void
c_fortran_zgssv_(int *iopt, int *n, int *nnz, int *nrhs,
doublecomplex *values, int *rowind, int *colptr,
doublecomplex *b, int *ldb,
fptr *f_factors, /* a handle containing the address
pointing to the factored matrices */
int *info)
{
/*
* This routine can be called from Fortran.
*
* iopt (input) int
* Specifies the operation:
* = 1, performs LU decomposition for the first time
* = 2, performs triangular solve
* = 3, free all the storage in the end
*
* f_factors (input/output) fptr*
* If iopt == 1, it is an output and contains the pointer pointing to
* the structure of the factored matrices.
* Otherwise, it it an input.
*
*/
SuperMatrix A, AC, B;
SuperMatrix *L, *U;
int *perm_r; /* row permutations from partial pivoting */
int *perm_c; /* column permutation vector */
int *etree; /* column elimination tree */
SCformat *Lstore;
NCformat *Ustore;
int i, panel_size, permc_spec, relax;
trans_t trans;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
factors_t *LUfactors;
trans = TRANS;
if ( *iopt == 1 ) { /* LU decomposition */
/* Set the default input options. */
set_default_options(&options);
/* Initialize the statistics variables. */
StatInit(&stat);
/* Adjust to 0-based indexing */
for (i = 0; i < *nnz; ++i) --rowind[i];
for (i = 0; i <= *n; ++i) --colptr[i];
zCreate_CompCol_Matrix(&A, *n, *n, *nnz, values, rowind, colptr,
SLU_NC, SLU_Z, SLU_GE);
L = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
U = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
if ( !(perm_r = intMalloc(*n)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(*n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(etree = intMalloc(*n)) ) ABORT("Malloc fails for etree[].");
/*
* Get column permutation vector perm_c[], according to permc_spec:
* permc_spec = 0: natural ordering
* permc_spec = 1: minimum degree on structure of A'*A
* permc_spec = 2: minimum degree on structure of A'+A
* permc_spec = 3: approximate minimum degree for unsymmetric matrices
*/
permc_spec = options.ColPerm;
get_perm_c(permc_spec, &A, perm_c);
sp_preorder(&options, &A, perm_c, etree, &AC);
panel_size = sp_ienv(1);
relax = sp_ienv(2);
zgstrf(&options, &AC, relax, panel_size, etree,
NULL, 0, perm_c, perm_r, L, U, &stat, info);
if ( *info == 0 ) {
Lstore = (SCformat *) L->Store;
Ustore = (NCformat *) U->Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz);
zQuerySpace(L, U, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
} else {
printf("zgstrf() error returns INFO= %d\n", *info);
if ( *info <= *n ) { /* factorization completes */
zQuerySpace(L, U, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
}
}
/* Restore to 1-based indexing */
for (i = 0; i < *nnz; ++i) ++rowind[i];
for (i = 0; i <= *n; ++i) ++colptr[i];
/* Save the LU factors in the factors handle */
LUfactors = (factors_t*) SUPERLU_MALLOC(sizeof(factors_t));
LUfactors->L = L;
LUfactors->U = U;
LUfactors->perm_c = perm_c;
LUfactors->perm_r = perm_r;
*f_factors = (fptr) LUfactors;
/* Free un-wanted storage */
SUPERLU_FREE(etree);
Destroy_SuperMatrix_Store(&A);
Destroy_CompCol_Permuted(&AC);
StatFree(&stat);
} else if ( *iopt == 2 ) { /* Triangular solve */
/* Initialize the statistics variables. */
StatInit(&stat);
/* Extract the LU factors in the factors handle */
LUfactors = (factors_t*) *f_factors;
L = LUfactors->L;
U = LUfactors->U;
perm_c = LUfactors->perm_c;
perm_r = LUfactors->perm_r;
zCreate_Dense_Matrix(&B, *n, *nrhs, b, *ldb, SLU_DN, SLU_Z, SLU_GE);
/* Solve the system A*X=B, overwriting B with X. */
zgstrs (trans, L, U, perm_c, perm_r, &B, &stat, info);
Destroy_SuperMatrix_Store(&B);
StatFree(&stat);
} else if ( *iopt == 3 ) { /* Free storage */
/* Free the LU factors in the factors handle */
LUfactors = (factors_t*) *f_factors;
SUPERLU_FREE (LUfactors->perm_r);
SUPERLU_FREE (LUfactors->perm_c);
Destroy_SuperNode_Matrix(LUfactors->L);
Destroy_CompCol_Matrix(LUfactors->U);
SUPERLU_FREE (LUfactors->L);
SUPERLU_FREE (LUfactors->U);
SUPERLU_FREE (LUfactors);
} else {
fprintf(stderr,"Invalid iopt=%d passed to c_fortran_zgssv()\n",*iopt);
exit(-1);
}
}
void
zgssvx(superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r,
int *etree, char *equed, double *R, double *C,
