NAG Library Manual, Mark 30
```    Program f04bafe

!     F04BAF Example Program Text

!     Mark 30.0 Release. NAG Copyright 2024.

!     .. Use Statements ..
Use nag_library, Only: f04baf, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: errbnd, rcond
Integer                          :: i, ierr, ifail, lda, ldb, n, nrhs
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), b(:,:)
Integer, Allocatable             :: ipiv(:)
!     .. Executable Statements ..
Write (nout,*) 'F04BAF Example Program Results'
Write (nout,*)
Flush (nout)
!     Skip heading in data file
lda = n
ldb = n
Allocate (a(lda,n),b(ldb,nrhs),ipiv(n))
!     Read A and B from data file

!     Solve the equations AX = B for X

!     ifail: behaviour on error exit
!            =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 1
Call f04baf(n,nrhs,a,lda,ipiv,b,ldb,rcond,errbnd,ifail)

If (ifail==0) Then
!       Print solution, estimate of condition number and approximate
!       error bound

ierr = 0
Call x04caf('General',' ',n,nrhs,b,ldb,'Solution',ierr)

Write (nout,*)
Write (nout,*) 'Estimate of condition number'
Write (nout,99999) 1.0E0_nag_wp/rcond
Write (nout,*)
Write (nout,*) 'Estimate of error bound for computed solutions'
Write (nout,99999) errbnd
Else If (ifail==n+1) Then
!       Matrix A is numerically singular.  Print estimate of
!       reciprocal of condition number and solution

Write (nout,*)
Write (nout,*) 'Estimate of reciprocal of condition number'
Write (nout,99999) rcond
Write (nout,*)
Flush (nout)

ierr = 0
Call x04caf('General',' ',n,nrhs,b,ldb,'Solution',ierr)

Else If (ifail>0 .And. ifail<=n) Then
!       The upper triangular matrix U is exactly singular.  Print
!       details of factorization
Write (nout,*)
Flush (nout)

ierr = 0
Call x04caf('General',' ',n,n,a,lda,'Details of factorization',ierr)

!       Print pivot indices
Write (nout,*)
Write (nout,*) 'Pivot indices'
Write (nout,99998) ipiv(1:n)
Else
Write (nout,99997) ifail
End If

99999 Format (6X,1P,E9.1)
99998 Format ((1X,7I11))
99997 Format (1X,' ** F04BAF returned with IFAIL = ',I5)
End Program f04bafe
```