NAG Library Manual, Mark 28.3
Interfaces:  FL   CL   CPP   AD 

NAG AD Library Introduction
Example description
    Program f11jb_a1w_fe

!     F11JB_A1W_F Example Program Text

!     Mark 28.3 Release. NAG Copyright 2022.

!     .. Use Statements ..
      Use iso_c_binding, Only: c_ptr
      Use nagad_library, Only: f11ja_a1w_f, f11jb_a1w_f, f11za_a1w_f,          &
                               f11zb_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
      Type (nagad_a1w_w_rtype)         :: dscale, dtol
      Integer                          :: i, ifail, j, la, lfill, liwork, n,   &
                                          nnz, nnzc, npivm
      Character (1)                    :: check, mic, pstrat
!     .. Local Arrays ..
      Type (nagad_a1w_w_rtype), Allocatable :: a(:), x(:), y(:)
      Real (Kind=nag_wp), Allocatable  :: ar(:), dxdy(:,:), yr(:)
      Integer, Allocatable             :: icol(:), ipiv(:), irow(:), istr(:),  &
                                          iwork(:), perm_fwd(:), perm_inv(:)
!     .. Executable Statements ..
      Write (nout,*) 'F11JB_A1W_F Example Program Results'
!     Skip heading in data file
      Read (nin,*)

!     Read order of matrix and number of nonzero entries

      Read (nin,*) n
      Read (nin,*) nnz

      la = 3*nnz
      liwork = 2*la + 7*n + 1

      Allocate (a(la),x(n),y(n),icol(la),ipiv(n),irow(la),istr(n+1),           &
        iwork(liwork),perm_fwd(n),perm_inv(n))
      Allocate (ar(la),yr(n),dxdy(n,n))

!     Read the matrix A
      Do i = 1, nnz
        Read (nin,*) ar(i), irow(i), icol(i)
      End Do
      a(1:nnz) = ar(1:nnz)

!     Read the vector y
      Read (nin,*) yr(1:n)
      y = yr

!     Create AD tape
      Call x10za_a1w_f

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

!     Calculate Cholesky factorization
      lfill = -1
      dtol = 0.0E0_nag_wp
      mic = 'N'
      dscale = 0.0E0_nag_wp
      pstrat = 'M'

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

      iwork = 0
!     Compute reverse Cuthill-McKee permutation for bandwidth reduction
      Call do_rcm(ad_handle,irow,icol,a,y,istr,perm_fwd,perm_inv,iwork)

      ifail = 0
      Call f11ja_a1w_f(ad_handle,n,nnz,a,la,irow,icol,lfill,dtol,mic,dscale,   &
        pstrat,ipiv,istr,nnzc,npivm,iwork,liwork,ifail)

!     Check the output value of NPIVM
      If (npivm/=0) Then
        Write (nout,99998) 'Factorization is not complete', npivm
      Else
!       Solve P L D L^T P^T x = y
        x = 0.0_nag_wp
        check = 'C'
        ifail = 0
        Call f11jb_a1w_f(ad_handle,n,a,la,irow,icol,ipiv,istr,check,y,x,ifail)
!       Output results
        Write (nout,*) ' Solution of linear system with Reverse Cuthill-McKee'
        Write (nout,99999)(x(perm_inv(i))%value,i=1,n)

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

        Write (nout,*)
        Write (nout,*) ' Derivatives of solution X w.r.t. RHS Y (A inverse)'
        Write (nout,*)
!       Setup evaluation of derivatives via adjoints
        Do i = 1, n
          Call nagad_a1w_ir_zero_adjoints
          Call nagad_a1w_inc_derivative(x(perm_inv(i)),1.0_nag_wp)
          ifail = 0
          Call nagad_a1w_ir_interpret_adjoint_sparse(ifail)

!         Get derivatives
          Do j = 1, n
            dxdy(i,j) = nagad_a1w_get_derivative(y(perm_inv(j)))
          End Do
        End Do
        Call x04caf('General',' ',n,n,dxdy,n,'       dx(i)/dy(j)',ifail)

      End If

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

99999 Format (1X,E16.4)
99998 Format (1X,A,I20)
    Contains
      Subroutine do_rcm(ad_handle,irow,icol,a,y,istr,perm_fwd,perm_inv,iwork)

!       .. Use Statements ..
        Use iso_c_binding, Only: c_ptr
        Use nag_library, Only: f11yef
!       .. Parameters ..
        Logical, Parameter             :: lopts(5) = (/.False.,.False.,.True., &
                                          .True.,.True./)
!       .. Scalar Arguments ..
        Type (c_ptr)                   :: ad_handle
!       .. Array Arguments ..
        Type (nagad_a1w_w_rtype), Intent (Inout) :: a(la), y(n)
        Integer, Intent (Inout)        :: icol(la), irow(la), istr(n+1),       &
                                          iwork(*)
        Integer, Intent (Out)          :: perm_fwd(n), perm_inv(n)
!       .. Local Scalars ..
        Integer                        :: i, ifail, j, nnz_cs, nnz_scs
!       .. Local Arrays ..
        Type (nagad_a1w_w_rtype), Allocatable :: rwork(:)
        Integer                        :: info(4), mask(1)
!       .. Intrinsic Procedures ..
        Intrinsic                      :: size
!       .. Executable Statements ..

!       SCS to CS, must add the upper triangle entries.
        j = nnz + 1
        Do i = 1, nnz
          If (irow(i)>icol(i)) Then
!           strictly lower triangle, add the transposed
            a(j) = a(i)
            irow(j) = icol(i)
            icol(j) = irow(i)
            j = j + 1
          End If
        End Do
        nnz_cs = j - 1

!       Reorder, CS to CCS, icolzp in istr
        ifail = 0
        Call f11za_a1w_f(ad_handle,n,nnz_cs,a,icol,irow,'F','F',istr,iwork,    &
          ifail)

!       Calculate reverse Cuthill-McKee
        ifail = 0
        Call f11yef(n,nnz_cs,istr,irow,lopts,mask,perm_fwd,info,ifail)

!       compute inverse perm, in perm_inv(1:n)
        Do i = 1, n
          perm_inv(perm_fwd(i)) = i
        End Do

!       Apply permutation on column/row indices
        icol(1:nnz_cs) = perm_inv(icol(1:nnz_cs))
        irow(1:nnz_cs) = perm_inv(irow(1:nnz_cs))

!       restrict to lower triangle, SCS format
!       copying entries upwards
        j = 1
        Do i = 1, nnz_cs
          If (irow(i)>=icol(i)) Then
!           non-upper triangle, bubble up
            a(j) = a(i)
            icol(j) = icol(i)
            irow(j) = irow(i)
            j = j + 1
          End If
        End Do
        nnz_scs = j - 1

!       sort
        ifail = 0
        Call f11zb_a1w_f(ad_handle,n,nnz_scs,a,irow,icol,'S','K',istr,iwork,   &
          ifail)

!       permute rhs vector
        Allocate (rwork(size(perm_fwd)))
        rwork(:) = y(perm_fwd(:))
        y(:) = rwork(:)
        Deallocate (rwork)
      End Subroutine do_rcm
    End Program f11jb_a1w_fe