SuperMatrix *L, SuperMatrix *U, void *work, int lwork,
SuperMatrix *B, SuperMatrix *X, double *recip_pivot_growth,
double *rcond, double *ferr, double *berr,
mem_usage_t *mem_usage, SuperLUStat_t *stat, int *info )
{
DNformat *Bstore, *Xstore;
doublecomplex *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;
double amax, anorm, bignum, smlnum, colcnd, rowcnd, rcmax, rcmin;
int relax, panel_size;
double diag_pivot_thresh, drop_tol;
double t0; /* temporary time */
double *utime;
/* External functions */
extern double zlangs(char *, SuperMatrix *);
extern double dlamch_(char *);
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 = dlamch_("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 (!nofact && options->Fact != DOFACT && options->Fact != SamePattern &&
options->Fact != SamePattern_SameRowPerm &&
!notran && options->Trans != TRANS && options->Trans != CONJ &&
!equil && options->Equil != NO)
*info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
(A->Stype != SLU_NC && A->Stype != SLU_NR) ||
A->Dtype != SLU_Z || 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 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_Z ||
B->Mtype != SLU_GE )
*info = -13;
else if ( X->ncol < 0 || Xstore->lda < SUPERLU_MAX(0, A->nrow) ||
(B->ncol != 0 && B->ncol != X->ncol) ||
X->Stype != SLU_DN ||
X->Dtype != SLU_Z || X->Mtype != SLU_GE )
*info = -14;
}
}
if (*info != 0) {
i = -(*info);
xerbla_("zgssvx", &i);
return;
}
/* Initialization for factor parameters */
panel_size = sp_ienv(1);
relax = sp_ienv(2);
diag_pivot_thresh = options->DiagPivotThresh;
drop_tol = 0.0;
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) );
zCreate_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. */
zgsequ(AA, R, C, &rowcnd, &colcnd, &amax, &info1);
if ( info1 == 0 ) {
/* Equilibrate matrix A. */
zlaqgs(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 ( 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) {
zd_mult(&Bmat[i+j*ldb], &Bmat[i+j*ldb], R[i]);
}
}
} else if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
zd_mult(&Bmat[i+j*ldb], &Bmat[i+j*ldb], C[i]);
}
}
}
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_();
zgstrf(options, &AC, drop_tol, 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 = zPivotGrowth(*info, AA, perm_c, L, U);
}
return;
}
/* Compute the reciprocal pivot growth factor *recip_pivot_growth. */
*recip_pivot_growth = zPivotGrowth(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 = zlangs(norm, AA);
zgscon(norm, L, U, anorm, rcond, stat, info);
utime[RCOND] = SuperLU_timer_() - t0;
}
if ( nrhs > 0 ) {
/* 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_();
zgstrs (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 ) {
zgsrfs(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) {
zd_mult(&Xmat[i+j*ldx], &Xmat[i+j*ldx], C[i]);
}
}
} else if ( rowequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
zd_mult(&Xmat[i+j*ldx], &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 < dlamch_("E") ) *info = A->ncol + 1;
}
if ( nofact ) {
zQuerySpace(L, U, mem_usage);
Destroy_CompCol_Permuted(&AC);
}
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
}
void
zgssv(superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r,
SuperMatrix *L, SuperMatrix *U, SuperMatrix *B,
SuperLUStat_t *stat, int *info )
{
DNformat *Bstore;
SuperMatrix *AA;/* 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 */
double drop_tol = 0.;
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_Z || 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_Z || B->Mtype != SLU_GE )
*info = -7;
if ( *info != 0 ) {
i = -(*info);
xerbla_("zgssv", &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) );
zCreate_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. */
zgstrf(options, &AC, drop_tol, 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. */
zgstrs (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);
}
}
main(int argc, char *argv[])
{
/*
* Purpose
* =======
*
* ZDRIVE is the main test program for the DOUBLE COMPLEX linear
* equation driver routines ZGSSV and ZGSSVX.
*
* The program is invoked by a shell script file -- ztest.csh.
* The output from the tests are written into a file -- ztest.out.
