```    Program f07mhfe

!     F07MHF Example Program Text

!     Mark 27.0 Release. NAG Copyright 2019.

!     .. Use Statements ..
Use nag_library, Only: dsyrfs, dsytrf, dsytrs, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Integer                          :: i, ifail, info, lda, ldaf, ldb, ldx, &
lwork, n, nrhs
Character (1)                    :: uplo
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), af(:,:), b(:,:), berr(:),    &
ferr(:), work(:), x(:,:)
Integer, Allocatable             :: ipiv(:), iwork(:)
!     .. Executable Statements ..
Write (nout,*) 'F07MHF Example Program Results'
!     Skip heading in data file
lda = n
ldaf = n
ldb = n
ldx = n
lwork = 64*n
Allocate (a(lda,n),af(ldaf,n),b(ldb,nrhs),berr(nrhs),ferr(nrhs),         &
work(lwork),x(ldx,n),ipiv(n),iwork(n))

!     Read A and B from data file, and copy A to AF and B to X

If (uplo=='U') Then
Do i = 1, n
af(i,i:n) = a(i,i:n)
End Do
Else If (uplo=='L') Then
Do i = 1, n
af(i,1:i) = a(i,1:i)
End Do
End If

x(1:n,1:nrhs) = b(1:n,1:nrhs)

!     Factorize A in the array AF
!     The NAG name equivalent of dsytrf is f07mdf
Call dsytrf(uplo,n,af,ldaf,ipiv,work,lwork,info)

Write (nout,*)
Flush (nout)
If (info==0) Then

!       Compute solution in the array X
!       The NAG name equivalent of dsytrs is f07mef
Call dsytrs(uplo,n,nrhs,af,ldaf,ipiv,x,ldx,info)

!       Improve solution, and compute backward errors and
!       estimated bounds on the forward errors
!       The NAG name equivalent of dsyrfs is f07mhf
Call dsyrfs(uplo,n,nrhs,a,lda,af,ldaf,ipiv,b,ldb,x,ldx,ferr,berr,work, &
iwork,info)

!       Print solution

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04caf('General',' ',n,nrhs,x,ldx,'Solution(s)',ifail)

Write (nout,*)
Write (nout,*) 'Backward errors (machine-dependent)'
Write (nout,99999) berr(1:nrhs)
Write (nout,*) 'Estimated forward error bounds (machine-dependent)'
Write (nout,99999) ferr(1:nrhs)
Else
Write (nout,*) 'The factor D is singular'
End If

99999 Format ((3X,1P,7E11.1))
End Program f07mhfe
```