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.