! ! 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 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 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_sminres.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_sminres.f90 ! ! Subroutine: psb_sminres ! This subroutine implements the MINRES 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. ! ! subroutine psb_sminres_vect(a,prec,b,x,eps,desc_a,info,& & itmax,iter,err,itrace,istop,cond) use psb_base_mod use psb_prec_mod use psb_s_linsolve_conv_mod use psb_linsolve_mod implicit none type(psb_sspmat_type), intent(in) :: a Type(psb_desc_type), Intent(in) :: desc_a class(psb_sprec_type), intent(inout) :: prec 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, istop integer(psb_ipk_), Optional, Intent(out) :: iter Real(psb_spk_), Optional, Intent(out) :: err, cond ! = Local data real(psb_spk_), allocatable, target :: aux(:) type(psb_s_vect_type), allocatable, target :: wwrk(:) type(psb_s_vect_type), pointer :: y, r1, r2, v, w, w1, w2, wtmp, res real(psb_spk_) :: alfa, beta, beta1, dbar, delta, denom real(psb_spk_) :: epsln, gamma, gbar, oldb, oldeps, phi, phibar real(psb_spk_) :: rhs1, rhs2, s, zeta, betatmp real(psb_spk_) :: rotx(1), roty(1) real(psb_spk_) :: cs real(psb_spk_) :: sn integer(psb_ipk_) :: itmax_, istop_, naux, itx, itrace_, n_col, n_row, err_act 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, errnum, errden, deps logical :: do_cond logical :: converged real(psb_spk_) :: epsmach real(psb_spk_) :: gmax, gmin, tnorm2, ynorm2 real(psb_spk_) :: rni, xni, bni, ani, bn2, r0n2 real(psb_spk_) :: dotv character(len=20) :: name character(len=*), parameter :: methdname='MINRES' info = psb_success_ name = 'psb_sminres' 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_ = psb_get_istop_default() endif if (.not.psb_is_valid_istop(istop_)) then info=psb_err_invalid_istop_ err=info call psb_errpush(info,name,i_err=(/istop_/)) goto 9999 end if ! ! istop_ = 1: normwise backward error, infinity norm ! istop_ = 2: ||r||/||b|| norm 2 ! select case(istop_) case(psb_istop_ani_,psb_istop_bn2_,& & psb_istop_rn2_abs_, psb_istop_rrn2_) ! nothing needed case default ! should never get here info=psb_err_internal_error_ err=info call psb_errpush(info,name,a_err="invalid istop_") goto 9999 end select 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=9_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 if (present(itmax)) then itmax_ = itmax else itmax_ = 1000 endif if (present(itrace)) then itrace_ = itrace else itrace_ = 0 end if y => wwrk(1) r1 => wwrk(2) r2 => wwrk(3) v => wwrk(4) w => wwrk(5) w1 => wwrk(6) w2 => wwrk(7) wtmp => wwrk(8) res => wwrk(9) do_cond = present(cond) epsmach = epsilon(sone) ! res = b - A*x call psb_geaxpby(sone,b,szero,res,desc_a,info) if (info == psb_success_) call psb_spmm(-sone,a,x,sone,res,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 select case(istop_) case(psb_istop_ani_) ani = psb_spnrmi(a,desc_a,info) bni = psb_geamax(b,desc_a,info) case(psb_istop_bn2_) bn2 = psb_genrm2(b,desc_a,info) case(psb_istop_rn2_abs_) ! nothing needed case(psb_istop_rrn2_) r0n2 = psb_genrm2(res,desc_a,info) end select if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if errnum = szero errden = sone deps = eps converged = .false. if ((itrace_ > 0).and.(me == 0)) call log_header(methdname) ! y = beta1 * P' * v1, with v1 the first Lanczos vector. call psb_geaxpby(sone,res,szero,y,desc_a,info) if (info == psb_success_) call psb_geaxpby(sone,res,szero,r1,desc_a,info) if (info == psb_success_) call prec%apply(res,y,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 dotv = psb_gedot(res,y,desc_a,info) if (dotv < -epsmach*max(sone,abs(dotv))) then info=psb_err_pivot_too_small_ call psb_errpush(info,name,a_err='MINRES breakdown: negative (r,z)') goto 9999 end if if (dotv < szero) dotv = szero beta1 = sqrt(dotv) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if ! If beta1 is numerically zero, x is already acceptable. if (abs(beta1) <= epsmach) then itx = 0 converged = .true. if (do_cond) cond = szero select case(istop_) case(psb_istop_ani_) rni = psb_geamax(res,desc_a,info) xni = psb_geamax(x,desc_a,info) errnum = rni errden = ani*xni + bni case(psb_istop_bn2_) errnum = abs(beta1) errden = bn2 case(psb_istop_rn2_abs_) errnum = abs(beta1) errden = sone case(psb_istop_rrn2_) errnum = abs(beta1) errden = r0n2 end select if (errden == szero) errden = sone if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if end if beta = beta1 oldb = szero dbar = szero epsln = szero phibar = beta1 rhs1 = beta1 rhs2 = szero cs = -sone sn = szero itx = 0 if (do_cond) then tnorm2 = 0.0_psb_spk_ ynorm2 = 0.0_psb_spk_ gmax = 0.0_psb_spk_ gmin = huge(sone) end if call psb_geaxpby(sone,r1,szero,r2,desc_a,info) if (info == psb_success_) call psb_geaxpby(szero,x,szero,w,desc_a,info) if (info == psb_success_) call psb_geaxpby(szero,x,szero,w1,desc_a,info) if (info == psb_success_) call psb_geaxpby(szero,x,szero,w2,desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if if (.not.converged) then do while (itx < itmax_) if (abs(beta) <= epsmach) exit itx = itx + 1 s = sone/beta call psb_geaxpby(s,y,szero,v,desc_a,info) if (info == psb_success_) call psb_spmm(sone,a,v,szero,y,desc_a,info,work=aux) if (itx >= 2 .and. info == psb_success_) then call psb_geaxpby((-beta/oldb),r1,sone,y,desc_a,info) end if if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if alfa = psb_gedot(v,y,desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if call psb_geaxpby((-alfa/beta),r2,sone,y,desc_a,info) if (info == psb_success_) call psb_geaxpby(sone,r2,szero,r1,desc_a,info) if (info == psb_success_) call psb_geaxpby(sone,y,szero,r2,desc_a,info) if (info == psb_success_) call prec%apply(r2,y,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 oldb = beta dotv = psb_gedot(r2,y,desc_a,info) if (dotv < -epsmach*max(sone,abs(dotv))) then info=psb_err_pivot_too_small_ call psb_errpush(info,name,a_err='MINRES breakdown: negative (r2,z2)') goto 9999 end if if (dotv < szero) dotv = szero beta = sqrt(dotv) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if if (do_cond) then tnorm2 = tnorm2 + abs(alfa)**2 + abs(oldb)**2 + abs(beta)**2 if (itx == 1) then gmax = abs(alfa) gmin = gmax end if end if oldeps = epsln delta = dbar gbar = alfa rotx(1) = delta roty(1) = gbar call srot(1,rotx,1,roty,1,cs,sn) delta = rotx(1) gbar = -roty(1) epsln = szero dbar = beta rotx(1) = epsln roty(1) = dbar call srot(1,rotx,1,roty,1,cs,sn) epsln = rotx(1) dbar = -roty(1) gamma = gbar betatmp = beta call srotg(gamma,betatmp,cs,sn) if (abs(gamma) <= epsmach) exit phi = phibar phibar = szero rotx(1) = phi roty(1) = phibar call srot(1,rotx,1,roty,1,cs,-sn) phi = rotx(1) phibar = roty(1) denom = sone/gamma call psb_geaxpby(sone,w2,szero,w1,desc_a,info) if (info == psb_success_) call psb_geaxpby(sone,w,szero,w2,desc_a,info) if (info == psb_success_) call psb_geaxpby(sone,v,szero,wtmp,desc_a,info) if (info == psb_success_) call psb_geaxpby(-oldeps,w1,sone,wtmp,desc_a,info) if (info == psb_success_) call psb_geaxpby(-delta,w2,sone,wtmp,desc_a,info) if (info == psb_success_) call psb_geaxpby(denom,wtmp,szero,w,desc_a,info) if (info == psb_success_) call psb_geaxpby(phi,w,sone,x,desc_a,info) if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if if (do_cond) then gmax = max(gmax,abs(gamma)) gmin = min(gmin,abs(gamma)) zeta = rhs1/gamma ynorm2 = ynorm2 + abs(zeta)**2 rhs1 = rhs2 - delta*zeta rhs2 = -epsln*zeta end if select case(istop_) case(psb_istop_ani_) ! Compute true residual only for the ANI stopping criterion. call psb_geaxpby(sone,b,szero,res,desc_a,info) if (info == psb_success_) call psb_spmm(-sone,a,x,sone,res,desc_a,info,work=aux) if (info == psb_success_) rni = psb_geamax(res,desc_a,info) if (info == psb_success_) xni = psb_geamax(x,desc_a,info) errnum = rni errden = ani*xni + bni case(psb_istop_bn2_) errnum = abs(phibar) errden = bn2 case(psb_istop_rn2_abs_) errnum = abs(phibar) errden = sone case(psb_istop_rrn2_) errnum = abs(phibar) errden = r0n2 end select if (errden == szero) errden = sone if (info /= psb_success_) then info=psb_err_from_subroutine_non_ call psb_errpush(info,name) goto 9999 end if if (itrace_ > 0) & & call log_conv(methdname,me,itx,itrace_,errnum,errden,deps) if (errnum <= eps*errden) then converged = .true. exit end if end do end if if ((.not.converged) .and. (itx >= itmax_)) then if (debug_level >= psb_debug_ext_)& & write(debug_unit,*) me,' ',trim(name),': MINRES reached iteration limit' end if if (do_cond) then if (gmin > 0.0_psb_spk_) then cond = gmax/gmin else cond = huge(sone) end if end if call log_end(methdname,me,itx,itrace_,errnum,errden,deps,err=derr,iter=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_sminres_vect