|
|
|
!!$ 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_dcgstabl.f90
|
|
|
|
!
|
|
|
|
! Subroutine: psb_dcgstabl
|
|
|
|
!
|
|
|
|
! 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.
|
|
|
|
! istop - integer(optional). The stopping criterium.
|
|
|
|
!
|
|
|
|
Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,&
|
|
|
|
&itmax,iter,err,itrace,irst,istop)
|
|
|
|
use psb_serial_mod
|
|
|
|
use psb_descriptor_type
|
|
|
|
use psb_prec_type
|
|
|
|
use psb_psblas_mod
|
|
|
|
use psb_tools_mod
|
|
|
|
use psb_const_mod
|
|
|
|
use psb_prec_mod
|
|
|
|
use psb_error_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)), Pointer :: aux(:),wwrk(:,:)
|
|
|
|
Real(Kind(1.d0)), Pointer :: ww(:), q(:), r(:), rt0(:), p(:), v(:), &
|
|
|
|
& s(:), t(:), z(:), f(:), uh(:,:), rh(:,:), &
|
|
|
|
& gamma(:), gamma1(:), gamma2(:), taum(:,:), sigma(:),&
|
|
|
|
&pv1(:), pv2(:), pm1(:,:), pm2(:,:)
|
|
|
|
Integer, Pointer :: iperm(:), ipnull(:), ipsave(:)
|
|
|
|
Real(Kind(1.d0)) ::rerr
|
|
|
|
Integer ::litmax, liter, naux, m, mglob, it, itrac,&
|
|
|
|
& nprows,npcols,me,mecol, n_row, n_col, nl, err_act
|
|
|
|
Character ::diagl, diagu
|
|
|
|
Logical, Parameter :: exchange=.True., noexchange=.False.
|
|
|
|
Integer, Parameter :: ione=1
|
|
|
|
Integer, Parameter :: irmax = 8
|
|
|
|
Integer :: itx, i, isvch, ich, icontxt,listop,j, int_err(5)
|
|
|
|
Logical :: do_renum_left
|
|
|
|
Real(Kind(1.d0)), Parameter :: one=1.d0, zero=0.d0, epstol=1.d-35
|
|
|
|
Logical, Parameter :: debug = .False.
|
|
|
|
Real(Kind(1.d0)) :: alpha, beta, rho, rho_old, rni, xni, bni, ani,bn2,&
|
|
|
|
& omega, tau
|
|
|
|
character(len=20) :: name,ch_err
|
|
|
|
|
|
|
|
info = 0
|
|
|
|
name = 'psb_dcgstabl'
|
|
|
|
call psb_erractionsave(err_act)
|
|
|
|
|
|
|
|
If (debug) Write(0,*) 'entering psb_dbicgstabl'
|
|
|
|
icontxt = desc_a%matrix_data(psb_ctxt_)
|
|
|
|
Call blacs_gridinfo(icontxt,nprows,npcols,me,mecol)
|
|
|
|
|
|
|
|
If (debug) Write(0,*) 'psb_dbicgstabl: from gridinfo',nprows,npcols,me
|
|
|
|
|
|
|
|
mglob = desc_a%matrix_data(psb_m_)
|
|
|
|
n_row = desc_a%matrix_data(psb_n_row_)
|
|
|
|
n_col = desc_a%matrix_data(psb_n_col_)
|
|
|
|
|
|
|
|
if (present(istop)) then
|
|
|
|
listop = istop
|
|
|
|
else
|
|
|
|
listop = 1
|
|
|
|
endif
|
|
|
|
!
|
|
|
|
! LISTOP = 1: Normwise backward error, infinity norm
|
|
|
|
! LISTOP = 2: ||r||/||b|| norm 2
|
|
|
|
!
