main(int argc, char *argv[])
{
SuperMatrix A;
NCformat *Astore;
double *a;
int *asub, *xa;
int *perm_c; /* column permutation vector */
int *perm_r; /* row permutations from partial pivoting */
SuperMatrix L; /* factor L */
SCformat *Lstore;
SuperMatrix U; /* factor U */
NCformat *Ustore;
SuperMatrix B;
int nrhs, ldx, info, m, n, nnz;
double *xact, *rhs;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
/* Now we modify the default options to use the symmetric mode. */
options.SymmetricMode = YES;
options.ColPerm = MMD_AT_PLUS_A;
options.DiagPivotThresh = 0.001;
#if 1
/* Read matrix A from a file in Harwell-Boeing format.*/
if (argc < 2)
{
printf("Usage:\n%s [OPTION] < [INPUT] > [OUTPUT]\nOPTION:\n"
"-h -hb:\n\t[INPUT] is a Harwell-Boeing format matrix.\n"
"-r -rb:\n\t[INPUT] is a Rutherford-Boeing format matrix.\n"
"-t -triplet:\n\t[INPUT] is a triplet format matrix.\n",
argv[0]);
return 0;
}
else
{
switch (argv[1][1])
{
case 'H':
case 'h':
printf("Input a Harwell-Boeing format matrix:\n");
dreadhb(&m, &n, &nnz, &a, &asub, &xa);
break;
case 'R':
case 'r':
printf("Input a Rutherford-Boeing format matrix:\n");
dreadrb(&m, &n, &nnz, &a, &asub, &xa);
break;
case 'T':
case 't':
printf("Input a triplet format matrix:\n");
dreadtriple(&m, &n, &nnz, &a, &asub, &xa);
break;
default:
printf("Unrecognized format.\n");
return 0;
}
}
#else
/* Read the matrix in Harwell-Boeing format. */
dreadhb(&m, &n, &nnz, &a, &asub, &xa);
#endif
dCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_D, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
nrhs = 1;
if ( !(rhs = doubleMalloc(m * nrhs)) ) ABORT("Malloc fails for rhs[].");
dCreate_Dense_Matrix(&B, m, nrhs, rhs, m, SLU_DN, SLU_D, SLU_GE);
xact = doubleMalloc(n * nrhs);
ldx = n;
dGenXtrue(n, nrhs, xact, ldx);
dFillRHS(options.Trans, nrhs, xact, ldx, &A, &B);
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
/* Initialize the statistics variables. */
StatInit(&stat);
dgssv(&options, &A, perm_c, perm_r, &L, &U, &B, &stat, &info);
if ( info == 0 ) {
/* This is how you could access the solution matrix. */
double *sol = (double*) ((DNformat*) B.Store)->nzval;
/* Compute the infinity norm of the error. */
dinf_norm_error(nrhs, &B, xact);
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 - n);
printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);
dQuerySpace(&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("dgssv() error returns INFO= %d\n", info);
if ( info <= n ) { /* factorization completes */
dQuerySpace(&L, &U, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
}
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhs);
SUPERLU_FREE (xact);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
}
main(int argc, char *argv[])
{
/*
* Purpose
* =======
*
* The driver program DLINSOLX2.
*
* This example illustrates how to use DGSSVX to solve systems repeatedly
* with the same sparsity pattern of matrix A.
* In this case, the column permutation vector perm_c is computed once.
