LIS_INT lis_idr1(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR r,t,v,av,*dX,*dR,*P;
LIS_SCALAR om, h;
LIS_SCALAR M,m,c;
LIS_REAL bnrm2, nrm2, tol;
LIS_REAL angle;
LIS_INT i,j,k,s,oldest;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes,tim;
unsigned long init[4]={0x123, 0x234, 0x345, 0x456}, length=4;
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];
conv = solver->options[LIS_OPTIONS_CONV_COND];
s = 1;
ptimes = 0.0;
r = solver->work[0];
t = solver->work[1];
v = solver->work[2];
av = solver->work[3];
P = &solver->work[4];
dX = &solver->work[4+s];
dR = &solver->work[4+2*s];
angle = 0.7;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
init_by_array(init, length);
for(i=0;i<n;i++)
{
P[0]->value[i] = genrand_real1();
}
/*
lis_vector_copy(r,P[0]);
*/
lis_idrs_orth(s,P);
#ifdef PRE_RIGHT
times = lis_wtime();
lis_psolve(solver, r, dX[0]);
ptimes += lis_wtime()-times;
LIS_MATVEC(A,dX[0],dR[0]);
#else
#ifdef PRE_BOTH
times = lis_wtime();
lis_psolve_right(solver, r, t);
ptimes += lis_wtime()-times;
LIS_MATVEC(A,t,av);
lis_vector_print(av);
times = lis_wtime();
lis_psolve_left(solver, av, v);
ptimes += lis_wtime()-times;
#endif
#endif
/*
lis_idrs_omega(dR[k],r,angle,&om);
*/
lis_vector_dot(dR[0],dR[0],&h);
lis_vector_dot(dR[0],r,&om);
om = om / h;
lis_vector_scale(om,dX[0]);
lis_vector_scale(-om,dR[0]);
lis_vector_axpy(1.0,dX[0],x);
lis_vector_axpy(1.0,dR[0],r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[1] =
nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 )
printf("iter: %5d residual = %e\n", 1, nrm2);
}
if( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = 1;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
lis_vector_dot(P[0],dR[0],&M);
iter = s;
oldest = 0;
lis_vector_dot(P[0],r,&m);
while( iter<=maxiter )
{
tim = lis_wtime();
/* solve Mc=m */
c = m/M;
for(i=0;i<n;i++)
{
v->value[i] = r->value[i] + -c*dR[0]->value[i];
}
/*
lis_vector_copy(r,v);
lis_vector_axpy(-c,dR[0],v);
*/
#ifdef PRE_RIGHT
times = lis_wtime();
lis_psolve(solver, v, av);
ptimes += lis_wtime()-times;
LIS_MATVEC(A,av,t);
#else
#ifdef PRE_BOTH
times = lis_wtime();
lis_psolve_right(solver, v, t);
ptimes += lis_wtime()-times;
LIS_MATVEC(A,t,av);
times = lis_wtime();
lis_psolve_left(solver, av, t);
ptimes += lis_wtime()-times;
#endif
#endif
/*
lis_idrs_omega(t,v,angle,&om);
lis_vector_dot(t,t,&h);
lis_vector_dot(t,v,&om);
*/
h = t->value[0]*t->value[0];
om = t->value[0]*v->value[0];
for(i=1;i<n;i++)
{
h += t->value[i]*t->value[i];
om += t->value[i]*v->value[i];
}
om = om / h;
/*
printf("i=%d om = %lf\n",iter,om);
*/
#if 0
lis_vector_scale(-om,t);
for(j=0;j<s;j++)
{
lis_vector_axpy(-c[j],dR[j],t);
}
lis_vector_copy(t,dR[oldest]);
lis_vector_scale(om,av);
for(j=0;j<s;j++)
{
lis_vector_axpy(-c[j],dX[j],av);
}
lis_vector_copy(av,dX[oldest]);
#else
for(i=0;i<n;i++)
{
h = om*av->value[i];
h -= dX[0]->value[i] * c;
dX[0]->value[i] = h;
h = -om*t->value[i];
h -= dR[0]->value[i] * c;
dR[0]->value[i] = h;
}
#endif
lis_vector_axpy(1.0,dR[0],r);
lis_vector_axpy(1.0,dX[0],x);
iter++;
/* 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( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
lis_vector_dot(P[0],dR[0],&h);
m += h;
M = h;
/* solve Mc=m */
c = m/M;
for(i=0;i<n;i++)
{
v->value[i] = r->value[i] + -c*dR[0]->value[i];
}
/*
lis_vector_copy(r,v);
lis_vector_axpy(-c,dR[0],v);
*/
#ifdef PRE_RIGHT
times = lis_wtime();
lis_psolve(solver, v, av);
ptimes += lis_wtime()-times;
#endif
#if 0
lis_vector_scale(om,av);
for(j=0;j<s;j++)
{
lis_vector_axpy(-c[j],dX[j],av);
}
lis_vector_copy(av,dX[oldest]);
#else
for(i=0;i<n;i++)
{
h = om*av->value[i];
h -= dX[0]->value[i] * c;
dX[0]->value[i] = h;
}
#endif
LIS_MATVEC(A,dX[0],dR[0]);
lis_vector_scale(-1.0,dR[0]);
lis_vector_axpy(1.0,dR[0],r);
lis_vector_axpy(1.0,dX[0],x);
iter++;
/* 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( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
lis_vector_dot(P[0],dR[0],&h);
m += h;
M = h;
tim = lis_wtime() - tim;
/*
printf("update m,M: %e\n",tim);
*/
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
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_orthomin_quad(LIS_SOLVER solver)
{
LIS_Comm comm;
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR x;
LIS_VECTOR r, rtld, *p, *ap, *aptld;
LIS_QUAD *dotsave;
LIS_QUAD_PTR alpha, beta, tmp, one;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,output,conv;
double time,ptime;
LIS_INT m,l,lmax,ip,ip0;
LIS_DEBUG_FUNC_IN;
comm = LIS_COMM_WORLD;
A = solver->A;
M = solver->precon;
x = solver->x;
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];
ptime = 0.0;
LIS_QUAD_SCALAR_MALLOC(alpha,0,1);
LIS_QUAD_SCALAR_MALLOC(beta,1,1);
LIS_QUAD_SCALAR_MALLOC(tmp,3,1);
LIS_QUAD_SCALAR_MALLOC(one,4,1);
r = solver->work[0];
rtld = solver->work[1];
p = &solver->work[2];
ap = &solver->work[ (m+1)+2];
aptld = &solver->work[2*(m+1)+2];
one.hi[0] = 1.0;
one.lo[0] = 0.0;
dotsave = (LIS_QUAD *)lis_malloc( sizeof(LIS_QUAD) * (m+1),"lis_orthomin_quad::dotsave" );
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,M,r,rtld,&bnrm2) )
{
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
iter=1;
while( iter<=maxiter )
{
ip = (iter-1) % (m+1);
/* p[ip] = rtld */
lis_vector_copyex_mm(rtld,p[ip]);
/* ap[ip] = A*p[ip] */
/* aptld[ip] = M^-1 ap[ip] */
lis_matvec(A,p[ip],ap[ip]);
time = lis_wtime();
lis_psolve(solver, ap[ip], aptld[ip]);
ptime += lis_wtime()-time;
lmax = _min(m,iter-1);
for(l=1;l<=lmax;l++)
{
ip0 = (ip+m+1-l) % (m+1);
/* beta = -<Ar[ip],Ap[ip0]> / <Ap[ip0],Ap[ip0]> */
lis_vector_dotex_mmm(aptld[ip],aptld[ip0],&beta);
lis_quad_mul((LIS_QUAD *)beta.hi,(LIS_QUAD *)beta.hi,&dotsave[l-1]);
lis_quad_minus((LIS_QUAD *)beta.hi);
lis_vector_axpyex_mmm(beta,p[ip0] ,p[ip]);
lis_vector_axpyex_mmm(beta,ap[ip0] ,ap[ip]);
lis_vector_axpyex_mmm(beta,aptld[ip0],aptld[ip]);
}
for(l=m-1;l>0;l--)
{
dotsave[l] = dotsave[l-1];
}
lis_vector_dotex_mmm(aptld[ip],aptld[ip],&tmp);
dotsave[0].hi = tmp.hi[0];
dotsave[0].lo = tmp.lo[0];
/* test breakdown */
if( tmp.hi[0]==0.0 && tmp.lo[0]==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
lis_free(dotsave);
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
lis_quad_div(&dotsave[0],(LIS_QUAD *)one.hi,&dotsave[0]);
/* alpha = <rtld,Aptld[ip]> */
lis_vector_dotex_mmm(rtld,aptld[ip],&alpha);
lis_quad_mul((LIS_QUAD *)alpha.hi,(LIS_QUAD *)alpha.hi,&dotsave[0]);
lis_vector_axpyex_mmm( alpha,p[ip],x);
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,ap[ip],r);
lis_vector_axpyex_mmm(alpha,aptld[ip],rtld);
lis_quad_minus((LIS_QUAD *)alpha.hi);
/* 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 ) lis_print_rhistory(comm,iter,nrm2);
}
if( tol > nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
