LIS_INT lis_cgs_switch(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,rtld, p,phat, q, qhat, u, uhat, vhat;
LIS_QUAD_PTR alpha, beta, rho, rho_old, tmpdot1, one;
LIS_REAL bnrm2, nrm2, tol, tol2;
LIS_INT iter,maxiter,n,output,conv;
LIS_INT iter2,maxiter2;
double times,ptimes;
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];
maxiter2 = solver->options[LIS_OPTIONS_SWITCH_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
tol2 = solver->params[LIS_PARAMS_SWITCH_RESID-LIS_OPTIONS_LEN];
ptimes = 0.0;
r = solver->work[0];
rtld = solver->work[1];
p = solver->work[2];
phat = solver->work[3];
q = solver->work[4];
qhat = solver->work[5];
u = solver->work[5];
uhat = solver->work[6];
vhat = solver->work[6];
LIS_QUAD_SCALAR_MALLOC(alpha,0,1);
LIS_QUAD_SCALAR_MALLOC(beta,1,1);
LIS_QUAD_SCALAR_MALLOC(rho,2,1);
LIS_QUAD_SCALAR_MALLOC(rho_old,3,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot1,4,1);
LIS_QUAD_SCALAR_MALLOC(one,6,1);
rho_old.hi[0] = 1.0;
rho_old.lo[0] = 0.0;
alpha.hi[0] = 1.0;
alpha.lo[0] = 0.0;
one.hi[0] = 1.0;
one.lo[0] = 0.0;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol2 = solver->tol_switch;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0, q);
lis_vector_set_allex_nm(0.0, p);
uhat->precision = LIS_PRECISION_DEFAULT;
p->precision = LIS_PRECISION_DEFAULT;
phat->precision = LIS_PRECISION_DEFAULT;
for( iter=1; iter<=maxiter2; iter++ )
{
/* rho = <rtld,r> */
lis_vector_dot(rtld,r,&rho.hi[0]);
/* test breakdown */
if( rho.hi[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
beta.hi[0] = (rho.hi[0] / rho_old.hi[0]);
/* u = r + beta*q */
lis_vector_axpyz(beta.hi[0],q,r,u);
/* p = u + beta*(q + beta*p) */
lis_vector_xpay(q,beta.hi[0],p);
lis_vector_xpay(u,beta.hi[0],p);
/* phat = M^-1 * p */
times = lis_wtime();
lis_psolve(solver, p, phat);
ptimes += lis_wtime()-times;
/* v = A * phat */
LIS_MATVEC(A,phat,vhat);
/* tmpdot1 = <rtld,vhat> */
lis_vector_dot(rtld,vhat,&tmpdot1.hi[0]);
/* test breakdown */
if( tmpdot1.hi[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
alpha.hi[0] = rho.hi[0] / tmpdot1.hi[0];
/* q = u - alpha*vhat */
lis_vector_axpyz(-alpha.hi[0],vhat,u,q);
/* phat = u + q */
/* uhat = M^-1 * (u + q) */
lis_vector_axpyz(1.0,u,q,phat);
times = lis_wtime();
lis_psolve(solver, phat, uhat);
ptimes += lis_wtime()-times;
/* x = x + alpha*uhat */
lis_vector_axpy(alpha.hi[0],uhat,x);
/* qhat = A * uhat */
LIS_MATVEC(A,uhat,qhat);
/* r = r - alpha*qhat */
lis_vector_axpy(-alpha.hi[0],qhat,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
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( nrm2 <= tol2 )
{
solver->iter = iter;
solver->iter2 = iter;
solver->ptimes = ptimes;
break;
}
rho_old.hi[0] = rho.hi[0];
}
uhat->precision = LIS_PRECISION_QUAD;
p->precision = LIS_PRECISION_QUAD;
phat->precision = LIS_PRECISION_QUAD;
solver->options[LIS_OPTIONS_INITGUESS_ZEROS] = LIS_FALSE;
lis_vector_copyex_mn(x,solver->xx);
rho_old.hi[0] = 1.0;
lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2);
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0, q);
lis_vector_set_allex_nm(0.0, p);
for( iter2=iter+1; iter2<=maxiter; iter2++ )
{
/* rho = <rtld,r> */
lis_vector_dotex_mmm(rtld,r,&rho);
/* test breakdown */
if( rho.hi[0]==0.0 && rho.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
/* u = r + beta*q */
lis_vector_axpyzex_mmmm(beta,q,r,u);
/* p = u + beta*(q + beta*p) */
lis_vector_xpayex_mmm(q,beta,p);
lis_vector_xpayex_mmm(u,beta,p);
/* phat = M^-1 * p */
times = lis_wtime();
lis_psolve(solver, p, phat);
ptimes += lis_wtime()-times;
/* v = A * phat */
LIS_MATVEC(A,phat,vhat);
/* tmpdot1 = <rtld,vhat> */
lis_vector_dotex_mmm(rtld,vhat,&tmpdot1);
/* test breakdown */
if( tmpdot1.hi[0]==0.0 && tmpdot1.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot1.hi);
/* q = u - alpha*vhat */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyzex_mmmm(alpha,vhat,u,q);
/* phat = u + q */
/* uhat = M^-1 * (u + q) */
lis_vector_axpyzex_mmmm(one,u,q,phat);
times = lis_wtime();
lis_psolve(solver, phat, uhat);
ptimes += lis_wtime()-times;
/* x = x + alpha*uhat */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,uhat,x);
/* qhat = A * uhat */
LIS_MATVEC(A,uhat,qhat);
/* r = r - alpha*qhat */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,qhat,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter2] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) printf("iter: %5d residual = %e\n", iter2, nrm2);
}
if( tol > nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
rho_old.hi[0] = rho.hi[0];
rho_old.lo[0] = rho.lo[0];
}
solver->retcode = LIS_MAXITER;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_crs_quad(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,rtld, p, q, u, z, ap, map, uq, auq;
LIS_QUAD_PTR alpha, beta, rho, rho_old, tmpdot1, one;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes;
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];
conv = solver->options[LIS_OPTIONS_CONV_COND];
ptimes = 0.0;
r = solver->work[0];
rtld = solver->work[1];
p = solver->work[2];
z = solver->work[3];
u = solver->work[3];
uq = solver->work[3];
q = solver->work[4];
ap = solver->work[4];
map = solver->work[5];
auq = solver->work[5];
LIS_QUAD_SCALAR_MALLOC(alpha,0,1);
LIS_QUAD_SCALAR_MALLOC(beta,1,1);
LIS_QUAD_SCALAR_MALLOC(rho,2,1);
LIS_QUAD_SCALAR_MALLOC(rho_old,3,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot1,4,1);
LIS_QUAD_SCALAR_MALLOC(one,6,1);
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,p);
LIS_MATVECT(A,p,rtld);
lis_vector_set_allex_nm(0.0,q);
lis_vector_set_allex_nm(0.0,p);
rho_old.hi[0] = 1.0;
rho_old.lo[0] = 0.0;
one.hi[0] = 1.0;
one.lo[0] = 0.0;
for( iter=1; iter<=maxiter; iter++ )
{
/* z = M^-1 * r */
/* rho = <rtld,z> */
times = lis_wtime();
lis_psolve(solver, r, z);
ptimes += lis_wtime()-times;
lis_vector_dotex_mmm(rtld,z,&rho);
/* test breakdown */
if( rho.hi[0]==0.0 && rho.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = rho / rho_old */
/* u = z + beta*q */
/* p = u + beta*(q + beta*p) */
/* ap = A * p */
/* map = M^-1 * ap */
/* tmpdot1 = <rtld,map> */
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
lis_vector_axpyzex_mmmm(beta,q,z,u);
lis_vector_xpayex_mmm(q,beta,p);
lis_vector_xpayex_mmm(u,beta,p);
LIS_MATVEC(A,p,ap);
times = lis_wtime();
lis_psolve(solver, ap, map);
ptimes += lis_wtime()-times;
