```    Program f08kdfe

!     F08KDF Example Program Text

!     Mark 26.2 Release. NAG Copyright 2017.

!     .. Use Statements ..
Use nag_library, Only: ddisna, dgesdd, nag_wp, x02ajf, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nb = 64, nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: eps, serrbd
Integer                          :: i, ifail, info, lda, ldu, lwork, m,  &
n
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), rcondu(:), rcondv(:), s(:),  &
u(:,:), uerrbd(:), verrbd(:),        &
work(:)
Real (Kind=nag_wp)               :: dummy(1,1)
Integer, Allocatable             :: iwork(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max, min, nint
!     .. Executable Statements ..
Write (nout,*) 'F08KDF Example Program Results'
Write (nout,*)
!     Skip heading in data file
lda = m
ldu = m
Allocate (a(lda,n),rcondu(m),rcondv(m),s(m),u(ldu,m),uerrbd(m),          &
verrbd(m),iwork(8*min(m,n)))

!     Use routine workspace query to get optimal workspace.
lwork = -1
!     The NAG name equivalent of dgesdd is f08kdf
Call dgesdd('Overwrite A by tranpose(V)',m,n,a,lda,s,u,ldu,dummy,1,      &
dummy,lwork,iwork,info)

!     Make sure that there is enough workspace for block size nb.
lwork = max((5*m+9)*m+n+nb*(m+n),nint(dummy(1,1)))
Allocate (work(lwork))

!     Read the m by n matrix A from data file

!     Compute the singular values and left and right singular vectors
!     of A (A = U*S*(V**T), m.le.n)

!     The NAG name equivalent of dgesdd is f08kdf
Call dgesdd('Overwrite A by tranpose(V)',m,n,a,lda,s,u,ldu,dummy,1,work, &
lwork,iwork,info)

If (info==0) Then

!       Print solution

Write (nout,*) 'Singular values'
Write (nout,99999) s(1:m)
Flush (nout)

!       Normalize so that u(1,j)>=0
Do i = 1, m
If (u(1,i)<0.0_nag_wp) Then
u(1:m,i) = -u(1:m,i)
a(i,1:n) = -a(i,1:n)
End If
End Do
!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04caf('General',' ',m,m,u,ldu,'Left singular vectors',ifail)

Write (nout,*)
Flush (nout)

Call x04caf('General',' ',m,n,a,lda,'Right singular vectors by row '// &
'(first m rows of V**T)',ifail)

!       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

Do i = 1, m
uerrbd(i) = serrbd/rcondu(i)
verrbd(i) = serrbd/rcondv(i)
End Do

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

Write (nout,*)
Write (nout,*) 'Error estimate for the singular values'
Write (nout,99998) serrbd
Write (nout,*)
Write (nout,*) 'Error estimates for the left singular vectors'
Write (nout,99998) uerrbd(1:m)
Write (nout,*)
Write (nout,*) 'Error estimates for the right singular vectors'
Write (nout,99998) verrbd(1:m)
Else
Write (nout,99997) 'Failure in DGESDD. INFO =', info
End If

99999 Format (3X,(8F8.4))
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4)
End Program f08kdfe
```