* The following data structures will be reused in the subsequent call to
* DGSSVX: perm_c, etree
*
*/
char equed[1];
yes_no_t equil;
trans_t trans;
SuperMatrix A, A1, L, U;
SuperMatrix B, B1, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
double *a, *a1;
int *asub, *xa, *asub1, *xa1;
int *perm_r; /* row permutations from partial pivoting */
int *perm_c; /* column permutation vector */
int *etree;
void *work;
int info, lwork, nrhs, ldx;
int i, j, m, n, nnz;
double *rhsb, *rhsb1, *rhsx, *xact;
double *R, *C;
double *ferr, *berr;
double u, rpg, rcond;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
extern void parse_command_line();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Defaults */
lwork = 0;
nrhs = 1;
equil = YES;
u = 1.0;
trans = NOTRANS;
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
/* Can use command line input to modify the defaults. */
parse_command_line(argc, argv, &lwork, &u, &equil, &trans);
options.Equil = equil;
options.DiagPivotThresh = u;
options.Trans = trans;
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) {
ABORT("DLINSOLX: cannot allocate work[]");
}
}
/* Read matrix A from a file in Harwell-Boeing format.*/
dreadhb(&m, &n, &nnz, &a, &asub, &xa);
if ( !(a1 = doubleMalloc(nnz)) ) ABORT("Malloc fails for a1[].");
if ( !(asub1 = intMalloc(nnz)) ) ABORT("Malloc fails for asub1[].");
if ( !(xa1 = intMalloc(n+1)) ) ABORT("Malloc fails for xa1[].");
for (i = 0; i < nnz; ++i) {
a1[i] = a[i];
asub1[i] = asub[i];
}
for (i = 0; i < n+1; ++i) xa1[i] = xa[i];
dCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_D, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
if ( !(rhsb = doubleMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsb1 = doubleMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb1[].");
if ( !(rhsx = doubleMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
dCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_D, SLU_GE);
dCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_D, SLU_GE);
xact = doubleMalloc(n * nrhs);
ldx = n;
dGenXtrue(n, nrhs, xact, ldx);
dFillRHS(trans, nrhs, xact, ldx, &A, &B);
for (j = 0; j < nrhs; ++j)
for (i = 0; i < m; ++i) rhsb1[i+j*m] = rhsb[i+j*m];
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(R = (double *) SUPERLU_MALLOC(A.nrow * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (double *) SUPERLU_MALLOC(A.ncol * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for C[].");
if ( !(ferr = (double *) SUPERLU_MALLOC(nrhs * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for ferr[].");
if ( !(berr = (double *) SUPERLU_MALLOC(nrhs * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for berr[].");
/* Initialize the statistics variables. */
StatInit(&stat);
/* ------------------------------------------------------------
WE SOLVE THE LINEAR SYSTEM FOR THE FIRST TIME: AX = B
------------------------------------------------------------*/
dgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("First system: dgssvx() returns info %d\n", info);
if ( info == 0 || info == n+1 ) {
/* This is how you could access the solution matrix. */
double *sol = (double*) ((DNformat*) X.Store)->nzval;
if ( options.PivotGrowth ) printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber )
printf("Recip. condition number = %e\n", rcond);
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 - n);
printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
if ( options.IterRefine ) {
printf("Iterative Refinement:\n");
printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for (i = 0; i < nrhs; ++i)
printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
Destroy_CompCol_Matrix(&A);
Destroy_Dense_Matrix(&B);
if ( lwork >= 0 ) { /* Deallocate storage associated with L and U. */
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
/* ------------------------------------------------------------
NOW WE SOLVE ANOTHER LINEAR SYSTEM: A1*X = B1
ONLY THE SPARSITY PATTERN OF A1 IS THE SAME AS THAT OF A.
------------------------------------------------------------*/
options.Fact = SamePattern;
StatInit(&stat); /* Initialize the statistics variables. */
dCreate_CompCol_Matrix(&A1, m, n, nnz, a1, asub1, xa1,
SLU_NC, SLU_D, SLU_GE);
dCreate_Dense_Matrix(&B1, m, nrhs, rhsb1, m, SLU_DN, SLU_D, SLU_GE);
dgssvx(&options, &A1, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B1, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("\nSecond system: dgssvx() returns info %d\n", info);
if ( info == 0 || info == n+1 ) {
/* This is how you could access the solution matrix. */
double *sol = (double*) ((DNformat*) X.Store)->nzval;
if ( options.PivotGrowth ) printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber )
printf("Recip. condition number = %e\n", rcond);
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 - n);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
if ( options.IterRefine ) {
printf("Iterative Refinement:\n");
printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for (i = 0; i < nrhs; ++i)
printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
Destroy_CompCol_Matrix(&A1);
Destroy_Dense_Matrix(&B1);
Destroy_Dense_Matrix(&X);
if ( lwork >= 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
}
int main(int argc, char *argv[])
{
/*
* Purpose
* =======
*
* DDRIVE is the main test program for the DOUBLE linear
* equation driver routines DGSSV and DGSSVX.
