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NAME

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

           CHARACTER       DIRECT, SIDE, STOREV, TRANS

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

           INTEGER         DESCC( * ), DESCV( * )

           COMPLEX*16      C( * ), T( * ), V( * ), WORK( * )

PURPOSE

       PZLARZB 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.

       Q is a product of k elementary reflectors as returned by PZTZRZF.

       Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

       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 H is formed from a product of elementary reflectors = 'F': H = H(1)
               H(2) . . . H(k) (Forward, not supported yet)
               = 'B': H = H(k) . . . H(2) H(1) (Backward)

       STOREV  (global input) CHARACTER
               Indicates how the vectors which define the elementary reflectors are stored:
               = 'C': Columnwise                        (not supported yet)
               = '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).

       L       (global input) INTEGER
               The  columns  of the distributed submatrix sub( A ) containing the meaningful part
               of the Householder reflectors.  If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >=  L
               >= 0.

       V       (local input) COMPLEX*16 pointer into the local memory
               to   an   array  of  dimension  (LLD_V,  LOCc(JV+M-1))  if  SIDE  =  'L',  (LLD_V,
               LOCc(JV+N-1)) if SIDE = 'R'. It contains  the  local  pieces  of  the  distributed
               vectors  V  representing  the  Householder  transformation as returned by PZTZRZF.
               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*16 array, dimension MB_V by MB_V
               The lower triangular matrix T in the representation of the block reflector.

       C       (local input/local output) COMPLEX*16 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*16 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