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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.