main(int argc, char *argv[])
{
/*
* Purpose
* =======
*
* SDRIVE is the main test program for the FLOAT linear
* equation driver routines SGSSV and SGSSVX.
*
* The program is invoked by a shell script file -- stest.csh.
* The output from the tests are written into a file -- stest.out.
*
* =====================================================================
*/
float *a, *a_save;
int *asub, *asub_save;
int *xa, *xa_save;
SuperMatrix A, B, X, L, U;
SuperMatrix ASAV, AC;
GlobalLU_t Glu; /* Not needed on return. */
mem_usage_t mem_usage;
int *perm_r; /* row permutation from partial pivoting */
int *perm_c, *pc_save; /* column permutation */
int *etree;
float zero = 0.0;
float *R, *C;
float *ferr, *berr;
float *rwork;
float *wwork;
void *work;
int info, lwork, nrhs, panel_size, relax;
int m, n, nnz;
float *xact;
float *rhsb, *solx, *bsav;
int ldb, ldx;
float rpg, rcond;
int i, j, k1;
float rowcnd, colcnd, amax;
int maxsuper, rowblk, colblk;
int prefact, nofact, equil, iequed;
int nt, nrun, nfail, nerrs, imat, fimat, nimat;
int nfact, ifact, itran;
int kl, ku, mode, lda;
int zerot, izero, ioff;
double u;
float anorm, cndnum;
float *Afull;
float result[NTESTS];
superlu_options_t options;
fact_t fact;
trans_t trans;
SuperLUStat_t stat;
static char matrix_type[8];
static char equed[1], path[4], sym[1], dist[1];
FILE *fp;
/* Fixed set of parameters */
int iseed[] = {1988, 1989, 1990, 1991};
static char equeds[] = {'N', 'R', 'C', 'B'};
static fact_t facts[] = {FACTORED, DOFACT, SamePattern,
SamePattern_SameRowPerm};
static trans_t transs[] = {NOTRANS, TRANS, CONJ};
/* Some function prototypes */
extern int sgst01(int, int, SuperMatrix *, SuperMatrix *,
SuperMatrix *, int *, int *, float *);
extern int sgst02(trans_t, int, int, int, SuperMatrix *, float *,
int, float *, int, float *resid);
extern int sgst04(int, int, float *, int,
float *, int, float rcond, float *resid);
extern int sgst07(trans_t, int, int, SuperMatrix *, float *, int,
float *, int, float *, int,
float *, float *, float *);
extern int slatb4_slu(char *, int *, int *, int *, char *, int *, int *,
float *, int *, float *, char *);
extern int slatms_slu(int *, int *, char *, int *, char *, float *d,
int *, float *, float *, int *, int *,
char *, float *, int *, float *, int *);
extern int sp_sconvert(int, int, float *, int, int, int,
float *a, int *, int *, int *);
/* Executable statements */
strcpy(path, "SGE");
nrun = 0;
nfail = 0;
nerrs = 0;
/* Defaults */
lwork = 0;
n = 1;
nrhs = 1;
panel_size = sp_ienv(1);
relax = sp_ienv(2);
u = 1.0;
strcpy(matrix_type, "LA");
parse_command_line(argc, argv, matrix_type, &n,
&panel_size, &relax, &nrhs, &maxsuper,
&rowblk, &colblk, &lwork, &u, &fp);
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) {
fprintf(stderr, "expert: cannot allocate %d bytes\n", lwork);
exit (-1);
}
}
/* Set the default input options. */
set_default_options(&options);
options.DiagPivotThresh = u;
options.PrintStat = NO;
options.PivotGrowth = YES;
options.ConditionNumber = YES;
options.IterRefine = SLU_SINGLE;
if ( strcmp(matrix_type, "LA") == 0 ) {
/* Test LAPACK matrix suite. */
m = n;
lda = SUPERLU_MAX(n, 1);
nnz = n * n; /* upper bound */
fimat = 1;
nimat = NTYPES;
Afull = floatCalloc(lda * n);
sallocateA(n, nnz, &a, &asub, &xa);
} else {
/* Read a sparse matrix */
