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_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_gmres_quad(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
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_QUAD_PTR rnorm;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes;
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[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_quad::h" );
cs = (m+1)*h_dim;
sn = (m+2)*h_dim;
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;
iter=0;
while( iter<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
{
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);
ptimes += lis_wtime()-times;
/* v = Az */
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);
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]) * bnrm2;
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 */
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 + yv */
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 */
times = lis_wtime();
lis_psolve(solver, z, r);
ptimes += lis_wtime()-times;
/* x = x + r */
lis_vector_axpyex_mmm(one,r,x);
if( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->iter2 = 0;
solver->resid = nrm2;
solver->ptimes = ptimes;
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 = iter+1;
solver->iter2 = 0;
solver->resid = nrm2;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
