!!$
!!$ Parallel Sparse BLAS version 3.0
!!$ (C) Copyright 2006, 2007, 2008, 2009, 2010
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari CNRS-IRIT, Toulouse
!!$
!!$ Contributions to this routine:
!!$ Daniela di Serafino Second University of Naples
!!$ Pasqua D'Ambra ICAR-CNR
!!$
!!$ 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.
!!$
!!$
!!$ 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 C
!!$ C [5] G. Sleijpen, D. Fokkema C
!!$ C BICGSTAB(L) for linear equations involving unsymmetric C
!!$ C matrices with complex spectrum C
!!$ C Electronic Trans. on Numer. Analysis, Vol. 1, pp. 11-32, C
!!$ C Sep. 1993 C
!!$ C C
!!$ C C
!!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
! File: psb_crgmres.f90
!
! Subroutine: psb_crgmres
! This subroutine implements the restarted GMRES method with right
! preconditioning.
!
! Arguments:
!
! a - type(psb_cspmat_type) Input: sparse matrix containing A.
! prec - class(psb_cprec_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.
! 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.
! irst - integer(optional) Input: restart parameter
!
!!$Subroutine psb_crgmres(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,istop)
!!$ use psb_base_mod
!!$ use psb_prec_mod
!!$ use psb_c_krylov_conv_mod
!!$ use psb_krylov_mod
!!$ implicit none
!!$
!!$! = Parameters
!!$ Type(psb_cspmat_type), Intent(in) :: a
!!$ class(psb_cprec_type), Intent(in) :: prec
!!$ Type(psb_desc_type), Intent(in) :: desc_a
!!$ complex(psb_spk_), Intent(in) :: b(:)
!!$ complex(psb_spk_), Intent(inout) :: x(:)
!!$ Real(psb_spk_), Intent(in) :: eps
!!$ integer(psb_ipk_), intent(out) :: info
!!$ integer(psb_ipk_), Optional, Intent(in) :: itmax, itrace, irst,istop
!!$ integer(psb_ipk_), Optional, Intent(out) :: iter
!!$ Real(psb_spk_), Optional, Intent(out) :: err
!!$! = local data
!!$ complex(psb_spk_), allocatable, target :: aux(:),w(:),w1(:), v(:,:)
!!$ complex(psb_spk_), allocatable :: c(:),s(:), h(:,:), rs(:),rst(:),xt(:)
!!$ Real(psb_spk_) :: tmp
!!$ complex(psb_spk_) :: rti, rti1, scal
!!$ integer(psb_ipk_) ::litmax, naux, mglob, it,k, itrace_,&
!!$ & np,me, n_row, n_col, nl, int_err(5)
!!$ Logical, Parameter :: exchange=.True., noexchange=.False.
!!$ integer(psb_ipk_), Parameter :: irmax = 8
!!$ integer(psb_ipk_) :: itx, i, isvch, ictxt,istop_, err_act
!!$ integer(psb_ipk_) :: debug_level, debug_unit
!!$ Real(psb_dpk_) :: rni, xni, bni, ani,bn2
!!$ real(psb_dpk_) :: errnum, errden, deps, derr
!!$ character(len=20) :: name
!!$ character(len=*), parameter :: methdname='RGMRES'
!!$
!!$ info = psb_success_
!!$ name = 'psb_cgmres'
!!$ call psb_erractionsave(err_act)
!!$ debug_unit = psb_get_debug_unit()
!!$ debug_level = psb_get_debug_level()
!!$
!!$ ictxt = desc_a%get_context()
!!$ Call psb_info(ictxt, me, np)
!!$ if (debug_level >= psb_debug_ext_)&
!!$ & write(debug_unit,*) me,' ',trim(name),': from psb_info',np
!!$
!!$ 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
!!$ !
!!$ ! ISTOP_ = 1: Normwise backward error, infinity norm
!!$ ! ISTOP_ = 2: ||r||/||b||, 2-norm
!!$ !
