double LisMPIDiscreteVector::getNorm2()
{
double val = .0;
int err = lis_vector_nrm2(_v, &val);
CHKERR(err);
return val;
}
void lis_vector_nrm2_f(LIS_VECTOR_F *x, LIS_REAL *value, LIS_INT *ierr)
{
LIS_DEBUG_FUNC_IN;
*ierr = lis_vector_nrm2((LIS_VECTOR)LIS_V2P(x),value);
if( *ierr ) return;
LIS_DEBUG_FUNC_OUT;
return;
}
LIS_INT lis_solver_get_residual_nrm2_r(LIS_VECTOR r, LIS_SOLVER solver, LIS_REAL *res)
{
LIS_DEBUG_FUNC_IN;
lis_vector_nrm2(r,res);
*res = *res * solver->bnrm;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
void lis_idrs_orth(LIS_INT s, LIS_VECTOR *P)
{
LIS_INT n,i,j;
LIS_REAL r;
LIS_SCALAR d;
n = P[0]->n;
for(j=0;j<s;j++)
{
lis_vector_nrm2(P[j],&r);
r = 1.0/r;
lis_vector_scale(r,P[j]);
for(i=j+1;i<s;i++)
{
lis_vector_dot(P[j],P[i],&d);
lis_vector_axpy(-d,P[j],P[i]);
}
}
}
LIS_INT lis_jacobi(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR d,r,t,s;
LIS_REAL bnrm2,nrm2,tol;
LIS_INT iter,maxiter,output;
double time,ptime;
LIS_DEBUG_FUNC_IN;
A = solver->A;
b = solver->b;
x = solver->x;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
ptime = 0.0;
r = solver->work[0];
t = solver->work[1];
s = solver->work[2];
d = solver->work[3];
lis_vector_nrm2(b,&bnrm2);
bnrm2 = 1.0 / bnrm2;
lis_matrix_get_diagonal(A,d);
lis_vector_reciprocal(d);
for( iter=1; iter<=maxiter; iter++ )
{
/* x += D^{-1}(b - Ax) */
time = lis_wtime();
lis_psolve(solver,x,s);
ptime += lis_wtime() - time;
lis_matvec(A,s,t);
/* lis_matvec(A,x,t);*/
lis_vector_axpyz(-1,t,b,r);
lis_vector_nrm2(r,&nrm2);
lis_vector_pmul(r,d,r);
lis_vector_axpy(1,r,x);
/* convergence check */
nrm2 = nrm2 * bnrm2;
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol >= nrm2 )
{
time = lis_wtime();
lis_psolve(solver,x,s);
ptime += lis_wtime() - time;
lis_vector_copy(s,x);
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
lis_psolve(solver,x,s);
lis_vector_copy(s,x);
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_fgmres(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,s, *z, *v;
LIS_SCALAR *h;
LIS_SCALAR aa,bb,rr,a2,b2,t;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes;
LIS_REAL rnorm;
LIS_INT i,j,k,m;
LIS_INT ii,i1,iiv,i1v,iih,i1h,jj;
LIS_INT h_dim;
LIS_INT cs,sn;
LIS_DEBUG_FUNC_IN;
A = solver->A;
M = solver->precon;
b = solver->b;
x = solver->x;
n = A->n;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
m = solver->options[LIS_OPTIONS_RESTART];
conv = solver->options[LIS_OPTIONS_CONV_COND];
h_dim = m+1;
ptimes = 0.0;
s = solver->work[0];
r = solver->work[1];
z = &solver->work[2];
v = &solver->work[m+2];
h = (LIS_SCALAR *)lis_malloc( sizeof(LIS_SCALAR) * (h_dim+1) * (h_dim+2),"lis_gmres::h" );
cs = (m+1)*h_dim;
sn = (m+2)*h_dim;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,v[0],&bnrm2) )
{
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
rnorm = 1.0 / bnrm2;
iter=0;
while( iter<maxiter )
{
/* first column of V */
/* v = r / ||r||_2 */
lis_vector_scale(bnrm2,v[0]);
/* s = ||r||_2 e_1 */
lis_vector_set_all(0,s);
s->value[0] = rnorm;
i = 0;
do
{
iter++;
i++;
ii = i-1;
i1 = i;
iiv = i-1;
i1v = i;
iih = (i-1)*h_dim;
i1h = i*h_dim;
/* z = M^-1 v */
times = lis_wtime();
lis_psolve(solver, v[iiv], z[iiv]);
ptimes += lis_wtime()-times;
/* v = Az */
LIS_MATVEC(A,z[iiv], v[i1v]);
for(k=0;k<i;k++)
{
/* h[k,i] = <w,v[k]> */
/* w = w - h[k,i]v[k] */
lis_vector_dot(v[i1v],v[k],&t);
h[k + iih] = t;
lis_vector_axpy(-t,v[k],v[i1v]);
}
/* h[i+1,i] = ||w|| */
/* v[i+1] = w / h[i+1,i] */
lis_vector_nrm2(v[i1v],&t);
h[i1 + iih] = t;
lis_vector_scale(1.0/t,v[i1v]);
for(k=1;k<=ii;k++)
{
jj = k-1;
t = h[jj + iih];
aa = h[jj + cs]*t;
aa += h[jj + sn]*h[k + iih];
bb = -h[jj + sn]*t;
bb += h[jj + cs]*h[k + iih];
h[jj + iih] = aa;
h[k + iih] = bb;
}
aa = h[ii + iih];
bb = h[i1 + iih];
a2 = aa*aa;
b2 = bb*bb;
rr = sqrt(a2 + b2);
if( rr==0.0 ) rr=1.0e-17;
h[ii + cs] = aa / rr;
h[ii + sn] = bb / rr;
s->value[i1] = -h[ii + sn]*s->value[ii];
s->value[ii] = h[ii + cs]*s->value[ii];
aa = h[ii + cs]*h[ii + iih];
aa += h[ii + sn]*h[i1 + iih];
h[ii + iih] = aa;
/* convergence check */
nrm2 = fabs(s->value[i1]);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) printf("iter: %5d residual = %e\n", iter, nrm2);
}
if( tol >= nrm2 ) break;
} while( i<m && iter <maxiter );
/* Solve H*Y =S for upper triangular H */
s->value[ii] = s->value[ii] / h[ii + iih];
for(k=1;k<=ii;k++)
{
jj = ii-k;
t = s->value[jj];
for(j=jj+1;j<=ii;j++)
{
t -= h[jj + j*h_dim]*s->value[j];
}
s->value[jj] = t / h[jj + jj*h_dim];
}
/* x = x + zy */
for(j=0;j<=ii;j++)
{
lis_vector_axpy(s->value[j],z[j],x);
}
if( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
LIS_MATVEC(A,x,v[0]);
lis_vector_xpay(b,-1.0,v[0]);
lis_vector_nrm2(v[0],&rnorm);
bnrm2 = 1.0 / rnorm;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter+1;
solver->resid = nrm2;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_eii_quad(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_SCALAR evalue, ievalue;
LIS_SCALAR lshift;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,iter2,output;
LIS_REAL nrm2,resid;
LIS_QUAD_PTR qdot_xz;
LIS_VECTOR z,q;
LIS_SOLVER solver;
double time,itime,ptime,p_c_time,p_i_time;
LIS_INT err;
LIS_PRECON precon;
LIS_INT nsol, precon_type;
char solvername[128], preconname[128];
LIS_DEBUG_FUNC_IN;
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
lshift = esolver->lshift;
output = esolver->options[LIS_EOPTIONS_OUTPUT];
A = esolver->A;
x = esolver->x;
if (esolver->options[LIS_EOPTIONS_INITGUESS_ONES] )
{
lis_vector_set_all(1.0,x);
}
evalue = 1.0;
z = esolver->work[0];
q = esolver->work[1];
LIS_QUAD_SCALAR_MALLOC(qdot_xz,0,1);
iter=0;
ievalue = 1/(evalue);
#ifdef _LONG__DOUBLE
if( output & (A->my_rank==0) ) printf("local shift : %Le\n", lshift);
#else
if( output & (A->my_rank==0) ) printf("local shift : %e\n", lshift);
#endif
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p none -precision quad",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_solver_get_solvername(nsol, solvername);
lis_solver_get_preconname(precon_type, preconname);
if( output & (A->my_rank==0) ) printf("linear solver : %s\n", solvername);
if( output & (A->my_rank==0) ) printf("preconditioner : %s\n", preconname);
/* create preconditioner */
solver->A = A;
err = lis_precon_create(solver, &precon);
if( err )
{
lis_solver_work_destroy(solver);
solver->retcode = err;
return err;
}
while (iter<emaxiter)
{
iter = iter+1;
/* x = x / ||x||_2 */
lis_vector_nrm2(x, &nrm2);
lis_vector_scale(1/nrm2, x);
/* z = (A - lshift I)^-1 * x */
lis_solve_kernel(A, x, z, solver, precon);
lis_solver_get_iter(solver,&iter2);
/* 1/evalue = <x,z> */
lis_vector_dotex_mmm(x, z, &qdot_xz);
lis_quad_minus((LIS_QUAD *)qdot_xz.hi);
lis_vector_axpyzex_mmmm(qdot_xz,x,z,q);
lis_quad_minus((LIS_QUAD *)qdot_xz.hi);
ievalue = qdot_xz.hi[0];
/* resid = ||z - 1/evalue * x||_2 / |1/evalue| */
lis_vector_nrm2(q, &resid);
resid = fabs(resid/ievalue);
/* x = z */
lis_vector_copy(z,x);
/* convergence check */
lis_solver_get_timeex(solver,&time,&itime,&ptime,&p_c_time,&p_i_time);
esolver->ptime += solver->ptime;
esolver->itime += solver->itime;
esolver->p_c_time += solver->p_c_time;
esolver->p_i_time += solver->p_i_time;
if( output )
{
if( output & LIS_EPRINT_MEM ) esolver->rhistory[iter] = resid;
if( output & LIS_EPRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,resid);
}
if( tol >= resid )
{
esolver->retcode = LIS_SUCCESS;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = 1/ievalue;
lis_vector_nrm2(x, &nrm2);
lis_vector_scale(1/nrm2, x);
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_precon_destroy(precon);
lis_solver_destroy(solver);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
lis_precon_destroy(precon);
esolver->retcode = LIS_MAXITER;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = 1/ievalue;
lis_vector_nrm2(x, &nrm2);
lis_vector_scale(1/nrm2, x);
if (lshift != 0)
{
lis_matrix_shift_diagonal(A, -lshift);
}
lis_solver_destroy(solver);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_gmres(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR r,s,z,*v;
LIS_SCALAR *h;
LIS_SCALAR aa,bb,rr,a2,b2,t;
LIS_REAL tnrm2;
LIS_REAL bnrm2,nrm2,tol;
LIS_INT iter,maxiter,n,output;
double time,ptime;
LIS_REAL rnorm;
LIS_INT i,j,k,m;
LIS_INT ii,i1,iiv,i1v,iih,jj;
LIS_INT h_dim;
LIS_INT cs,sn;
LIS_DEBUG_FUNC_IN;
A = solver->A;
b = solver->b;
x = solver->x;
n = A->n;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
m = solver->options[LIS_OPTIONS_RESTART];
h_dim = m+1;
ptime = 0.0;
s = solver->work[0];
r = solver->work[1];
z = solver->work[2];
v = &solver->work[3];
h = (LIS_SCALAR *)lis_malloc( sizeof(LIS_SCALAR)*(h_dim+1)*(h_dim+2),"lis_gmres::h" );
cs = (m+1)*h_dim;
sn = (m+2)*h_dim;
/* r = M^-1 * (b - A * x) */
lis_matvec(A,x,z);
lis_vector_xpay(b,-1.0,z);
lis_psolve(solver,z,v[0]);
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,v[0],&bnrm2) )
{
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
iter=0;
while( iter<maxiter )
{
/* first column of V */
/* v = r / ||r||_2 */
lis_vector_nrm2(v[0],&rnorm);
lis_vector_scale(1.0/rnorm,v[0]);
/* s = ||r||_2 e_1 */
lis_vector_set_all(0,s);
s->value[0] = rnorm;
i = 0;
do
{
iter++;
i++;
ii = i-1;
i1 = i;
iiv = i-1;
i1v = i;
iih = (i-1)*h_dim;
/* z = M^-1 * v */
time = lis_wtime();
lis_psolve(solver,v[iiv],z);
ptime += lis_wtime()-time;
/* w = A * z */
lis_matvec(A,z,v[i1v]);
for(k=0;k<i;k++)
{
/* h[k,i] = <w,v[k]> */
/* w = w - h[k,i] * v[k] */
lis_vector_dot(v[i1v],v[k],&t);
h[k+iih] = t;
lis_vector_axpy(-t,v[k],v[i1v]);
}
/* h[i+1,i] = ||w|| */
/* v[i+1] = w / h[i+1,i] */
lis_vector_nrm2(v[i1v],&tnrm2);
h[i1+iih] = tnrm2;
lis_vector_scale(1.0/tnrm2,v[i1v]);
for(k=1;k<=ii;k++)
{
jj = k-1;
t = h[jj+iih];
aa = h[jj+cs]*t;
aa += h[jj+sn]*h[k+iih];
bb = -h[jj+sn]*t;
bb += h[jj+cs]*h[k+iih];
h[jj+iih] = aa;
h[k+iih] = bb;
}
aa = h[ii+iih];
bb = h[i1+iih];
a2 = aa*aa;
b2 = bb*bb;
rr = sqrt(a2+b2);
if( rr==0.0 ) rr=1.0e-17;
h[ii+cs] = aa/rr;
h[ii+sn] = bb/rr;
s->value[i1] = -h[ii+sn]*s->value[ii];
s->value[ii] = h[ii+cs]*s->value[ii];
aa = h[ii+cs]*h[ii+iih];
aa += h[ii+sn]*h[i1+iih];
h[ii+iih] = aa;
/* convergence check */
nrm2 = sabs(s->value[i1])*bnrm2;
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol >= nrm2 ) break;
} while( i<m && iter <maxiter );
/* Solve H * Y = S for upper Hessenberg matrix H */
s->value[ii] = s->value[ii]/h[ii+iih];
for(k=1;k<=ii;k++)
{
jj = ii-k;
t = s->value[jj];
for(j=jj+1;j<=ii;j++)
{
t -= h[jj+j*h_dim]*s->value[j];
}
s->value[jj] = t/h[jj+jj*h_dim];
}
/* z = z + y * v */
#ifdef _OPENMP
#pragma omp parallel for private(k)
#endif
for(k=0;k<n;k++)
{
z->value[k] = s->value[0]*v[0]->value[k];
}
for(j=1;j<=ii;j++)
{
lis_vector_axpy(s->value[j],v[j],z);