fimat = nimat = 0;
sreadhb(fp, &m, &n, &nnz, &a, &asub, &xa);
}
sallocateA(n, nnz, &a_save, &asub_save, &xa_save);
rhsb = floatMalloc(m * nrhs);
bsav = floatMalloc(m * nrhs);
solx = floatMalloc(n * nrhs);
ldb = m;
ldx = n;
sCreate_Dense_Matrix(&B, m, nrhs, rhsb, ldb, SLU_DN, SLU_S, SLU_GE);
sCreate_Dense_Matrix(&X, n, nrhs, solx, ldx, SLU_DN, SLU_S, SLU_GE);
xact = floatMalloc(n * nrhs);
etree = intMalloc(n);
perm_r = intMalloc(n);
perm_c = intMalloc(n);
pc_save = intMalloc(n);
R = (float *) SUPERLU_MALLOC(m*sizeof(float));
C = (float *) SUPERLU_MALLOC(n*sizeof(float));
ferr = (float *) SUPERLU_MALLOC(nrhs*sizeof(float));
berr = (float *) SUPERLU_MALLOC(nrhs*sizeof(float));
j = SUPERLU_MAX(m,n) * SUPERLU_MAX(4,nrhs);
rwork = (float *) SUPERLU_MALLOC(j*sizeof(float));
for (i = 0; i < j; ++i) rwork[i] = 0.;
if ( !R ) ABORT("SUPERLU_MALLOC fails for R");
if ( !C ) ABORT("SUPERLU_MALLOC fails for C");
if ( !ferr ) ABORT("SUPERLU_MALLOC fails for ferr");
if ( !berr ) ABORT("SUPERLU_MALLOC fails for berr");
if ( !rwork ) ABORT("SUPERLU_MALLOC fails for rwork");
wwork = floatCalloc( SUPERLU_MAX(m,n) * SUPERLU_MAX(4,nrhs) );
for (i = 0; i < n; ++i) perm_c[i] = pc_save[i] = i;
options.ColPerm = MY_PERMC;
for (imat = fimat; imat <= nimat; ++imat) { /* All matrix types */
if ( imat ) {
/* Skip types 5, 6, or 7 if the matrix size is too small. */
zerot = (imat >= 5 && imat <= 7);
if ( zerot && n < imat-4 )
continue;
/* Set up parameters with SLATB4 and generate a test matrix
with SLATMS. */
slatb4_slu(path, &imat, &n, &n, sym, &kl, &ku, &anorm, &mode,
&cndnum, dist);
slatms_slu(&n, &n, dist, iseed, sym, &rwork[0], &mode, &cndnum,
&anorm, &kl, &ku, "No packing", Afull, &lda,
&wwork[0], &info);
if ( info ) {
printf(FMT3, "SLATMS", info, izero, n, nrhs, imat, nfail);
continue;
}
/* For types 5-7, zero one or more columns of the matrix
to test that INFO is returned correctly. */
if ( zerot ) {
if ( imat == 5 ) izero = 1;
else if ( imat == 6 ) izero = n;
else izero = n / 2 + 1;
ioff = (izero - 1) * lda;
if ( imat < 7 ) {
for (i = 0; i < n; ++i) Afull[ioff + i] = zero;
} else {
for (j = 0; j < n - izero + 1; ++j)
for (i = 0; i < n; ++i)
Afull[ioff + i + j*lda] = zero;
}
} else {
izero = 0;
}
/* Convert to sparse representation. */
sp_sconvert(n, n, Afull, lda, kl, ku, a, asub, xa, &nnz);
} else {
izero = 0;
zerot = 0;
}
sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
/* Save a copy of matrix A in ASAV */
sCreate_CompCol_Matrix(&ASAV, m, n, nnz, a_save, asub_save, xa_save,
SLU_NC, SLU_S, SLU_GE);
sCopy_CompCol_Matrix(&A, &ASAV);
/* Form exact solution. */
sGenXtrue(n, nrhs, xact, ldx);
StatInit(&stat);
for (iequed = 0; iequed < 4; ++iequed) {
*equed = equeds[iequed];
if (iequed == 0) nfact = 4;
else nfact = 1; /* Only test factored, pre-equilibrated matrix */
for (ifact = 0; ifact < nfact; ++ifact) {
fact = facts[ifact];
options.Fact = fact;
for (equil = 0; equil < 2; ++equil) {
options.Equil = equil;
prefact = ( options.Fact == FACTORED ||
options.Fact == SamePattern_SameRowPerm );
/* Need a first factor */
nofact = (options.Fact != FACTORED); /* Not factored */
/* Restore the matrix A. */
sCopy_CompCol_Matrix(&ASAV, &A);
if ( zerot ) {
if ( prefact ) continue;
} else if ( options.Fact == FACTORED ) {
if ( equil || iequed ) {
