LIS_INT lis_epi(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_SCALAR evalue;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,output;
LIS_INT nprocs,my_rank;
LIS_REAL nrm2,resid;
LIS_VECTOR z,q;
double times, ptimes;
LIS_DEBUG_FUNC_IN;
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
A = esolver->A;
x = esolver->x;
if (esolver->options[LIS_EOPTIONS_INITGUESS_ONES] )
{
lis_vector_set_all(1.0,x);
}
z = esolver->work[0];
q = esolver->work[1];
iter=0;
while (iter<emaxiter)
{
iter = iter+1;
/* x = x / ||x||_2 */
lis_vector_nrm2(x, &nrm2);
lis_vector_scale(1/nrm2, x);
/* z = A * x */
lis_matvec(A,x,z);
/* evalue = <x,z> */
lis_vector_dot(x, z, &evalue);
/* resid = ||z - evalue * x||_2 / |evalue| */
lis_vector_axpyz(-evalue,x,z,q);
lis_vector_nrm2(q, &resid);
resid = fabs(resid / evalue);
/* x = z */
lis_vector_copy(z, x);
/* convergence check */
if( output )
{
if( output & LIS_EPRINT_MEM ) esolver->residual[iter] = resid;
if( output & LIS_EPRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,resid);
}
if( tol >= resid )
{
esolver->retcode = LIS_SUCCESS;
esolver->iter = iter;
esolver->resid = resid;
esolver->evalue[0] = evalue;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
esolver->retcode = LIS_MAXITER;
esolver->iter = iter;
esolver->resid = resid;
esolver->evalue[0] = evalue;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT 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_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_bicgsafe_switch(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,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,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];
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 */
times = lis_wtime();
lis_psolve(solver, r, rhat);
ptimes += lis_wtime()-times;
/* 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 */
times = lis_wtime();
lis_psolve(solver, t, that);
lis_psolve(solver, ptld, phat);
lis_psolve(solver, t0, t0hat);
ptimes += lis_wtime()-times;
/* 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->residual[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->ptimes = ptimes;
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 */
times = lis_wtime();
lis_psolve(solver, r, rhat);
ptimes += lis_wtime()-times;
/* 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 */
times = lis_wtime();
lis_psolve(solver, t, that);
lis_psolve(solver, ptld, phat);
lis_psolve(solver, t0, t0hat);
ptimes += lis_wtime()-times;
/* 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->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;
}
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_minres(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR v1,v2,v3,v4,w0,w1,w2;
LIS_REAL nrm2,tol;
LIS_SCALAR alpha,beta2,beta3;
LIS_SCALAR gamma1,gamma2,gamma3;
LIS_SCALAR delta,eta;
LIS_SCALAR sigma1,sigma2,sigma3;
LIS_SCALAR rho1,rho2,rho3;
LIS_SCALAR r0_euc,r_euc;
LIS_INT iter,maxiter,output;
double time,ptime;
LIS_DEBUG_FUNC_IN;
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 && A->my_rank==0 ) lis_print_rhistory(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_bicgsafe(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
LIS_VECTOR b,x;
LIS_VECTOR r, rtld, mr, amr, t, mt, p, ap;
LIS_VECTOR y, u, au, z;
LIS_SCALAR alpha, beta, rho, rho_old;
LIS_SCALAR qsi, eta;
LIS_SCALAR tmp, tmpdot[5];
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];
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);
times = lis_wtime();
lis_psolve(solver, r, mr);
ptimes += lis_wtime()-times;
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 */
times = lis_wtime();
lis_psolve(solver, t, mt);
ptimes += lis_wtime()-times;
/* 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->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;
}
/* 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 */
times = lis_wtime();
lis_psolve(solver, r, mr);
