Program f08bbfe

!     F08BBF Example Program Text

!     Mark 28.3 Release. NAG Copyright 2022.

!     .. Use Statements ..
      Use nag_library, Only: dgemqrt, dgeqrt, dnrm2, dtpmqrt, dtpqrt, dtrtrs,  &
                             nag_wp, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nbmax = 64, nin = 5, nout = 6
!     .. Local Scalars ..
      Integer                          :: i, ifail, info, j, lda, ldb, ldt,    &
                                          lwork, m, n, nb, nrhs
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), b(:,:), c(:,:), rnorm(:),    &
                                          t(:,:), work(:)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: max, min
!     .. Executable Statements ..
      Write (nout,*) 'F08BBF Example Program Results'
      Write (nout,*)
      Flush (nout)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) m, n, nrhs
      lda = m
      ldb = m
      nb = min(m,n,nbmax)
      ldt = nb
      lwork = nb*max(n,m)
      Allocate (a(lda,n),b(ldb,nrhs),c(ldb,nrhs),rnorm(nrhs),t(ldt,min(m,      &
        n)),work(lwork))

!     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)

      c(1:m,1:nrhs) = b(1:m,1:nrhs)
!     Compute the QR factorization of first n rows of A
!     The NAG name equivalent of dgeqrt is f08abf
      Call dgeqrt(n,n,nb,a,lda,t,ldt,work,info)

!     Compute C = (C1) = (Q**T)*B, storing the result in C
!                  (C2)
!     The NAG name equivalent of dgemqrt is f08acf
      Call dgemqrt('Left','Transpose',n,nrhs,n,nb,a,lda,t,ldt,c,ldb,work,info)

      b(1:n,1:nrhs) = c(1:n,1:nrhs)
!     Compute least squares solutions for first n rows by back-substitution in
!     R*X = C1
!     The NAG name equivalent of dtrtrs is f07tef
      Call dtrtrs('Upper','No transpose','Non-Unit',n,nrhs,a,lda,c,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 solution using first n rows

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

      End If

!     Now add the remaining rows and perform QR update
!     The NAG name equivalent of dtpqrt is f08bbf
      Call dtpqrt(m-n,n,0,nb,a,lda,a(n+1,1),lda,t,ldt,work,info)

!     Apply orthogonal transformations to C
!     The NAG name equivalent of dtpmqrt is f08bcf
      Call dtpmqrt('Left','Transpose',m-n,nrhs,n,0,nb,a(n+1,1),lda,t,ldt,b,    &
        ldb,b(5,1),ldb,work,info)
!     Compute least squares solutions for first n rows by bac-substitution 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
        Write (nout,*)
        Flush (nout)
        ifail = 0
        Call x04caf('G',' ',n,nrhs,b,ldb,                                      &
          'Least squares solution(s) for all rows',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 f08bbfe