void lis_solver_get_precon_f(LIS_SOLVER_F *solver, LIS_INT *nsol, LIS_INT *ierr) { LIS_DEBUG_FUNC_IN; *ierr = lis_solver_get_precon((LIS_SOLVER)LIS_V2P(solver),nsol); LIS_DEBUG_FUNC_OUT; return; }
bool LisLinearSolver::solve(LisMatrix &A, LisVector &b, LisVector &x) { finalizeMatrixAssembly(A); INFO("------------------------------------------------------------------"); INFO("*** LIS solver computation"); // Create solver LIS_SOLVER solver; int ierr = lis_solver_create(&solver); if (!checkLisError(ierr)) return false; lis_solver_set_option( const_cast<char*>(_lis_option._option_string.c_str()), solver); #ifdef _OPENMP INFO("-> number of threads: %i", (int) omp_get_max_threads()); #endif { int precon; ierr = lis_solver_get_precon(solver, &precon); INFO("-> precon: %i", precon); } { int slv; ierr = lis_solver_get_solver(solver, &slv); INFO("-> solver: %i", slv); } // solve INFO("-> solve"); ierr = lis_solve(A.getRawMatrix(), b.getRawVector(), x.getRawVector(), solver); if (!checkLisError(ierr)) return false; LIS_INT linear_solver_status; ierr = lis_solver_get_status(solver, &linear_solver_status); if (!checkLisError(ierr)) return false; INFO("-> status: %d", linear_solver_status); { int iter = 0; ierr = lis_solver_get_iter(solver, &iter); if (!checkLisError(ierr)) return false; INFO("-> iteration: %d", iter); } { double resid = 0.0; ierr = lis_solver_get_residualnorm(solver, &resid); if (!checkLisError(ierr)) return false; INFO("-> residual: %g", resid); } { double time, itime, ptime, p_ctime, p_itime; ierr = lis_solver_get_timeex(solver, &time, &itime, &ptime, &p_ctime, &p_itime); if (!checkLisError(ierr)) return false; INFO("-> time total (s): %g", time); INFO("-> time iterations (s): %g", itime); INFO("-> time preconditioning (s): %g", ptime); INFO("-> time precond. create (s): %g", p_ctime); INFO("-> time precond. iter (s): %g", p_itime); } // Clear solver ierr = lis_solver_destroy(solver); if (!checkLisError(ierr)) return false; INFO("------------------------------------------------------------------"); return linear_solver_status == LIS_SUCCESS; }
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_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_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; }