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NAME

       PCLAPV2  -  applie  either  P (permutation matrix indicated by IPIV) or
       inv(  P  )  to  a  M-by-N  distributed  matrix  sub(   A   )   denoting
       A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting

SYNOPSIS

       SUBROUTINE PCLAPV2( DIREC,  ROWCOL,  M,  N, A, IA, JA, DESCA, IPIV, IP,
                           JP, DESCIP )

           CHARACTER       DIREC, ROWCOL

           INTEGER         IA, IP, JA, JP, M, N

           INTEGER         DESCA( * ), DESCIP( * ), IPIV( * )

           COMPLEX         A( * )

PURPOSE

       PCLAPV2 applies either P (permutation matrix indicated by IPIV) or inv(
       P   )   to   a   M-by-N   distributed   matrix   sub(   A   )  denoting
       A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting.  The pivot
       vector  should  be aligned with the distributed matrix A.  For pivoting
       the rows of sub( A ), IPIV should be distributed along a process column
       and  replicated  over  all  process  rows.   Similarly,  IPIV should be
       distributed along a process row and replicated over all process columns
       for column pivoting.

       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

       DIREC   (global input) CHARACTER
               Specifies in which order the  permutation  is  applied:  =  ’F’
               (Forward)  Applies pivots Forward from top of matrix.  Computes
               P * sub( A ); = ’B’ (Backward)  Applies  pivots  Backward  from
               bottom of matrix. Computes inv( P ) * sub( A ).

       ROWCOL  (global input) CHARACTER
               Specifies if the rows or columns are to be permuted: = ’R’ Rows
               will be permuted, = ’C’ Columns will be permuted.

       M       (global input) INTEGER
               The number of rows to be operated on, i.e. the number  of  rows
               of the distributed submatrix sub( A ). 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( A ). N >= 0.

       A       (local input/local output) COMPLEX pointer into the
               local memory to an array of  dimension  (LLD_A,  LOCc(JA+N-1)).
               On  entry,  this  local  array contains the local pieces of the
               distributed matrix sub(  A  )  to  which  the  row  or  columns
               interchanges  will be applied. On exit, this array contains the
               local pieces of the permuted distributed matrix.

       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.

       IPIV    (input) INTEGER array, dimension >= LOCr(M_A)+MB_A if
               ROWCOL  =  ’R’,  LOCc(N_A)+NB_A  otherwise.  It  contains   the
               pivoting information. IPIV(i) is the global row (column), local
               row (column) i was swapped with.  The last piece of  the  array
               of size MB_A (resp. NB_A) is used as workspace. IPIV is tied to
               the distributed matrix A.

       IP      (global input) INTEGER
               IPIV’s global row index, which points to the beginning  of  the
               submatrix which is to be operated on.

       JP      (global input) INTEGER
               IPIV’s  global  column  index, which points to the beginning of
               the submatrix which is to be operated on.

       DESCIP  (global and local input) INTEGER array of dimension 8
               The array descriptor for the distributed matrix IPIV.