LIS_INT main(LIS_INT argc, char* argv[])
{
LIS_SCALAR *a,*q,*r;
LIS_INT m,n,nn;
LIS_INT i,j,ii,jj,nnz,qriter;
double time,time0;
LIS_REAL qrerr;
LIS_DEBUG_FUNC_IN;
lis_initialize(&argc, &argv);
if( argc < 3 )
{
printf("Usage: %s m n\n", argv[0]);
CHKERR(1);
}
m = atoi(argv[1]);
n = atoi(argv[2]);
if( m<=0 || n<=0 )
{
printf("m=%d <=0 or n=%d <=0\n", m,n);
CHKERR(1);
}
printf("\n");
/* create arrays */
nn = m*n;
a = (LIS_SCALAR *)malloc(nn*nn*sizeof(LIS_SCALAR));
q = (LIS_SCALAR *)malloc(nn*nn*sizeof(LIS_SCALAR));
r = (LIS_SCALAR *)malloc(nn*nn*sizeof(LIS_SCALAR));
/* define two-dimensional Laplacian */
lis_array_set_all(nn*nn,(LIS_SCALAR)0.0,a);
nnz = 0;
for(ii=0;ii<nn;ii++)
{
i = ii/m;
j = ii - i*m;
if( i>0 ) { jj = ii - m; a[ii + jj * nn] = -1.0; nnz++;}
if( i<n-1 ) { jj = ii + m; a[ii + jj * nn] = -1.0; nnz++;}
if( j>0 ) { jj = ii - 1; a[ii + jj * nn] = -1.0; nnz++;}
if( j<m-1 ) { jj = ii + 1; a[ii + jj * nn] = -1.0; nnz++;}
jj = ii; a[ii + jj * nn] = 4.0; nnz++;
}
printf("matrix size = %d x %d (%d nonzero entries)\n\n", nn,nn,nnz);
/* solve eigenproblem */
time0 = lis_wtime();
lis_array_qr(nn,a,q,r,&qriter,&qrerr);
time = lis_wtime() - time0;
printf("QR : number of iterations = %d\n", qriter);
printf("QR : elapsed time = %e sec.\n", time);
printf("QR : eigensolver = %e sec.\n", time);
#ifdef _LONG__DOUBLE
printf("QR : 2-norm of A(2,1) = %Le\n\n", qrerr);
#else
printf("QR : 2-norm of A(2,1) = %e\n\n", qrerr);
#endif
lis_finalize();
LIS_DEBUG_FUNC_OUT;
return 0;
}
LIS_INT lis_ecg(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_SCALAR evalue;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,iter3,nsolver,i,j,output;
LIS_INT nprocs,my_rank;
LIS_REAL nrm2,resid,resid3;
LIS_SCALAR lshift;
LIS_VECTOR b,D,r,w,p,Aw,Ax,Ap,ones,Ds;
LIS_SCALAR *SA, *SB, *SW, *v3, *SAv3, *SBv3, *z3, *q3, *SBz3, evalue3, ievalue3;
LIS_SOLVER solver;
LIS_PRECON precon;
LIS_MATRIX A0;
LIS_VECTOR x0,z,q;
double times,itimes,ptimes,p_c_times,p_i_times;
LIS_INT nsol, precon_type;
char solvername[128], preconname[128];
A = esolver->A;
x = esolver->x;
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
lshift = esolver->lshift;
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
SA = (LIS_SCALAR *)lis_malloc(3*3*sizeof(LIS_SCALAR), "lis_ecg::SA");
SB = (LIS_SCALAR *)lis_malloc(3*3*sizeof(LIS_SCALAR), "lis_ecg::SB");
SW = (LIS_SCALAR *)lis_malloc(3*3*sizeof(LIS_SCALAR), "lis_ecg::SW");
v3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::v3");
SAv3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::SAv3");
SBv3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::SBv3");
SBz3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::SBz3");
z3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::z3");
q3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::q3");
b = esolver->work[0];
D = esolver->work[1];
Ds = esolver->work[2];
r = esolver->work[3];
w = esolver->work[4];
p = esolver->work[5];
Aw = esolver->work[6];
Ax = esolver->work[7];
Ap = esolver->work[8];
lis_vector_set_all(1.0,b);
lis_vector_nrm2(b, &nrm2);
lis_vector_scale(1/nrm2, b);
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p ilu",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_get_solvername(nsol, solvername);
