You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
462 lines
15 KiB
Fortran
462 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
|
|
Integer ::litmax, liter, naux, m, mglob, it,k, itrace_,&
|
|
& np,me, n_row, n_col, nl, int_err(5)
|
|
Character :: diagl, diagu
|
|
Logical, Parameter :: exchange=.True., noexchange=.False.
|
|
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
|
|
|
|
diagl = 'u'
|
|
diagu = 'u'
|
|
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)
|
|
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)
|
|
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)
|
|
|
|
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
|
|
|
|
|