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NAME

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

           CHARACTER       SIDE, TRANS

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

           INTEGER         DESCA( * ), DESCC( * )

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

PURPOSE

       PSORMHR   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 IHI-ILO elementary reflectors, as
       returned by PSGEHRD:

       Q = H(ilo) H(ilo+1) . . . H(ihi-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.

       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.

       ILO     (global input) INTEGER
               IHI      (global  input)  INTEGER  ILO and IHI must have the same values as in the
               previous call of PSGEHRD. Q is equal to the unit matrix except in the  distributed
               submatrix  Q(ia+ilo:ia+ihi-1,ia+ilo:ja+ihi-1).   If SIDE = 'L', 1 <= ILO <= IHI <=
               max(1,M); if SIDE = 'R', 1 <= ILO <= IHI <= max(1,N); ILO  and  IHI  are  relative
               indexes.

       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'.  The  vectors  which  define  the  elementary
               reflectors, as returned by PSGEHRD.

       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+M-2)
               if  SIDE  =  'L',  and  LOCc(JA+N-2) if SIDE = 'R'. This array contains the scalar
               factors TAU(j) of the elementary reflectors H(j) as returned by  PSGEHRD.  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

               IAA  =  IA  + ILO; JAA = JA+ILO-1; If SIDE = 'L', MI = IHI-ILO; NI = N; ICC = IC +
               ILO; JCC = JC; LWORK >= MAX( (NB_A*(NB_A-1))/2, (NqC0 + MpC0)*NB_A ) + NB_A * NB_A
               else  if SIDE = 'R', MI = M; NI = IHI-ILO; ICC = IC; JCC = JC + ILO; 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 )