}
/* r = M^-1 * z */
time = lis_wtime();
lis_psolve(solver,z,r);
ptime += lis_wtime()-time;
/* x = x + r */
lis_vector_axpy(1,r,x);
if( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
for(j=1;j<=i;j++)
{
jj = i1-j+1;
s->value[jj-1] = -h[jj-1+sn]*s->value[jj];
s->value[jj] = h[jj-1+cs]*s->value[jj];
}
for(j=0;j<=i1;j++)
{
t = s->value[j];
if( j==0 ) t = t-1.0;
lis_vector_axpy(t,v[j],v[0]);
}
}
solver->retcode = LIS_MAXITER;
solver->iter = iter+1;
solver->resid = nrm2;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_solver_get_initial_residual(LIS_SOLVER solver, LIS_PRECON M, LIS_VECTOR t, LIS_VECTOR r, LIS_SCALAR *bnrm2)
{
LIS_INT output,conv;
#ifdef USE_QUAD_PRECISION
LIS_INT i;
#endif
LIS_MATRIX A;
LIS_VECTOR x,b,p,xx;
LIS_SCALAR nrm2;
LIS_REAL tol,tol_w,tol_switch;
LIS_DEBUG_FUNC_IN;
A = solver->A;
b = solver->b;
x = solver->x;
xx = solver->xx;
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
tol_w = solver->params[LIS_PARAMS_RESID_WEIGHT-LIS_OPTIONS_LEN];
tol_switch = solver->params[LIS_PARAMS_SWITCH_RESID-LIS_OPTIONS_LEN];
/* Initial Residual */
if( M==NULL )
{
p = r;
}
else
{
p = t;
}
if( !solver->options[LIS_OPTIONS_INITGUESS_ZEROS] )
{
#ifndef USE_QUAD_PRECISION
lis_matvec(A,x,p); /* p = Ax */
lis_vector_xpay(b,-1,p); /* p = b - p */
#else
if( solver->precision==LIS_PRECISION_DOUBLE )
{
lis_matvec(A,x,p); /* p = Ax */
lis_vector_xpay(b,-1,p); /* p = b - p */
}
else
{
lis_matvec(A,xx,p); /* p = Ax */
lis_vector_xpay(b,-1,p); /* p = b - p */
#ifdef _OPENMP
#pragma omp parallel for private(i)
#endif
for(i=0;i<A->n;i++)
{
p->value_lo[i] = 0.0;
}
}
#endif
}
else
{
#ifndef USE_QUAD_PRECISION
lis_vector_copy(b,p);
#else
if( solver->precision==LIS_PRECISION_DOUBLE )
{
lis_vector_copy(b,p);
}
else
{
lis_vector_copyex_nm(b,p);
}
#endif
}
switch(conv)
{
case LIS_CONV_COND_NRM2_R:
lis_vector_nrm2(p,&nrm2);
*bnrm2 = nrm2;
solver->tol = tol;
solver->tol_switch = tol_switch;
break;
case LIS_CONV_COND_NRM2_B:
lis_vector_nrm2(p,&nrm2);
lis_vector_nrm2(b,bnrm2);
solver->tol = tol;
solver->tol_switch = tol_switch;
break;
case LIS_CONV_COND_NRM1_B:
lis_vector_nrm1(p,&nrm2);
lis_vector_nrm1(b,bnrm2);
solver->tol = *bnrm2*tol_w + tol;
solver->tol_switch = *bnrm2*tol_w + tol_switch;
break;
}
if( *bnrm2 == 0.0 )
{
*bnrm2 = 1.0;
}
else
{
*bnrm2 = 1.0 / *bnrm2;
}
solver->bnrm = *bnrm2;
nrm2 = nrm2 * *bnrm2;
if( output && (r->precision==LIS_PRECISION_QUAD && solver->precision!=LIS_PRECISION_SWITCH) )
{
if( output & LIS_PRINT_MEM ) solver->residual[0] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) printf("iter: %5d residual = %e\n", 0, nrm2);
}
if( nrm2 <= solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN] )
{
solver->retcode = LIS_SUCCESS;
solver->iter = 1;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_FAILS;
}
if( M!=NULL )
{
/* r = M^-1 * p */
lis_psolve(solver, p, r);
}
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
LIS_INT lis_gs(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR r,t,s;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,output;
double time,ptime;
LIS_INT err;
LIS_DEBUG_FUNC_IN;
A = solver->A;
b = solver->b;
x = solver->x;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
ptime = 0.0;
r = solver->work[0];
t = solver->work[1];
s = solver->work[2];
lis_vector_nrm2(b,&bnrm2);
bnrm2 = 1.0 / bnrm2;
err = lis_matrix_split(A);
if( err ) return err;
if( A->use_wd!=LIS_SOLVER_GS )
{
if( !A->WD )
{
err = lis_matrix_diag_duplicate(A->D,&A->WD);
if( err ) return err;
}
lis_matrix_diag_copy(A->D,A->WD);
lis_matrix_diag_inverse(A->WD);
A->use_wd = LIS_SOLVER_GS;
}
for( iter=1; iter<=maxiter; iter++ )
{
/* x += (D-L)^{-1}(b - Ax) */
time = lis_wtime();
lis_psolve(solver,x,s);
ptime += lis_wtime() - time;
lis_matvec(A,s,t);
/* lis_matvec(A,x,t);*/
lis_vector_axpyz(-1,t,b,r);
lis_vector_nrm2(r,&nrm2);
lis_matrix_solve(A,r,t,LIS_MATRIX_LOWER);
lis_vector_axpy(1,t,x);
/* convergence check */
nrm2 = nrm2 * bnrm2;
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol >= nrm2 )
{
time = lis_wtime();
lis_psolve(solver,x,s);
ptime += lis_wtime() - time;
lis_vector_copy(s,x);
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
lis_psolve(solver,x,s);
lis_vector_copy(s,x);
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_epi_quad(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_SCALAR evalue;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,output;
LIS_INT nprocs,my_rank;
LIS_REAL nrm2,resid;
LIS_QUAD_PTR qdot_xz;
LIS_VECTOR z,q;
double times, ptimes;
LIS_DEBUG_FUNC_IN;
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
A = esolver->A;
x = esolver->x;
if (esolver->options[LIS_EOPTIONS_INITGUESS_ONES] )
{
lis_vector_set_all(1.0,x);
}
z = esolver->work[0];
q = esolver->work[1];
LIS_QUAD_SCALAR_MALLOC(qdot_xz,0,1);
iter=0;
while (iter<emaxiter)
{
iter = iter+1;
/* x = x / ||x||_2 */
lis_vector_nrm2(x, &nrm2);
lis_vector_scale(1/nrm2, x);
/* z = A * x */
lis_matvec(A,x,z);
/* evalue = <x,z> */
lis_vector_dotex_mmm(x, z, &qdot_xz);
lis_quad_minus((LIS_QUAD *)qdot_xz.hi);
/* resid = ||z - evalue * x||_2 / |evalue| */
lis_vector_axpyzex_mmmm(qdot_xz,x,z,q);
lis_quad_minus((LIS_QUAD *)qdot_xz.hi);
lis_vector_nrm2(q, &resid);
evalue = qdot_xz.hi[0];
resid = fabs(resid / evalue);
/* x = z */
lis_vector_copy(z, x);
/* convergence check */
if( output )
{
if( output & LIS_EPRINT_MEM ) esolver->residual[iter] = resid;
if( output & LIS_EPRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,resid);
}
if( tol >= resid )
{
esolver->retcode = LIS_SUCCESS;
esolver->iter = iter;
esolver->resid = resid;
esolver->evalue[0] = evalue;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
esolver->retcode = LIS_MAXITER;
esolver->iter = iter;
esolver->resid = resid;
esolver->evalue[0] = evalue;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT main(LIS_INT argc, char* argv[])
{
LIS_MATRIX A,A0;
LIS_VECTOR b,x,v;
LIS_SCALAR ntimes,nmflops,nnrm2;
LIS_SCALAR *value;
LIS_INT nprocs,my_rank;
int int_nprocs,int_my_rank;
LIS_INT nthreads, maxthreads;
LIS_INT gn,nnz,mode;
LIS_INT i,j,jj,j0,j1,l,k,n,np,h,ih;
LIS_INT m,nn,ii;
LIS_INT block;
LIS_INT rn,rmin,rmax,rb;
LIS_INT is,ie,clsize,ci,*iw;
LIS_INT err,iter,matrix_type;
LIS_INT *ptr,*index;
double mem,val,ra,rs,ri,ria,ca,time,time2,convtime,val2,nnzs,nnzap,nnzt;
double commtime,comptime,flops;
FILE *file;
char path[1024];
LIS_DEBUG_FUNC_IN;
lis_initialize(&argc, &argv);
#ifdef USE_MPI
MPI_Comm_size(MPI_COMM_WORLD,&int_nprocs);
MPI_Comm_rank(MPI_COMM_WORLD,&int_my_rank);
nprocs = int_nprocs;
my_rank = int_my_rank;
#else
nprocs = 1;
my_rank = 0;
#endif
if( argc < 4 )
{
if( my_rank==0 ) printf("Usage: spmvtest5 matrix_filename matrix_type iter [block] \n");
lis_finalize();
exit(0);
}
file = fopen(argv[1], "r");
if( file==NULL ) CHKERR(1);
matrix_type = atoi(argv[2]);
iter = atoi(argv[3]);
if (argv[4] == NULL) {
block = 2;
}
else {
block = atoi(argv[4]);
}
if( matrix_type<1 || matrix_type>11 )
{
if( my_rank==0 ) printf("matrix_type=%d <1 or matrix_type=%d >11\n",matrix_type,matrix_type);
CHKERR(1);
}
if( iter<=0 )
{
if( my_rank==0 ) printf("iter=%d <= 0\n",iter);
CHKERR(1);
}
if( my_rank==0 )
{
printf("\n");
printf("number of processes = %d\n",nprocs);
}
#ifdef _OPENMP
if( my_rank==0 )
{
nthreads = omp_get_num_procs();
maxthreads = omp_get_max_threads();
printf("max number of threads = %d\n", nthreads);
printf("number of threads = %d\n", maxthreads);
}
#else
nthreads = 1;
maxthreads = 1;
#endif
/* create matrix and vectors */
lis_matrix_create(LIS_COMM_WORLD,&A0);
err = lis_input(A0,NULL,NULL,argv[1]);
CHKERR(err);
n = A0->n;
gn = A0->gn;
nnz = A0->nnz;
np = A0->np-n;
#ifdef USE_MPI
MPI_Allreduce(&nnz,&i,1,LIS_MPI_INT,MPI_SUM,A0->comm);
nnzap = (double)i / (double)nprocs;
nnzt = ((double)nnz -nnzap)*((double)nnz -nnzap);
nnz = i;
MPI_Allreduce(&nnzt,&nnzs,1,MPI_DOUBLE,MPI_SUM,A0->comm);
nnzs = (nnzs / (double)nprocs)/nnzap;
MPI_Allreduce(&np,&i,1,LIS_MPI_INT,MPI_SUM,A0->comm);
np = i;
#endif
if( my_rank==0 )
{
printf("block size of BSR and BSC = %d x %d\n",block,block);
printf("iteration count = %d\n\n",iter);
}
err = lis_vector_duplicate(A0,&x);
if( err ) CHKERR(err);
err = lis_vector_duplicate(A0,&b);
if( err ) CHKERR(err);
lis_matrix_get_range(A0,&is,&ie);
for(i=0;i<n;i++)
{
err = lis_vector_set_value(LIS_INS_VALUE,i+is,1.0,x);
}
lis_matrix_duplicate(A0,&A);
lis_matrix_set_type(A,matrix_type);
err = lis_matrix_convert(A0,A);
if( err ) CHKERR(err);
if( A->matrix_type==LIS_MATRIX_BSR || A->matrix_type==LIS_MATRIX_BSC )
{
A->bnr = block;
A->bnc = block;
}
comptime = 0.0;
commtime = 0.0;
for(i=0;i<iter;i++)
{
#ifdef USE_MPI
MPI_Barrier(A->comm);
time = lis_wtime();
lis_send_recv(A->commtable,x->value);
commtime += lis_wtime() - time;
#endif
time2 = lis_wtime();
lis_matvec(A,x,b);
comptime += lis_wtime() - time2;
}
lis_vector_nrm2(b,&val);
if( my_rank==0 )
{
flops = 2.0*nnz*iter*1.0e-6 / comptime;
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
}
lis_matrix_destroy(A);
lis_matrix_destroy(A0);
lis_vector_destroy(b);
lis_vector_destroy(x);
lis_finalize();
LIS_DEBUG_FUNC_OUT;
return 0;
}
LIS_INT main(LIS_INT argc, char* argv[])
{
LIS_MATRIX A,A0;
LIS_VECTOR b,x,v;
LIS_SCALAR ntimes,nmflops,nnrm2;
LIS_SCALAR *value;
LIS_INT nprocs,my_rank;
int int_nprocs,int_my_rank;
LIS_INT nthreads, maxthreads;
LIS_INT gn,nnz,mode;
LIS_INT i,ii,j,jj,j0,j1,l,k,n,np,h,ih;
LIS_INT rn,rmin,rmax,rb;
LIS_INT is,ie,clsize,ci,*iw;
LIS_INT err,iter,matrix_type,s,ss,se;
LIS_INT *ptr,*index;
double mem,ra,rs,ri,ria,ca,time,time2,convtime,nnzs,nnzap,nnzt;
LIS_SCALAR val;
double commtime,comptime,flops;
FILE *file;
char path[1024];
LIS_DEBUG_FUNC_IN;
lis_initialize(&argc, &argv);
#ifdef USE_MPI
MPI_Comm_size(MPI_COMM_WORLD,&int_nprocs);
MPI_Comm_rank(MPI_COMM_WORLD,&int_my_rank);
nprocs = int_nprocs;
my_rank = int_my_rank;
#else
nprocs = 1;
my_rank = 0;
#endif
if( argc < 3 )
{
if( my_rank==0 )
{
printf("Usage: %s n iter [matrix_type]\n", argv[0]);
}
CHKERR(1);
}
n = atoi(argv[1]);
iter = atoi(argv[2]);
if (argv[3] == NULL) {
s = 0;
}
else {
s = atoi(argv[3]);
}
if( n<=0 )
{
#ifdef _LONGLONG
if( my_rank==0 ) printf("n=%lld <=0\n",n);
#else
if( my_rank==0 ) printf("n=%d <=0\n",n);
#endif
CHKERR(1);
}
if( iter<=0 )
{
#ifdef _LONGLONG
if( my_rank==0 ) printf("iter=%lld <= 0\n",iter);
#else
if( my_rank==0 ) printf("iter=%d <= 0\n",iter);
#endif
CHKERR(1);
}
if( s<0 || s>11 )
{
#ifdef _LONGLONG
if( my_rank==0 ) printf("matrix_type=%lld < 0 or matrix_type=%lld > 11\n",s,s);
#else
if( my_rank==0 ) printf("matrix_type=%d < 0 or matrix_type=%d > 11\n",s,s);
#endif
CHKERR(1);
}
if( my_rank==0 )
{
printf("\n");
#ifdef _LONGLONG
printf("number of processes = %lld\n",nprocs);