*
* The program is invoked by a shell script file -- dtest.csh.
* The output from the tests are written into a file -- dtest.out.
*
* =====================================================================
*/
double *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;
double zero = 0.0;
double *R, *C;
double *ferr, *berr;
double *rwork;
double *wwork;
void *work;
int info, lwork, nrhs, panel_size, relax;
int m, n, nnz;
double *xact;
double *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;
double *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];
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 dgst01(int, int, SuperMatrix *, SuperMatrix *,
SuperMatrix *, int *, int *, double *);
extern int dgst02(trans_t, int, int, int, SuperMatrix *, double *,
int, double *, int, double *resid);
extern int dgst04(int, int, double *, int,
double *, int, double rcond, double *resid);
extern int dgst07(trans_t, int, int, SuperMatrix *, double *, int,
double *, int, double *, int,
double *, double *, double *);
extern int dlatb4_slu(char *, int *, int *, int *, char *, int *, int *,
double *, int *, double *, char *);
extern int dlatms_slu(int *, int *, char *, int *, char *, double *d,
int *, double *, double *, int *, int *,
char *, double *, int *, double *, int *);
extern int sp_dconvert(int, int, double *, int, int, int,
double *a, int *, int *, int *);
/* Executable statements */
strcpy(path, "DGE");
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_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 = doubleCalloc(lda * n);
dallocateA(n, nnz, &a, &asub, &xa);
} else {
/* Read a sparse matrix */
fimat = nimat = 0;
dreadhb(fp, &m, &n, &nnz, &a, &asub, &xa);
}
dallocateA(n, nnz, &a_save, &asub_save, &xa_save);
rhsb = doubleMalloc(m * nrhs);
bsav = doubleMalloc(m * nrhs);
solx = doubleMalloc(n * nrhs);
ldb = m;
ldx = n;
dCreate_Dense_Matrix(&B, m, nrhs, rhsb, ldb, SLU_DN, SLU_D, SLU_GE);
dCreate_Dense_Matrix(&X, n, nrhs, solx, ldx, SLU_DN, SLU_D, SLU_GE);
xact = doubleMalloc(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 = doubleCalloc( 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 DLATB4 and generate a test matrix
with DLATMS. */
dlatb4_slu(path, &imat, &n, &n, sym, &kl, &ku, &anorm, &mode,
&cndnum, dist);
dlatms_slu(&n, &n, dist, iseed, sym, &rwork[0], &mode, &cndnum,
&anorm, &kl, &ku, "No packing", Afull, &lda,
&wwork[0], &info);
if ( info ) {
printf(FMT3, "DLATMS", 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_dconvert(n, n, Afull, lda, kl, ku, a, asub, xa, &nnz);
} else {
izero = 0;
zerot = 0;
}
dCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_D, SLU_GE);
/* Save a copy of matrix A in ASAV */
dCreate_CompCol_Matrix(&ASAV, m, n, nnz, a_save, asub_save, xa_save,
SLU_NC, SLU_D, SLU_GE);
dCopy_CompCol_Matrix(&A, &ASAV);
/* Form exact solution. */
dGenXtrue(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. */
dCopy_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. */
dgsequ(&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. */
dlaqgs(&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. */
dgstrf(&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. */
dCopy_CompCol_Matrix(&ASAV, &A);
/* Set the right hand side. */
dFillRHS(trans, nrhs, xact, ldx, &A, &B);
dCopy_Dense_Matrix(m, nrhs, rhsb, ldb, bsav, ldb);
/*----------------
* Test dgssv
*----------------*/
if ( options.Fact == DOFACT && itran == 0) {
/* Not yet factored, and untransposed */
dCopy_Dense_Matrix(m, nrhs, rhsb, ldb, solx, ldx);
dgssv(&options, &A, perm_c, perm_r, &L, &U, &X,