|
|
|
|
|
|
|
|
if ((listop < 1 ).or.(listop > 2 ) ) then
|
|
|
|
write(0,*) 'psb_bicgstabl: invalid istop',listop
|
|
|
|
info=5001
|
|
|
|
int_err=listop
|
|
|
|
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
|
|
|
|
itrac = itrace
|
|
|
|
Else
|
|
|
|
itrac = -1
|
|
|
|
End If
|
|
|
|
|
|
|
|
If (Present(irst)) Then
|
|
|
|
nl = irst
|
|
|
|
If (debug) Write(0,*) 'present: irst: ',irst,nl
|
|
|
|
Else
|
|
|
|
nl = 1
|
|
|
|
If (debug) Write(0,*) 'not present: irst: ',irst,nl
|
|
|
|
Endif
|
|
|
|
|
|
|
|
naux=4*n_col
|
|
|
|
Allocate(aux(naux),gamma(0:nl),gamma1(nl),&
|
|
|
|
&gamma2(nl),taum(nl,nl),sigma(nl), stat=info)
|
|
|
|
|
|
|
|
If (info.Ne.0) Then
|
|
|
|
info=4000
|
|
|
|
call psb_errpush(info,name)
|
|
|
|
goto 9999
|
|
|
|
End If
|
|
|
|
Call psb_alloc(mglob,10,wwrk,desc_a,info)
|
|
|
|
Call psb_alloc(mglob,nl+1,uh,desc_a,info,js=0)
|
|
|
|
Call psb_alloc(mglob,nl+1,rh,desc_a,info,js=0)
|
|
|
|
Call psb_asb(wwrk,desc_a,info)
|
|
|
|
Call psb_asb(uh,desc_a,info)
|
|
|
|
Call psb_asb(rh,desc_a,info)
|
|
|
|
if (info.ne.0) Then
|
|
|
|
info=4011
|
|
|
|
call psb_errpush(info,name)
|
|
|
|
goto 9999
|
|
|
|
End If
|
|
|
|
|
|
|
|
q => wwrk(:,1)
|
|
|
|
r => wwrk(:,2)
|
|
|
|
p => wwrk(:,3)
|
|
|
|
v => wwrk(:,4)
|
|
|
|
f => wwrk(:,5)
|
|
|
|
s => wwrk(:,6)
|
|
|
|
t => wwrk(:,7)
|
|
|
|
z => wwrk(:,8)
|
|
|
|
ww => wwrk(:,9)
|
|
|
|
rt0 => wwrk(:,10)
|
|
|
|
|
|
|
|
! ensure global coherence for convergence checks.
|
|
|
|
Call blacs_get(icontxt,16,isvch)
|
|
|
|
ich = 1
|
|
|
|
Call blacs_set(icontxt,16,ich)
|
|
|
|
|
|
|
|
if (listop == 1) then
|
|
|
|
ani = psb_nrmi(a,desc_a,info)
|
|
|
|
bni = psb_amax(b,desc_a,info)
|
|
|
|
else if (listop == 2) then
|
|
|
|
bn2 = psb_nrm2(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
|
|
|
|
!!$
|
|
|
|
!!$ r0 = b-ax0
|
|
|
|
!!$
|
|
|
|
If (debug) Write(0,*) 'restart: ',itx,it
|
|
|
|
If (itx.Ge.itmax) Exit restart
|
|
|
|
it = 0
|
|
|
|
Call psb_axpby(one,b,zero,r,desc_a,info)
|
|
|
|
Call psb_spmm(-one,a,x,one,r,desc_a,info,work=aux)
|
|
|
|
|
|
|
|
call psb_prcaply(prec,r,desc_a,info)
|
|
|
|
|
|
|
|
Call psb_axpby(one,r,zero,rt0,desc_a,info)
|
|
|
|
Call psb_axpby(one,r,zero,rh(:,0),desc_a,info)
|
|
|
|
Call psb_axpby(zero,r,zero,uh(:,0),desc_a,info)
|
|
|
|
if (info.ne.0) Then
|
|
|
|
info=4011
|
|
|
|
call psb_errpush(info,name)
|
|
|
|
goto 9999
|
|
|
|
End If
|
|
|
|
|
|
|
|
rho = one
|
|
|
|
alpha = zero
|
|
|
|
omega = one
|
|
|
|
|
|
|
|
If (debug) Write(0,*) 'on entry to amax: b: ',Size(b)
|
|
|