#else
printf("number of processes = %d\n",nprocs);
#endif
}
#ifdef _OPENMP
nthreads = omp_get_num_procs();
maxthreads = omp_get_max_threads();
if( my_rank==0 )
{
#ifdef _LONGLONG
printf("max number of threads = %lld\n", nthreads);
printf("number of threads = %lld\n", maxthreads);
#else
printf("max number of threads = %d\n", nthreads);
printf("number of threads = %d\n", maxthreads);
#endif
}
#else
nthreads = 1;
maxthreads = 1;
#endif
/* create matrix and vectors */
lis_matrix_create(LIS_COMM_WORLD,&A0);
lis_matrix_set_size(A0,0,n);
lis_matrix_get_size(A0,&n,&gn);
lis_matrix_get_range(A0,&is,&ie);
k = 0;
for(i=is;i<ie;i++)
{
if( i>0 ) lis_matrix_set_value(LIS_INS_VALUE,i,i-1,-1.0,A0);
if( i<gn-1 ) lis_matrix_set_value(LIS_INS_VALUE,i,i+1,-1.0,A0);
lis_matrix_set_value(LIS_INS_VALUE,i,i,2.0,A0);
}
err = lis_matrix_assemble(A0);
CHKERR(err);
n = A0->n;
gn = A0->gn;
nnz = A0->nnz;
np = A0->np-n;
#ifdef USE_MPI
MPI_Allreduce(&nnz,&i,1,LIS_MPI_INT,MPI_SUM,A0->comm);
nnzap = (double)i / (double)nprocs;
nnzt = ((double)nnz -nnzap)*((double)nnz -nnzap);
nnz = i;
MPI_Allreduce(&nnzt,&nnzs,1,MPI_DOUBLE,MPI_SUM,A0->comm);
nnzs = (nnzs / (double)nprocs)/nnzap;
MPI_Allreduce(&np,&i,1,LIS_MPI_INT,MPI_SUM,A0->comm);
np = i;
#endif
if( my_rank==0 )
{
#ifdef _LONGLONG
printf("matrix size = %lld x %lld (%lld nonzero entries)\n",gn,gn,nnz);
printf("iteration count = %lld\n\n",iter);
#else
printf("matrix size = %d x %d (%d nonzero entries)\n",gn,gn,nnz);
printf("iteration count = %d\n\n",iter);
#endif
}
err = lis_vector_duplicate(A0,&x);
if( err ) CHKERR(err);
err = lis_vector_duplicate(A0,&b);
if( err ) CHKERR(err);
lis_matrix_get_range(A0,&is,&ie);
for(i=0;i<n;i++)
{
err = lis_vector_set_value(LIS_INS_VALUE,i+is,1.0,x);
}
/*
MPI version of VBR is not implemented.
DNS is also excluded to reduce memory usage.
*/
if (s==0)
{
ss = 1;
se = 11;
}
else
{
ss = s;
se = s+1;
}
for (matrix_type=ss;matrix_type<se;matrix_type++)
{
if ( nprocs>1 && matrix_type==9 ) continue;
lis_matrix_duplicate(A0,&A);
lis_matrix_set_type(A,matrix_type);
err = lis_matrix_convert(A0,A);
if( err ) CHKERR(err);
comptime = 0.0;
commtime = 0.0;
for(i=0;i<iter;i++)
{
#ifdef USE_MPI
MPI_Barrier(A->comm);
time = lis_wtime();
lis_send_recv(A->commtable,x->value);
commtime += lis_wtime() - time;
MPI_Barrier(A->comm);
#endif
time2 = lis_wtime();
lis_matvec(A,x,b);
comptime += lis_wtime() - time2;
}
lis_vector_nrm2(b,&val);
if( my_rank==0 )
{
flops = 2.0*nnz*iter*1.0e-6 / comptime;
#ifdef USE_MPI
#ifdef _LONG__DOUBLE
#ifdef _LONGLONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#endif
#else
#ifdef _LONGLONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#endif
#endif
#else
#ifdef _LONG__DOUBLE
#ifdef _LONGLONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#endif
#else
#ifdef _LONGLONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#endif
#endif
#endif
}
lis_matrix_destroy(A);
}
lis_matrix_destroy(A0);
lis_vector_destroy(b);
lis_vector_destroy(x);
lis_finalize();
LIS_DEBUG_FUNC_OUT;
return 0;
}
LIS_INT lis_esi_quad(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_VECTOR x, Ax;
LIS_SCALAR xAx, xx, mu, lshift;
LIS_INT ss;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT i,j,k;
LIS_SCALAR evalue,dotvr;
LIS_INT iter,giter,output,niesolver;
LIS_INT nprocs,my_rank;
LIS_REAL nrm2,dot,resid,resid0;
LIS_QUAD_PTR qdot_vv, qdot_vr;
LIS_VECTOR *v,r,q;
LIS_SOLVER solver;
LIS_PRECON precon;
double times,itimes,ptimes,p_c_times,p_i_times;
LIS_INT err;
LIS_INT nsol, precon_type;
char solvername[128], preconname[128];
LIS_DEBUG_FUNC_IN;
A = esolver->A;
x = esolver->x;
ss = esolver->options[LIS_EOPTIONS_SUBSPACE];
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
lshift = esolver->lshift;
output = esolver->options[LIS_EOPTIONS_OUTPUT];
niesolver = esolver->options[LIS_EOPTIONS_INNER_ESOLVER];
r = esolver->work[0];
q = esolver->work[1];
v = &esolver->work[2];
Ax = esolver->work[3];
LIS_QUAD_SCALAR_MALLOC(qdot_vv,0,1);
LIS_QUAD_SCALAR_MALLOC(qdot_vr,1,1);
lis_vector_set_all(1.0,r);
lis_vector_nrm2(r, &nrm2);
lis_vector_scale(1/nrm2,r);
switch ( niesolver )
{
case LIS_ESOLVER_II:
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p ilu -precision quad",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);
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
break;
case LIS_ESOLVER_AII:
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p ilu -precision quad",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);
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
lis_vector_set_all(1.0,q);
lis_solve(A, q, x, solver);
lis_precon_create(solver, &precon);
solver->precon = precon;
break;
case LIS_ESOLVER_RQI:
lis_solver_create(&solver);
lis_solver_set_option("-p ilu -precision quad -maxiter 10",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);
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
break;
}
giter=0;
j=0;
while (j<ss)
{
lis_vector_duplicate(A,&esolver->evector[j]);
j = j+1;
lis_vector_copy(r, v[j]);
if (niesolver==LIS_ESOLVER_II || niesolver==LIS_ESOLVER_RQI)
{
/* create preconditioner */
solver->A = A;
err = lis_precon_create(solver, &precon);
if( err )
{
lis_solver_work_destroy(solver);
solver->retcode = err;
return err;
}
}
if (niesolver==LIS_ESOLVER_RQI)
{
lis_vector_nrm2(x, &nrm2);
lis_vector_scale(1/nrm2, x);
lis_matvec(A, x, Ax);
lis_vector_dot(x, Ax, &xAx);
lis_vector_dot(x, x, &xx);
mu = xAx / xx;
}
iter = 0;
while (iter<emaxiter)
{
/* diagonalization */
iter = iter+1;
giter = giter+1;
for (k=1;k<j;k++)
{
lis_vector_dotex_mmm(v[j], v[k], &qdot_vv);
lis_quad_minus((LIS_QUAD *)qdot_vv.hi);
lis_vector_axpyex_mmm(qdot_vv,v[k],v[j]);
}
switch( niesolver )
{
case LIS_ESOLVER_PI:
lis_matvec(A,v[j],r);
break;
case LIS_ESOLVER_II:
lis_solve_kernel(A, v[j], r, solver, precon);
break;
case LIS_ESOLVER_AII:
lis_psolve(solver, v[j], r);
break;
case LIS_ESOLVER_RQI:
lis_vector_nrm2(v[j], &nrm2);
lis_vector_scale(1/nrm2, v[j]);
lis_matrix_shift_diagonal(A, -mu);
lis_solve_kernel(A, v[j], r, solver, precon);
lis_matrix_shift_diagonal(A, mu);
break;
}
if ( j==1 && ( niesolver==LIS_ESOLVER_II || niesolver==LIS_ESOLVER_AII || niesolver==LIS_ESOLVER_RQI ))
{
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_vector_nrm2(r, &nrm2);
lis_vector_dotex_mmm(v[j], r, &qdot_vr);
lis_quad_minus((LIS_QUAD *)qdot_vr.hi);
lis_vector_axpyzex_mmmm(qdot_vr,v[j],r,q);
lis_quad_minus((LIS_QUAD *)qdot_vr.hi);
dotvr = qdot_vr.hi[0];
mu = mu + 1/dotvr;
lis_vector_nrm2(q, &resid);
resid = fabs(resid / dotvr);
lis_vector_scale(1/nrm2,r);
lis_vector_copy(r, v[j]);
if ( j==1 )
{
if( output & LIS_PRINT_MEM ) esolver->residual[iter] = resid;
if( output & LIS_PRINT_OUT ) printf("iter: %5d residual = %e\n", iter, resid);
esolver->iter = iter;
esolver->resid = resid;
}
if (tol>resid) break;
}
if (niesolver==LIS_ESOLVER_II || niesolver==LIS_ESOLVER_RQI)
{
lis_precon_destroy(precon);
}
switch ( niesolver )
{
case LIS_ESOLVER_PI:
esolver->evalue[j-1] = dotvr;
break;
case LIS_ESOLVER_II:
esolver->evalue[j-1] = 1/dotvr;
break;
case LIS_ESOLVER_AII:
esolver->evalue[j-1] = 1/dotvr;
break;
case LIS_ESOLVER_RQI:
esolver->evalue[j-1] = mu;
break;
}
lis_vector_copy(v[j], esolver->evector[j-1]);
if (A->my_rank==0 && ss>1)
{
#ifdef _LONGLONG
printf("Subspace: mode number = %lld\n", j-1);
#else
printf("Subspace: mode number = %d\n", j-1);
#endif
printf("Subspace: eigenvalue = %e\n", esolver->evalue[j-1]);
#ifdef _LONGLONG
printf("Subspace: number of iterations = %lld\n",iter);
#else
printf("Subspace: number of iterations = %d\n",iter);
#endif
printf("Subspace: relative residual 2-norm = %e\n",resid);
}
}
lis_vector_copy(esolver->evector[esolver->options[LIS_EOPTIONS_MODE]], esolver->x);
switch ( niesolver )
{
case LIS_ESOLVER_II:
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_solver_destroy(solver);
break;
case LIS_ESOLVER_AII:
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_precon_destroy(precon);
lis_solver_destroy(solver);
break;
case LIS_ESOLVER_RQI:
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_solver_destroy(solver);
break;
}
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
LIS_INT lis_epi(LIS_ESOLVER esolver)
{
LIS_Comm comm;
LIS_MATRIX A;
LIS_VECTOR v,y,q;
LIS_SCALAR theta;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,output;
LIS_SCALAR oshift,ishift;
LIS_REAL nrm2,resid;
LIS_DEBUG_FUNC_IN;
comm = LIS_COMM_WORLD;
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
#ifdef _COMPLEX
oshift = esolver->params[LIS_EPARAMS_SHIFT - LIS_EOPTIONS_LEN] + esolver->params[LIS_EPARAMS_SHIFT_IM - LIS_EOPTIONS_LEN] * _Complex_I;
#else
oshift = esolver->params[LIS_EPARAMS_SHIFT - LIS_EOPTIONS_LEN];
#endif
A = esolver->A;
v = esolver->x;
if (esolver->options[LIS_EOPTIONS_INITGUESS_ONES] )
{
lis_vector_set_all(1.0,v);
}
y = esolver->work[0];
q = esolver->work[1];
if ( esolver->ishift != 0.0 ) oshift = ishift;
if ( oshift != 0.0 ) lis_matrix_shift_diagonal(A, oshift);
if( output )
{
#ifdef _COMPLEX
lis_printf(comm,"shift : (%e, %e)\n", (double)creal(oshift), (double)cimag(oshift));
#else
lis_printf(comm,"shift : %e\n", (double)oshift);
#endif
}
iter=0;
while (iter<emaxiter)
{
iter = iter+1;
/* v = v / ||v||_2 */
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
/* y = A * v */
lis_matvec(A,v,y);
/* theta = <v,y> */
lis_vector_dot(v, y, &theta);
/* resid = ||y - theta * v||_2 / |theta| */
lis_vector_axpyz(-theta, v, y, q);
lis_vector_nrm2(q, &resid);
resid = resid / fabs(theta);
/* v = y */
lis_vector_copy(y, v);
/* convergence check */
if( output )
{
if( output & LIS_EPRINT_MEM ) esolver->rhistory[iter] = resid;
if( output & LIS_EPRINT_OUT ) lis_print_rhistory(comm,iter,resid);
}
if( tol >= resid )
{
esolver->retcode = LIS_SUCCESS;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = theta + oshift;
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
if ( oshift != 0.0 ) lis_matrix_shift_diagonal(A, -oshift);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
esolver->retcode = LIS_MAXITER;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = theta + oshift;
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
if ( oshift != 0.0 ) lis_matrix_shift_diagonal(A, -oshift);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT main(LIS_INT argc, char* argv[])
{
LIS_MATRIX A,A0;
LIS_VECTOR b,x;
LIS_SCALAR *value;
LIS_INT nprocs,my_rank;
int int_nprocs,int_my_rank;
LIS_INT nthreads,maxthreads;
LIS_INT gn,nnz,np;
LIS_INT i,j,k,si,sj,sk,ii,jj,ctr;
LIS_INT l,m,n,nn;
LIS_INT is,ie;
LIS_INT err,iter,matrix_type,storage,ss,se;
LIS_INT *ptr,*index;
double time,time2,nnzs,nnzap,nnzt;
LIS_SCALAR val;
double commtime,comptime,flops;
LIS_DEBUG_FUNC_IN;