&stat, &info);
if ( info && info != izero ) {
printf(FMT3, "dgssv",
info, izero, n, nrhs, imat, nfail);
} else {
/* Reconstruct matrix from factors and
compute residual. */
dgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
nt = 1;
if ( izero == 0 ) {
/* Compute residual of the computed
solution. */
dCopy_Dense_Matrix(m, nrhs, rhsb, ldb,
wwork, ldb);
dgst02(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, "dgssv", 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 dgssv */
/*----------------
* Test dgssvx
*----------------*/
/* Equilibrate the matrix if fact = FACTORED and
equed = 'R', 'C', or 'B'. */
if ( options.Fact == FACTORED &&
(equil || iequed) && n > 0 ) {
dlaqgs(&A, R, C, rowcnd, colcnd, amax, equed);
}
/* Solve the system and compute the condition number
and error bounds using dgssvx. */
dgssvx(&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, "dgssvx",
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. */
dgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
k1 = 0;
} else {
k1 = 1;
}
if ( !info ) {
/* Compute residual of the computed solution.*/
dCopy_Dense_Matrix(m, nrhs, bsav, ldb,
wwork, ldb);
dgst02(trans, m, n, nrhs, &ASAV, solx, ldx,
wwork, ldb, &result[1]);
/* Check solution from generated exact
solution. */
dgst04(n, nrhs, solx, ldx, xact, ldx, rcond,
&result[2]);
/* Check the error bounds from iterative
refinement. */
dgst07(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, "dgssvx",
options.Fact, trans, *equed,
n, imat, i, result[i]);
++nfail;
}
}
nrun += NTESTS;
} /* if .. info == 0 */
} /* else .. end of testing dgssvx */
} /* 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("DGE", 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;
}
main(int argc, char *argv[])
{
SuperMatrix A, AC, L, U, B;
NCformat *Astore;
SCPformat *Lstore;
NCPformat *Ustore;
superlumt_options_t superlumt_options;
pxgstrf_shared_t pxgstrf_shared;
pdgstrf_threadarg_t *pdgstrf_threadarg;
int nprocs;
fact_t fact;
trans_t trans;
yes_no_t refact, usepr;
double u, drop_tol;
double *a;
int *asub, *xa;
int *perm_c; /* column permutation vector */
int *perm_r; /* row permutations from partial pivoting */
void *work;
int info, lwork, nrhs, ldx;
int m, n, nnz, permc_spec, panel_size, relax;
int i, firstfact;
double *rhsb, *xact;
Gstat_t Gstat;
flops_t flopcnt;
void parse_command_line();
/* Default parameters to control factorization. */
nprocs = 1;
fact = EQUILIBRATE;
trans = NOTRANS;
panel_size = sp_ienv(1);
relax = sp_ienv(2);
u = 1.0;
usepr = NO;
drop_tol = 0.0;
work = NULL;
lwork = 0;
nrhs = 1;
/* Get the number of processes from command line. */
parse_command_line(argc, argv, &nprocs);
/* Read the input matrix stored in Harwell-Boeing format. */
dreadhb(&m, &n, &nnz, &a, &asub, &xa);
/* Set up the sparse matrix data structure for A. */
dCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_D, SLU_GE);
if (!(rhsb = doubleMalloc(m * nrhs))) SUPERLU_ABORT("Malloc fails for rhsb[].");
dCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_D, SLU_GE);
xact = doubleMalloc(n * nrhs);
ldx = n;
dGenXtrue(n, nrhs, xact, ldx);
dFillRHS(trans, nrhs, xact, ldx, &A, &B);
if (!(perm_r = intMalloc(m))) SUPERLU_ABORT("Malloc fails for perm_r[].");
if (!(perm_c = intMalloc(n))) SUPERLU_ABORT("Malloc fails for perm_c[].");
/********************************
* THE FIRST TIME FACTORIZATION *
********************************/
/* ------------------------------------------------------------
Allocate storage and initialize statistics variables.
