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!!$
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!!$
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!!$ MLD2P4
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!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
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!!$ based on PSBLAS (Parallel Sparse BLAS v.2.0)
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!!$
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!!$ (C) Copyright 2006 Alfredo Buttari University of Rome Tor Vergata
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!!$ Pasqua D'Ambra ICAR-CNR, Naples
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!!$ Daniela di Serafino Second University of Naples
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!!$ Salvatore Filippone University of Rome Tor Vergata
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!!$
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!!$ Redistribution and use in source and binary forms, with or without
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!!$ modification, are permitted provided that the following conditions
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!!$ are met:
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!!$ 1. Redistributions of source code must retain the above copyright
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!!$ notice, this list of conditions and the following disclaimer.
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!!$ 2. Redistributions in binary form must reproduce the above copyright
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!!$ notice, this list of conditions, and the following disclaimer in the
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!!$ documentation and/or other materials provided with the distribution.
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!!$ 3. The name of the PSBLAS group or the names of its contributors may
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!!$ not be used to endorse or promote products derived from this
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!!$ software without specific written permission.
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!!$
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!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS
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!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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!!$ POSSIBILITY OF SUCH DAMAGE.
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!!$
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!!$
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!
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! This is a partial duplication of material already present in the Krylov
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! part of the PSBLAS subtree. This is not as bad as it sounds, since
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! 1. There is no actual computation here, these are just wrappers around
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! the actual methods, so very little code is necessary;
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! 2. Changing the wrappers enables issuing error messages with a subroutine
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! name coherent with what the user sees;
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! 3. At the very least we would need a layer renaming the PSBLAS krylov interfaces,
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! so we are doing approx. the same amount of (re)coding.
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!
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Module mld_krylov_mod
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interface mld_krylov
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module procedure mld_dkrylov, mld_zkrylov
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end interface
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interface psb_cg
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subroutine psb_dcg(a,prec,b,x,eps,&
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& desc_a,info,itmax,iter,err,itrace,istop)
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use psb_base_mod
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use psb_prec_mod
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type(psb_dspmat_type), intent(in) :: a
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type(psb_desc_type), intent(in) :: desc_a
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real(kind(1.d0)), intent(in) :: b(:)
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real(kind(1.d0)), intent(inout) :: x(:)
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real(kind(1.d0)), intent(in) :: eps
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type(psb_dprec_type), intent(in) :: prec
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integer, intent(out) :: info
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integer, optional, intent(in) :: itmax, itrace,istop
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integer, optional, intent(out) :: iter
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real(kind(1.d0)), optional, intent(out) :: err
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end subroutine psb_dcg
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end interface
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interface psb_bicg
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subroutine psb_dbicg(a,prec,b,x,eps,&
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& desc_a,info,itmax,iter,err,itrace,istop)
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use psb_base_mod
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use psb_prec_mod
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type(psb_dspmat_type), intent(in) :: a
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type(psb_desc_type), intent(in) :: desc_a
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real(kind(1.d0)), intent(in) :: b(:)
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real(kind(1.d0)), intent(inout) :: x(:)
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real(kind(1.d0)), intent(in) :: eps
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type(psb_dprec_type), intent(in) :: prec
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integer, intent(out) :: info
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integer, optional, intent(in) :: itmax, itrace,istop
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integer, optional, intent(out) :: iter
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real(kind(1.d0)), optional, intent(out) :: err
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end subroutine psb_dbicg
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end interface
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interface psb_bicgstab
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subroutine psb_dcgstab(a,prec,b,x,eps,&
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& desc_a,info,itmax,iter,err,itrace,istop)
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use psb_base_mod
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use psb_prec_mod
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type(psb_dspmat_type), intent(in) :: a
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type(psb_desc_type), intent(in) :: desc_a
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real(kind(1.d0)), intent(in) :: b(:)
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real(kind(1.d0)), intent(inout) :: x(:)
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real(kind(1.d0)), intent(in) :: eps
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type(psb_dprec_type), intent(in) :: prec
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integer, intent(out) :: info
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integer, optional, intent(in) :: itmax, itrace,istop
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integer, optional, intent(out) :: iter
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real(kind(1.d0)), optional, intent(out) :: err
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end subroutine psb_dcgstab
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subroutine psb_zcgstab(a,prec,b,x,eps,&
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& desc_a,info,itmax,iter,err,itrace,istop)
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use psb_base_mod
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use psb_prec_mod
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type(psb_zspmat_type), intent(in) :: a
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type(psb_desc_type), intent(in) :: desc_a
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complex(kind(1.d0)), intent(in) :: b(:)
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complex(kind(1.d0)), intent(inout) :: x(:)
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real(kind(1.d0)), intent(in) :: eps
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type(psb_zprec_type), intent(in) :: prec
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integer, intent(out) :: info
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integer, optional, intent(in) :: itmax, itrace,istop
