```    Program f08kzfe

!     F08KZF Example Program Text

!     Mark 27.0 Release. NAG Copyright 2019.

!     .. Use Statements ..
Use nag_library, Only: nag_wp, zgesvdx
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: vl, vu
Integer                          :: i, il, info, iu, lda, ldu, ldvt,     &
liwork, lrwork, lwork, m, n, ns
Character (1)                    :: range
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), u(:,:), vt(:,:), work(:)
Real (Kind=nag_wp), Allocatable  :: rwork(:), s(:)
Integer, Allocatable             :: iwork(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: nint
!     .. Executable Statements ..
Write (nout,*) 'F08KZF Example Program Results'
Write (nout,*)
!     Skip heading in data file
Read (nin,*) m, n
lda = m
ldu = m
ldvt = n
lwork = 2*n**2 + 4*n
lrwork = 2*n*2 + 34*n
liwork = 12*n
Allocate (a(lda,n),s(n),vt(ldvt,n),u(ldu,m),iwork(liwork),work(lwork),   &
rwork(lrwork))

!     Read the m by n matrix A from data file

!     Read range for selected singular values

If (range=='I' .Or. range=='i') Then
Read (nin,*) il, iu
Else If (range=='V' .Or. range=='v') Then
Read (nin,*) vl, vu
End If

!     Compute the singular values and left and right singular vectors
!     of A.

!     The NAG name equivalent of zgesvd is f08kzf
Call zgesvdx('V','V',range,m,n,a,lda,vl,vu,il,iu,ns,s,u,ldu,vt,ldvt,     &
work,lwork,rwork,iwork,info)

If (info/=0) Then
Write (nout,99999) 'Failure in ZGESVDX. INFO =', info
99999   Format (1X,A,I4)
Go To 100
End If

!     Print the selected singular values of A

Write (nout,*) 'Singular values of A:'
Write (nout,99998) s(1:ns)
99998 Format (1X,4(3X,F11.4))

Call compute_error_bounds(m,ns,s)

100   Continue

Contains
Subroutine compute_error_bounds(m,n,s)

!       Error estimates for singular values and vectors is computed
!       and printed here.

!       .. Use Statements ..
Use nag_library, Only: ddisna, nag_wp, x02ajf, x02amf
!       .. Implicit None Statement ..
Implicit None
!       .. Scalar Arguments ..
Integer, Intent (In)           :: m, n
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (In) :: s(n)
!       .. Local Scalars ..
Real (Kind=nag_wp)             :: eps, serrbd
Integer                        :: i, info, nl
!       .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: rcondu(:), rcondv(:), uerrbd(:),    &
verrbd(:)
!       .. Executable Statements ..
Allocate (rcondu(n),rcondv(n),uerrbd(n),verrbd(n))

!       Get the machine precision, EPS and compute the approximate
!       error bound for the computed singular values.  Note that for
!       the 2-norm, S(1) = norm(A)

eps = x02ajf()
serrbd = eps*s(1)

!       Call DDISNA (F08FLF) to estimate reciprocal condition
!       numbers for the singular vectors

Call ddisna('Left',m,n,s,rcondu,info)
Call ddisna('Right',m,n,s,rcondv,info)

!       Compute the error estimates for the singular vectors

nl = n
Do i = 1, n
If (s(i)<x02amf()) Then
nl = i - 1
Else
uerrbd(i) = serrbd/rcondu(i)
End If
verrbd(i) = serrbd/rcondv(i)

End Do

!       Print the approximate error bounds for the singular values
!       and vectors

Write (nout,*)
Write (nout,*) 'Error estimates (as multiples of machine precision):'
Write (nout,*) '  for the singular values'
Write (nout,99999) nint(serrbd/x02ajf())
Write (nout,*)
Write (nout,*) '  for the left (non-zero) singular vectors'
Write (nout,99999) nint(uerrbd(1:nl)/x02ajf())
Write (nout,*)
Write (nout,*) '  for the right singular vectors'
Write (nout,99999) nint(verrbd(1:n)/x02ajf())

99999   Format (4X,6I11)

End Subroutine compute_error_bounds

End Program f08kzfe
```