!!$
!!$ if ((istop_ < 1 ).or.(istop_ > 2 ) ) then
!!$ info=psb_err_invalid_istop_
!!$ int_err(1)=istop_
!!$ err=info
!!$ call psb_errpush(info,name,i_err=int_err)
!!$ goto 9999
!!$ endif
!!$
!!$ if (present(itmax)) then
!!$ litmax = itmax
!!$ else
!!$ litmax = 1000
!!$ endif
!!$
!!$ if (present(itrace)) then
!!$ itrace_ = itrace
!!$ else
!!$ itrace_ = 0
!!$ end if
!!$
!!$ if (present(irst)) then
!!$ nl = irst
!!$ if (debug_level >= psb_debug_ext_) &
!!$ & write(debug_unit,*) me,' ',trim(name),&
!!$ & ' present: irst: ',irst,nl
!!$ else
!!$ nl = 10
!!$ if (debug_level >= psb_debug_ext_) &
!!$ & write(debug_unit,*) me,' ',trim(name),&
!!$ & ' not present: irst: ',irst,nl
!!$ endif
!!$ if (nl <=0 ) then
!!$ info=psb_err_invalid_istop_
!!$ int_err(1)=nl
!!$ err=info
!!$ call psb_errpush(info,name,i_err=int_err)
!!$ goto 9999
!!$ endif
!!$
!!$ call psb_chkvect(mglob,ione,size(x,1),ione,ione,desc_a,info)
!!$ if(info /= psb_success_) then
!!$ info=psb_err_from_subroutine_
!!$ call psb_errpush(info,name,a_err='psb_chkvect on X')
!!$ goto 9999
!!$ end if
!!$ call psb_chkvect(mglob,ione,size(b,ione),ione,ione,desc_a,info)
!!$ if(info /= psb_success_) then
!!$ info=psb_err_from_subroutine_
!!$ call psb_errpush(info,name,a_err='psb_chkvect on B')
!!$ goto 9999
!!$ end if
!!$
!!$
!!$ naux=4*n_col
!!$ allocate(aux(naux),h(nl+1,nl+1),&
!!$ &c(nl+1),s(nl+1),rs(nl+1), rst(nl+1),stat=info)
!!$
!!$ if (info == psb_success_) Call psb_geall(v,desc_a,info,n=nl+1)
!!$ if (info == psb_success_) Call psb_geall(w,desc_a,info)
!!$ if (info == psb_success_) Call psb_geall(w1,desc_a,info)
!!$ if (info == psb_success_) Call psb_geall(xt,desc_a,info)
!!$ if (info == psb_success_) Call psb_geasb(v,desc_a,info)
!!$ if (info == psb_success_) Call psb_geasb(w,desc_a,info)
!!$ if (info == psb_success_) Call psb_geasb(w1,desc_a,info)
!!$ if (info == psb_success_) Call psb_geasb(xt,desc_a,info)
!!$ if (info /= psb_success_) then
!!$ info=psb_err_from_subroutine_non_
!!$ call psb_errpush(info,name)
!!$ goto 9999
!!$ end if
!!$ if (debug_level >= psb_debug_ext_) &
!!$ & write(debug_unit,*) me,' ',trim(name),&
!!$ & ' Size of V,W,W1 ',size(v),size(v,1),&
!!$ & size(w),size(w,1),size(w1),size(w1,1), size(v(:,1))
!!$
!!$
!!$ if (istop_ == 1) then
!!$ ani = psb_spnrmi(a,desc_a,info)
!!$ bni = psb_geamax(b,desc_a,info)
!!$ else if (istop_ == 2) then
!!$ bn2 = psb_genrm2(b,desc_a,info)
!!$ endif
!!$ errnum = dzero
!!$ errden = done
!!$ deps = eps
!!$ if (info /= psb_success_) then
!!$ info=psb_err_from_subroutine_non_
!!$ call psb_errpush(info,name)
!!$ goto 9999
!!$ end if
!!$ if ((itrace_ > 0).and.(me == 0)) call log_header(methdname)
!!$
!!$ itx = 0
!!$ restart: do
!!$
!!$ ! compute r0 = b-ax0
!!$ ! check convergence
!!$ ! compute v1 = r0/||r0||_2
!!$
!!$ if (debug_level >= psb_debug_ext_) &
!!$ & write(debug_unit,*) me,' ',trim(name),&
!!$ & ' restart: ',itx,it
!!$ it = 0
!!$ call psb_geaxpby(cone,b,czero,v(:,1),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_spmm(-cone,a,x,cone,v(:,1),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
!!$
!!$ rs(1) = psb_genrm2(v(:,1),desc_a,info)
!!$ rs(2:) = czero
!!$ if (info /= psb_success_) Then
!!$ info=psb_err_from_subroutine_non_
!!$ call psb_errpush(info,name)
!!$ goto 9999
!!$ end if
!!$ scal=done/rs(1) ! rs(1) MIGHT BE VERY SMALL - USE DSCAL TO DEAL WITH IT?