lis_get_preconname(precon_type, preconname);
printf("solver : %s %d\n", solvername, nsol);
printf("precon : %s %d\n", preconname, precon_type);
lis_solve(A, b, x, solver);
lis_vector_copy(b,Ax);
lis_vector_nrm2(x, &nrm2);
lis_vector_set_all(0.0,p);
lis_vector_set_all(0.0,Ap);
lis_precon_create(solver, &precon);
solver->precon = precon;
iter=0;
while (iter<emaxiter)
{
iter = iter + 1;
lis_vector_dot(x,Ax,&evalue);
lis_vector_axpyz(-(evalue),x,Ax,r);
lis_vector_nrm2(r, &nrm2);
resid = fabs(nrm2/(evalue));
if( output )
{
if( output & LIS_EPRINT_MEM ) esolver->residual[iter] = resid;
if( output & LIS_EPRINT_OUT && A->my_rank==0 ) printf("iter: %5d residual = %e\n", iter, resid);
}
if (resid<tol) break;
lis_psolve(solver, x, w);
lis_vector_copy(x,Aw);
lis_vector_nrm2(w, &nrm2);
lis_vector_dot(w,Aw,&SA[0]);
lis_vector_dot(x,Aw,&SA[3]);
lis_vector_dot(p,Aw,&SA[6]);
SA[1] = SA[3];
lis_vector_dot(x,Ax,&SA[4]);
lis_vector_dot(p,Ax,&SA[7]);
SA[2] = SA[6];
SA[5] = SA[7];
lis_vector_dot(p,Ap,&SA[8]);
lis_vector_dot(w,w,&SB[0]);
lis_vector_dot(x,w,&SB[3]);
lis_vector_dot(p,w,&SB[6]);
SB[1] = SB[3];
lis_vector_dot(x,x,&SB[4]);
lis_vector_dot(p,x,&SB[7]);
SB[2] = SB[6];
SB[5] = SB[7];
lis_vector_dot(p,p,&SB[8]);
lis_array_set_all(3, 1.0, v3);
iter3=0;
while (iter3<emaxiter)
{
iter3 = iter3 + 1;
lis_array_nrm2(3, v3, &nrm2);
lis_array_scale(3, 1/nrm2, v3);
lis_array_matvec(3, SB, v3, SBv3, LIS_INS_VALUE);
lis_array_invvec(3, SA, SBv3, z3);
lis_array_dot2(3, SBv3, z3, &ievalue3);
if (ievalue3==0)
{
printf("ievalue3 is zero\n");
lis_precon_destroy(precon);
lis_solver_destroy(solver);
esolver->iter = iter;
esolver->resid = resid;
esolver->evalue[0] = evalue;
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_free(SA);
lis_free(SB);
lis_free(SW);
lis_free(v3);
lis_free(SAv3);
lis_free(SBv3);
lis_free(SBz3);
lis_free(z3);
lis_free(q3);
return LIS_BREAKDOWN;
}
lis_array_axpyz(3, -ievalue3, SBv3, z3, q3);
lis_array_nrm2(3, q3, &resid3);
resid3 = fabs(resid3 / ievalue3);
if (resid3<1e-12) break;
lis_array_copy(3,z3,v3);
}
evalue3 = 1 / ievalue3;
lis_vector_scale(v3[0],w);
lis_vector_axpy(v3[2],p,w);
lis_vector_xpay(w,v3[1],x);
lis_vector_copy(w,p);
lis_vector_scale(v3[0],Aw);
lis_vector_axpy(v3[2],Ap,Aw);
lis_vector_xpay(Aw,v3[1],Ax);
lis_vector_copy(Aw,Ap);
lis_vector_nrm2(x,&nrm2);
lis_vector_scale(1/nrm2,x);
lis_vector_scale(1/nrm2,Ax);
lis_vector_nrm2(p,&nrm2);
lis_vector_scale(1/nrm2,p);
lis_vector_scale(1/nrm2,Ap);
lis_solver_get_timeex(solver,×,&itimes,&ptimes,&p_c_times,&p_i_times);
esolver->ptimes += solver->ptimes;
esolver->itimes += solver->itimes;
esolver->p_c_times += solver->p_c_times;
esolver->p_i_times += solver->p_i_times;
}
lis_precon_destroy(precon);
lis_solver_destroy(solver);
esolver->iter = iter;
esolver->resid = resid;
esolver->evalue[0] = evalue;
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_free(SA);
lis_free(SB);
lis_free(SW);
lis_free(v3);
lis_free(SAv3);
lis_free(SBv3);
lis_free(SBz3);
lis_free(z3);
lis_free(q3);
if (resid<tol)
{
esolver->retcode = LIS_SUCCESS;
return LIS_SUCCESS;
}
else
{
esolver->retcode = LIS_MAXITER;
return LIS_MAXITER;
}
}