NAG Library Manual, Mark 28.3
```    Program f11ddfe

!     F11DDF Example Program Text

!     Mark 28.3 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: f11bdf, f11bef, f11bff, f11ddf, f11xaf, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: anorm, omega, sigmax, stplhs,        &
stprhs, tol
Integer                          :: i, ifail, irevcm, iterm, itn, la,    &
liwork, lwneed, lwork, m, maxitn,    &
monit, n, nnz
Character (1)                    :: ckddf, ckxaf, norm, precon, trans,   &
weight
Character (8)                    :: method
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:), b(:), rdiag(:), wgt(:),        &
work(:), x(:)
Integer, Allocatable             :: icol(:), irow(:), iwork(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max
!     .. Executable Statements ..
Write (nout,*) 'F11DDF Example Program Results'
Write (nout,*)
!     Skip heading in data file

la = 3*nnz
lwork = max(n*(m+3)+m*(m+5)+101,7*n+100,(2*n+m)*(m+2)+n+100,10*n+100)
liwork = 2*n + 1
Allocate (a(la),b(n),rdiag(n),wgt(n),work(lwork),x(n),icol(la),irow(la), &
iwork(liwork))

Do i = 1, nnz
End Do

!     Read right-hand side vector b and initial approximate solution x

!     Call F11BDF to initialize solver

weight = 'N'
monit = 0

!     ifail: behaviour on error exit
!             =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call f11bdf(method,precon,norm,weight,iterm,n,m,tol,maxitn,anorm,sigmax, &
monit,lwneed,work,lwork,ifail)

!     Calculate reciprocal diagonal matrix elements if necessary

If (precon=='P' .Or. precon=='p') Then

iwork(1:n) = 0

Do i = 1, nnz
If (irow(i)==icol(i)) Then
iwork(irow(i)) = iwork(irow(i)) + 1
If (a(i)/=0.E0_nag_wp) Then
rdiag(irow(i)) = 1.E0_nag_wp/a(i)
Else
Write (nout,*) 'Matrix has a zero diagonal element'
Go To 100
End If
End If
End Do

Do i = 1, n
If (iwork(i)==0) Then
Write (nout,*) 'Matrix has a missing diagonal element'
Go To 100
End If
If (iwork(i)>=2) Then
Write (nout,*) 'Matrix has a multiple diagonal element'
Go To 100
End If
End Do

End If

!     Call F11BEF to solve the linear system

irevcm = 0
ckxaf = 'C'
ckddf = 'C'

loop: Do
ifail = 0
Call f11bef(irevcm,x,b,wgt,work,lwork,ifail)

Select Case (irevcm)
Case (1)
!         Compute matrix-vector product
trans = 'N'

Call f11xaf(trans,n,nnz,a,irow,icol,ckxaf,x,b,ifail)

ckxaf = 'N'
Case (-1)
!         Compute transposed matrix-vector product
trans = 'T'

Call f11xaf(trans,n,nnz,a,irow,icol,ckxaf,x,b,ifail)

ckxaf = 'N'
Case (2)

!         SSOR preconditioning
trans = 'N'

Call f11ddf(trans,n,nnz,a,irow,icol,rdiag,omega,ckddf,x,b,iwork,     &
ifail)

ckddf = 'N'
Case (4)
!         Termination

ifail = 0
Call f11bff(itn,stplhs,stprhs,anorm,sigmax,work,lwork,ifail)

Write (nout,'(A,I10,A)') ' Converged in', itn, ' iterations'
Write (nout,'(A,1P,E16.3)') ' Matrix norm =', anorm
Write (nout,'(A,1P,E16.3)') ' Final residual norm =', stplhs
Write (nout,*)

!         Output x
Write (nout,*) '           X'
Write (nout,'(1X,1P,E16.4)') x(1:n)
Exit loop
Case Default
Exit loop
End Select
End Do loop

100   Continue

End Program f11ddfe
```