lis_free(dotsave);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
iter++;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
lis_free(dotsave);
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_crs(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_VECTOR r,rtld, p, q, u, z, ap, map, uq, auq;
LIS_SCALAR 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;
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];
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];
/* 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);
rho_old = 1.0;
lis_vector_set_all(0,q);
lis_vector_set_all(0,p);
for( iter=1; iter<=maxiter; iter++ )
{
/* z = M^-1 * r */
/* rho = <rtld,z> */
time = lis_wtime();
lis_psolve(solver, r, z);
ptime += lis_wtime()-time;
lis_vector_dot(rtld,z,&rho);
/* test breakdown */
if( rho==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> */
beta = rho / rho_old;
lis_vector_axpyz(beta,q,z,u);
lis_vector_xpay(q,beta,p);
lis_vector_xpay(u,beta,p);
lis_matvec(A,p,ap);
time = lis_wtime();
lis_psolve(solver, ap, map);
ptime += lis_wtime()-time;
lis_vector_dot(rtld,map,&tmpdot1);
/* test breakdown */
if( tmpdot1==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 */
alpha = rho / tmpdot1;
lis_vector_axpyz(-alpha,map,u,q);
lis_vector_axpyz(1,u,q,uq);
lis_matvec(A,uq,auq);
lis_vector_axpy(alpha,uq,x);
lis_vector_axpy(-alpha,auq,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 = rho;
}
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_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_bicgstab(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,rtld, t,p,v, s, phat, shat;
LIS_SCALAR alpha, beta, omega, rho, rho_old, tmpdot1, tmpdot2;
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;
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];
alpha = (LIS_SCALAR)1.0;
omega = (LIS_SCALAR)1.0;
rho_old = (LIS_SCALAR)1.0;
lis_vector_set_all(0.0,p);
lis_vector_set_all(0.0,phat);
lis_vector_set_all(0.0,s);
lis_vector_set_all(0.0,shat);
/* 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);
for( iter=1; iter<=maxiter; iter++ )
{
/* rho = <rtld,r> */
lis_vector_dot(rtld,r,&rho);
/* test breakdown */
if( rho==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = 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 = (rho / rho_old) * (alpha / omega);
/* p = r + beta*(p - omega*v) */
lis_vector_axpy(-omega,v,p);
lis_vector_xpay(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_dot(rtld,v,&tmpdot1);
/* test breakdown */
/* */
/* alpha = rho / tmpdot1 */
alpha = rho / tmpdot1;
/* s = r - alpha*v */
lis_vector_axpy(-alpha,v,r);
/* Early check for tolerance */
lis_solver_get_residual[conv](s,solver,&nrm2);
/* lis_vector_nrm2(s,&nrm2);
nrm2 = nrm2 * bnrm2;*/
if( nrm2 <= tol )
{
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,phat,x);
solver->retcode = LIS_SUCCESS;
solver->iter = 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_dot(t,s,&tmpdot1);
lis_vector_dot(t,t,&tmpdot2);
omega = tmpdot1 / tmpdot2;
/* x = x + alpha*phat + omega*shat */
lis_vector_axpy(alpha,phat,x);
lis_vector_axpy(omega,shat,x);
/* r = s - omega*t */
lis_vector_axpy(-omega,t,r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
/* lis_vector_nrm2(r,&nrm2);
nrm2 = nrm2 * 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 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
if( omega==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
rho_old = rho;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_bicgsafe(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_VECTOR r, rtld, mr, amr, t, mt, p, ap;
LIS_VECTOR y, u, au, z;
LIS_SCALAR alpha, beta;
LIS_REAL rho, rho_old;
LIS_SCALAR qsi, eta;
LIS_SCALAR tmp, tmpdot[5];
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];
mr = solver->work[2];
amr = solver->work[3];
p = solver->work[4];
ap = solver->work[5];
t = solver->work[6];
mt = solver->work[7];
y = solver->work[8];
u = solver->work[9];
z = solver->work[10];
au = solver->work[11];
/* 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);
time = lis_wtime();
lis_psolve(solver, r, mr);
ptime += lis_wtime()-time;
lis_matvec(A,mr,amr);
lis_vector_dot(rtld,r,&rho_old);
lis_vector_copy(amr,ap);
lis_vector_copy(mr,p);
beta = 0.0;
for( iter=1; iter<=maxiter; iter++ )
{
/* tmpdot[0] = <rtld,ap> */
/* alpha = rho_old / tmpdot[0] */
lis_vector_dot(rtld,ap,&tmpdot[0]);
alpha = rho_old / tmpdot[0];
/* tmpdot[0] = <y,y> */
/* tmpdot[1] = <amr,r> */
/* tmpdot[2] = <y,r> */
/* tmpdot[3] = <amr,y> */
/* tmpdot[4] = <amr,amr> */
lis_vector_dot(y,y,&tmpdot[0]);
lis_vector_dot(amr,r,&tmpdot[1]);
lis_vector_dot(y,r,&tmpdot[2]);
lis_vector_dot(amr,y,&tmpdot[3]);
lis_vector_dot(amr,amr,&tmpdot[4]);
if(iter==1)
{
qsi = tmpdot[1] / tmpdot[4];
eta = 0.0;
}
else
{
tmp = tmpdot[4]*tmpdot[0] - tmpdot[3]*tmpdot[3];
qsi = (tmpdot[0]*tmpdot[1] - tmpdot[2]*tmpdot[3]) / tmp;
eta = (tmpdot[4]*tmpdot[2] - tmpdot[3]*tmpdot[1]) / tmp;
}
/* t = qsi*ap + eta*y */
lis_vector_copy(y,t);
lis_vector_scale(eta,t);
lis_vector_axpy(qsi,ap,t);
/* mt = M^-1 * t */
time = lis_wtime();
lis_psolve(solver, t, mt);
ptime += lis_wtime()-time;
/* u = mt + eta*beta*u */
/* au = A * u */
lis_vector_xpay(mt,eta*beta,u);
lis_matvec(A,u,au);
/* z = qsi*mr + eta*z - alpha*u */
lis_vector_scale(eta,z);
lis_vector_axpy(qsi,mr,z);
lis_vector_axpy(-alpha,u,z);
/* y = qsi*amr + eta*y - alpha*au */
lis_vector_scale(eta,y);
lis_vector_axpy(qsi,amr,y);
lis_vector_axpy(-alpha,au,y);
/* x = x + alpha*p + z */
lis_vector_axpy(alpha,p,x);
lis_vector_axpy(1.0,z,x);
/* r = r - alpha*ap - y */
lis_vector_axpy(-alpha,ap,r);
lis_vector_axpy(-1.0,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 = <rtld,r> */
lis_vector_dot(rtld,r,&rho);
if( rho==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) */
beta = (rho / rho_old) * (alpha / qsi);
/* mr = M^-1 * r */
/* amr = A * mr */
time = lis_wtime();
lis_psolve(solver, r, mr);
ptime += lis_wtime()-time;
lis_matvec(A,mr,amr);
/* p = mr + beta*(p - u) */
/* ap = amr + beta*(ap - au) */
lis_vector_axpy(-1.0,u,p);
lis_vector_xpay(mr,beta,p);
lis_vector_axpy(-1.0,au,ap);
lis_vector_xpay(amr,beta,ap);
rho_old = rho;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
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_bicrsafe_quad(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_VECTOR r, rtld, artld, mr, amr, p, ap, map;
LIS_VECTOR y, my, u, au, 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;
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];
mr = solver->work[2];
amr = solver->work[3];
p = solver->work[4];
ap = solver->work[5];
map = solver->work[6];
my = solver->work[7];
y = solver->work[8];
u = solver->work[9];
z = solver->work[10];
