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494 lines
15 KiB
Fortran
494 lines
15 KiB
Fortran
! File: psb_dbgmres.f90
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!
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! Subroutine: psb_dbgmres
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! This subroutine implements the BGMRES method with right preconditioning.
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!
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! Arguments:
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!
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! a - type(psb_dspmat_type) Input: sparse matrix containing A.
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! prec - class(psb_dprec_type) Input: preconditioner
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! b - real,dimension(:,:) Input: vector containing the
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! right hand side B
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! x - real,dimension(:,:) Input/Output: vector containing the
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! initial guess and final solution X.
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! eps - real Input: Stopping tolerance; the iteration is
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! stopped when the error estimate |err| <= eps
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! desc_a - type(psb_desc_type). Input: The communication descriptor.
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! info - integer. Output: Return code
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!
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! itmax - integer(optional) Input: maximum number of iterations to be
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! performed.
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!
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! iter - integer(optional) Output: how many iterations have been
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! performed.
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! performed.
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! err - real (optional) Output: error estimate on exit. If the
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! denominator of the estimate is exactly
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! 0, it is changed into 1.
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! itrace - integer(optional) Input: print an informational message
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! with the error estimate every itrace
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! iterations
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! istop - integer(optional) Input: stopping criterion, or how
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! to estimate the error.
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! 1: err = |r|/(|a||x|+|b|); here the iteration is
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! stopped when |r| <= eps * (|a||x|+|b|)
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! 2: err = |r|/|b|; here the iteration is
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! stopped when |r| <= eps * |b|
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! where r is the (preconditioned, recursive
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! estimate of) residual.
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!
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subroutine psb_dbgmres_multivect(a, prec, b, x, eps, desc_a, info, itmax, iter, err, itrace, istop)
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use psb_base_mod
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use psb_prec_mod
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use psb_d_krylov_conv_mod
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use psb_krylov_mod
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implicit none
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type(psb_dspmat_type), intent(in) :: a
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type(psb_desc_type), intent(in) :: desc_a
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class(psb_dprec_type), intent(inout) :: prec
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type(psb_d_multivect_type), intent(inout) :: b
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type(psb_d_multivect_type), intent(inout) :: x
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real(psb_dpk_), intent(in) :: eps
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integer(psb_ipk_), intent(out) :: info
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integer(psb_ipk_), optional, intent(in) :: itmax, itrace, istop
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integer(psb_ipk_), optional, intent(out) :: iter
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real(psb_dpk_), optional, intent(out) :: err
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real(psb_dpk_), allocatable :: aux(:), c(:,:), s(:,:), h(:,:), beta(:,:)
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type(psb_d_multivect_type), allocatable :: v(:)
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type(psb_d_multivect_type) :: w, pd
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integer(psb_ipk_) :: naux, itrace_, n_row, n_col, nrhs, nrep
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integer(psb_lpk_) :: mglob, n_add, ncv
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integer(psb_ipk_) :: i, j, k, istop_, err_act, idx_i, idx_j, idx
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integer(psb_ipk_) :: debug_level, debug_unit
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type(psb_ctxt_type) :: ctxt
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integer(psb_ipk_) :: np, me, itx
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real(psb_dpk_), allocatable :: r0n2(:), rmn2(:)
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real(psb_dpk_) :: errnum, errden
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real(psb_dpk_) :: deps, derr
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character(len=20) :: name
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character(len=*), parameter :: methdname='BGMRES'
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info = psb_success_
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name = 'psb_dbgmres'
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call psb_erractionsave(err_act)
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debug_unit = psb_get_debug_unit()
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debug_level = psb_get_debug_level()
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ctxt = desc_a%get_context()
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call psb_info(ctxt, me, np)
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if (debug_level >= psb_debug_ext_) &
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& write(debug_unit,*) me,' ',trim(name),': from psb_info',np
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if (.not.allocated(b%v)) then
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info = psb_err_invalid_vect_state_
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call psb_errpush(info,name)
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goto 9999
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endif
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if (.not.allocated(x%v)) then
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info = psb_err_invalid_vect_state_
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call psb_errpush(info,name)
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goto 9999
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endif
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mglob = desc_a%get_global_rows()
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n_row = desc_a%get_local_rows()
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n_col = desc_a%get_local_cols()
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if (present(istop)) then
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istop_ = istop
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else
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istop_ = 1
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endif
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if (istop_ /= 1) then
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info=psb_err_invalid_istop_
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err=info
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call psb_errpush(info,name,i_err=(/istop_/))
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goto 9999