ptimes += lis_wtime()-times;
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_gmres_switch(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_PRECON M;
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,conv;
LIS_INT iter2,maxiter2;
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];
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];
m = solver->options[LIS_OPTIONS_RESTART];
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_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;
/* 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;
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_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->residual[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 triangular 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];
}
/* x = x + yv */
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 */
times = lis_wtime();
lis_psolve(solver, z, r);
ptimes += lis_wtime()-times;
/* x = x + r */
lis_vector_axpy(1,r,x);
if( tol2 >= nrm2 )
{
solver->iter = iter;
solver->iter2 = iter;
solver->ptimes = ptimes;
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;
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);
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[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 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 = iter2;
solver->iter2 = iter;
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 = iter2+1;
solver->iter2 = iter;
solver->resid = nrm2;
lis_free(h);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_gmres(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[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;
/* 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;
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_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]) * bnrm2;
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 ) 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 + yv */
#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 */
times = lis_wtime();
lis_psolve(solver, z, r);
ptimes += lis_wtime()-times;
/* x = x + r */
lis_vector_axpy(1,r,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;
}
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_eii_quad(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_SCALAR evalue, ievalue;
LIS_SCALAR lshift;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,iter2,output;
LIS_REAL nrm2,resid;
LIS_QUAD_PTR qdot_xz;
LIS_VECTOR z,q;
LIS_SOLVER solver;
double time,itime,ptime,p_c_time,p_i_time;
LIS_INT err;
LIS_PRECON precon;
LIS_INT nsol, precon_type;
char solvername[128], preconname[128];
LIS_DEBUG_FUNC_IN;
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
lshift = esolver->lshift;
output = esolver->options[LIS_EOPTIONS_OUTPUT];
A = esolver->A;
x = esolver->x;
if (esolver->options[LIS_EOPTIONS_INITGUESS_ONES] )
{
lis_vector_set_all(1.0,x);
}
evalue = 1.0;
z = esolver->work[0];
q = esolver->work[1];
LIS_QUAD_SCALAR_MALLOC(qdot_xz,0,1);
iter=0;
ievalue = 1/(evalue);
#ifdef _LONG__DOUBLE
if( output & (A->my_rank==0) ) printf("local shift : %Le\n", lshift);
#else
if( output & (A->my_rank==0) ) printf("local shift : %e\n", lshift);
#endif
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p none -precision quad",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_solver_get_solvername(nsol, solvername);
lis_solver_get_preconname(precon_type, preconname);
if( output & (A->my_rank==0) ) printf("linear solver : %s\n", solvername);
if( output & (A->my_rank==0) ) printf("preconditioner : %s\n", preconname);
/* create preconditioner */
solver->A = A;
err = lis_precon_create(solver, &precon);
if( err )
{
lis_solver_work_destroy(solver);
solver->retcode = err;
return err;
}
while (iter<emaxiter)
{
iter = iter+1;
/* x = x / ||x||_2 */
lis_vector_nrm2(x, &nrm2);
lis_vector_scale(1/nrm2, x);
/* z = (A - lshift I)^-1 * x */