au = solver->work[11];
artld = solver->work[12];
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);
/* 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_matvect(A,rtld,artld);
time = lis_wtime();
lis_psolve(solver, r, mr);
ptime += lis_wtime()-time;
lis_matvec(A,mr,amr);
lis_vector_dotex_mmm(rtld,amr,&rho_old);
lis_vector_copyex_mm(amr,ap);
lis_vector_copyex_mm(mr,p);
one.hi[0] = -1.0;
one.lo[0] = 0.0;
for( iter=1; iter<=maxiter; iter++ )
{
/* map = M^-1 * ap */
time = lis_wtime();
lis_psolve(solver, ap, map);
ptime += lis_wtime()-time;
/* tmpdot[0] = <artld,map> */
/* alpha = rho_old / tmpdot[0] */
lis_vector_dotex_mmm(artld,map,&tmpdot[0]);
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho_old.hi,(LIS_QUAD *)tmpdot[0].hi);
/* tmpdot[0] = <y,y> */
/* tmpdot[1] = <amr,r> */
/* tmpdot[2] = <y,r> */
/* tmpdot[3] = <amr,y> */
/* tmpdot[4] = <amr,amr> */
lis_vector_dotex_mmm(y,y,&tmpdot[0]);
lis_vector_dotex_mmm(amr,r,&tmpdot[1]);
lis_vector_dotex_mmm(y,r,&tmpdot[2]);
lis_vector_dotex_mmm(amr,y,&tmpdot[3]);
lis_vector_dotex_mmm(amr,amr,&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*map + eta*my + eta*beta*u */
/* au = A * u */
lis_quad_mul((LIS_QUAD *)tmp.hi,(LIS_QUAD *)eta.hi,(LIS_QUAD *)beta.hi);
lis_vector_scaleex_mm(tmp,u);
lis_vector_axpyex_mmm(qsi,map,u);
lis_vector_axpyex_mmm(eta,my,u);
lis_matvec(A,u,au);
/* z = qsi*mr + eta*z - alpha*u */
lis_vector_scaleex_mm(eta,z);
lis_vector_axpyex_mmm(qsi,mr,z);
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,u,z);
/* y = qsi*amr + eta*y - alpha*au */
/* my = M^-1 * y */
lis_vector_scaleex_mm(eta,y);
lis_vector_axpyex_mmm(qsi,amr,y);
lis_vector_axpyex_mmm(alpha,au,y);
time = lis_wtime();
lis_psolve(solver, y, my);
ptime += lis_wtime()-time;
/* x = x + alpha*p + z */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,p,x);
lis_quad_minus((LIS_QUAD *)one.hi);
lis_vector_axpyex_mmm(one,z,x);
/* r = r - alpha*ap - y */
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_quad_minus((LIS_QUAD *)one.hi);
lis_vector_axpyex_mmm(alpha,ap,r);
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;
}
/* mr = mr - alpha*map - my */
/* amr = A * mr */
/* rho = <rtld,amr> */
lis_vector_axpyex_mmm(alpha,map,mr);
lis_vector_axpyex_mmm(one,my,mr);
lis_matvec(A,mr,amr);
lis_vector_dotex_mmm(rtld,amr,&rho);
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_minus((LIS_QUAD *)alpha.hi);
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);
/* p = mr + beta*(p - u) */
/* ap = amr + beta*(ap - au) */
lis_vector_axpyex_mmm(one,u,p);
lis_vector_xpayex_mmm(mr,beta,p);
lis_vector_axpyex_mmm(one,au,ap);
lis_vector_xpayex_mmm(amr,beta,ap);
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_gs(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR r,t,s;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,output;
double time,ptime;
LIS_INT err;
LIS_DEBUG_FUNC_IN;
A = solver->A;
b = solver->b;
x = solver->x;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
ptime = 0.0;
r = solver->work[0];
t = solver->work[1];
s = solver->work[2];
lis_vector_nrm2(b,&bnrm2);
bnrm2 = 1.0 / bnrm2;
err = lis_matrix_split(A);
if( err ) return err;
if( A->use_wd!=LIS_SOLVER_GS )
{
if( !A->WD )
{
err = lis_matrix_diag_duplicate(A->D,&A->WD);
if( err ) return err;
}
lis_matrix_diag_copy(A->D,A->WD);
lis_matrix_diag_inverse(A->WD);
A->use_wd = LIS_SOLVER_GS;
}
for( iter=1; iter<=maxiter; iter++ )
{
/* x += (D-L)^{-1}(b - Ax) */
time = lis_wtime();
lis_psolve(solver,x,s);
ptime += lis_wtime() - time;
lis_matvec(A,s,t);
/* lis_matvec(A,x,t);*/
lis_vector_axpyz(-1,t,b,r);
lis_vector_nrm2(r,&nrm2);
lis_matrix_solve(A,r,t,LIS_MATRIX_LOWER);
lis_vector_axpy(1,t,x);
/* convergence check */
nrm2 = nrm2 * bnrm2;
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol >= nrm2 )
{
time = lis_wtime();
lis_psolve(solver,x,s);
ptime += lis_wtime() - time;
lis_vector_copy(s,x);
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
lis_psolve(solver,x,s);
lis_vector_copy(s,x);
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_idrs(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR r,t,v,av,*dX,*dR,*P;
LIS_SCALAR om, h;
LIS_SCALAR *M,*m,*c,*MM;
LIS_REAL bnrm2, nrm2, tol;
LIS_REAL angle;
LIS_INT i,j,k,s,oldest;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes,tim;
unsigned long init[4]={0x123, 0x234, 0x345, 0x456}, length=4;
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];
conv = solver->options[LIS_OPTIONS_CONV_COND];
s = solver->options[LIS_OPTIONS_IDRS_RESTART];
ptimes = 0.0;
r = solver->work[0];
t = solver->work[1];
v = solver->work[2];
av = solver->work[3];
dX = &solver->work[4];
P = &solver->work[4+s];
dR = &solver->work[4+2*s];
angle = 0.7;
m = (LIS_SCALAR *)lis_malloc(s*sizeof(LIS_SCALAR), "lis_idrs::m");
c = (LIS_SCALAR *)lis_malloc(s*sizeof(LIS_SCALAR), "lis_idrs::c");
M = (LIS_SCALAR *)lis_malloc(s*s*sizeof(LIS_SCALAR), "lis_idrs::M");
MM = (LIS_SCALAR *)lis_malloc(s*s*sizeof(LIS_SCALAR),
"lis_idrs::M");
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,r,&bnrm2) )
{
lis_free2(4,m,c,M,MM);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
init_by_array(init, length);
for(k=0;k<s;k++)
{
for(i=0;i<n;i++)
{
P[k]->value[i] = genrand_real1();
}
}
lis_idrs_orth(s,P);
for( k=0; k<s; k++ )
{
#ifdef PRE_RIGHT
times = lis_wtime();
lis_psolve(solver, r, dX[k]);
ptimes += lis_wtime()-times;
LIS_MATVEC(A,dX[k],dR[k]);
#endif
lis_vector_dot(dR[k],dR[k],&h);
lis_vector_dot(dR[k],r,&om);
om = om / h;
lis_vector_scale(om,dX[k]);
lis_vector_scale(-om,dR[k]);
lis_vector_axpy(1.0,dX[k],x);
lis_vector_axpy(1.0,dR[k],r);
/* convergence check */
lis_solver_get_residual[conv](r,solver,&nrm2);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[k+1] =
nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 )
printf("iter: %5d residual = %e\n", k+1, nrm2);
}
if( tol >= nrm2 )
{
lis_free2(4,m,c,M,MM);
solver->retcode = LIS_SUCCESS;
solver->iter = k+1;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
for(i=0;i<s;i++)
{
lis_vector_dot(P[i],dR[k],&M[k*s+i]);
}
}
iter = s;
oldest = 0;
for(i=0;i<s;i++)
{
lis_vector_dot(P[i],r,&m[i]);
}
while( iter<=maxiter )
{
tim = lis_wtime();
lis_array_solve(s,M,m,c,MM); /* solve Mc=m */
lis_vector_copy(r,v);
for(j=0;j<s;j++)
{
lis_vector_axpy(-c[j],dR[j],v);
}
if( (iter%(s+1))==s )
{
#ifdef PRE_RIGHT
times = lis_wtime();
lis_psolve(solver, v, av);
ptimes += lis_wtime()-times;
LIS_MATVEC(A,av,t);
#endif
lis_vector_dot(t,t,&h);
lis_vector_dot(t,v,&om);
om = om / h;
#if 0
lis_vector_scale(-om,t);
for(j=0;j<s;j++)
{
lis_vector_axpy(-c[j],dR[j],t);
}
lis_vector_copy(t,dR[oldest]);
lis_vector_scale(om,av);
for(j=0;j<s;j++)
{
lis_vector_axpy(-c[j],dX[j],av);
}
lis_vector_copy(av,dX[oldest]);
#else
