NAG Library Manual, Mark 28.4
```    Program f08kufe

!     F08KUF Example Program Text

!     Mark 28.4 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: f06tff, f06thf, nag_wp, x04dbf, zgebrd, zgelqf,   &
zgeqrf, zunglq, zungqr, zunmbr
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Complex (Kind=nag_wp), Parameter :: zero = (0.0E0_nag_wp,0.0E0_nag_wp)
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Integer                          :: i, ic, ifail, info, lda, ldph, ldu,  &
lwork, m, n
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), ph(:,:), tau(:), taup(:),  &
tauq(:), u(:,:), work(:)
Real (Kind=nag_wp), Allocatable  :: d(:), e(:)
Character (1)                    :: clabs(1), rlabs(1)
!     .. Executable Statements ..
Write (nout,*) 'F08KUF Example Program Results'
!     Skip heading in data file
Do ic = 1, 2
lda = m
ldph = n
ldu = m
lwork = 64*(m+n)
Allocate (a(lda,n),ph(ldph,n),tau(n),taup(n),tauq(n),u(ldu,n),         &
work(lwork),d(n),e(n-1))

!       Read A from data file

If (m>=n) Then

!         Compute the QR factorization of A
!         The NAG name equivalent of zgeqrf is f08asf
Call zgeqrf(m,n,a,lda,tau,work,lwork,info)

!         Copy A to U
Call f06tff('Lower',m,n,a,lda,u,ldu)

!         Form Q explicitly, storing the result in U
!         The NAG name equivalent of zungqr is f08atf
Call zungqr(m,n,n,u,ldu,tau,work,lwork,info)

!         Copy R to PH (used as workspace)
Call f06tff('Upper',n,n,a,lda,ph,ldph)

!         Set the strictly lower triangular part of R to zero
Call f06thf('Lower',n-1,n-1,zero,zero,ph(2,1),ldph)

!         Bidiagonalize R
!         The NAG name equivalent of zgebrd is f08ksf
Call zgebrd(n,n,ph,ldph,d,e,tauq,taup,work,lwork,info)

!         Update Q, storing the result in U
!         The NAG name equivalent of zunmbr is f08kuf
Call zunmbr('Q','Right','No transpose',m,n,n,ph,ldph,tauq,u,ldu,     &
work,lwork,info)

!         Print bidiagonal form and matrix Q

Write (nout,*)
Write (nout,*) 'Example 1: bidiagonal matrix B'
Write (nout,*) 'Diagonal'
Write (nout,99999) d(1:n)
Write (nout,*) 'Superdiagonal'
Write (nout,99999) e(1:n-1)
Write (nout,*)
Flush (nout)

!         ifail: behaviour on error exit
!                =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04dbf('General',' ',m,n,u,ldu,'Bracketed','F7.4',              &
'Example 1: matrix Q','Integer',rlabs,'Integer',clabs,80,0,ifail)

Else

!         Compute the LQ factorization of A
!         The NAG name equivalent of zgelqf is f08avf
Call zgelqf(m,n,a,lda,tau,work,lwork,info)

!         Copy A to PH
Call f06tff('Upper',m,n,a,lda,ph,ldph)

!         Form Q explicitly, storing the result in PH
!         The NAG name equivalent of zunglq is f08awf
Call zunglq(n,n,m,ph,ldph,tau,work,lwork,info)

!         Copy L to U (used as workspace)
Call f06tff('Lower',m,m,a,lda,u,ldu)

!         Set the strictly upper triangular part of L to zero
Call f06thf('Upper',m-1,m-1,zero,zero,u(1,2),ldu)

!         Bidiagonalize L
!         The NAG name equivalent of zgebrd is f08ksf
Call zgebrd(m,m,u,ldu,d,e,tauq,taup,work,lwork,info)

!         Update P**H, storing the result in PH
!         The NAG name equivalent of zunmbr is f08kuf
Call zunmbr('P','Left','Conjugate transpose',m,n,m,u,ldu,taup,ph,    &
ldph,work,lwork,info)

!         Print bidiagonal form and matrix P**H

Write (nout,*)
Write (nout,*) 'Example 2: bidiagonal matrix B'
Write (nout,*) 'Diagonal'
Write (nout,99999) d(1:m)
Write (nout,*) 'Superdiagonal'
Write (nout,99999) e(1:m-1)
Write (nout,*)
Flush (nout)

ifail = 0
Call x04dbf('General',' ',m,n,ph,ldph,'Bracketed','F7.4',            &
'Example 2: matrix P**H','Integer',rlabs,'Integer',clabs,80,0,     &
ifail)

End If
Deallocate (a,ph,tau,taup,tauq,u,work,d,e)
End Do

99999 Format (3X,(8F8.4))
End Program f08kufe
```