/* Compute row and column scale factors to
equilibrate matrix A. */
sgsequ(&A, R, C, &rowcnd, &colcnd, &amax, &info);
/* Force equilibration. */
if ( !info && n > 0 ) {
if ( strncmp(equed, "R", 1)==0 ) {
rowcnd = 0.;
colcnd = 1.;
} else if ( strncmp(equed, "C", 1)==0 ) {
rowcnd = 1.;
colcnd = 0.;
} else if ( strncmp(equed, "B", 1)==0 ) {
rowcnd = 0.;
colcnd = 0.;
}
}
/* Equilibrate the matrix. */
slaqgs(&A, R, C, rowcnd, colcnd, amax, equed);
}
}
if ( prefact ) { /* Need a factor for the first time */
/* Save Fact option. */
fact = options.Fact;
options.Fact = DOFACT;
/* Preorder the matrix, obtain the column etree. */
sp_preorder(&options, &A, perm_c, etree, &AC);
/* Factor the matrix AC. */
sgstrf(&options, &AC, relax, panel_size,
etree, work, lwork, perm_c, perm_r, &L, &U,
&Glu, &stat, &info);
if ( info ) {
printf("** First factor: info %d, equed %c\n",
info, *equed);
if ( lwork == -1 ) {
printf("** Estimated memory: %d bytes\n",
info - n);
exit(0);
}
}
Destroy_CompCol_Permuted(&AC);
/* Restore Fact option. */
options.Fact = fact;
} /* if .. first time factor */
for (itran = 0; itran < NTRAN; ++itran) {
trans = transs[itran];
options.Trans = trans;
/* Restore the matrix A. */
sCopy_CompCol_Matrix(&ASAV, &A);
/* Set the right hand side. */
sFillRHS(trans, nrhs, xact, ldx, &A, &B);
sCopy_Dense_Matrix(m, nrhs, rhsb, ldb, bsav, ldb);
/*----------------
* Test sgssv
*----------------*/
if ( options.Fact == DOFACT && itran == 0) {
/* Not yet factored, and untransposed */
sCopy_Dense_Matrix(m, nrhs, rhsb, ldb, solx, ldx);
sgssv(&options, &A, perm_c, perm_r, &L, &U, &X,
&stat, &info);
if ( info && info != izero ) {
printf(FMT3, "sgssv",
info, izero, n, nrhs, imat, nfail);
} else {
/* Reconstruct matrix from factors and
compute residual. */
sgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
nt = 1;
if ( izero == 0 ) {
/* Compute residual of the computed
solution. */
sCopy_Dense_Matrix(m, nrhs, rhsb, ldb,
wwork, ldb);
sgst02(trans, m, n, nrhs, &A, solx,
ldx, wwork,ldb, &result[1]);
nt = 2;
}
/* Print information about the tests that
did not pass the threshold. */
for (i = 0; i < nt; ++i) {
if ( result[i] >= THRESH ) {
printf(FMT1, "sgssv", n, i,
result[i]);
++nfail;
}
}
nrun += nt;
} /* else .. info == 0 */
/* Restore perm_c. */
for (i = 0; i < n; ++i) perm_c[i] = pc_save[i];
if (lwork == 0) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
} /* if .. end of testing sgssv */
/*----------------
* Test sgssvx
*----------------*/
/* Equilibrate the matrix if fact = FACTORED and
equed = 'R', 'C', or 'B'. */
if ( options.Fact == FACTORED &&
(equil || iequed) && n > 0 ) {
slaqgs(&A, R, C, rowcnd, colcnd, amax, equed);
}
/* Solve the system and compute the condition number
and error bounds using sgssvx. */
sgssvx(&options, &A, perm_c, perm_r, etree,
equed, R, C, &L, &U, work, lwork, &B, &X, &rpg,
&rcond, ferr, berr, &Glu,
&mem_usage, &stat, &info);
if ( info && info != izero ) {
printf(FMT3, "sgssvx",
info, izero, n, nrhs, imat, nfail);
if ( lwork == -1 ) {
printf("** Estimated memory: %.0f bytes\n",
mem_usage.total_needed);
exit(0);
}
} else {
if ( !prefact ) {
/* Reconstruct matrix from factors and
compute residual. */
sgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
k1 = 0;
} else {
k1 = 1;
}
if ( !info ) {
/* Compute residual of the computed solution.*/
