NAG Library Manual, Mark 29
```    Program f07abfe

!     F07ABF Example Program Text

!     Mark 29.0 Release. NAG Copyright 2023.

!     .. Use Statements ..
Use nag_library, Only: dgesvx, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: rcond
Integer                          :: i, ifail, info, lda, ldaf, ldb, ldx, &
n, nrhs
Character (1)                    :: equed
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), af(:,:), b(:,:), berr(:),    &
c(:), ferr(:), r(:), work(:), x(:,:)
Integer, Allocatable             :: ipiv(:), iwork(:)
!     .. Executable Statements ..
Write (nout,*) 'F07ABF Example Program Results'
Write (nout,*)
Flush (nout)
!     Skip heading in data file
lda = n
ldaf = n
ldb = n
ldx = n
Allocate (a(lda,n),af(ldaf,n),b(ldb,nrhs),berr(nrhs),c(n),ferr(nrhs),    &
r(n),work(4*n),x(ldx,nrhs),ipiv(n),iwork(n))

!     Read A and B from data file

!     Solve the equations AX = B for X

!     The NAG name equivalent of dgesvx is f07abf
Call dgesvx('Equilibration','No transpose',n,nrhs,a,lda,af,ldaf,ipiv,    &
equed,r,c,b,ldb,x,ldx,rcond,ferr,berr,work,iwork,info)

If ((info==0) .Or. (info==n+1)) Then

!       Print solution, error bounds, condition number, the form
!       of equilibration and the pivot growth factor

!       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,*)
Write (nout,*) 'Estimated forward error bounds (machine-dependent)'
Write (nout,99999) ferr(1:nrhs)
Write (nout,*)
If (equed=='N') Then
Write (nout,*) 'A has not been equilibrated'
Else If (equed=='R') Then
Write (nout,*) 'A has been row scaled as diag(R)*A'
Else If (equed=='C') Then
Write (nout,*) 'A has been column scaled as A*diag(C)'
Else If (equed=='B') Then
Write (nout,*)                                                       &
'A has been row and column scaled as diag(R)*A*diag(C)'
End If
Write (nout,*)
Write (nout,*) 'Reciprocal condition number estimate of scaled matrix'
Write (nout,99999) rcond
Write (nout,*)
Write (nout,*) 'Estimate of reciprocal pivot growth factor'
Write (nout,99999) work(1)

If (info==n+1) Then
Write (nout,*)
Write (nout,*) 'The matrix A is singular to working precision'
End If
Else
Write (nout,99998) 'The (', info, ',', info, ')',                      &
' element of the factor U is zero'
End If

99999 Format ((3X,1P,7E11.1))
99998 Format (1X,A,I3,A,I3,A,A)
End Program f07abfe
```