lis_vector_dotex_mmm(rtld,map,&tmpdot1);
/* test breakdown */
if( tmpdot1.hi[0]==0.0 && tmpdot1.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
/* q = u - alpha*map */
/* uq = u + q */
/* auq = A * uq */
/* x = x + alpha*uq */
/* r = r - alpha*auq */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot1.hi);
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyzex_mmmm(alpha,map,u,q);
lis_vector_axpyzex_mmmm(one,u,q,uq);
LIS_MATVEC(A,uq,auq);
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,uq,x);
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,auq,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter] = nrm2;
if( output & LIS_PRINT_OUT ) printf("iter: %5d residual = %e\n", iter, nrm2);
}
if( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
rho_old.hi[0] = rho.hi[0];
rho_old.lo[0] = rho.lo[0];
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
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_cgs_quad(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_VECTOR r,rtld, p,phat, q, qhat, u, uhat, vhat;
LIS_QUAD_PTR alpha, beta, rho, rho_old, tmpdot1, one;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,output,conv;
double time,ptime;
LIS_DEBUG_FUNC_IN;
A = solver->A;
x = solver->x;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
ptime = 0.0;
r = solver->work[0];
rtld = solver->work[1];
p = solver->work[2];
phat = solver->work[3];
q = solver->work[4];
qhat = solver->work[5];
u = solver->work[5];
uhat = solver->work[6];
vhat = solver->work[6];
LIS_QUAD_SCALAR_MALLOC(alpha,0,1);
LIS_QUAD_SCALAR_MALLOC(beta,1,1);
LIS_QUAD_SCALAR_MALLOC(rho,2,1);
LIS_QUAD_SCALAR_MALLOC(rho_old,3,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot1,4,1);
LIS_QUAD_SCALAR_MALLOC(one,6,1);
rho_old.hi[0] = 1.0;
rho_old.lo[0] = 0.0;
alpha.hi[0] = 1.0;
alpha.lo[0] = 0.0;
one.hi[0] = 1.0;
one.lo[0] = 0.0;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0, q);
lis_vector_set_allex_nm(0.0, p);
for( iter=1; iter<=maxiter; iter++ )
{
/* rho = <rtld,r> */
lis_vector_dotex_mmm(rtld,r,&rho);
/* test breakdown */
if( rho.hi[0]==0.0 && rho.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
/* u = r + beta*q */
lis_vector_axpyzex_mmmm(beta,q,r,u);
/* p = u + beta*(q + beta*p) */
lis_vector_xpayex_mmm(q,beta,p);
lis_vector_xpayex_mmm(u,beta,p);
/* phat = M^-1 * p */
time = lis_wtime();
lis_psolve(solver, p, phat);
ptime += lis_wtime()-time;
/* v = A * phat */
lis_matvec(A,phat,vhat);
/* tmpdot1 = <rtld,vhat> */
lis_vector_dotex_mmm(rtld,vhat,&tmpdot1);
/* test breakdown */
if( tmpdot1.hi[0]==0.0 && tmpdot1.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot1.hi);
/* q = u - alpha*vhat */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyzex_mmmm(alpha,vhat,u,q);
/* phat = u + q */
/* uhat = M^-1 * (u + q) */
lis_vector_axpyzex_mmmm(one,u,q,phat);
time = lis_wtime();
lis_psolve(solver, phat, uhat);
ptime += lis_wtime()-time;
/* x = x + alpha*uhat */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,uhat,x);
/* qhat = A * uhat */
lis_matvec(A,uhat,qhat);
/* r = r - alpha*qhat */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,qhat,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
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 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
rho_old.hi[0] = rho.hi[0];
rho_old.lo[0] = rho.lo[0];
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_bicg_switch(LIS_SOLVER solver)
{
LIS_MATRIX A,At;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,rtld, z,ztld,p, ptld, q, qtld;
LIS_QUAD_PTR alpha, beta, rho, rho_old, tmpdot1;
LIS_REAL bnrm2, nrm2, tol, tol2;
LIS_INT iter,maxiter,n,output,conv;
LIS_INT iter2,maxiter2;
double times,ptimes;
LIS_DEBUG_FUNC_IN;
A = solver->A;
At = solver->A;
M = solver->precon;
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];
conv = solver->options[LIS_OPTIONS_CONV_COND];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
tol2 = solver->params[LIS_PARAMS_SWITCH_RESID-LIS_OPTIONS_LEN];
ptimes = 0.0;
r = solver->work[0];
rtld = solver->work[1];
z = solver->work[2];
ztld = solver->work[3];
p = solver->work[4];
ptld = solver->work[5];
q = solver->work[2];
qtld = solver->work[3];
LIS_QUAD_SCALAR_MALLOC(alpha,0,1);
LIS_QUAD_SCALAR_MALLOC(beta,1,1);
LIS_QUAD_SCALAR_MALLOC(rho,2,1);
LIS_QUAD_SCALAR_MALLOC(rho_old,3,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot1,4,1);
rho_old.hi[0] = 1.0;
rho_old.lo[0] = 0.0;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol2 = solver->tol_switch;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0, p);
lis_vector_set_allex_nm(0.0, ptld);
r->precision = LIS_PRECISION_DEFAULT;
rtld->precision = LIS_PRECISION_DEFAULT;
p->precision = LIS_PRECISION_DEFAULT;
ptld->precision = LIS_PRECISION_DEFAULT;
for( iter=1; iter<=maxiter2; iter++ )
{
/* z = M^-1 * r */
/* ztld = M^-T * rtld */
times = lis_wtime();
lis_psolve(solver, r, z);
lis_psolvet(solver, rtld, ztld);
ptimes += lis_wtime()-times;
/* rho = <z,rtld> */
lis_vector_dot(z,rtld,&rho.hi[0]);
/* test breakdown */
if( rho.hi[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
beta.hi[0] = rho.hi[0] / rho_old.hi[0];
/* p = z + beta*p */
/* ptld = ztld + beta*ptld */
/* q = A * p */
/* qtld = A^T * ptld */
lis_vector_xpay(z,beta.hi[0],p);
LIS_MATVEC(A,p,q);
lis_vector_xpay(ztld,beta.hi[0],ptld);
LIS_MATVECT(At,ptld,qtld);
/* tmpdot1 = <ptld,q> */
lis_vector_dot(ptld,q,&tmpdot1.hi[0]);
/* test breakdown */
if( tmpdot1.hi[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
alpha.hi[0] = rho.hi[0] / tmpdot1.hi[0];
/* x = x + alpha*p */
lis_vector_axpy(alpha.hi[0],p,x);
/* r = r - alpha*q */
lis_vector_axpy(-alpha.hi[0],q,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( nrm2 <= tol2 )
{
solver->iter = iter;
solver->iter2 = iter;
solver->ptimes = ptimes;
break;
}
/* rtld = rtld - alpha*qtld */
lis_vector_axpy(-alpha.hi[0],qtld,rtld);
rho_old.hi[0] = rho.hi[0];
}
r->precision = LIS_PRECISION_QUAD;
rtld->precision = LIS_PRECISION_QUAD;
p->precision = LIS_PRECISION_QUAD;
ptld->precision = LIS_PRECISION_QUAD;
/* solver->precon->precon_type = 0;*/
solver->options[LIS_OPTIONS_INITGUESS_ZEROS] = LIS_FALSE;
lis_vector_copyex_mn(x,solver->xx);
rho_old.hi[0] = 1.0;
lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2);
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0, p);
lis_vector_set_allex_nm(0.0, ptld);