!!$
!!$ if (debug_level >= psb_debug_ext_) &
!!$ & write(debug_unit,*) me,' ',trim(name),&
!!$ & ' on entry to amax: b: ',Size(b),rs(1),scal
!!$
!!$ !
!!$ ! check convergence
!!$ !
!!$ if (istop_ == 1) then
!!$ rni = psb_geamax(v(:,1),desc_a,info)
!!$ xni = psb_geamax(x,desc_a,info)
!!$ errnum = rni
!!$ errden = (ani*xni+bni)
!!$ else if (istop_ == 2) then
!!$ rni = psb_genrm2(v(:,1),desc_a,info)
!!$ errnum = rni
!!$ errden = bn2
!!$ endif
!!$ if (info /= psb_success_) then
!!$ info=psb_err_from_subroutine_non_
!!$ call psb_errpush(info,name)
!!$ goto 9999
!!$ end if
!!$
!!$ if (errnum <= deps*errden) exit restart
!!$
!!$ if (itrace_ > 0) &
!!$ & call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
!!$
!!$ v(:,1) = v(:,1) * scal
!!$
!!$ if (itx >= litmax) exit restart
!!$
!!$ !
!!$ ! inner iterations
!!$ !
!!$
!!$ inner: Do i=1,nl
!!$ itx = itx + 1
!!$
!!$ call prec%apply(v(:,i),w1,desc_a,info)
!!$ Call psb_spmm(cone,a,w1,czero,w,desc_a,info,work=aux)
!!$ !
!!$
!!$ do k = 1, i
!!$ h(k,i) = psb_gedot(v(:,k),w,desc_a,info)
!!$ call psb_geaxpby(-h(k,i),v(:,k),cone,w,desc_a,info)
!!$ end do
!!$ h(i+1,i) = psb_genrm2(w,desc_a,info)
!!$ scal=done/h(i+1,i)
!!$ call psb_geaxpby(scal,w,czero,v(:,i+1),desc_a,info)
!!$ do k=2,i
!!$ call crot(1,h(k-1,i),1,h(k,i),1,real(c(k-1)),s(k-1))
!!$ enddo
!!$
!!$ rti = h(i,i)
!!$ rti1 = h(i+1,i)
!!$ call crotg(rti,rti1,tmp,s(i))
!!$ c(i) = cmplx(tmp,szero)
!!$ call crot(1,h(i,i),1,h(i+1,i),1,real(c(i)),s(i))
!!$ h(i+1,i) = czero
!!$ call crot(1,rs(i),1,rs(i+1),1,real(c(i)),s(i))
!!$
!!$ if (istop_ == 1) then
!!$ !
!!$ ! build x and then compute the residual and its infinity norm
!!$ !