*
* =====================================================================
*/
doublecomplex *a, *a_save;
int *asub, *asub_save;
int *xa, *xa_save;
SuperMatrix A, B, X, L, U;
SuperMatrix ASAV, AC;
mem_usage_t mem_usage;
int *perm_r; /* row permutation from partial pivoting */
int *perm_c, *pc_save; /* column permutation */
int *etree;
doublecomplex zero = {0.0, 0.0};
double *R, *C;
double *ferr, *berr;
double *rwork;
doublecomplex *wwork;
void *work;
int info, lwork, nrhs, panel_size, relax;
int m, n, nnz;
doublecomplex *xact;
doublecomplex *rhsb, *solx, *bsav;
int ldb, ldx;
double rpg, rcond;
int i, j, k1;
double 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;
double anorm, cndnum;
doublecomplex *Afull;
double 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];
/* 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 zgst01(int, int, SuperMatrix *, SuperMatrix *,
SuperMatrix *, int *, int *, double *);
extern int zgst02(trans_t, int, int, int, SuperMatrix *, doublecomplex *,
int, doublecomplex *, int, double *resid);
extern int zgst04(int, int, doublecomplex *, int,
doublecomplex *, int, double rcond, double *resid);
extern int zgst07(trans_t, int, int, SuperMatrix *, doublecomplex *, int,
doublecomplex *, int, doublecomplex *, int,
double *, double *, double *);
extern int zlatb4_(char *, int *, int *, int *, char *, int *, int *,
double *, int *, double *, char *);
extern int zlatms_(int *, int *, char *, int *, char *, double *d,
int *, double *, double *, int *, int *,
char *, doublecomplex *, int *, doublecomplex *, int *);
extern int sp_zconvert(int, int, doublecomplex *, int, int, int,
doublecomplex *a, int *, int *, int *);
/* Executable statements */
strcpy(path, "ZGE");
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);
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 = DOUBLE;
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 = doublecomplexCalloc(lda * n);
zallocateA(n, nnz, &a, &asub, &xa);
} else {
/* Read a sparse matrix */
fimat = nimat = 0;
zreadhb(&m, &n, &nnz, &a, &asub, &xa);
}
zallocateA(n, nnz, &a_save, &asub_save, &xa_save);
rhsb = doublecomplexMalloc(m * nrhs);
bsav = doublecomplexMalloc(m * nrhs);
solx = doublecomplexMalloc(n * nrhs);
ldb = m;
ldx = n;
zCreate_Dense_Matrix(&B, m, nrhs, rhsb, ldb, SLU_DN, SLU_Z, SLU_GE);
zCreate_Dense_Matrix(&X, n, nrhs, solx, ldx, SLU_DN, SLU_Z, SLU_GE);
xact = doublecomplexMalloc(n * nrhs);
etree = intMalloc(n);
perm_r = intMalloc(n);
perm_c = intMalloc(n);
pc_save = intMalloc(n);
R = (double *) SUPERLU_MALLOC(m*sizeof(double));
C = (double *) SUPERLU_MALLOC(n*sizeof(double));
ferr = (double *) SUPERLU_MALLOC(nrhs*sizeof(double));
berr = (double *) SUPERLU_MALLOC(nrhs*sizeof(double));
j = SUPERLU_MAX(m,n) * SUPERLU_MAX(4,nrhs);
rwork = (double *) SUPERLU_MALLOC(j*sizeof(double));
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 = doublecomplexCalloc( 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 ZLATB4 and generate a test matrix
with ZLATMS. */
zlatb4_(path, &imat, &n, &n, sym, &kl, &ku, &anorm, &mode,
&cndnum, dist);
zlatms_(&n, &n, dist, iseed, sym, &rwork[0], &mode, &cndnum,
&anorm, &kl, &ku, "No packing", Afull, &lda,
&wwork[0], &info);
if ( info ) {
printf(FMT3, "ZLATMS", 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_zconvert(n, n, Afull, lda, kl, ku, a, asub, xa, &nnz);
} else {
izero = 0;
zerot = 0;
}
zCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_Z, SLU_GE);
/* Save a copy of matrix A in ASAV */
zCreate_CompCol_Matrix(&ASAV, m, n, nnz, a_save, asub_save, xa_save,
SLU_NC, SLU_Z, SLU_GE);
zCopy_CompCol_Matrix(&A, &ASAV);
/* Form exact solution. */
zGenXtrue(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. */
zCopy_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. */
zgsequ(&A, R, C, &rowcnd, &colcnd, &amax, &info);
/* Force equilibration. */
if ( !info && n > 0 ) {
if ( lsame_(equed, "R") ) {
rowcnd = 0.;
colcnd = 1.;
} else if ( lsame_(equed, "C") ) {
rowcnd = 1.;
colcnd = 0.;
} else if ( lsame_(equed, "B") ) {
rowcnd = 0.;
colcnd = 0.;
}
}
/* Equilibrate the matrix. */
zlaqgs(&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. */
zgstrf(&options, &AC, relax, panel_size,
etree, work, lwork, perm_c, perm_r, &L, &U,
&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. */
zCopy_CompCol_Matrix(&ASAV, &A);
/* Set the right hand side. */
zFillRHS(trans, nrhs, xact, ldx, &A, &B);
zCopy_Dense_Matrix(m, nrhs, rhsb, ldb, bsav, ldb);
/*----------------
* Test zgssv
*----------------*/
if ( options.Fact == DOFACT && itran == 0) {
/* Not yet factored, and untransposed */
