!!$ !!$ 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. 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File: psb_zgcr.f90 !! !! Contributors: Ambra Abdullahi (UNITOV) and Pasqua D’Ambra (IAC-CNR) !! !!$ 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 [4] Notay, Yvan C !!$ C Aggregation-based algebraic multigrid method C !!$ C SIAM Journal on Scientific Computing 34, C !!$ C pp. A2288-A2316, 2012 C !!$ C C !!$ C C !!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ! File: psb_zgcr.f90 ! ! Subroutine: psb_zgcr ! This subroutine implements the GCR method. ! ! ! Arguments: ! ! a - type(psb_zspmat_type) Input: sparse matrix containing A. ! prec - class(psb_zprec_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 ! subroutine psb_zgcr_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_z_krylov_conv_mod use psb_krylov_mod implicit none type(psb_zspmat_type), intent(in) :: a Type(psb_desc_type), Intent(in) :: desc_a class(psb_zprec_type), intent(inout) :: prec type(psb_z_vect_type), Intent(inout) :: b type(psb_z_vect_type), Intent(inout) :: x real(psb_dpk_), 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_dpk_), Optional, Intent(out) :: err ! = local data complex(psb_dpk_), allocatable :: alpha(:), h(:,:) type(psb_z_vect_type), allocatable :: z(:), c(:), c_scale(:) type(psb_z_vect_type) :: r real(psb_dpk_) :: r_norm, b_norm, a_norm, derr integer(psb_ipk_) :: n_col, mglob, naux, err_act integer(psb_ipk_) :: debug_level, debug_unit integer(psb_ipk_) :: np, me, ictxt integer(psb_ipk_) :: i, j, it, itx, istop_, itmax_, itrace_, nl, m, nrst complex(psb_dpk_) :: hjj complex(psb_dpk_), allocatable, target :: aux(:) character(len=20) :: name type(psb_itconv_type) :: stopdat character(len=*), parameter :: methdname='GCR' integer(psb_ipk_) ::int_err(5) info = psb_success_ name = 'psb_zgcr' 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 (.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_col = desc_a%get_local_cols() if (present(istop)) then istop_ = istop else istop_ = 2 endif ! ! ISTOP_ = 1: Normwise backward error, infinity norm ! ISTOP_ = 2: ||r||/||b||, 2-norm ! if ((istop_ < 1 ).or.(istop_ > 2 ) ) then info=psb_err_invalid_istop_ int_err(1)=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_)& & 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 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 = 10 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 naux=4*n_col allocate(aux(naux),h(nl+1,nl+1),& &c_scale(nl+1),c(nl+1),z(nl+1), alpha(nl+1), stat=info) h = zzero if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if call psb_geasb(r, desc_a,info, scratch=.true.,mold=x%v) do i =1,nl+1 call psb_geasb(c(i), desc_a,info, scratch=.true.,mold=x%v) call psb_geasb(z(i), desc_a,info, scratch=.true.,mold=x%v) call psb_geasb(c_scale(i), desc_a,info, scratch=.true.,mold=x%v) end do itx = 0 nrst = -1 call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info) restart: do if (itx>= itmax_) exit restart h = zzero it = 0 ! compute r0 = b-ax0 if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if call psb_geaxpby(zone, b, zzero, r, desc_a, info) call psb_spmm(-zone,a,x,zone,r,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 (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) exit restart nrst = nrst + 1 iteration: do itx = itx + 1 it = it + 1 j = it !Apply preconditioner call prec%apply(r,z(j),desc_a,info,work=aux) call psb_spmm(zone,a,z(j),zzero,c(1),desc_a,info,work=aux) do i =1, j - 1 h(i,j) = psb_gedot(c_scale(i), c(i), desc_a, info) call psb_geaxpby(zone, c(i), zzero, c(i+1), desc_a, info) call psb_geaxpby(-h(i,j), c_scale(i), zone, c(i+1), desc_a, info) end do h(j,j) = psb_norm2(c(j), desc_a, info) hjj = zone/h(j,j) call psb_geaxpby(hjj, c(j), zzero, c_scale(j), desc_a, info) alpha(j) = psb_gedot(c_scale(j), r, desc_a, info) !Update residual call psb_geaxpby(zone, r, zzero, r, desc_a, info) call psb_geaxpby(-alpha(j), c_scale(j), zone, r, desc_a, info) if (psb_check_conv(methdname,itx,x,r,desc_a,stopdat,info)) exit restart if (j >= irst) exit iteration end do iteration m = j !Compute solution call ztrsm('l','u','n','n',m,1,zone,h,size(h,1),alpha,size(alpha,1)) if (nrst == 0 ) then call x%set(zzero) endif do i=1,m call psb_geaxpby(alpha(i), z(i), zone, x, desc_a, info) enddo end do restart m = j !Compute solution call ztrsm('l','u','n','n',m,1,zone,h,size(h,1),alpha,size(alpha,1)) call x%set(zzero) do i=1,m call psb_geaxpby(alpha(i), z(i), zone, x, desc_a, info) enddo iter = j call psb_end_conv(methdname,itx,desc_a,stopdat,info,derr,iter) if (present(err)) err = derr if (info == psb_success_) call psb_gefree(r,desc_a,info) do j = 1,m if (info == psb_success_) call psb_gefree(z(j),desc_a,info) if (info == psb_success_) call psb_gefree(c_scale(j),desc_a,info) enddo do i =1,nl+1 if (info == psb_success_) call psb_gefree(c(i),desc_a,info) end do if (info == psb_success_) deallocate(aux,h,c_scale,z,c,alpha,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 continue call psb_erractionrestore(err_act) if (err_act.eq.psb_act_abort_) then call psb_error() return end if return end subroutine psb_zgcr_vect