!!$
!!$ Parallel Sparse BLAS version 2.2
!!$ (C) Copyright 2006/2007/2008
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari University of Rome Tor Vergata
!!$
!!$ 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_zrgmres.f90
!
! Subroutine: psb_zrgmres
! This subroutine implements the restarted GMRES method with right
! preconditioning.
!
! Arguments:
!
! a - type(psb_zspmat_type) Input: sparse matrix containing A.
! prec - type(psb_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.
! 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|/|b|; here the iteration is
! stopped when |r| <= eps * |b|
! 2: err = |r|/(|a||x|+|b|); here the iteration is
! stopped when |r| <= eps * (|a||x|+|b|)
! where r is the (preconditioned, recursive
! estimate of) residual.
! irst - integer(optional) Input: restart parameter
!
Subroutine psb_zrgmres(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,istop)
use psb_base_mod
use psb_prec_mod
use psb_krylov_mod, psb_protect_name => psb_zrgmres
implicit none
!!$ Parameters
Type(psb_zspmat_type), Intent(in) :: a
Type(psb_zprec_type), Intent(in) :: prec
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
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 data
complex(Kind(1.d0)), allocatable, target :: aux(:),w(:),w1(:), v(:,:)
complex(Kind(1.d0)), allocatable :: c(:),s(:), h(:,:), rs(:),rst(:),xt(:)
Real(Kind(1.d0)) :: tmp
complex(kind(1.d0)) :: rti, rti1, scal
Integer ::litmax, naux, mglob, it,k, itrace_,&
& np,me, n_row, n_col, nl, int_err(5)
Logical, Parameter :: exchange=.True., noexchange=.False.
Integer, Parameter :: irmax = 8
Integer :: itx, i, isvch, ictxt,istop_, err_act
integer :: debug_level, debug_unit
Real(Kind(1.d0)) :: rni, xni, bni, ani,bn2
real(kind(1.d0)), external :: dznrm2
real(kind(1.d0)) :: errnum, errden
character(len=20) :: name
character(len=*), parameter :: methdname='RGMRES'
info = 0
name = 'psb_zgmres'
call psb_erractionsave(err_act)
debug_unit = psb_get_debug_unit()
debug_level = psb_get_debug_level()
ictxt = psb_cd_get_context(desc_a)
Call psb_info(ictxt, me, np)
if (debug_level >= psb_debug_ext_)&
& write(debug_unit,*) me,' ',trim(name),': from psb_info',np
mglob = psb_cd_get_global_rows(desc_a)
n_row = psb_cd_get_local_rows(desc_a)
n_col = psb_cd_get_local_cols(desc_a)
if (present(istop)) then
istop_ = istop
else
istop_ = 1
endif
!
! ISTOP_ = 1: Normwise backward error, infinity norm
! ISTOP_ = 2: ||r||/||b||, 2-norm
!
if ((istop_ < 1 ).or.(istop_ > 2 ) ) then
info=5001
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=5001
int_err(1)=nl
err=info
call psb_errpush(info,name,i_err=int_err)
goto 9999
endif
call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info)
if(info /= 0) then
info=4010
call psb_errpush(info,name,a_err='psb_chkvect on X')
goto 9999
end if
call psb_chkvect(mglob,1,size(b,1),1,1,desc_a,info)
if(info /= 0) then
info=4010
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 == 0) Call psb_geall(v,desc_a,info,n=nl+1)
if (info == 0) Call psb_geall(w,desc_a,info)
if (info == 0) Call psb_geall(w1,desc_a,info)
if (info == 0) Call psb_geall(xt,desc_a,info)
if (info == 0) Call psb_geasb(v,desc_a,info)
if (info == 0) Call psb_geasb(w,desc_a,info)
if (info == 0) Call psb_geasb(w1,desc_a,info)
if (info == 0) Call psb_geasb(xt,desc_a,info)
if (info /= 0) then
info=4011
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))
! Ensure global coherence for convergence checks.
call psb_set_coher(ictxt,isvch)
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
if (info /= 0) then
info=4011
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(zone,b,zzero,v(:,1),desc_a,info)
if (info /= 0) then
info=4011
call psb_errpush(info,name)
goto 9999
end if
call psb_spmm(-zone,a,x,zone,v(:,1),desc_a,info,work=aux)
if (info /= 0) Then
info=4011
call psb_errpush(info,name)
goto 9999
End If
rs(1) = psb_genrm2(v(:,1),desc_a,info)
rs(2:) = zzero
if (info /= 0) Then
info=4011
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 /= 0) then
info=4011
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,eps)
v(:,1) = v(:,1) * scal
if (itx >= litmax) exit restart
!
! inner iterations
!
inner: Do i=1,nl
itx = itx + 1
call psb_precaply(prec,v(:,i),w1,desc_a,info)
Call psb_spmm(zone,a,w1,zzero,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),zone,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,zzero,v(:,i+1),desc_a,info)
do k=2,i
call zrot(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 zrotg(rti,rti1,tmp,s(i))
c(i) = cmplx(tmp,dzero)
call zrot(1,h(i,i),1,h(i+1,i),1,real(c(i)),s(i))
h(i+1,i) = zzero
call zrot(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 = zzero
call ztrsm('l','u','n','n',i,1,zone,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),zone,xt,desc_a,info)
end do
call psb_precaply(prec,xt,desc_a,info)
call psb_geaxpby(zone,x,zone,xt,desc_a,info)
call psb_geaxpby(zone,b,zzero,w1,desc_a,info)
call psb_spmm(-zone,a,xt,zone,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
x = xt
else if (istop_ == 2) then
!