!!$ rst = rs
!!$ xt = czero
!!$ call ctrsm('l','u','n','n',i,1,cone,h,size(h,1),rst,size(rst,1))
!!$ if (debug_level >= psb_debug_ext_) &
!!$ & write(debug_unit,*) me,' ',trim(name),&
!!$ & ' Rebuild x-> RS:',rst(1:nl)
!!$ do k=1, i
!!$ call psb_geaxpby(rst(k),v(:,k),cone,xt,desc_a,info)
!!$ end do
!!$ call prec%apply(xt,desc_a,info)
!!$ call psb_geaxpby(cone,x,cone,xt,desc_a,info)
!!$ call psb_geaxpby(cone,b,czero,w1,desc_a,info)
!!$ call psb_spmm(-cone,a,xt,cone,w1,desc_a,info,work=aux)
!!$ rni = psb_geamax(w1,desc_a,info)
!!$ xni = psb_geamax(xt,desc_a,info)
!!$ errnum = rni
!!$ errden = (ani*xni+bni)
!!$ !
!!$
!!$ else if (istop_ == 2) then
!!$ !
!!$ ! compute the residual 2-norm as byproduct of the solution
!!$ ! procedure of the least-squares problem
!!$ !
!!$ rni = abs(rs(i+1))
!!$ errnum = rni
!!$ errden = bn2
!!$ endif
!!$
!!$ If (errnum <= deps*errden) Then
!!$
!!$ if (istop_ == 1) then
!!$ x = xt
!!$ else if (istop_ == 2) then
!!$ !
!!$ ! build x
!!$ !
!!$ call ctrsm('l','u','n','n',i,1,cone,h,size(h,1),rs,size(rs,1))
!!$ if (debug_level >= psb_debug_ext_) &
!!$ & write(debug_unit,*) me,' ',trim(name),&
!!$ & ' Rebuild x-> RS:',rs(1:nl)
!!$ w1 = czero
!!$ do k=1, i
!!$ call psb_geaxpby(rs(k),v(:,k),cone,w1,desc_a,info)
!!$ end do
!!$ call prec%apply(w1,w,desc_a,info)
!!$ call psb_geaxpby(cone,w,cone,x,desc_a,info)
!!$ end if
!!$
!!$ exit restart
!!$
!!$ end if
!!$
!!$ if (itrace_ > 0) &
!!$ & call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
!!$
!!$ end do inner
!!$
!!$ if (istop_ == 1) then
!!$ x = xt
!!$ else if (istop_ == 2) then
!!$ !
!!$ ! build x
!!$ !
!!$ call ctrsm('l','u','n','n',nl,1,cone,h,size(h,1),rs,size(rs,1))
!!$ if (debug_level >= psb_debug_ext_) &
!!$ & write(debug_unit,*) me,' ',trim(name),&
!!$ & ' Rebuild x-> RS:',rs(1:nl)
!!$ w1 = czero
!!$ do k=1, nl
!!$ call psb_geaxpby(rs(k),v(:,k),cone,w1,desc_a,info)
!!$ end do
!!$ call prec%apply(w1,w,desc_a,info)
!!$ call psb_geaxpby(cone,w,cone,x,desc_a,info)
!!$ end if
!!$
!!$ end do restart
!!$ if (itrace_ > 0) &
!!$ & call log_conv(methdname,me,itx,ione,errnum,errden,deps)
!!$
!!$ call log_end(methdname,me,itx,errnum,errden,deps,err=derr,iter=iter)
!!$
!!$ if (present(err)) then
!!$ err = derr
!!$ end if
!!$
!!$
!!$ deallocate(aux,h,c,s,rs,rst, stat=info)
!!$ if (info == psb_success_) call psb_gefree(v,desc_a,info)
!!$ if (info == psb_success_) call psb_gefree(w,desc_a,info)
!!$ if (info == psb_success_) call psb_gefree(w1,desc_a,info)
!!$ if (info == psb_success_) call psb_gefree(xt,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_erractionrestore(err_act)
!!$ return
!!$
!!$9999 continue
!!$ call psb_erractionrestore(err_act)
!!$ if (err_act == psb_act_abort_) then
!!$ call psb_error()
!!$ return
!!$ end if
!!$ return
!!$
!!$End Subroutine psb_crgmres
subroutine psb_crgmres_vect(a,prec,b,x,eps,desc_a,info,&
& itmax,iter,err,itrace,irst,istop)