lis_initialize(&argc, &argv);
#ifdef USE_MPI
MPI_Comm_size(MPI_COMM_WORLD,&int_nprocs);
MPI_Comm_rank(MPI_COMM_WORLD,&int_my_rank);
nprocs = int_nprocs;
my_rank = int_my_rank;
#else
nprocs = 1;
my_rank = 0;
#endif
if( argc < 5 )
{
if( my_rank==0 )
{
printf("Usage: %s l m n iter [matrix_type]\n", argv[0]);
}
CHKERR(1);
}
l = atoi(argv[1]);
m = atoi(argv[2]);
n = atoi(argv[3]);
iter = atoi(argv[4]);
if (argv[5] == NULL) {
storage = 0;
}
else {
storage = atoi(argv[5]);
}
if( iter<=0 )
{
#ifdef _LONG__LONG
if( my_rank==0 ) printf("iter=%lld <= 0\n",iter);
#else
if( my_rank==0 ) printf("iter=%d <= 0\n",iter);
#endif
CHKERR(1);
}
if( l<=0 || m<=0 || n<=0 )
{
#ifdef _LONG__LONG
if( my_rank==0 ) printf("l=%lld <=0, m=%lld <=0 or n=%lld <=0\n",l,m,n);
#else
if( my_rank==0 ) printf("l=%d <=0, m=%d <=0 or n=%d <=0\n",l,m,n);
#endif
CHKERR(1);
}
if( storage<0 || storage>11 )
{
#ifdef _LONG__LONG
if( my_rank==0 ) printf("matrix_type=%lld < 0 or matrix_type=%lld > 11\n",storage,storage);
#else
if( my_rank==0 ) printf("matrix_type=%d < 0 or matrix_type=%d > 11\n",storage,storage);
#endif
CHKERR(1);
}
if( my_rank==0 )
{
printf("\n");
#ifdef _LONG__LONG
printf("number of processes = %lld\n",nprocs);
#else
printf("number of processes = %d\n",nprocs);
#endif
}
#ifdef _OPENMP
nthreads = omp_get_num_procs();
maxthreads = omp_get_max_threads();
if( my_rank==0 )
{
#ifdef _LONG__LONG
printf("max number of threads = %lld\n", nthreads);
printf("number of threads = %lld\n", maxthreads);
#else
printf("max number of threads = %d\n", nthreads);
printf("number of threads = %d\n", maxthreads);
#endif
}
#else
nthreads = 1;
maxthreads = 1;
#endif
/* create matrix and vectors */
nn = l*m*n;
err = lis_matrix_create(LIS_COMM_WORLD,&A0);
err = lis_matrix_set_size(A0,0,nn);
CHKERR(err);
ptr = (LIS_INT *)malloc((A0->n+1)*sizeof(LIS_INT));
if( ptr==NULL ) CHKERR(1);
index = (LIS_INT *)malloc(27*A0->n*sizeof(LIS_INT));
if( index==NULL ) CHKERR(1);
value = (LIS_SCALAR *)malloc(27*A0->n*sizeof(LIS_SCALAR));
if( value==NULL ) CHKERR(1);
lis_matrix_get_range(A0,&is,&ie);
ctr = 0;
for(ii=is;ii<ie;ii++)
{
i = ii/(m*n);
j = (ii - i*m*n)/n;
k = ii - i*m*n - j*n;
for(si=-1;si<=1;si++) {
if( i+si>-1 && i+si<l ) {
for(sj=-1;sj<=1;sj++) {
if( j+sj>-1 && j+sj<m ) {
for(sk=-1;sk<=1;sk++) {
if( k+sk>-1 && k+sk<n ) {
jj = ii + si*m*n + sj*n + sk;
index[ctr] = jj;
if( jj==ii ) { value[ctr++] = 26.0;}
else { value[ctr++] = -1.0;}
}
}
}
}
}
}
ptr[ii-is+1] = ctr;
}
ptr[0] = 0;
err = lis_matrix_set_csr(ptr[ie-is],ptr,index,value,A0);
CHKERR(err);
err = lis_matrix_assemble(A0);
CHKERR(err);
n = A0->n;
gn = A0->gn;
nnz = A0->nnz;
np = A0->np-n;
#ifdef USE_MPI
MPI_Allreduce(&nnz,&i,1,LIS_MPI_INT,MPI_SUM,A0->comm);
nnzap = (double)i / (double)nprocs;
nnzt = ((double)nnz -nnzap)*((double)nnz -nnzap);
nnz = i;
MPI_Allreduce(&nnzt,&nnzs,1,MPI_DOUBLE,MPI_SUM,A0->comm);
nnzs = (nnzs / (double)nprocs)/nnzap;
MPI_Allreduce(&np,&i,1,LIS_MPI_INT,MPI_SUM,A0->comm);
np = i;
#endif
if( my_rank==0 )
{
#ifdef _LONG__LONG
printf("matrix size = %lld x %lld (%lld nonzero entries)\n",gn,gn,nnz);
printf("number of iterations = %lld\n\n",iter);
#else
printf("matrix size = %d x %d (%d nonzero entries)\n",gn,gn,nnz);
printf("number of iterations = %d\n\n",iter);
#endif
}
err = lis_vector_duplicate(A0,&x);
if( err ) CHKERR(err);
err = lis_vector_duplicate(A0,&b);
if( err ) CHKERR(err);
lis_matrix_get_range(A0,&is,&ie);
for(i=0;i<n;i++)
{
err = lis_vector_set_value(LIS_INS_VALUE,i+is,1.0,x);
}
for(i=0;i<n;i++)
{
lis_sort_id(A0->ptr[i],A0->ptr[i+1]-1,A0->index,A0->value);
}
/*
MPI version of VBR is not implemented.
DNS is also excluded to reduce memory usage.
*/
if (storage==0)
{
ss = 1;
se = 11;
}
else
{
ss = storage;
se = storage+1;
}
for (matrix_type=ss;matrix_type<se;matrix_type++)
{
if ( nprocs>1 && matrix_type==9 ) continue;
lis_matrix_duplicate(A0,&A);
lis_matrix_set_type(A,matrix_type);
err = lis_matrix_convert(A0,A);
if( err ) CHKERR(err);
comptime = 0.0;
commtime = 0.0;
for(i=0;i<iter;i++)
{
#ifdef USE_MPI
MPI_Barrier(A->comm);
time = lis_wtime();
lis_send_recv(A->commtable,x->value);
commtime += lis_wtime() - time;
#endif
time2 = lis_wtime();
lis_matvec(A,x,b);
comptime += lis_wtime() - time2;
}
lis_vector_nrm2(b,&val);
if( my_rank==0 )
{
flops = 2.0*nnz*iter*1.0e-6 / comptime;
#ifdef USE_MPI
#ifdef _LONG__DOUBLE
#ifdef _LONG__LONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#endif
#else
#ifdef _LONG__LONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#endif
#endif
#else
#ifdef _LONG__DOUBLE
#ifdef _LONG__LONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#endif
#else
#ifdef _LONG__LONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#endif
#endif
#endif
}
lis_matrix_destroy(A);
}
lis_matrix_destroy(A0);
lis_vector_destroy(b);
lis_vector_destroy(x);
lis_finalize();
LIS_DEBUG_FUNC_OUT;
return 0;
}
LIS_INT lis_egpi(LIS_ESOLVER esolver)
{
LIS_Comm comm;
LIS_MATRIX A,B;
LIS_VECTOR w,v,y,q;
LIS_SCALAR eta,theta;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,iter2,output;
LIS_SCALAR oshift,ishift;
LIS_REAL nrm2,resid;
LIS_SOLVER solver;
double time,itime,ptime,p_c_time,p_i_time;
LIS_INT err;
LIS_PRECON precon;
LIS_INT nsol, precon_type;
char solvername[128], preconname[128];
LIS_DEBUG_FUNC_IN;
comm = LIS_COMM_WORLD;
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
#ifdef _COMPLEX
oshift = esolver->params[LIS_EPARAMS_SHIFT - LIS_EOPTIONS_LEN] + esolver->params[LIS_EPARAMS_SHIFT_IM - LIS_EOPTIONS_LEN] * _Complex_I;
#else
oshift = esolver->params[LIS_EPARAMS_SHIFT - LIS_EOPTIONS_LEN];
#endif
A = esolver->A;
B = esolver->B;
v = esolver->x;
if (esolver->options[LIS_EOPTIONS_INITGUESS_ONES] )
{
lis_vector_set_all(1.0,v);
}
w = esolver->work[0];
y = esolver->work[1];
q = esolver->work[2];
if ( esolver->ishift != 0.0 ) oshift = ishift;
if ( oshift != 0.0 ) lis_matrix_shift_matrix(A, B, oshift);
if( output )
{
#ifdef _COMPLEX
lis_printf(comm,"shift : (%e, %e)\n", (double)creal(oshift), (double)cimag(oshift));
#else
lis_printf(comm,"shift : %e\n", (double)oshift);
#endif
}
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p none",solver);
err = lis_solver_set_optionC(solver);
CHKERR(err);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_solver_get_solvername(nsol, solvername);
lis_solver_get_preconname(precon_type, preconname);
if( output )
{
lis_printf(comm,"linear solver : %s\n", solvername);
lis_printf(comm,"preconditioner : %s\n", preconname);
}
/* create preconditioner */
solver->A = B;
err = lis_precon_create(solver, &precon);
if( err )
{
lis_solver_work_destroy(solver);
solver->retcode = err;
return err;
}
iter=0;
while (iter<emaxiter)
{
iter = iter+1;
/* v = v / ||v||_2 */
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
/* w = A * v */
lis_matvec(A, v, w);
/* v = v / <v,w>^1/2, w = w / <v,w>^1/2 */
lis_vector_dot(v, w, &eta);
eta = sqrt(eta);
lis_vector_scale(1.0/eta, v);
lis_vector_scale(1.0/eta, w);
/* y = B^-1 * w */
err = lis_solve_kernel(B, w, y, solver, precon);
if( err )
{
lis_solver_work_destroy(solver);
solver->retcode = err;
return err;
}
lis_solver_get_iter(solver, &iter2);
/* theta = <w,y> */
lis_vector_dot(w, y, &theta);
/* resid = ||y - theta * v||_2 / |theta| */
lis_vector_axpyz(-theta, v, y, q);
lis_vector_nrm2(q, &resid);
resid = resid / fabs(theta);
/* v = y */
lis_vector_copy(y, v);
/* convergence check */
lis_solver_get_timeex(solver,&time,&itime,&ptime,&p_c_time,&p_i_time);
esolver->ptime += solver->ptime;
esolver->itime += solver->itime;
esolver->p_c_time += solver->p_c_time;
esolver->p_i_time += solver->p_i_time;
if( output )
{
if( output & LIS_EPRINT_MEM ) esolver->rhistory[iter] = resid;
if( output & LIS_EPRINT_OUT ) lis_print_rhistory(comm,iter,resid);
}
if( tol >= resid )
{
esolver->retcode = LIS_SUCCESS;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = theta + oshift;
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
if ( oshift != 0.0 ) lis_matrix_shift_matrix(A, B, -oshift);
lis_precon_destroy(precon);
lis_solver_destroy(solver);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
lis_precon_destroy(precon);
esolver->retcode = LIS_MAXITER;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = theta + oshift;
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
if ( oshift != 0.0 ) lis_matrix_shift_matrix(A, B, -oshift);
lis_solver_destroy(solver);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_solve_kernel(LIS_MATRIX A, LIS_VECTOR b, LIS_VECTOR x, LIS_SOLVER solver, LIS_PRECON precon)
{
LIS_INT nsolver, precon_type, maxiter;
LIS_INT err;
LIS_SCALAR *residual;
LIS_VECTOR xx;
LIS_INT output;
LIS_INT scale;
LIS_INT conv_cond;
LIS_INT precision,is_use_at,storage,block;
LIS_INT i,n,np;
double p_c_times, p_i_times,itimes;
LIS_SCALAR nrm2,tol,tol_w;
LIS_VECTOR t;
LIS_VECTOR bb;
LIS_MATRIX AA,B;
LIS_MATRIX At;
char buf[64];
LIS_DEBUG_FUNC_IN;
nsolver = solver->options[LIS_OPTIONS_SOLVER];
precon_type = solver->options[LIS_OPTIONS_PRECON];
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
scale = solver->options[LIS_OPTIONS_SCALE];
precision = solver->options[LIS_OPTIONS_PRECISION];
is_use_at = solver->options[LIS_OPTIONS_USE_AT];
storage = solver->options[LIS_OPTIONS_STORAGE];
block = solver->options[LIS_OPTIONS_STORAGE_BLOCK];
conv_cond = solver->options[LIS_OPTIONS_CONV_COND];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
tol_w = solver->params[LIS_PARAMS_RESID_WEIGHT-LIS_OPTIONS_LEN];
solver->precision = precision;
if( nsolver < 1 || nsolver > LIS_SOLVERS_LEN )
{
LIS_SETERR2(LIS_ERR_ILL_ARG,"Parameter LIS_OPTIONS_SOLVER is %d (Set between 1 to %d)\n",nsolver, LIS_SOLVERS_LEN);
return LIS_ERR_ILL_ARG;
}
if( precon_type < 0 || precon_type > precon_register_type )
{
LIS_SETERR2(LIS_ERR_ILL_ARG,"Parameter LIS_OPTIONS_PRECON is %d (Set between 0 to %d)\n",precon_type, precon_register_type-1);
return LIS_ERR_ILL_ARG;
}
if( maxiter<0 )
{
LIS_SETERR1(LIS_ERR_ILL_ARG,"Parameter LIS_OPTIONS_MAXITER(=%d) is less than 0\n",maxiter);
return LIS_ERR_ILL_ARG;
}
#ifdef USE_MPI
if( precon_type == LIS_PRECON_TYPE_SAAMG && solver->A->nprocs < 2)
{
LIS_SETERR1(LIS_ERR_ILL_ARG,"Parameter A->nprocs (=%d) is less than 2 (Set more than 1 when using parallel version of SAAMG)\n",solver->A->nprocs);
return LIS_ERR_ILL_ARG;
}
#endif
#ifdef USE_QUAD_PRECISION
if( precision==LIS_PRECISION_QUAD && lis_solver_execute_quad[nsolver]==NULL )
{
LIS_SETERR1(LIS_ERR_NOT_IMPLEMENTED,"Quad precision solver %s is not implemented\n",lis_solvername[nsolver]);
return LIS_ERR_NOT_IMPLEMENTED;
}
else if( precision==LIS_PRECISION_SWITCH && lis_solver_execute_switch[nsolver]==NULL )
{
LIS_SETERR1(LIS_ERR_NOT_IMPLEMENTED,"Switch solver %s is not implemented\n",lis_solvername[nsolver]);