for( iter2=iter+1; iter2<=maxiter; iter2++ )
{
/* z = M^-1 * r */
/* ztld = M^-T * rtld */
times = lis_wtime();
lis_psolve(solver, r, z);
lis_psolvet(solver, rtld, ztld);
/* memset(z->value_lo,0,n*sizeof(LIS_SCALAR));
memset(ztld->value_lo,0,n*sizeof(LIS_SCALAR));*/
ptimes += lis_wtime()-times;
/* rho = <z,rtld> */
lis_vector_dotex_mmm(z,rtld,&rho);
/* printf("rho = %e %e\n",rho.hi[0],rho.lo[0]);*/
/* test breakdown */
if( rho.hi[0]==0.0 && rho.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter2;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
/* p = z + beta*p */
/* ptld = ztld + beta*ptld */
/* q = A * p */
/* qtld = A^T * ptld */
lis_vector_xpayex_mmm(z,beta,p);
LIS_MATVEC(A,p,q);
lis_vector_xpayex_mmm(ztld,beta,ptld);
LIS_MATVECT(At,ptld,qtld);
/* tmpdot1 = <ptld,q> */
lis_vector_dotex_mmm(ptld,q,&tmpdot1);
/* test breakdown */
if( tmpdot1.hi[0]==0.0 && tmpdot1.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter2;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot1.hi);
/* x = x + alpha*p */
lis_vector_axpyex_mmm(alpha,p,x);
/* r = r - alpha*q */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,q,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter2] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol > nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* rtld = rtld - alpha*qtld */
lis_vector_axpyex_mmm(alpha,qtld,rtld);
rho_old.hi[0] = rho.hi[0];
rho_old.lo[0] = rho.lo[0];
}
solver->retcode = LIS_MAXITER;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
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_psolve_adds(LIS_SOLVER solver, LIS_VECTOR B, LIS_VECTOR X)
{
LIS_INT i,k,n,np,iter,ptype;
LIS_SCALAR *b,*x,*w,*r,*rl;
LIS_VECTOR W,R;
LIS_PRECON precon;
LIS_QUAD_DECLAR;
LIS_DEBUG_FUNC_IN;
precon = solver->precon;
n = precon->A->n;
np = precon->A->np;
W = precon->work[0];
R = precon->work[1];
b = B->value;
x = X->value;
w = W->value;
r = R->value;
rl = R->value_lo;
iter = solver->options[LIS_OPTIONS_ADDS_ITER];
ptype = solver->options[LIS_OPTIONS_PRECON];
#ifdef USE_QUAD_PRECISION
if( solver->precision==LIS_PRECISION_DEFAULT )
{
#endif
lis_vector_set_all(0.0,X);
lis_vector_copy(B,R);
for(k=0;k<iter+1;k++)
{
for(i=n;i<np;i++)
{
r[i] = 0.0;
}
lis_psolve_xxx[ptype](solver,R,W);
#ifdef _OPENMP
#pragma omp parallel for private(i)
#endif
for(i=0;i<n;i++)
{
x[i] += w[i];
}
if(k!=iter)
{
lis_matvec(precon->A,X,R);
#ifdef _OPENMP
#pragma omp parallel for private(i)
#endif
for(i=0;i<n;i++)
{
r[i] = b[i] - r[i];
}
}
}
#ifdef USE_QUAD_PRECISION
}
else
{
lis_vector_set_allex_nm(0.0,X);
lis_vector_copyex_mm(B,R);
for(k=0;k<iter+1;k++)
{
for(i=n;i<np;i++)
{
r[i] = 0.0;
rl[i] = 0.0;
}
lis_psolve_xxx[ptype](solver,R,W);
for(i=0;i<n;i++)
{
#ifndef USE_SSE2
LIS_QUAD_ADD(X->value[i],X->value_lo[i],X->value[i],X->value_lo[i],W->value[i],W->value_lo[i]);
#else
LIS_QUAD_ADD_SSE2(X->value[i],X->value_lo[i],X->value[i],X->value_lo[i],W->value[i],W->value_lo[i]);
#endif
/* x[i] += w[i];*/
}
if(k==iter) break;
lis_matvec(precon->A,X,R);
for(i=0;i<n;i++)
{
#ifndef USE_SSE2
LIS_QUAD_ADD(R->value[i],R->value_lo[i],B->value[i],B->value_lo[i],-R->value[i],-R->value_lo[i]);
#else
LIS_QUAD_ADD_SSE2(R->value[i],R->value_lo[i],B->value[i],B->value_lo[i],-R->value[i],-R->value_lo[i]);
#endif
/* r[i] = b[i] - r[i];*/
}
}
}
#endif
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
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 lis_psolvet_hybrid(LIS_SOLVER solver, LIS_VECTOR B, LIS_VECTOR X)
{
LIS_VECTOR xx;
LIS_SOLVER solver2;
LIS_INT nsolver;
LIS_PRECON precon;
/*
* Mx = b
* M = A
*/
LIS_DEBUG_FUNC_IN;
precon = solver->precon;
solver2 = precon->solver;
xx = precon->solver->x;
nsolver = solver2->options[LIS_OPTIONS_SOLVER];
solver2->b = B;
LIS_MATVEC = lis_matvect;
LIS_MATVECT = lis_matvec;
if( solver2->options[LIS_OPTIONS_INITGUESS_ZEROS] )
{
#ifdef USE_QUAD_PRECISION
if( solver->precision==LIS_PRECISION_DEFAULT )
{
#endif
lis_vector_set_all(0,xx);
#ifdef USE_QUAD_PRECISION
}
else
{
lis_vector_set_allex_nm(0,xx);
}
#endif
}
else
{
#ifdef USE_QUAD_PRECISION
if( solver->precision==LIS_PRECISION_DEFAULT )
{
#endif
lis_vector_copy(B,xx);
#ifdef USE_QUAD_PRECISION
}
else
{
lis_vector_copyex_mm(B,xx);
}
#endif
}
/* execute solver */
lis_solver_execute[nsolver](solver2);
#ifdef USE_QUAD_PRECISION
if( solver->precision==LIS_PRECISION_DEFAULT )
{
#endif
lis_vector_copy(solver2->x,X);
#ifdef USE_QUAD_PRECISION
}
else
{
lis_vector_copyex_mm(solver2->x,X);
}
#endif
LIS_MATVEC = lis_matvec;
LIS_MATVECT = lis_matvect;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
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;
}
LIS_INT lis_esolve(LIS_MATRIX A, LIS_VECTOR x, LIS_SCALAR *evalue0, LIS_ESOLVER esolver)
{
LIS_INT nesolver,niesolver,emaxiter;
LIS_SCALAR *evalue;
LIS_VECTOR *evector;
LIS_SCALAR *resid;
LIS_SCALAR *rhistory;
LIS_INT *iter,*iter2;
LIS_INT err;
LIS_INT output;
LIS_INT ss, mode;
double time;
double gshift;
LIS_INT estorage,eblock;
LIS_MATRIX B;
LIS_INT eprecision;
LIS_VECTOR xx;
LIS_DEBUG_FUNC_IN;
/* begin parameter check */
err = lis_matrix_check(A,LIS_MATRIX_CHECK_ALL);
if( err ) return err;
if( x==NULL )
{
LIS_SETERR(LIS_ERR_ILL_ARG,"vector x is undefined\n");
return LIS_ERR_ILL_ARG;
}
if( A->n!=x->n )
{
return LIS_ERR_ILL_ARG;
}
if( A->gn<=0 )
{
LIS_SETERR1(LIS_ERR_ILL_ARG,"Size n(=%d) of matrix A is less than 0\n",A->gn);
return LIS_ERR_ILL_ARG;
}
nesolver = esolver->options[LIS_EOPTIONS_ESOLVER];
niesolver = esolver->options[LIS_EOPTIONS_INNER_ESOLVER];
ss = esolver->options[LIS_EOPTIONS_SUBSPACE];
mode = esolver->options[LIS_EOPTIONS_MODE];
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
gshift = esolver->params[LIS_EPARAMS_SHIFT - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
estorage = esolver->options[LIS_EOPTIONS_STORAGE];
eblock = esolver->options[LIS_EOPTIONS_STORAGE_BLOCK];
eprecision = esolver->options[LIS_EOPTIONS_PRECISION];
esolver->eprecision = eprecision;
if( nesolver < 1 || nesolver > LIS_ESOLVER_LEN )
{
LIS_SETERR2(LIS_ERR_ILL_ARG,"Parameter LIS_EOPTIONS_ESOLVER is %d (Set between 1 to %d)\n",nesolver, LIS_ESOLVER_LEN);
return LIS_ERR_ILL_ARG;
}
if( niesolver < 1 || niesolver > 7 )
{
LIS_SETERR1(LIS_ERR_ILL_ARG,"Parameter LIS_EOPTIONS_INNER_ESOLVER is %d (Set between 1 to 7)\n", niesolver);
return LIS_ERR_ILL_ARG;
}
if ( esolver->options[LIS_EOPTIONS_ESOLVER] == LIS_ESOLVER_SI && niesolver > 4 )