for(i=0;i<n;i++)
{
h = om*av->value[i];
for(j=0;j<s;j++)
{
h -= dX[j]->value[i] * c[j];
}
dX[oldest]->value[i] = h;
}
for(i=0;i<n;i++)
{
h = -om*t->value[i];
for(j=0;j<s;j++)
{
h -= dR[j]->value[i] * c[j];
}
dR[oldest]->value[i] = h;
}
#endif
}
else
{
#ifdef PRE_RIGHT
times = lis_wtime();
lis_psolve(solver, v, av);
ptimes += lis_wtime()-times;
#endif
#if 0
lis_vector_scale(om,av);
for(j=0;j<s;j++)
{
lis_vector_axpy(-c[j],dX[j],av);
}
lis_vector_copy(av,dX[oldest]);
#else
for(i=0;i<n;i++)
{
h = om*av->value[i];
for(j=0;j<s;j++)
{
h -= dX[j]->value[i] * c[j];
}
dX[oldest]->value[i] = h;
}
#endif
LIS_MATVEC(A,dX[oldest],dR[oldest]);
lis_vector_scale(-1.0,dR[oldest]);
}
lis_vector_axpy(1.0,dR[oldest],r);
lis_vector_axpy(1.0,dX[oldest],x);
iter++;
/* 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( tol >= nrm2 )
{
lis_free2(4,m,c,M,MM);
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
for(i=0;i<s;i++)
{
lis_vector_dot(P[i],dR[oldest],&h);
m[i] += h;
M[oldest*s+i] = h;
}
oldest++;
if( oldest==s ) oldest = 0;
tim = lis_wtime() - tim;
/*
printf("update m,M: %e\n",tim);
*/
}
lis_free2(4,m,c,M,MM);
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_solver_get_initial_residual(LIS_SOLVER solver, LIS_PRECON M, LIS_VECTOR t, LIS_VECTOR r, LIS_SCALAR *bnrm2)
{
LIS_INT output,conv;
#ifdef USE_QUAD_PRECISION
LIS_INT i;
#endif
LIS_MATRIX A;
LIS_VECTOR x,b,p,xx;
LIS_SCALAR nrm2;
LIS_REAL tol,tol_w,tol_switch;
LIS_DEBUG_FUNC_IN;
A = solver->A;
b = solver->b;
x = solver->x;
xx = solver->xx;
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
tol_w = solver->params[LIS_PARAMS_RESID_WEIGHT-LIS_OPTIONS_LEN];
tol_switch = solver->params[LIS_PARAMS_SWITCH_RESID-LIS_OPTIONS_LEN];
/* Initial Residual */
if( M==NULL )
{
p = r;
}
else
{
p = t;
}
if( !solver->options[LIS_OPTIONS_INITGUESS_ZEROS] )
{
#ifndef USE_QUAD_PRECISION
lis_matvec(A,x,p); /* p = Ax */
lis_vector_xpay(b,-1,p); /* p = b - p */
#else
if( solver->precision==LIS_PRECISION_DOUBLE )
{
lis_matvec(A,x,p); /* p = Ax */
lis_vector_xpay(b,-1,p); /* p = b - p */
}
else
{
lis_matvec(A,xx,p); /* p = Ax */
lis_vector_xpay(b,-1,p); /* p = b - p */
#ifdef _OPENMP
#pragma omp parallel for private(i)
#endif
for(i=0;i<A->n;i++)
{
p->value_lo[i] = 0.0;
}
}
#endif
}
else
{
#ifndef USE_QUAD_PRECISION
lis_vector_copy(b,p);
#else
if( solver->precision==LIS_PRECISION_DOUBLE )
{
lis_vector_copy(b,p);
}
else
{
lis_vector_copyex_nm(b,p);
}
#endif
}
switch(conv)
{
case LIS_CONV_COND_NRM2_R:
lis_vector_nrm2(p,&nrm2);
*bnrm2 = nrm2;
solver->tol = tol;
solver->tol_switch = tol_switch;
break;
case LIS_CONV_COND_NRM2_B:
lis_vector_nrm2(p,&nrm2);
lis_vector_nrm2(b,bnrm2);
solver->tol = tol;
solver->tol_switch = tol_switch;
break;
case LIS_CONV_COND_NRM1_B:
lis_vector_nrm1(p,&nrm2);
lis_vector_nrm1(b,bnrm2);
solver->tol = *bnrm2*tol_w + tol;
solver->tol_switch = *bnrm2*tol_w + tol_switch;
break;
}
if( *bnrm2 == 0.0 )
{
*bnrm2 = 1.0;
}
else
{
*bnrm2 = 1.0 / *bnrm2;
}
solver->bnrm = *bnrm2;
nrm2 = nrm2 * *bnrm2;
if( output && (r->precision==LIS_PRECISION_QUAD && solver->precision!=LIS_PRECISION_SWITCH) )
{
if( output & LIS_PRINT_MEM ) solver->residual[0] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) printf("iter: %5d residual = %e\n", 0, nrm2);
}
if( nrm2 <= solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN] )
{
solver->retcode = LIS_SUCCESS;
solver->iter = 1;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_FAILS;
}
if( M!=NULL )
{
/* r = M^-1 * p */
lis_psolve(solver, p, r);
}
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
LIS_INT lis_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_bicg(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_SCALAR alpha, beta, rho, rho_old, tmpdot1;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
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];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
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];
rho_old = (LIS_SCALAR)1.0;
/* 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_all(0, p);
lis_vector_set_all(0, ptld);
for( iter=1; iter<=maxiter; 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);
/* printf("rho = %e\n",rho);*/
/* test breakdown */
if( rho==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
beta = rho / rho_old;
/* p = z + beta*p */
/* ptld = ztld + beta*ptld */
/* q = A * p */
/* qtld = A^T * ptld */
lis_vector_xpay(z,beta,p);
LIS_MATVEC(A,p,q);
lis_vector_xpay(ztld,beta,ptld);
LIS_MATVECT(At,ptld,qtld);
/* tmpdot1 = <ptld,q> */
lis_vector_dot(ptld,q,&tmpdot1);
/* printf("tmpdot1 = %e\n",tmpdot1);*/
/* test breakdown */
if( tmpdot1==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
alpha = rho / tmpdot1;
/* x = x + alpha*p */
lis_vector_axpy(alpha,p,x);
/* r = r - alpha*q */
lis_vector_axpy(-alpha,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( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* rtld = rtld - alpha*qtld */
lis_vector_axpy(-alpha,qtld,rtld);
rho_old = rho;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_bicrstab(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,rtld, p, s, ap, ms, map, ams, z;
LIS_SCALAR alpha, beta, omega, rho, rho_old, tmpdot1, tmpdot2;
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;
rtld = solver->work[0];
r = solver->work[1];
s = solver->work[2];
ms = solver->work[3];
ams = solver->work[4];
p = solver->work[5];
ap = solver->work[6];
map = solver->work[7];
z = solver->work[8];
/* 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);
times = lis_wtime();
lis_psolve(solver, r, z);
ptimes += lis_wtime()-times;
lis_vector_copy(z,p);
lis_vector_dot(rtld,z,&rho_old);
for( iter=1; iter<=maxiter; iter++ )
{
/* ap = A * p */
/* map = M^-1 * ap */
/* tmpdot1 = <rtld,map> */
/* alpha = rho_old / tmpdot1 */
/* s = r - alpha*ap */
LIS_MATVEC(A,p,ap);
times = lis_wtime();
lis_psolve(solver, ap, map);
ptimes += lis_wtime()-times;
lis_vector_dot(rtld,map,&tmpdot1);
alpha = rho_old / tmpdot1;
lis_vector_axpyz(-alpha,ap,r,s);
/* Early check for tolerance */
lis_solver_get_residual[conv](s,solver,&nrm2);
if( nrm2 <= tol )
{
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,p,x);
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* ms = z - alpha*map */
/* ams = A * ms */
/* tmpdot1 = <ams,s> */
/* tmpdot2 = <ams,ams> */
/* omega = tmpdot1 / tmpdot2 */
lis_vector_axpyz(-alpha,map,z,ms);
LIS_MATVEC(A,ms,ams);
lis_vector_dot(ams,s,&tmpdot1);
lis_vector_dot(ams,ams,&tmpdot2);
omega = tmpdot1 / tmpdot2;
/* x = x + alpha*p + omega*ms */
/* r = s - omega*ams */
lis_vector_axpy(alpha,p,x);
lis_vector_axpy(omega,ms,x);
lis_vector_axpyz(-omega,ams,s,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( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* z = M^-1 * r */