return LIS_ERR_NOT_IMPLEMENTED;
}
if( solver->options[LIS_OPTIONS_SWITCH_MAXITER]==-1 )
{
solver->options[LIS_OPTIONS_SWITCH_MAXITER] = maxiter;
}
#endif
err = lis_solver_check_params[nsolver](solver);
if( err )
{
solver->retcode = err;
return err;
}
/* end parameter check */
solver->A = A;
solver->b = b;
/* create initial vector */
#ifndef USE_QUAD_PRECISION
err = lis_vector_duplicate(A,&xx);
#else
if( precision==LIS_PRECISION_DOUBLE )
{
err = lis_vector_duplicate(A,&xx);
}
else
{
err = lis_vector_duplicateex(LIS_PRECISION_QUAD,A,&xx);
}
#endif
if( err )
{
solver->retcode = err;
return err;
}
if( solver->options[LIS_OPTIONS_INITGUESS_ZEROS] )
{
if( output ) lis_printf(A->comm,"initial vector x = 0\n");
#ifndef USE_QUAD_PRECISION
lis_vector_set_all(0.0,xx);
#else
if( precision==LIS_PRECISION_DOUBLE )
{
lis_vector_set_all(0.0,xx);
}
else
{
lis_vector_set_allex_nm(0.0,xx);
}
#endif
}
else
{
if( output ) lis_printf(A->comm,"initial vector x = user defined\n");
#ifndef USE_QUAD_PRECISION
lis_vector_copy(x,xx);
#else
if( precision==LIS_PRECISION_DOUBLE )
{
lis_vector_copy(x,xx);
}
else
{
lis_vector_copyex_nm(x,xx);
}
#endif
}
/* create residual history vector */
if( solver->residual ) lis_free(solver->residual);
residual = (LIS_SCALAR *)lis_malloc((maxiter+2)*sizeof(LIS_SCALAR),"lis_solve::residual");
if( residual==NULL )
{
LIS_SETERR_MEM((maxiter+2)*sizeof(LIS_SCALAR));
lis_vector_destroy(xx);
solver->retcode = err;
return err;
}
residual[0] = 1.0;
n = A->n;
np = A->np;
t = NULL;
At = NULL;
p_c_times = lis_wtime();
if( precon_type==LIS_PRECON_TYPE_IS )
{
if( solver->d==NULL )
{
err = lis_vector_duplicate(A,&solver->d);
if( err )
{
return err;
}
}
if( !A->is_scaled )
{
lis_matrix_scaling(A,b,solver->d,LIS_SCALE_JACOBI);
}
else if( !b->is_scaled )
{
#ifdef _OPENMP
#pragma omp parallel for
#endif
for(i=0;i<n;i++)
{
b->value[i] = b->value[i]*solver->d->value[i];
}
}
if( nsolver >= LIS_SOLVER_JACOBI && nsolver <= LIS_SOLVER_SOR )
{
solver->options[LIS_OPTIONS_ISLEVEL] = 0;
}
}
else if( nsolver >= LIS_SOLVER_JACOBI && nsolver <= LIS_SOLVER_SOR && precon_type!=LIS_PRECON_TYPE_NONE )
{
if( solver->d==NULL )
{
err = lis_vector_duplicate(A,&solver->d);
if( err )
{
return err;
}
}
if( !A->is_scaled )
{
lis_matrix_scaling(A,b,solver->d,LIS_SCALE_JACOBI);
}
}
else if( scale )
{
if( storage==LIS_MATRIX_BSR && scale==LIS_SCALE_JACOBI )
{
if( A->matrix_type!=LIS_MATRIX_BSR )
{
err = lis_matrix_duplicate(A,&B);
if( err ) return err;
lis_matrix_set_blocksize(B,block,block,NULL,NULL);
lis_matrix_set_type(B,storage);
err = lis_matrix_convert(A,B);
if( err ) return err;
lis_matrix_storage_destroy(A);
lis_matrix_DLU_destroy(A);
lis_matrix_diag_destroy(A->WD);
if( A->l2g_map ) lis_free( A->l2g_map );
if( A->commtable ) lis_commtable_destroy( A->commtable );
if( A->ranges ) lis_free( A->ranges );
err = lis_matrix_copy_struct(B,A);
if( err ) return err;
lis_free(B);
}
err = lis_matrix_split(A);
if( err ) return err;
err = lis_matrix_diag_duplicate(A->D,&solver->WD);
if( err ) return err;
lis_matrix_diag_copy(A->D,solver->WD);
lis_matrix_diag_inverse(solver->WD);
lis_matrix_bscaling_bsr(A,solver->WD);
lis_vector_duplicate(A,&t);
lis_matrix_diag_matvec(solver->WD,b,t);
lis_vector_copy(t,b);
lis_vector_destroy(t);
t = NULL;
}
else
{
if( solver->d==NULL )
{
err = lis_vector_duplicate(A,&solver->d);
if( err )
{
return err;
}
}
if( scale==LIS_SCALE_JACOBI && nsolver==LIS_SOLVER_CG )
{
scale = LIS_SCALE_SYMM_DIAG;
}
if( !A->is_scaled )
{
lis_matrix_scaling(A,b,solver->d,scale);
}
else if( !b->is_scaled )
{
#ifdef _OPENMP
#pragma omp parallel for
#endif
for(i=0;i<n;i++)
{
b->value[i] = b->value[i]*solver->d->value[i];
}
}
}
}
/* precon_type = precon->precon_type;*/
if( precon_type==LIS_PRECON_TYPE_IS )
{
if( nsolver < LIS_SOLVER_JACOBI || nsolver > LIS_SOLVER_SOR )
{
AA = solver->A;
bb = solver->b;
}
else
{
AA = precon->A;
bb = precon->Pb;
}
}
else
{
AA = A;
bb = b;
}
p_c_times = lis_wtime() - p_c_times;
itimes = lis_wtime();
/* Matrix Convert */
solver->A = AA;
solver->b = bb;
err = lis_matrix_convert_self(solver);
if( err )
{
lis_vector_destroy(xx);
lis_solver_work_destroy(solver);
lis_free(residual);
solver->retcode = err;
return err;
}
block = solver->A->bnr;
if( A->my_rank==0 )
{
if( output ) printf("precision : %s\n", lis_precisionname[precision]);
if( output ) printf("solver : %s %d\n", lis_solvername[nsolver],nsolver);
switch( precon_type )
{
case LIS_PRECON_TYPE_ILU:
i = solver->options[LIS_OPTIONS_FILL];
if( A->matrix_type==LIS_MATRIX_BSR || A->matrix_type==LIS_MATRIX_VBR )
{
if( output ) sprintf(buf,"Block %s(%d)",lis_preconname[precon_type],i);
}
else
{
if( output ) sprintf(buf,"%s(%d)",lis_preconname[precon_type],i);
}
break;
default:
if( output ) sprintf(buf,"%s",lis_preconname[precon_type]);
break;
}
if( solver->options[LIS_OPTIONS_ADDS] && precon_type )
{
if( output ) printf("precon : %s + additive schwarz\n", buf);
}
else
{
if( output ) printf("precon : %s\n", buf);
}
}
switch(conv_cond)
{
case LIS_CONV_COND_NRM2_R:
case LIS_CONV_COND_NRM2_B:
if( A->my_rank==0 )
{
if( output ) ("CONV_COND : ||r||_2 <= %6.1e*||r_0||_2\n", tol);
}
break;
case LIS_CONV_COND_NRM1_B:
lis_vector_nrm1(b,&nrm2);
nrm2 = nrm2*tol_w + tol;
if( A->my_rank==0 )
{
if( output ) printf("conv_cond : ||r||_1 <= %6.1e*||b||_1 + %6.1e = %6.1e\n", tol_w,tol,nrm2);
}
break;
}
if( A->my_rank==0 )
{
if( AA->matrix_type==LIS_MATRIX_BSR || AA->matrix_type==LIS_MATRIX_BSC )
{
if( output ) printf("storage : %s(%d x %d)\n", lis_storagename[AA->matrix_type-1],block,block);
}
else
{
if( output ) printf("storage : %s\n", lis_storagename[AA->matrix_type-1]);
}
}
/* create work vector */
err = lis_solver_malloc_work[nsolver](solver);
if( err )
{
lis_vector_destroy(xx);
lis_precon_destroy(precon);
solver->retcode = err;
return err;
}
if( nsolver==LIS_SOLVER_BICG && is_use_at )
{
if( output ) lis_printf(A->comm,"Use At\n");
lis_matrix_duplicate(AA,&At);
lis_matrix_set_type(At,LIS_USE_AT_TYPE[AA->matrix_type]);
lis_matrix_convert(AA,At);
solver->At = At;
}
solver->x = xx;
solver->xx = x;
solver->precon = precon;
solver->residual = residual;
/* execute solver */
#ifndef USE_QUAD_PRECISION
err = lis_solver_execute[nsolver](solver);
#else
if( precision==LIS_PRECISION_DOUBLE )
{
err = lis_solver_execute[nsolver](solver);
}
else if( precision==LIS_PRECISION_QUAD )
{
err = lis_solver_execute_quad[nsolver](solver);
}
else if( precision==LIS_PRECISION_SWITCH )
{
err = lis_solver_execute_switch[nsolver](solver);
}
#endif
solver->retcode = err;
if( scale==LIS_SCALE_SYMM_DIAG && precon_type!=LIS_PRECON_TYPE_IS)
{
#ifdef _OPENMP
#pragma omp parallel for
#endif
for(i=0;i<n;i++)
{
x->value[i] = xx->value[i]*solver->d->value[i];
}
}
else
{
#ifndef USE_QUAD_PRECISION
lis_vector_copy(xx,x);
#else
if( precision==LIS_PRECISION_DOUBLE )
{
lis_vector_copy(xx,x);
}
else
{
lis_vector_copyex_mn(xx,x);
}
#endif
}
itimes = lis_wtime() - itimes - solver->ptimes;
p_i_times = solver->ptimes;
solver->ptimes = p_c_times + p_i_times;
solver->p_c_times = p_c_times;
solver->p_i_times = p_i_times;
solver->times = solver->ptimes + itimes;
solver->itimes = itimes;
lis_solver_work_destroy(solver);
lis_vector_duplicate(A,&t);
xx->precision = LIS_PRECISION_DEFAULT;
lis_matvec(A,xx,t);
lis_vector_xpay(b,-1.0,t);
if( scale==LIS_SCALE_SYMM_DIAG && precon_type!=LIS_PRECON_TYPE_IS)
{
#ifdef _OPENMP
#pragma omp parallel for
#endif
for(i=0;i<n;i++)
{
t->value[i] = t->value[i]/solver->d->value[i];
}
}
lis_vector_nrm2(t,&nrm2);
/*
solver->resid = nrm2;
*/
if( A->my_rank==0 )
{
if( err )
{
if( output ) printf("lis_solve : %s(code=%d)\n\n",lis_returncode[err],err);
}
else
{
if( output ) printf("lis_solve : normal end\n\n");
}
}
if( precision==LIS_PRECISION_DOUBLE )
{
solver->iter2 = solver->iter;
}
else if( precision==LIS_PRECISION_QUAD )
{
solver->iter2 = 0;
}
lis_vector_destroy(t);
/* lis_vector_destroy(d);*/
lis_vector_destroy(xx);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
LIS_INT main(LIS_INT argc, char* argv[])
{
LIS_MATRIX A,A0;
LIS_VECTOR b,x;
LIS_INT nprocs,my_rank;
int int_nprocs,int_my_rank;
LIS_INT nthreads, maxthreads;
LIS_INT nnz;
LIS_INT i,n,np;
LIS_INT block;
LIS_INT is,ie;
LIS_INT err,iter,matrix_type;
double time,time2,nnzs,nnzap,nnzt;
LIS_SCALAR val;
double commtime,comptime,flops;
char path[1024];
FILE *file;
LIS_DEBUG_FUNC_IN;
lis_initialize(&argc, &argv);
#ifdef USE_MPI
MPI_Comm_size(MPI_COMM_WORLD,&int_nprocs);
MPI_Comm_rank(MPI_COMM_WORLD,&int_my_rank);
nprocs = int_nprocs;
my_rank = int_my_rank;
#else
nprocs = 1;
my_rank = 0;
#endif
if( argc < 3 )
{
if( my_rank==0 )
{
printf("Usage: %s matrix_filename_list iter [block] \n", argv[0]);
}
lis_finalize();
exit(0);
}
file = fopen(argv[1], "r");
if( file==NULL ) CHKERR(1);
iter = atoi(argv[2]);
if (argv[3] == NULL) {
block = 2;
}
else {
block = atoi(argv[3]);
}
if( iter<=0 )
{
#ifdef _LONG__LONG
printf("iter=%lld <= 0\n",iter);
#else
printf("iter=%d <= 0\n",iter);
#endif
CHKERR(1);
}
if( my_rank==0 )
{
printf("\n");
#ifdef _LONG__LONG
printf("number of processes = %lld\n",nprocs);
#else
printf("number of processes = %d\n",nprocs);
#endif
}
#ifdef _OPENMP
if( my_rank==0 )
{
nthreads = omp_get_num_procs();
maxthreads = omp_get_max_threads();
#ifdef _LONG__LONG
printf("max number of threads = %lld\n", nthreads);
printf("number of threads = %lld\n", maxthreads);
#else
printf("max number of threads = %d\n", nthreads);
printf("number of threads = %d\n", maxthreads);
#endif
}
#else
nthreads = 1;
maxthreads = 1;
#endif
/* create matrix and vectors */
while( fscanf(file, "%s\n", path)==1 )
{
if( my_rank==0 )
{
printf("matrix_filename = %s\n", path);
}
lis_matrix_create(LIS_COMM_WORLD,&A0);
err = lis_input(A0,NULL,NULL,path);
if( err ) CHKERR(err);
n = A0->n;
nnz = A0->nnz;
np = A0->np-n;
#ifdef USE_MPI
MPI_Allreduce(&nnz,&i,1,LIS_MPI_INT,MPI_SUM,A0->comm);
nnzap = (double)i / (double)nprocs;
nnzt = ((double)nnz -nnzap)*((double)nnz -nnzap);
nnz = i;
MPI_Allreduce(&nnzt,&nnzs,1,MPI_DOUBLE,MPI_SUM,A0->comm);
nnzs = (nnzs / (double)nprocs)/nnzap;
MPI_Allreduce(&np,&i,1,LIS_MPI_INT,MPI_SUM,A0->comm);
np = i;
#endif
if( my_rank==0 )
{
#ifdef _LONG__LONG
printf("block size of BSR and BSC = %lld x %lld\n",block,block);
printf("number of iterations = %lld\n\n",iter);
#else
printf("block size of BSR and BSC = %d x %d\n",block,block);
printf("number of iterations = %d\n\n",iter);
#endif
}
err = lis_vector_duplicate(A0,&x);
if( err ) CHKERR(err);
err = lis_vector_duplicate(A0,&b);
if( err ) CHKERR(err);
lis_matrix_get_range(A0,&is,&ie);
for(i=0;i<n;i++)
{
err = lis_vector_set_value(LIS_INS_VALUE,i+is,1.0,x);
}
/*
MPI version of VBR is not implemented.