zCopy_Dense_Matrix(m, nrhs, rhsb, ldb, solx, ldx);
zgssv(&options, &A, perm_c, perm_r, &L, &U, &X,
&stat, &info);
if ( info && info != izero ) {
printf(FMT3, "zgssv",
info, izero, n, nrhs, imat, nfail);
} else {
/* Reconstruct matrix from factors and
compute residual. */
zgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
nt = 1;
if ( izero == 0 ) {
/* Compute residual of the computed
solution. */
zCopy_Dense_Matrix(m, nrhs, rhsb, ldb,
wwork, ldb);
zgst02(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, "zgssv", 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 zgssv */
/*----------------
* Test zgssvx
*----------------*/
/* Equilibrate the matrix if fact = FACTORED and
equed = 'R', 'C', or 'B'. */
if ( options.Fact == FACTORED &&
(equil || iequed) && n > 0 ) {
zlaqgs(&A, R, C, rowcnd, colcnd, amax, equed);
}
/* Solve the system and compute the condition number
and error bounds using zgssvx. */
zgssvx(&options, &A, perm_c, perm_r, etree,
equed, R, C, &L, &U, work, lwork, &B, &X, &rpg,
&rcond, ferr, berr, &mem_usage, &stat, &info);
if ( info && info != izero ) {
printf(FMT3, "zgssvx",
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. */
zgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
k1 = 0;
} else {
k1 = 1;
}
if ( !info ) {
/* Compute residual of the computed solution.*/
zCopy_Dense_Matrix(m, nrhs, bsav, ldb,
wwork, ldb);
zgst02(trans, m, n, nrhs, &ASAV, solx, ldx,
wwork, ldb, &result[1]);
/* Check solution from generated exact
solution. */
zgst04(n, nrhs, solx, ldx, xact, ldx, rcond,
&result[2]);
/* Check the error bounds from iterative
refinement. */
zgst07(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, "zgssvx",
options.Fact, trans, *equed,
n, imat, i, result[i]);
++nfail;
}
}
nrun += NTESTS;
} /* if .. info == 0 */
} /* else .. end of testing zgssvx */
} /* 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
} /* for imat ... */
/* Print a summary of the results. */
PrintSumm("ZGE", nfail, nrun, nerrs);
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);
Destroy_CompCol_Matrix(&A);
Destroy_CompCol_Matrix(&ASAV);
if ( lwork > 0 ) {
SUPERLU_FREE (work);
Destroy_SuperMatrix_Store(&L);
Destroy_SuperMatrix_Store(&U);
}
StatFree(&stat);
return 0;
}
void
zgssvx(char *fact, char *trans, char *refact,
SuperMatrix *A, factor_param_t *factor_params, int *perm_c,
int *perm_r, int *etree, char *equed, double *R, double *C,
SuperMatrix *L, SuperMatrix *U, void *work, int lwork,
SuperMatrix *B, SuperMatrix *X, double *recip_pivot_growth,
double *rcond, double *ferr, double *berr,
mem_usage_t *mem_usage, int *info )
{
/*
* Purpose
* =======
*
* ZGSSVX solves the system of linear equations A*X=B or A'*X=B, using
* the LU factorization from zgstrf(). Error bounds on the solution and
* a condition estimate are also provided. It performs the following steps:
*
* 1. If A is stored column-wise (A->Stype = SLU_NC):
*
* 1.1. If fact = 'E', scaling factors are computed to equilibrate the
* system:
* trans = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
* trans = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
* trans = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
* Whether or not the system will be equilibrated depends on the
* scaling of the matrix A, but if equilibration is used, A is
* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if trans='N')
* or diag(C)*B (if trans = 'T' or 'C').
*
* 1.2. Permute columns of A, forming A*Pc, where Pc is a permutation
* matrix that usually preserves sparsity.
* For more details of this step, see sp_preorder.c.
*
* 1.3. If fact = 'N' or 'E', the LU decomposition is used to factor the
* matrix A (after equilibration if fact = 'E') as Pr*A*Pc = L*U,
* with Pr determined by partial pivoting.
*
* 1.4. Compute the reciprocal pivot growth factor.
*
* 1.5. If some U(i,i) = 0, so that U is exactly singular, then the
* routine returns with info = i. Otherwise, the factored form of
* A is used to estimate the condition number of the matrix A. If
* the reciprocal of the condition number is less than machine
* precision, info = A->ncol+1 is returned as a warning, but the
* routine still goes on to solve for X and computes error bounds
* as described below.
*
* 1.6. The system of equations is solved for X using the factored form
* of A.
*
* 1.7. Iterative refinement is applied to improve the computed solution
* matrix and calculate error bounds and backward error estimates
* for it.
*
* 1.8. If equilibration was used, the matrix X is premultiplied by
* diag(C) (if trans = 'N') or diag(R) (if trans = 'T' or 'C') so
* that it solves the original system before equilibration.