sCopy_Dense_Matrix(m, nrhs, bsav, ldb,
wwork, ldb);
sgst02(trans, m, n, nrhs, &ASAV, solx, ldx,
wwork, ldb, &result[1]);
/* Check solution from generated exact
solution. */
sgst04(n, nrhs, solx, ldx, xact, ldx, rcond,
&result[2]);
/* Check the error bounds from iterative
refinement. */
sgst07(trans, n, nrhs, &ASAV, bsav, ldb,
solx, ldx, xact, ldx, ferr, berr,
&result[3]);
/* Print information about the tests that did
not pass the threshold. */
for (i = k1; i < NTESTS; ++i) {
if ( result[i] >= THRESH ) {
printf(FMT2, "sgssvx",
options.Fact, trans, *equed,
n, imat, i, result[i]);
++nfail;
}
}
nrun += NTESTS;
} /* if .. info == 0 */
} /* else .. end of testing sgssvx */
} /* for itran ... */
if ( lwork == 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
} /* for equil ... */
} /* for ifact ... */
} /* for iequed ... */
#if 0
if ( !info ) {
PrintPerf(&L, &U, &mem_usage, rpg, rcond, ferr, berr, equed);
}
#endif
Destroy_SuperMatrix_Store(&A);
Destroy_SuperMatrix_Store(&ASAV);
StatFree(&stat);
} /* for imat ... */
/* Print a summary of the results. */
PrintSumm("SGE", nfail, nrun, nerrs);
if ( strcmp(matrix_type, "LA") == 0 ) SUPERLU_FREE (Afull);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (bsav);
SUPERLU_FREE (solx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (pc_save);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
SUPERLU_FREE (rwork);
SUPERLU_FREE (wwork);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
#if 0
Destroy_CompCol_Matrix(&A);
Destroy_CompCol_Matrix(&ASAV);
#else
SUPERLU_FREE(a); SUPERLU_FREE(asub); SUPERLU_FREE(xa);
SUPERLU_FREE(a_save); SUPERLU_FREE(asub_save); SUPERLU_FREE(xa_save);
#endif
if ( lwork > 0 ) {
SUPERLU_FREE (work);
Destroy_SuperMatrix_Store(&L);
Destroy_SuperMatrix_Store(&U);
}
return 0;
}
void
sgssv(superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r,
SuperMatrix *L, SuperMatrix *U, SuperMatrix *B,
SuperLUStat_t *stat, 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 = SLU_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 = SLU_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
* =========
*
* options (input) superlu_options_t*
* The structure defines the input parameters to control
* how the LU decomposition will be performed and how the
* system will be solved.
*
* 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 = SLU_NC or SLU_NR; Dtype = SLU_S; Mtype = SLU_GE.
* In the future, more general A may be handled.
*
* perm_c (input/output) int*
* If A->Stype = SLU_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.
* If A->Stype = SLU_NR, column permutation vector of size A->nrow
* which describes permutation of columns of transpose(A)
* (rows of A) as described above.
*
* If options->ColPerm = MY_PERMC or options->Fact = SamePattern or
* options->Fact = SamePattern_SameRowPerm, it is an input argument.
* 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.
* Otherwise, it is an output argument.
*
* perm_r (input/output) int*
* If A->Stype = SLU_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 = SLU_NR, permutation vector of size A->ncol, which
* determines permutation of rows of transpose(A)
* (columns of A) as described above.
*
* If options->RowPerm = MY_PERMR or
* options->Fact = SamePattern_SameRowPerm, perm_r is an
* input argument.
