Program f08me_a1w_fe

!     F08MEF Example Program Text

!     Mark 30.3 Release. NAG Copyright 2024.

!     .. Use Statements ..
      Use iso_c_binding, Only: c_ptr
      Use nagad_library, Only: f08me_a1w_f, nagad_a1w_get_derivative,          &
                               nagad_a1w_inc_derivative,                       &
                               nagad_a1w_ir_interpret_adjoint_sparse,          &
                               nagad_a1w_ir_register_variable,                 &
                               nagad_a1w_ir_remove, nagad_a1w_ir_zero_adjoints &
                               , nagad_a1w_w_rtype, x10aa_a1w_f, x10ab_a1w_f,  &
                               x10za_a1w_f, Assignment (=)
      Use nag_library, Only: nag_wp, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Type (c_ptr)                     :: ad_handle
      Integer                          :: i, ifail, ldc, ldu, ldvt, n
      Character (1)                    :: uplo
!     .. Local Arrays ..
      Type (nagad_a1w_w_rtype), Allocatable :: c(:,:), d(:), d_in(:), e(:),    &
                                          e_in(:), u(:,:), vt(:,:), work(:)
      Real (Kind=nag_wp), Allocatable  :: dr(:), dsdd(:,:), dsde(:,:), er(:),  &
                                          ur(:,:), vtr(:,:)
!     .. Executable Statements ..
      Write (nout,*) 'F08ME_A1W_F Example Program Results'
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n
      ldc = 1
      ldu = n
      ldvt = n
      Allocate (c(ldc,1),d(n),e(n-1),u(ldu,n),vt(ldvt,n),work(4*n))
      Allocate (d_in(n),e_in(n-1),dr(n),er(n-1),ur(ldu,n),vtr(ldvt,n))
      Allocate (dsdd(n,n),dsde(n,n-1))

!     Read B from data file

      Read (nin,*) dr(1:n)
      Read (nin,*) er(1:n-1)

      Read (nin,*) uplo

      d_in = dr
      e_in = er
!     Initialize U and VT to be the unit matrix
      u = 0.0_nag_wp
      vt = 0.0_nag_wp
      Do i = 1, n
        u(i,i) = 1.0_nag_wp
        vt(i,i) = 1.0_nag_wp
      End Do
!     Create AD tape
      Call x10za_a1w_f

!     Create AD configuration data object
      ifail = 0
      Call x10aa_a1w_f(ad_handle,ifail)

!     Register variables to differentiate w.r.t.
      Call nagad_a1w_ir_register_variable(d_in)
      Call nagad_a1w_ir_register_variable(e_in)

      d = d_in
      e = e_in
!     Calculate the SVD of B
      ifail = 0
      Call f08me_a1w_f(ad_handle,uplo,n,n,n,0,d,e,u,ldu,vt,ldvt,c,ldc,work,    &
        ifail)

      Write (nout,*)
!     Print singular values, left & right singular vectors

      Write (nout,*) 'Singular values'
      Write (nout,99999) d(1:n)%value
      Write (nout,*)
      Flush (nout)

      ur = u
      ifail = 0
      Call x04caf('General',' ',n,n,ur,ldu,'Left singular vectors, by column', &
        ifail)

      vtr = vt
      ifail = 0
      Call x04caf('General',' ',n,n,vtr,ldvt,'Right singular vectors, by row', &
        ifail)

      Write (nout,*)
      Flush (nout)

      Write (nout,*)
      Write (nout,*) ' Derivatives calculated: First order adjoints'
      Write (nout,*) ' Computational mode    : algorithmic'

      Write (nout,*)
      Write (nout,*) ' Derivatives of S.V.s w.r.t. d, e on input:'
!     Setup evaluation of derivatives via adjoints
      Do i = 1, n
        Call nagad_a1w_ir_zero_adjoints
        Call nagad_a1w_inc_derivative(d(i),1.0_nag_wp)
        ifail = 0
        Call nagad_a1w_ir_interpret_adjoint_sparse(ifail)

!       Get derivatives
        dsdd(i,1:n) = nagad_a1w_get_derivative(d_in(1:n))
        dsde(i,1:n-1) = nagad_a1w_get_derivative(e_in(1:n-1))
      End Do
      ifail = 0
      Call x04caf('General',' ',n,n,dsdd,n,' dS_i/dD_j',ifail)
      Write (nout,*)
      ifail = 0
      Call x04caf('General',' ',n,n-1,dsde,n,' dS_i/dE_j',ifail)

!     Remove computational data object and tape
      Call x10ab_a1w_f(ad_handle,ifail)
      Call nagad_a1w_ir_remove

99999 Format (3X,(8F8.4))
    End Program f08me_a1w_fe