lis_solve_kernel(A, x, z, solver, precon);
lis_solver_get_iter(solver,&iter2);
/* 1/evalue = <x,z> */
lis_vector_dotex_mmm(x, z, &qdot_xz);
lis_quad_minus((LIS_QUAD *)qdot_xz.hi);
lis_vector_axpyzex_mmmm(qdot_xz,x,z,q);
lis_quad_minus((LIS_QUAD *)qdot_xz.hi);
ievalue = qdot_xz.hi[0];
/* resid = ||z - 1/evalue * x||_2 / |1/evalue| */
lis_vector_nrm2(q, &resid);
resid = fabs(resid/ievalue);
/* x = z */
lis_vector_copy(z,x);
/* convergence check */
lis_solver_get_timeex(solver,&time,&itime,&ptime,&p_c_time,&p_i_time);
esolver->ptime += solver->ptime;
esolver->itime += solver->itime;
esolver->p_c_time += solver->p_c_time;
esolver->p_i_time += solver->p_i_time;
if( output )
{
if( output & LIS_EPRINT_MEM ) esolver->rhistory[iter] = resid;
if( output & LIS_EPRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,resid);
}
if( tol >= resid )
{
esolver->retcode = LIS_SUCCESS;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = 1/ievalue;
lis_vector_nrm2(x, &nrm2);
lis_vector_scale(1/nrm2, x);
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_precon_destroy(precon);
lis_solver_destroy(solver);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
lis_precon_destroy(precon);
esolver->retcode = LIS_MAXITER;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = 1/ievalue;
lis_vector_nrm2(x, &nrm2);
lis_vector_scale(1/nrm2, x);
if (lshift != 0)
{
lis_matrix_shift_diagonal(A, -lshift);
}
lis_solver_destroy(solver);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_eai_quad(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_INT ss,ic;
LIS_INT emaxiter,iter0,hqriter;
LIS_REAL tol,hqrerr,D;
LIS_INT i,j;
LIS_INT output, niesolver;
LIS_REAL nrm2,resid0;
LIS_VECTOR *v,w;
LIS_SCALAR *h,*hq,*hr,evalue,evalue0;
LIS_SOLVER solver;
LIS_ESOLVER esolver2;
char esolvername[128],solvername[128],preconname[128];
LIS_INT nsol,precon_type;
ss = esolver->options[LIS_EOPTIONS_SUBSPACE];
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
niesolver = esolver->options[LIS_EOPTIONS_INNER_ESOLVER];
h = (LIS_SCALAR *)lis_malloc(ss*ss*sizeof(LIS_SCALAR), "lis_eai_quad::h");
hq = (LIS_SCALAR *)lis_malloc(ss*ss*sizeof(LIS_SCALAR), "lis_eai_quad::hq");
hr = (LIS_SCALAR *)lis_malloc(ss*ss*sizeof(LIS_SCALAR), "lis_eai_quad::hr");
A = esolver->A;
w = esolver->work[0];
v = &esolver->work[1];
lis_vector_set_all(0.0,v[0]);
lis_vector_set_all(1.0,w);
lis_vector_nrm2(w, &nrm2);
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p none",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_solver_get_solvername(nsol, solvername);
lis_solver_get_preconname(precon_type, preconname);
lis_esolver_get_esolvername(niesolver, esolvername);
if( A->my_rank==0 ) printf("inner eigensolver : %s\n", esolvername);
if( A->my_rank==0 ) printf("linear solver : %s\n", solvername);
if( A->my_rank==0 ) printf("preconditioner : %s\n", preconname);
for (i=0;i<ss*ss;i++) h[i] = 0.0;
j=-1;
while (j<ss-1)
{
j = j+1;
lis_vector_copy(w, v[j]);
/* w = A * v(j) */
lis_matvec(A, v[j], w);
/* reorthogonalization */
for (i=0;i<=j;i++)
{
/* h(i,j) = <v(i), w> */
lis_vector_dot(v[i], w, &h[i+j*ss]);
/* w = w - h(i,j) * v(i) */
lis_vector_axpy(-h[i+j*ss], v[i], w);
}
/* h(j+1,j) = ||w||_2 */
lis_vector_nrm2(w, &h[j+1+j*ss]);
/* convergence check */
if (fabs(h[j+1+j*ss])<tol) break;
/* v(j+1) = w / h(i+1,j) */
lis_vector_scale(1/h[j+1+j*ss],w);
lis_vector_copy(w,v[j+1]);
}
/* compute eigenvalues of a real upper
Hessenberg matrix H(j) = SH'(j)S^* */
lis_array_qr(ss,h,hq,hr,&hqriter,&hqrerr);
if( A->my_rank==0 )
{
#ifdef _LONG__LONG
printf("size of subspace : %lld\n\n", ss);
#else
printf("size of subspace : %d\n\n", ss);
#endif
if( output ) printf("approximate eigenvalues in subspace:\n\n");
i=0;
while (i<ss-1)
{
i = i + 1;
if (fabs(h[i+(i-1)*ss])<tol)
{
#ifdef _LONG__LONG
printf("Arnoldi: mode number = %lld\n",i-1);
#else
printf("Arnoldi: mode number = %d\n",i-1);
#endif
#ifdef _LONG__DOUBLE
printf("Arnoldi: eigenvalue = %Le\n",h[i-1+(i-1)*ss]);
