Provided by: scalapack-doc_1.5-10_all bug

NAME

       PDLARFB  -  applie a real block reflector Q or its transpose Q**T to a real distributed M-
       by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1)

SYNOPSIS

       SUBROUTINE PDLARFB( 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( * )

           DOUBLE          PRECISION C( * ), T( * ), V( * ), WORK( * )

PURPOSE

       PDLARFB applies a real block reflector Q or its transpose Q**T to a real distributed M-by-
       N matrix sub( C ) = 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**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.

       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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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