C( * ), TAU( * ), WORK( * )

PURPOSE

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

       If VECT = ’P’, PSORMBR overwrites sub( C ) with

                            SIDE = ’L’           SIDE = ’R’
       TRANS = ’N’:      P * sub( C )          sub( C ) * P
       TRANS = ’T’:      P**T * sub( C )       sub( C ) * P**T

       Here Q and P**T are the orthogonal distributed matrices  determined  by
       PSGEBRD  when  reducing  a  real  distributed  matrix  A(IA:*,JA:*)  to
       bidiagonal form: A(IA:*,JA:*) = Q * B * P**T. Q and P**T are defined as
       products of elementary reflectors H(i) and G(i) respectively.

       Let nq = m if SIDE = ’L’ and nq = n if SIDE = ’R’. Thus nq is the order
       of the orthogonal matrix Q or P**T that is applied.

       If VECT = ’Q’, A(IA:*,JA:*) is assumed to have been an NQ-by-K matrix:
       if nq >= k, Q = H(1) H(2) . . . H(k);
       if nq < k, Q = H(1) H(2) . . . H(nq-1).

       If VECT = ’P’, A(IA:*,JA:*) is assumed to have been a K-by-NQ matrix:
       if k < nq, P = G(1) G(2) . . . G(k);
       if k >= nq, P = G(1) G(2) . . . G(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

       VECT    (global input) CHARACTER
               = ’Q’: apply Q or Q**T;
               = ’P’: apply P or P**T.

       SIDE    (global input) CHARACTER
               = ’L’: apply Q, Q**T, P or P**T from the Left;
               = ’R’: apply Q, Q**T, P or P**T from the Right.

       TRANS   (global input) CHARACTER
               = ’N’:  No transpose, apply Q or P;
               = ’T’:  Transpose, apply Q**T or P**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
               If   VECT  =  ’Q’,  the  number  of  columns  in  the  original
               distributed matrix reduced by PSGEBRD.   If  VECT  =  ’P’,  the
               number  of  rows  in the original distributed matrix reduced by
               PSGEBRD.  K >= 0.

       A       (local input) REAL pointer into the local memory
               to  an  array  of  dimension  (LLD_A,LOCc(JA+MIN(NQ,K)-1))   if
               VECT=’Q’,  and  (LLD_A,LOCc(JA+NQ-1))  if VECT = ’P’. NQ = M if
               SIDE = ’L’, and NQ = N otherwise. The vectors which define  the
               elementary  reflectors  H(i) and G(i), whose products determine
               the matrices Q and P, as returned by PSGEBRD.  If VECT  =  ’Q’,
               LLD_A   >=  max(1,LOCr(IA+NQ-1));  if  VECT  =  ’P’,  LLD_A  >=
               max(1,LOCr(IA+MIN(NQ,K)-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) REAL array, dimension
               LOCc(JA+MIN(NQ,K)-1) if VECT  =  ’Q’,  LOCr(IA+MIN(NQ,K)-1)  if
               VECT  =  ’P’,  TAU(i)  must  contain  the  scalar factor of the
               elementary  reflector H(i) or G(i), which determines Q or P, as
               returned by PDGEBRD in its array argument TAUQ or TAUP.  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, if VECT=’Q’, sub( C ) is overwritten by  Q*sub(  C  )  or
               Q’*sub(  C ) or sub( C )*Q’ or sub( C )*Q; if VECT=’P, sub( C )
               is overwritten by P*sub( C ) or P’*sub( C ) or sub(  C  )*P  or
               sub( C )*P’.

       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’, NQ = M; if( (VECT = ’Q’ and NQ >= K)
               or (VECT <> ’Q’ and NQ > K)  ),  IAA=IA;  JAA=JA;  MI=M;  NI=N;
               ICC=IC;  JCC=JC; else IAA=IA+1; JAA=JA; MI=M-1; NI=N; ICC=IC+1;
               JCC=JC; end if else if SIDE = ’R’, NQ = N; if( (VECT = ’Q’  and
               NQ  >=  K) or (VECT <> ’Q’ and NQ > K) ), IAA=IA; JAA=JA; MI=M;
               NI=N; ICC=IC; JCC=JC;  else  IAA=IA;  JAA=JA+1;  MI=M;  NI=N-1;
               ICC=IC; JCC=JC+1; end if end if

               If  VECT = ’Q’, If SIDE = ’L’, LWORK >= MAX( (NB_A*(NB_A-1))/2,
               (NqC0 + MpC0)*NB_A ) + NB_A * NB_A else if SIDE = ’R’, 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 else if VECT <> ’Q’, if SIDE =
               ’L’, LWORK >= MAX( (MB_A*(MB_A-1))/2, (  MpC0  +  MAX(  MqA0  +
               NUMROC(  NUMROC(  MI+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 end if

               where LCMP = LCM / NPROW, 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 ), IACOL =  INDXG2P(
               JAA,  NB_A,  MYCOL,  CSRC_A, NPCOL ), MqA0 = NUMROC( MI+ICOFFA,
               NB_A, MYCOL, IACOL, NPCOL ), 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 ),

               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   VECT   =   ’Q’,  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  )  else If SIDE = ’L’, (
               MB_A.EQ.MB_C  .AND.  ICOFFA.EQ.IROFFC  )  If  SIDE  =  ’R’,   (
               NB_A.EQ.NB_C  .AND. ICOFFA.EQ.ICOFFC .AND. IACOL.EQ.ICCOL ) end
               if