void lis_vector_axpyz_f(LIS_SCALAR *alpha, LIS_VECTOR_F *x, LIS_VECTOR_F *y, LIS_VECTOR_F *z, LIS_INT *ierr)
{
LIS_DEBUG_FUNC_IN;
*ierr = lis_vector_axpyz(*alpha,(LIS_VECTOR)LIS_V2P(x),(LIS_VECTOR)LIS_V2P(y),(LIS_VECTOR)LIS_V2P(z));
if( *ierr ) return;
LIS_DEBUG_FUNC_OUT;
return;
}
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_crs(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_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];
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> */
times = lis_wtime();
lis_psolve(solver, r, z);
ptimes += lis_wtime()-times;
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);
times = lis_wtime();
lis_psolve(solver, ap, map);
ptimes += lis_wtime()-times;
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->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 = rho;
}
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_cgs(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR 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,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];
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 */
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_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);
time = lis_wtime();
lis_psolve(solver, phat, uhat);
ptime += lis_wtime()-time;
/* 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->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_esi(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_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_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",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",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 -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_dot(v[j], v[k], &dot);
lis_vector_axpy(-dot, 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_dot(v[j],r,&dotvr);
mu = mu + 1/dotvr;
lis_vector_axpyz(-dotvr,v[j],r,q);
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_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_ecr(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_VECTOR x;
LIS_SCALAR evalue;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,i,j,output;
LIS_INT nprocs,my_rank;
LIS_REAL nrm2,resid;
LIS_SCALAR lshift;
LIS_VECTOR r,p,Ax,Ar,Ap;
LIS_SCALAR alpha, beta;
LIS_SCALAR rAp, rp, ApAp, pAp, pp, ArAp, pAr;
double times,itimes,ptimes,p_c_times,p_i_times;
A = esolver->A;
x = esolver->x;
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
lshift = esolver->lshift;
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
r = esolver->work[0];
p = esolver->work[1];
Ax = esolver->work[2];
Ar = esolver->work[3];
Ap = esolver->work[4];
lis_vector_set_all(1.0,x);
lis_vector_nrm2(x,&nrm2);
lis_vector_scale(1/nrm2,x);
lis_matvec(A,x,Ax);
lis_vector_dot(x,Ax,&evalue);
lis_vector_axpyz(-evalue,x,Ax,r);
lis_vector_scale(-1.0,r);
lis_vector_copy(r,p);
lis_matvec(A,p,Ap);
iter=0;
while (iter<emaxiter)
{
iter = iter + 1;
lis_vector_dot(r,Ap,&rAp);
lis_vector_dot(r,p,&rp);
lis_vector_dot(Ap,Ap,&ApAp);
lis_vector_dot(p,Ap,&pAp);
lis_vector_dot(p,p,&pp);
alpha = (rAp - evalue * rp) / (ApAp - evalue * (2.0 * pAp - evalue * pp));
lis_vector_axpy(alpha,p,x);
lis_matvec(A,x,Ax);
lis_vector_dot(x,Ax,&evalue);
lis_vector_nrm2(x, &nrm2);
evalue = evalue / (nrm2 * nrm2);
lis_vector_axpyz(-evalue,x,Ax,r);
lis_vector_scale(-1.0,r);
lis_matvec(A,r,Ar);
lis_vector_dot(Ar,Ap,&ArAp);
lis_vector_dot(p,Ar,&pAr);
lis_vector_dot(r,Ap,&rAp);
lis_vector_dot(r,p,&rp);
beta = - (ArAp - evalue * ((pAr + rAp) - evalue * rp))/ (ApAp - evalue * (2.0 * pAp - evalue * pp));
lis_vector_xpay(r,beta,p);
lis_vector_nrm2(r,&nrm2);
resid = fabs(nrm2 / (evalue));
if( output )
{
if( output & LIS_EPRINT_MEM ) esolver->residual[iter] = resid;
if( output & LIS_EPRINT_OUT && A->my_rank==0 ) printf("iter: %5d residual = %e\n", iter, resid);
}
if (resid<tol) break;
}
esolver->iter = iter;
esolver->resid = resid;
esolver->evalue[0] = evalue;
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
if (resid<tol)
{
esolver->retcode = LIS_SUCCESS;
return LIS_SUCCESS;
}
else
{
esolver->retcode = LIS_MAXITER;
return LIS_MAXITER;
}
}
LIS_INT lis_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_egpi(LIS_ESOLVER esolver)
{
LIS_Comm comm;
LIS_MATRIX A,B;
LIS_VECTOR w,v,y,q;
LIS_SCALAR eta,theta;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,iter2,output;
LIS_SCALAR oshift,ishift;
LIS_REAL nrm2,resid;
LIS_SOLVER solver;
double time,itime,ptime,p_c_time,p_i_time;
LIS_INT err;
LIS_PRECON precon;
LIS_INT nsol, precon_type;
char solvername[128], preconname[128];
LIS_DEBUG_FUNC_IN;
comm = LIS_COMM_WORLD;
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
#ifdef _COMPLEX
oshift = esolver->params[LIS_EPARAMS_SHIFT - LIS_EOPTIONS_LEN] + esolver->params[LIS_EPARAMS_SHIFT_IM - LIS_EOPTIONS_LEN] * _Complex_I;
#else
oshift = esolver->params[LIS_EPARAMS_SHIFT - LIS_EOPTIONS_LEN];
#endif
A = esolver->A;
B = esolver->B;
v = esolver->x;
if (esolver->options[LIS_EOPTIONS_INITGUESS_ONES] )
{
lis_vector_set_all(1.0,v);
}
w = esolver->work[0];
y = esolver->work[1];
q = esolver->work[2];
if ( esolver->ishift != 0.0 ) oshift = ishift;
if ( oshift != 0.0 ) lis_matrix_shift_matrix(A, B, oshift);
if( output )
{
#ifdef _COMPLEX
lis_printf(comm,"shift : (%e, %e)\n", (double)creal(oshift), (double)cimag(oshift));
#else
lis_printf(comm,"shift : %e\n", (double)oshift);
#endif
}
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p none",solver);
err = lis_solver_set_optionC(solver);
CHKERR(err);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_solver_get_solvername(nsol, solvername);
lis_solver_get_preconname(precon_type, preconname);
if( output )
{
lis_printf(comm,"linear solver : %s\n", solvername);
lis_printf(comm,"preconditioner : %s\n", preconname);
}
/* create preconditioner */
solver->A = B;
err = lis_precon_create(solver, &precon);
if( err )
{
lis_solver_work_destroy(solver);
solver->retcode = err;
return err;
}
iter=0;
while (iter<emaxiter)
{
iter = iter+1;
/* v = v / ||v||_2 */
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
/* w = A * v */
lis_matvec(A, v, w);
/* v = v / <v,w>^1/2, w = w / <v,w>^1/2 */
lis_vector_dot(v, w, &eta);
eta = sqrt(eta);
lis_vector_scale(1.0/eta, v);
lis_vector_scale(1.0/eta, w);
/* y = B^-1 * w */
err = lis_solve_kernel(B, w, y, solver, precon);
if( err )
{
lis_solver_work_destroy(solver);
solver->retcode = err;
return err;
}
lis_solver_get_iter(solver, &iter2);
/* theta = <w,y> */
lis_vector_dot(w, y, &theta);
/* resid = ||y - theta * v||_2 / |theta| */
lis_vector_axpyz(-theta, v, y, q);
lis_vector_nrm2(q, &resid);
resid = resid / fabs(theta);
/* v = y */
lis_vector_copy(y, v);
/* convergence check */
lis_solver_get_timeex(solver,&time,&itime,&ptime,&p_c_time,&p_i_time);
esolver->ptime += solver->ptime;
esolver->itime += solver->itime;
esolver->p_c_time += solver->p_c_time;
esolver->p_i_time += solver->p_i_time;
if( output )
{
if( output & LIS_EPRINT_MEM ) esolver->rhistory[iter] = resid;
if( output & LIS_EPRINT_OUT ) lis_print_rhistory(comm,iter,resid);
}
if( tol >= resid )
{
esolver->retcode = LIS_SUCCESS;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = theta + oshift;
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
if ( oshift != 0.0 ) lis_matrix_shift_matrix(A, B, -oshift);
lis_precon_destroy(precon);
lis_solver_destroy(solver);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
lis_precon_destroy(precon);
esolver->retcode = LIS_MAXITER;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = theta + oshift;
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
if ( oshift != 0.0 ) lis_matrix_shift_matrix(A, B, -oshift);
lis_solver_destroy(solver);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_epi(LIS_ESOLVER esolver)
{
LIS_Comm comm;
LIS_MATRIX A;
LIS_VECTOR v,y,q;
LIS_SCALAR theta;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT iter,output;
LIS_SCALAR oshift,ishift;
LIS_REAL nrm2,resid;
LIS_DEBUG_FUNC_IN;
comm = LIS_COMM_WORLD;
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
output = esolver->options[LIS_EOPTIONS_OUTPUT];
#ifdef _COMPLEX
oshift = esolver->params[LIS_EPARAMS_SHIFT - LIS_EOPTIONS_LEN] + esolver->params[LIS_EPARAMS_SHIFT_IM - LIS_EOPTIONS_LEN] * _Complex_I;
#else
oshift = esolver->params[LIS_EPARAMS_SHIFT - LIS_EOPTIONS_LEN];
#endif
A = esolver->A;
v = esolver->x;
if (esolver->options[LIS_EOPTIONS_INITGUESS_ONES] )
{
lis_vector_set_all(1.0,v);
}
y = esolver->work[0];
q = esolver->work[1];
if ( esolver->ishift != 0.0 ) oshift = ishift;
if ( oshift != 0.0 ) lis_matrix_shift_diagonal(A, oshift);
if( output )
{
#ifdef _COMPLEX
lis_printf(comm,"shift : (%e, %e)\n", (double)creal(oshift), (double)cimag(oshift));
#else
lis_printf(comm,"shift : %e\n", (double)oshift);
#endif
}
iter=0;
while (iter<emaxiter)
{
iter = iter+1;
/* v = v / ||v||_2 */
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
/* y = A * v */
lis_matvec(A,v,y);
/* theta = <v,y> */
lis_vector_dot(v, y, &theta);
/* resid = ||y - theta * v||_2 / |theta| */
lis_vector_axpyz(-theta, v, y, q);
lis_vector_nrm2(q, &resid);
resid = resid / fabs(theta);
/* v = y */
lis_vector_copy(y, v);
/* convergence check */
if( output )
{
if( output & LIS_EPRINT_MEM ) esolver->rhistory[iter] = resid;
if( output & LIS_EPRINT_OUT ) lis_print_rhistory(comm,iter,resid);
}
if( tol >= resid )
{
esolver->retcode = LIS_SUCCESS;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = theta + oshift;
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
if ( oshift != 0.0 ) lis_matrix_shift_diagonal(A, -oshift);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
esolver->retcode = LIS_MAXITER;
esolver->iter[0] = iter;
esolver->resid[0] = resid;
esolver->evalue[0] = theta + oshift;
lis_vector_nrm2(v, &nrm2);
lis_vector_scale(1.0/nrm2, v);
if ( oshift != 0.0 ) lis_matrix_shift_diagonal(A, -oshift);
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT 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_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_gs(LIS_SOLVER solver)
{
LIS_MATRIX A;
LIS_VECTOR b,x;
LIS_VECTOR r,t,s;
LIS_REAL bnrm2, nrm2, tol;
LIS_INT iter,maxiter,output;
double time,ptime;
LIS_INT err;
LIS_DEBUG_FUNC_IN;
A = solver->A;
b = solver->b;
x = solver->x;
maxiter = solver->options[LIS_OPTIONS_MAXITER];
output = solver->options[LIS_OPTIONS_OUTPUT];
tol = solver->params[LIS_PARAMS_RESID-LIS_OPTIONS_LEN];
ptime = 0.0;
r = solver->work[0];
t = solver->work[1];
s = solver->work[2];
lis_vector_nrm2(b,&bnrm2);
bnrm2 = 1.0 / bnrm2;
err = lis_matrix_split(A);
if( err ) return err;
if( A->use_wd!=LIS_SOLVER_GS )
{
if( !A->WD )
{
err = lis_matrix_diag_duplicate(A->D,&A->WD);
if( err ) return err;
}
lis_matrix_diag_copy(A->D,A->WD);
lis_matrix_diag_inverse(A->WD);
A->use_wd = LIS_SOLVER_GS;
}
for( iter=1; iter<=maxiter; iter++ )
{
/* x += (D-L)^{-1}(b - Ax) */
time = lis_wtime();
lis_psolve(solver,x,s);
ptime += lis_wtime() - time;
lis_matvec(A,s,t);
/* lis_matvec(A,x,t);*/
lis_vector_axpyz(-1,t,b,r);
lis_vector_nrm2(r,&nrm2);
lis_matrix_solve(A,r,t,LIS_MATRIX_LOWER);
lis_vector_axpy(1,t,x);
/* convergence check */
nrm2 = nrm2 * bnrm2;
if( output )
{
if( output & LIS_PRINT_MEM ) solver->rhistory[iter] = nrm2;
if( output & LIS_PRINT_OUT && A->my_rank==0 ) lis_print_rhistory(iter,nrm2);
}
if( tol >= nrm2 )
{
time = lis_wtime();
lis_psolve(solver,x,s);
ptime += lis_wtime() - time;
lis_vector_copy(s,x);
solver->retcode = LIS_SUCCESS;
solver->iter = iter;
solver->resid = nrm2;
solver->ptime = ptime;
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
}
lis_psolve(solver,x,s);
lis_vector_copy(s,x);
solver->retcode = LIS_MAXITER;
solver->iter = iter;
solver->resid = nrm2;
LIS_DEBUG_FUNC_OUT;
return LIS_MAXITER;
}
LIS_INT lis_epi(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_eii(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_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];
iter=0;
ievalue = 1/(evalue);
#ifdef _LONG__DOUBLE
if( output & (A->my_rank==0) ) printf("local shift : %Le\n", lshift);
#else
#if defined(_COMPLEX)
if( output & (A->my_rank==0) ) printf("local shift : "CFMT"\n", cfmt(lshift));
#else
if( output & (A->my_rank==0) ) printf("local shift : %e\n", lshift);
#endif
#endif
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
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);
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_dot(x, z, &ievalue);
/* resid = ||z - 1/evalue * x||_2 / |1/evalue| */
lis_vector_axpyz(-ievalue,x,z,q);
lis_vector_nrm2(q, &resid);
resid = sabs(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;
}