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integer, optional, intent(out) :: iter
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real(kind(1.d0)), optional, intent(out) :: err
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end subroutine psb_zcgstab
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end interface
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interface psb_bicgstabl
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Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,&
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&itmax,iter,err, itrace,irst,istop)
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use psb_base_mod
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use psb_prec_mod
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Type(psb_dspmat_type), Intent(in) :: a
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Type(psb_desc_type), Intent(in) :: desc_a
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type(psb_dprec_type), intent(in) :: prec
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Real(Kind(1.d0)), Intent(in) :: b(:)
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Real(Kind(1.d0)), Intent(inout) :: x(:)
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Real(Kind(1.d0)), Intent(in) :: eps
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integer, intent(out) :: info
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Integer, Optional, Intent(in) :: itmax, itrace, irst,istop
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Integer, Optional, Intent(out) :: iter
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Real(Kind(1.d0)), Optional, Intent(out) :: err
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end subroutine psb_dcgstabl
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end interface
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interface psb_rgmres
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Subroutine psb_dgmresr(a,prec,b,x,eps,desc_a,info,&
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&itmax,iter,err,itrace,irst,istop)
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use psb_base_mod
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use psb_prec_mod
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Type(psb_dspmat_type), Intent(in) :: a
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Type(psb_desc_type), Intent(in) :: desc_a
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type(psb_dprec_type), intent(in) :: prec
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Real(Kind(1.d0)), Intent(in) :: b(:)
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Real(Kind(1.d0)), Intent(inout) :: x(:)
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Real(Kind(1.d0)), Intent(in) :: eps
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integer, intent(out) :: info
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Integer, Optional, Intent(in) :: itmax, itrace, irst,istop
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Integer, Optional, Intent(out) :: iter
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Real(Kind(1.d0)), Optional, Intent(out) :: err
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end subroutine psb_dgmresr
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Subroutine psb_zgmresr(a,prec,b,x,eps,desc_a,info,&
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&itmax,iter,err,itrace,irst,istop)
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use psb_base_mod
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use psb_prec_mod
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Type(psb_zspmat_type), Intent(in) :: a
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Type(psb_desc_type), Intent(in) :: desc_a
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type(psb_zprec_type), intent(in) :: prec
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complex(Kind(1.d0)), Intent(in) :: b(:)
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complex(Kind(1.d0)), Intent(inout) :: x(:)
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Real(Kind(1.d0)), Intent(in) :: eps
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integer, intent(out) :: info
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Integer, Optional, Intent(in) :: itmax, itrace, irst,istop
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Integer, Optional, Intent(out) :: iter
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Real(Kind(1.d0)), Optional, Intent(out) :: err
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end subroutine psb_zgmresr
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end interface
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interface psb_cgs
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subroutine psb_dcgs(a,prec,b,x,eps,desc_a,info,&
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&itmax,iter,err,itrace,istop)
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use psb_base_mod
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use psb_prec_mod
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type(psb_dspmat_type), intent(in) :: a
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type(psb_desc_type), intent(in) :: desc_a
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type(psb_dprec_type), intent(in) :: prec
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real(kind(1.d0)), intent(in) :: b(:)
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real(kind(1.d0)), intent(inout) :: x(:)
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real(kind(1.d0)), intent(in) :: eps
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integer, intent(out) :: info
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integer, optional, intent(in) :: itmax, itrace,istop
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integer, optional, intent(out) :: iter
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real(kind(1.d0)), optional, intent(out) :: err
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end subroutine psb_dcgs
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subroutine psb_zcgs(a,prec,b,x,eps,&
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& desc_a,info,itmax,iter,err,itrace,istop)
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use psb_base_mod
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use psb_prec_mod
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type(psb_zspmat_type), intent(in) :: a
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type(psb_desc_type), intent(in) :: desc_a
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complex(kind(1.d0)), intent(in) :: b(:)
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complex(kind(1.d0)), intent(inout) :: x(:)
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real(kind(1.d0)), intent(in) :: eps
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type(psb_zprec_type), intent(in) :: prec
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integer, intent(out) :: info
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integer, optional, intent(in) :: itmax, itrace,istop
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integer, optional, intent(out) :: iter
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real(kind(1.d0)), optional, intent(out) :: err
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end subroutine psb_zcgs
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end interface
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contains
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!
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! File: mld_krylov_mod.f90
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!
|
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! Subroutine: mld_dkrylov
|
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|
|
!
|
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|
|
! Front-end for the Krylov subspace iterations, real version
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!
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! Arguments:
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|
!
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! methd - character The specific method; can take the values:
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! CG
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! CGS
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! BICG
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! BICGSTAB
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! BICGSTABL
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! RGMRES
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|
!
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! a - type(<psb_dspmat_type>) Input: sparse matrix containing A.
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|
! prec - type(<mld_dprec_type>) Input: preconditioner
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|
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! b - real,dimension(:) Input: vector containing the
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|
|
! right hand side B
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|
! x - real,dimension(:) Input/Output: vector containing the
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|
|
! initial guess and final solution X.