! build x
!
call ztrsm('l','u','n','n',i,1,zone,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 = zzero
do k=1, i
call psb_geaxpby(rs(k),v(:,k),zone,w1,desc_a,info)
end do
call psb_precaply(prec,w1,w,desc_a,info)
call psb_geaxpby(zone,w,zone,x,desc_a,info)
end if
exit restart
end if
if (itrace_ > 0) &
& call log_conv(methdname,me,itx,itrace_,errnum,errden,eps)
end do inner
if (istop_ == 1) then
x = xt
else if (istop_ == 2) then
!
! build x
!
call ztrsm('l','u','n','n',nl,1,zone,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 = zzero
do k=1, nl
call psb_geaxpby(rs(k),v(:,k),zone,w1,desc_a,info)
end do
call psb_precaply(prec,w1,w,desc_a,info)
call psb_geaxpby(zone,w,zone,x,desc_a,info)
end if
end do restart
if (itrace_ > 0) &
& call log_conv(methdname,me,itx,1,errnum,errden,eps)
call log_end(methdname,me,itx,errnum,errden,eps,err=err,iter=iter)
deallocate(aux,h,c,s,rs,rst, stat=info)
if (info == 0) call psb_gefree(v,desc_a,info)
if (info == 0) call psb_gefree(w,desc_a,info)
if (info == 0) call psb_gefree(w1,desc_a,info)
if (info == 0) call psb_gefree(xt,desc_a,info)
if (info /= 0) then
info=4011
call psb_errpush(info,name)
goto 9999
end if
! restore external global coherence behaviour
call psb_restore_coher(ictxt,isvch)
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
contains
subroutine zrot( n, cx, incx, cy, incy, c, s )
!
! -- lapack auxiliary routine (version 3.0) --
! univ. of tennessee, univ. of california berkeley, nag ltd.,
! courant institute, argonne national lab, and rice university
! october 31, 1992
!
! .. scalar arguments ..
integer incx, incy, n
real(kind(1.d0)) c
complex(kind(1.d0)) s
! ..
! .. array arguments ..
complex(kind(1.d0)) cx( * ), cy( * )
! ..
!
! purpose
! =======
!
! zrot applies a plane rotation, where the cos (c) is real and the
! sin (s) is complex, and the vectors cx and cy are complex.
!
! arguments
! =========
!
! n (input) integer
! the number of elements in the vectors cx and cy.
!
! cx (input/output) complex*16 array, dimension (n)
! on input, the vector x.
! on output, cx is overwritten with c*x + s*y.
!
! incx (input) integer
! the increment between successive values of cy. incx <> 0.
!
! cy (input/output) complex*16 array, dimension (n)
! on input, the vector y.
! on output, cy is overwritten with -conjg(s)*x + c*y.
!
! incy (input) integer
! the increment between successive values of cy. incx <> 0.
!
! c (input) double precision
! s (input) complex*16
! c and s define a rotation
! [ c s ]
! [ -conjg(s) c ]
! where c*c + s*conjg(s) = 1.0.
!
! =====================================================================
!
! .. local scalars ..
integer i, ix, iy
complex(kind(1.d0)) stemp
! ..
! .. intrinsic functions ..
intrinsic dconjg
! ..
! .. executable statements ..
!
if( n <= 0 ) return
if( incx == 1 .and. incy == 1 ) then
!
! code for both increments equal to 1
!
do i = 1, n
stemp = c*cx(i) + s*cy(i)
cy(i) = c*cy(i) - dconjg(s)*cx(i)
cx(i) = stemp
end do
else
!
! code for unequal increments or equal increments not equal to 1
!
ix = 1
iy = 1
if( incx < 0 )ix = ( -n+1 )*incx + 1
if( incy < 0 )iy = ( -n+1 )*incy + 1
do i = 1, n
stemp = c*cx(ix) + s*cy(iy)
cy(iy) = c*cy(iy) - dconjg(s)*cx(ix)
cx(ix) = stemp
ix = ix + incx
iy = iy + incy
end do
end if
return
return
end subroutine zrot
!
!
subroutine zrotg(ca,cb,c,s)
complex(kind(1.d0)) ca,cb,s
real(kind(1.d0)) c
real(kind(1.d0)) norm,scale
complex(kind(1.d0)) alpha
!
if (cdabs(ca) == 0.0d0) then
!
c = 0.0d0
s = (1.0d0,0.0d0)
ca = cb
return
end if
!
scale = cdabs(ca) + cdabs(cb)
norm = scale*dsqrt((cdabs(ca/dcmplx(scale,0.0d0)))**2 +&
& (cdabs(cb/dcmplx(scale,0.0d0)))**2)
alpha = ca /cdabs(ca)
c = cdabs(ca) / norm
s = alpha * dconjg(cb) / norm
ca = alpha * norm
!
return
end subroutine zrotg
End Subroutine psb_zrgmres