#include <math.h>
#include "superlu_ddefs.h"
Data Types | |
type | etree_node |
Defines | |
#define | IRECV_U |
Functions/Subroutines | |
static void | pdgstrf2 (superlu_options_t *options, int_t nsupers, int_t k0, int_t k, double thresh, Glu_persist_t *Glu_persist, gridinfo_t *grid, LocalLU_t *Llu, MPI_Request *U_diag_blk_send_req, SuperLUStat_t *stat, int *info) |
static void | pdgstrs2 (int_t, int_t, int_t, Glu_persist_t *, gridinfo_t *, LocalLU_t *, SuperLUStat_t *) |
int | superlu_sort_perm (const void *arg1, const void *arg2) |
int_t | pdgstrf (superlu_options_t *options, int m, int n, double anorm, LUstruct_t *LUstruct, gridinfo_t *grid, SuperLUStat_t *stat, int *info) |
-- Distributed SuperLU routine (version 3.0) -- Lawrence Berkeley National Lab, Univ. of California Berkeley. July 12, 2011
Modified: September 1, 1999 Feburary 7, 2001 use MPI_Isend/MPI_Irecv October 15, 2008 latency-reducing panel factorization July 12, 2011 static-scheduling and arbitray look-ahead
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. ( pdgstrf2(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 ) { pdgstrf2(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; } }
#define IRECV_U |
int_t pdgstrf | ( | superlu_options_t * | options, | |
int | m, | |||
int | n, | |||
double | anorm, | |||
LUstruct_t * | LUstruct, | |||
gridinfo_t * | grid, | |||
SuperLUStat_t * | stat, | |||
int * | info | |||
) |
Purpose =======
PDGSTRF 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_ddefs.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_ddefs.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.
static void pdgstrf2 | ( | superlu_options_t * | options, | |
int_t | nsupers, | |||
int_t | k0, | |||
int_t | k, | |||
double | thresh, | |||
Glu_persist_t * | Glu_persist, | |||
gridinfo_t * | grid, | |||
LocalLU_t * | Llu, | |||
MPI_Request * | U_diag_blk_send_req, | |||
SuperLUStat_t * | stat, | |||
int * | info | |||
) | [static] |
Purpose ======= Panel factorization -- block column k
Factor diagonal and subdiagonal blocks and test for exact singularity. Only the column processes that own block column *k* participate 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.
U_diag_blk_send_req (input/output) MPI_Request* List of send requests to send down the diagonal block of U.
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.
ALWAYS SEND TO ALL OTHERS - TO FIX
static void pdgstrs2 | ( | int_t | m, | |
int_t | k0, | |||
int_t | k, | |||
Glu_persist_t * | Glu_persist, | |||
gridinfo_t * | grid, | |||
LocalLU_t * | Llu, | |||
SuperLUStat_t * | stat | |||
) | [static] |
int superlu_sort_perm | ( | const void * | arg1, | |
const void * | arg2 | |||
) |