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|
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! eps - real Input: Stopping tolerance; the iteration is
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|
|
! stopped when the error estimate
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|
! |err| <= eps
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|
! desc_a - type(<psb_desc_type>). Input: The communication descriptor.
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|
! info - integer. Output: Return code
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|
!
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! itmax - integer(optional) Input: maximum number of iterations to be
|
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|
|
! performed.
|
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|
|
! iter - integer(optional) Output: how many iterations have been
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|
|
! performed.
|
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|
! err - real (optional) Output: error estimate on exit
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|
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! itrace - integer(optional) Input: print an informational message
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|
|
|
! with the error estimate every itrace
|
|
|
|
|
! iterations
|
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|
|
|
! irst - integer(optional) Input: restart parameter for RGMRES and
|
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|
|
|
! BICGSTAB(L) methods
|
|
|
|
|
! istop - integer(optional) Input: stopping criterion, or how
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|
|
! to estimate the error.
|
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|
! 1: err = |r|/|b|
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! 2: err = |r|/(|a||x|+|b|)
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|
|
! where r is the (preconditioned, recursive
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|
|
! estimate of) residual
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!
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|
|
Subroutine mld_dkrylov(method,a,prec,b,x,eps,desc_a,info,&
|
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&itmax,iter,err,itrace,irst,istop)
|
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use psb_base_mod
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|
use psb_prec_mod
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|
|
character(len=*) :: method
|
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|
|
Type(psb_dspmat_type), Intent(in) :: a
|
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|
|
|
Type(psb_desc_type), Intent(in) :: desc_a
|
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|
|
|
type(psb_dprec_type), intent(in) :: prec
|
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|
|
|
Real(Kind(1.d0)), Intent(in) :: b(:)
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|
|
|
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
|
|
|
|
|
|
|
|
|
|
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)
|
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|
|
|
case('RGMRES')
|
|
|
|
|
call psb_rgmres(a,prec,b,x,eps,desc_a,info,&
|
|
|
|
|
&itmax,iter,err,itrace,irst,istop)
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|
|
|
case('BICGSTABL')
|
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|
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|
call psb_bicgstabl(a,prec,b,x,eps,desc_a,info,&
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|
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|
&itmax,iter,err,itrace,irst,istop)
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|
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|
case default
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|
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|
if (me==0) write(0,*) 'Warning: Unknown method ',method,&
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|
|
|
|
& ' in ',name,' defaulting to BiCGSTAB'
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|
|
|
|
call psb_bicgstab(a,prec,b,x,eps,desc_a,info,&
|
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|
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|
&itmax,iter,err,itrace,istop)
|
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|
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|
end select
|
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if(info/=0) then
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|
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call psb_errpush(info,name)
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goto 9999
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end if
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call psb_erractionrestore(err_act)
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|
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return
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|
9999 continue
|
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|
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call psb_erractionrestore(err_act)
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|
|
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if (err_act.eq.psb_act_abort_) then
|
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|
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call psb_error(ictxt)
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return
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end if
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|
end subroutine mld_dkrylov
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!
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! File: mld_krylov_mod.f90
|
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|
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!
|
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|
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! Subroutine: mld_zkrylov
|
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|
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|
!
|
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|
! Front-end for the Krylov subspace iterations, complexversion
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|
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|
!
|
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|
! Arguments:
|
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|
!
|
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|
! methd - character The specific method; can take the values:
|
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|
! CGS
|
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|
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|
! BICGSTAB
|
|
|
|
|
! RGMRES
|
|
|
|
|
!
|
|
|
|
|
! a - type(<psb_zspmat_type>) Input: sparse matrix containing A.
|
|
|
|
|
! prec - type(<mld_zprec_type>) Input: preconditioner
|
|
|
|
|
! b - complex,dimension(:) Input: vector containing the
|
|
|
|
|
! right hand side B
|
|
|
|
|
! x - complex,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.
|
|
|
|
|
! err - real (optional) Output: error estimate on exit
|
|
|
|
|
! itrace - integer(optional) Input: print an informational message
|
|
|
|
|
! with the error estimate every itrace
|
|
|
|
|
! iterations
|
|
|
|
|
! irst - integer(optional) Input: restart parameter for RGMRES and
|
|
|
|
|
! BICGSTAB(L) methods
|
|
|
|
|
! istop - integer(optional) Input: stopping criterion, or how
|
|
|
|
|
! to estimate the error.
|
|
|
|
|
! 1: err = |r|/|b|
|
|
|
|
|
! 2: err = |r|/(|a||x|+|b|)
|
|
|
|
|
! where r is the (preconditioned, recursive
|
|
|
|
|
! estimate of) residual
|
|
|
|
|
!
|
|
|
|
|
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
|
|
|
|
|
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
|
|
|
|
|
|
|
|
|
|
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
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
