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NAME

       PZGETRF  -  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 PZGETRF( M, N, A, IA, JA, DESCA, IPIV, INFO )

           INTEGER         IA, INFO, JA, M, N

           INTEGER         DESCA( * ), IPIV( * )

           COMPLEX*16      A( * )

PURPOSE

       PZGETRF  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) COMPLEX*16 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.