! 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. ! ! Parameters: ! a - type(). The sparse matrix containing A. ! prec - type(). The data structure containing the preconditioner. ! b - real,dimension(:). The right hand side. ! x - real,dimension(:). The vector of unknowns. ! eps - real. The error tolerance. ! desc_a - type(). The communication descriptor. ! info - integer. Eventually returns an error code. ! itmax - integer(optional). The maximum number of iterations. ! iter - integer(optional). The number of iterations performed. ! err - real(optional). The error on return. ! itrace - integer(optional). The unit to write messages onto. ! istop - integer(optional). The stopping criterium. ! Subroutine psb_dcg(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err, itrace, istop) use psb_serial_mod use psb_descriptor_type use psb_prec_type use psb_psblas_mod use psb_tools_mod use psb_const_mod use psb_prec_mod use psb_error_mod implicit none !!$ Parameters Type(psb_dspmat_type), Intent(in) :: a Type(psb_dprec_type), Intent(in) :: prec Type(psb_desc_type), Intent(in) :: desc_a Real(Kind(1.d0)), Intent(in) :: b(:) Real(Kind(1.d0)), Intent(inout) :: x(:) Real(Kind(1.d0)), Intent(in) :: eps integer, intent(out) :: info Integer, Optional, Intent(in) :: itmax, itrace, istop Integer, Optional, Intent(out) :: iter Real(Kind(1.d0)), Optional, Intent(out) :: err !!$ Local data real(kind(1.d0)), pointer :: aux(:), q(:), p(:),& & r(:), z(:), w(:), wwrk(:,:) real(kind(1.d0)) ::rerr real(kind(1.d0)) ::alpha, beta, rho, rho_old, rni, xni, bni, ani,bn2,& & sigma integer :: litmax, liter, listop, naux, m, mglob, it, itrac,& & nprows,npcols,me,mecol, n_col, isvch, ich, icontxt, n_row,err_act, int_err(5) character ::diagl, diagu logical, parameter :: exchange=.true., noexchange=.false. integer, parameter :: ione=1 real(kind(1.d0)), parameter :: one=1.d0, zero=0.d0, epstol=1.d-35 character(len=20) :: name,ch_err info = 0 name = 'psb_dcg' call psb_erractionsave(err_act) icontxt = desc_a%matrix_data(psb_ctxt_) call blacs_gridinfo(icontxt,nprows,npcols,me,mecol) mglob = desc_a%matrix_data(psb_m_) n_row = desc_a%matrix_data(psb_n_row_) n_col = desc_a%matrix_data(psb_n_col_) if (present(istop)) then listop = istop else listop = 1 endif ! ! LISTOP = 1: Normwise backward error, infinity norm ! LISTOP = 2: ||r||/||b|| norm 2 ! !!$ If ((prec%prec < min_prec_).Or.(prec%prec > max_prec_) ) Then !!$ Write(0,*) 'F90_CG: Invalid IPREC',prec%prec !!$ If (Present(ierr)) ierr=-1 !!$ Return !!$ Endif if ((listop < 1 ).or.(listop > 2 ) ) then write(0,*) 'psb_cg: invalid istop',listop info=5001 int_err(1)=listop err=info call psb_errpush(info,name,i_err=int_err) goto 9999 endif naux=4*n_col allocate(aux(naux), stat=info) call psb_dalloc(mglob,5,wwrk,desc_a,info) call psb_asb(wwrk,desc_a,info) if (info.ne.0) then info=4011 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 litmax = itmax else litmax = 1000 endif if (present(itrace)) then itrac = itrace else itrac = -1 end if !!$ DIAGL = 'U' !!$ DIAGU = 'R' ! Ensure global coherence for convergence checks. call blacs_get(icontxt,16,isvch) ich = 1 call blacs_set(icontxt,16,ich) !!$ !!$ r0 = b-Ax0 !!$ call psb_axpby(one,b,zero,r,desc_a,info) call psb_spmm(-one,a,x,one,r,desc_a,info,work=aux) if (info.ne.0) then info=4011 call psb_errpush(info,name) goto 9999 end if rho = zero if (listop == 1) then ani = psb_nrmi(a,desc_a,info) bni = psb_amax(b,desc_a,info) else if (listop == 2) then bn2 = psb_nrm2(b,desc_a,info) endif if (info.ne.0) then info=4011 call psb_errpush(info,name) goto 9999 end if iteration: do it = 1, itmax !!$ !!$ solve mz = r !!$ Note: the overlapped preconditioner (if overlap is non empty) !!$ is non-symmetric: M^{-1} = \Lambda P^T K^{-1} P !!$ For CG we use instead !!$ M^{-1} = \sqrt{\Lambda} P^T K^{-1} P \sqrt{\Lambda} !!$ Keep track of the old symmetrized stuf, might come in useful. !!$ CALL F90_PSAXPBY(ONE,R,ZERO,Z,DECOMP_DATA) !!$ CALL F90_PSOVRL(Z,DECOMP_DATA,& !!$ & UPDATE_TYPE=SQUARE_ROOT_,CHOICE=NOEXCHANGE) !!$ CALL F90_PSSPSM(ONE,L,Z,ZERO,W,DECOMP_DATA,& !!$ & TRANS='N',UNIT=DIAGL,CHOICE=NONE_,WORK=AUX) !!$ CALL F90_PSSPSM(ONE,U,W,ZERO,Z,DECOMP_DATA,& !!$ & TRANS='N',UNIT=DIAGU,CHOICE=NONE_,DIAG=VDIAG,WORK=AUX) !!$ CALL F90_PSOVRL(Z,DECOMP_DATA,& !!$ & UPDATE_TYPE=SQUARE_ROOT_) !!$ CALL F90_PSHALO(Z,DECOMP_DATA) Call psb_prcaply(prec,r,z,desc_a,info,work=aux) rho_old = rho rho = psb_dot(r,z,desc_a,info) if (it==1) then call psb_axpby(one,z,zero,p,desc_a,info) else if (rho_old==zero) then write(0,*) 'CG Iteration breakdown' exit iteration endif beta = rho/rho_old call psb_axpby(one,z,beta,p,desc_a,info) end if call psb_spmm(one,a,p,zero,q,desc_a,info,work=aux) sigma = psb_dot(p,q,desc_a,info) if (sigma==zero) then write(0,*) 'CG Iteration breakdown' exit iteration endif alpha = rho/sigma call psb_axpby(alpha,p,one,x,desc_a,info) call psb_axpby(-alpha,q,one,r,desc_a,info) if (listop == 1) Then rni = psb_amax(r,desc_a,info) xni = psb_amax(x,desc_a,info) rerr = rni/(ani*xni+bni) If (itrac /= -1) Then If (me.Eq.0) Write(itrac,'(a,i4,5(2x,es10.4))') 'cg: ',it,rerr,rni,bni,& &xni,ani Endif Else If (listop == 2) Then rni = psb_nrm2(r,desc_a,info) rerr = rni/bn2 If (itrac /= -1) Then If (me.Eq.0) Write(itrac,'(a,i4,3(2x,es10.4)))') 'cg: ',it,rerr,rni,bn2 Endif Endif if (rerr<=eps) then exit iteration end if end do iteration if (present(err)) err=rerr if (present(iter)) iter = it if (rerr>eps) then write(0,*) 'CG Failed to converge to ',eps,& & ' in ',litmax,' iterations ' info=it end if deallocate(aux) call psb_free(wwrk,desc_a,info) ! restore external global coherence behaviour call blacs_set(icontxt,16,isvch) if (info.ne.0) then 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.act_abort) then call psb_error() return end if return end subroutine psb_dcg