PZGETRF(3) ScaLAPACK routine of NEC Numeric Library Collection PZGETRF(3)
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 diago-
nal 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 algo-
rithm.
Notes
=====
Each global data object is described by an associated description vec-
tor. This vector stores the information required to establish the map-
ping 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 col-
umn.
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 fac-
torization 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.
ScaLAPACK routine 31 October 2017 PZGETRF(3)