Program f08befe

!     F08BEF Example Program Text

!     Mark 29.2 Release. NAG Copyright 2023.

!     .. 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
      Read (nin,*)
      Read (nin,*) m, n, nrhs
      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

      Read (nin,*)(a(i,1:n),i=1,m)
      Read (nin,*)(b(i,1:nrhs),i=1,m)

!     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))) Then
          Exit loop
        End If
      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 back-substitution 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