```    Program f08befe

!     F08BEF Example Program Text

!     Mark 25 Release. NAG Copyright 2014.

!     .. Use Statements ..
Use nag_library, Only: dgeqpf, dormqr, dtrsv, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Real (Kind=nag_wp), Parameter    :: zero = 0.0E0_nag_wp
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: tol
Integer                          :: i, ifail, info, k, lda, ldb, ldx,    &
lwork, m, n, nrhs
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), b(:,:), tau(:), work(:),     &
x(:,:)
Integer, Allocatable             :: jpvt(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: abs
!     .. Executable Statements ..
Write (nout,*) 'F08BEF Example Program Results'
!     Skip heading in data file
lda = m
ldb = m
ldx = m
lwork = 64*n
Allocate (a(lda,n),b(ldb,nrhs),tau(n),work(lwork),x(ldx,nrhs),jpvt(n))

!     Read A and B from data file

!     Initialize JPVT to be zero so that all columns are free

jpvt(1:n) = 0

!     Compute the QR factorization of A

!     The NAG name equivalent of dgeqpf is f08bef
Call dgeqpf(m,n,a,lda,jpvt,tau,work,info)

!     Choose TOL to reflect the relative accuracy of the input data

tol = 0.01E0_nag_wp

!     Determine which columns of R to use

loop: Do k = 1, n
If (abs(a(k,k))<=tol*abs(a(1,1))) Exit loop
End Do loop

!     Compute C = (Q**T)*B, storing the result in B

k = k - 1

!     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 solution by backsubstitution in R*B = C
Do i = 1, nrhs

!       The NAG name equivalent of dtrsv is f06pjf
Call dtrsv('Upper','No transpose','Non-Unit',k,a,lda,b(1,i),1)

!       Set the unused elements of the I-th solution vector to zero

b(k+1:n,i) = zero

End Do

!     Unscramble the least-squares solution stored in B

Do i = 1, n
x(jpvt(i),1:nrhs) = b(i,1:nrhs)
End Do

!     Print least-squares solution

Write (nout,*)
Flush (nout)

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

End Program f08befe
```