! File: psb_dbgmres.f90 ! ! Subroutine: psb_dbgmres ! This subroutine implements the BGMRES method with right preconditioning. ! ! Arguments: ! ! a - type(psb_dspmat_type) Input: sparse matrix containing A. ! prec - class(psb_dprec_type) Input: preconditioner ! b - real,dimension(:,:) Input: vector containing the ! right hand side B ! x - real,dimension(:,:) Input/Output: vector containing the ! initial guess and final solution X. ! eps - real Input: Stopping tolerance; the iteration is ! stopped when the error estimate |err| <= eps ! desc_a - type(psb_desc_type). Input: The communication descriptor. ! info - integer. Output: Return code ! ! itmax - integer(optional) Input: maximum number of iterations to be ! performed. ! ! iter - integer(optional) Output: how many iterations have been ! performed. ! performed. ! err - real (optional) Output: error estimate on exit. If the ! denominator of the estimate is exactly ! 0, it is changed into 1. ! itrace - integer(optional) Input: print an informational message ! with the error estimate every itrace ! iterations ! itrs - integer(optional) Input: iteration number parameter ! istop - integer(optional) Input: stopping criterion, or how ! to estimate the error. ! 1: err = |r|/(|a||x|+|b|); here the iteration is ! stopped when |r| <= eps * (|a||x|+|b|) ! 2: err = |r|/|b|; here the iteration is ! stopped when |r| <= eps * |b| ! where r is the (preconditioned, recursive ! estimate of) residual. ! subroutine psb_dbgmres_multivect(a, prec, b, x, eps, desc_a, info, itmax, iter, err, itrace, itrs, istop) use psb_base_mod use psb_prec_mod use psb_d_krylov_conv_mod use psb_krylov_mod implicit none type(psb_dspmat_type), intent(in) :: a type(psb_desc_type), Intent(in) :: desc_a class(psb_dprec_type), intent(inout) :: prec type(psb_d_multivect_type), Intent(inout) :: b type(psb_d_multivect_type), Intent(inout) :: x real(psb_dpk_), Intent(in) :: eps integer(psb_ipk_), intent(out) :: info integer(psb_ipk_), Optional, Intent(in) :: itmax, itrace, itrs, istop integer(psb_ipk_), Optional, Intent(out) :: iter real(psb_dpk_), Optional, Intent(out) :: err real(psb_dpk_), allocatable :: aux(:), h(:,:), beta(:,:) type(psb_d_multivect_type), allocatable :: v(:) type(psb_d_multivect_type) :: v_tot, w real(psb_dpk_) :: t1, t2 real(psb_dpk_) :: rti, rti1 integer(psb_ipk_) :: litmax, naux, itrace_, n_row, n_col, nrep integer(psb_lpk_) :: mglob, m, n, n_add integer(psb_ipk_) :: n_ integer(psb_ipk_) :: i, j, istop_, err_act, idx_i, idx_j, idx integer(psb_ipk_) :: debug_level, debug_unit type(psb_ctxt_type) :: ctxt integer(psb_ipk_) :: np, me, itx real(psb_dpk_) :: rni, xni, bni, ani, bn2, r0n2 real(psb_dpk_) :: errnum, errden, deps, derr character(len=20) :: name character(len=*), parameter :: methdname='BGMRES' info = psb_success_ name = 'psb_dbgmres' call psb_erractionsave(err_act) debug_unit = psb_get_debug_unit() debug_level = psb_get_debug_level() ctxt = desc_a%get_context() call psb_info(ctxt, me, np) if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),': from psb_info',np if (.not.allocated(b%v)) then info = psb_err_invalid_vect_state_ call psb_errpush(info,name) goto 9999 endif if (.not.allocated(x%v)) then info = psb_err_invalid_vect_state_ call psb_errpush(info,name) goto 9999 endif mglob = desc_a%get_global_rows() n_row = desc_a%get_local_rows() n_col = desc_a%get_local_cols() if (present(istop)) then istop_ = istop else istop_ = 2 endif if ((istop_ < 1 ).or.(istop_ > 2 ) ) then info=psb_err_invalid_istop_ err=info call psb_errpush(info,name,i_err=(/istop_/)) goto 9999 endif if (present(itmax)) then litmax = itmax else litmax = 1000 endif if (present(itrace)) then itrace_ = itrace else itrace_ = 0 end if if (present(itrs)) then nrep = itrs if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' present: itrs: ',itrs,nrep else nrep = 10 if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' not present: itrs: ',itrs,nrep endif if (nrep <=0 ) then info=psb_err_invalid_irst_ err=info call psb_errpush(info,name,i_err=(/nrep/)) goto 9999 endif m = x%get_nrows() n = x%get_ncols() call psb_chkvect(m,n,x%get_nrows(),lone,lone,desc_a,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='psb_chkvect