use psb_base_mod
use psb_prec_mod
use psb_c_krylov_conv_mod
use psb_krylov_mod
implicit none
type(psb_cspmat_type), intent(in) :: a
Type(psb_desc_type), Intent(in) :: desc_a
class(psb_cprec_type), intent(inout) :: prec
type(psb_c_vect_type), Intent(inout) :: b
type(psb_c_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, irst,istop
integer(psb_ipk_), Optional, Intent(out) :: iter
Real(psb_spk_), Optional, Intent(out) :: err
! = local data
complex(psb_spk_), allocatable :: aux(:)
complex(psb_spk_), allocatable :: c(:), s(:), h(:,:), rs(:), rst(:)
type(psb_c_vect_type), allocatable :: v(:)
type(psb_c_vect_type) :: w, w1, xt
real(psb_spk_) :: tmp
complex(psb_spk_) :: scal, gm, rti, rti1
integer(psb_ipk_) ::litmax, naux, mglob, it,k, itrace_,&
& n_row, n_col, nl, int_err(5)
Logical, Parameter :: exchange=.True., noexchange=.False., use_srot=.true.
integer(psb_ipk_), Parameter :: irmax = 8
integer(psb_ipk_) :: itx, i, istop_, err_act
integer(psb_ipk_) :: debug_level, debug_unit
integer(psb_ipk_) :: ictxt, np, me
Real(psb_spk_) :: rni, xni, bni, ani,bn2, dt
real(psb_dpk_) :: errnum, errden, deps, derr
character(len=20) :: name
character(len=*), parameter :: methdname='RGMRES'
info = psb_success_
name = 'psb_sgmres'
call psb_erractionsave(err_act)
debug_unit = psb_get_debug_unit()
debug_level = psb_get_debug_level()
ictxt = desc_a%get_context()
Call psb_info(ictxt, me, np)
if (debug_level >= psb_debug_ext_)&
& write(debug_unit,*) me,' ',trim(name),': from psb_info',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
!
! ISTOP_ = 1: Normwise backward error, infinity norm
! ISTOP_ = 2: ||r||/||b||, 2-norm
!
if ((istop_ < 1 ).or.(istop_ > 2 ) ) then
info=psb_err_invalid_istop_
int_err(1)=istop_
err=info
call psb_errpush(info,name,i_err=int_err)
goto 9999
endif
if (present(itmax)) then
litmax = itmax
else
litmax = 1000
endif
if (present(itrace)) then
itrace_ = itrace
else
itrace_ = 0
end if
if (present(irst)) then
nl = irst
if (debug_level >= psb_debug_ext_) &
& write(debug_unit,*) me,' ',trim(name),&
& ' present: irst: ',irst,nl
else
nl = 10
if (debug_level >= psb_debug_ext_) &
& write(debug_unit,*) me,' ',trim(name),&
& ' not present: irst: ',irst,nl
endif
if (nl <=0 ) then
info=psb_err_invalid_istop_
int_err(1)=nl
err=info
call psb_errpush(info,name,i_err=int_err)
goto 9999
endif
call psb_chkvect(mglob,ione,x%get_nrows(),ione,ione,desc_a,info)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='psb_chkvect on X')
goto 9999
end if
call psb_chkvect(mglob,ione,b%get_nrows(),ione,ione,desc_a,info)
if(info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='psb_chkvect on B')
goto 9999
end if
naux=4*n_col
allocate(aux(naux),h(nl+1,nl+1),&
&c(nl+1),s(nl+1),rs(nl+1), rst(nl+1),stat=info)
if (info == psb_success_) call psb_geall(v,desc_a,info,n=nl+1)
if (info == psb_success_) call psb_geall(w,desc_a,info)
if (info == psb_success_) call psb_geall(w1,desc_a,info)