{
LIS_SETERR1(LIS_ERR_ILL_ARG,"Parameter LIS_EOPTIONS_INNER_ESOLVER is %d (Set between 1 to 4 for Subspace)\n", niesolver);
return LIS_ERR_ILL_ARG;
}
if ( esolver->options[LIS_EOPTIONS_ESOLVER] == LIS_ESOLVER_LI && niesolver == LIS_ESOLVER_PI )
{
LIS_SETERR1(LIS_ERR_ILL_ARG,"Parameter LIS_EOPTIONS_INNER_ESOLVER is %d (Set between 2 to 7 for Lanczos)\n", niesolver);
return LIS_ERR_ILL_ARG;
}
if ( esolver->options[LIS_EOPTIONS_ESOLVER] == LIS_ESOLVER_AI && (( niesolver == LIS_ESOLVER_PI ) || ( niesolver == LIS_ESOLVER_CG) || ( niesolver == LIS_ESOLVER_JD)) )
{
LIS_SETERR1(LIS_ERR_ILL_ARG,"Parameter LIS_EOPTIONS_INNER_ESOLVER is %d (Set between 2 to 4 or 6 for Arnoldi)\n", niesolver);
return LIS_ERR_ILL_ARG;
}
if ( esolver->options[LIS_EOPTIONS_ESOLVER] == LIS_ESOLVER_SI && ss > A->gn )
{
LIS_SETERR2(LIS_ERR_ILL_ARG,"Parameter LIS_EOPTIONS_SUBSPACE is %d (Set less than or equal to matrix size %d for Subspace)\n", ss, A->gn);
return LIS_ERR_ILL_ARG;
}
if (( esolver->options[LIS_EOPTIONS_ESOLVER] == LIS_ESOLVER_LI || esolver->options[LIS_EOPTIONS_ESOLVER] == LIS_ESOLVER_AI ) && ss > A->gn )
{
LIS_SETERR2(LIS_ERR_ILL_ARG,"Parameter LIS_EOPTIONS_SUBSPACE is %d (Set less than or equal to matrix size %d for Lanczos and Arnoldi)\n", ss, A->gn);
return LIS_ERR_ILL_ARG;
}
if ( esolver->options[LIS_EOPTIONS_ESOLVER] == LIS_ESOLVER_SI && mode >= ss )
{
LIS_SETERR2(LIS_ERR_ILL_ARG,"Parameter LIS_EOPTIONS_MODE is %d (Set less than subspace size %d for Subspace)\n", mode, ss);
return LIS_ERR_ILL_ARG;
}
if ( esolver->options[LIS_EOPTIONS_ESOLVER] == ( LIS_ESOLVER_LI || LIS_ESOLVER_AI ) && mode >= ss )
{
LIS_SETERR2(LIS_ERR_ILL_ARG,"Parameter LIS_EOPTIONS_MODE is %d (Set less than subspace size %d for Lanczos or Arnoldi)\n", mode, ss);
return LIS_ERR_ILL_ARG;
}
#ifdef USE_QUAD_PRECISION
if( eprecision==LIS_PRECISION_QUAD && lis_esolver_execute_quad[nesolver]==NULL )
{
LIS_SETERR1(LIS_ERR_NOT_IMPLEMENTED,"Quad precision eigensolver %s is not implemented\n",lis_esolvername[nesolver]);
return LIS_ERR_NOT_IMPLEMENTED;
}
else if( eprecision==LIS_PRECISION_SWITCH && lis_esolver_execute_switch[nesolver]==NULL )
{
LIS_SETERR1(LIS_ERR_NOT_IMPLEMENTED,"Switch esolver %s is not implemented\n",lis_esolvername[nesolver]);
return LIS_ERR_NOT_IMPLEMENTED;
}
if( esolver->options[LIS_EOPTIONS_SWITCH_MAXITER]==-1 )
{
esolver->options[LIS_EOPTIONS_SWITCH_MAXITER] = emaxiter;
}
#endif
/* create eigenvalue array */
if( esolver->evalue ) lis_free(esolver->evalue);
evalue = (LIS_SCALAR *)lis_malloc((ss+2)*sizeof(LIS_SCALAR),"lis_esolve::evalue");
if( evalue==NULL )
{
LIS_SETERR_MEM((ss+2)*sizeof(LIS_SCALAR));
esolver->retcode = err;
return err;
}
evalue[0] = 1.0;
evalue[ss-1] = 1.0;
/* create residual norm array */
if( esolver->resid ) lis_free(esolver->resid);
resid = (LIS_SCALAR *)lis_malloc((ss+2)*sizeof(LIS_SCALAR),"lis_esolve::resid");
if( resid==NULL )
{
LIS_SETERR_MEM((ss+2)*sizeof(LIS_SCALAR));
esolver->retcode = err;
return err;
}
/* create number of iterations array */
if( esolver->iter ) lis_free(esolver->iter);
iter = (LIS_INT *)lis_malloc((ss+2)*sizeof(LIS_SCALAR),"lis_esolve::iter");
if( iter==NULL )
{
LIS_SETERR_MEM((ss+2)*sizeof(LIS_SCALAR));
esolver->retcode = err;
return err;
}
/* create quad precision number of iterations array */
if( esolver->iter2 ) lis_free(esolver->iter2);
iter2 = (LIS_INT *)lis_malloc((ss+2)*sizeof(LIS_SCALAR),"lis_esolve::iter2");
if( iter2==NULL )
{
LIS_SETERR_MEM((ss+2)*sizeof(LIS_SCALAR));
esolver->retcode = err;
return err;
}
/* create initial vector */
#ifndef USE_QUAD_PRECISION
err = lis_vector_duplicate(A,&xx);
#else
if( eprecision==LIS_PRECISION_DOUBLE )
{
err = lis_vector_duplicate(A,&xx);
}
else
{
err = lis_vector_duplicateex(LIS_PRECISION_QUAD,A,&xx);
}
#endif
if( err )
{
esolver->retcode = err;
return err;
}
if( esolver->options[LIS_EOPTIONS_INITGUESS_ONES] )
{
if( output ) lis_printf(A->comm,"initial vector x : 1\n");
#ifndef USE_QUAD_PRECISION
lis_vector_set_all(1.0,xx);
#else
if( eprecision==LIS_PRECISION_DOUBLE )
{
lis_vector_set_all(1.0,xx);
}
else
{
lis_vector_set_allex_nm(1.0,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( eprecision==LIS_PRECISION_DOUBLE )
{
lis_vector_copy(x,xx);
}
else
{
lis_vector_copyex_nm(x,xx);
}
#endif
}
/* global shift */
if ( output ) if( A->my_rank==0 ) printf("shift : %e\n", gshift);
/* create eigenvector array */
if( esolver->evector ) lis_free(esolver->evector);
evector = (LIS_VECTOR *)lis_malloc((ss+2)*sizeof(LIS_VECTOR),"lis_esolve::evector");
if( evector==NULL )
{
LIS_SETERR_MEM((ss+2)*sizeof(LIS_VECTOR));
esolver->retcode = err;
return err;
}
/* create residual history array */
if( esolver->rhistory ) lis_free(esolver->rhistory);
rhistory = (LIS_SCALAR *)lis_malloc((emaxiter+2)*sizeof(LIS_SCALAR),"lis_esolve::rhistory");
if( rhistory==NULL )
{
LIS_SETERR_MEM((emaxiter+2)*sizeof(LIS_SCALAR));
lis_vector_destroy(xx);
esolver->retcode = err;
return err;
}
/* convert matrix */
if( estorage>0 && A->matrix_type!=estorage )
{
err = lis_matrix_duplicate(A,&B);
if( err ) return err;
lis_matrix_set_blocksize(B,eblock,eblock,NULL,NULL);
lis_matrix_set_type(B,estorage);
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);
}
esolver->A = A;
esolver->evalue = evalue;
esolver->x = x;
esolver->evector = evector;
rhistory[0] = 1.0;
esolver->rhistory = rhistory;
esolver->resid = resid;
esolver->iter = iter;
esolver->iter2 = iter2;
if( A->my_rank==0 )
{
#ifdef _LONG__DOUBLE
if ( output ) printf("precision : long double\n");
#else
if ( output ) printf("precision : %s\n", lis_eprecisionname[eprecision]);
#endif
#ifdef _LONG__LONG
if ( output ) printf("eigensolver : %s\n", lis_esolvername[nesolver]);
#else
if ( output ) printf("eigensolver : %s\n", lis_esolvername[nesolver]);
#endif
}
if( A->my_rank==0 )
{
#ifdef _LONG__DOUBLE
if ( output ) printf("convergence condition : ||lx-Ax||_2 <= %6.1Le * ||lx||_2\n", esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN]);
#else
if ( output ) printf("convergence condition : ||lx-Ax||_2 <= %6.1e * ||lx||_2\n", esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN]);
#endif
}
if( A->my_rank==0 )
{
if( A->matrix_type==LIS_MATRIX_BSR || A->matrix_type==LIS_MATRIX_BSC )
{
#ifdef _LONG__LONG
if ( output ) printf("matrix storage format : %s(%lld x %lld)\n", lis_estoragename[A->matrix_type-1],eblock,eblock);