DNS is also excluded to reduce memory usage.
*/
for (matrix_type=1;matrix_type<11;matrix_type++)
{
if ( nprocs>1 && matrix_type==9 ) continue;
lis_matrix_duplicate(A0,&A);
lis_matrix_set_type(A,matrix_type);
err = lis_matrix_convert(A0,A);
if( err ) CHKERR(err);
if( my_rank==0 )
{
if( A->matrix_type==LIS_MATRIX_BSR || A->matrix_type==LIS_MATRIX_BSC )
{
A->bnr = block;
A->bnc = block;
}
}
comptime = 0.0;
commtime = 0.0;
for(i=0;i<iter;i++)
{
#ifdef USE_MPI
MPI_Barrier(A->comm);
time = lis_wtime();
lis_send_recv(A->commtable,x->value);
commtime += lis_wtime() - time;
#endif
time2 = lis_wtime();
lis_matvec(A,x,b);
comptime += lis_wtime() - time2;
}
lis_vector_nrm2(b,&val);
if( my_rank==0 )
{
flops = 2.0*nnz*iter*1.0e-6 / comptime;
#ifdef USE_MPI
#ifdef _LONG__DOUBLE
#ifdef _LONG__LONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#endif
#else
#ifdef _LONG__LONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, communication = %e sec, communication/computation = %3.3f %%, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,commtime,commtime/comptime*100,val);
#endif
#endif
#else
#ifdef _LONG__DOUBLE
#ifdef _LONG__LONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %Le\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#endif
#else
#ifdef _LONG__LONG
printf("matrix_type = %2lld (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#else
printf("matrix_type = %2d (%s), computation = %e sec, %8.3f MFLOPS, 2-norm = %e\n",matrix_type,lis_storagename2[matrix_type-1],comptime,flops,val);
#endif
#endif
#endif
}
lis_matrix_destroy(A);
}
lis_matrix_destroy(A0);
lis_vector_destroy(b);
lis_vector_destroy(x);
}
fclose(file);
lis_finalize();
LIS_DEBUG_FUNC_OUT;
return 0;
}
LIS_INT lis_fgmres_quad(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR r,s,*z,*v;
LIS_QUAD *h;
LIS_QUAD_PTR aa,bb,rr,a2,b2,t,one,tmp;
LIS_REAL bnrm2,nrm2,tol;
LIS_INT iter,maxiter,n,output;
double time,ptime;
LIS_REAL rnorm;
LIS_INT i,j,k,m;
LIS_INT ii,i1,iiv,i1v,iih,jj;
LIS_INT h_dim;
LIS_INT cs,sn;
LIS_DEBUG_FUNC_IN;
A = solver->A;
b = solver->b;
x = solver->x;
n = A->n;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
m = solver->options[LIS_OPTIONS_RESTART];
h_dim = m+1;
ptime = 0.0;
s = solver->work[0];
r = solver->work[1];
z = &solver->work[2];
v = &solver->work[m+2];
h = (LIS_QUAD *)lis_malloc( sizeof(LIS_QUAD)*(h_dim+1)*(h_dim+2),"lis_fgmres_quad::h" );
cs = (m+1)*h_dim;
sn = (m+2)*h_dim;
LIS_QUAD_SCALAR_MALLOC(aa,0,1);
LIS_QUAD_SCALAR_MALLOC(bb,1,1);
LIS_QUAD_SCALAR_MALLOC(rr,2,1);
LIS_QUAD_SCALAR_MALLOC(a2,3,1);
LIS_QUAD_SCALAR_MALLOC(b2,4,1);
LIS_QUAD_SCALAR_MALLOC(t,5,1);
LIS_QUAD_SCALAR_MALLOC(tmp,6,1);
LIS_QUAD_SCALAR_MALLOC(one,7,1);
one.hi[0] = 1.0;
one.lo[0] = 0.0;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,v[0],&bnrm2) )
{
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
rnorm = 1.0/bnrm2;
iter=0;
while( iter<maxiter )
{
/* first column of V */
/* v = r / ||r||_2 */
lis_vector_scaleex_nm(bnrm2,v[0]);
/* s = ||r||_2 e_1 */
lis_vector_set_allex_nm(0.0,s);
s->value[0] = rnorm;
s->value_lo[0] = 0.0;
i = 0;
do
{
iter++;
i++;
ii = i-1;
i1 = i;
iiv = i-1;
i1v = i;
iih = (i-1)*h_dim;
/* z = M^-1 * v */
time = lis_wtime();
lis_psolve(solver,v[iiv],z[iiv]);
ptime += lis_wtime()-time;
/* w = A * z */
lis_matvec(A,z[iiv], v[i1v]);
for(k=0;k<i;k++)
{
/* h[k,i] = <w,v[k]> */
/* w = w - h[k,i] * v[k] */
lis_vector_dotex_mmm(v[i1v],v[k],&t);
h[k+iih].hi = t.hi[0];
h[k+iih].lo = t.lo[0];
lis_quad_minus((LIS_QUAD *)t.hi);
lis_vector_axpyex_mmm(t,v[k],v[i1v]);
}
/* h[i+1,i] = ||w|| */
/* v[i+1] = w / h[i+1,i] */
lis_vector_nrm2ex_mm(v[i1v],&t);
h[i1+iih].hi = t.hi[0];
h[i1+iih].lo = t.lo[0];
lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)one.hi,(LIS_QUAD *)t.hi);
lis_vector_scaleex_mm(tmp,v[i1v]);
for(k=1;k<=ii;k++)
{
jj = k-1;
t.hi[0] = h[jj+iih].hi;
t.lo[0] = h[jj+iih].lo;
lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[jj+cs],(LIS_QUAD *)t.hi);
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+sn],(LIS_QUAD *)&h[k+iih]);
lis_quad_add((LIS_QUAD *)aa.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi);
lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)&h[jj+sn],(LIS_QUAD *)t.hi);
lis_quad_minus((LIS_QUAD *)bb.hi);
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+cs],(LIS_QUAD *)&h[k+iih]);
lis_quad_add((LIS_QUAD *)bb.hi,(LIS_QUAD *)bb.hi,(LIS_QUAD *)tmp.hi);
h[jj+iih].hi = aa.hi[0];
h[jj+iih].lo = aa.lo[0];
h[k+iih].hi = bb.hi[0];
h[k+iih].lo = bb.lo[0];
}
aa.hi[0] = h[ii+iih].hi;
aa.lo[0] = h[ii+iih].lo;
bb.hi[0] = h[i1+iih].hi;
bb.lo[0] = h[i1+iih].lo;
lis_quad_sqr((LIS_QUAD *)a2.hi,(LIS_QUAD *)aa.hi);
lis_quad_sqr((LIS_QUAD *)b2.hi,(LIS_QUAD *)bb.hi);
lis_quad_add((LIS_QUAD *)rr.hi,(LIS_QUAD *)a2.hi,(LIS_QUAD *)b2.hi);
lis_quad_sqrt((LIS_QUAD *)rr.hi,(LIS_QUAD *)rr.hi);
if( rr.hi[0]==0.0 )
{
rr.hi[0]=1.0e-17;
rr.lo[0]=0.0;
}
lis_quad_div((LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)aa.hi,(LIS_QUAD *)rr.hi);
lis_quad_div((LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)bb.hi,(LIS_QUAD *)rr.hi);
tmp.hi[0] = s->value[ii];
tmp.lo[0] = s->value_lo[ii];
lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)tmp.hi);
lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)tmp.hi);
lis_quad_minus((LIS_QUAD *)aa.hi);
s->value[i1] = aa.hi[0];
s->value_lo[i1] = aa.lo[0];
s->value[ii] = bb.hi[0];
s->value_lo[ii] = bb.lo[0];
lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)&h[ii+iih]);
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)&h[i1+iih]);
lis_quad_add((LIS_QUAD *)aa.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi);
h[ii+iih].hi = aa.hi[0];
h[ii+iih].lo = aa.lo[0];
/* convergence check */
nrm2 = fabs(s->value[i1]);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol >= nrm2 ) break;
} while( i<m && iter <maxiter );
/* Solve H * Y = S for upper Hessenberg matrix H */
tmp.hi[0] = s->value[ii];
tmp.lo[0] = s->value_lo[ii];
lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[ii+iih]);
s->value[ii] = tmp.hi[0];
s->value_lo[ii] = tmp.lo[0];
for(k=1;k<=ii;k++)
{
jj = ii-k;
t.hi[0] = s->value[jj];
t.lo[0] = s->value_lo[jj];
for(j=jj+1;j<=ii;j++)
{
tmp.hi[0] = s->value[j];
tmp.lo[0] = s->value_lo[j];
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+j*h_dim]);
lis_quad_sub((LIS_QUAD *)t.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)tmp.hi);
}
lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)&h[jj+jj*h_dim]);
s->value[jj] = tmp.hi[0];
s->value_lo[jj] = tmp.lo[0];
}
/* x = x + y * z */
for(j=0;j<=ii;j++)
{
aa.hi[0] = s->value[j];
aa.lo[0] = s->value_lo[j];
lis_vector_axpyex_mmm(aa,z[j],x);
}
if( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
lis_matvec(A,x,v[0]);
lis_vector_xpay(b,-1.0,v[0]);
memset(v[0]->value_lo,0,n*sizeof(LIS_SCALAR));
lis_vector_nrm2(v[0],&rnorm);
bnrm2 = 1.0/rnorm;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter+1;
solver->resid = nrm2;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
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;
}
}
LIS_INT lis_gmres_switch(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR r,s,z,*v;
LIS_QUAD *h;
LIS_SCALAR *hd;
LIS_QUAD_PTR aa,bb,rr,a2,b2,t,one,tmp;
LIS_QUAD_PTR rnorm;
LIS_REAL bnrm2,nrm2,tol,tol2;
LIS_INT iter,maxiter,n,output;
LIS_INT iter2,maxiter2;
double time,ptime;
LIS_INT i,j,k,m;
LIS_INT ii,i1,iiv,i1v,iih,jj;
LIS_INT h_dim;
LIS_INT cs,sn;
LIS_DEBUG_FUNC_IN;
A = solver->A;
b = solver->b;
x = solver->x;
n = A->n;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
maxiter2 = solver->options[LIS_OPTIONS_SWITCH_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
tol2 = solver->params[LIS_PARAMS_SWITCH_RESID-LIS_OPTIONS_LEN];
m = solver->options[LIS_OPTIONS_RESTART];
h_dim = m+1;
ptime = 0.0;
s = solver->work[0];
r = solver->work[1];
z = solver->work[2];
v = &solver->work[3];
LIS_QUAD_SCALAR_MALLOC(aa,0,1);
LIS_QUAD_SCALAR_MALLOC(bb,1,1);
LIS_QUAD_SCALAR_MALLOC(rr,2,1);
LIS_QUAD_SCALAR_MALLOC(a2,3,1);
LIS_QUAD_SCALAR_MALLOC(b2,4,1);
LIS_QUAD_SCALAR_MALLOC(t,5,1);
LIS_QUAD_SCALAR_MALLOC(tmp,6,1);
LIS_QUAD_SCALAR_MALLOC(one,7,1);
LIS_QUAD_SCALAR_MALLOC(rnorm,8,1);
h = (LIS_QUAD *)lis_malloc( sizeof(LIS_QUAD)*(h_dim+1)*(h_dim+2),"lis_gmres_switch::h" );
hd = (LIS_SCALAR *)h;
cs = (m+1)*h_dim;
sn = (m+2)*h_dim;
one.hi[0] = 1.0;
one.lo[0] = 0.0;
z->precision = LIS_PRECISION_DEFAULT;
/* r = M^-1 * (b - A * x) */
lis_matvec(A,x,z);
lis_vector_xpay(b,-1.0,z);
lis_psolve(solver,z,v[0]);
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,v[0],&bnrm2) )
{
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol2 = solver->tol_switch;
iter=0;
while( iter<maxiter2 )
{
/* first column of V */
/* v = r / ||r||_2 */
lis_vector_nrm2(v[0],&rnorm.hi[0]);
lis_vector_scale(1.0/rnorm.hi[0],v[0]);
/* s = ||r||_2 e_1 */
lis_vector_set_all(0,s);
s->value[0] = rnorm.hi[0];
i = 0;
do
{
iter++;
i++;
ii = i-1;
i1 = i;
iiv = i-1;
i1v = i;
iih = (i-1)*h_dim;
/* z = M^-1 * v */
time = lis_wtime();
lis_psolve(solver,v[iiv],z);
ptime += lis_wtime()-time;
/* w = A * z */
lis_matvec(A,z, v[i1v]);
for(k=0;k<i;k++)
{