*
* 2. If A is stored row-wise (A->Stype = SLU_NR), apply the above algorithm
* to the transpose of A:
*
* 2.1. If fact = 'E', scaling factors are computed to equilibrate the
* system:
* trans = 'N': diag(R)*A'*diag(C) *inv(diag(C))*X = diag(R)*B
* trans = 'T': (diag(R)*A'*diag(C))**T *inv(diag(R))*X = diag(C)*B
* trans = 'C': (diag(R)*A'*diag(C))**H *inv(diag(R))*X = diag(C)*B
* Whether or not the system will be equilibrated depends on the
* scaling of the matrix A, but if equilibration is used, A' is
* overwritten by diag(R)*A'*diag(C) and B by diag(R)*B
* (if trans='N') or diag(C)*B (if trans = 'T' or 'C').
*
* 2.2. Permute columns of transpose(A) (rows of A),
* forming transpose(A)*Pc, where Pc is a permutation matrix that
* usually preserves sparsity.
* For more details of this step, see sp_preorder.c.
*
* 2.3. If fact = 'N' or 'E', the LU decomposition is used to factor the
* transpose(A) (after equilibration if fact = 'E') as
* Pr*transpose(A)*Pc = L*U with the permutation Pr determined by
* partial pivoting.
*
* 2.4. Compute the reciprocal pivot growth factor.
*
* 2.5. If some U(i,i) = 0, so that U is exactly singular, then the
* routine returns with info = i. Otherwise, the factored form
* of transpose(A) is used to estimate the condition number of the
* matrix A. If the reciprocal of the condition number
* is less than machine precision, info = A->nrow+1 is returned as
* a warning, but the routine still goes on to solve for X and
* computes error bounds as described below.
*
* 2.6. The system of equations is solved for X using the factored form
* of transpose(A).
*
* 2.7. Iterative refinement is applied to improve the computed solution
* matrix and calculate error bounds and backward error estimates
* for it.
*
* 2.8. If equilibration was used, the matrix X is premultiplied by
* diag(C) (if trans = 'N') or diag(R) (if trans = 'T' or 'C') so
* that it solves the original system before equilibration.
*
* See supermatrix.h for the definition of 'SuperMatrix' structure.
*
* Arguments
* =========
*
* fact (input) char*
* Specifies whether or not the factored form of the matrix
* A is supplied on entry, and if not, whether the matrix A should
* be equilibrated before it is factored.
* = 'F': On entry, L, U, perm_r and perm_c contain the factored
* form of A. If equed is not 'N', the matrix A has been
* equilibrated with scaling factors R and C.
* A, L, U, perm_r are not modified.
* = 'N': The matrix A will be factored, and the factors will be
* stored in L and U.
* = 'E': The matrix A will be equilibrated if necessary, then
* factored into L and U.
*
* trans (input) char*
* Specifies the form of the system of equations:
* = 'N': A * X = B (No transpose)
* = 'T': A**T * X = B (Transpose)
* = 'C': A**H * X = B (Transpose)
*
* refact (input) char*
* Specifies whether we want to re-factor the matrix.
* = 'N': Factor the matrix A.
* = 'Y': Matrix A was factored before, now we want to re-factor
* matrix A with perm_r and etree as inputs. Use
* the same storage for the L\U factors previously allocated,
* expand it if necessary. User should insure to use the same
* memory model. In this case, perm_r may be modified due to
* different pivoting determined by diagonal threshold.
* If fact = 'F', then refact is not accessed.
*
* A (input/output) SuperMatrix*
* Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number
* of the linear equations is A->nrow. Currently, the type of A can be:
* Stype = SLU_NC or SLU_NR, Dtype = SLU_Z, Mtype = SLU_GE.
* In the future, more general A may be handled.
*
* On entry, If fact = 'F' and equed is not 'N', then A must have
* been equilibrated by the scaling factors in R and/or C.
* A is not modified if fact = 'F' or 'N', or if fact = 'E' and
* equed = 'N' on exit.
*
* On exit, if fact = 'E' and equed is not 'N', A is scaled as follows:
* If A->Stype = SLU_NC:
* equed = 'R': A := diag(R) * A
* equed = 'C': A := A * diag(C)
* equed = 'B': A := diag(R) * A * diag(C).
* If A->Stype = SLU_NR:
* equed = 'R': transpose(A) := diag(R) * transpose(A)
* equed = 'C': transpose(A) := transpose(A) * diag(C)
* equed = 'B': transpose(A) := diag(R) * transpose(A) * diag(C).
*
* factor_params (input) factor_param_t*
* The structure defines the input scalar parameters, consisting of
* the following fields. If factor_params = NULL, the default
* values are used for all the fields; otherwise, the values
* are given by the user.
* - panel_size (int): Panel size. A panel consists of at most
* panel_size consecutive columns. If panel_size = -1, use
* default value 8.
