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NAME

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

SYNOPSIS

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

           CHARACTER*1     DIREC, PIVROC, ROWCOL

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

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

           DOUBLE          PRECISION A( * )

PURPOSE

       PDLAPIV applies either P (permutation matrix indicated by IPIV) or inv(
       P   )   to   a   general   M-by-N   distributed   matrix  sub(  A  )  =
       A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting. The  pivot
       vector  may  be distributed across a process row or a column. The pivot
       vector should be aligned with the distributed matrix  A.  This  routine
       will  transpose  the pivot vector if necessary.  For example if the row
       pivots should be applied to the columns of sub( A  ),  pass  ROWCOL=’C’
       and PIVROC=’C’.

       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

       Restrictions
       ============

       IPIV must always be a distributed vector (not  a  matrix).   Thus:  IF(
       ROWPIV .EQ. ’C’ ) THEN
          JP must be 1
       ELSE
          IP must be 1
       END IF

       The  following  restrictions  apply  when  IPIV must be transposed: IF(
       ROWPIV.EQ.’C’ .AND. PIVROC.EQ.’C’) THEN
           DESCIP(MB_) must equal DESCA(NB_)
       ELSE IF( ROWPIV.EQ.’R" .AND. PIVROC.EQ.’R’) THEN
           DESCIP(NB_) must equal DESCA(MB_)
       END IF

ARGUMENTS

       DIREC   (global input) CHARACTER*1
               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*1
               Specifies if the rows or columns are to be permuted: = ’R’ Rows
               will be permuted, = ’C’ Columns will be permuted.

       PIVROC  (global input) CHARACTER*1
               Specifies whether IPIV is distributed over  a  process  row  or
               column:  =  ’R’  IPIV distributed over a process row = ’C’ IPIV
               distributed over a process column

       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) DOUBLE PRECISION pointer into the
               local memory to an array of  dimension  (LLD_A,  LOCc(JA+N-1)).
               On   entry,  this  array  contains  the  local  pieces  of  the
               distributed submatrix sub( A )  to  which  the  row  or  column
               interchanges  will be applied. On exit, the local pieces of the
               permuted distributed submatrix.

       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    (local input) INTEGER array, dimension >= LOCr(M_A)+MB_A
               if  ROWCOL=’R’,  otherwise  LOCc(N_A)+NB_A.  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.  This array is
               tied to the distributed matrix A.

       IWORK   (local workspace) INTEGER array, dimension (LDW)
               where  LDW  is   equal   to   the   workspace   necessary   for
               transposition, and the storage of the tranposed IPIV:

               Let  LCM  be the least common multiple of NPROW and NPCOL.  IF(
               ROWCOL.EQ.’R’ .AND. PIVROC.EQ.’R’ ) THEN IF(  NPROW.EQ.NPCOL  )
               THEN  LDW  =  LOCr(  N_P  + MOD(JP-1, NB_P) ) + NB_P ELSE LDW =
               LOCr(   N_P   +   MOD(JP-1,   NB_P)   )   +   NB_P   *    CEIL(
               CEIL(LOCc(N_P)/NB_P)   /   (LCM/NPCOL)   )   END  IF  ELSE  IF(
               ROWCOL.EQ.’C’ .AND. PIVROC.EQ.’C’ ) THEN IF(  NPROW.EQ.NPCOL  )
               THEN  LDW  =  LOCc(  M_P  + MOD(IP-1, MB_P) ) + MB_P ELSE LDW =
               LOCc(   M_P   +   MOD(IP-1,   MB_P)   )   +   MB_P   *    CEIL(
               CEIL(LOCr(M_P)/MB_P)  /  (LCM/NPROW) ) END IF ELSE IWORK is not
               referenced.  END IF