------------------------------------------------------------*/
StatAlloc(n, nprocs, panel_size, relax, &Gstat);
StatInit(n, nprocs, &Gstat);
/* ------------------------------------------------------------
Get column permutation vector perm_c[], according to permc_spec:
permc_spec = 0: natural ordering
permc_spec = 1: minimum degree ordering on structure of A'*A
permc_spec = 2: minimum degree ordering on structure of A'+A
permc_spec = 3: approximate minimum degree for unsymmetric matrices
------------------------------------------------------------*/
permc_spec = 1;
get_perm_c(permc_spec, &A, perm_c);
/* ------------------------------------------------------------
Initialize the option structure superlumt_options using the
user-input parameters;
Apply perm_c to the columns of original A to form AC.
------------------------------------------------------------*/
refact= NO;
pdgstrf_init(nprocs, fact, trans, refact, panel_size, relax,
u, usepr, drop_tol, perm_c, perm_r,
work, lwork, &A, &AC, &superlumt_options, &Gstat);
/* ------------------------------------------------------------
Compute the LU factorization of A.
The following routine will create nprocs threads.
------------------------------------------------------------*/
pdgstrf(&superlumt_options, &AC, perm_r, &L, &U, &Gstat, &info);
flopcnt = 0;
for (i = 0; i < nprocs; ++i) flopcnt += Gstat.procstat[i].fcops;
Gstat.ops[FACT] = flopcnt;
/* ------------------------------------------------------------
Solve the system A*X=B, overwriting B with X.
------------------------------------------------------------*/
dgstrs(trans, &L, &U, perm_r, perm_c, &B, &Gstat, &info);
printf("\n** Result of sparse LU **\n");
dinf_norm_error(nrhs, &B, xact); /* Check inf. norm of the error */
Destroy_CompCol_Permuted(&AC); /* Free extra arrays in AC. */
/*********************************
* THE SUBSEQUENT FACTORIZATIONS *
*********************************/
/* ------------------------------------------------------------
Re-initialize statistics variables and options used by the
factorization routine pdgstrf().
------------------------------------------------------------*/
StatInit(n, nprocs, &Gstat);
refact= YES;
pdgstrf_init(nprocs, fact, trans, refact, panel_size, relax,
u, usepr, drop_tol, perm_c, perm_r,
work, lwork, &A, &AC, &superlumt_options, &Gstat);
/* ------------------------------------------------------------
Compute the LU factorization of A.
The following routine will create nprocs threads.
------------------------------------------------------------*/
pdgstrf(&superlumt_options, &AC, perm_r, &L, &U, &Gstat, &info);
flopcnt = 0;
for (i = 0; i < nprocs; ++i) flopcnt += Gstat.procstat[i].fcops;
Gstat.ops[FACT] = flopcnt;
/* ------------------------------------------------------------
Re-generate right-hand side B, then solve A*X= B.
------------------------------------------------------------*/
dFillRHS(trans, nrhs, xact, ldx, &A, &B);
dgstrs(trans, &L, &U, perm_r, perm_c, &B, &Gstat, &info);
/* ------------------------------------------------------------
Deallocate storage after factorization.