#else
if ( output ) printf("matrix storage format : %s(%d x %d)\n", lis_estoragename[A->matrix_type-1],eblock,eblock);
#endif
}
else
{
if ( output ) printf("matrix storage format : %s\n", lis_estoragename[A->matrix_type-1]);
}
}
time = lis_wtime();
esolver->ptime = 0;
esolver->itime = 0;
esolver->p_c_time = 0;
esolver->p_i_time = 0;
if (gshift != 0.0) lis_matrix_shift_diagonal(A, gshift);
/* create work vector */
err = lis_esolver_malloc_work[nesolver](esolver);
if( err )
{
lis_vector_destroy(xx);
esolver->retcode = err;
return err;
}
esolver->x = xx;
esolver->xx = x;
/* execute esolver */
#ifndef USE_QUAD_PRECISION
err = lis_esolver_execute[nesolver](esolver);
#else
if( eprecision==LIS_PRECISION_DOUBLE )
{
err = lis_esolver_execute[nesolver](esolver);
}
else if( eprecision==LIS_PRECISION_QUAD )
{
err = lis_esolver_execute_quad[nesolver](esolver);
}
else if( eprecision==LIS_PRECISION_SWITCH )
{
err = lis_esolver_execute_switch[nesolver](esolver);
}
#endif
esolver->retcode = err;
*evalue0 = esolver->evalue[0];
lis_vector_copy(esolver->x, x);
esolver->time = lis_wtime() - time;
lis_matrix_shift_diagonal(A, -gshift);
if( A->my_rank==0 )
{
if( err )
{
#ifdef _LONG__LONG
if ( output ) printf("eigensolver status : %s(code=%lld)\n\n",lis_ereturncode[err],err);
#else
if ( output ) printf("eigensolver status : %s(code=%d)\n\n",lis_ereturncode[err],err);
#endif
}
else
{
if ( output ) printf("eigensolver status : normal end\n\n");
}
}
if( eprecision==LIS_PRECISION_DOUBLE )
{
esolver->iter2[mode] = esolver->iter[mode];
}
else if( eprecision==LIS_PRECISION_QUAD )
{
esolver->iter2[mode] = 0;
}
lis_vector_destroy(xx);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
LIS_INT lis_bicgstab_switch(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,rtld, t,p,v, s, phat, shat;
LIS_QUAD_PTR alpha, beta, omega, rho, rho_old, tmpdot1, tmpdot2;
LIS_REAL bnrm2, nrm2, tol, tol2;
LIS_INT iter,maxiter,n,output,conv;
LIS_INT iter2,maxiter2;
double times,ptimes;
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];
maxiter2 = solver->options[LIS_OPTIONS_SWITCH_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
tol2 = solver->params[LIS_PARAMS_SWITCH_RESID-LIS_OPTIONS_LEN];
ptimes = 0.0;
rtld = solver->work[0];
r = solver->work[1];
s = solver->work[1];
t = solver->work[2];
p = solver->work[3];
v = solver->work[4];
phat = solver->work[5];
shat = solver->work[6];
LIS_QUAD_SCALAR_MALLOC(alpha,0,1);
LIS_QUAD_SCALAR_MALLOC(beta,1,1);
LIS_QUAD_SCALAR_MALLOC(rho,2,1);
LIS_QUAD_SCALAR_MALLOC(rho_old,3,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot1,4,1);
LIS_QUAD_SCALAR_MALLOC(omega,6,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot2,7,1);
rho_old.hi[0] = 1.0;
rho_old.lo[0] = 0.0;
alpha.hi[0] = 1.0;
alpha.lo[0] = 0.0;
omega.hi[0] = 1.0;
omega.lo[0] = 0.0;
lis_vector_set_allex_nm(0.0, p);
lis_vector_set_allex_nm(0.0, phat);
lis_vector_set_allex_nm(0.0, s);
lis_vector_set_allex_nm(0.0, shat);
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol2 = solver->tol_switch;
lis_solver_set_shadowresidual(solver,r,rtld);
s->precision = LIS_PRECISION_DEFAULT;
shat->precision = LIS_PRECISION_DEFAULT;
p->precision = LIS_PRECISION_DEFAULT;
phat->precision = LIS_PRECISION_DEFAULT;
for( iter=1; iter<=maxiter2; iter++ )
{
/* rho = <rtld,r> */
lis_vector_dot(rtld,r,&rho.hi[0]);
/* test breakdown */
if( rho.hi[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
if( iter==1 )
{
lis_vector_copy(r,p);
}
else
{
/* beta = (rho / rho_old) * (alpha / omega) */
beta.hi[0] = (rho.hi[0] / rho_old.hi[0]) * (alpha.hi[0] / omega.hi[0]);
/* p = r + beta*(p - omega*v) */
lis_vector_axpy(-omega.hi[0],v,p);
lis_vector_xpay(r,beta.hi[0],p);
}
/* phat = M^-1 * p */
times = lis_wtime();
lis_psolve(solver, p, phat);
ptimes += lis_wtime()-times;
/* v = A * phat */
LIS_MATVEC(A,phat,v);
/* tmpdot1 = <rtld,v> */
lis_vector_dot(rtld,v,&tmpdot1.hi[0]);
/* test breakdown */
/* */
/* alpha = rho / tmpdot1 */
alpha.hi[0] = rho.hi[0] / tmpdot1.hi[0];
/* s = r - alpha*v */
lis_vector_axpy(-alpha.hi[0],v,r);
/* Early check for tolerance */
lis_solver_get_residual[conv](s,solver,&nrm2);
if( nrm2 <= tol2 )
{
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);
}
lis_vector_axpy(alpha.hi[0],phat,x);
solver->iter = iter;
solver->iter2 = iter;
solver->ptimes = ptimes;
break;
}
/* shat = M^-1 * s */
times = lis_wtime();
lis_psolve(solver, s, shat);
ptimes += lis_wtime()-times;
/* t = A * shat */
LIS_MATVEC(A,shat,t);
/* tmpdot1 = <t,s> */
/* tmpdot2 = <t,t> */
/* omega = tmpdot1 / tmpdot2 */
lis_vector_dot(t,s,&tmpdot1.hi[0]);
lis_vector_dot(t,t,&tmpdot2.hi[0]);
omega.hi[0] = tmpdot1.hi[0] / tmpdot2.hi[0];
/* x = x + alpha*phat + omega*shat */
lis_vector_axpy(alpha.hi[0],phat,x);
lis_vector_axpy(omega.hi[0],shat,x);
/* r = s - omega*t */
lis_vector_axpy(-omega.hi[0],t,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
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( nrm2 <= tol2 )
{
solver->iter = iter;
solver->iter2 = iter;
solver->ptimes = ptimes;
break;
}
if( omega.hi[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
rho_old.hi[0] = rho.hi[0];
}
s->precision = LIS_PRECISION_QUAD;
shat->precision = LIS_PRECISION_QUAD;
p->precision = LIS_PRECISION_QUAD;
phat->precision = LIS_PRECISION_QUAD;
solver->options[LIS_OPTIONS_INITGUESS_ZEROS] = LIS_FALSE;
lis_vector_copyex_mn(x,solver->xx);
rho_old.hi[0] = 1.0;
alpha.hi[0] = 1.0;
omega.hi[0] = 1.0;
lis_vector_set_allex_nm(0.0, p);
lis_vector_set_allex_nm(0.0, phat);
lis_vector_set_allex_nm(0.0, s);
lis_vector_set_allex_nm(0.0, shat);
/* Initial Residual */
lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2);
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,rtld);
for( iter2=iter+1; iter2<=maxiter; iter2++ )
{
/* rho = <rtld,r> */
lis_vector_dotex_mmm(rtld,r,&rho);
/* test breakdown */
if( rho.hi[0]==0.0 && rho.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
if( iter2==1 )
{
lis_vector_copyex_mm(r,p);
}
else
{
/* beta = (rho / rho_old) * (alpha / omega) */
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
lis_quad_div((LIS_QUAD *)tmpdot1.hi,(LIS_QUAD *)alpha.hi,(LIS_QUAD *)omega.hi);
lis_quad_mul((LIS_QUAD *)beta.hi,(LIS_QUAD *)beta.hi,(LIS_QUAD *)tmpdot1.hi);
/* p = r + beta*(p - omega*v) */
lis_quad_minus((LIS_QUAD *)omega.hi);
lis_vector_axpyex_mmm(omega,v,p);
lis_vector_xpayex_mmm(r,beta,p);