/* rho = <rtld,z> */
times = lis_wtime();
lis_psolve(solver, r, z);
ptimes += lis_wtime()-times;
lis_vector_dot(rtld,z,&rho);
if( rho==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) * (alpha / omega) */
/* p = z + beta*(p - omega*map) */
beta = (rho / rho_old) * (alpha / omega);
lis_vector_axpy(-omega,map,p);
lis_vector_xpay(z,beta,p);
rho_old = rho;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_bicr_quad(LIS_SOLVER solver)
{
LIS_MATRIX A,At;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,rtld, z,ztld,p, ptld, ap, map, az, aptld;
LIS_QUAD_PTR alpha, beta, rho, rho_old, tmpdot1;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
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];
output = solver->options[LIS_OPTIONS_OUTPUT];
conv = solver->options[LIS_OPTIONS_CONV_COND];
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];
ap = solver->work[6];
az = solver->work[7];
map = solver->work[8];
aptld = solver->work[9];
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);
/* 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_psolve(solver, r, z);
lis_psolvet(solver, rtld, ztld);
lis_vector_copyex_mm(z,p);
lis_vector_copyex_mm(ztld,ptld);
LIS_MATVEC(A,z,ap);
lis_vector_dotex_mmm(ap,ztld,&rho_old);
for( iter=1; iter<=maxiter; iter++ )
{
/* aptld = A^T * ptld */
/* map = M^-1 * ap */
LIS_MATVECT(A,ptld,aptld);
times = lis_wtime();
lis_psolve(solver, ap, map);
ptimes += lis_wtime()-times;
/* tmpdot1 = <map,aptld> */
lis_vector_dotex_mmm(map,aptld,&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_old / tmpdot1 */
/* x = x + alpha*p */
/* r = r - alpha*ap */
lis_quad_div((LIS_QUAD *)alpha.hi,(LIS_QUAD *)rho_old.hi,(LIS_QUAD *)tmpdot1.hi);
lis_vector_axpyex_mmm(alpha,p,x);
lis_quad_minus((LIS_QUAD *)alpha.hi);
lis_vector_axpyex_mmm(alpha,ap,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( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
/* rtld = rtld - alpha*aptld */
/* z = z - alpha*map */
/* ztld = M^-T * rtld */
/* az = A * z */
/* rho = <az,ztld> */
lis_vector_axpyex_mmm(alpha,aptld,rtld);
lis_vector_axpyex_mmm(alpha,map,z);
times = lis_wtime();
lis_psolvet(solver, rtld, ztld);
ptimes += lis_wtime()-times;
LIS_MATVEC(A,z,az);
lis_vector_dotex_mmm(az,ztld,&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 */
/* p = z + beta*p */
/* ptld = ztld + beta*ptld */
/* ap = az + beta*ap */
lis_quad_div((LIS_QUAD *)beta.hi,(LIS_QUAD *)rho.hi,(LIS_QUAD *)rho_old.hi);
lis_vector_xpayex_mmm(z,beta,p);
lis_vector_xpayex_mmm(ztld,beta,ptld);
lis_vector_xpayex_mmm(az,beta,ap);
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_ecg(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_SCALAR evalue;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,iter3,nsolver,i,j,output;
LIS_INT nprocs,my_rank;
LIS_REAL nrm2,resid,resid3;
LIS_SCALAR lshift;
LIS_VECTOR b,D,r,w,p,Aw,Ax,Ap,ones,Ds;
LIS_SCALAR *SA, *SB, *SW, *v3, *SAv3, *SBv3, *z3, *q3, *SBz3, evalue3, ievalue3;
LIS_SOLVER solver;
LIS_PRECON precon;
LIS_MATRIX A0;
LIS_VECTOR x0,z,q;
double times,itimes,ptimes,p_c_times,p_i_times;
LIS_INT nsol, precon_type;
char solvername[128], preconname[128];
A = esolver->A;
x = esolver->x;
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
lshift = esolver->lshift;
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
SA = (LIS_SCALAR *)lis_malloc(3*3*sizeof(LIS_SCALAR), "lis_ecg::SA");
SB = (LIS_SCALAR *)lis_malloc(3*3*sizeof(LIS_SCALAR), "lis_ecg::SB");
SW = (LIS_SCALAR *)lis_malloc(3*3*sizeof(LIS_SCALAR), "lis_ecg::SW");
v3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::v3");
SAv3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::SAv3");
SBv3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::SBv3");
SBz3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::SBz3");
z3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::z3");
q3 = (LIS_SCALAR *)lis_malloc(3*sizeof(LIS_SCALAR), "lis_ecg::q3");
b = esolver->work[0];
D = esolver->work[1];
Ds = esolver->work[2];
r = esolver->work[3];
w = esolver->work[4];
p = esolver->work[5];
Aw = esolver->work[6];
Ax = esolver->work[7];
Ap = esolver->work[8];
lis_vector_set_all(1.0,b);
lis_vector_nrm2(b, &nrm2);
lis_vector_scale(1/nrm2, b);
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p ilu",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_get_solvername(nsol, solvername);
lis_get_preconname(precon_type, preconname);
printf("solver : %s %d\n", solvername, nsol);
printf("precon : %s %d\n", preconname, precon_type);
lis_solve(A, b, x, solver);
lis_vector_copy(b,Ax);
lis_vector_nrm2(x, &nrm2);
lis_vector_set_all(0.0,p);
lis_vector_set_all(0.0,Ap);
lis_precon_create(solver, &precon);
solver->precon = precon;
iter=0;
while (iter<emaxiter)
{
iter = iter + 1;
lis_vector_dot(x,Ax,&evalue);
lis_vector_axpyz(-(evalue),x,Ax,r);
lis_vector_nrm2(r, &nrm2);
resid = fabs(nrm2/(evalue));
if( output )
{
if( output & LIS_EPRINT_MEM ) esolver->residual[iter] = resid;
if( output & LIS_EPRINT_OUT && A->my_rank==0 ) printf("iter: %5d residual = %e\n", iter, resid);
}
if (resid<tol) break;
lis_psolve(solver, x, w);
lis_vector_copy(x,Aw);
lis_vector_nrm2(w, &nrm2);
lis_vector_dot(w,Aw,&SA[0]);
lis_vector_dot(x,Aw,&SA[3]);
lis_vector_dot(p,Aw,&SA[6]);
SA[1] = SA[3];
lis_vector_dot(x,Ax,&SA[4]);
lis_vector_dot(p,Ax,&SA[7]);
SA[2] = SA[6];
SA[5] = SA[7];
lis_vector_dot(p,Ap,&SA[8]);
lis_vector_dot(w,w,&SB[0]);
lis_vector_dot(x,w,&SB[3]);
lis_vector_dot(p,w,&SB[6]);
SB[1] = SB[3];
lis_vector_dot(x,x,&SB[4]);
lis_vector_dot(p,x,&SB[7]);
SB[2] = SB[6];
SB[5] = SB[7];
lis_vector_dot(p,p,&SB[8]);
lis_array_set_all(3, 1.0, v3);
iter3=0;
while (iter3<emaxiter)
{
iter3 = iter3 + 1;
lis_array_nrm2(3, v3, &nrm2);
lis_array_scale(3, 1/nrm2, v3);
lis_array_matvec(3, SB, v3, SBv3, LIS_INS_VALUE);
lis_array_invvec(3, SA, SBv3, z3);
lis_array_dot2(3, SBv3, z3, &ievalue3);
if (ievalue3==0)
{
printf("ievalue3 is zero\n");
lis_precon_destroy(precon);
lis_solver_destroy(solver);
esolver->iter = iter;
esolver->resid = resid;
esolver->evalue[0] = evalue;
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_free(SA);
lis_free(SB);
lis_free(SW);
lis_free(v3);
lis_free(SAv3);
lis_free(SBv3);
lis_free(SBz3);
lis_free(z3);
lis_free(q3);
return LIS_BREAKDOWN;
}
lis_array_axpyz(3, -ievalue3, SBv3, z3, q3);
lis_array_nrm2(3, q3, &resid3);
resid3 = fabs(resid3 / ievalue3);
if (resid3<1e-12) break;
lis_array_copy(3,z3,v3);
}
evalue3 = 1 / ievalue3;
lis_vector_scale(v3[0],w);
lis_vector_axpy(v3[2],p,w);
lis_vector_xpay(w,v3[1],x);
lis_vector_copy(w,p);
lis_vector_scale(v3[0],Aw);
lis_vector_axpy(v3[2],Ap,Aw);
lis_vector_xpay(Aw,v3[1],Ax);
lis_vector_copy(Aw,Ap);
lis_vector_nrm2(x,&nrm2);
