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
- SUBROUTINE PZGETRF(
- M, N, A, IA, JA, DESCA, IPIV, INFO )
INTEGER IA, INFO, JA, M, N INTEGER DESCA( * ), IPIV( * ) COMPLEX*16 A( * )
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 ).
- 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.