}
/* phat = M^-1 * p */
times = lis_wtime();
lis_psolve(solver, p, phat);
ptimes += lis_wtime()-times;
/* v = A * phat */
LIS_MATVEC(A,phat,v);
/* tmpdot1 = <rtld,v> */
lis_vector_dotex_mmm(rtld,v,&tmpdot1);
/* test breakdown */
/* */
/* alpha = rho / tmpdot1 */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot1.hi);
/* s = r - alpha*v */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,v,r);
/* Early check for tolerance */
lis_solver_get_residual[conv](s,solver,&nrm2);
if( tol > nrm2 )
{
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter2] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) printf("iter: %5d residual = %e\n", iter2, nrm2);
}
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,phat,x);
solver->retcode = LIS_SUCCESS;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* shat = M^-1 * s */
times = lis_wtime();
lis_psolve(solver, s, shat);
ptimes += lis_wtime()-times;
/* t = A * shat */
LIS_MATVEC(A,shat,t);
/* tmpdot1 = <t,s> */
/* tmpdot2 = <t,t> */
/* omega = tmpdot1 / tmpdot2 */
lis_vector_dotex_mmm(t,s,&tmpdot1);
lis_vector_dotex_mmm(t,t,&tmpdot2);
lis_quad_div((LIS_QUAD *)omega.hi,(LIS_QUAD *)tmpdot1.hi,(LIS_QUAD *)tmpdot2.hi);
/* x = x + alpha*phat + omega*shat */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,phat,x);
lis_vector_axpyex_mmm(omega,shat,x);
/* r = s - omega*t */
lis_quad_minus((LIS_QUAD *)omega.hi);
lis_vector_axpyex_mmm(omega,t,r);
lis_quad_minus((LIS_QUAD *)omega.hi);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter2] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) printf("iter: %5d residual = %e\n", iter2, nrm2);
}
if( tol > nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
if( omega.hi[0]==0.0 && omega.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
rho_old.hi[0] = rho.hi[0];
rho_old.lo[0] = rho.lo[0];
}
solver->retcode = LIS_MAXITER;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_bicgsafe_switch(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_VECTOR r, rtld, rhat, p, ptld, phat;
LIS_VECTOR t, ttld, that, t0, t0hat;
LIS_VECTOR y, w, u, z;
LIS_QUAD_PTR alpha, beta, rho, rho_old;
LIS_QUAD_PTR qsi, eta, one;
LIS_QUAD_PTR tmp, tmpdot[5];
LIS_REAL bnrm2, nrm2, tol, tol2;
LIS_INT iter,maxiter,output,conv;
LIS_INT iter2,maxiter2;
double time,ptime;
LIS_DEBUG_FUNC_IN;
A = solver->A;
x = solver->x;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
maxiter2 = solver->options[LIS_OPTIONS_SWITCH_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
tol2 = solver->params[LIS_PARAMS_SWITCH_RESID-LIS_OPTIONS_LEN];
ptime = 0.0;
rtld = solver->work[0];
r = solver->work[1];
rhat = solver->work[2];
p = solver->work[3];
ptld = solver->work[4];
phat = solver->work[5];
t = solver->work[6];
ttld = solver->work[7];
that = solver->work[8];
t0 = solver->work[9];
t0hat = solver->work[10];
y = solver->work[11];
w = solver->work[12];
u = solver->work[13];
z = solver->work[14];
LIS_QUAD_SCALAR_MALLOC(alpha,0,1);
LIS_QUAD_SCALAR_MALLOC(beta,1,1);
LIS_QUAD_SCALAR_MALLOC(rho,2,1);
LIS_QUAD_SCALAR_MALLOC(rho_old,3,1);
LIS_QUAD_SCALAR_MALLOC(qsi,4,1);
LIS_QUAD_SCALAR_MALLOC(eta,5,1);
LIS_QUAD_SCALAR_MALLOC(tmp,6,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[0],7,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[1],8,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[2],9,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[3],10,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[4],11,1);
LIS_QUAD_SCALAR_MALLOC(one,13,1);
rho_old.hi[0] = 1.0;
rho_old.lo[0] = 0.0;
alpha.hi[0] = 1.0;
alpha.lo[0] = 0.0;
qsi.hi[0] = 1.0;
qsi.lo[0] = 0.0;
one.hi[0] = -1.0;
one.lo[0] = 0.0;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol2 = solver->tol_switch;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0, ttld);
lis_vector_set_allex_nm(0.0, ptld);
lis_vector_set_allex_nm(0.0, p);
lis_vector_set_allex_nm(0.0, u);
lis_vector_set_allex_nm(0.0, t);
lis_vector_set_allex_nm(0.0, t0);
for( iter=1; iter<=maxiter2; iter++ )
{
/* rho = <rtld,r> */
lis_vector_dot(rtld,r,&rho.hi[0]);
/* test breakdown */
if( rho.hi[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) * (alpha / qsi) */
beta.hi[0] = (rho.hi[0] / rho_old.hi[0]) * (alpha.hi[0] / qsi.hi[0]);
/* w = ttld + beta*ptld */
lis_vector_axpyz(beta.hi[0],ptld,ttld,w);
/* rhat = M^-1 * r */
time = lis_wtime();
lis_psolve(solver, r, rhat);
ptime += lis_wtime()-time;
/* p = rhat + beta*(p - u) */
lis_vector_axpy(-1,u,p);
lis_vector_xpay(rhat,beta.hi[0],p);
/* ptld = A * p */
lis_matvec(A,p,ptld);
/* tmpdot[0] = <rtld,ptld> */
lis_vector_dot(rtld,ptld,&tmpdot[0].hi[0]);
/* test breakdown */
/* */
/* alpha = rho / tmpdot[0] */
alpha.hi[0] = rho.hi[0] / tmpdot[0].hi[0];
/* y = t - r + alpha*(-w + ptld) */
lis_vector_axpyz(-1,w,ptld,y);
lis_vector_xpay(t,alpha.hi[0],y);
lis_vector_axpy(-1,r,y);
/* t = r - alpha*ptld */
lis_vector_axpyz(-alpha.hi[0],ptld,r,t);
/* that = M^-1 * t */
/* phat = M^-1 * ptld */
/* t0hat = M^-1 * t0 */
time = lis_wtime();
lis_psolve(solver, t, that);
lis_psolve(solver, ptld, phat);
lis_psolve(solver, t0, t0hat);
ptime += lis_wtime()-time;
/* ttld = A * that */
lis_matvec(A,that,ttld);
/* tmpdot[0] = <y,y> */
/* tmpdot[1] = <ttld,t> */
/* tmpdot[2] = <y,t> */
/* tmpdot[3] = <ttld,y> */
/* tmpdot[4] = <ttld,ttld> */
lis_vector_dot(y,y,&tmpdot[0].hi[0]);
lis_vector_dot(ttld,t,&tmpdot[1].hi[0]);
lis_vector_dot(y,t,&tmpdot[2].hi[0]);
lis_vector_dot(ttld,y,&tmpdot[3].hi[0]);
lis_vector_dot(ttld,ttld,&tmpdot[4].hi[0]);
if(iter==1)
{
qsi.hi[0] = tmpdot[1].hi[0] / tmpdot[4].hi[0];
eta.hi[0] = 0.0;
}
else
{
tmp.hi[0] = tmpdot[4].hi[0]*tmpdot[0].hi[0] - tmpdot[3].hi[0]*tmpdot[3].hi[0];
qsi.hi[0] = (tmpdot[0].hi[0]*tmpdot[1].hi[0] - tmpdot[2].hi[0]*tmpdot[3].hi[0]) / tmp.hi[0];
eta.hi[0] = (tmpdot[4].hi[0]*tmpdot[2].hi[0] - tmpdot[3].hi[0]*tmpdot[1].hi[0]) / tmp.hi[0];
}
/* u = qsi*phat + eta*(t0hat - rhat + beta*u) */
lis_vector_xpay(t0hat,beta.hi[0],u);
lis_vector_axpy(-1,rhat,u);
lis_vector_scale(eta.hi[0],u);
lis_vector_axpy(qsi.hi[0],phat,u);
/* z = qsi*rhat + eta*z - alpha*u */
lis_vector_scale(eta.hi[0],z);
lis_vector_axpy(qsi.hi[0],rhat,z);
lis_vector_axpy(-alpha.hi[0],u,z);
/* x = x + alpha*p + z */
lis_vector_axpy(alpha.hi[0],p,x);
lis_vector_axpy(1,z,x);
/* r = t - eta*y - qsi*ttld */
lis_vector_axpyz(-eta.hi[0],y,t,r);