|
|
|
|
|
if (listop == 1) then
|
|
|
|
rni = psb_amax(r,desc_a,info)
|
|
|
|
xni = psb_amax(x,desc_a,info)
|
|
|
|
rerr = rni/(ani*xni+bni)
|
|
|
|
if (itrac /= -1) then
|
|
|
|
If (me == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'bicgstab(l): ',&
|
|
|
|
& itx,rerr,rni,bni,xni,ani
|
|
|
|
endif
|
|
|
|
else if (listop == 2) then
|
|
|
|
rni = psb_nrm2(r,desc_a,info)
|
|
|
|
rerr = rni/bn2
|
|
|
|
if (itrac /= -1) then
|
|
|
|
If (me == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'bicgstab(l): ',&
|
|
|
|
& itx,rerr,rni,bn2
|
|
|
|
endif
|
|
|
|
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
|
|
|
|
|
|
|
|
iteration: Do
|
|
|
|
it = it + nl
|
|
|
|
itx = itx + nl
|
|
|
|
rho = -omega*rho
|
|
|
|
If (debug) Write(0,*) 'iteration: ',itx, rho,rh(1,0)
|
|
|
|
|
|
|
|
Do j = 0, nl -1
|
|
|
|
If (debug) Write(0,*) 'bicg part: ',j, nl
|
|
|
|
rho_old = rho
|
|
|
|
rho = psb_dot(rh(:,j),rt0,desc_a,info)
|
|
|
|
If (rho==zero) Then
|
|
|
|
If (debug) Write(0,*) 'bi-cgstab iteration breakdown r',rho
|
|
|
|
Exit iteration
|
|
|
|
Endif
|
|
|
|
beta = alpha*rho/rho_old
|
|
|
|
If (debug) Write(0,*) 'bicg part: ',alpha,beta,rho,rho_old
|
|
|
|
rho_old = rho
|
|
|
|
Call psb_axpby(one,rh(:,0:j),-beta,uh(:,0:j),desc_a,info)
|
|
|
|
If (debug) Write(0,*) 'bicg part: ',rh(1,0),beta
|
|
|
|
Call psb_spmm(one,a,uh(:,j),zero,uh(:,j+1),desc_a,info,work=aux)
|
|
|
|
|
|
|
|
call psb_prcaply(prec,uh(:,j+1),desc_a,info)
|
|
|
|
|
|
|
|
gamma(j) = psb_dot(uh(:,j+1),rt0,desc_a,info)
|
|
|
|
If (gamma(j)==zero) Then
|
|
|
|
If (debug) Write(0,*) 'bi-cgstab iteration breakdown s2',gamma(j)
|
|
|
|
Exit iteration
|
|
|
|
Endif
|
|
|
|
alpha = rho/gamma(j)
|
|
|
|
If (debug) Write(0,*) 'bicg part: alpha=r/g ',alpha,rho,gamma(j)
|
|
|
|
|
|
|
|
Call psb_axpby(-alpha,uh(:,1:j+1),one,rh(:,0:j),desc_a,info)
|
|
|
|
Call psb_axpby(alpha,uh(:,0),one,x,desc_a,info)
|
|
|
|
Call psb_spmm(one,a,rh(:,j),zero,rh(:,j+1),desc_a,info,work=aux)
|
|
|
|
|
|
|
|
call psb_prcaply(prec,rh(:,j+1),desc_a,info)
|
|
|
|
|
|
|
|
Enddo
|
|
|
|
|
|
|
|
Do j=1, nl
|
|
|
|
If (debug) Write(0,*) 'mod g-s part: ',j, nl,rh(1,0)
|
|
|
|
Do i=1, j-1
|
|
|
|
taum(i,j) = psb_dot(rh(:,i),rh(:,j),desc_a,info)
|
|
|
|
taum(i,j) = taum(i,j)/sigma(i)
|
|
|
|
Call psb_axpby(-taum(i,j),rh(:,i),one,rh(:,j),desc_a,info)
|
|
|
|
Enddo
|
|
|
|
If (debug) Write(0,*) 'mod g-s part: dot prod '
|
|
|
|
sigma(j) = psb_dot(rh(:,j),rh(:,j),desc_a,info)
|
|
|
|
gamma1(j) = psb_dot(rh(:,0),rh(:,j),desc_a,info)
|
|
|
|
