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

NAME

       PCLAPIV  - 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 PCLAPIV( 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( * )

           COMPLEX         A( * )

PURPOSE

       PCLAPIV 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) COMPLEX 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