lis_vector_axpy(-qsi.hi[0],ttld,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
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 )
{
solver->iter = iter;
solver->iter2 = iter;
solver->ptime = ptime;
break;
}
lis_vector_copy(t,t0);
rho_old.hi[0] = rho.hi[0];
}
r->precision = LIS_PRECISION_QUAD;
p->precision = LIS_PRECISION_QUAD;
t->precision = LIS_PRECISION_QUAD;
t0->precision = LIS_PRECISION_QUAD;
ptld->precision = LIS_PRECISION_QUAD;
that->precision = LIS_PRECISION_QUAD;
solver->options[LIS_OPTIONS_INITGUESS_ZEROS] = LIS_FALSE;
lis_vector_copyex_mn(x,solver->xx);
rho_old.hi[0] = 1.0;
alpha.hi[0] = 1.0;
qsi.hi[0] = 1.0;
one.hi[0] = -1.0;
/* Initial Residual */
lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2);
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0, ttld);
lis_vector_set_allex_nm(0.0, ptld);
lis_vector_set_allex_nm(0.0, p);
lis_vector_set_allex_nm(0.0, u);
lis_vector_set_allex_nm(0.0, t);
lis_vector_set_allex_nm(0.0, t0);
for( iter2=iter+1; iter2<=maxiter; iter2++ )
{
/* rho = <rtld,r> */
lis_vector_dotex_mmm(rtld,r,&rho);
/* test breakdown */
if( rho.hi[0]==0.0 && rho.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) * (alpha / qsi) */
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)alpha.hi,(LIS_QUAD *)qsi.hi);
lis_quad_mul((LIS_QUAD *)beta.hi,(LIS_QUAD *)beta.hi,(LIS_QUAD *)tmp.hi);
/* w = ttld + beta*ptld */
lis_vector_axpyzex_mmmm(beta,ptld,ttld,w);
/* rhat = M^-1 * r */
time = lis_wtime();
lis_psolve(solver, r, rhat);
ptime += lis_wtime()-time;
/* p = rhat + beta*(p - u) */
lis_vector_axpyex_mmm(one,u,p);
lis_vector_xpayex_mmm(rhat,beta,p);
/* ptld = A * p */
lis_matvec(A,p,ptld);
/* tmpdot[0] = <rtld,ptld> */
lis_vector_dotex_mmm(rtld,ptld,&tmpdot[0]);
/* test breakdown */
/* */
/* alpha = rho / tmpdot[0] */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot[0].hi);
/* y = t - r + alpha*(-w + ptld) */
lis_vector_axpyzex_mmmm(one,w,ptld,y);
lis_vector_xpayex_mmm(t,alpha,y);
lis_vector_axpyex_mmm(one,r,y);
/* t = r - alpha*ptld */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyzex_mmmm(alpha,ptld,r,t);
/* that = M^-1 * t */
/* phat = M^-1 * ptld */
/* t0hat = M^-1 * t0 */
time = lis_wtime();
lis_psolve(solver, t, that);
lis_psolve(solver, ptld, phat);
lis_psolve(solver, t0, t0hat);
ptime += lis_wtime()-time;
/* ttld = A * that */
lis_matvec(A,that,ttld);
/* tmpdot[0] = <y,y> */
/* tmpdot[1] = <ttld,t> */
/* tmpdot[2] = <y,t> */
/* tmpdot[3] = <ttld,y> */
/* tmpdot[4] = <ttld,ttld> */
lis_vector_dotex_mmm(y,y,&tmpdot[0]);
lis_vector_dotex_mmm(ttld,t,&tmpdot[1]);
lis_vector_dotex_mmm(y,t,&tmpdot[2]);
lis_vector_dotex_mmm(ttld,y,&tmpdot[3]);
lis_vector_dotex_mmm(ttld,ttld,&tmpdot[4]);
if(iter==1)
{
lis_quad_div((LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmpdot[1].hi,(LIS_QUAD *)tmpdot[4].hi);
eta.hi[0] = 0.0;
eta.lo[0] = 0.0;
}
else
{
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmpdot[4].hi,(LIS_QUAD *)tmpdot[0].hi);
lis_quad_sqr((LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmpdot[3].hi);
lis_quad_sub((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)qsi.hi);
lis_quad_mul((LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmpdot[0].hi,(LIS_QUAD *)tmpdot[1].hi);
lis_quad_mul((LIS_QUAD *)eta.hi,(LIS_QUAD *)tmpdot[2].hi,(LIS_QUAD *)tmpdot[3].hi);
lis_quad_sub((LIS_QUAD *)qsi.hi,(LIS_QUAD *)qsi.hi,(LIS_QUAD *)eta.hi);
lis_quad_div((LIS_QUAD *)qsi.hi,(LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmp.hi);
lis_quad_mul((LIS_QUAD *)eta.hi,(LIS_QUAD *)tmpdot[4].hi,(LIS_QUAD *)tmpdot[2].hi);
lis_quad_mul((LIS_QUAD *)tmpdot[0].hi,(LIS_QUAD *)tmpdot[3].hi,(LIS_QUAD *)tmpdot[1].hi);
lis_quad_sub((LIS_QUAD *)eta.hi,(LIS_QUAD *)eta.hi,(LIS_QUAD *)tmpdot[0].hi);
lis_quad_div((LIS_QUAD *)eta.hi,(LIS_QUAD *)eta.hi,(LIS_QUAD *)tmp.hi);
}
/* u = qsi*phat + eta*(t0hat - rhat + beta*u) */
lis_vector_xpayex_mmm(t0hat,beta,u);
lis_vector_axpyex_mmm(one,rhat,u);
lis_vector_scaleex_mm(eta,u);
lis_vector_axpyex_mmm(qsi,phat,u);
/* z = qsi*rhat + eta*z - alpha*u */
lis_vector_scaleex_mm(eta,z);
lis_vector_axpyex_mmm(qsi,rhat,z);
lis_vector_axpyex_mmm(alpha,u,z);
/* x = x + alpha*p + z */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_quad_minus((LIS_QUAD *)one.hi);
lis_vector_axpyex_mmm(alpha,p,x);
lis_vector_axpyex_mmm(one,z,x);
lis_quad_minus((LIS_QUAD *)one.hi);
/* r = t - eta*y - qsi*ttld */
lis_quad_minus((LIS_QUAD *)eta.hi);
lis_quad_minus((LIS_QUAD *)qsi.hi);
lis_vector_axpyzex_mmmm(eta,y,t,r);
lis_vector_axpyex_mmm(qsi,ttld,r);
lis_quad_minus((LIS_QUAD *)eta.hi);
lis_quad_minus((LIS_QUAD *)qsi.hi);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
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 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter2;
solver->iter2 = iter;
solver->resid = nrm2;
solver->ptime = ptime;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
lis_vector_copyex_mm(t,t0);
rho_old.hi[0] = rho.hi[0];
rho_old.lo[0] = rho.lo[0];
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->iter2 = iter2;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_bicgsafe_quad(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_VECTOR r, rtld, rhat, p, ptld;
LIS_VECTOR t, ttld;
LIS_VECTOR y, v, u, utld, z;
LIS_QUAD_PTR alpha, beta, rho, rho_old;
LIS_QUAD_PTR qsi, eta;
LIS_QUAD_PTR tmp, tmpdot[5],one;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,output,conv;
double time,ptime;
LIS_DEBUG_FUNC_IN;
A = solver->A;
x = solver->x;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
ptime = 0.0;
rtld = solver->work[0];
r = solver->work[1];
rhat = solver->work[2];
p = solver->work[3];
ptld = solver->work[4];
t = solver->work[5];
ttld = solver->work[6];
y = solver->work[7];
v = solver->work[8];
u = solver->work[9];
z = solver->work[10];
utld = solver->work[11];
LIS_QUAD_SCALAR_MALLOC(alpha,0,1);
LIS_QUAD_SCALAR_MALLOC(beta,1,1);
LIS_QUAD_SCALAR_MALLOC(rho,2,1);
LIS_QUAD_SCALAR_MALLOC(rho_old,3,1);
LIS_QUAD_SCALAR_MALLOC(qsi,4,1);
LIS_QUAD_SCALAR_MALLOC(eta,5,1);
LIS_QUAD_SCALAR_MALLOC(tmp,6,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[0],7,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[1],8,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[2],9,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[3],10,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot[4],11,1);
LIS_QUAD_SCALAR_MALLOC(one,13,1);
rho_old.hi[0] = 1.0;
