#include "pdsp_defs.h"
#include "util.h"
void
pdgssv(int nprocs, SuperMatrix *A, int *perm_c, int *perm_r,
SuperMatrix *L, SuperMatrix *U, SuperMatrix *B, int *info )
{
/*
* -- SuperLU MT routine (version 1.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* August 15, 1997
*
* Purpose
* =======
*
* pdgssv() solves the system of linear equations A*X=B, using the parallel
* LU factorization routine pdgstrf(). It performs the following steps:
*
* 1. If A is stored column-wise (A->Stype = NC):
*
* 1.1. Permute the columns of A, forming A*Pc, where Pc is a
* permutation matrix.
* For more details of this step, see sp_preorder.c.
*
* 1.2. Factor A as Pr*A*Pc=L*U with the permutation Pr determined
* by Gaussian elimination with partial pivoting.
* L is unit lower triangular with offdiagonal entries
* bounded by 1 in magnitude, and U is upper triangular.
*
* 1.3. Solve the system of equations A*X=B using the factored
* form of A.
*
* 2. If A is stored row-wise (A->Stype = NR), apply the above algorithm
* to the tranpose of A:
*
* 2.1. Permute columns of tranpose(A) (rows of A),
* forming transpose(A)*Pc, where Pc is a permutation matrix.
* For more details of this step, see sp_preorder.c.
*
* 2.2. Factor A as Pr*transpose(A)*Pc=L*U with the permutation Pr
* determined by Gaussian elimination with partial pivoting.
* L is unit lower triangular with offdiagonal entries
* bounded by 1 in magnitude, and U is upper triangular.
*
* 2.3. Solve the system of equations A*X=B using the factored
* form of A.
*
* See supermatrix.h for the definition of "SuperMatrix" structure.
*
*
* Arguments
* =========
*
* nprocs (input) int
* Number of processes (or threads) to be spawned and used to perform
* the LU factorization by pdgstrf(). There is a single thread of
* control to call pdgstrf(), and all threads spawned by pdgstrf()
* are terminated before returning from pdgstrf().
*
* A (input) SuperMatrix*
* Matrix A in A*X=B, of dimension (A->nrow, A->ncol), where
* A->nrow = A->ncol. Currently, the type of A can be:
* Stype = NC or NR; Dtype = _D; Mtype = GE. In the future,
* more general A will be handled.
*
* perm_c (input/output) int*
* If A->Stype=NC, column permutation vector of size A->ncol,
* which defines the permutation matrix Pc; perm_c[i] = j means
* column i of A is in position j in A*Pc.
* On exit, perm_c may be overwritten by the product of the input
* perm_c and a permutation that postorders the elimination tree
* of Pc'*A'*A*Pc; perm_c is not changed if the elimination tree
* is already in postorder.
*
* If A->Stype=NR, column permutation vector of size A->nrow
* which describes permutation of columns of tranpose(A)
* (rows of A) as described above.
*
* perm_r (output) int*,
* If A->Stype=NR, row permutation vector of size A->nrow,
* which defines the permutation matrix Pr, and is determined
* by partial pivoting. perm_r[i] = j means row i of A is in
* position j in Pr*A.
*
* If A->Stype=NR, permutation vector of size A->ncol, which
* determines permutation of rows of transpose(A)
* (columns of A) as described above.
*
* L (output) SuperMatrix*
* The factor L from the factorization
* Pr*A*Pc=L*U (if A->Stype=NC) or
* Pr*transpose(A)*Pc=L*U (if A->Stype=NR).
* Uses compressed row subscripts storage for supernodes, i.e.,
* L has types: Stype = SCP, Dtype = _D, Mtype = TRLU.
*
* U (output) SuperMatrix*
* The factor U from the factorization
* Pr*A*Pc=L*U (if A->Stype=NC) or
* Pr*transpose(A)*Pc=L*U (if A->Stype=NR).
* Use column-wise storage scheme, i.e., U has types:
* Stype = NCP, Dtype = _D, Mtype = TRU.
*
* B (input/output) SuperMatrix*
* B has types: Stype = DN, Dtype = _D, Mtype = GE.
* On entry, the right hand side matrix.
* On exit, the solution matrix if info = 0;
*
* info (output) int*
* = 0: successful exit
* > 0: if info = i, and i is
* <= A->ncol: U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* so the solution could not be computed.
