```    Program f08aefe

!     F08AEF Example Program Text

!     Mark 25 Release. NAG Copyright 2014.

!     .. Use Statements ..
Use nag_library, Only: dgeqrf, dnrm2, dormqr, dtrtrs, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nb = 64, nin = 5, nout = 6
!     .. Local Scalars ..
Integer                          :: i, ifail, info, j, lda, ldb, lwork,  &
m, n, nrhs
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), b(:,:), rnorm(:), tau(:),    &
work(:)
!     .. Executable Statements ..
Write (nout,*) 'F08AEF Example Program Results'
Write (nout,*)
Flush (nout)
!     Skip heading in data file
lda = m
ldb = m
lwork = nb*n
Allocate (a(lda,n),b(ldb,nrhs),rnorm(nrhs),tau(n),work(lwork))

!     Read A and B from data file

!     Compute the QR factorization of A
!     The NAG name equivalent of dgeqrf is f08aef
Call dgeqrf(m,n,a,lda,tau,work,lwork,info)

!     Compute C = (C1) = (Q**T)*B, storing the result in B
!                 (C2)
!     The NAG name equivalent of dormqr is f08agf
Call dormqr('Left','Transpose',m,nrhs,n,a,lda,tau,b,ldb,work,lwork,info)

!     Compute least-squares solutions by backsubstitution in
!     R*X = C1
!     The NAG name equivalent of dtrtrs is f07tef
Call dtrtrs('Upper','No transpose','Non-Unit',n,nrhs,a,lda,b,ldb,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

!       Print least-squares solutions

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04caf('General',' ',n,nrhs,b,ldb,'Least-squares solution(s)', &
ifail)

!       Compute and print estimates of the square roots of the residual
!       sums of squares

!       The NAG name equivalent of dnrm2 is f06ejf
Do j = 1, nrhs
rnorm(j) = dnrm2(m-n,b(n+1,j),1)
End Do

Write (nout,*)
Write (nout,*) 'Square root(s) of the residual sum(s) of squares'
Write (nout,99999) rnorm(1:nrhs)
End If

99999 Format (5X,1P,7E11.2)
End Program f08aefe
```