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endif
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if (present(itmax)) then
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nrep = itmax
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else
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nrep = 10
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endif
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if (present(itrace)) then
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itrace_ = itrace
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else
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itrace_ = 0
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end if
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ncv = x%get_ncols()
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call psb_chkvect(mglob,ncv,x%get_nrows(),lone,lone,desc_a,info)
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if(info /= psb_success_) then
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info=psb_err_from_subroutine_
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call psb_errpush(info,name,a_err='psb_chkvect on X')
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goto 9999
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end if
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ncv = b%get_ncols()
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call psb_chkvect(mglob,ncv,b%get_nrows(),lone,lone,desc_a,info)
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if(info /= psb_success_) then
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info=psb_err_from_subroutine_
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call psb_errpush(info,name,a_err='psb_chkvect on B')
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goto 9999
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end if
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naux = 4*n_col
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nrhs = x%get_ncols()
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allocate(aux(naux),c(nrep*nrhs,nrhs),s(nrep*nrhs,nrhs),h((nrep+1)*nrhs,nrep*nrhs),&
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& beta((nrep+1)*nrhs,nrhs),r0n2(nrhs),rmn2(nrhs),stat=info)
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if (info == psb_success_) call psb_geall(v,desc_a,info,m=nrep+1,n=nrhs)
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if (info == psb_success_) call psb_geall(w,desc_a,info,n=nrhs)
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if (info == psb_success_) call psb_geall(pd,desc_a,info,n=nrhs)
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if (info == psb_success_) call psb_geasb(v(1),desc_a,info,mold=x%v,n=nrhs)
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if (info == psb_success_) call psb_geasb(w,desc_a,info,mold=x%v,n=nrhs)
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if (info == psb_success_) call psb_geasb(pd,desc_a,info,mold=x%v,n=nrhs)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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if (debug_level >= psb_debug_ext_) &
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& write(debug_unit,*) me,' ',trim(name),&
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& ' Size of V,W ',v(1)%get_nrows(),size(v),&
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& w%get_nrows()
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! Compute norm2 of R(0)
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if (istop_ == 1) then
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call psb_geaxpby(done,b,dzero,v(1),desc_a,info)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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call psb_spmm(-done,a,x,done,v(1),desc_a,info,work=aux)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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r0n2 = psb_genrm2(v(1),desc_a,info)
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endif
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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h = dzero
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c = dzero
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s = dzero
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beta = dzero
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itx = 0
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deps = eps
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n_add = nrhs-1
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if ((itrace_ > 0).and.(me == psb_root_)) call log_header(methdname)
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! BGMRES algorithm
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! STEP 1: Compute R(0) = B - A*X(0)
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! Store B in V(1)
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call psb_geaxpby(done,b,dzero,v(1),desc_a,info)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! Store R(0) in V(1)
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call psb_spmm(-done,a,x,done,v(1),desc_a,info,work=aux)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! STEP 2: Compute QR_fact(R(0))
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beta(1:nrhs,1:nrhs) = mgs_qr_fact(v(1))
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! STEP 3: Outer loop
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outer: do j=1,nrep
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! Assembly next iteration
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call psb_geasb(v(j+1),desc_a,info,mold=x%v,n=nrhs)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! Update itx counter
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itx = itx + 1
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! Compute j index for H operations
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idx_j = (j-1)*nrhs+1
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! STEP 4: Compute W = AV(j)
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call psb_spmm(done,a,v(j),dzero,w,desc_a,info,work=aux)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! STEP 5: Inner loop
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inner: do i=1,j
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! Compute i index for H operations
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idx_i = (i-1)*nrhs+1
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! STEP 6: Compute H(i,j) = (V(i)**T)*W
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h(idx_i:idx_i+n_add,idx_j:idx_j+n_add) = psb_gedot(v(i),w,desc_a,info)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! STEP 7: Compute W = W - V(i)*H(i,j)
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! Compute product V(i)*H(i,j)
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call psb_geprod(v(i),h(idx_i:idx_i+n_add,idx_j:idx_j+n_add),pd,desc_a,info)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! Compute W
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call psb_geaxpby(-done,pd,done,w,desc_a,info)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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end do inner
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! STEP 8: Compute QR_fact(W)
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! Store R in H(j+1,j)
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h(idx_j+nrhs:idx_j+nrhs+n_add,idx_j:idx_j+n_add) = mgs_qr_fact(w)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! Store Q in V(j+1)
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call psb_geaxpby(done,w,dzero,v(j+1),desc_a,info)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! STEP 9: Compute Givens rotation
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rmn2 = givens_rotation(j)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! Compute residues
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if (istop_ == 1) then
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errnum = sum(rmn2)/size(rmn2)
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errden = sum(r0n2)/size(r0n2)
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end if
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! Check convergence
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if (errnum <= eps*errden) then
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exit outer
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end if
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! Log update
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if (itrace_ > 0) call log_conv(methdname,me,itx,ione,errnum,errden,deps)
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end do outer
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! STEP 10: X(m) = X(0) + VT(m)*Y(m)