rho_old.lo[0] = 0.0;
alpha.hi[0] = 1.0;
alpha.lo[0] = 0.0;
qsi.hi[0] = 1.0;
qsi.lo[0] = 0.0;
one.hi[0] = -1.0;
one.lo[0] = 0.0;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0,p);
lis_vector_set_allex_nm(0.0,u);
lis_vector_set_allex_nm(0.0,ptld);
lis_vector_set_allex_nm(0.0,utld);
for( iter=1; iter<=maxiter; iter++ )
{
/* rho = <rtld,r> */
lis_vector_dotex_mmm(rtld,r,&rho);
/* test breakdown */
if( rho.hi[0]==0.0 && rho.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) * (alpha / qsi) */
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
lis_quad_div((LIS_QUAD *)tmp.hi,(LIS_QUAD *)alpha.hi,(LIS_QUAD *)qsi.hi);
lis_quad_mul((LIS_QUAD *)beta.hi,(LIS_QUAD *)beta.hi,(LIS_QUAD *)tmp.hi);
/* rhat = M^-1 * r */
/* v = A * rhat */
time = lis_wtime();
lis_psolve(solver, r, rhat);
ptime += lis_wtime()-time;
lis_matvec(A,rhat,v);
/* p = rhat + beta*(p - u) */
lis_vector_axpyex_mmm(one,u,p);
lis_vector_xpayex_mmm(rhat,beta,p);
/* ptld = v + beta*(ptld - utld) */
lis_vector_axpyex_mmm(one,utld,ptld);
lis_vector_xpayex_mmm(v,beta,ptld);
/* tmpdot[0] = <rtld,ptld> */
lis_vector_dotex_mmm(rtld,ptld,&tmpdot[0]);
/* test breakdown */
/* */
/* alpha = rho / tmpdot[0] */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot[0].hi);
/* tmpdot[0] = <y,y> */
/* tmpdot[1] = <v,r> */
/* tmpdot[2] = <y,r> */
/* tmpdot[3] = <v,y> */
/* tmpdot[4] = <v,v> */
lis_vector_dotex_mmm(y,y,&tmpdot[0]);
lis_vector_dotex_mmm(v,r,&tmpdot[1]);
lis_vector_dotex_mmm(y,r,&tmpdot[2]);
lis_vector_dotex_mmm(v,y,&tmpdot[3]);
lis_vector_dotex_mmm(v,v,&tmpdot[4]);
if(iter==1)
{
lis_quad_div((LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmpdot[1].hi,(LIS_QUAD *)tmpdot[4].hi);
eta.hi[0] = 0.0;
eta.lo[0] = 0.0;
}
else
{
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmpdot[4].hi,(LIS_QUAD *)tmpdot[0].hi);
lis_quad_sqr((LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmpdot[3].hi);
lis_quad_sub((LIS_QUAD *)tmp.hi,(LIS_QUAD *)tmp.hi,(LIS_QUAD *)qsi.hi);
lis_quad_mul((LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmpdot[0].hi,(LIS_QUAD *)tmpdot[1].hi);
lis_quad_mul((LIS_QUAD *)eta.hi,(LIS_QUAD *)tmpdot[2].hi,(LIS_QUAD *)tmpdot[3].hi);
lis_quad_sub((LIS_QUAD *)qsi.hi,(LIS_QUAD *)qsi.hi,(LIS_QUAD *)eta.hi);
lis_quad_div((LIS_QUAD *)qsi.hi,(LIS_QUAD *)qsi.hi,(LIS_QUAD *)tmp.hi);
lis_quad_mul((LIS_QUAD *)eta.hi,(LIS_QUAD *)tmpdot[4].hi,(LIS_QUAD *)tmpdot[2].hi);
lis_quad_mul((LIS_QUAD *)tmpdot[0].hi,(LIS_QUAD *)tmpdot[3].hi,(LIS_QUAD *)tmpdot[1].hi);
lis_quad_sub((LIS_QUAD *)eta.hi,(LIS_QUAD *)eta.hi,(LIS_QUAD *)tmpdot[0].hi);
lis_quad_div((LIS_QUAD *)eta.hi,(LIS_QUAD *)eta.hi,(LIS_QUAD *)tmp.hi);
}
/* t = qsi*ptld + eta*y */
lis_vector_copyex_mm(y,t);
lis_vector_scaleex_mm(eta,t);
lis_vector_axpyex_mmm(qsi,ptld,t);
/* ttld = M^-1 * t */
time = lis_wtime();
lis_psolve(solver, t, ttld);
ptime += lis_wtime()-time;
/* u = ttld + eta*beta*u */
/* utld = A * u */
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)eta.hi,(LIS_QUAD *)beta.hi);
lis_vector_xpayex_mmm(ttld,tmp,u);
lis_matvec(A,u,utld);
/* z = qsi*rhat + eta*z - alpha*u */
lis_vector_scaleex_mm(eta,z);
lis_vector_axpyex_mmm(qsi,rhat,z);
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,u,z);
/* y = qsi*v + eta*y - alpha*utld */
lis_vector_scaleex_mm(eta,y);
lis_vector_axpyex_mmm(qsi,v,y);
lis_vector_axpyex_mmm(alpha,utld,y);
lis_quad_minus((LIS_QUAD *)alpha.hi);
/* x = x + alpha*p + z */
lis_vector_axpyex_mmm(alpha,p,x);
lis_quad_minus((LIS_QUAD *)one.hi);
lis_vector_axpyex_mmm(one,z,x);
lis_quad_minus((LIS_QUAD *)one.hi);
/* r = r - alpha*ptld - y */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,ptld,r);
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(one,y,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
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 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
rho_old.hi[0] = rho.hi[0];
rho_old.lo[0] = rho.lo[0];
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_bicg_quad(LIS_SOLVER solver)
{
LIS_MATRIX A,At;
LIS_VECTOR x;
LIS_VECTOR r,rtld, z,ztld,p, ptld, q, qtld;
LIS_QUAD_PTR alpha, beta, rho, rho_old, tmpdot1;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,output,conv;
double time,ptime;
LIS_DEBUG_FUNC_IN;
A = solver->A;
At = solver->A;
x = solver->x;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
ptime = 0.0;
r = solver->work[0];
rtld = solver->work[1];
z = solver->work[2];
ztld = solver->work[3];
p = solver->work[4];
ptld = solver->work[5];
q = solver->work[2];
qtld = solver->work[3];
LIS_QUAD_SCALAR_MALLOC(alpha,0,1);
LIS_QUAD_SCALAR_MALLOC(beta,1,1);
LIS_QUAD_SCALAR_MALLOC(rho,2,1);
LIS_QUAD_SCALAR_MALLOC(rho_old,3,1);
LIS_QUAD_SCALAR_MALLOC(tmpdot1,4,1);
rho_old.hi[0] = 1.0;
rho_old.lo[0] = 0.0;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
lis_solver_set_shadowresidual(solver,r,rtld);
lis_vector_set_allex_nm(0.0, p);
lis_vector_set_allex_nm(0.0, ptld);
for( iter=1; iter<=maxiter; iter++ )
{
/* z = M^-1 * r */
/* ztld = M^-T * rtld */
time = lis_wtime();
lis_psolve(solver, r, z);
lis_psolvet(solver, rtld, ztld);
ptime += lis_wtime()-time;
/* rho = <z,rtld> */
lis_vector_dotex_mmm(z,rtld,&rho);
/* printf("rho = %e %e\n",rho.hi[0],rho.lo[0]);*/
/* test breakdown */
if( rho.hi[0]==0.0 && rho.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
/* printf("beta = %e %e\n",beta.hi[0],beta.lo[0]);*/
/* p = z + beta*p */
/* ptld = ztld + beta*ptld */
/* q = A * p */
/* qtld = A^T * ptld */
lis_vector_xpayex_mmm(z,beta,p);
lis_matvec(A,p,q);
lis_vector_xpayex_mmm(ztld,beta,ptld);
lis_matvect(At,ptld,qtld);
/* tmpdot1 = <ptld,q> */
lis_vector_dotex_mmm(ptld,q,&tmpdot1);
/* printf("tmpdot1 = %e %e\n",tmpdot1.hi[0],tmpdot1.lo[0]);*/
/* test breakdown */
if( tmpdot1.hi[0]==0.0 && tmpdot1.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)tmpdot1.hi);
/* printf("alpha = %e %e\n",alpha.hi[0],alpha.lo[0]);*/
/* x = x + alpha*p */
lis_vector_axpyex_mmm(alpha,p,x);
/* r = r - alpha*q */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,q,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
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 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* rtld = rtld - alpha*qtld */
lis_vector_axpyex_mmm(alpha,qtld,rtld);
rho_old.hi[0] = rho.hi[0];
rho_old.lo[0] = rho.lo[0];
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
