!!$ !!$ Parallel Sparse BLAS version 3.4 !!$ (C) Copyright 2006, 2010, 2015 !!$ 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 !!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ! ! File: psb_cbicg.f90 ! ! Subroutine: psb_cbicg ! This subroutine implements the BiCG method. ! ! Arguments: ! ! a - type(psb_cspmat_type) Input: sparse matrix containing A. ! prec - class(psb_cprec_type) Input: preconditioner ! b(:) - complex Input: vector containing the ! right hand side B ! x(:) - complex 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. ! 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. ! ! subroutine psb_cbicg_vect(a,prec,b,x,eps,desc_a,info,& & itmax,iter,err,itrace,istop) use psb_base_mod use psb_prec_mod use psb_c_krylov_conv_mod use psb_krylov_mod implicit none type(psb_cspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a class(psb_cprec_type), intent(inout) :: prec type(psb_c_vect_type), Intent(inout) :: b type(psb_c_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, istop integer(psb_ipk_), optional, intent(out) :: iter real(psb_spk_), optional, intent(out) :: err ! !$ local data complex(psb_spk_), allocatable, target :: aux(:) type(psb_c_vect_type), allocatable, target :: wwrk(:) type(psb_c_vect_type), pointer :: ww, q, r, p,& & zt, pt, z, rt, qt integer(psb_ipk_) :: int_err(5) integer(psb_ipk_) :: itmax_, naux, mglob, it, itrace_,& & n_row, n_col, istop_, err_act integer(psb_ipk_) :: debug_level, debug_unit logical, parameter :: exchange=.true., noexchange=.false. integer(psb_ipk_), parameter :: irmax = 8 integer(psb_ipk_) :: itx integer(psb_ipk_) :: ictxt, np, me complex(psb_spk_) :: alpha, beta, rho, rho_old, sigma real(psb_dpk_) :: derr type(psb_itconv_type) :: stopdat character(len=20) :: name,ch_err character(len=*), parameter :: methdname='BiCG' info = psb_success_ name = 'psb_cbicg' 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 mglob = desc_a%get_global_rows() n_row = desc_a%get_local_rows() n_col = desc_a%get_local_cols() 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 if (present(istop)) then istop_ = istop else istop_ = 2 endif ! ! istop_ = 1: normwise backward error, infinity norm ! istop_ = 2: ||r||/||b|| norm 2 ! if ((istop_ < 1 ).or.(istop_ > 2 ) ) then info=psb_err_invalid_istop_ int_err=istop_ 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_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='psb_chkvect on X') goto 9999 end if 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 B') goto 9999 end if naux=4*n_col allocate(aux(naux),stat=info) if (info == psb_success_) call psb_geall(wwrk,desc_a,info,n=9_psb_ipk_) if (info == psb_success_) call psb_geasb(wwrk,desc_a,info,mold=x%v) if(info /= psb_success_) then info=psb_err_from_subroutine_non_ ch_err='psb_asb' err=info call psb_errpush(info,name,a_err=ch_err) goto 9999 end if q => wwrk(1) qt => wwrk(2) r => wwrk(3) rt => wwrk(4) p => wwrk(5) pt => wwrk(6) z => wwrk(7) zt => wwrk(8) ww => wwrk(9) if (present(itmax)) then itmax_ = itmax else itmax_ = 1000 endif if (present(itrace)) then itrace_ = itrace else itrace_ = 0 end if itx = 0 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 restart: do ! !$ ! !$ r0 = b-ax0 ! !$ if (itx >= itmax_) exit restart it = 0 call psb_geaxpby(cone,b,czero,r,desc_a,info) if (info == psb_success_) call psb_spmm(-cone,a,x,cone,r,desc_a,info,work=aux) if (debug_level >= psb_debug_ext_)& & write(debug_unit,*) me,' ',trim(name),' Done spmm',info if (info == psb_success_) call psb_geaxpby(cone,r,czero,rt,desc_a,info) if(info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if rho = czero ! Perhaps we already satisfy the convergence criterion... 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 + 1 itx = itx + 1 if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),'iteration: ',itx call prec%apply(r,z,desc_a,info,work=aux) if (info == psb_success_) call prec%apply(rt,zt,desc_a,info,trans='c',work=aux) rho_old = rho rho = psb_gedot(rt,z,desc_a,info) if (rho == czero) then if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' iteration breakdown r',rho exit iteration endif if (it == 1) then call psb_geaxpby(cone,z,czero,p,desc_a,info) call psb_geaxpby(cone,zt,czero,pt,desc_a,info) else beta = (rho/rho_old) call psb_geaxpby(cone,z,beta,p,desc_a,info) call psb_geaxpby(cone,zt,beta,pt,desc_a,info) end if call psb_spmm(cone,a,p,czero,q,desc_a,info,& & work=aux) call psb_spmm(cone,a,pt,czero,qt,desc_a,info,& & work=aux,trans='c') sigma = psb_gedot(pt,q,desc_a,info) if (sigma == czero) then if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' iteration breakdown s1', sigma exit iteration endif alpha = rho/sigma call psb_geaxpby(alpha,p,cone,x,desc_a,info) call psb_geaxpby(-alpha,q,cone,r,desc_a,info) call psb_geaxpby(-alpha,qt,cone,rt,desc_a,info) 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 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(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 call psb_error_handler(err_act) return end subroutine psb_cbicg_vect