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! Compute Y(m)
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call dtrsm('L','U','N','N',itx*nrhs,nrhs,done,h,size(h,1),beta,size(beta,1))
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! Loop product
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do i=1,itx
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! Compute index for Y products
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idx = (i-1)*nrhs+1
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! Compute product V(i)*Y(i)
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call psb_geprod(v(i),beta(idx:idx+n_add,:),pd,desc_a,info)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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! Add product to X(m)
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call psb_geaxpby(done,pd,done,x,desc_a,info)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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end do
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! END algorithm
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if (itrace_ > 0) call log_conv(methdname,me,itx,ione,errnum,errden,deps)
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call log_end(methdname,me,itx,itrace_,errnum,errden,deps,err=derr,iter=iter)
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if (present(err)) err = derr
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if (info == psb_success_) call psb_gefree(v,desc_a,info)
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if (info == psb_success_) call psb_gefree(w,desc_a,info)
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if (info == psb_success_) call psb_gefree(pd,desc_a,info)
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if (info == psb_success_) deallocate(aux,c,s,h,beta,r0n2,rmn2,stat=info)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_non_
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call psb_errpush(info,name)
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goto 9999
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end if
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call psb_erractionrestore(err_act)
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return
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9999 call psb_error_handler(err_act)
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return
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contains
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! Modified Gram-Schmidt QR factorization
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function mgs_qr_fact(mv) result(res)
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implicit none
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! I/O parameters
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type(psb_d_multivect_type), intent(inout) :: mv
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real(psb_dpk_), allocatable :: res(:,:)
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! Utils
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real(psb_dpk_) :: scal
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integer(psb_ipk_) :: i, j
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! Allocate output
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allocate(res(nrhs,nrhs))
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! Initialize params
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res = dzero
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! Start factorization
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do i=1,nrhs
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! Compute R(i,i) = nrm2(W(:,i))
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res(i,i) = psb_genrm2(mv,i,desc_a,info)
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! Compute 1/R(i,i)
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scal = done/res(i,i)
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! Compute W(:,i) = W(:,i)/R(i,i)
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call psb_geaxpby(i,i,scal,mv,dzero,mv,desc_a,info)
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! Iterate over columns
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do j=i+1,nrhs
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! Compute R(i,j) = W(:,i)'*W(:,j)
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res(i,j) = psb_gedot(i,j,mv,mv,desc_a,info)
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! Compute W(:,j) = W(:,j) - R(i,j)*W(:,i)
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call psb_geaxpby(i,j,-res(i,j),mv,done,mv,desc_a,info)
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end do
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end do
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end function mgs_qr_fact
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function givens_rotation(rep) result(res)
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! I/O parameters
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real(psb_dpk_), allocatable :: res(:)
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integer(psb_ipk_), intent(in) :: rep
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! Utils
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integer(psb_ipk_) :: i, j, idx_rep, idx_col, idx, back_idx
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real(psb_dpk_) :: rti, rti1
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! Initialize params
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idx_rep = (rep-1)*nrhs+1
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idx = done
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! Old rotations for new columns in H
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do i=nrhs+1,rep*nrhs
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! Do nrhs rotation for each new column
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do j=1,nrhs
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call drot(nrhs,h((i-1)-(j-1),idx_rep:idx_rep+n_add),1,&
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& h(i-(j-1),idx_rep:idx_rep+n_add),1,c(idx,j),s(idx,j))
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end do
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! Update C and S row idx
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idx = idx + done
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end do
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! Rotations for new columns
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do i=1,nrhs
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! Compute col idx
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idx_col = idx_rep+(i-1)
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do j=1,nrhs
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! Compute backward idx
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back_idx = idx_rep+nrhs+(i-j)
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! Generate Givens rotation
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rti = h(back_idx-1,idx_col)
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rti1 = h(back_idx,idx_col)
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call drotg(rti,rti1,c(idx_col,j),s(idx_col,j))
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! Apply Givens rotation to H
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call drot(nrhs-(i-1),h(back_idx-1,idx_col:idx_rep+n_add),1,&
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& h(back_idx,idx_col:idx_rep+n_add),&
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& 1,c(idx_col,j),s(idx_col,j))
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! Eliminate rotated values
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h(back_idx,idx_rep:idx_col) = dzero
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! Apply Givens rotation to G=E1*Beta
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call drot(j,beta(back_idx-1,nrhs-(j-1):nrhs),&
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& 1,beta(back_idx,nrhs-(j-1):nrhs),1,&
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& c(idx_col,j),s(idx_col,j))
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end do
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end do
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! Compute residues
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res = sum(beta(idx_rep+nrhs:idx_rep+nrhs+n_add,:)**2,dim=1)
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end function givens_rotation
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end subroutine psb_dbgmres_multivect
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