PDLAPIV(3)    ScaLAPACK routine of NEC Numeric Library Collection   PDLAPIV(3)



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 vec-
       tor.  This vector stores the information required to establish the map-
       ping 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  col-
       umn.
       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( ROW-
       PIV.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 bot-
               tom 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  dis-
               tributed  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 (LIPIV) where LIPIV is
               when  ROWCOL='R'  or  'r':  >=  LOCr(  IA+M-1  ) + MB_A      if
               PIVROC='C' or 'c', >= LOCc( M + MOD(JP-1,NB_P) ) if  PIVROC='R'
               or   'r',   and,   when   ROWCOL='C'  or  'c':  >=  LOCr(  N  +
               MOD(IP-1,MB_P) ) if PIVROC='C' or 'c', >= LOCc( JA+N-1 ) + NB_A
               if  PIVROC='R' or 'r'.  This array contains the pivoting infor-
               mation. IPIV(i) is the global row (column), local row  (column)
               i  was  swapped with.  When ROWCOL='R' or 'r' and PIVROC='C' or
               'c', or ROWCOL='C' or 'c' and PIVROC='R' or 'r', the last piece
               of  this  array of size MB_A (resp. NB_A) is used as workspace.
               In those cases, this array is tied to the distributed matrix A.

       IP      (global input) INTEGER
               The row index in the global array P indicating the first row of
               sub( P ).

       JP      (global input) INTEGER
               The column index in the global array  P  indicating  the  first
               column of sub( P ).

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

       IWORK   (local workspace) INTEGER array, dimension (LDW)
               where  LDW  is  equal to the workspace necessary for transposi-
               tion, 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(  ROW-
               COL.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



ScaLAPACK routine               31 October 2017                     PDLAPIV(3)