* - relax (int): To control degree of relaxing supernodes. If the
* number of nodes (columns) in a subtree of the elimination
* tree is less than relax, this subtree is considered as one
* supernode, regardless of the row structures of those columns.
* If relax = -1, use default value 8.
* - diag_pivot_thresh (double): Diagonal pivoting threshold.
* At step j of the Gaussian elimination, if
* abs(A_jj) >= diag_pivot_thresh * (max_(i>=j) abs(A_ij)),
* then use A_jj as pivot. 0 <= diag_pivot_thresh <= 1.
* If diag_pivot_thresh = -1, use default value 1.0,
* which corresponds to standard partial pivoting.
* - drop_tol (double): Drop tolerance threshold. (NOT IMPLEMENTED)
* At step j of the Gaussian elimination, if
* abs(A_ij)/(max_i abs(A_ij)) < drop_tol,
* then drop entry A_ij. 0 <= drop_tol <= 1.
* If drop_tol = -1, use default value 0.0, which corresponds to
* standard Gaussian elimination.
*
* 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.
* 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 = SLU_NR, column permutation vector of size A->nrow,
* which describes permutation of columns of transpose(A)
* (rows of A) as described above.
*
* 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 refact is not 'Y', perm_r is output argument;
* If refact = 'Y', the pivoting routine will try to use the input
* perm_r, unless a certain threshold criterion is violated.
* In that case, perm_r is overwritten by a new permutation
* determined by partial pivoting or diagonal threshold pivoting.
*
* etree (input/output) int*, dimension (A->ncol)
* Elimination tree of Pc'*A'*A*Pc.
* If fact is not 'F' and refact = 'Y', etree is an input argument,
* otherwise it is an output argument.
* Note: etree is a vector of parent pointers for a forest whose
* vertices are the integers 0 to A->ncol-1; etree[root]==A->ncol.
*
* equed (input/output) char*
* Specifies the form of equilibration that was done.
* = 'N': No equilibration.
* = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
* = 'C': Column equilibration, i.e., A was postmultiplied by diag(C).
* = 'B': Both row and column equilibration, i.e., A was replaced
* by diag(R)*A*diag(C).
* If fact = 'F', equed is an input argument, otherwise it is
* an output argument.
*
* R (input/output) double*, dimension (A->nrow)
* The row scale factors for A or transpose(A).
* If equed = 'R' or 'B', A (if A->Stype = SLU_NC) or transpose(A)
* (if A->Stype = SLU_NR) is multiplied on the left by diag(R).
* If equed = 'N' or 'C', R is not accessed.
* If fact = 'F', R is an input argument; otherwise, R is output.
* If fact = 'F' and equed = 'R' or 'B', each element of R must
* be positive.
*
* C (input/output) double*, dimension (A->ncol)
* The column scale factors for A or transpose(A).
* If equed = 'C' or 'B', A (if A->Stype = SLU_NC) or transpose(A)
* (if A->Stype = SLU_NR) is multiplied on the right by diag(C).
* If equed = 'N' or 'R', C is not accessed.
* If fact = 'F', C is an input argument; otherwise, C is output.
* If fact = 'F' and equed = 'C' or 'B', each element of C must
* be positive.
*
* 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 = SC, Dtype = SLU_Z, Mtype = 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_Z, Mtype = TRU.
*
* work (workspace/output) void*, size (lwork) (in bytes)
* User supplied workspace, should be large enough
* to hold data structures for factors L and U.
* On exit, if fact is not 'F', L and U point to this array.
*
* lwork (input) int
* Specifies the size of work array in bytes.
* = 0: allocate space internally by system malloc;
* > 0: use user-supplied work array of length lwork in bytes,
* returns error if space runs out.
* = -1: the routine guesses the amount of space needed without
* performing the factorization, and returns it in
* mem_usage->total_needed; no other side effects.
*
* See argument 'mem_usage' for memory usage statistics.
*
* B (input/output) SuperMatrix*
* B has types: Stype = SLU_DN, Dtype = SLU_Z, Mtype = SLU_GE.
* On entry, the right hand side matrix.
* On exit,
* if equed = 'N', B is not modified; otherwise
* if A->Stype = SLU_NC:
* if trans = 'N' and equed = 'R' or 'B', B is overwritten by
* diag(R)*B;
* if trans = 'T' or 'C' and equed = 'C' of 'B', B is
* overwritten by diag(C)*B;
* if A->Stype = SLU_NR:
* if trans = 'N' and equed = 'C' or 'B', B is overwritten by
* diag(C)*B;
* if trans = 'T' or 'C' and equed = 'R' of 'B', B is
* overwritten by diag(R)*B.
*
* X (output) SuperMatrix*
* X has types: Stype = SLU_DN, Dtype = SLU_Z, Mtype = SLU_GE.