lis_vector_scale(1/nrm2,x);
lis_vector_scale(1/nrm2,Ax);
lis_vector_nrm2(p,&nrm2);
lis_vector_scale(1/nrm2,p);
lis_vector_scale(1/nrm2,Ap);
lis_solver_get_timeex(solver,×,&itimes,&ptimes,&p_c_times,&p_i_times);
esolver->ptimes += solver->ptimes;
esolver->itimes += solver->itimes;
esolver->p_c_times += solver->p_c_times;
esolver->p_i_times += solver->p_i_times;
}
lis_precon_destroy(precon);
lis_solver_destroy(solver);
esolver->iter = iter;
esolver->resid = resid;
esolver->evalue[0] = evalue;
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_free(SA);
lis_free(SB);
lis_free(SW);
lis_free(v3);
lis_free(SAv3);
lis_free(SBv3);
lis_free(SBz3);
lis_free(z3);
lis_free(q3);
if (resid<tol)
{
esolver->retcode = LIS_SUCCESS;
return LIS_SUCCESS;
}
else
{
esolver->retcode = LIS_MAXITER;
return LIS_MAXITER;
}
}
LIS_INT lis_gmres(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR r,s,z,*v;
LIS_SCALAR *h;
LIS_SCALAR aa,bb,rr,a2,b2,t;
LIS_REAL tnrm2;
LIS_REAL bnrm2,nrm2,tol;
LIS_INT iter,maxiter,n,output;
double time,ptime;
LIS_REAL rnorm;
LIS_INT i,j,k,m;
LIS_INT ii,i1,iiv,i1v,iih,jj;
LIS_INT h_dim;
LIS_INT cs,sn;
LIS_DEBUG_FUNC_IN;
A = solver->A;
b = solver->b;
x = solver->x;
n = A->n;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
m = solver->options[LIS_OPTIONS_RESTART];
h_dim = m+1;
ptime = 0.0;
s = solver->work[0];
r = solver->work[1];
z = solver->work[2];
v = &solver->work[3];
h = (LIS_SCALAR *)lis_malloc( sizeof(LIS_SCALAR)*(h_dim+1)*(h_dim+2),"lis_gmres::h" );
cs = (m+1)*h_dim;
sn = (m+2)*h_dim;
/* r = M^-1 * (b - A * x) */
lis_matvec(A,x,z);
lis_vector_xpay(b,-1.0,z);
lis_psolve(solver,z,v[0]);
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,v[0],&bnrm2) )
{
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
iter=0;
while( iter<maxiter )
{
/* first column of V */
/* v = r / ||r||_2 */
lis_vector_nrm2(v[0],&rnorm);
lis_vector_scale(1.0/rnorm,v[0]);
/* s = ||r||_2 e_1 */
lis_vector_set_all(0,s);
s->value[0] = rnorm;
i = 0;
do
{
iter++;
i++;
ii = i-1;
i1 = i;
iiv = i-1;
i1v = i;
iih = (i-1)*h_dim;
/* z = M^-1 * v */
time = lis_wtime();
lis_psolve(solver,v[iiv],z);
ptime += lis_wtime()-time;
/* w = A * z */
lis_matvec(A,z,v[i1v]);
for(k=0;k<i;k++)
{
/* h[k,i] = <w,v[k]> */
/* w = w - h[k,i] * v[k] */
lis_vector_dot(v[i1v],v[k],&t);
h[k+iih] = t;
lis_vector_axpy(-t,v[k],v[i1v]);
}
/* h[i+1,i] = ||w|| */
/* v[i+1] = w / h[i+1,i] */
lis_vector_nrm2(v[i1v],&tnrm2);
h[i1+iih] = tnrm2;
lis_vector_scale(1.0/tnrm2,v[i1v]);
for(k=1;k<=ii;k++)
{
jj = k-1;
t = h[jj+iih];
aa = h[jj+cs]*t;
aa += h[jj+sn]*h[k+iih];
bb = -h[jj+sn]*t;
bb += h[jj+cs]*h[k+iih];
h[jj+iih] = aa;
h[k+iih] = bb;
}
aa = h[ii+iih];
bb = h[i1+iih];
a2 = aa*aa;
b2 = bb*bb;
rr = sqrt(a2+b2);
if( rr==0.0 ) rr=1.0e-17;
h[ii+cs] = aa/rr;
h[ii+sn] = bb/rr;
s->value[i1] = -h[ii+sn]*s->value[ii];
s->value[ii] = h[ii+cs]*s->value[ii];
aa = h[ii+cs]*h[ii+iih];
aa += h[ii+sn]*h[i1+iih];
h[ii+iih] = aa;
/* convergence check */
nrm2 = sabs(s->value[i1])*bnrm2;
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol >= nrm2 ) break;
} while( i<m && iter <maxiter );
/* Solve H * Y = S for upper Hessenberg matrix H */
s->value[ii] = s->value[ii]/h[ii+iih];
for(k=1;k<=ii;k++)
{
jj = ii-k;
t = s->value[jj];
for(j=jj+1;j<=ii;j++)
{
t -= h[jj+j*h_dim]*s->value[j];
}
s->value[jj] = t/h[jj+jj*h_dim];
}
/* z = z + y * v */
#ifdef _OPENMP
#pragma omp parallel for private(k)
#endif
for(k=0;k<n;k++)
{
z->value[k] = s->value[0]*v[0]->value[k];
}
for(j=1;j<=ii;j++)
{
lis_vector_axpy(s->value[j],v[j],z);
}
/* r = M^-1 * z */
time = lis_wtime();
lis_psolve(solver,z,r);
ptime += lis_wtime()-time;
/* x = x + r */
lis_vector_axpy(1,r,x);
if( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
for(j=1;j<=i;j++)
{
jj = i1-j+1;
s->value[jj-1] = -h[jj-1+sn]*s->value[jj];
s->value[jj] = h[jj-1+cs]*s->value[jj];
}
for(j=0;j<=i1;j++)
{
t = s->value[j];
if( j==0 ) t = t-1.0;
lis_vector_axpy(t,v[j],v[0]);
}
}
solver->retcode = LIS_MAXITER;
solver->iter = iter+1;
solver->resid = nrm2;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_fgmres(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r,s, *z, *v;
LIS_SCALAR *h;
LIS_SCALAR aa,bb,rr,a2,b2,t;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,n,output,conv;
double times,ptimes;
LIS_REAL rnorm;
LIS_INT i,j,k,m;
LIS_INT ii,i1,iiv,i1v,iih,i1h,jj;
LIS_INT h_dim;
LIS_INT cs,sn;
LIS_DEBUG_FUNC_IN;
A = solver->A;
M = solver->precon;
b = solver->b;
x = solver->x;
n = A->n;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
m = solver->options[LIS_OPTIONS_RESTART];
conv = solver->options[LIS_OPTIONS_CONV_COND];
h_dim = m+1;
ptimes = 0.0;
s = solver->work[0];
r = solver->work[1];
z = &solver->work[2];
v = &solver->work[m+2];
h = (LIS_SCALAR *)lis_malloc( sizeof(LIS_SCALAR) * (h_dim+1) * (h_dim+2),"lis_gmres::h" );
cs = (m+1)*h_dim;
sn = (m+2)*h_dim;
/* Initial Residual */
if( lis_solver_get_initial_residual(solver,NULL,NULL,v[0],&bnrm2) )
{
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
tol = solver->tol;
rnorm = 1.0 / bnrm2;
iter=0;
while( iter<maxiter )
{
/* first column of V */
/* v = r / ||r||_2 */
lis_vector_scale(bnrm2,v[0]);
/* s = ||r||_2 e_1 */
lis_vector_set_all(0,s);
s->value[0] = rnorm;
i = 0;
do
{
iter++;
i++;
ii = i-1;
i1 = i;
iiv = i-1;
i1v = i;
iih = (i-1)*h_dim;
i1h = i*h_dim;
/* z = M^-1 v */
times = lis_wtime();
lis_psolve(solver, v[iiv], z[iiv]);
ptimes += lis_wtime()-times;
/* v = Az */
LIS_MATVEC(A,z[iiv], v[i1v]);
for(k=0;k<i;k++)
{
/* h[k,i] = <w,v[k]> */
/* w = w - h[k,i]v[k] */
lis_vector_dot(v[i1v],v[k],&t);
h[k + iih] = t;
lis_vector_axpy(-t,v[k],v[i1v]);
}
/* h[i+1,i] = ||w|| */
/* v[i+1] = w / h[i+1,i] */
lis_vector_nrm2(v[i1v],&t);
h[i1 + iih] = t;
lis_vector_scale(1.0/t,v[i1v]);
for(k=1;k<=ii;k++)
{
jj = k-1;
t = h[jj + iih];
aa = h[jj + cs]*t;
aa += h[jj + sn]*h[k + iih];
bb = -h[jj + sn]*t;
bb += h[jj + cs]*h[k + iih];
h[jj + iih] = aa;
h[k + iih] = bb;
}
aa = h[ii + iih];
bb = h[i1 + iih];
a2 = aa*aa;
b2 = bb*bb;
rr = sqrt(a2 + b2);
if( rr==0.0 ) rr=1.0e-17;
h[ii + cs] = aa / rr;
h[ii + sn] = bb / rr;
s->value[i1] = -h[ii + sn]*s->value[ii];
s->value[ii] = h[ii + cs]*s->value[ii];
aa = h[ii + cs]*h[ii + iih];
aa += h[ii + sn]*h[i1 + iih];
h[ii + iih] = aa;
/* convergence check */
nrm2 = fabs(s->value[i1]);
if( output )
{
if( output & LIS_PRINT_MEM ) solver->residual[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) printf("iter: %5d residual = %e\n", iter, nrm2);
}
if( tol >= nrm2 ) break;
} while( i<m && iter <maxiter );
/* Solve H*Y =S for upper triangular H */
s->value[ii] = s->value[ii] / h[ii + iih];
for(k=1;k<=ii;k++)
{
jj = ii-k;
t = s->value[jj];
for(j=jj+1;j<=ii;j++)
{
t -= h[jj + j*h_dim]*s->value[j];
}
s->value[jj] = t / h[jj + jj*h_dim];