* otherwise it is an output argument.
*
* L (output) SuperMatrix*
* The factor L from the factorization
* Pr*A*Pc=L*U (if A->Stype = SLU_NC) or
* Pr*transpose(A)*Pc=L*U (if A->Stype = SLU_NR).
* Uses compressed row subscripts storage for supernodes, i.e.,
* L has types: Stype = SLU_SC, Dtype = SLU_S, Mtype = SLU_TRLU.
*
* U (output) SuperMatrix*
* The factor U from the factorization
* Pr*A*Pc=L*U (if A->Stype = SLU_NC) or
* Pr*transpose(A)*Pc=L*U (if A->Stype = SLU_NR).
* Uses column-wise storage scheme, i.e., U has types:
* Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_TRU.
*
* B (input/output) SuperMatrix*
* B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
* On entry, the right hand side matrix.
* On exit, the solution matrix if info = 0;
*
* stat (output) SuperLUStat_t*
* Record the statistics on runtime and doubleing-point operation count.
* See util.h for the definition of 'SuperLUStat_t'.
*
* 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.
*
*/
DNformat *Bstore;
SuperMatrix *AA = NULL;/* A in SLU_NC format used by the factorization routine.*/
SuperMatrix AC; /* Matrix postmultiplied by Pc */
int lwork = 0, *etree, i;
/* Set default values for some parameters */
int panel_size; /* panel size */
int relax; /* no of columns in a relaxed snodes */
int permc_spec;
trans_t trans = NOTRANS;
double *utime;
double t; /* Temporary time */
/* Test the input parameters ... */
*info = 0;
Bstore = B->Store;
if ( options->Fact != DOFACT ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
(A->Stype != SLU_NC && A->Stype != SLU_NR) ||
A->Dtype != SLU_S || A->Mtype != SLU_GE )
*info = -2;
else if ( B->ncol < 0 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_S || B->Mtype != SLU_GE )
*info = -7;
if ( *info != 0 ) {
i = -(*info);
xerbla_("sgssv", &i);
return;
}
utime = stat->utime;
/* Convert A to SLU_NC format when necessary. */
if ( A->Stype == SLU_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,
SLU_NC, A->Dtype, A->Mtype);
trans = TRANS;
} else {
if ( A->Stype == SLU_NC ) AA = A;
}
t = SuperLU_timer_();
/*
* Get column permutation vector perm_c[], according to permc_spec:
* permc_spec = NATURAL: natural ordering
* permc_spec = MMD_AT_PLUS_A: minimum degree on structure of A'+A
* permc_spec = MMD_ATA: minimum degree on structure of A'*A
* permc_spec = COLAMD: approximate minimum degree column ordering
* permc_spec = MY_PERMC: the ordering already supplied in perm_c[]
*/
permc_spec = options->ColPerm;
if ( permc_spec != MY_PERMC && options->Fact == DOFACT )
get_perm_c(permc_spec, AA, perm_c);
utime[COLPERM] = SuperLU_timer_() - t;
etree = intMalloc(A->ncol);
t = SuperLU_timer_();
sp_preorder(options, AA, perm_c, etree, &AC);
utime[ETREE] = SuperLU_timer_() - t;
panel_size = sp_ienv(1);
relax = sp_ienv(2);
/*printf("Factor PA = LU ... relax %d\tw %d\tmaxsuper %d\trowblk %d\n",
relax, panel_size, sp_ienv(3), sp_ienv(4));*/
t = SuperLU_timer_();
/* Compute the LU factorization of A. */
sgstrf(options, &AC, relax, panel_size,
etree, NULL, lwork, perm_c, perm_r, L, U, stat, info);
utime[FACT] = SuperLU_timer_() - t;
t = SuperLU_timer_();
if ( *info == 0 ) {
/* Solve the system A*X=B, overwriting B with X. */
sgstrs (trans, L, U, perm_c, perm_r, B, stat, info);
}
utime[SOLVE] = SuperLU_timer_() - t;
