/*! @file ditersol.c
* \brief Example #1 showing how to use ILU to precondition GMRES
*
* <pre>
* -- SuperLU routine (version 4.2) --
* Lawrence Berkeley National Laboratory
* November, 2010
* August, 2011
*
* This example shows that ILU is computed from the equilibrated matrix,
* and the preconditioned GMRES is applied to the equilibrated system.
* The driver routine DGSISX is called twice to perform factorization
* and apply preconditioner separately.
*
* Note that DGSISX performs the following factorization:
* Pr*Dr*A*Dc*Pc^T ~= LU
* with Pr being obtained from MC64 statically then partial pivoting
* dybamically. On return, A is overwritten as A1 = Dr*A*Dc.
*
* We can solve the transformed system, A1*y = Dr*B, using FGMRES.
* B is first overwritten as Dr*B.
* Then GMRES step requires requires 2 procedures:
* 1) Apply preconditioner M^{-1} = Pc^T*U^{-1}*L^{-1}*Pr
* 2) Matrix-vector multiplication: w = A1*v
*
* </pre>
*/
#include "slu_ddefs.h"
superlu_options_t *GLOBAL_OPTIONS;
double *GLOBAL_R, *GLOBAL_C;
int *GLOBAL_PERM_C, *GLOBAL_PERM_R;
SuperMatrix *GLOBAL_A, *GLOBAL_L, *GLOBAL_U;
SuperLUStat_t *GLOBAL_STAT;
mem_usage_t *GLOBAL_MEM_USAGE;
void dpsolve(int n,
double x[], /* solution */
double y[] /* right-hand side */
)
{
SuperMatrix *A = GLOBAL_A, *L = GLOBAL_L, *U = GLOBAL_U;
SuperLUStat_t *stat = GLOBAL_STAT;
int *perm_c = GLOBAL_PERM_C, *perm_r = GLOBAL_PERM_R;
char equed[1] = {'N'};
double *R = GLOBAL_R, *C = GLOBAL_C;
superlu_options_t *options = GLOBAL_OPTIONS;
mem_usage_t *mem_usage = GLOBAL_MEM_USAGE;
int info;
static DNformat X, Y;
static SuperMatrix XX = {SLU_DN, SLU_D, SLU_GE, 1, 1, &X};
static SuperMatrix YY = {SLU_DN, SLU_D, SLU_GE, 1, 1, &Y};
double rpg, rcond;
XX.nrow = YY.nrow = n;
X.lda = Y.lda = n;
X.nzval = x;
Y.nzval = y;
#if 0
dcopy_(&n, y, &i_1, x, &i_1);
dgstrs(NOTRANS, L, U, perm_c, perm_r, &XX, stat, &info);
#else
dgsisx(options, A, perm_c, perm_r, NULL, equed, R, C,
L, U, NULL, 0, &YY, &XX, &rpg, &rcond, mem_usage, stat, &info);
#endif
}
void dmatvec_mult(double alpha, double x[], double beta, double y[])
{
SuperMatrix *A = GLOBAL_A;
sp_dgemv("N", alpha, A, x, 1, beta, y, 1);
}
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;
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);
/* Generate the right-hand side */
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. */
B.ncol = 0; /* not to perform triangular solution */
dgsisx(&options, &A, perm_c, perm_r, etree, equed, R, C, &L, &U, work,
lwork, &B, &X, &rpg, &rcond, &mem_usage, &stat, &info);
/* Set RHS for GMRES. */
if (!(b = doubleMalloc(m))) ABORT("Malloc fails for b[].");
if (*equed == 'R' || *equed == 'B') {
for (i = 0; i < n; ++i) b[i] = rhsb[i] * R[i];
} else {
for (i = 0; i < m; i++) b[i] = rhsb[i];
}
printf("dgsisx(): info %d, equed %c\n", info, equed[0]);
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);
}
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
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;
GLOBAL_OPTIONS = &options;
GLOBAL_R = R;
GLOBAL_C = C;
GLOBAL_MEM_USAGE = &mem_usage;
/* Set the options to do solve-only. */
options.Fact = FACTORED;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
/* Set the variables used by GMRES. */
restrt = SUPERLU_MIN(n / 3 + 1, 50);
maxit = 1000;
iter = maxit;
resid = 1e-8;
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 *);
/* Initial guess */
for (i = 0; i < n; i++) x[i] = zero;
t = SuperLU_timer_();
/* Call GMRES */
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;
}