#else
printf("Arnoldi: eigenvalue = %e\n",h[i-1+(i-1)*ss]);
#endif
esolver->evalue[i-1] = h[i-1+(i-1)*ss];
}
else
{
D = (h[i-1+(i-1)*ss]-h[i+i*ss]) * (h[i-1+(i-1)*ss]-h[i+i*ss])
+ 4 * h[i-1+i*ss] * h[i+(i-1)*ss];
if (D<0)
{
#ifdef _LONG__LONG
printf("Arnoldi: mode number = %lld\n",i-1);
#else
printf("Arnoldi: mode number = %d\n",i-1);
#endif
#ifdef _LONG__DOUBLE
printf("Arnoldi: eigenvalue = %Le + %Le i\n", (h[i-1+(i-1)*ss]+h[i+i*ss])/2, sqrt(-D)/2);
#else
printf("Arnoldi: eigenvalue = %e + %e i\n", (h[i-1+(i-1)*ss]+h[i+i*ss])/2, sqrt(-D)/2);
#endif
#ifdef _LONG__LONG
printf("Arnoldi: mode number = %lld\n",i);
#else
printf("Arnoldi: mode number = %d\n",i);
#endif
#ifdef _LONG__DOUBLE
printf("Arnoldi: eigenvalue = %Le - %Le i\n", (h[i-1+(i-1)*ss]+h[i+i*ss])/2, sqrt(-D)/2);
#else
printf("Arnoldi: eigenvalue = %e - %e i\n", (h[i-1+(i-1)*ss]+h[i+i*ss])/2, sqrt(-D)/2);
#endif
esolver->evalue[i-1] = (h[i-1+(i-1)*ss]+h[i+i*ss])/2;
esolver->evalue[i] = (h[i-1+(i-1)*ss]+h[i+i*ss])/2;
i=i+1;
}
else
{
#ifdef _LONG__LONG
printf("Arnoldi: mode number = %lld\n",i-1);
#else
printf("Arnoldi: mode number = %d\n",i-1);
#endif
#ifdef _LONG__DOUBLE
printf("Arnoldi: eigenvalue = %Le\n",h[i-1+(i-1)*ss]);
#else
printf("Arnoldi: eigenvalue = %e\n",h[i-1+(i-1)*ss]);
#endif
esolver->evalue[i-1] = h[i-1+(i-1)*ss];
}
}
}
if (i<ss)
{
#ifdef _LONG__LONG
printf("Arnoldi: mode number = %lld\n",i);
#else
printf("Arnoldi: mode number = %d\n",i);
#endif
#ifdef _LONG__DOUBLE
printf("Arnoldi: eigenvalue = %Le\n",h[i+i*ss]);
#else
printf("Arnoldi: eigenvalue = %e\n",h[i+i*ss]);
#endif
}
if( output ) printf("\n");
if( output ) printf("compute refined (real) eigenpairs, where imaginary parts are currently neglected:\n\n");
}
lis_esolver_create(&esolver2);
esolver2->options[LIS_EOPTIONS_ESOLVER] = niesolver;
esolver2->options[LIS_EOPTIONS_SUBSPACE] = 1;
esolver2->options[LIS_EOPTIONS_MAXITER] = emaxiter;
esolver2->options[LIS_EOPTIONS_OUTPUT] = esolver->options[LIS_EOPTIONS_OUTPUT];
esolver2->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN] = tol;
esolver2->eprecision = LIS_PRECISION_QUAD;
/* compute refined (real) eigenpairs, where imaginary parts are currently neglected */
for (i=0;i<ss;i++)
{
lis_vector_duplicate(A, &esolver->evector[i]);
esolver2->lshift = -(esolver->evalue[i]);
lis_esolve(A, esolver->evector[i], &evalue, esolver2);
lis_esolver_work_destroy(esolver2);
esolver->evalue[i] = evalue - esolver2->lshift;
esolver->iter[i] = esolver2->iter[0];
esolver->resid[i] = esolver2->resid[0];
if (i==0)
{
evalue0 = esolver->evalue[0];
iter0 = esolver2->iter[0];
resid0 = esolver2->resid[0];
if( output & LIS_EPRINT_MEM )
{
for (ic=0;ic<iter0+1;ic++)
{
esolver->rhistory[ic] = esolver2->rhistory[ic];
}
}
esolver->ptime = esolver2->ptime;
esolver->itime = esolver2->itime;
esolver->p_c_time = esolver2->p_c_time;
esolver->p_i_time = esolver2->p_i_time;
}
if (A->my_rank==0)
{
#ifdef _LONG__LONG
if( output ) printf("Arnoldi: mode number = %lld\n", i);
#else
if( output ) printf("Arnoldi: mode number = %d\n", i);
#endif
#ifdef _LONG__DOUBLE
if( output ) printf("Arnoldi: eigenvalue = %Le\n", esolver->evalue[i]);
#else
if( output ) printf("Arnoldi: eigenvalue = %e\n", esolver->evalue[i]);
#endif
#ifdef _LONG__LONG
if( output ) printf("Arnoldi: number of iterations = %lld\n",esolver2->iter[0]);
#else
if( output ) printf("Arnoldi: number of iterations = %d\n",esolver2->iter[0]);
#endif
#ifdef _LONG__DOUBLE
if( output ) printf("Arnoldi: relative residual = %Le\n\n",esolver2->resid[0]);
#else
if( output ) printf("Arnoldi: relative residual = %e\n\n",esolver2->resid[0]);
#endif
}
}
esolver->evalue[0] = evalue0;
esolver->iter[0] = iter0;
esolver->resid[0] = resid0;
lis_vector_copy(esolver->evector[0], esolver->x);
lis_esolver_destroy(esolver2);
lis_free(h);
lis_free(hq);
lis_free(hr);
lis_solver_destroy(solver);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