------------------------------------------------------------*/
pxgstrf_finalize(&superlumt_options, &AC);
printf("\n** Result of sparse LU **\n");
dinf_norm_error(nrhs, &B, xact); /* Check inf. norm of the error */
Lstore = (SCPformat *) L.Store;
Ustore = (NCPformat *) 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 - n);
fflush(stdout);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (xact);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
if ( lwork >= 0 ) {
Destroy_SuperNode_SCP(&L);
Destroy_CompCol_NCP(&U);
}
StatFree(&Gstat);
}
int main(int argc, char *argv[])
{
void dmatvec_mult(double alpha, double x[], double beta, double y[]);
void dpsolve(int n, double x[], double y[]);
extern int dfgmr( int n,
void (*matvec_mult)(double, double [], double, double []),
void (*psolve)(int n, double [], double[]),
double *rhs, double *sol, double tol, int restrt, int *itmax,
FILE *fits);
extern int dfill_diag(int n, NCformat *Astore);
char equed[1] = {'B'};
yes_no_t equil;
trans_t trans;
SuperMatrix A, L, U;
SuperMatrix B, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
double *a;
int *asub, *xa;
int *etree;
int *perm_c; /* column permutation vector */
int *perm_r; /* row permutations from partial pivoting */
int nrhs, ldx, lwork, info, m, n, nnz;
double *rhsb, *rhsx, *xact;
double *work = NULL;
double *R, *C;
double u, rpg, rcond;
double zero = 0.0;
double one = 1.0;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
int restrt, iter, maxit, i;
double resid;
double *x, *b;
#ifdef DEBUG
extern int num_drop_L, num_drop_U;
#endif
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Defaults */
lwork = 0;
nrhs = 1;
equil = YES;
u = 0.1; /* u=1.0 for complete factorization */
trans = NOTRANS;
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 0.1; //different from complete LU
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
options.RowPerm = LargeDiag;
options.ILU_DropTol = 1e-4;
options.ILU_FillTol = 1e-2;
options.ILU_FillFactor = 10.0;
options.ILU_DropRule = DROP_BASIC | DROP_AREA;
options.ILU_Norm = INF_NORM;
options.ILU_MILU = SILU;
*/
ilu_set_default_options(&options);
/* Modify the defaults. */
options.PivotGrowth = YES; /* Compute reciprocal pivot growth */
options.ConditionNumber = YES;/* Compute reciprocal condition number */
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) ABORT("Malloc fails for work[].");
}
/* Read matrix A from a file in Harwell-Boeing format.*/
if (argc < 2)
{
printf("Usage:\n%s [OPTION] < [INPUT] > [OUTPUT]\nOPTION:\n"
"-h -hb:\n\t[INPUT] is a Harwell-Boeing format matrix.\n"
"-r -rb:\n\t[INPUT] is a Rutherford-Boeing format matrix.\n"
"-t -triplet:\n\t[INPUT] is a triplet format matrix.\n",
argv[0]);
return 0;
}
else
{
switch (argv[1][1])
{
case 'H':
case 'h':
printf("Input a Harwell-Boeing format matrix:\n");
dreadhb(&m, &n, &nnz, &a, &asub, &xa);
break;
case 'R':
case 'r':
printf("Input a Rutherford-Boeing format matrix:\n");
dreadrb(&m, &n, &nnz, &a, &asub, &xa);
break;
case 'T':
case 't':
printf("Input a triplet format matrix:\n");
dreadtriple(&m, &n, &nnz, &a, &asub, &xa);
break;
default:
printf("Unrecognized format.\n");
return 0;
}
}
dCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_D, SLU_GE);
Astore = A.Store;
dfill_diag(n, Astore);
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
fflush(stdout);
if ( !(rhsb = doubleMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsx = doubleMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
dCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_D, SLU_GE);
dCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_D, SLU_GE);
xact = doubleMalloc(n * nrhs);
ldx = n;
dGenXtrue(n, nrhs, xact, ldx);
dFillRHS(trans, nrhs, xact, ldx, &A, &B);
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(R = (double *) SUPERLU_MALLOC(A.nrow * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (double *) SUPERLU_MALLOC(A.ncol * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for C[].");
info = 0;
#ifdef DEBUG
num_drop_L = 0;
num_drop_U = 0;
#endif
/* Initialize the statistics variables. */
StatInit(&stat);
/* Compute the incomplete factorization and compute the condition number
and pivot growth using dgsisx. */
dgsisx(&options, &A, perm_c, perm_r, etree, equed, R, C, &L, &U, work,
lwork, &B, &X, &rpg, &rcond, &mem_usage, &stat, &info);
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("dgsisx(): info %d\n", info);
if (info > 0 || rcond < 1e-8 || rpg > 1e8)
printf("WARNING: This preconditioner might be unstable.\n");
if ( info == 0 || info == n+1 ) {
if ( options.PivotGrowth == YES )
printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber == YES )
printf("Recip. condition number = %e\n", rcond);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
printf("n(A) = %d, nnz(A) = %d\n", n, Astore->nnz);
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 - n);
printf("Fill ratio: nnz(F)/nnz(A) = %.3f\n",
((double)(Lstore->nnz) + (double)(Ustore->nnz) - (double)n)
/ (double)Astore->nnz);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
fflush(stdout);
/* Set the global variables. */
GLOBAL_A = &A;
GLOBAL_L = &L;
GLOBAL_U = &U;
GLOBAL_STAT = &stat;
GLOBAL_PERM_C = perm_c;
GLOBAL_PERM_R = perm_r;
/* Set the variables used by GMRES. */
restrt = SUPERLU_MIN(n / 3 + 1, 50);
maxit = 1000;
iter = maxit;
resid = 1e-8;
if (!(b = doubleMalloc(m))) ABORT("Malloc fails for b[].");
if (!(x = doubleMalloc(n))) ABORT("Malloc fails for x[].");
if (info <= n + 1)
{
int i_1 = 1;
double maxferr = 0.0, nrmA, nrmB, res, t;
double temp;
extern double dnrm2_(int *, double [], int *);
extern void daxpy_(int *, double *, double [], int *, double [], int *);
/* Call GMRES. */
for (i = 0; i < n; i++) b[i] = rhsb[i];
for (i = 0; i < n; i++) x[i] = zero;
t = SuperLU_timer_();
dfgmr(n, dmatvec_mult, dpsolve, b, x, resid, restrt, &iter, stdout);
t = SuperLU_timer_() - t;
/* Output the result. */
nrmA = dnrm2_(&(Astore->nnz), (double *)((DNformat *)A.Store)->nzval,
&i_1);
nrmB = dnrm2_(&m, b, &i_1);
sp_dgemv("N", -1.0, &A, x, 1, 1.0, b, 1);
res = dnrm2_(&m, b, &i_1);
resid = res / nrmB;
printf("||A||_F = %.1e, ||B||_2 = %.1e, ||B-A*X||_2 = %.1e, "
"relres = %.1e\n", nrmA, nrmB, res, resid);
if (iter >= maxit)
{
if (resid >= 1.0) iter = -180;
else if (resid > 1e-8) iter = -111;
}
printf("iteration: %d\nresidual: %.1e\nGMRES time: %.2f seconds.\n",
iter, resid, t);
/* Scale the solution back if equilibration was performed. */
if (*equed == 'C' || *equed == 'B')
for (i = 0; i < n; i++) x[i] *= C[i];
for (i = 0; i < m; i++) {
maxferr = SUPERLU_MAX(maxferr, fabs(x[i] - xact[i]));
}
printf("||X-X_true||_oo = %.1e\n", maxferr);
}
#ifdef DEBUG
printf("%d entries in L and %d entries in U dropped.\n",
num_drop_L, num_drop_U);
#endif
fflush(stdout);
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (rhsx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
if ( lwork >= 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
SUPERLU_FREE(b);
SUPERLU_FREE(x);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
return 0;
}
