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psblas3/krylov/psb_dgmresr.f90

473 lines
15 KiB
Fortran

!!$
!!$ Parallel Sparse BLAS v2.0
!!$ (C) Copyright 2006 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_dgmresr.f90
!
! Subroutine: psb_dgmres
! This subroutine implements the restarted GMRES method with right
! preconditioning.
!
! Parameters:
! a - type(<psb_dspmat_type>). The sparse matrix containing A.
! prec - type(<psb_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(<psb_desc_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.
! irst - integer(optional). The restart value.
! istop - integer(optional). The stopping criterium.
!
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
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, irst,istop
Integer, Optional, Intent(out) :: iter
Real(Kind(1.d0)), Optional, Intent(out) :: err
!!$ local data
Real(Kind(1.d0)), allocatable, target :: aux(:),w(:),w1(:), v(:,:)
Real(Kind(1.d0)), allocatable :: c(:),s(:), h(:,:), rs(:),rst(:),xt(:)
Real(Kind(1.d0)) :: rerr, scal, gm, rti, rti1
Integer ::litmax, liter, naux, m, mglob, it,k, itrace_,&
& np,me, n_row, n_col, nl, int_err(5)
Logical, Parameter :: exchange=.True., noexchange=.False., use_drot=.true.
Integer, Parameter :: irmax = 8
Integer :: itx, i, isvch, ich, ictxt,istop_, err_act
Logical, Parameter :: debug = .false.
Real(Kind(1.d0)) :: rni, xni, bni, ani,bn2, dt
real(kind(1.d0)), external :: dnrm2
character(len=20) :: name
info = 0
name = 'psb_dgmres'
call psb_erractionsave(err_act)
If (debug) Write(0,*) 'entering psb_dgmres'
ictxt = psb_cd_get_context(desc_a)
Call psb_info(ictxt, me, np)
If (debug) Write(0,*) 'psb_dgmres: from gridinfo',np,me
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
write(0,*) 'psb_dgmres: invalid istop',istop_
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) Write(0,*) 'present: irst: ',irst,nl
Else
nl = 10
If (debug) Write(0,*) 'not present: irst: ',irst,nl
Endif
if (nl <=0 ) then
write(0,*) 'psb_dgmres: invalid irst ',nl
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.ne.0) Then
info=4011
call psb_errpush(info,name)
goto 9999
End If
if (debug) write(0,*) '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
if (info.ne.0) Then
info=4011
call psb_errpush(info,name)
goto 9999
End If
itx = 0
restart: Do
! compute r0 = b-ax0
! check convergence
! compute v1 = r0/||r0||_2
If (debug) Write(0,*) 'restart: ',itx,it
it = 0
Call psb_geaxpby(done,b,dzero,v(:,1),desc_a,info)
if (info.ne.0) Then
info=4011
call psb_errpush(info,name)
goto 9999
End If
Call psb_spmm(-done,a,x,done,v(:,1),desc_a,info,work=aux)
if (info.ne.0) Then
info=4011
call psb_errpush(info,name)
goto 9999
End If
rs(1) = psb_genrm2(v(:,1),desc_a,info)
rs(2:) = dzero
if (info.ne.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) Write(0,*) '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)
rerr = rni/(ani*xni+bni)
else if (istop_ == 2) then
rni = psb_genrm2(v(:,1),desc_a,info)
rerr = rni/bn2
endif
if (info.ne.0) Then
info=4011
call psb_errpush(info,name)
goto 9999
End If
If (rerr<=eps) Then
Exit restart
End If
If (itrace_ > 0) then
if ((mod(itx,itrace_)==0).and.(me == 0))&
& write(*,'(a,i4,3(2x,es10.4))') 'gmres(l): ',itx,rerr
end If
v(:,1) = v(:,1) * scal
If (itx.Ge.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(done,a,w1,dzero,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),done,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,dzero,v(:,i+1),desc_a,info)
if (use_drot) then
do k=2,i
call drot(1,h(k-1,i),1,h(k,i),1,c(k-1),s(k-1))
enddo
rti = h(i,i)
rti1 = h(i+1,i)
call drotg(rti,rti1,c(i),s(i))
call drot(1,h(i,i),1,h(i+1,i),1,c(i),s(i))
h(i+1,i) = dzero
call drot(1,rs(i),1,rs(i+1),1,c(i),s(i))
else
do k=2,i
dt = h(k-1,i)
h(k-1,i) = c(k-1)*dt + s(k-1)*h(k,i)
h(k,i) = -s(k-1)*dt + c(k-1)*h(k,i)
enddo
gm = safe_dn2(h(i,i),h(i+1,i))
if (debug) write(0,*) 'GM : ',gm
gm = max(gm,epstol)
c(i) = h(i,i)/gm
s(i) = h(i+1,i)/gm
rs(i+1) = -s(i)*rs(i)
rs(i) = c(i)*rs(i)
h(i,i) = c(i)*h(i,i)+s(i)*h(i+1,i)
endif
if (istop_ == 1) then
!
