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 MbyN distributed matrix sub( A ) = (IA:IA+M1,JA:JA+N1) 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 rightlooking 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+N1)). On entry, this array contains the local pieces of the MbyN 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 ith argument is an array and the jentry had an illegal value, then INFO = (i*100+j), if the ith argument is a scalar and had an illegal value, then INFO = i. > 0: If INFO = K, U(IA+K1,JA+K1) 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.