!!$ !!$ Parallel Sparse BLAS version 3.1 !!$ (C) Copyright 2006, 2007, 2008, 2009, 2010, 2012, 2013 !!$ Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari CNRS-IRIT, Toulouse !!$ !!$ Redistribution and use in source and binary forms, with or without !!$ modification, are permitted provided that the following conditions !!$ are met: !!$ 1. Redistributions of source code must retain the above copyright !!$ notice, this list of conditions and the following disclaimer. !!$ 2. Redistributions in binary form must reproduce the above copyright !!$ notice, this list of conditions, and the following disclaimer in the !!$ documentation and/or other materials provided with the distribution. !!$ 3. The name of the PSBLAS group or the names of its contributors may !!$ not be used to endorse or promote products derived from this !!$ software without specific written permission. !!$ !!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS !!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED !!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR !!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS !!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR !!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF !!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS !!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN !!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) !!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE !!$ POSSIBILITY OF SUCH DAMAGE. !!$ !!$ !!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC !!$ C C !!$ C References: C !!$ C [1] Duff, I., Marrone, M., Radicati, G., and Vittoli, C. C !!$ C Level 3 basic linear algebra subprograms for sparse C !!$ C matrices: a user level interface C !!$ C ACM Trans. Math. Softw., 23(3), 379-401, 1997. C !!$ C C !!$ C C !!$ C [2] S. Filippone, M. Colajanni C !!$ C PSBLAS: A library for parallel linear algebra C !!$ C computation on sparse matrices C !!$ C ACM Trans. on Math. Softw., 26(4), 527-550, Dec. 2000. C !!$ C C !!$ C [3] M. Arioli, I. Duff, M. Ruiz C !!$ C Stopping criteria for iterative solvers C !!$ C SIAM J. Matrix Anal. Appl., Vol. 13, pp. 138-144, 1992 C !!$ C C !!$ C C !!$ C [4] R. Barrett et al C !!$ C Templates for the solution of linear systems C !!$ C SIAM, 1993 C !!$ C C !!$ C C !!$ C [5] G. Sleijpen, D. Fokkema C !!$ C BICGSTAB(L) for linear equations involving unsymmetric C !!$ C matrices with complex spectrum C !!$ C Electronic Trans. on Numer. Analysis, Vol. 1, pp. 11-32, C !!$ C Sep. 1993 C !!$ C C !!$ C C !!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ! File: psb_scgstabl.f90 ! ! Subroutine: psb_scgstabl ! Implements the BICGSTAB(L) method ! ! ! Arguments: ! ! a - type(psb_sspmat_type) Input: sparse matrix containing A. ! prec - class(psb_sprec_type) Input: preconditioner ! b(:) - real Input: vector containing the ! right hand side B ! x(:) - real 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 ! 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. ! irst - integer(optional) Input: restart parameter L ! ! ! Subroutine psb_scgstabl_vect(a,prec,b,x,eps,desc_a,info,& & itmax,iter,err,itrace,irst,istop) use psb_base_mod use psb_prec_mod use psb_s_krylov_conv_mod use psb_krylov_mod implicit none type(psb_sspmat_type), intent(in) :: a class(psb_sprec_type), Intent(inout) :: prec Type(psb_desc_type), Intent(in) :: desc_a type(psb_s_vect_type), Intent(inout) :: b type(psb_s_vect_type), Intent(inout) :: x Real(psb_spk_), Intent(in) :: eps integer(psb_ipk_), intent(out) :: info