! build x and then compute the residual and its infinity norm
!
rst = rs
xt = dzero
call dtrsm('l','u','n','n',i,1,done,h,size(h,1),rst,size(rst,1))
if (debug) write(0,*) 'Rebuild x-> RS:',rst(1:nl)
do k=1, i
call psb_geaxpby(rst(k),v(:,k),done,xt,desc_a,info)
end do
call psb_precaply(prec,xt,desc_a,info)
call psb_geaxpby(done,x,done,xt,desc_a,info)
call psb_geaxpby(done,b,dzero,w1,desc_a,info)
call psb_spmm(-done,a,xt,done,w1,desc_a,info,work=aux)
rni = psb_geamax(w1,desc_a,info)
xni = psb_geamax(xt,desc_a,info)
rerr = rni/(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))
rerr = rni/bn2
endif
if (rerr < eps ) then
if (istop_ == 1) then
x = xt
else if (istop_ == 2) then
!
! build x
!
call dtrsm('l','u','n','n',i,1,done,h,size(h,1),rs,size(rs,1))
if (debug) write(0,*) 'Rebuild x-> RS:',rs(21:nl)
w1 = dzero
do k=1, i
call psb_geaxpby(rs(k),v(:,k),done,w1,desc_a,info)
end do
call psb_precaply(prec,w1,w,desc_a,info)
call psb_geaxpby(done,w,done,x,desc_a,info)
end if
exit restart
end if
If (itrace_ > 0) then
if ((mod(itx,itrace_)==0).and.(me == 0))&
& write(*,'(a,i4,3(2x,es10.4))') 'gmres(l): ',itx,rerr
end If
end Do inner
if (istop_ == 1) then
x = xt
else if (istop_ == 2) then
!
! build x
!
call dtrsm('l','u','n','n',nl,1,done,h,size(h,1),rs,size(rs,1))
if (debug) write(0,*) 'Rebuild x-> RS:',rs(21:nl)
w1 = dzero
do k=1, nl
call psb_geaxpby(rs(k),v(:,k),done,w1,desc_a,info)
end do
call psb_precaply(prec,w1,w,desc_a,info)
call psb_geaxpby(done,w,done,x,desc_a,info)
end if
End Do restart
If (itrace_ > 0) then
if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'gmres(l): ',itx,rerr
end If
If (Present(err)) err=rerr
If (Present(iter)) iter = itx
If ((rerr>eps).and. (me == 0)) Then
Write(0,*) 'gmresr(l) failed to converge to ',eps,&
& ' in ',itx,' iterations '
End If
Deallocate(aux,h,c,s,rs,rst, stat=info)
Call psb_gefree(v,desc_a,info)
Call psb_gefree(w,desc_a,info)
Call psb_gefree(w1,desc_a,info)
Call psb_gefree(xt,desc_a,info)
! restore external global coherence behaviour
call psb_restore_coher(ictxt,isvch)
if (info /= 0) then
info=4011
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()
return
end if
return
contains
function safe_dn2(a,b)
real(kind(1.d0)), intent(in) :: a, b
real(kind(1.d0)) :: safe_dn2
real(kind(1.d0)) :: t
t = max(abs(a),abs(b))
if (t==0.d0) then
safe_dn2 = 0.d0
else
safe_dn2 = t * sqrt(abs(a/t)**2 + abs(b/t)**2)
endif
return
end function safe_dn2
End Subroutine psb_dgmresr