NAME

       PDGETRF   -   compute   an  LU  factorization  of  a  general  M-by-N  distributed  matrix  sub(  A  )  =
       (IA:IA+M-1,JA:JA+N-1) using partial pivoting with row interchanges

SYNOPSIS

       SUBROUTINE PDGETRF( M, N, A, IA, JA, DESCA, IPIV, INFO )

           INTEGER         IA, INFO, JA, M, N

           INTEGER         DESCA( * ), IPIV( * )

           DOUBLE          PRECISION A( * )

PURPOSE

       PDGETRF  computes  an  LU  factorization  of  a  general  M-by-N  distributed   matrix   sub(   A   )   =
       (IA:IA+M-1,JA:JA+N-1) using partial pivoting with row interchanges.

       The  factorization  has  the  form  sub(  A  )  =  P * L * U, where P is a permutation matrix, L is lower
       triangular with unit diagonal ele- ments (lower trapezoidal if m > n), and U is upper  triangular  (upper
       trapezoidal if m < n). L and U are stored in sub( A ).

       This is the right-looking Parallel Level 3 BLAS version of the algorithm.

       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

       This routine requires square block decomposition ( MB_A = NB_A ).

ARGUMENTS

       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 M-by-N distributed matrix sub( A )  to  be  factored.  On  exit,  this  array
               contains  the  local  pieces  of the factors L and U from the factorization sub( A ) = P*L*U; the
               unit diagonal ele- ments of L are not stored.

       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 output) INTEGER array, dimension ( LOCr(M_A)+MB_A )
               This array contains the pivoting information.  IPIV(i) -> The global row local row i was  swapped
               with.  This array is tied to the distributed matrix A.

       INFO    (global output) INTEGER
               = 0:  successful exit
               <  0:   If  the  i-th  argument  is  an  array  and the j-entry had an illegal value, then INFO =
               -(i*100+j), if the i-th argument is a scalar and had an illegal value, then INFO = -i.  > 0:   If
               INFO = K, U(IA+K-1,JA+K-1) is exactly zero.  The factorization has been completed, but the factor
               U is exactly singular, and division by zero will occur if  it  is  used  to  solve  a  system  of
               equations.