if (info == psb_success_) call psb_geall(xt,desc_a,info)
if (info == psb_success_) call psb_geasb(v,desc_a,info,mold=x%v)
if (info == psb_success_) call psb_geasb(w,desc_a,info,mold=x%v)
if (info == psb_success_) call psb_geasb(w1,desc_a,info,mold=x%v)
if (info == psb_success_) call psb_geasb(xt,desc_a,info,mold=x%v)
if (info /= psb_success_) then
info=psb_err_from_subroutine_non_
call psb_errpush(info,name)
goto 9999
end if
if (debug_level >= psb_debug_ext_) &
& write(debug_unit,*) me,' ',trim(name),&
& ' Size of V,W,W1 ',v(1)%get_nrows(),size(v),&
& w%get_nrows(),w1%get_nrows()
if (istop_ == 1) then
ani = psb_spnrmi(a,desc_a,info)
bni = psb_geamax(b,desc_a,info)
else if (istop_ == 2) then
bn2 = psb_genrm2(b,desc_a,info)
endif
errnum = czero
errden = cone
deps = eps
if (info /= psb_success_) then
info=psb_err_from_subroutine_non_
call psb_errpush(info,name)
goto 9999
end if
if ((itrace_ > 0).and.(me == 0)) call log_header(methdname)
itx = 0
restart: do
! compute r0 = b-ax0
! check convergence
! compute v1 = r0/||r0||_2
if (debug_level >= psb_debug_ext_) &
& write(debug_unit,*) me,' ',trim(name),&
& ' restart: ',itx,it
it = 0
call psb_geaxpby(cone,b,czero,v(1),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_spmm(-cone,a,x,cone,v(1),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
rs(1) = psb_genrm2(v(1),desc_a,info)
rs(2:) = czero
if (info /= psb_success_) then
info=psb_err_from_subroutine_non_
call psb_errpush(info,name)
goto 9999
end if
scal=cone/rs(1) ! rs(1) MIGHT BE VERY SMALL - USE DSCAL TO DEAL WITH IT?
if (debug_level >= psb_debug_ext_) &
& write(debug_unit,*) me,' ',trim(name),&
& ' on entry to amax: b: ',b%get_nrows(),rs(1),scal
!
! check convergence
!
if (istop_ == 1) then
rni = psb_geamax(v(1),desc_a,info)
xni = psb_geamax(x,desc_a,info)
errnum = rni
errden = (ani*xni+bni)
else if (istop_ == 2) then
rni = psb_genrm2(v(1),desc_a,info)
errnum = rni
errden = bn2
endif
if (info /= psb_success_) then
info=psb_err_from_subroutine_non_
call psb_errpush(info,name)
goto 9999
end if
if (errnum <= eps*errden) exit restart
if (itrace_ > 0) &
& call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
call v(1)%scal(scal) !v(1) = v(1) * scal
if (itx >= litmax) exit restart
!
! inner iterations
!
inner: Do i=1,nl
itx = itx + 1
call prec%apply(v(i),w1,desc_a,info)
call psb_spmm(cone,a,w1,czero,w,desc_a,info,work=aux)
!
do k = 1, i
h(k,i) = psb_gedot(v(k),w,desc_a,info)
call psb_geaxpby(-h(k,i),v(k),cone,w,desc_a,info)
end do
h(i+1,i) = psb_genrm2(w,desc_a,info)
scal=cone/h(i+1,i)
call psb_geaxpby(scal,w,czero,v(i+1),desc_a,info)
do k=2,i
call crot(1,h(k-1,i),1,h(k,i),1,real(c(k-1)),s(k-1))
enddo
rti = h(i,i)
rti1 = h(i+1,i)
call crotg(rti,rti1,tmp,s(i))
c(i) = cmplx(tmp,szero)
call crot(1,h(i,i),1,h(i+1,i),1,real(c(i)),s(i))
h(i+1,i) = czero
call crot(1,rs(i),1,rs(i+1),1,real(c(i)),s(i))
if (istop_ == 1) then
!
