! ! Parallel Sparse BLAS version 3.5 ! (C) Copyright 2006-2018 ! Salvatore Filippone ! Alfredo Buttari ! ! 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 ! CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC ! File: psb_dcgs.f90 ! ! Subroutine: psb_dcgs ! Implements the Conjugate Gradient Squared method. ! ! Arguments: ! ! a - type(psb_dspmat_type) Input: sparse matrix containing A. ! prec - class(psb_dprec_type) Input: preconditioner ! b - real,dimension(:) Input: vector containing the ! right hand side B ! x - real,dimension(:) 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. ! Subroutine psb_dcgs_vect(a,prec,b,x,eps,desc_a,info,& & itmax,iter,err,itrace,istop) use psb_base_mod use psb_prec_mod use psb_d_krylov_conv_mod use psb_krylov_mod implicit none type(psb_dspmat_type), intent(in) :: a Type(psb_desc_type), Intent(in) :: desc_a class(psb_dprec_type), intent(inout) :: prec type(psb_d_vect_type), Intent(inout) :: b type(psb_d_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,istop integer(psb_ipk_), Optional, Intent(out) :: iter Real(psb_dpk_), Optional, Intent(out) :: err ! = local data real(psb_dpk_), allocatable, target :: aux(:) type(psb_d_vect_type), allocatable, target :: wwrk(:) type(psb_d_vect_type), pointer :: ww, q, r, p, v,& & s, z, f, rt, qt, uv integer(psb_ipk_) :: itmax_, naux, it, itrace_,& & n_row, n_col,istop_, itx, err_act integer(psb_lpk_) :: mglob type(psb_ctxt_type) :: ctxt integer(psb_ipk_) :: np, me integer(psb_ipk_) :: debug_level, debug_unit real(psb_dpk_) :: alpha, beta, rho, rho_old, sigma real(psb_dpk_) :: derr type(psb_itconv_type) :: stopdat character(len=20) :: name character(len=*), parameter :: methdname='CGS' info = psb_success_ name = 'psb_dcgs' call psb_erractionsave(err_act) debug_unit = psb_get_debug_unit() debug_level = psb_get_debug_level() ctxt = desc_a%get_context() Call psb_info(ctxt, me, np) if (debug_level >= psb_debug_ext_)& & write(debug_unit,*) me,' ',trim(name),': from psb_info',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_row = desc_a%get_local_rows() n_col = desc_a%get_local_cols() If (Present(istop)) Then istop_ = istop Else istop_ = 2 Endif call psb_chkvect(mglob,lone,x%get_nrows(),lone,lone,desc_a,info) if (info == psb_success_) call psb_chkvect(mglob,lone,b%get_nrows(),lone,lone,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),stat=info) if (info == psb_success_) Call psb_geall(wwrk,desc_a,info,n=11_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_ call psb_errpush(info,name) goto 9999 End If q => wwrk(1) qt => wwrk(2) r => wwrk(3) rt => wwrk(4) p => wwrk(5) v => wwrk(6) uv => wwrk(7) z => wwrk(8) f => wwrk(9) s => wwrk(10) ww => wwrk(11) 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,x,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(done,b,dzero,r,desc_a,info) if (info == psb_success_) call psb_spmm(-done,a,x,done,r,desc_a,info,work=aux) if (info == psb_success_) call psb_geaxpby(done,r,dzero,rt,desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if ! 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 rho = dzero iteration: do it = it + 1 itx = itx + 1 if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),'iteration: ',itx rho_old = rho rho = psb_gedot(rt,r,desc_a,info) if (rho == dzero) 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(done,r,dzero,uv,desc_a,info) if (info == psb_success_) call psb_geaxpby(done,r,dzero,p,desc_a,info) else beta = (rho/rho_old) call psb_geaxpby(done,r,dzero,uv,desc_a,info) if (info == psb_success_) call psb_geaxpby(beta,q,done,uv,desc_a,info) if (info == psb_success_) call psb_geaxpby(done,q,beta,p,desc_a,info) if (info == psb_success_) call psb_geaxpby(done,uv,beta,p,desc_a,info) end if if (info == psb_success_) call prec%apply(p,f,desc_a,info,work=aux) if (info == psb_success_) call psb_spmm(done,a,f,dzero,v,desc_a,info,& & work=aux) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='First loop part ') goto 9999 end if sigma = psb_gedot(rt,v,desc_a,info) if (sigma == dzero) then if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),& & ' iteration breakdown s1', sigma exit iteration endif alpha = rho/sigma if (info == psb_success_) call psb_geaxpby(done,uv,dzero,q,desc_a,info) if (info == psb_success_) call psb_geaxpby(-alpha,v,done,q,desc_a,info) if (info == psb_success_) call psb_geaxpby(done,uv,dzero,s,desc_a,info) if (info == psb_success_) call psb_geaxpby(done,q,done,s,desc_a,info) if (info == psb_success_) call prec%apply(s,z,desc_a,info,work=aux) if (info == psb_success_) call psb_geaxpby(alpha,z,done,x,desc_a,info) if (info == psb_success_) call psb_spmm(done,a,z,dzero,qt,desc_a,info,& & work=aux) if (info == psb_success_) call psb_geaxpby(-alpha,qt,done,r,desc_a,info) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='X update ') goto 9999 end if 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_dcgs_vect