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NAME

       PCLARFB - applie a complex block reflector Q or its conjugate transpose
       Q**H  to  a  complex  M-by-N  distributed  matrix  sub(  C  )  denoting
       C(IC:IC+M-1,JC:JC+N-1), from the left or the right

SYNOPSIS

       SUBROUTINE PCLARFB( SIDE,  TRANS,  DIRECT,  STOREV, M, N, K, V, IV, JV,
                           DESCV, T, C, IC, JC, DESCC, WORK )

           CHARACTER       SIDE, TRANS, DIRECT, STOREV

           INTEGER         IC, IV, JC, JV, K, M, N

           INTEGER         DESCC( * ), DESCV( * )

           COMPLEX         C( * ), T( * ), V( * ), WORK( * )

PURPOSE

       PCLARFB applies a complex block reflector Q or its conjugate  transpose
       Q**H  to  a  complex  M-by-N  distributed  matrix  sub(  C  )  denoting
       C(IC:IC+M-1,JC:JC+N-1), from the left or the right.

       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**H from the Left;
               = ’R’: apply Q or Q**H from the Right.

       TRANS   (global input) CHARACTER
               = ’N’:  No transpose, apply Q;
               = ’C’:  Conjugate transpose, apply Q**H.

       DIRECT  (global input) CHARACTER
               Indicates  how  Q  is  formed  from  a  product  of  elementary
               reflectors = ’F’: Q = H(1) H(2) . . . H(k) (Forward)
               = ’B’: Q = H(k) . . . H(2) H(1) (Backward)

       STOREV  (global input) CHARACTER
               Indicates  how  the  vectors  which   define   the   elementary
               reflectors are stored:
               = ’C’: Columnwise
               = ’R’: Rowwise

       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  order  of  the  matrix  T  (=  the  number  of  elementary
               reflectors whose product defines the block reflector).

       V       (local input) COMPLEX pointer into the local memory
               to an array of dimension ( LLD_V, LOCc(JV+K-1) )  if  STOREV  =
               ’C’,  (  LLD_V, LOCc(JV+M-1)) if STOREV = ’R’ and SIDE = ’L’, (
               LLD_V, LOCc(JV+N-1) ) if STOREV  =  ’R’  and  SIDE  =  ’R’.  It
               contains   the  local  pieces  of  the  distributed  vectors  V
               representing  the  Householder  transformation.   See   further
               details.    If   STOREV   =  ’C’  and  SIDE  =  ’L’,  LLD_V  >=
               MAX(1,LOCr(IV+M-1)); if STOREV = ’C’ and SIDE = ’R’,  LLD_V  >=
               MAX(1,LOCr(IV+N-1)); if STOREV = ’R’, LLD_V >= LOCr(IV+K-1).

       IV      (global input) INTEGER
               The row index in the global array V indicating the first row of
               sub( V ).

       JV      (global input) INTEGER
               The column index in the global array  V  indicating  the  first
               column of sub( V ).

       DESCV   (global and local input) INTEGER array of dimension DLEN_.
               The array descriptor for the distributed matrix V.

       T       (local input) COMPLEX array, dimension MB_V by MB_V
               if  STOREV  =  ’R’ and NB_V by NB_V if STOREV = ’C’. The trian-
               gular matrix T in the representation of the block reflector.

       C       (local input/local output) COMPLEX pointer into the
               local memory to an array of dimension (LLD_C,LOCc(JC+N-1)).  On
               entry,  the M-by-N 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) COMPLEX array, dimension (LWORK)
               If  STOREV  =  ’C’, if SIDE = ’L’, LWORK >= ( NqC0 + MpC0 ) * K
               else if SIDE = ’R’, LWORK >= (  NqC0  +  MAX(  NpV0  +  NUMROC(
               NUMROC( N+ICOFFC, NB_V, 0, 0, NPCOL ), NB_V, 0, 0, LCMQ ), MpC0
               ) ) * K end if else if STOREV = ’R’, if SIDE = ’L’, LWORK >=  (
               MpC0  + MAX( MqV0 + NUMROC( NUMROC( M+IROFFC, MB_V, 0, 0, NPROW
               ), MB_V, 0, 0, LCMP ), NqC0 ) ) * K else if SIDE =  ’R’,  LWORK
               >= ( MpC0 + NqC0 ) * K end if end if

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

               IROFFV = MOD( IV-1, MB_V ), ICOFFV = MOD( JV-1, NB_V ), IVROW =
               INDXG2P( IV, MB_V, MYROW, RSRC_V, NPROW ), IVCOL = INDXG2P( JV,
               NB_V,  MYCOL,  CSRC_V,  NPCOL ), MqV0 = NUMROC( M+ICOFFV, NB_V,
               MYCOL, IVCOL, NPCOL ), NpV0 = NUMROC(  N+IROFFV,  MB_V,  MYROW,
               IVROW, NPROW ),

               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 ), NpC0 = NUMROC(  N+ICOFFC,  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
               subroutine BLACS_GRIDINFO.

               Alignment requirements ======================

               The    distributed    submatrices     V(IV:*,     JV:*)     and
               C(IC:IC+M-1,JC:JC+N-1)  must  verify some alignment properties,
               namely the following expressions should be true:

               If STOREV = ’Columnwise’ If SIDE = ’Left’, ( MB_V.EQ.MB_C .AND.
               IROFFV.EQ.IROFFC  .AND.  IVROW.EQ.ICROW  ) If SIDE = ’Right’, (
               MB_V.EQ.NB_C  .AND.  IROFFV.EQ.ICOFFC  )  else  if   STOREV   =
               ’Rowwise’    If   SIDE   =   ’Left’,   (   NB_V.EQ.MB_C   .AND.
               ICOFFV.EQ.IROFFC ) If SIDE  =  ’Right’,  (  NB_V.EQ.NB_C  .AND.
               ICOFFV.EQ.ICOFFC .AND. IVCOL.EQ.ICCOL ) end if