!!$ !!$ !!$ MLD2P4 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package !!$ based on PSBLAS (Parallel Sparse BLAS v.2.0) !!$ !!$ (C) Copyright 2006 Alfredo Buttari University of Rome Tor Vergata !!$ Pasqua D'Ambra ICAR-CNR, Naples !!$ Daniela di Serafino Second University of Naples !!$ Salvatore Filippone University of Rome Tor Vergata !!$ !!$ 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 MLD2P4 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 MLD2P4 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: mld_krylov_mod.f90. ! ! Module: mld_krylov_mod. ! Contains: mld_dkrylov, mld_zkrylov. ! ! This module defines the interfaces to the real and complex versions of the ! routines implementing Krylov solvers: ! - mld_krylov : driver providing a general interface to the Krylov ! solvers available in PSBLAS; ! - psb_cg : Conjugate Gradient (CG) solver (real version only); ! - psb_bicg : BiConjugate Gradient (BiCG) solver (real version only); ! - psb_bicgstab : BiConjugate Gradient Stabilized (BiCGStab) solver; ! - psb_bicgstabl : BiCGStab(l) solver (real version only); ! - psb_rgmres : Generalized Minimal Residual (GMRES) solver with ! Restarting; ! - psb_cgs : Conjugate Gradient Squared (CGS) solver. ! ! This is a partial duplication of material already present in the Krylov ! part of the PSBLAS subtree. This is not bad since ! 1. there is no actual computation here, these are just wrappers around ! the actual methods, so very little code is necessary; ! 2. these wrappers enable issuing error messages with a subroutine name ! coherent with what the user sees; ! 3. at the very least we would need a layer renaming the PSBLAS krylov ! interfaces, so we are doing approximately the same amount of (re)coding. ! Module mld_krylov_mod interface mld_krylov module procedure mld_dkrylov, mld_zkrylov end interface interface psb_cg subroutine psb_dcg(a,prec,b,x,eps,& & desc_a,info,itmax,iter,err,itrace,istop) use psb_base_mod use psb_prec_mod type(psb_dspmat_type), intent(in) :: a 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 type(psb_dprec_type), intent(in) :: prec integer, intent(out) :: info integer, optional, intent(in) :: itmax, itrace,istop integer, optional, intent(out) :: iter real(kind(1.d0)), optional, intent(out) :: err end subroutine psb_dcg end interface interface psb_bicg subroutine psb_dbicg(a,prec,b,x,eps,& & desc_a,info,itmax,iter,err,itrace,istop) use psb_base_mod use psb_prec_mod type(psb_dspmat_type), intent(in) :: a 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 type(psb_dprec_type), intent(in) :: prec integer, intent(out) :: info integer, optional, intent(in) :: itmax, itrace,istop integer, optional, intent(out) :: iter real(kind(1.d0)), optional, intent(out) :: err end subroutine psb_dbicg end interface interface psb_bicgstab subroutine psb_dcgstab(a,prec,b,x,eps,& & desc_a,info,itmax,iter,err,itrace,istop) use psb_base_mod use psb_prec_mod type(psb_dspmat_type), intent(in) :: a 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 type(psb_dprec_type), intent(in) :: prec integer, intent(out) :: info integer, optional, intent(in) :: itmax, itrace,istop integer, optional, intent(out) :: iter real(kind(1.d0)), optional, intent(out) :: err end subroutine psb_dcgstab subroutine psb_zcgstab(a,prec,b,x,eps,& & desc_a,info,itmax,iter,err,itrace,istop) use psb_base_mod use psb_prec_mod type(psb_zspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a complex(kind(1.d0)), intent(in) :: b(:) complex(kind(1.d0)), intent(inout) :: x(:) real(kind(1.d0)), intent(in) :: eps type(psb_zprec_type), intent(in) :: prec integer, intent(out) :: info integer, optional, intent(in) :: itmax, itrace,istop integer, optional, intent(out) :: iter real(kind(1.d0)), optional, intent(out) :: err end subroutine psb_zcgstab end interface interface psb_bicgstabl Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err, itrace,irst,istop) use psb_base_mod use psb_prec_mod Type(psb_dspmat_type), Intent(in) :: a Type(psb_desc_type), Intent(in) :: desc_a type(psb_dprec_type), intent(in) :: prec 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, irst,istop Integer, Optional, Intent(out) :: iter Real(Kind(1.d0)), Optional, Intent(out) :: err end subroutine psb_dcgstabl end interface interface psb_rgmres Subroutine