/* h[k,i] = <w,v[k]> */
/* w = w - h[k,i] * v[k] */
lis_vector_dot(v[i1v],v[k],&t.hi[0]);
hd[k+iih] = t.hi[0];
lis_vector_axpy(-t.hi[0],v[k],v[i1v]);
}
/* h[i+1,i] = ||w|| */
/* v[i+1] = w / h[i+1,i] */
lis_vector_nrm2(v[i1v],&t.hi[0]);
hd[i1+iih] = t.hi[0];
lis_vector_scale(1.0/t.hi[0],v[i1v]);
for(k=1;k<=ii;k++)
{
jj = k-1;
t.hi[0] = hd[jj+iih];
aa.hi[0] = hd[jj+cs]*t.hi[0];
aa.hi[0] += hd[jj+sn]*hd[k+iih];
bb.hi[0] = -hd[jj+sn]*t.hi[0];
bb.hi[0] += hd[jj+cs]*hd[k+iih];
hd[jj+iih] = aa.hi[0];
hd[k+iih] = bb.hi[0];
}
aa.hi[0] = hd[ii+iih];
bb.hi[0] = hd[i1+iih];
a2.hi[0] = aa.hi[0]*aa.hi[0];
b2.hi[0] = bb.hi[0]*bb.hi[0];
rr.hi[0] = sqrt(a2.hi[0]+b2.hi[0]);
if( rr.hi[0]==0.0 ) rr.hi[0]=1.0e-17;
hd[ii+cs] = aa.hi[0]/rr.hi[0];
hd[ii+sn] = bb.hi[0]/rr.hi[0];
s->value[i1] = -hd[ii+sn]*s->value[ii];
s->value[ii] = hd[ii+cs]*s->value[ii];
aa.hi[0] = hd[ii+cs]*hd[ii+iih];
aa.hi[0] += hd[ii+sn]*hd[i1+iih];
hd[ii+iih] = aa.hi[0];
/* convergence check */
nrm2 = fabs(s->value[i1])*bnrm2;
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol2 >= nrm2 ) break;
} while( i<m && iter <maxiter2 );
/* Solve H * Y = S for upper Hessenberg matrix H */
s->value[ii] = s->value[ii]/hd[ii+iih];
for(k=1;k<=ii;k++)
{
jj = ii-k;
t.hi[0] = s->value[jj];
for(j=jj+1;j<=ii;j++)
{
t.hi[0] -= hd[jj+j*h_dim]*s->value[j];
}
s->value[jj] = t.hi[0]/hd[jj+jj*h_dim];
}
/* z = z + y * v */
for(k=0;k<n;k++)
{
z->value[k] = s->value[0]*v[0]->value[k];
}
for(j=1;j<=ii;j++)
{
lis_vector_axpy(s->value[j],v[j],z);
}
/* r = M^-1 * z */
time = lis_wtime();
lis_psolve(solver,z,r);
ptime += lis_wtime()-time;
/* x = x + r */
lis_vector_axpy(1,r,x);
if( tol2 >= nrm2 )
{
solver->iter = iter;
solver->iter2 = iter;
solver->ptime = ptime;
break;
}
for(j=1;j<=i;j++)
{
jj = i1-j+1;
s->value[jj-1] = -hd[jj-1+sn]*s->value[jj];
s->value[jj] = hd[jj-1+cs]*s->value[jj];
}
for(j=0;j<=i1;j++)
{
t.hi[0] = s->value[j];
if( j==0 ) t.hi[0] = t.hi[0]-1.0;
lis_vector_axpy(t.hi[0],v[j],v[0]);
}
}
/* Initial Residual */
z->precision = LIS_PRECISION_QUAD;
solver->options[LIS_OPTIONS_INITGUESS_ZEROS] = LIS_FALSE;
lis_vector_copyex_mn(x,solver->xx);
lis_solver_get_initial_residual(solver,NULL,NULL,v[0],&bnrm2);
tol = solver->tol;
iter2=iter;
while( iter2<maxiter )
{
/* first column of V */
/* v = r / ||r||_2 */
lis_vector_nrm2ex_mm(v[0],&rnorm);
lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)one.hi,(LIS_QUAD *)rnorm.hi);
lis_vector_scaleex_mm(tmp,v[0]);
/* s = ||r||_2 e_1 */
lis_vector_set_allex_nm(0.0,s);
s->value[0] = rnorm.hi[0];
s->value_lo[0] = rnorm.lo[0];
i = 0;
do
{
iter2++;
i++;
ii = i-1;
i1 = i;
iiv = i-1;
i1v = i;
iih = (i-1)*h_dim;
/* z = M^-1 * v */
time = lis_wtime();
lis_psolve(solver,v[iiv],z);
ptime += lis_wtime()-time;
/* w = A * z */
lis_matvec(A,z, v[i1v]);
for(k=0;k<i;k++)
{
/* h[k,i] = <w,v[k]> */
/* w = w - h[k,i] * v[k] */
lis_vector_dotex_mmm(v[i1v],v[k],&t);
h[k+iih].hi = t.hi[0];
h[k+iih].lo = t.lo[0];
lis_quad_minus((LIS_QUAD *)t.hi);
lis_vector_axpyex_mmm(t,v[k],v[i1v]);
}
/* h[i+1,i] = ||w|| */
/* v[i+1] = w / h[i+1,i] */
lis_vector_nrm2ex_mm(v[i1v],&t);
h[i1+iih].hi = t.hi[0];
h[i1+iih].lo = t.lo[0];
lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)one.hi,(LIS_QUAD *)t.hi);
lis_vector_scaleex_mm(tmp,v[i1v]);
for(k=1;k<=ii;k++)
{
jj = k-1;
t.hi[0] = h[jj+iih].hi;
t.lo[0] = h[jj+iih].lo;
lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[jj+cs],(LIS_QUAD *)t.hi);
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+sn],(LIS_QUAD *)&h[k+iih]);
lis_quad_add((LIS_QUAD *)aa.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi);
lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)&h[jj+sn],(LIS_QUAD *)t.hi);
lis_quad_minus((LIS_QUAD *)bb.hi);
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+cs],(LIS_QUAD *)&h[k+iih]);
lis_quad_add((LIS_QUAD *)bb.hi,(LIS_QUAD *)bb.hi,(LIS_QUAD *)tmp.hi);
h[jj+iih].hi = aa.hi[0];
h[jj+iih].lo = aa.lo[0];
h[k+iih].hi = bb.hi[0];
h[k+iih].lo = bb.lo[0];
}
aa.hi[0] = h[ii+iih].hi;
aa.lo[0] = h[ii+iih].lo;
bb.hi[0] = h[i1+iih].hi;
bb.lo[0] = h[i1+iih].lo;
lis_quad_sqr((LIS_QUAD *)a2.hi,(LIS_QUAD *)aa.hi);
lis_quad_sqr((LIS_QUAD *)b2.hi,(LIS_QUAD *)bb.hi);
lis_quad_add((LIS_QUAD *)rr.hi,(LIS_QUAD *)a2.hi,(LIS_QUAD *)b2.hi);
lis_quad_sqrt((LIS_QUAD *)rr.hi,(LIS_QUAD *)rr.hi);
lis_quad_div((LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)aa.hi,(LIS_QUAD *)rr.hi);
lis_quad_div((LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)bb.hi,(LIS_QUAD *)rr.hi);
tmp.hi[0] = s->value[ii];
tmp.lo[0] = s->value_lo[ii];
lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)tmp.hi);
lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)tmp.hi);
lis_quad_minus((LIS_QUAD *)aa.hi);
s->value[i1] = aa.hi[0];
s->value_lo[i1] = aa.lo[0];
s->value[ii] = bb.hi[0];
s->value_lo[ii] = bb.lo[0];
lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)&h[ii+cs],(LIS_QUAD *)&h[ii+iih]);
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[ii+sn],(LIS_QUAD *)&h[i1+iih]);
lis_quad_add((LIS_QUAD *)aa.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi);
h[ii+iih].hi = aa.hi[0];
h[ii+iih].lo = aa.lo[0];
/* convergence check */
nrm2 = fabs(s->value[i1])*bnrm2;
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter2] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol >= nrm2 ) break;
} while( i<m && iter2 <maxiter );
/* Solve H * Y = S for upper Hessenberg matrix H */
tmp.hi[0] = s->value[ii];
tmp.lo[0] = s->value_lo[ii];
lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[ii+iih]);
s->value[ii] = tmp.hi[0];
s->value_lo[ii] = tmp.lo[0];
for(k=1;k<=ii;k++)
{
jj = ii-k;
t.hi[0] = s->value[jj];
t.lo[0] = s->value_lo[jj];
for(j=jj+1;j<=ii;j++)
{
tmp.hi[0] = s->value[j];
tmp.lo[0] = s->value_lo[j];
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj+j*h_dim]);
lis_quad_sub((LIS_QUAD *)t.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)tmp.hi);
}
lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)&h[jj+jj*h_dim]);
s->value[jj] = tmp.hi[0];
s->value_lo[jj] = tmp.lo[0];
}
/* z = z + y * v */
for(k=0;k<n;k++)
{
aa.hi[0] = s->value[0];
aa.lo[0] = s->value_lo[0];
bb.hi[0] = v[0]->value[k];
bb.lo[0] = v[0]->value_lo[k];
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)aa.hi,(LIS_QUAD *)bb.hi);
z->value[k] = tmp.hi[0];
z->value_lo[k] = tmp.lo[0];
}
for(j=1;j<=ii;j++)
{
aa.hi[0] = s->value[j];
aa.lo[0] = s->value_lo[j];
lis_vector_axpyex_mmm(aa,v[j],z);
}
/* r = M^-1 * z */
time = lis_wtime();
lis_psolve(solver,z,r);
ptime += lis_wtime()-time;
/* x = x + r */
lis_vector_axpyex_mmm(one,r,x);
if( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
solver->ptime = ptime;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
for(j=1;j<=i;j++)
{
jj = i1-j+1;
tmp.hi[0] = s->value[jj];
tmp.lo[0] = s->value_lo[jj];
lis_quad_mul((LIS_QUAD *)aa.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj-1+sn]);
lis_quad_mul((LIS_QUAD *)bb.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)&h[jj-1+cs]);
lis_quad_minus((LIS_QUAD *)aa.hi);
s->value[jj-1] = aa.hi[0];
s->value_lo[jj-1] = aa.lo[0];
s->value[jj] = bb.hi[0];
s->value_lo[jj] = bb.lo[0];
}
for(j=0;j<=i1;j++)
{
t.hi[0] = s->value[j];
t.lo[0] = s->value_lo[j];
if( j==0 )
{
lis_quad_sub((LIS_QUAD *)t.hi,(LIS_QUAD *)t.hi,(LIS_QUAD *)one.hi);
}
lis_vector_axpyex_mmm(t,v[j],v[0]);
}
}
solver->retcode = LIS_MAXITER;
solver->iter = iter2+1;
solver->iter2 = iter;
solver->resid = nrm2;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_ecr(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_SCALAR evalue;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,i,j,output;
LIS_INT nprocs,my_rank;
LIS_REAL nrm2,resid;
LIS_SCALAR lshift;
LIS_VECTOR r,p,Ax,Ar,Ap;
LIS_SCALAR alpha, beta;
LIS_SCALAR rAp, rp, ApAp, pAp, pp, ArAp, pAr;
double times,itimes,ptimes,p_c_times,p_i_times;
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);
r = esolver->work[0];
p = esolver->work[1];
Ax = esolver->work[2];
Ar = esolver->work[3];
Ap = esolver->work[4];
lis_vector_set_all(1.0,x);
lis_vector_nrm2(x,&nrm2);
lis_vector_scale(1/nrm2,x);
lis_matvec(A,x,Ax);
lis_vector_dot(x,Ax,&evalue);
lis_vector_axpyz(-evalue,x,Ax,r);
lis_vector_scale(-1.0,r);
lis_vector_copy(r,p);
lis_matvec(A,p,Ap);
iter=0;
while (iter<emaxiter)
{
iter = iter + 1;
lis_vector_dot(r,Ap,&rAp);
lis_vector_dot(r,p,&rp);
lis_vector_dot(Ap,Ap,&ApAp);
lis_vector_dot(p,Ap,&pAp);
lis_vector_dot(p,p,&pp);
alpha = (rAp - evalue * rp) / (ApAp - evalue * (2.0 * pAp - evalue * pp));
lis_vector_axpy(alpha,p,x);
lis_matvec(A,x,Ax);
lis_vector_dot(x,Ax,&evalue);
lis_vector_nrm2(x, &nrm2);
evalue = evalue / (nrm2 * nrm2);
lis_vector_axpyz(-evalue,x,Ax,r);
lis_vector_scale(-1.0,r);
lis_matvec(A,r,Ar);
lis_vector_dot(Ar,Ap,&ArAp);
lis_vector_dot(p,Ar,&pAr);
lis_vector_dot(r,Ap,&rAp);
lis_vector_dot(r,p,&rp);
beta = - (ArAp - evalue * ((pAr + rAp) - evalue * rp))/ (ApAp - evalue * (2.0 * pAp - evalue * pp));
lis_vector_xpay(r,beta,p);
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;
}
esolver->iter = iter;
esolver->resid = resid;
esolver->evalue[0] = evalue;
