pzgstrf_irecv.c File Reference
Performs LU factorization in parallel. More...
Include dependency graph for pzgstrf_irecv.c:
Functions | |
| static void | pzgstrf2 (superlu_options_t *, int_t, double, Glu_persist_t *, gridinfo_t *, LocalLU_t *, SuperLUStat_t *, int *) |
| static void | pzgstrs2 (int_t, int_t, Glu_persist_t *, gridinfo_t *, LocalLU_t *, SuperLUStat_t *) |
| int_t | pzgstrf (superlu_options_t *options, int m, int n, double anorm, LUstruct_t *LUstruct, gridinfo_t *grid, SuperLUStat_t *stat, int *info) |
| static int | probe_recv (int iam, int source, int tag, MPI_Datatype datatype, MPI_Comm comm, int buf_size) |
Detailed Description
Performs LU factorization in parallel.
Copyright (c) 2003, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from U.S. Dept. of Energy)
All rights reserved.
The source code is distributed under BSD license, see the file License.txt at the top-level directory.
-- Distributed SuperLU routine (version 1.0) --
Lawrence Berkeley National Lab, Univ. of California Berkeley.
September 1, 1999
Modified:
Feburary 7, 2001 use MPI_Isend/MPI_Irecv
Sketch of the algorithm
=======================
The following relations hold:
* A_kk = L_kk * U_kk
* L_ik = Aik * U_kk^(-1)
* U_kj = L_kk^(-1) * A_kj
----------------------------------
| | |
----|-----------------------------
| | \ U_kk| |
| | \ | U_kj |
| |L_kk \ | || |
----|-------|---------||----------
| | | \/ |
| | | |
| | | |
| | | |
| | L_ik ==> A_ij |
| | | |
| | | |
| | | |
----------------------------------
Handle the first block of columns separately.
* Factor diagonal and subdiagonal blocks and test for exact
singularity. ( pzgstrf2(0), one column at a time )
* Compute block row of U
* Update trailing matrix
Loop over the remaining blocks of columns.
mycol = MYCOL( iam, grid );
myrow = MYROW( iam, grid );
N = nsupers;
For (k = 1; k < N; ++k) {
krow = PROW( k, grid );
kcol = PCOL( k, grid );
Pkk = PNUM( krow, kcol, grid );
* Factor diagonal and subdiagonal blocks and test for exact
singularity.
if ( mycol == kcol ) {
pzgstrf2(k), one column at a time
}
* Parallel triangular solve
if ( iam == Pkk ) multicast L_k,k to this process row;
if ( myrow == krow && mycol != kcol ) {
Recv L_k,k from process Pkk;
for (j = k+1; j < N; ++j)
if ( PCOL( j, grid ) == mycol && A_k,j != 0 )
U_k,j = L_k,k \ A_k,j;
}
* Parallel rank-k update
if ( myrow == krow ) multicast U_k,k+1:N to this process column;
if ( mycol == kcol ) multicast L_k+1:N,k to this process row;
if ( myrow != krow ) {
Pkj = PNUM( krow, mycol, grid );
Recv U_k,k+1:N from process Pkj;
}
if ( mycol != kcol ) {
Pik = PNUM( myrow, kcol, grid );
Recv L_k+1:N,k from process Pik;
}
for (j = k+1; k < N; ++k) {
for (i = k+1; i < N; ++i)
if ( myrow == PROW( i, grid ) && mycol == PCOL( j, grid )
&& L_i,k != 0 && U_k,j != 0 )
A_i,j = A_i,j - L_i,k * U_k,j;
}
}
Remaining issues
(1) Use local indices for L subscripts and SPA. [DONE]
Function Documentation
◆ probe_recv()
|
static |
◆ pzgstrf()
| int_t pzgstrf | ( | superlu_options_t * | options, |
| int | m, | ||
| int | n, | ||
| double | anorm, | ||
| LUstruct_t * | LUstruct, | ||
| gridinfo_t * | grid, | ||
| SuperLUStat_t * | stat, | ||
| int * | info | ||
| ) |
Purpose
=======
PZGSTRF performs the LU factorization in parallel.
Arguments
=========
options (input) superlu_options_t*
The structure defines the input parameters to control
how the LU decomposition will be performed.
The following field should be defined:
o ReplaceTinyPivot (yes_no_t)
Specifies whether to replace the tiny diagonals by
sqrt(epsilon)*norm(A) during LU factorization.
m (input) int
Number of rows in the matrix.
n (input) int
Number of columns in the matrix.
anorm (input) double
The norm of the original matrix A, or the scaled A if
equilibration was done.
LUstruct (input/output) LUstruct_t*
The data structures to store the distributed L and U factors.
The following fields should be defined:
o Glu_persist (input) Glu_persist_t*
Global data structure (xsup, supno) replicated on all processes,
describing the supernode partition in the factored matrices
L and U:
xsup[s] is the leading column of the s-th supernode,
supno[i] is the supernode number to which column i belongs.
o Llu (input/output) LocalLU_t*
The distributed data structures to store L and U factors.
See superlu_zdefs.h for the definition of 'LocalLU_t'.
grid (input) gridinfo_t*
The 2D process mesh. It contains the MPI communicator, the number
of process rows (NPROW), the number of process columns (NPCOL),
and my process rank. It is an input argument to all the
parallel routines.
Grid can be initialized by subroutine SUPERLU_GRIDINIT.
See superlu_zdefs.h for the definition of 'gridinfo_t'.
stat (output) SuperLUStat_t*
Record the statistics on runtime and floating-point operation count.
See util.h for the definition of 'SuperLUStat_t'.
info (output) int*
= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, U(i,i) 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.
Here is the call graph for this function:
◆ pzgstrf2()
|
static |
Purpose
=======
Factor diagonal and subdiagonal blocks and test for exact singularity.
Only the process column that owns block column *k* participates
in the work.
Arguments
=========
k (input) int (global)
The column number of the block column to be factorized.
thresh (input) double (global)
The threshold value = s_eps * anorm.
Glu_persist (input) Glu_persist_t*
Global data structures (xsup, supno) replicated on all processes.
grid (input) gridinfo_t*
The 2D process mesh.
Llu (input/output) LocalLU_t*
Local data structures to store distributed L and U matrices.
stat (output) SuperLUStat_t*
Record the statistics about the factorization.
See SuperLUStat_t structure defined in util.h.
info (output) int*
= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, U(i,i) 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.
Here is the caller graph for this function:
◆ pzgstrs2()
|
static |
Here is the caller graph for this function:
