NAG Library Manual, Mark 27.3
```    Program f08zsfe

!     F08ZSF Example Program Text

!     Mark 27.3 Release. NAG Copyright 2021.

!     .. Use Statements ..
Use nag_library, Only: dznrm2, nag_wp, zgemv, zggqrf, ztrtrs, zunmqr,    &
zunmrq
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Complex (Kind=nag_wp), Parameter :: one = (1.0E0_nag_wp,0.0E0_nag_wp)
Complex (Kind=nag_wp), Parameter :: zero = (0.0E0_nag_wp,0.0E0_nag_wp)
Integer, Parameter               :: nb = 64, nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: rnorm
Integer                          :: i, info, lda, ldb, lwork, m, n, p
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), b(:,:), d(:), taua(:),     &
taub(:), work(:), y(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max, min
!     .. Executable Statements ..
Write (nout,*) 'F08ZSF Example Program Results'
Write (nout,*)
!     Skip heading in data file
lda = n
ldb = n
lwork = nb*(m+p)
Allocate (a(lda,m),b(ldb,p),d(n),taua(m),taub(m+p),work(lwork),y(p))

!     Read A, B and D from data file

!     Compute the generalized QR factorization of (A,B) as
!     A = Q*(R),   B = Q*(T11 T12)*Z
!            (0)          ( 0  T22)
!     The NAG name equivalent of zggqrf is f08zsf
Call zggqrf(n,m,p,a,lda,taua,b,ldb,taub,work,lwork,info)

!     Compute c = (c1) = (Q**H)*d, storing the result in D
!                  (c2)
!     The NAG name equivalent of zunmqr is f08auf
Call zunmqr('Left','Conjugate transpose',n,1,m,a,lda,taua,d,n,work,      &
lwork,info)

!     Putting Z*y = w = (w1), set w1 = 0, storing the result in Y1
!                        (w2)
y(1:m+p-n) = zero

If (n>m) Then

!       Copy c2 into Y2

y(m+p-n+1:p) = d(m+1:n)

!       Solve T22*w2 = c2 for w2, storing result in Y2

!       The NAG name equivalent of ztrtrs is f07tsf
Call ztrtrs('Upper','No transpose','Non-unit',n-m,1,b(m+1,m+p-n+1),    &
ldb,y(m+p-n+1),n-m,info)

If (info>0) Then
Write (nout,*)                                                       &
'The upper triangular factor, T22, of B is singular, '
Write (nout,*) 'the least squares solution could not be computed'
Go To 100
End If

!       Compute estimate of the square root of the residual sum of
!       squares norm(y) = norm(w2)
!       The NAG name equivalent of dznrm2 is f06jjf
rnorm = dznrm2(n-m,y(m+p-n+1),1)

!       Form c1 - T12*w2 in D
!       The NAG name equivalent of zgemv is f06saf
Call zgemv('No transpose',m,n-m,-one,b(1,m+p-n+1),ldb,y(m+p-n+1),1,    &
one,d,1)
End If

!     Solve R*x = c1 - T12*w2 for x
!     The NAG name equivalent of ztrtrs is f07tsf
Call ztrtrs('Upper','No transpose','Non-unit',m,1,a,lda,d,m,info)

If (info>0) Then
Write (nout,*) 'The upper triangular factor, R, of A is singular, '
Write (nout,*) 'the least squares solution could not be computed'
Else

!       Compute y = (Z**H)*w
!       The NAG name equivalent of zunmrq is f08cxf
Call zunmrq('Left','Conjugate transpose',p,1,min(n,p),b(max(1,         &
n-p+1),1),ldb,taub,y,p,work,lwork,info)

!       Print least squares solution x
Write (nout,*) 'Generalized least squares solution'
Write (nout,99999) d(1:m)

!       Print residual vector y
Write (nout,*)
Write (nout,*) 'Residual vector'
Write (nout,99998) y(1:p)

!       Print estimate of the square root of the residual sum of
!       squares
Write (nout,*)
Write (nout,*) 'Square root of the residual sum of squares'
Write (nout,99997) rnorm
End If
100   Continue

99999 Format (3(' (',F9.4,',',F9.4,')',:))
99998 Format (3(' (',1P,E9.2,',',1P,E9.2,')',:))
99997 Format (1X,1P,E10.2)
End Program f08zsfe
```