SUPERLU_FREE (etree);
Destroy_CompCol_Permuted(&AC);
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
}
void
sgssvx(superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r,
int *etree, char *equed, float *R, float *C,
SuperMatrix *L, SuperMatrix *U, void *work, int lwork,
SuperMatrix *B, SuperMatrix *X, float *recip_pivot_growth,
float *rcond, float *ferr, float *berr,
mem_usage_t *mem_usage, SuperLUStat_t *stat, int *info )
{
DNformat *Bstore, *Xstore;
float *Bmat, *Xmat;
int ldb, ldx, nrhs;
SuperMatrix *AA;/* A in SLU_NC format used by the factorization routine.*/
SuperMatrix AC; /* Matrix postmultiplied by Pc */
int colequ, equil, nofact, notran, rowequ, permc_spec;
trans_t trant;
char norm[1];
int i, j, info1;
float amax, anorm, bignum, smlnum, colcnd, rowcnd, rcmax, rcmin;
int relax, panel_size;
float diag_pivot_thresh;
double t0; /* temporary time */
double *utime;
/* External functions */
extern float slangs(char *, SuperMatrix *);
Bstore = B->Store;
Xstore = X->Store;
Bmat = Bstore->nzval;
Xmat = Xstore->nzval;
ldb = Bstore->lda;
ldx = Xstore->lda;
nrhs = B->ncol;
*info = 0;
nofact = (options->Fact != FACTORED);
equil = (options->Equil == YES);
notran = (options->Trans == NOTRANS);
if ( nofact ) {
*(unsigned char *)equed = 'N';
rowequ = FALSE;
colequ = FALSE;
} else {
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
smlnum = slamch_("Safe minimum");
bignum = 1. / smlnum;
}
#if 0
printf("dgssvx: Fact=%4d, Trans=%4d, equed=%c\n",
options->Fact, options->Trans, *equed);
#endif
/* Test the input parameters */
if (options->Fact != DOFACT && options->Fact != SamePattern &&
options->Fact != SamePattern_SameRowPerm &&
options->Fact != FACTORED &&
options->Trans != NOTRANS && options->Trans != TRANS &&
options->Trans != CONJ &&
options->Equil != NO && options->Equil != YES)
*info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
(A->Stype != SLU_NC && A->Stype != SLU_NR) ||
A->Dtype != SLU_S || A->Mtype != SLU_GE )
*info = -2;
else if (options->Fact == FACTORED &&
!(rowequ || colequ || lsame_(equed, "N")))
*info = -6;
else {
if (rowequ) {
rcmin = bignum;
rcmax = 0.;
for (j = 0; j < A->nrow; ++j) {
rcmin = SUPERLU_MIN(rcmin, R[j]);
rcmax = SUPERLU_MAX(rcmax, R[j]);
}
if (rcmin <= 0.) *info = -7;
else if ( A->nrow > 0)
rowcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
else rowcnd = 1.;
}
if (colequ && *info == 0) {
rcmin = bignum;
rcmax = 0.;
for (j = 0; j < A->nrow; ++j) {
rcmin = SUPERLU_MIN(rcmin, C[j]);
rcmax = SUPERLU_MAX(rcmax, C[j]);
}
if (rcmin <= 0.) *info = -8;
else if (A->nrow > 0)
colcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
else colcnd = 1.;
}
if (*info == 0) {
if ( lwork < -1 ) *info = -12;
else if ( B->ncol < 0 ) *info = -13;
else if ( B->ncol > 0 ) { /* no checking if B->ncol=0 */
if ( Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_S ||
B->Mtype != SLU_GE )
*info = -13;
}
if ( X->ncol < 0 ) *info = -14;
else if ( X->ncol > 0 ) { /* no checking if X->ncol=0 */
if ( Xstore->lda < SUPERLU_MAX(0, A->nrow) ||
(B->ncol != 0 && B->ncol != X->ncol) ||
X->Stype != SLU_DN ||
X->Dtype != SLU_S || X->Mtype != SLU_GE )
*info = -14;
}
}
}
if (*info != 0) {
i = -(*info);
xerbla_("sgssvx", &i);
return;
}
/* Initialization for factor parameters */
panel_size = sp_ienv(1);
relax = sp_ienv(2);