psb_dgmresr(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,irst,istop) use psb_base_mod use psb_prec_mod Type(psb_dspmat_type), Intent(in) :: a Type(psb_desc_type), Intent(in) :: desc_a type(psb_dprec_type), intent(in) :: prec 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, irst,istop Integer, Optional, Intent(out) :: iter Real(Kind(1.d0)), Optional, Intent(out) :: err end subroutine psb_dgmresr Subroutine psb_zgmresr(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,irst,istop) use psb_base_mod use psb_prec_mod Type(psb_zspmat_type), Intent(in) :: a Type(psb_desc_type), Intent(in) :: desc_a type(psb_zprec_type), intent(in) :: prec complex(Kind(1.d0)), Intent(in) :: b(:) complex(Kind(1.d0)), Intent(inout) :: x(:) Real(Kind(1.d0)), Intent(in) :: eps integer, intent(out) :: info Integer, Optional, Intent(in) :: itmax, itrace, irst,istop Integer, Optional, Intent(out) :: iter Real(Kind(1.d0)), Optional, Intent(out) :: err end subroutine psb_zgmresr end interface interface psb_cgs subroutine psb_dcgs(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,istop) use psb_base_mod use psb_prec_mod type(psb_dspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a type(psb_dprec_type), intent(in) :: prec 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 end subroutine psb_dcgs subroutine psb_zcgs(a,prec,b,x,eps,& & desc_a,info,itmax,iter,err,itrace,istop) use psb_base_mod use psb_prec_mod type(psb_zspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a complex(kind(1.d0)), intent(in) :: b(:) complex(kind(1.d0)), intent(inout) :: x(:) real(kind(1.d0)), intent(in) :: eps type(psb_zprec_type), intent(in) :: prec integer, intent(out) :: info integer, optional, intent(in) :: itmax, itrace,istop integer, optional, intent(out) :: iter real(kind(1.d0)), optional, intent(out) :: err end subroutine psb_zcgs end interface contains ! ! Subroutine: mld_dkrylov/mld_zkrylov. ! Version: real/complex. ! Note: internal subroutine of module mld_krylov_mod. ! ! This routine solves a linear system ! ! Ax = b ! ! by using one of following preconditioned Krylov solvers: CG, BiCG, BiCGStab, ! BiCGStab(l), Restarted GMRES, CGS. The preconditioning is applied as right ! preconditioning. ! ! The user can choose among two stopping criteria: ! ! - one based on the normwise backward error in the infinity norm, i.e. ! ! ||r_i||_inf < eps * (||A||_inf * ||x_i||_inf + ||b||_inf); ! ! - the other based on the relative residual reduction in the 2-norm, i.e. ! ! ||r_i||_2 < eps * ||b||_2. ! ! In the above formulae, x_i is the approximate solution and r_i = b - A*x_i ! is the corresponding residual at the i-th iteration. ! ! This routine is a driver that provides a general interface to the Krylov ! solvers implemented in PSBLAS. These solvers can use all the preconditioners ! available in MLD2P4. ! ! ! Arguments: ! method - character(len=*), input. ! The Krylov method to be applied. The following values are ! are allowed in the real case: 'cg', 'bicg', 'bicgstab', ! 'bicgstabl', 'rgmres', 'cgs' (and all the upper/lower case ! variants). The same values except 'cg', 'bicg' and 'bicgstabl' ! are allowed in the complex case. ! a - type(psb_dspmat_type)/type(psb_zspmat_type), input. ! The sparse matrix structure containing the local part of the ! matrix A. ! prec - type(mld_dprec_type)/type(mld_zprec_type), input. ! The preconditioner data structure containing the local part ! of the preconditioner to be applied. ! b - real(kind(1.d0))/complex(kind(1.d0)), dimension(:), input. ! The local part of the right-hand side. ! x - real(kind(1.d0))/complex(kind(1.d0)), dimension(:), input/output. ! The local part of the approximate solution. In input it ! contains an initial guess of the solution, while, in output, ! the approximation computed by the selected Krylov solver. ! eps - real(kind(1.d0)), input. ! The tolerance used in the stopping criterion. ! desc_a - type(psb_desc_type), input. ! The communication descriptor associated to a. ! info - integer, output. ! Error code. ! itmax - integer, optional, input. ! The maximum number of iterations to be performed. If itmax ! is not present, a maximum number of 1000 iterations is ! assumed. ! iter - integer, optional, output. ! The number of iterations actually performed. ! err - real(kind(1.d0)), optional, output. ! An