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/*
* -- SuperLU routine (version 2.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* November 15, 1997
*
*/
#include "ssp_defs.h"
#include "util.h"
void
sgssv(SuperMatrix *A, int *perm_c, int *perm_r, SuperMatrix *L,
SuperMatrix *U, SuperMatrix *B, int *info )
{
/*
* Purpose
* =======
*
* SGSSV solves the system of linear equations A*X=B, using the
* LU factorization from SGSTRF. 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 transpose of A:
*
* 2.1. Permute columns of transpose(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
* =========
*
* A (input) SuperMatrix*
* Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number
* of linear equations is A->nrow. Currently, the type of A can be:
* Stype = NC or NR; Dtype = S_; 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 transpose(A)
* (rows of A) as described above.
*
* perm_r (output) int*
* If A->Stype = NC, 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 = SC, Dtype = S_, 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).
* Uses column-wise storage scheme, i.e., U has types:
* Stype = NC, Dtype = S_, Mtype = TRU.
*
* B (input/output) SuperMatrix*
* B has types: Stype = DN, Dtype = S_, 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.
*
*/
double t1; /* Temporary time */
char refact[1], trans[1];
DNformat *Bstore;
SuperMatrix *AA; /* A in NC format used by the factorization routine.*/
SuperMatrix AC; /* Matrix postmultiplied by Pc */
int lwork = 0, *etree, i;
/* Set default values for some parameters */
float diag_pivot_thresh = 1.0;
float drop_tol = 0;
int panel_size; /* panel size */
int relax; /* no of columns in a relaxed snodes */
double *utime;
extern SuperLUStat_t SuperLUStat;
/* Test the input parameters ... */
*info = 0;
Bstore = B->Store;
if ( A->nrow != A->ncol || A->nrow < 0 ||
(A->Stype != NC && A->Stype != NR) ||
A->Dtype != S_ || A->Mtype != GE )
*info = -1;
else if ( B->ncol < 0 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->Stype != DN || B->Dtype != S_ || B->Mtype != GE )
*info = -6;
if ( *info != 0 ) {
i = -(*info);
xerbla_("sgssv", &i);
return;
}
*refact = 'N';
*trans = 'N';
panel_size = sp_ienv(1);
relax = sp_ienv(2);
StatInit(panel_size, relax);
utime = SuperLUStat.utime;
/* Convert A to NC format when necessary. */
if ( A->Stype == NR ) {
NRformat *Astore = A->Store;
AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
sCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz,
Astore->nzval, Astore->colind, Astore->rowptr,
NC, A->Dtype, A->Mtype);
*trans = 'T';
} else if ( A->Stype == NC ) AA = A;
etree = intMalloc(A->ncol);
t1 = SuperLU_timer_();
sp_preorder(refact, AA, perm_c, etree, &AC);
utime[ETREE] = SuperLU_timer_() - t1;
/*printf("Factor PA = LU ... relax %d\tw %d\tmaxsuper %d\trowblk %d\n",
relax, panel_size, sp_ienv(3), sp_ienv(4));*/
t1 = SuperLU_timer_();
/* Compute the LU factorization of A. */
sgstrf(refact, &AC, diag_pivot_thresh, drop_tol, relax, panel_size,
etree, NULL, lwork, perm_r, perm_c, L, U, info);
utime[FACT] = SuperLU_timer_() - t1;
t1 = SuperLU_timer_();
if ( *info == 0 ) {
/* Solve the system A*X=B, overwriting B with X. */
sgstrs (trans, L, U, perm_r, perm_c, B, info);
}
utime[SOLVE] = SuperLU_timer_() - t1;
SUPERLU_FREE (etree);
Destroy_CompCol_Permuted(&AC);
if ( A->Stype == NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
PrintStat( &SuperLUStat );
StatFree();
}
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