* If info = 0 or info = A->ncol+1, X contains the solution matrix
* to the original system of equations. Note that A and B are modified
* on exit if equed is not 'N', and the solution to the equilibrated
* system is inv(diag(C))*X if trans = 'N' and equed = 'C' or 'B',
* or inv(diag(R))*X if trans = 'T' or 'C' and equed = 'R' or 'B'.
*
* recip_pivot_growth (output) double*
* The reciprocal pivot growth factor max_j( norm(A_j)/norm(U_j) ).
* The infinity norm is used. If recip_pivot_growth is much less
* than 1, the stability of the LU factorization could be poor.
*
* rcond (output) double*
* The estimate of the reciprocal condition number of the matrix A
* after equilibration (if done). If rcond is less than the machine
* precision (in particular, if rcond = 0), the matrix is singular
* to working precision. This condition is indicated by a return
* code of info > 0.
*
* FERR (output) double*, dimension (B->ncol)
* The estimated forward error bound for each solution vector
* X(j) (the j-th column of the solution matrix X).
* If XTRUE is the true solution corresponding to X(j), FERR(j)
* is an estimated upper bound for the magnitude of the largest
* element in (X(j) - XTRUE) divided by the magnitude of the
* largest element in X(j). The estimate is as reliable as
* the estimate for RCOND, and is almost always a slight
* overestimate of the true error.
*
* BERR (output) double*, dimension (B->ncol)
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in
* any element of A or B that makes X(j) an exact solution).
*
* mem_usage (output) mem_usage_t*
* Record the memory usage statistics, consisting of following fields:
* - for_lu (float)
* The amount of space used in bytes for L\U data structures.
* - total_needed (float)
* The amount of space needed in bytes to perform factorization.
* - expansions (int)
* The number of memory expansions during the LU factorization.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 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 and error bounds
* could not be computed.
* = A->ncol+1: U is nonsingular, but RCOND is less than machine
* precision, meaning that the matrix is singular to
* working precision. Nevertheless, the solution and
* error bounds are computed because there are a number
* of situations where the computed solution can be more
* accurate than the value of RCOND would suggest.
* > A->ncol+1: number of bytes allocated when memory allocation
* failure occurred, plus A->ncol.
*
*/
DNformat *Bstore, *Xstore;
doublecomplex *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;
char trant[1], norm[1];
int i, j, info1;
double amax, anorm, bignum, smlnum, colcnd, rowcnd, rcmax, rcmin;
int relax, panel_size;
double diag_pivot_thresh, drop_tol;
double t0; /* temporary time */
double *utime;
extern SuperLUStat_t SuperLUStat;
/* External functions */
extern double zlangs(char *, SuperMatrix *);
extern double dlamch_(char *);
Bstore = B->Store;
Xstore = X->Store;
Bmat = Bstore->nzval;
Xmat = Xstore->nzval;
ldb = Bstore->lda;
ldx = Xstore->lda;
nrhs = B->ncol;
#if 0
printf("zgssvx: fact=%c, trans=%c, refact=%c, equed=%c\n",
*fact, *trans, *refact, *equed);
#endif
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
notran = lsame_(trans, "N");
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rowequ = FALSE;
colequ = FALSE;
} else {
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
smlnum = dlamch_("Safe minimum");
bignum = 1. / smlnum;
}
/* Test the input parameters */
if (!nofact && !equil && !lsame_(fact, "F")) *info = -1;
else if (!notran && !lsame_(trans, "T") && !lsame_(trans, "C")) *info = -2;
else if ( !(lsame_(refact,"Y") || lsame_(refact, "N")) ) *info = -3;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
(A->Stype != SLU_NC && A->Stype != SLU_NR) ||
A->Dtype != SLU_Z || A->Mtype != SLU_GE )
*info = -4;
else if (lsame_(fact, "F") && !(rowequ || colequ || lsame_(equed, "N")))
*info = -9;
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 = -10;
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 = -11;
else if (A->nrow > 0)
colcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
else colcnd = 1.;
}
if (*info == 0) {
if ( lwork < -1 ) *info = -15;
else if ( B->ncol < 0 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_Z ||
B->Mtype != SLU_GE )
*info = -16;
else if ( X->ncol < 0 || Xstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->ncol != X->ncol || X->Stype != SLU_DN ||
X->Dtype != SLU_Z || X->Mtype != SLU_GE )
*info = -17;
}
}
if (*info != 0) {
i = -(*info);
xerbla_("zgssvx", &i);
return;
}
/* Default values for factor_params */
panel_size = sp_ienv(1);
relax = sp_ienv(2);
diag_pivot_thresh = 1.0;
drop_tol = 0.0;
if ( factor_params != NULL ) {
if ( factor_params->panel_size != -1 )
panel_size = factor_params->panel_size;
