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456 lines
14 KiB
Fortran
456 lines
14 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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! itrs - integer(optional) Input: iteration number parameter
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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, itrs, 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, itrs, 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(:), h(:,:), vt(:,:), beta(:,:), y(:,:)
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type(psb_d_multivect_type), allocatable :: v(:)
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type(psb_d_multivect_type) :: w, r0, rm
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real(psb_dpk_) :: t1, t2
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real(psb_dpk_) :: rti, rti1
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integer(psb_ipk_) :: litmax, 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, col, 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_), allocatable :: 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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litmax = itmax
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else
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litmax = 1000
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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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if (present(itrs)) then
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nrep = itrs
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if (debug_level >= psb_debug_ext_) &
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& write(debug_unit,*) me,' ',trim(name),&
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& ' present: itrs: ',itrs,nrep
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else
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nrep = 10
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if (debug_level >= psb_debug_ext_) &
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& write(debug_unit,*) me,' ',trim(name),&
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& ' not present: itrs: ',itrs,nrep
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endif
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if (nrep <=0 ) then
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info=psb_err_invalid_irst_
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err=info
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call psb_errpush(info,name,i_err=(/nrep/))
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goto 9999
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endif
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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),h((nrep+1)*nrhs,nrep*nrhs),y(nrep*nrhs,nrhs),&
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& vt(n_row,(nrep+1)*nrhs),r0n2(nrhs),rmn2(nrhs),&
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& errnum(nrhs),errden(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(r0,desc_a,info,n=nrhs)
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if (info == psb_success_) call psb_geall(rm,desc_a,info,n=nrhs)
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if (info == psb_success_) call psb_geasb(v,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(r0,desc_a,info,mold=x%v,n=nrhs)
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if (info == psb_success_) call psb_geasb(rm,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,r0,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,r0,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(r0,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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y = dzero
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errnum = dzero
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errden = done
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deps = eps
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itx = 0
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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 = psb_geqrfact(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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! Add V(1) to VT
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vt(:,1:nrhs) = v(1)%get_vect()
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! STEP 3: Outer loop
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outer: do j=1,nrep
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! Update itx counter
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itx = itx + 1
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if (itx >= litmax) exit outer
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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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! TODO
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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_geprod(v(i),w,desc_a,info,trans=.true.)
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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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call psb_geaxpby(-done,&
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& psb_geprod(v(i),h(idx_i:idx_i+n_add,idx_j:idx_j+n_add),desc_a,info,global=.false.),&
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& 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) = psb_geqrfact(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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! 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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! Add V(j+1) to VT
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idx = j*nrhs+1
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vt(:,idx:idx+n_add) = v(j+1)%get_vect()
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! STEP 9: Compute Y(j)
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call frobenius_norm_min(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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! Copy R(0) in R(j)
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call psb_geaxpby(done,r0,dzero,rm,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 R(j) = R(0) - VT(j+1)*H(j)*Y(j)
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call psb_geaxpby(-done,psb_geprod(psb_geprod(vt(:,1:(j+1)*nrhs),h(1:(j+1)*nrhs,1:j*nrhs),&
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& desc_a,info,global=.false.),&
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& y(1:j*nrhs,1:nrhs),desc_a,info,global=.false.),done,rm,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 nrm2 of each column of R(j)
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rmn2 = psb_genrm2(rm,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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! Set error num and den
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errnum = rmn2
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errden = r0n2
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end if
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! TODO Check convergence (max o media)
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if (maxval(errnum).le.(eps*maxval(errden))) then
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! Exit algorithm
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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,maxval(errnum),maxval(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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call psb_geaxpby(done,psb_geprod(vt(:,1:j*nrhs),y(1:j*nrhs,:),desc_a,info,global=.false.),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 algorithm
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if (itrace_ > 0) call log_conv(methdname,me,itx,ione,maxval(errnum),maxval(errden),deps)
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call log_end(methdname,me,itx,itrace_,maxval(errnum),maxval(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(r0,desc_a,info)
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if (info == psb_success_) call psb_gefree(rm,desc_a,info)
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if (info == psb_success_) deallocate(aux,h,y,vt,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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! Minimize Frobenius norm
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subroutine frobenius_norm_min(rep)
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implicit none
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integer(psb_ipk_), intent(in) :: rep
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integer(psb_ipk_) :: lwork
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real(psb_dpk_), allocatable :: work(:), beta_e1(:,:)
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real(psb_dpk_), allocatable :: h_temp(:,:)
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integer(psb_ipk_) :: m_h, n_h, mn
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! Initialize params
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h_temp = h
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m_h = (rep+1)*nrhs
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n_h = rep*nrhs
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mn = min(m_h,n_h)
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lwork = max(1,mn+max(mn,nrhs))
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allocate(work(lwork))
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! Compute E1*beta
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allocate(beta_e1(m_h,nrhs))
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beta_e1 = dzero
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beta_e1(1:nrhs,1:nrhs) = beta
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! Compute min Frobenius norm
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call dgels('N',m_h,n_h,nrhs,h_temp(1:m_h,1:n_h),m_h,beta_e1,m_h,work,lwork,info)
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! Set solution
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y = beta_e1(1:n_h,1:nrhs)
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! Deallocate
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deallocate(work,h_temp,beta_e1)
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return
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end subroutine frobenius_norm_min
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end subroutine psb_dbgmres_multivect
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