Program f08ga_t1w_fe

!     F08GA_T1W_F Example Program Text
!     Mark 28.3 Release. NAG Copyright 2022.

!     .. Use Statements ..
      Use iso_c_binding, Only: c_ptr
      Use nagad_library, Only: f08ga_t1w_f, nagad_t1w_w_rtype, x10aa_t1w_f,    &
                               x10ab_t1w_f, Assignment (=)
      Use nag_library, Only: nag_wp, x02ajf, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
      Character (1), Parameter         :: uplo = 'U'
!     .. Local Scalars ..
      Type (c_ptr)                     :: ad_handle
      Real (Kind=nag_wp)               :: eerrbd, eps
      Integer                          :: i, ifail, info, j, n
!     .. Local Arrays ..
      Type (nagad_t1w_w_rtype), Allocatable :: ap(:), ap_in(:), w(:), work(:), &
                                          w_in(:)
      Type (nagad_t1w_w_rtype)         :: dummy(1,1)
      Real (Kind=nag_wp), Allocatable  :: dwda(:,:), wr(:)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: abs, max
!     .. Executable Statements ..
      Write (nout,*) 'F08GA_T1W_F Example Program Results'
      Write (nout,*)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n

      Allocate (ap((n*(n+1))/2),w(n),w_in(n),work(3*n))
      Allocate (ap_in((n*(n+1))/2),dwda(n,n),wr(n))

      ifail = 0
      Call x10aa_t1w_f(ad_handle,ifail)

!     Read the upper triangular part of the matrix A from data file

      ap_in = 0.0_nag_wp
      w_in = 0.0_nag_wp
      Read (nin,*)((ap_in(i+(j*(j-1))/2)%value,j=i,n),i=1,n)

      Do j = 1, n

        ap = ap_in
        w = w_in
        ap(j*(j+1)/2)%tangent = 1.0_nag_wp
!       Solve the symmetric eigenvalue problem
!       The NAG name equivalent of dspev_t1w is f08ga_t1w_f
        Call f08ga_t1w_f(ad_handle,'No vectors',uplo,n,ap,w,dummy,1,work,info)

        If (info/=0) Then
          Write (nout,99997) 'Failure in dspev_t1w. info =', info
          Go To 100
        End If

        If (j==1) Then
          wr(1:n) = w(1:n)%value
        End If

        Do i = 1, n
          dwda(i,j) = w(i)%tangent
        End Do

      End Do

      Write (nout,*) 'Eigenvalues'
      Write (nout,99999) wr(1:n)

!     Get the machine precision, EPS and compute the approximate
!     error bound for the computed eigenvalues.  Note that for
!     the 2-norm, max( abs(W(i)) ) = norm(A), and since the
!     eigenvalues are returned in ascending order
!     max( abs(W(i)) ) = max( abs(W(1)), abs(W(n)))

      eps = x02ajf()
      eerrbd = eps*max(abs(wr(1)),abs(wr(n)))

!     Print the approximate error bound for the eigenvalues

      Write (nout,*)
      Write (nout,*) 'Error estimate for the eigenvalues'
      Write (nout,99998) eerrbd

      Write (nout,*)
      Write (nout,*) 'Derivatives of eigenvalues w.r.t. diagonal of A'
      ifail = 0
      Call x04caf('General',' ',n,n,dwda,n,'dW_i/dA_jj',ifail)

100   Continue
      Call x10ab_t1w_f(ad_handle,ifail)
99999 Format (3X,(8F8.4))
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4)
    End Program f08ga_t1w_fe