integer(psb_ipk_), Optional, Intent(in) :: itmax, itrace, irst,istop integer(psb_ipk_), Optional, Intent(out) :: iter Real(psb_spk_), Optional, Intent(out) :: err ! = local data real(psb_spk_), allocatable, target :: aux(:), gamma(:),& & gamma1(:), gamma2(:), taum(:,:), sigma(:) type(psb_s_vect_type), allocatable, target :: wwrk(:),uh(:), rh(:) type(psb_s_vect_type), Pointer :: ww, q, r, rt0, p, v, & & s, t, z, f integer(psb_ipk_) :: itmax_, naux, mglob, it, itrace_,& & n_row, n_col, nl, err_act Logical, Parameter :: exchange=.True., noexchange=.False. integer(psb_ipk_), Parameter :: irmax = 8 integer(psb_ipk_) :: itx, i, istop_,j, k, int_err(5) integer(psb_ipk_) :: debug_level, debug_unit integer(psb_ipk_) :: ictxt, np, me real(psb_spk_) :: alpha, beta, rho, rho_old, rni, xni, bni, ani,bn2,& & omega real(psb_dpk_) :: derr type(psb_itconv_type) :: stopdat character(len=20) :: name character(len=*), parameter :: methdname='BiCGStab(L)' info = psb_success_ name = 'psb_scgstabl' call psb_erractionsave(err_act) debug_unit = psb_get_debug_unit() debug_level = psb_get_debug_level() ictxt = desc_a%get_context() Call psb_info(ictxt, me, np) if (debug_level >= psb_debug_ext_)& & write(debug_unit,*) me,' ',trim(name),': from psb_info',np if (.not.allocated(x%v)) then info = psb_err_invalid_vect_state_ call psb_errpush(info,name) goto 9999 endif if (.not.allocated(b%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 (present(itmax)) then itmax_ = itmax else itmax_ = 1000 endif if (present(itrace)) then itrace_ = itrace else itrace_ = 0 end if if (present(irst)) then nl = irst if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & 'present: irst: ',irst,nl else nl = 1 if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' not present: irst: ',irst,nl endif if (nl <=0 ) then info=psb_err_invalid_istop_ int_err(1)=nl err=info call psb_errpush(info,name,i_err=int_err) goto 9999 endif call psb_chkvect(mglob,ione,x%get_nrows(),ione,ione,desc_a,info) if (info == psb_success_) call psb_chkvect(mglob,ione,b%get_nrows(),ione,ione,desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='psb_chkvect on X/B') goto 9999 end if naux=4*n_col allocate(aux(naux),gamma(0:nl),gamma1(nl),& &gamma2(nl),taum(nl,nl),sigma(nl), stat=info) if (info /= psb_success_) then info=psb_err_alloc_dealloc_ call psb_errpush(info,name) goto 9999 end if if (info == psb_success_) Call psb_geall(wwrk,desc_a,info,n=10_psb_ipk_) if (info == psb_success_) Call psb_geall(uh,desc_a,info,n=nl+1,lb=izero) if (info == psb_success_) Call psb_geall(rh,desc_a,info,n=nl+1,lb=izero) if (info == psb_success_) Call psb_geasb(wwrk,desc_a,info,mold=x%v) if (info == psb_success_) Call psb_geasb(uh,desc_a,info,mold=x%v) if (info == psb_success_) Call psb_geasb(rh,desc_a,info,mold=x%v) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if q => wwrk(1) r => wwrk(2) p => wwrk(3) v => wwrk(4) f => wwrk(5) s => wwrk(6) t => wwrk(7) z => wwrk(8) ww => wwrk(9) rt0 => wwrk(10) call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info) if (info /= psb_success_) Then call psb_errpush(psb_err_from_subroutine_non_,name) goto 9999 End If itx = 0 restart: do ! = ! = r0 = b-ax0 ! = if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),' restart: ',itx,it if (itx >= itmax_) exit restart it = 0 call psb_geaxpby(sone,b,szero,r,desc_a,info) if (info == psb_success_) call psb_spmm(-sone,a,x,sone,r,desc_a,info,work=aux) if (info == psb_success_) call prec%apply(r,desc_a,info) if (info == psb_success_) call psb_geaxpby(sone,r,szero,rt0,desc_a,info) if (info == psb_success_) call