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
if (resid<tol)
{
esolver->retcode = LIS_SUCCESS;
return LIS_SUCCESS;
}
else
{
esolver->retcode = LIS_MAXITER;
return LIS_MAXITER;
}
}
LIS_INT lis_minres(LIS_SOLVER solver)
{
LIS_Comm comm;
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR v1,v2,v3,v4,w0,w1,w2;
LIS_REAL nrm2,tol;
LIS_SCALAR alpha;
LIS_REAL beta2,beta3;
LIS_SCALAR gamma1,gamma2,gamma3;
LIS_SCALAR delta,eta;
LIS_SCALAR sigma1,sigma2,sigma3;
LIS_SCALAR rho1,rho2,rho3;
LIS_REAL r0_euc,r_euc;
LIS_INT iter,maxiter,output;
double time,ptime;
LIS_DEBUG_FUNC_IN;
comm = LIS_COMM_WORLD;
A = solver->A;
b = solver->b;
x = solver->x;
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
ptime = 0.0;
v1 = solver->work[0];
v2 = solver->work[1];
v3 = solver->work[2];
v4 = solver->work[3];
w0 = solver->work[4];
w1 = solver->work[5];
w2 = solver->work[6];
/* Lanczos algorithm */
lis_matvec(A,x,v2);
lis_vector_xpay(b,-1.0,v2);
time = lis_wtime();
lis_psolve(solver,v2,v3);
ptime += lis_wtime()-time;
lis_vector_copy(v3,v2);
/* Compute elements of Hermitian tridiagonal matrix */
lis_vector_nrm2(v2,&r_euc);
eta = beta2 = r0_euc = r_euc;
gamma2 = gamma1 = 1.0;
sigma2 = sigma1 = 0.0;
lis_vector_set_all(0.0,v1);
lis_vector_set_all(0.0,w0);
lis_vector_set_all(0.0,w1);
nrm2 = r_euc / r0_euc;
for(iter=1;iter<=maxiter;iter++)
{
/* Lanczos algorithm */
lis_vector_scale(1.0 / beta2,v2);
lis_matvec(A,v2,v3);
time = lis_wtime();
lis_psolve(solver,v3,v4);
ptime += lis_wtime()-time;
lis_vector_dot(v2,v4,&alpha);
lis_vector_axpy(-alpha,v2,v4);
lis_vector_axpy(-beta2,v1,v4);
lis_vector_nrm2(v4,&beta3);
/* Compute elements of Hermitian tridiagonal matrix */
delta = gamma2 * alpha - gamma1 * sigma2 * beta2;
rho1 = sqrt(delta * delta + beta3 * beta3);
rho2 = sigma2 * alpha + gamma1 * gamma2 * beta2;
rho3 = sigma1 * beta2;
gamma3 = delta / rho1;
sigma3 = beta3 / rho1;
lis_vector_axpyz(-rho3,w0,v2,w2);
lis_vector_axpy(-rho2,w1,w2);
lis_vector_scale(1.0 / rho1,w2);
lis_vector_axpy(gamma3 * eta,w2,x);
/* convergence check */
r_euc *= fabs(sigma3);
nrm2 = r_euc / r0_euc;
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
if( output & LIS_PRINT_OUT ) lis_print_rhistory(comm,iter,nrm2);
}
if( nrm2 <= tol )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
eta *= -sigma3;
lis_vector_copy(v2,v1);
lis_vector_copy(v4,v2);
lis_vector_copy(w1,w0);
lis_vector_copy(w2,w1);
beta2 = beta3;
gamma1 = gamma2;
gamma2 = gamma3;
sigma1 = sigma2;
sigma2 = sigma3;
}
lis_vector_destroy(v1);
lis_vector_destroy(v2);
lis_vector_destroy(v3);
lis_vector_destroy(v4);
lis_vector_destroy(w0);
lis_vector_destroy(w1);
lis_vector_destroy(w2);
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_eai_quad(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_INT ss,ic;
LIS_INT emaxiter,iter0,hqriter;
LIS_REAL tol,hqrerr,D;
LIS_INT i,j;
LIS_INT output, niesolver;
LIS_REAL nrm2,resid0;
LIS_VECTOR *v,w;
LIS_SCALAR *h,*hq,*hr,evalue,evalue0;
LIS_SOLVER solver;
LIS_ESOLVER esolver2;
char esolvername[128],solvername[128],preconname[128];
LIS_INT nsol,precon_type;
ss = esolver->options[LIS_EOPTIONS_SUBSPACE];
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
niesolver = esolver->options[LIS_EOPTIONS_INNER_ESOLVER];
h = (LIS_SCALAR *)lis_malloc(ss*ss*sizeof(LIS_SCALAR), "lis_eai_quad::h");
hq = (LIS_SCALAR *)lis_malloc(ss*ss*sizeof(LIS_SCALAR), "lis_eai_quad::hq");
hr = (LIS_SCALAR *)lis_malloc(ss*ss*sizeof(LIS_SCALAR), "lis_eai_quad::hr");
A = esolver->A;
w = esolver->work[0];
v = &esolver->work[1];
lis_vector_set_all(0.0,v[0]);
lis_vector_set_all(1.0,w);
lis_vector_nrm2(w, &nrm2);
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p none",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_solver_get_solvername(nsol, solvername);
lis_solver_get_preconname(precon_type, preconname);
lis_esolver_get_esolvername(niesolver, esolvername);
if( A->my_rank==0 ) printf("inner eigensolver : %s\n", esolvername);
if( A->my_rank==0 ) printf("linear solver : %s\n", solvername);
if( A->my_rank==0 ) printf("preconditioner : %s\n", preconname);
for (i=0;i<ss*ss;i++) h[i] = 0.0;
j=-1;
while (j<ss-1)
{
j = j+1;
lis_vector_copy(w, v[j]);
/* w = A * v(j) */
lis_matvec(A, v[j], w);
/* reorthogonalization */
for (i=0;i<=j;i++)
{
/* h(i,j) = <v(i), w> */
lis_vector_dot(v[i], w, &h[i+j*ss]);
/* w = w - h(i,j) * v(i) */
lis_vector_axpy(-h[i+j*ss], v[i], w);
}
/* h(j+1,j) = ||w||_2 */
lis_vector_nrm2(w, &h[j+1+j*ss]);
/* convergence check */
if (fabs(h[j+1+j*ss])<tol) break;
/* v(j+1) = w / h(i+1,j) */
lis_vector_scale(1/h[j+1+j*ss],w);
lis_vector_copy(w,v[j+1]);
}
/* compute eigenvalues of a real upper
Hessenberg matrix H(j) = SH'(j)S^* */
lis_array_qr(ss,h,hq,hr,&hqriter,&hqrerr);
if( A->my_rank==0 )
{
#ifdef _LONG__LONG
printf("size of subspace : %lld\n\n", ss);
#else
printf("size of subspace : %d\n\n", ss);
#endif
if( output ) printf("approximate eigenvalues in subspace:\n\n");
i=0;
while (i<ss-1)
{
i = i + 1;
if (fabs(h[i+(i-1)*ss])<tol)
{
#ifdef _LONG__LONG
printf("Arnoldi: mode number = %lld\n",i-1);
#else
printf("Arnoldi: mode number = %d\n",i-1);
#endif
#ifdef _LONG__DOUBLE
printf("Arnoldi: eigenvalue = %Le\n",h[i-1+(i-1)*ss]);
#else
printf("Arnoldi: eigenvalue = %e\n",h[i-1+(i-1)*ss]);
#endif
esolver->evalue[i-1] = h[i-1+(i-1)*ss];
}
else
{
D = (h[i-1+(i-1)*ss]-h[i+i*ss]) * (h[i-1+(i-1)*ss]-h[i+i*ss])
+ 4 * h[i-1+i*ss] * h[i+(i-1)*ss];
if (D<0)
{
#ifdef _LONG__LONG
printf("Arnoldi: mode number = %lld\n",i-1);
#else
printf("Arnoldi: mode number = %d\n",i-1);
#endif
#ifdef _LONG__DOUBLE
printf("Arnoldi: eigenvalue = %Le + %Le i\n", (h[i-1+(i-1)*ss]+h[i+i*ss])/2, sqrt(-D)/2);
#else
printf("Arnoldi: eigenvalue = %e + %e i\n", (h[i-1+(i-1)*ss]+h[i+i*ss])/2, sqrt(-D)/2);
#endif
#ifdef _LONG__LONG
printf("Arnoldi: mode number = %lld\n",i);
#else
printf("Arnoldi: mode number = %d\n",i);
#endif
#ifdef _LONG__DOUBLE
printf("Arnoldi: eigenvalue = %Le - %Le i\n", (h[i-1+(i-1)*ss]+h[i+i*ss])/2, sqrt(-D)/2);
#else
printf("Arnoldi: eigenvalue = %e - %e i\n", (h[i-1+(i-1)*ss]+h[i+i*ss])/2, sqrt(-D)/2);
#endif
esolver->evalue[i-1] = (h[i-1+(i-1)*ss]+h[i+i*ss])/2;
esolver->evalue[i] = (h[i-1+(i-1)*ss]+h[i+i*ss])/2;
i=i+1;
}
else
{
#ifdef _LONG__LONG
printf("Arnoldi: mode number = %lld\n",i-1);
#else
printf("Arnoldi: mode number = %d\n",i-1);
#endif
#ifdef _LONG__DOUBLE
printf("Arnoldi: eigenvalue = %Le\n",h[i-1+(i-1)*ss]);
#else
printf("Arnoldi: eigenvalue = %e\n",h[i-1+(i-1)*ss]);
#endif
esolver->evalue[i-1] = h[i-1+(i-1)*ss];
}
}
}
if (i<ss)
{
#ifdef _LONG__LONG
printf("Arnoldi: mode number = %lld\n",i);
#else
printf("Arnoldi: mode number = %d\n",i);
#endif
#ifdef _LONG__DOUBLE
printf("Arnoldi: eigenvalue = %Le\n",h[i+i*ss]);
#else
printf("Arnoldi: eigenvalue = %e\n",h[i+i*ss]);
#endif
}
if( output ) printf("\n");
if( output ) printf("compute refined (real) eigenpairs, where imaginary parts are currently neglected:\n\n");
}
lis_esolver_create(&esolver2);
esolver2->options[LIS_EOPTIONS_ESOLVER] = niesolver;
esolver2->options[LIS_EOPTIONS_SUBSPACE] = 1;
esolver2->options[LIS_EOPTIONS_MAXITER] = emaxiter;
esolver2->options[LIS_EOPTIONS_OUTPUT] = esolver->options[LIS_EOPTIONS_OUTPUT];
esolver2->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN] = tol;
esolver2->eprecision = LIS_PRECISION_QUAD;
/* compute refined (real) eigenpairs, where imaginary parts are currently neglected */
for (i=0;i<ss;i++)
{
lis_vector_duplicate(A, &esolver->evector[i]);
esolver2->lshift = -(esolver->evalue[i]);
lis_esolve(A, esolver->evector[i], &evalue, esolver2);
lis_esolver_work_destroy(esolver2);
esolver->evalue[i] = evalue - esolver2->lshift;
esolver->iter[i] = esolver2->iter[0];
esolver->resid[i] = esolver2->resid[0];
if (i==0)
{
evalue0 = esolver->evalue[0];
iter0 = esolver2->iter[0];
resid0 = esolver2->resid[0];
if( output & LIS_EPRINT_MEM )
{
for (ic=0;ic<iter0+1;ic++)
{
esolver->rhistory[ic] = esolver2->rhistory[ic];
}
}
esolver->ptime = esolver2->ptime;
esolver->itime = esolver2->itime;
esolver->p_c_time = esolver2->p_c_time;
esolver->p_i_time = esolver2->p_i_time;
}
if (A->my_rank==0)
{
#ifdef _LONG__LONG
if( output ) printf("Arnoldi: mode number = %lld\n", i);
#else
if( output ) printf("Arnoldi: mode number = %d\n", i);
#endif
#ifdef _LONG__DOUBLE
if( output ) printf("Arnoldi: eigenvalue = %Le\n", esolver->evalue[i]);
#else
if( output ) printf("Arnoldi: eigenvalue = %e\n", esolver->evalue[i]);
#endif
#ifdef _LONG__LONG
if( output ) printf("Arnoldi: number of iterations = %lld\n",esolver2->iter[0]);
#else
if( output ) printf("Arnoldi: number of iterations = %d\n",esolver2->iter[0]);
#endif
#ifdef _LONG__DOUBLE
if( output ) printf("Arnoldi: relative residual = %Le\n\n",esolver2->resid[0]);
#else
if( output ) printf("Arnoldi: relative residual = %e\n\n",esolver2->resid[0]);
#endif
}
}
esolver->evalue[0] = evalue0;
esolver->iter[0] = iter0;
esolver->resid[0] = resid0;
lis_vector_copy(esolver->evector[0], esolver->x);
lis_esolver_destroy(esolver2);
lis_free(h);
lis_free(hq);
lis_free(hr);
lis_solver_destroy(solver);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