* > A->ncol: number of bytes allocated when memory allocation
* failure occurred, plus A->ncol.
*
*/
trans_t trans;
NCformat *Astore;
DNformat *Bstore;
SuperMatrix *AA; /* A in NC format used by the factorization routine.*/
SuperMatrix AC; /* Matrix postmultiplied by Pc */
int i, n, panel_size, relax;
yes_no_t refact, usepr;
double diag_pivot_thresh, drop_tol;
void *work;
int lwork;
pdgstrf_options_t pdgstrf_options;
Gstat_t Gstat;
double t; /* Temporary time */
double *utime;
flops_t *ops, flopcnt;
/* ------------------------------------------------------------
Test the input parameters.
------------------------------------------------------------*/
Astore = A->Store;
Bstore = B->Store;
*info = 0;
if ( nprocs <= 0 ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
(A->Stype != SLU_NC && A->Stype != SLU_NR) ||
A->Dtype != SLU_D || A->Mtype != SLU_GE )
*info = -2;
else if ( B->ncol < 0 || Bstore->lda < MAX(1, A->nrow) ) *info = -7;
if ( *info != 0 ) {
i = -(*info);
xerbla_("pdgssv", &i);
return;
}
#if 0
/* Use the best sequential code.
if this part is commented out, we will use the parallel code
run on one processor. */
if ( nprocs == 1 ) {
return;
}
#endif
refact = NO;
trans = NOTRANS;
panel_size = sp_ienv(1);
relax = sp_ienv(2);
diag_pivot_thresh = 1.0;
usepr = NO;
drop_tol = 0.0;
work = NULL;
lwork = 0;
/* ------------------------------------------------------------
Allocate storage and initialize statistics variables.
------------------------------------------------------------*/
n = A->ncol;
StatAlloc(n, nprocs, panel_size, relax, &Gstat);
StatInit(n, nprocs, &Gstat);
utime = Gstat.utime;
ops = Gstat.ops;
/* ------------------------------------------------------------
Convert A to NC format when necessary.
------------------------------------------------------------*/
if ( A->Stype == SLU_NR ) {
NRformat *Astore = A->Store;
AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
dCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz,
Astore->nzval, Astore->colind, Astore->rowptr,
SLU_NC, A->Dtype, A->Mtype);
trans = TRANS;
} else if ( A->Stype == SLU_NC ) AA = A;
/* ------------------------------------------------------------
Initialize the option structure pdgstrf_options using the
user-input parameters;
Apply perm_c to the columns of original A to form AC.
------------------------------------------------------------*/
pdgstrf_init(nprocs, refact, panel_size, relax,
diag_pivot_thresh, usepr, drop_tol, perm_c, perm_r,
work, lwork, AA, &AC, &pdgstrf_options, &Gstat);
/* ------------------------------------------------------------
Compute the LU factorization of A.
The following routine will create nprocs threads.
------------------------------------------------------------*/
pdgstrf(&pdgstrf_options, &AC, perm_r, L, U, &Gstat, info);
flopcnt = 0;
for (i = 0; i < nprocs; ++i) flopcnt += Gstat.procstat[i].fcops;
ops[FACT] = flopcnt;
#if ( PRNTlevel==1 )
printf("nprocs = %d, flops %e, Mflops %.2f\n",
nprocs, flopcnt, flopcnt/utime[FACT]*1e-6);
printf("Parameters: w %d, relax %d, maxsuper %d, rowblk %d, colblk %d\n",
sp_ienv(1), sp_ienv(2), sp_ienv(3), sp_ienv(4), sp_ienv(5));
fflush(stdout);
#endif
/* ------------------------------------------------------------
Solve the system A*X=B, overwriting B with X.
------------------------------------------------------------*/
if ( *info == 0 ) {
t = SuperLU_timer_();
dgstrs (trans, L, U, perm_r, perm_c, B, &Gstat, info);
utime[SOLVE] = SuperLU_timer_() - t;
ops[SOLVE] = ops[TRISOLVE];
}
/* ------------------------------------------------------------
Deallocate storage after factorization.
------------------------------------------------------------*/
pdgstrf_finalize(&pdgstrf_options, &AC);
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
/* ------------------------------------------------------------
Print timings, then deallocate statistic variables.
------------------------------------------------------------*/
/*PrintStat(&Gstat);*/
StatFree(&Gstat);
}
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