! BSD 3-Clause License ! ! Copyright (c) 2020, Fabio Durastante ! All rights reserved. ! ! 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. Neither the name of the copyright holder nor the names of its ! contributors may be used to endorse or promote products derived from ! this software without specific prior 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 COPYRIGHT HOLDER OR 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. ! ! This code is based on the psb_dcg.F90 code from PSBLAS ! ! 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. ! ! ! File: psb_dcg.f90 ! 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_dcg.f90 ! ! Subroutine: psb_dcg ! This subroutine implements the Conjugate Gradient method. ! ! ! Arguments: ! ! a - type(psb_dspmat_type) Input: sparse matrix containing A. ! prec - class(psb_dprec_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. ! ! subroutine psfun_dcg_vect(a,prec,b,eta,zeta,x,eps,desc_a,info,& & itmax,iter,err,itrace,istop,cond) !! Preconditioned Conjugate Gradient for shifted system \((\eta A + \zeta I)x = b \) 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 !! Distributed sparse matrix Type(psb_desc_type), Intent(in) :: desc_a !! Descriptor class(psb_dprec_type), intent(inout) :: prec !! Preconditioner type(psb_d_vect_type), Intent(inout) :: b !! Right-hand side real(psb_dpk_), intent(in) :: eta !! \(\eta\) of \((\eta A + \zeta I)x = b \) real(psb_dpk_), intent(in) :: zeta !! \(\zeta\) of \((\eta A + \zeta I)x = b \) type(psb_d_vect_type), Intent(inout) :: x !! Solution on exit, initial guess on entry Real(psb_dpk_), Intent(in) :: eps !! Tolerance for the solution integer(psb_ipk_), intent(out) :: info !! Flag integer(psb_ipk_), Optional, Intent(in) :: itmax, itrace, istop !! Auxiliary parameters integer(psb_ipk_), Optional, Intent(out) :: iter !! Final number of iteration Real(psb_dpk_), Optional, Intent(out) :: err,cond !! Auxiliary parameters ! = Local data real(psb_dpk_), allocatable, target :: aux(:),td(:),tu(:),eig(:),ewrk(:) integer(psb_mpk_), allocatable :: ibl(:), ispl(:), iwrk(:) type(psb_d_vect_type), allocatable, target :: wwrk(:) type(psb_d_vect_type), pointer :: q, p, r, z, w real(psb_dpk_) :: alpha, beta, rho, rho_old, sigma,alpha_old,beta_old integer(psb_ipk_) :: itmax_, istop_, naux, it, itx, itrace_,& & n_col, n_row,err_act, ieg,nspl, istebz integer(psb_lpk_) :: mglob integer(psb_ipk_) :: debug_level, debug_unit type(psb_ctxt_type) :: ctxt integer(psb_ipk_) :: np, me real(psb_dpk_) :: derr type(psb_itconv_type) :: stopdat logical :: do_cond character(len=20) :: name character(len=*), parameter :: methdname='CG' info = psb_success_ name = 'psb_dcg' 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 (.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=5_psb_ipk_) if (info == psb_success_) call psb_geasb(wwrk,desc_a,info,mold=x%v,scratch=.true.) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if p => wwrk(1) q => wwrk(2) r => wwrk(3) z => wwrk(4) w => wwrk(5) if (present(itmax)) then itmax_ = itmax else itmax_ = 1000 endif if (present(itrace)) then itrace_ = itrace else itrace_ = 0 end if do_cond=present(cond) if (do_cond) then istebz = 0 allocate(td(itmax_),tu(itmax_), eig(itmax_),& & ibl(itmax_),ispl(itmax_),iwrk(3*itmax_),ewrk(4*itmax_),& & stat=info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if end if itx=0 alpha = dzero restart: do ! = ! = r0 = b-Ax0 ! = if (itx>= itmax_) exit restart it = 0 call psb_geaxpby(done,b,dzero,r,desc_a,info) ! r <- b [ x0 = 0] ! r <- r - (η A + ζ I) x : We do it in two step : r <- r - ηA, r <- r - ζ x if (info == psb_success_) call psb_spmm(-eta,a,x,done,r,desc_a,info,work=aux) if (info == psb_success_) call psb_geaxpby(-zeta,x,done,r,desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if rho = dzero 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 iteration: do it = it + 1 itx = itx + 1 call prec%apply(r,z,desc_a,info,work=aux) rho_old = rho rho = psb_gedot(r,z,desc_a,info) if (it == 1) then call psb_geaxpby(done,z,dzero,p,desc_a,info) else if (rho_old == dzero) then if (debug_level >= psb_debug_ext_)& & write(debug_unit,*) me,' ',trim(name),& & ': CG Iteration breakdown rho' exit iteration endif beta = rho/rho_old call psb_geaxpby(done,z,beta,p,desc_a,info) end if ! We have here another product with a, thus we need to change it into a ! product with (η A + ζ I): q <- Ap => q <- η A p, q <- q + ζ p call psb_spmm(eta,a,p,dzero,q,desc_a,info,work=aux) call psb_geaxpby(zeta,p,done,q,desc_a,info) sigma = psb_gedot(p,q,desc_a,info) if (sigma == dzero) then if (debug_level >= psb_debug_ext_)& & write(debug_unit,*) me,' ',trim(name),& & ': CG Iteration breakdown sigma' exit iteration endif alpha_old = alpha alpha = rho/sigma if (do_cond) then istebz = istebz + 1 if (istebz == 1) then td(istebz) = done/alpha else td(istebz) = done/alpha + beta/alpha_old tu(istebz-1) = sqrt(beta)/alpha_old end if end if call psb_geaxpby(alpha,p,done,x,desc_a,info) call psb_geaxpby(-alpha,q,done,r,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 if (do_cond) then if (me == psb_root_) then #if defined(HAVE_LAPACK) call dstebz('A','E',istebz,dzero,dzero,0,0,-done,td,tu,& & ieg,nspl,eig,ibl,ispl,ewrk,iwrk,info) if (info < 0) then call psb_errpush(psb_err_from_subroutine_ai_,name,& & a_err='dstebz',i_err=(/info/)) info=psb_err_from_subroutine_ai_ goto 9999 end if cond = eig(ieg)/eig(1) #else cond = dzero #endif info=psb_success_ end if call psb_bcast(ctxt,cond) end if 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 psfun_dcg_vect