}
/* x = x + zy */
for(j=0;j<=ii;j++)
{
lis_vector_axpy(s->value[j],z[j],x);
}
if( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
LIS_MATVEC(A,x,v[0]);
lis_vector_xpay(b,-1.0,v[0]);
lis_vector_nrm2(v[0],&rnorm);
bnrm2 = 1.0 / rnorm;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter+1;
solver->resid = nrm2;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_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_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_cgs(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_SCALAR alpha, beta, rho, rho_old, tmpdot1;
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];
phat = solver->work[3];
q = solver->work[4];
qhat = solver->work[5];
u = solver->work[5];
uhat = solver->work[6];
vhat = solver->work[6];
alpha = (LIS_SCALAR)1.0;
rho_old = (LIS_SCALAR)1.0;
/* 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_all(0,q);
lis_vector_set_all(0,p);
for( iter=1; iter<=maxiter; iter++ )
{
/* rho = <rtld,r> */
lis_vector_dot(rtld,r,&rho);
/* test breakdown */
if( rho==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = (rho / rho_old) */
beta = (rho / rho_old);
/* u = r + beta*q */
lis_vector_axpyz(beta,q,r,u);
/* p = u + beta*(q + beta*p) */
lis_vector_xpay(q,beta,p);
lis_vector_xpay(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_dot(rtld,vhat,&tmpdot1);
/* test breakdown */
if( tmpdot1==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho / tmpdot1 */
alpha = rho / tmpdot1;
/* q = u - alpha*vhat */
lis_vector_axpyz(-alpha,vhat,u,q);
/* phat = u + q */
/* uhat = M^-1 * (u + q) */
lis_vector_axpyz(1,u,q,phat);
times = lis_wtime();
lis_psolve(solver, phat, uhat);
ptimes += lis_wtime()-times;
/* x = x + alpha*uhat */
lis_vector_axpy(alpha,uhat,x);
/* qhat = A * uhat */
LIS_MATVEC(A,uhat,qhat);
/* r = r - alpha*qhat */
lis_vector_axpy(-alpha,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( tol >= nrm2 )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptimes = ptimes;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
rho_old = rho;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_jacobi(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR d,r,t,s;
LIS_REAL bnrm2,nrm2,tol;
LIS_INT iter,maxiter,output;
double time,ptime;
LIS_DEBUG_FUNC_IN;
A = solver->A;
b = solver->b;
x = solver->x;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
ptime = 0.0;
r = solver->work[0];
t = solver->work[1];
s = solver->work[2];
d = solver->work[3];
lis_vector_nrm2(b,&bnrm2);
bnrm2 = 1.0 / bnrm2;
lis_matrix_get_diagonal(A,d);
lis_vector_reciprocal(d);
for( iter=1; iter<=maxiter; iter++ )
{
/* x += D^{-1}(b - Ax) */
time = lis_wtime();
lis_psolve(solver,x,s);
ptime += lis_wtime() - time;
lis_matvec(A,s,t);
/* lis_matvec(A,x,t);*/
lis_vector_axpyz(-1,t,b,r);
lis_vector_nrm2(r,&nrm2);
lis_vector_pmul(r,d,r);
lis_vector_axpy(1,r,x);
/* convergence check */
nrm2 = nrm2 * bnrm2;
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol >= nrm2 )
{
time = lis_wtime();
lis_psolve(solver,x,s);
ptime += lis_wtime() - time;
lis_vector_copy(s,x);
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
lis_psolve(solver,x,s);
lis_vector_copy(s,x);
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_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_esi_quad(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_VECTOR x, Ax;
LIS_SCALAR xAx, xx, mu, lshift;
LIS_INT ss;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT i,j,k;
LIS_SCALAR evalue,dotvr;
LIS_INT iter,giter,output,niesolver;
LIS_INT nprocs,my_rank;
LIS_REAL nrm2,dot,resid,resid0;
LIS_QUAD_PTR qdot_vv, qdot_vr;
LIS_VECTOR *v,r,q;
LIS_SOLVER solver;
LIS_PRECON precon;
double times,itimes,ptimes,p_c_times,p_i_times;
LIS_INT err;
LIS_INT nsol, precon_type;
char solvername[128], preconname[128];
LIS_DEBUG_FUNC_IN;
A = esolver->A;
x = esolver->x;
ss = esolver->options[LIS_EOPTIONS_SUBSPACE];
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
lshift = esolver->lshift;
output = esolver->options[LIS_EOPTIONS_OUTPUT];
niesolver = esolver->options[LIS_EOPTIONS_INNER_ESOLVER];
r = esolver->work[0];
q = esolver->work[1];
v = &esolver->work[2];
Ax = esolver->work[3];
LIS_QUAD_SCALAR_MALLOC(qdot_vv,0,1);
LIS_QUAD_SCALAR_MALLOC(qdot_vr,1,1);
lis_vector_set_all(1.0,r);
lis_vector_nrm2(r, &nrm2);
lis_vector_scale(1/nrm2,r);
switch ( niesolver )
{
case LIS_ESOLVER_II:
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p ilu -precision quad",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_get_solvername(nsol, solvername);
lis_get_preconname(precon_type, preconname);
printf("solver : %s %d\n", solvername, nsol);
printf("precon : %s %d\n", preconname, precon_type);
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
break;
case LIS_ESOLVER_AII:
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p ilu -precision quad",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_get_solvername(nsol, solvername);
lis_get_preconname(precon_type, preconname);
printf("solver : %s %d\n", solvername, nsol);
printf("precon : %s %d\n", preconname, precon_type);
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
lis_vector_set_all(1.0,q);
lis_solve(A, q, x, solver);
lis_precon_create(solver, &precon);
solver->precon = precon;
break;
case LIS_ESOLVER_RQI:
lis_solver_create(&solver);
lis_solver_set_option("-p ilu -precision quad -maxiter 10",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_get_solvername(nsol, solvername);
lis_get_preconname(precon_type, preconname);
printf("solver : %s %d\n", solvername, nsol);
printf("precon : %s %d\n", preconname, precon_type);
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
break;
}
giter=0;
j=0;
while (j<ss)
{
lis_vector_duplicate(A,&esolver->evector[j]);
j = j+1;
lis_vector_copy(r, v[j]);
if (niesolver==LIS_ESOLVER_II || niesolver==LIS_ESOLVER_RQI)
{
/* create preconditioner */
solver->A = A;
err = lis_precon_create(solver, &precon);
if( err )
{
lis_solver_work_destroy(solver);
solver->retcode = err;
return err;
}
}
if (niesolver==LIS_ESOLVER_RQI)
{
lis_vector_nrm2(x, &nrm2);
lis_vector_scale(1/nrm2, x);
lis_matvec(A, x, Ax);
lis_vector_dot(x, Ax, &xAx);
lis_vector_dot(x, x, &xx);
mu = xAx / xx;
}
iter = 0;
while (iter<emaxiter)
{
/* diagonalization */
iter = iter+1;
giter = giter+1;
for (k=1;k<j;k++)
{
lis_vector_dotex_mmm(v[j], v[k], &qdot_vv);
lis_quad_minus((LIS_QUAD *)qdot_vv.hi);
lis_vector_axpyex_mmm(qdot_vv,v[k],v[j]);
}
switch( niesolver )
{
case LIS_ESOLVER_PI:
lis_matvec(A,v[j],r);
break;
case LIS_ESOLVER_II:
lis_solve_kernel(A, v[j], r, solver, precon);
break;
case LIS_ESOLVER_AII:
lis_psolve(solver, v[j], r);
break;
case LIS_ESOLVER_RQI:
lis_vector_nrm2(v[j], &nrm2);
lis_vector_scale(1/nrm2, v[j]);