psb_geaxpby(sone,r,szero,rh(0),desc_a,info) if (info == psb_success_) call psb_geaxpby(szero,r,szero,uh(0),desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if rho = sone alpha = szero omega = sone if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' on entry to amax: b: ',b%get_nrows() if (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) exit restart if (info /= psb_success_) Then call psb_errpush(psb_err_from_subroutine_non_,name) goto 9999 End If iteration: do it = it + nl itx = itx + nl rho = -omega*rho if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' iteration: ',itx, rho do j = 0, nl -1 If (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),'bicg part: ',j, nl rho_old = rho rho = psb_gedot(rh(j),rt0,desc_a,info) if (rho == szero) then if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' bi-cgstab iteration breakdown r',rho exit iteration endif beta = alpha*rho/rho_old rho_old = rho do k=0, j ! = call psb_geaxpby(sone,rh(:,0:j),-beta,uh(:,0:j),desc_a,info) call psb_geaxpby(sone,rh(k),-beta,uh(k),desc_a,info) end do call psb_spmm(sone,a,uh(j),szero,uh(j+1),desc_a,info,work=aux) call prec%apply(uh(j+1),desc_a,info) gamma(j) = psb_gedot(uh(j+1),rt0,desc_a,info) if (gamma(j) == szero) then if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' bi-cgstab iteration breakdown s2',gamma(j) exit iteration endif alpha = rho/gamma(j) if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' bicg part: alpha=r/g ',alpha,rho,gamma(j) do k=0,j ! = call psb_geaxpby(-alpha,uh(:,1:j+1),sone,rh(:,0:j),desc_a,info) call psb_geaxpby(-alpha,uh(k+1),sone,rh(k),desc_a,info) end do call psb_geaxpby(alpha,uh(0),sone,x,desc_a,info) call psb_spmm(sone,a,rh(j),szero,rh(j+1),desc_a,info,work=aux) call prec%apply(rh(j+1),desc_a,info) enddo do j=1, nl if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' mod g-s part: ',j, nl do i=1, j-1 taum(i,j) = psb_gedot(rh(i),rh(j),desc_a,info) taum(i,j) = taum(i,j)/sigma(i) call psb_geaxpby(-taum(i,j),rh(i),sone,rh(j),desc_a,info) enddo sigma(j) = psb_gedot(rh(j),rh(j),desc_a,info) gamma1(j) = psb_gedot(rh(0),rh(j),desc_a,info) gamma1(j) = gamma1(j)/sigma(j) enddo gamma(nl) = gamma1(nl) omega = gamma(nl) do j=nl-1,1,-1 gamma(j) = gamma1(j) do i=j+1,nl gamma(j) = gamma(j) - taum(j,i) * gamma(i) enddo enddo do j=1,nl-1 gamma2(j) = gamma(j+1) do i=j+1,nl-1 gamma2(j) = gamma2(j) + taum(j,i) * gamma(i+1) enddo enddo call psb_geaxpby(gamma(1),rh(0),sone,x,desc_a,info) call psb_geaxpby(-gamma1(nl),rh(nl),sone,rh(0),desc_a,info) call psb_geaxpby(-gamma(nl),uh(nl),sone,uh(0),desc_a,info) do j=1, nl-1 call psb_geaxpby(-gamma(j),uh(j),sone,uh(0),desc_a,info) call psb_geaxpby(gamma2(j),rh(j),sone,x,desc_a,info) call psb_geaxpby(-gamma1(j),rh(j),sone,rh(0),desc_a,info) enddo if (psb_check_conv(methdname,itx,x,rh(0),desc_a,stopdat,info)) exit restart if (info /= psb_success_) Then call psb_errpush(psb_err_from_subroutine_non_,name) goto 9999 End If end do iteration end do restart call psb_end_conv(methdname,itx,desc_a,stopdat,info,derr,iter) if (present(err)) err = derr if (info == psb_success_) call psb_gefree(uh,desc_a,info) if (info == psb_success_) call psb_gefree(rh,desc_a,info) if (info == psb_success_) call psb_gefree(wwrk,desc_a,info) if (info == psb_success_) deallocate(aux,stat=info) if (info /= psb_success_) then call psb_errpush(info,name) goto 9999 end if call psb_erractionrestore(err_act) return 9999 continue call psb_erractionrestore(err_act) if (err_act == psb_act_abort_) then call psb_error() return end if return End Subroutine psb_scgstabl_vect