on X') goto 9999 end if call psb_chkvect(m,n,b%get_nrows(),lone,lone,desc_a,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='psb_chkvect on B') goto 9999 end if naux=4*n_col allocate(aux(naux),h((nrep+1)*n,nrep*n),stat=info) n_ = n if (info == psb_success_) call psb_geall(v,desc_a,info,m=nrep+1,n=n_) if (info == psb_success_) call psb_geall(v_tot,desc_a,info,n=(nrep+1)*n_) if (info == psb_success_) call psb_geall(w,desc_a,info,n=n_) if (info == psb_success_) call psb_geasb(v,desc_a,info,mold=x%v,n=n_) if (info == psb_success_) call psb_geasb(v_tot,desc_a,info,mold=x%v,n=(nrep+1)*n_) if (info == psb_success_) call psb_geasb(w,desc_a,info,mold=x%v,n=n_) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' Size of V,W ',v(1)%get_nrows(),size(v),& & w%get_nrows() if (istop_ == 1) then ani = psb_spnrmi(a,desc_a,info) bni = psb_geamax(b,desc_a,info) else if (istop_ == 2) then bn2 = psb_genrm2(b,desc_a,info) endif if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if errnum = dzero errden = done deps = eps itx = 0 n_add = n-1 if ((itrace_ > 0).and.(me == psb_root_)) call log_header(methdname) ! BGMRES algorithm ! TODO inserire timer operazioni tra mlv ! STEP 1: Compute R(0) = B - A*X(0) ! Store B in V(1) call psb_geaxpby(done,b,dzero,v(1),desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if ! Store R(0) in V(1) call psb_spmm(-done,a,x,done,v(1),desc_a,info,work=aux) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if ! STEP 2: Compute QR_fact(R(0)) beta = psb_geqrfact(v(1),desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if ! STEP 3: Outer loop outer: do j=1,nrep itx = itx + 1 ! Compute j index for H operations idx_j = (j-1)*n+1 ! STEP 4: Compute W = AV(j) call psb_spmm(done,a,v(j),dzero,w,desc_a,info,work=aux) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if if (itx >= litmax) exit outer ! STEP 5: Inner loop inner: do i=1,j ! Compute i index for H operations idx_i = (i-1)*n+1 ! STEP 6: Compute H(i,j) = V(i)_T*W h(idx_i:idx_i+n_add,idx_j:idx_j+n_add) = psb_gedot(v(i),w,desc_a,info,.true.) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if ! STEP 7: Compute W = W - V(i)*H(i,j) call psb_geaxpby(-done,psb_gedot(v(i),h(idx_i:idx_i+n_add,idx_j:idx_j+n_add),desc_a,info),done,w,desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if end do inner ! STEP 8: Compute QR_fact(W) ! Store R in H(j+1,j) h(idx_j+n:idx_j+n+n_add,idx_j:idx_j+n_add) = psb_geqrfact(w,desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if ! Store Q in V(j+1) call psb_geaxpby(done,w,dzero,v(j+1),desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if end do outer ! STEP 9: Compute Y(m) call frobenius_norm_min() if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if ! STEP 10: Compute V = {V(1),...,V(m)} do i=1,nrep+1 idx = (i-1)*n+1 v_tot%v%v(:,idx:idx+n_add) = v(i)%v%v(:,1:n) enddo ! STEP 11: X(m) = X(0) + V*Y(m) call psb_geaxpby(done,psb_gedot(v_tot,h,desc_a,info),done,x,desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if ! END algorithm if (itrace_ > 0) call log_conv(methdname,me,itx,ione,errnum,errden,deps) call log_end(methdname,me,itx,itrace_,errnum,errden,deps,err=derr,iter=iter) if (present(err)) err = derr if (info == psb_success_) call psb_gefree(v,desc_a,info) if (info == psb_success_) call psb_gefree(v_tot,desc_a,info) if (info == psb_success_) call psb_gefree(w,desc_a,info) if (info == psb_success_) deallocate(aux,h,stat=info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if call psb_erractionrestore(err_act) return 9999 call psb_error_handler(err_act) return contains ! Minimize Frobenius norm subroutine frobenius_norm_min() implicit none integer(psb_ipk_) :: lwork real(psb_dpk_), allocatable :: work(:), beta_e1(:,:) integer(psb_ipk_) :: m_h, n_h, mn ! Initialize params m_h = (nrep+1)*n n_h = nrep*n mn = min(m_h,n_h) lwork = max(1,mn+max(mn,n)) allocate(work(lwork)) ! Compute E1*beta allocate(beta_e1(m_h,n)) beta_e1 = dzero beta_e1(1:n,1:n) = beta ! Compute min Frobenius norm call dgels('N',m_h,n_h,n,h,m_h,beta_e1,m_h,work,lwork,info) deallocate(work,beta_e1) return end subroutine frobenius_norm_min end subroutine psb_dbgmres_multivect