estimate of the error in the computed solution, i.e. the ! relative backward error ||r|| / (||A||*||x||+||b||), where ! || || is the infinity norm, or the relative residual ! ||r||/||b||, where || || is the 2-norm, according to the ! selected stopping criterion (see istop below). ! itrace - integer, optional, input. ! If itrace>0 then information about convergence is printed ! every itrace iterations; otherwise it is ignored. If itrace ! is not present, itrace=0 is assumed. ! irst - integer, optional, input. ! The restart parameter used in the GMRES and BiCGSTAB(l) ! solvers. It is ignored if other solvers are chosen. If irst ! is not present, irst=10 is assumed for Restarded GMRES and ! irst=l=1 for BiCGStab(l) (note that BiCGStab(1)=BiCGStab). ! istop - integer, optional, input. ! The normwise backward error stopping criterion is used if ! istop=1; the relative residual one if istop=2. If istop ! is not present, istop=1 is assumed. ! Subroutine mld_dkrylov(method,a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,irst,istop) use psb_base_mod use psb_prec_mod ! Arguments character(len=*) :: method Type(psb_dspmat_type), Intent(in) :: a Type(psb_desc_type), Intent(in) :: desc_a type(psb_dprec_type), intent(in) :: prec 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, irst,istop Integer, Optional, Intent(out) :: iter Real(Kind(1.d0)), Optional, Intent(out) :: err ! Local variables integer :: ictxt,me,np,err_act character(len=20) :: name info = 0 name = 'mld_krylov' call psb_erractionsave(err_act) ictxt=psb_cd_get_context(desc_a) call psb_info(ictxt, me, np) select case(toupper(method)) case('CG') call psb_cg(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,istop) case('CGS') call psb_cgs(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,istop) case('BICG') call psb_bicg(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,istop) case('BICGSTAB') call psb_bicgstab(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,istop) case('RGMRES') call psb_rgmres(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,irst,istop) case('BICGSTABL') call psb_bicgstabl(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,irst,istop) case default if (me==0) write(0,*) 'Warning: Unknown method ',method,& & ' in ',name,' defaulting to BiCGSTAB' call psb_bicgstab(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,istop) end select if(info/=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.psb_act_abort_) then call psb_error(ictxt) return end if end subroutine mld_dkrylov Subroutine mld_zkrylov(method,a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,irst,istop) use psb_base_mod use psb_prec_mod ! Arguments character(len=*) :: method Type(psb_zspmat_type), Intent(in) :: a Type(psb_desc_type), Intent(in) :: desc_a type(psb_zprec_type), intent(in) :: prec complex(Kind(1.d0)), Intent(in) :: b(:) complex(Kind(1.d0)), Intent(inout) :: x(:) Real(Kind(1.d0)), Intent(in) :: eps integer, intent(out) :: info Integer, Optional, Intent(in) :: itmax, itrace, irst,istop Integer, Optional, Intent(out) :: iter Real(Kind(1.d0)), Optional, Intent(out) :: err ! Local variables integer :: ictxt,me,np,err_act character(len=20) :: name info = 0 name = 'mld_krylov' call psb_erractionsave(err_act) ictxt=psb_cd_get_context(desc_a) call psb_info(ictxt, me, np) select case(toupper(method)) !!$ case('CG') !!$ call psb_cg(a,prec,b,x,eps,desc_a,info,& !!$ &itmax,iter,err,itrace,istop) case('CGS') call psb_cgs(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,istop) !!$ case('BICG') !!$ call psb_bicg(a,prec,b,x,eps,desc_a,info,& !!$ &itmax,iter,err,itrace,istop) case('BICGSTAB') call psb_bicgstab(a,prec,b,x,eps,desc_a,info,& & itmax,iter,err,itrace,istop) case('RGMRES') call psb_rgmres(a,prec,b,x,eps,desc_a,info,& & itmax,iter,err,itrace,irst,istop) !!$ case('BICGSTABL') !!$ call psb_bicgstabl(a,prec,b,x,eps,desc_a,info,& !!$ &itmax,iter,err,itrace,irst,istop) case default if (me==0) write(0,*) 'Warning: Unknown method ',method,& & ' in ',name,' defaulting to BiCGSTAB' call psb_bicgstab(a,prec,b,x,eps,desc_a,info,& &itmax,iter,err,itrace,istop) end select if(info/=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.psb_act_abort_) then call psb_error(ictxt) return end if end subroutine mld_zkrylov end module mld_krylov_mod