diag_pivot_thresh = options->DiagPivotThresh;
utime = stat->utime;
/* Convert A to SLU_NC format when necessary. */
if ( A->Stype == SLU_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,
SLU_NC, A->Dtype, A->Mtype);
if ( notran ) { /* Reverse the transpose argument. */
trant = TRANS;
notran = 0;
} else {
trant = NOTRANS;
notran = 1;
}
} else { /* A->Stype == SLU_NC */
trant = options->Trans;
AA = A;
}
if ( nofact && equil ) {
t0 = SuperLU_timer_();
/* Compute row and column scalings to equilibrate the matrix A. */
sgsequ(AA, R, C, &rowcnd, &colcnd, &amax, &info1);
if ( info1 == 0 ) {
/* Equilibrate matrix A. */
slaqgs(AA, R, C, rowcnd, colcnd, amax, equed);
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
}
utime[EQUIL] = SuperLU_timer_() - t0;
}
if ( nofact ) {
t0 = SuperLU_timer_();
/*
* Gnet column permutation vector perm_c[], according to permc_spec:
* permc_spec = NATURAL: natural ordering
* permc_spec = MMD_AT_PLUS_A: minimum degree on structure of A'+A
* permc_spec = MMD_ATA: minimum degree on structure of A'*A
* permc_spec = COLAMD: approximate minimum degree column ordering
* permc_spec = MY_PERMC: the ordering already supplied in perm_c[]
*/
permc_spec = options->ColPerm;
if ( permc_spec != MY_PERMC && options->Fact == DOFACT )
get_perm_c(permc_spec, AA, perm_c);
utime[COLPERM] = SuperLU_timer_() - t0;
t0 = SuperLU_timer_();
sp_preorder(options, AA, perm_c, etree, &AC);
utime[ETREE] = SuperLU_timer_() - t0;
/* printf("Factor PA = LU ... relax %d\tw %d\tmaxsuper %d\trowblk %d\n",
relax, panel_size, sp_ienv(3), sp_ienv(4));
fflush(stdout); */
/* Compute the LU factorization of A*Pc. */
t0 = SuperLU_timer_();
sgstrf(options, &AC, relax, panel_size, etree,
work, lwork, perm_c, perm_r, L, U, stat, info);
utime[FACT] = SuperLU_timer_() - t0;
if ( lwork == -1 ) {
mem_usage->total_needed = *info - A->ncol;
return;
}
}
if ( options->PivotGrowth ) {
if ( *info > 0 ) {
if ( *info <= A->ncol ) {
/* Compute the reciprocal pivot growth factor of the leading
rank-deficient *info columns of A. */
*recip_pivot_growth = sPivotGrowth(*info, AA, perm_c, L, U);
}
return;
}
/* Compute the reciprocal pivot growth factor *recip_pivot_growth. */
*recip_pivot_growth = sPivotGrowth(A->ncol, AA, perm_c, L, U);
}
if ( options->ConditionNumber ) {
/* Estimate the reciprocal of the condition number of A. */
t0 = SuperLU_timer_();
if ( notran ) {
*(unsigned char *)norm = '1';
} else {
*(unsigned char *)norm = 'I';
}
anorm = slangs(norm, AA);
sgscon(norm, L, U, anorm, rcond, stat, info);
utime[RCOND] = SuperLU_timer_() - t0;
}
if ( nrhs > 0 ) {
/* Scale the right hand side if equilibration was performed. */
if ( notran ) {
if ( rowequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i)
Bmat[i + j*ldb] *= R[i];
}
} else if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i)
Bmat[i + j*ldb] *= C[i];
}
/* Compute the solution matrix X. */
for (j = 0; j < nrhs; j++) /* Save a copy of the right hand sides */
for (i = 0; i < B->nrow; i++)
Xmat[i + j*ldx] = Bmat[i + j*ldb];
t0 = SuperLU_timer_();
sgstrs (trant, L, U, perm_c, perm_r, X, stat, info);
utime[SOLVE] = SuperLU_timer_() - t0;
/* Use iterative refinement to improve the computed solution and compute
error bounds and backward error estimates for it. */
t0 = SuperLU_timer_();