lis_matrix_shift_diagonal(A, -mu);
lis_solve_kernel(A, v[j], r, solver, precon);
lis_matrix_shift_diagonal(A, mu);
break;
}
if ( j==1 && ( niesolver==LIS_ESOLVER_II || niesolver==LIS_ESOLVER_AII || niesolver==LIS_ESOLVER_RQI ))
{
lis_solver_get_timeex(solver,×,&itimes,&ptimes,&p_c_times,&p_i_times);
esolver->ptimes += solver->ptimes;
esolver->itimes += solver->itimes;
esolver->p_c_times += solver->p_c_times;
esolver->p_i_times += solver->p_i_times;
}
lis_vector_nrm2(r, &nrm2);
lis_vector_dotex_mmm(v[j], r, &qdot_vr);
lis_quad_minus((LIS_QUAD *)qdot_vr.hi);
lis_vector_axpyzex_mmmm(qdot_vr,v[j],r,q);
lis_quad_minus((LIS_QUAD *)qdot_vr.hi);
dotvr = qdot_vr.hi[0];
mu = mu + 1/dotvr;
lis_vector_nrm2(q, &resid);
resid = fabs(resid / dotvr);
lis_vector_scale(1/nrm2,r);
lis_vector_copy(r, v[j]);
if ( j==1 )
{
if( output & LIS_PRINT_MEM ) esolver->residual[iter] = resid;
if( output & LIS_PRINT_OUT ) printf("iter: %5d residual = %e\n", iter, resid);
esolver->iter = iter;
esolver->resid = resid;
}
if (tol>resid) break;
}
if (niesolver==LIS_ESOLVER_II || niesolver==LIS_ESOLVER_RQI)
{
lis_precon_destroy(precon);
}
switch ( niesolver )
{
case LIS_ESOLVER_PI:
esolver->evalue[j-1] = dotvr;
break;
case LIS_ESOLVER_II:
esolver->evalue[j-1] = 1/dotvr;
break;
case LIS_ESOLVER_AII:
esolver->evalue[j-1] = 1/dotvr;
break;
case LIS_ESOLVER_RQI:
esolver->evalue[j-1] = mu;
break;
}
lis_vector_copy(v[j], esolver->evector[j-1]);
if (A->my_rank==0 && ss>1)
{
#ifdef _LONGLONG
printf("Subspace: mode number = %lld\n", j-1);
#else
printf("Subspace: mode number = %d\n", j-1);
#endif
printf("Subspace: eigenvalue = %e\n", esolver->evalue[j-1]);
#ifdef _LONGLONG
printf("Subspace: number of iterations = %lld\n",iter);
#else
printf("Subspace: number of iterations = %d\n",iter);
#endif
printf("Subspace: relative residual 2-norm = %e\n",resid);
}
}
lis_vector_copy(esolver->evector[esolver->options[LIS_EOPTIONS_MODE]], esolver->x);
switch ( niesolver )
{
case LIS_ESOLVER_II:
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_solver_destroy(solver);
break;
case LIS_ESOLVER_AII:
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_precon_destroy(precon);
lis_solver_destroy(solver);
break;
case LIS_ESOLVER_RQI:
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_solver_destroy(solver);
break;
}
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
LIS_INT lis_minres(LIS_SOLVER solver)
{
LIS_Comm comm;
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR v1,v2,v3,v4,w0,w1,w2;
LIS_REAL nrm2,tol;
LIS_SCALAR alpha;
LIS_REAL beta2,beta3;
LIS_SCALAR gamma1,gamma2,gamma3;
LIS_SCALAR delta,eta;
LIS_SCALAR sigma1,sigma2,sigma3;
LIS_SCALAR rho1,rho2,rho3;
LIS_REAL r0_euc,r_euc;
LIS_INT iter,maxiter,output;
double time,ptime;
LIS_DEBUG_FUNC_IN;
comm = LIS_COMM_WORLD;
A = solver->A;
b = solver->b;
x = solver->x;
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
ptime = 0.0;
v1 = solver->work[0];
v2 = solver->work[1];
v3 = solver->work[2];
v4 = solver->work[3];
w0 = solver->work[4];
w1 = solver->work[5];
w2 = solver->work[6];
/* Lanczos algorithm */
lis_matvec(A,x,v2);
lis_vector_xpay(b,-1.0,v2);
time = lis_wtime();
lis_psolve(solver,v2,v3);
ptime += lis_wtime()-time;
lis_vector_copy(v3,v2);
/* Compute elements of Hermitian tridiagonal matrix */
lis_vector_nrm2(v2,&r_euc);
eta = beta2 = r0_euc = r_euc;
gamma2 = gamma1 = 1.0;
sigma2 = sigma1 = 0.0;
lis_vector_set_all(0.0,v1);
lis_vector_set_all(0.0,w0);
lis_vector_set_all(0.0,w1);
nrm2 = r_euc / r0_euc;
for(iter=1;iter<=maxiter;iter++)
{
/* Lanczos algorithm */
lis_vector_scale(1.0 / beta2,v2);
lis_matvec(A,v2,v3);
time = lis_wtime();
lis_psolve(solver,v3,v4);
ptime += lis_wtime()-time;
lis_vector_dot(v2,v4,&alpha);
lis_vector_axpy(-alpha,v2,v4);
lis_vector_axpy(-beta2,v1,v4);
lis_vector_nrm2(v4,&beta3);
/* Compute elements of Hermitian tridiagonal matrix */
delta = gamma2 * alpha - gamma1 * sigma2 * beta2;
rho1 = sqrt(delta * delta + beta3 * beta3);
rho2 = sigma2 * alpha + gamma1 * gamma2 * beta2;
rho3 = sigma1 * beta2;
gamma3 = delta / rho1;
sigma3 = beta3 / rho1;
lis_vector_axpyz(-rho3,w0,v2,w2);
lis_vector_axpy(-rho2,w1,w2);
lis_vector_scale(1.0 / rho1,w2);
lis_vector_axpy(gamma3 * eta,w2,x);
/* convergence check */
r_euc *= fabs(sigma3);
nrm2 = r_euc / r0_euc;
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
if( output & LIS_PRINT_OUT ) lis_print_rhistory(comm,iter,nrm2);
}
if( nrm2 <= tol )
{
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
eta *= -sigma3;
lis_vector_copy(v2,v1);
lis_vector_copy(v4,v2);
lis_vector_copy(w1,w0);
lis_vector_copy(w2,w1);
beta2 = beta3;
gamma1 = gamma2;
gamma2 = gamma3;
sigma1 = sigma2;
sigma2 = sigma3;
}
lis_vector_destroy(v1);
lis_vector_destroy(v2);
lis_vector_destroy(v3);
lis_vector_destroy(v4);
lis_vector_destroy(w0);
lis_vector_destroy(w1);
lis_vector_destroy(w2);
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_bicr(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_VECTOR r,rtld, z,ztld,p, ptld, ap, map, az, aptld;
LIS_SCALAR 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;
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];
ap = solver->work[6];
az = solver->work[7];
map = solver->work[8];
aptld = solver->work[9];
/* 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_psolve(solver, r, z);
lis_psolvet(solver, rtld, ztld);
lis_vector_copy(z,p);
lis_vector_copy(ztld,ptld);
lis_matvec(A,z,ap);
lis_vector_dot(ap,ztld,&rho_old);
for( iter=1; iter<=maxiter; iter++ )
{
/* aptld = A^T * ptld */
/* map = M^-1 * ap */
lis_matvect(A,ptld,aptld);
time = lis_wtime();
lis_psolve(solver, ap, map);
ptime += lis_wtime()-time;
/* tmpdot1 = <map,aptld> */
lis_vector_dot(map,aptld,&tmpdot1);
/* test breakdown */
if( tmpdot1==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* alpha = rho_old / tmpdot1 */
/* x = x + alpha*p */
/* r = r - alpha*ap */
alpha = rho_old / tmpdot1;
lis_vector_axpy(alpha,p,x);
lis_vector_axpy(-alpha,ap,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*aptld */
/* z = z - alpha*map */
/* ztld = M^-T * rtld */
/* az = A * z */
/* rho = <az,ztld> */
lis_vector_axpy(-alpha,aptld,rtld);
lis_vector_axpy(-alpha,map,z);
time = lis_wtime();
lis_psolvet(solver, rtld, ztld);
ptime += lis_wtime()-time;
lis_matvec(A,z,az);
lis_vector_dot(az,ztld,&rho);
/* test breakdown */
if( rho==0.0 )
{
solver->retcode = LIS_BREAKDOWN;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_BREAKDOWN;
}
/* beta = rho / rho_old */
/* p = z + beta*p */
/* ptld = ztld + beta*ptld */
/* ap = az + beta*ap */
beta = rho / rho_old;
lis_vector_xpay(z,beta,p);
lis_vector_xpay(ztld,beta,ptld);
lis_vector_xpay(az,beta,ap);
rho_old = rho;
}
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
