LIS_INT lis_solve(LIS_MATRIX A, LIS_VECTOR b, LIS_VECTOR x, LIS_SOLVER solver)
{
LIS_INT err;
LIS_PRECON precon;
LIS_DEBUG_FUNC_IN;
solver->A = A;
/* create preconditioner */
if( solver->options[LIS_OPTIONS_PRECON] < 0 || solver->options[LIS_OPTIONS_PRECON] > LIS_PRECONNAME_MAX )
{
LIS_SETERR2(LIS_ERR_ILL_ARG,"Parameter LIS_OPTIONS_PRECON is %d (Set between 0 to %d)\n",solver->options[LIS_OPTIONS_PRECON], LIS_PRECONNAME_MAX);
return LIS_ERR_ILL_ARG;
}
err = lis_precon_create(solver, &precon);
if( err )
{
lis_solver_work_destroy(solver);
solver->retcode = err;
return err;
}
/* Core Kernel of lis_solve() */
lis_solve_kernel(A, b, x, solver, precon);
lis_precon_destroy(precon);
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
void lis_solve_kernel_f(LIS_MATRIX_F *A, LIS_VECTOR_F b, LIS_VECTOR_F x, LIS_SOLVER_F *solver, LIS_PRECON *precon, LIS_INT *ierr)
{
LIS_DEBUG_FUNC_IN;
*ierr = lis_solve_kernel((LIS_MATRIX)LIS_V2P(A), (LIS_VECTOR)LIS_V2P(b), (LIS_VECTOR)LIS_V2P(x), (LIS_SOLVER)LIS_V2P(solver), (LIS_PRECON)LIS_V2P(precon));
if( *ierr ) return;
LIS_DEBUG_FUNC_OUT;
return;
}
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_esi_quad(LIS_ESOLVER esolver)
{
LIS_MATRIX A;
LIS_VECTOR x, Ax;
LIS_SCALAR xAx, xx, mu, lshift;
LIS_INT ss;
LIS_INT emaxiter;
LIS_REAL tol;
LIS_INT i,j,k;
LIS_SCALAR evalue,dotvr;
LIS_INT iter,giter,output,niesolver;
LIS_INT nprocs,my_rank;
LIS_REAL nrm2,dot,resid,resid0;
LIS_QUAD_PTR qdot_vv, qdot_vr;
LIS_VECTOR *v,r,q;
LIS_SOLVER solver;
LIS_PRECON precon;
double times,itimes,ptimes,p_c_times,p_i_times;
LIS_INT err;
LIS_INT nsol, precon_type;
char solvername[128], preconname[128];
LIS_DEBUG_FUNC_IN;
A = esolver->A;
x = esolver->x;
ss = esolver->options[LIS_EOPTIONS_SUBSPACE];
emaxiter = esolver->options[LIS_EOPTIONS_MAXITER];
tol = esolver->params[LIS_EPARAMS_RESID - LIS_EOPTIONS_LEN];
lshift = esolver->lshift;
output = esolver->options[LIS_EOPTIONS_OUTPUT];
niesolver = esolver->options[LIS_EOPTIONS_INNER_ESOLVER];
r = esolver->work[0];
q = esolver->work[1];
v = &esolver->work[2];
Ax = esolver->work[3];
LIS_QUAD_SCALAR_MALLOC(qdot_vv,0,1);
LIS_QUAD_SCALAR_MALLOC(qdot_vr,1,1);
lis_vector_set_all(1.0,r);
lis_vector_nrm2(r, &nrm2);
lis_vector_scale(1/nrm2,r);
switch ( niesolver )
{
case LIS_ESOLVER_II:
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p ilu -precision quad",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_get_solvername(nsol, solvername);
lis_get_preconname(precon_type, preconname);
printf("solver : %s %d\n", solvername, nsol);
printf("precon : %s %d\n", preconname, precon_type);
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
break;
case LIS_ESOLVER_AII:
lis_solver_create(&solver);
lis_solver_set_option("-i bicg -p ilu -precision quad",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_get_solvername(nsol, solvername);
lis_get_preconname(precon_type, preconname);
printf("solver : %s %d\n", solvername, nsol);
printf("precon : %s %d\n", preconname, precon_type);
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
lis_vector_set_all(1.0,q);
lis_solve(A, q, x, solver);
lis_precon_create(solver, &precon);
solver->precon = precon;
break;
case LIS_ESOLVER_RQI:
lis_solver_create(&solver);
lis_solver_set_option("-p ilu -precision quad -maxiter 10",solver);
lis_solver_set_optionC(solver);
lis_solver_get_solver(solver, &nsol);
lis_solver_get_precon(solver, &precon_type);
lis_get_solvername(nsol, solvername);
lis_get_preconname(precon_type, preconname);
printf("solver : %s %d\n", solvername, nsol);
printf("precon : %s %d\n", preconname, precon_type);
if( A->my_rank==0 ) printf("local shift = %e\n", lshift);
if (lshift != 0) lis_matrix_shift_diagonal(A, lshift);
break;
}
giter=0;
j=0;
while (j<ss)
{
lis_vector_duplicate(A,&esolver->evector[j]);
j = j+1;
lis_vector_copy(r, v[j]);
if (niesolver==LIS_ESOLVER_II || niesolver==LIS_ESOLVER_RQI)
{
/* create preconditioner */
solver->A = A;
err = lis_precon_create(solver, &precon);
if( err )
{
lis_solver_work_destroy(solver);
solver->retcode = err;
return err;
}
}
if (niesolver==LIS_ESOLVER_RQI)
{
lis_vector_nrm2(x, &nrm2);
lis_vector_scale(1/nrm2, x);
lis_matvec(A, x, Ax);
lis_vector_dot(x, Ax, &xAx);
lis_vector_dot(x, x, &xx);
mu = xAx / xx;
}
iter = 0;
while (iter<emaxiter)
{
/* diagonalization */
iter = iter+1;
giter = giter+1;
for (k=1;k<j;k++)
{
lis_vector_dotex_mmm(v[j], v[k], &qdot_vv);
lis_quad_minus((LIS_QUAD *)qdot_vv.hi);
lis_vector_axpyex_mmm(qdot_vv,v[k],v[j]);
}
switch( niesolver )
{
case LIS_ESOLVER_PI:
lis_matvec(A,v[j],r);
break;
case LIS_ESOLVER_II:
lis_solve_kernel(A, v[j], r, solver, precon);
break;
case LIS_ESOLVER_AII:
lis_psolve(solver, v[j], r);
break;
case LIS_ESOLVER_RQI:
lis_vector_nrm2(v[j], &nrm2);
lis_vector_scale(1/nrm2, v[j]);
lis_matrix_shift_diagonal(A, -mu);
lis_solve_kernel(A, v[j], r, solver, precon);
lis_matrix_shift_diagonal(A, mu);
break;
}
if ( j==1 && ( niesolver==LIS_ESOLVER_II || niesolver==LIS_ESOLVER_AII || niesolver==LIS_ESOLVER_RQI ))
{
lis_solver_get_timeex(solver,×,&itimes,&ptimes,&p_c_times,&p_i_times);
esolver->ptimes += solver->ptimes;
esolver->itimes += solver->itimes;
esolver->p_c_times += solver->p_c_times;
esolver->p_i_times += solver->p_i_times;
}
lis_vector_nrm2(r, &nrm2);
lis_vector_dotex_mmm(v[j], r, &qdot_vr);
lis_quad_minus((LIS_QUAD *)qdot_vr.hi);
lis_vector_axpyzex_mmmm(qdot_vr,v[j],r,q);
lis_quad_minus((LIS_QUAD *)qdot_vr.hi);
dotvr = qdot_vr.hi[0];
mu = mu + 1/dotvr;
lis_vector_nrm2(q, &resid);
resid = fabs(resid / dotvr);
lis_vector_scale(1/nrm2,r);
lis_vector_copy(r, v[j]);
if ( j==1 )
{
if( output & LIS_PRINT_MEM ) esolver->residual[iter] = resid;
if( output & LIS_PRINT_OUT ) printf("iter: %5d residual = %e\n", iter, resid);
esolver->iter = iter;
esolver->resid = resid;
}
if (tol>resid) break;
}
if (niesolver==LIS_ESOLVER_II || niesolver==LIS_ESOLVER_RQI)
{
lis_precon_destroy(precon);
}
switch ( niesolver )
{
case LIS_ESOLVER_PI:
esolver->evalue[j-1] = dotvr;
break;
case LIS_ESOLVER_II:
esolver->evalue[j-1] = 1/dotvr;
break;
case LIS_ESOLVER_AII:
esolver->evalue[j-1] = 1/dotvr;
break;
case LIS_ESOLVER_RQI:
esolver->evalue[j-1] = mu;
break;
}
lis_vector_copy(v[j], esolver->evector[j-1]);
if (A->my_rank==0 && ss>1)
{
#ifdef _LONGLONG
printf("Subspace: mode number = %lld\n", j-1);
#else
printf("Subspace: mode number = %d\n", j-1);
#endif
printf("Subspace: eigenvalue = %e\n", esolver->evalue[j-1]);
#ifdef _LONGLONG
printf("Subspace: number of iterations = %lld\n",iter);
#else
printf("Subspace: number of iterations = %d\n",iter);
#endif
printf("Subspace: relative residual 2-norm = %e\n",resid);
}
}
lis_vector_copy(esolver->evector[esolver->options[LIS_EOPTIONS_MODE]], esolver->x);
switch ( niesolver )
{
case LIS_ESOLVER_II:
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_solver_destroy(solver);
break;
case LIS_ESOLVER_AII:
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_precon_destroy(precon);
lis_solver_destroy(solver);
break;
case LIS_ESOLVER_RQI:
if (lshift != 0) lis_matrix_shift_diagonal(A, -lshift);
lis_solver_destroy(solver);
break;
}
LIS_DEBUG_FUNC_OUT;
return LIS_SUCCESS;
}
LIS_INT lis_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;
}
