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



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 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 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  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.

       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 con-
               tains 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 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',   (   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 )



ScaLAPACK routine               31 October 2017                     PSORMHR(3)