if ( factor_params->relax != -1 ) relax = factor_params->relax;
if ( factor_params->diag_pivot_thresh != -1 )
diag_pivot_thresh = factor_params->diag_pivot_thresh;
if ( factor_params->drop_tol != -1 )
drop_tol = factor_params->drop_tol;
}
StatInit(panel_size, relax);
utime = SuperLUStat.utime;
/* Convert A to SLU_NC format when necessary. */
if ( A->Stype == SLU_NR ) {
NRformat *Astore = A->Store;
AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
zCreate_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 = 'T';
notran = 0;
} else {
*trant = 'N';
notran = 1;
}
} else { /* A->Stype == SLU_NC */
*trant = *trans;
AA = A;
}
if ( equil ) {
t0 = SuperLU_timer_();
/* Compute row and column scalings to equilibrate the matrix A. */
zgsequ(AA, R, C, &rowcnd, &colcnd, &amax, &info1);
if ( info1 == 0 ) {
/* Equilibrate matrix A. */
zlaqgs(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;
}
/* 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) {
zd_mult(&Bmat[i + j*ldb], &Bmat[i + j*ldb], R[i]);
}
}
} else if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
zd_mult(&Bmat[i + j*ldb], &Bmat[i + j*ldb], C[i]);
}
}
if ( nofact || equil ) {
t0 = SuperLU_timer_();
sp_preorder(refact, 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_();
zgstrf(refact, &AC, diag_pivot_thresh, drop_tol, relax, panel_size,
etree, work, lwork, perm_r, perm_c, L, U, info);
utime[FACT] = SuperLU_timer_() - t0;
if ( lwork == -1 ) {
mem_usage->total_needed = *info - A->ncol;
return;
}
}
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 = zPivotGrowth(*info, AA, perm_c, L, U);
}
return;
}
/* Compute the reciprocal pivot growth factor *recip_pivot_growth. */
*recip_pivot_growth = zPivotGrowth(A->ncol, AA, perm_c, L, U);
/* Estimate the reciprocal of the condition number of A. */
t0 = SuperLU_timer_();
if ( notran ) {
*(unsigned char *)norm = '1';
} else {
*(unsigned char *)norm = 'I';
}
anorm = zlangs(norm, AA);
zgscon(norm, L, U, anorm, rcond, info);
utime[RCOND] = SuperLU_timer_() - t0;
/* 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_();
zgstrs (trant, L, U, perm_r, perm_c, X, 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_();
zgsrfs(trant, AA, L, U, perm_r, perm_c, equed, R, C, B,
X, ferr, berr, info);
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) {
zd_mult(&Xmat[i + j*ldx], &Xmat[i + j*ldx], C[i]);
}
}
} else if ( rowequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
zd_mult(&Xmat[i+ j*ldx], &Xmat[i+ j*ldx], R[i]);
}
}
/* Set INFO = A->ncol+1 if the matrix is singular to working precision. */
if ( *rcond < dlamch_("E") ) *info = A->ncol + 1;
zQuerySpace(L, U, panel_size, mem_usage);
if ( nofact || equil ) Destroy_CompCol_Permuted(&AC);
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
PrintStat( &SuperLUStat );
StatFree();
}
void
zgssv(SuperMatrix *A, int *perm_c, int *perm_r, SuperMatrix *L,
SuperMatrix *U, SuperMatrix *B, int *info )
{
/*
* Purpose
* =======
*
* ZGSSV solves the system of linear equations A*X=B, using the
* LU factorization from ZGSTRF. 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
* =========
*
* 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_Z; 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.
* 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 = SLU_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 = 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.
*
* 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 = SC, Dtype = SLU_Z, Mtype = 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_Z, Mtype = TRU.
*
* B (input/output) SuperMatrix*
* B has types: Stype = SLU_DN, Dtype = SLU_Z, Mtype = SLU_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 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 */
double diag_pivot_thresh = 1.0;
double 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 != SLU_NC && A->Stype != SLU_NR) ||
A->Dtype != SLU_Z || A->Mtype != SLU_GE )
*info = -1;
else if ( B->ncol < 0 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_Z || B->Mtype != SLU_GE )
*info = -6;
if ( *info != 0 ) {
i = -(*info);
xerbla_("zgssv", &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 SLU_NC format when necessary. */
if ( A->Stype == SLU_NR ) {
NRformat *Astore = A->Store;
AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
zCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz,
Astore->nzval, Astore->colind, Astore->rowptr,
SLU_NC, A->Dtype, A->Mtype);
*trans = 'T';
} else if ( A->Stype == SLU_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. */
zgstrf(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. */
zgstrs (trans, L, U, perm_r, perm_c, B, info);
}
utime[SOLVE] = SuperLU_timer_() - t1;
SUPERLU_FREE (etree);
Destroy_CompCol_Permuted(&AC);
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
PrintStat( &SuperLUStat );
StatFree();
}
