```    Program f11jbfe

!     F11JBF Example Program Text

!     Mark 25 Release. NAG Copyright 2014.

!     .. Use Statements ..
Use nag_library, Only: f11jaf, f11jbf, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter                   :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)                   :: dscale, dtol
Integer                              :: i, ifail, la, lfill, liwork, n,  &
nnz, nnzc, npivm
Character (1)                        :: check, mic, pstrat
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable      :: a(:), x(:), y(:)
Integer, Allocatable                 :: icol(:), ipiv(:), irow(:),       &
istr(:), iwork(:), perm_fwd(:),  &
perm_inv(:)
!     .. Executable Statements ..
Write (nout,*) 'F11JBF Example Program Results'
!     Skip heading in data file

!     Read order of matrix and number of non-zero entries

la = 3*nnz
liwork = 2*la + 7*n + 1

Allocate (a(la),x(n),y(n),icol(la),ipiv(n),irow(la),istr(n+1), &
iwork(liwork),perm_fwd(n),perm_inv(n))

Do i = 1, nnz
End Do

!     Calculate Cholesky factorization

lfill = -1
dtol = 0.0E0_nag_wp
mic = 'N'
dscale = 0.0E0_nag_wp
pstrat = 'M'

!     ifail: behaviour on error exit
!             =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call f11jaf(n,nnz,a,la,irow,icol,lfill,dtol,mic,dscale,pstrat,ipiv,istr, &
nnzc,npivm,iwork,liwork,ifail)

!     Check the output value of NPIVM
If (npivm/=0) Then
Write (nout,99998) 'Factorization is not complete', npivm
Else
!       Solve P L D L^T P^T x = y
check = 'C'
ifail = 0
Call f11jbf(n,a,la,irow,icol,ipiv,istr,check,y,x,ifail)
!       Output results
Write (nout,*) ' Solution of linear system'
Write (nout,99999) x(1:n)
End If

!     Compute reverse Cuthill-McKee permutation for bandwidth reduction
Call do_rcm(irow,icol,a,y,istr,perm_fwd,perm_inv,iwork)

ifail = 0
Call f11jaf(n,nnz,a,la,irow,icol,lfill,dtol,mic,dscale,pstrat,ipiv,istr, &
nnzc,npivm,iwork,liwork,ifail)

!     Check the output value of NPIVM
If (npivm/=0) Then
Write (nout,99998) 'Factorization is not complete', npivm
Else
!       Solve P L D L^T P^T x = y
ifail = 0
Call f11jbf(n,a,la,irow,icol,ipiv,istr,check,y,x,ifail)
!       Output results
Write (nout,*) ' Solution of linear system with Reverse Cuthill-McKee'
Write (nout,99999)(x(perm_inv(i)),i=1,n)
End If

99999 Format (1X,E16.4)
99998 Format (1X,A,I20)
Contains
Subroutine do_rcm(irow,icol,a,y,istr,perm_fwd,perm_inv,iwork)

!       .. Use Statements ..
Use nag_library, Only: f11yef, f11zaf, f11zbf
!       .. Parameters ..
Logical, Parameter                   ::                                &
lopts(5) = (/.False.,.False.,.True.,.True., &
.True./)
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout)   :: a(la), y(n)
Integer, Intent (Inout)              :: icol(la), irow(la), istr(n+1), &
iwork(*)
Integer, Intent (Out)                :: perm_fwd(n), perm_inv(n)
!       .. Local Scalars ..
Integer                              :: i, ifail, j, nnz_cs, nnz_scs
!       .. Local Arrays ..
Real (Kind=nag_wp), Allocatable      :: rwork(:)
!       .. Intrinsic Procedures ..
Intrinsic                            :: size
!       .. Executable Statements ..

!       SCS to CS, must add the upper triangle entries.
j = nnz + 1
Do i = 1, nnz
If (irow(i)>icol(i)) Then
!           strictly lower triangle, add the transposed
a(j) = a(i)
irow(j) = icol(i)
icol(j) = irow(i)
j = j + 1
End If
End Do
nnz_cs = j - 1

!       Reorder, CS to CCS, icolzp in istr
ifail = 0
Call f11zaf(n,nnz_cs,a,icol,irow,'F','F',istr,iwork,ifail)

!       Calculate reverse Cuthill-McKee
ifail = 0

!       compute inverse perm, in perm_inv(1:n)
Do i = 1, n
perm_inv(perm_fwd(i)) = i
End Do

!       Apply permutation on column/row indices
icol(1:nnz_cs) = perm_inv(icol(1:nnz_cs))
irow(1:nnz_cs) = perm_inv(irow(1:nnz_cs))

!       restrict to lower triangle, SCS format
!       copying entries upwards
j = 1
Do i = 1, nnz_cs
If (irow(i)>=icol(i)) Then
!           non-upper triangle, bubble up
a(j) = a(i)
icol(j) = icol(i)
irow(j) = irow(i)
j = j + 1
End If
End Do
nnz_scs = j - 1

!       sort
ifail = 0
Call f11zbf(n,nnz_scs,a,irow,icol,'S','K',istr,iwork,ifail)

!       permute rhs vector
Allocate (rwork(size(perm_fwd)))
rwork(:) = y(perm_fwd(:))
y(:) = rwork(:)
Deallocate (rwork)
End Subroutine do_rcm
End Program f11jbfe
```