If (debug) Write(0,*) 'mod g-s part: gamma1 ', &
|
|
|
|
&gamma1(j), sigma(j)
|
|
|
|
gamma1(j) = gamma1(j)/sigma(j)
|
|
|
|
Enddo
|
|
|
|
|
|
|
|
gamma(nl) = gamma1(nl)
|
|
|
|
omega = gamma(nl)
|
|
|
|
|
|
|
|
Do j=nl-1,1,-1
|
|
|
|
gamma(j) = gamma1(j)
|
|
|
|
Do i=j+1,nl
|
|
|
|
gamma(j) = gamma(j) - taum(j,i) * gamma(i)
|
|
|
|
Enddo
|
|
|
|
Enddo
|
|
|
|
If (debug) Write(0,*) 'first solve: ', gamma(:)
|
|
|
|
|
|
|
|
Do j=1,nl-1
|
|
|
|
gamma2(j) = gamma(j+1)
|
|
|
|
Do i=j+1,nl-1
|
|
|
|
gamma2(j) = gamma2(j) + taum(j,i) * gamma(i+1)
|
|
|
|
Enddo
|
|
|
|
Enddo
|
|
|
|
If (debug) Write(0,*) 'second solve: ', gamma(:)
|
|
|
|
|
|
|
|
Call psb_axpby(gamma(1),rh(:,0),one,x,desc_a,info)
|
|
|
|
Call psb_axpby(-gamma1(nl),rh(:,nl),one,rh(:,0),desc_a,info)
|
|
|
|
Call psb_axpby(-gamma(nl),uh(:,nl),one,uh(:,0),desc_a,info)
|
|
|
|
|
|
|
|
Do j=1, nl-1
|
|
|
|
Call psb_axpby(-gamma(j),uh(:,j),one,uh(:,0),desc_a,info)
|
|
|
|
Call psb_axpby(gamma2(j),rh(:,j),one,x,desc_a,info)
|
|
|
|
Call psb_axpby(-gamma1(j),rh(:,j),one,rh(:,0),desc_a,info)
|
|
|
|
Enddo
|
|
|
|
|
|
|
|
if (listop == 1) then
|
|
|
|
rni = psb_amax(rh(:,0),desc_a,info)
|
|
|
|
xni = psb_amax(x,desc_a,info)
|
|
|
|
rerr = rni/(ani*xni+bni)
|
|
|
|
if (itrac /= -1) then
|
|
|
|
If (me == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'bicgstab(l): ',&
|
|
|
|
& itx,rerr,rni,bni,xni,ani
|
|
|
|
endif
|
|
|
|
|
|
|
|
else if (listop == 2) then
|
|
|
|
|
|
|
|
rni = psb_nrm2(rh(:,0),desc_a,info)
|
|
|
|
rerr = rni/bn2
|
|
|
|
if (itrac /= -1) then
|
|
|
|
If (me == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'bicgstab(l): ',&
|
|
|
|
& itx,rerr,rni,bn2
|
|
|
|
endif
|
|
|
|
endif
|
|
|
|
|
|
|
|
If (rerr<=eps) Then
|
|
|
|
Exit restart
|
|
|
|
End If
|
|
|
|
|
|
|
|
If (itx.Ge.itmax) Exit restart
|
|
|
|
End Do iteration
|
|
|
|
End Do restart
|
|
|
|
|
|
|
|
If (Present(err)) err=rerr
|
|
|
|
If (Present(iter)) iter = itx
|
|
|
|
If (rerr>eps) Then
|
|
|
|
Write(0,*) 'bi-cgstabl failed to converge to ',eps,&
|
|
|
|
& ' in ',itx,' iterations '
|
|
|
|
End If
|
|
|
|
|
|
|
|
Deallocate(aux)
|
|
|
|
Call psb_free(wwrk,desc_a,info)
|
|
|
|
Call psb_free(uh,desc_a,info)
|
|
|
|
Call psb_free(rh,desc_a,info)
|
|
|
|
! restore external global coherence behaviour
|
|
|
|
Call blacs_set(icontxt,16,isvch)
|
|
|
|
|
|
|
|
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.act_abort) then
|
|
|
|
call psb_error()
|
|
|
|
return
|
|
|
|
end if
|
|
|
|
return
|
|
|
|
|
|
|
|
End Subroutine psb_dcgstabl
|
|
|
|
|
|
|
|
|