if ( options->IterRefine != NOREFINE ) {
sgsrfs(trant, AA, L, U, perm_c, perm_r, equed, R, C, B,
X, ferr, berr, stat, info);
} else {
for (j = 0; j < nrhs; ++j) ferr[j] = berr[j] = 1.0;
}
utime[REFINE] = SuperLU_timer_() - t0;
/* Transform the solution matrix X to a solution of the original system. */
if ( notran ) {
if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i)
Xmat[i + j*ldx] *= C[i];
}
} else if ( rowequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i)
Xmat[i + j*ldx] *= R[i];
}
} /* end if nrhs > 0 */
if ( options->ConditionNumber ) {
/* Set INFO = A->ncol+1 if the matrix is singular to working precision. */
if ( *rcond < slamch_("E") ) *info = A->ncol + 1;
}
if ( nofact ) {
sQuerySpace(L, U, mem_usage);
Destroy_CompCol_Permuted(&AC);
}
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
}
/* Here is a driver inspired by A. Sheffer's "cow flattener". */
static NLboolean __nlFactorize_SUPERLU(__NLContext *context, NLint *permutation) {
/* OpenNL Context */
__NLSparseMatrix* M = (context->least_squares)? &context->MtM: &context->M;
NLuint n = context->n;
NLuint nnz = __nlSparseMatrixNNZ(M); /* number of non-zero coeffs */
/* Compressed Row Storage matrix representation */
NLint *xa = __NL_NEW_ARRAY(NLint, n+1);
NLfloat *rhs = __NL_NEW_ARRAY(NLfloat, n);
NLfloat *a = __NL_NEW_ARRAY(NLfloat, nnz);
NLint *asub = __NL_NEW_ARRAY(NLint, nnz);
NLint *etree = __NL_NEW_ARRAY(NLint, n);
/* SuperLU variables */
SuperMatrix At, AtP;
NLint info, panel_size, relax;
superlu_options_t options;
/* Temporary variables */
NLuint i, jj, count;
__nl_assert(!(M->storage & __NL_SYMMETRIC));
__nl_assert(M->storage & __NL_ROWS);
__nl_assert(M->m == M->n);
/* Convert M to compressed column format */
for(i=0, count=0; i<n; i++) {
__NLRowColumn *Ri = M->row + i;
xa[i] = count;
for(jj=0; jj<Ri->size; jj++, count++) {
a[count] = Ri->coeff[jj].value;
asub[count] = Ri->coeff[jj].index;
}
}
xa[n] = nnz;
/* Free M, don't need it anymore at this point */
__nlSparseMatrixClear(M);
/* Create superlu A matrix transposed */
sCreate_CompCol_Matrix(
&At, n, n, nnz, a, asub, xa,
SLU_NC, /* Colum wise, no supernode */
SLU_S, /* floats */
SLU_GE /* general storage */
);
/* Set superlu options */
set_default_options(&options);
options.ColPerm = MY_PERMC;
options.Fact = DOFACT;
StatInit(&(context->slu.stat));
panel_size = sp_ienv(1); /* sp_ienv give us the defaults */
relax = sp_ienv(2);
/* Compute permutation and permuted matrix */
context->slu.perm_r = __NL_NEW_ARRAY(NLint, n);
context->slu.perm_c = __NL_NEW_ARRAY(NLint, n);
if ((permutation == NULL) || (*permutation == -1)) {
get_perm_c(3, &At, context->slu.perm_c);
if (permutation)
memcpy(permutation, context->slu.perm_c, sizeof(NLint)*n);
}
else
memcpy(context->slu.perm_c, permutation, sizeof(NLint)*n);
sp_preorder(&options, &At, context->slu.perm_c, etree, &AtP);
/* Decompose into L and U */
sgstrf(&options, &AtP, relax, panel_size,
etree, NULL, 0, context->slu.perm_c, context->slu.perm_r,
&(context->slu.L), &(context->slu.U), &(context->slu.stat), &info);
/* Cleanup */
Destroy_SuperMatrix_Store(&At);
Destroy_CompCol_Permuted(&AtP);
__NL_DELETE_ARRAY(etree);
__NL_DELETE_ARRAY(xa);
__NL_DELETE_ARRAY(rhs);
__NL_DELETE_ARRAY(a);
__NL_DELETE_ARRAY(asub);
context->slu.alloc_slu = NL_TRUE;
return (info == 0);
}
