NAG Library Manual, Mark 27.3
```    Program f11bdfe

!     F11BDF Example Program Text

!     Mark 27.3 Release. NAG Copyright 2021.

!     .. Use Statements ..
Use nag_library, Only: f11bdf, f11bef, f11bff, f11daf, f11dbf, f11xaf,   &
nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: anorm, dtol, sigmax, stplhs, stprhs, &
tol
Integer                          :: i, ifail, ifail1, irevcm, iterm,     &
itn, la, lfill, liwork, lwork,       &
lwreq, m, maxitn, monit, n, nnz,     &
nnzc, npivm
Character (8)                    :: method
Character (1)                    :: milu, norm, precon, pstrat, weight
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:), b(:), wgt(:), work(:), x(:)
Integer, Allocatable             :: icol(:), idiag(:), ipivp(:),         &
ipivq(:), irow(:), istr(:), iwork(:)
!     .. Executable Statements ..
Write (nout,*) 'F11BDF Example Program Results'

!     Skip heading in data file

la = 3*nnz
liwork = 7*n + 2
lwork = 200
Allocate (a(la),b(n),wgt(n),work(lwork),x(n),icol(la),idiag(n),ipivp(n), &
ipivq(n),irow(la),istr(n+1),iwork(liwork))

!     Read or initialize the parameters for the iterative solver

Read (nin,*) precon, norm, weight, iterm
anorm = 0.0E0_nag_wp
sigmax = 0.0E0_nag_wp

!     Read the parameters for the preconditioner

!     Read the nonzero elements of the matrix A

Do i = 1, nnz
End Do

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

!     Calculate incomplete LU factorization

milu = 'N'

!     ifail: behaviour on error exit
!             =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call f11daf(n,nnz,a,la,irow,icol,lfill,dtol,pstrat,milu,ipivp,ipivq,     &
istr,idiag,nnzc,npivm,iwork,liwork,ifail)

!     Call F11BDF to initialize the solver

ifail = 0
Call f11bdf(method,precon,norm,weight,iterm,n,m,tol,maxitn,anorm,sigmax, &
monit,lwreq,work,lwork,ifail)

!     Call repeatedly F11BEF to solve the equations
!     Note that the arrays B and X are overwritten

!     On final exit, X will contain the solution and B the
!     residual vector

irevcm = 0
lwreq = lwork

ifail = 1
loop: Do
Call f11bef(irevcm,x,b,wgt,work,lwreq,ifail)

If (irevcm/=4) Then
ifail1 = -1
Select Case (irevcm)
Case (-1)

Call f11xaf('Transpose',n,nnz,a,irow,icol,'No checking',x,b,       &
ifail1)

Case (1)

Call f11xaf('No transpose',n,nnz,a,irow,icol,'No checking',x,b,    &
ifail1)

Case (2)

Call f11dbf('No transpose',n,a,la,irow,icol,ipivp,ipivq,istr,      &
idiag,'No checking',x,b,ifail1)

Case (3)

ifail1 = 0
Call f11bff(itn,stplhs,stprhs,anorm,sigmax,work,lwreq,ifail1)

Write (nout,99999) itn, stplhs
Write (nout,99998)
Write (nout,99997)(x(i),b(i),i=1,n)
End Select
If (ifail1/=0) Then
irevcm = 6
End If
Else If (ifail/=0) Then
Write (nout,99993) ifail
Go To 100
Else
Exit loop
End If
End Do loop

!     Obtain information about the computation

ifail1 = 0
Call f11bff(itn,stplhs,stprhs,anorm,sigmax,work,lwreq,ifail1)

!     Print the output data

Write (nout,99996)
Write (nout,99995) 'Number of iterations for convergence:    ', itn
Write (nout,99994) 'Residual norm:                           ', stplhs
Write (nout,99994) 'Right-hand side of termination criterion:', stprhs
Write (nout,99994) '1-norm of matrix A:                      ', anorm

!     Output x

Write (nout,99998)
Write (nout,99997)(x(i),b(i),i=1,n)
100   Continue

99999 Format (/,1X,'Monitoring at iteration no.',I4,/,1X,1P,'residual no',     &
'rm: ',E14.4)
99998 Format (/,2X,'  Solution vector',2X,' Residual vector')
99997 Format (1X,1P,E16.4,1X,E16.4)
99996 Format (/,1X,'Final Results')
99995 Format (1X,A,I4)
99994 Format (1X,A,1P,E14.4)
99993 Format (1X,/,1X,' ** F11BEF returned with IFAIL = ',I5)
End Program f11bdfe
```