.TH PCGETRF l "12 May 1997" "LAPACK version 1.5" "LAPACK routine (version 1.5)"
.SH NAME
PCGETRF - 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
.SH SYNOPSIS
.TP 20
SUBROUTINE PCGETRF(
M, N, A, IA, JA, DESCA, IPIV, INFO )
.TP 20
.ti +4
INTEGER
IA, INFO, JA, M, N
.TP 20
.ti +4
INTEGER
DESCA( * ), IPIV( * )
.TP 20
.ti +4
COMPLEX
A( * )
.SH PURPOSE
PCGETRF 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.
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Notes
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=====
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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.
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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".
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NOTATION        STORED IN      EXPLANATION
.br
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
                               DTYPE_A = 1.
.br
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.
.br
M_A    (global) DESCA( M_ )    The number of rows in the global
                               array A.
.br
N_A    (global) DESCA( N_ )    The number of columns in the global
                               array A.
.br
MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
                               the rows of the array.
.br
NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
                               the columns of the array.
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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.
.br
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.
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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.
.br
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.
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The values of LOCr() and LOCc() may be determined via a call to the
ScaLAPACK tool function, NUMROC:
.br
        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:
.br
        LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
.br
        LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
.br

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

.SH ARGUMENTS
.TP 8
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.
.TP 8
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.
.TP 8
A       (local input/local output) COMPLEX 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.
.TP 8
IA      (global input) INTEGER
The row index in the global array A indicating the first
row of sub( A ).
.TP 8
JA      (global input) INTEGER
The column index in the global array A indicating the
first column of sub( A ).
.TP 8
DESCA   (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix A.
.TP 8
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.
.TP 8
INFO    (global output) INTEGER
= 0:  successful exit
.br
< 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.