! build x and then compute the residual and its infinity norm
!
rst = rs
call w1%set(czero)
call ctrsm('l','u','n','n',i,1,cone,h,size(h,1),rst,size(rst,1))
if (debug_level >= psb_debug_ext_) &
& write(debug_unit,*) me,' ',trim(name),&
& ' Rebuild x-> RS:',rst(1:nl)
do k=1, i
call psb_geaxpby(rst(k),v(k),cone,xt,desc_a,info)
end do
call prec%apply(xt,desc_a,info)
call psb_geaxpby(cone,x,cone,xt,desc_a,info)
call psb_geaxpby(cone,b,czero,w1,desc_a,info)
call psb_spmm(-cone,a,xt,cone,w1,desc_a,info,work=aux)
rni = psb_geamax(w1,desc_a,info)
xni = psb_geamax(xt,desc_a,info)
errnum = rni
errden = (ani*xni+bni)
!
else if (istop_ == 2) then
!
! compute the residual 2-norm as byproduct of the solution
! procedure of the least-squares problem
!
rni = abs(rs(i+1))
errnum = rni
errden = bn2
endif
if (errnum <= eps*errden) then
if (istop_ == 1) then
call psb_geaxpby(cone,xt,czero,x,desc_a,info)
! = x = xt
else if (istop_ == 2) then
!
! build x
!
call ctrsm('l','u','n','n',i,1,cone,h,size(h,1),rs,size(rs,1))
if (debug_level >= psb_debug_ext_) &
& write(debug_unit,*) me,' ',trim(name),&
& ' Rebuild x-> RS:',rs(1:nl)
call w1%set(czero)
do k=1, i
call psb_geaxpby(rs(k),v(k),cone,w1,desc_a,info)
end do
call prec%apply(w1,w,desc_a,info)
call psb_geaxpby(cone,w,cone,x,desc_a,info)
end if
exit restart
end if
if (itrace_ > 0) &
& call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
end do inner
if (istop_ == 1) then
call psb_geaxpby(cone,xt,czero,x,desc_a,info)! x = xt
else if (istop_ == 2) then
!
! build x
!
call ctrsm('l','u','n','n',nl,1,cone,h,size(h,1),rs,size(rs,1))
if (debug_level >= psb_debug_ext_) &
& write(debug_unit,*) me,' ',trim(name),&
& ' Rebuild x-> RS:',rs(1:nl)
call w1%set(czero)
do k=1, nl
call psb_geaxpby(rs(k),v(k),cone,w1,desc_a,info)
end do
call prec%apply(w1,w,desc_a,info)
call psb_geaxpby(cone,w,cone,x,desc_a,info)
end if
end do restart
if (itrace_ > 0) &
& call log_conv(methdname,me,itx,ione,errnum,errden,deps)
call log_end(methdname,me,itx,errnum,errden,deps,err=derr,iter=iter)
if (present(err)) err = derr
if (info == psb_success_) call psb_gefree(v,desc_a,info)
if (info == psb_success_) call psb_gefree(w,desc_a,info)
if (info == psb_success_) call psb_gefree(w1,desc_a,info)
if (info == psb_success_) call psb_gefree(xt,desc_a,info)
if (info == psb_success_) deallocate(aux,h,c,s,rs,rst, stat=info)
if (info /= psb_success_) then
info=psb_err_from_subroutine_non_
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 == psb_act_abort_) then
call psb_error()
return
end if
return
end subroutine psb_crgmres_vect