Program f08ga_a1w_fe
! F08GA_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: abs, f08ga_a1w_f, max, &
nagad_a1w_get_derivative, &
nagad_a1w_inc_derivative, &
nagad_a1w_ir_create => x10za_a1w_f, &
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, &
Assignment (=), Operator (*)
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
Type (nagad_a1w_w_rtype) :: eerrbd, eps
Integer :: i, ifail, info, j, n
! .. Local Arrays ..
Type (nagad_a1w_w_rtype), Allocatable :: ap(:), ap_in(:), w(:), work(:)
Type (nagad_a1w_w_rtype) :: dummy(1,1)
Real (Kind=nag_wp), Allocatable :: dwda(:,:)
! .. Executable Statements ..
Write (nout,*) 'F08GA_A1W_F Example Program Results'
Write (nout,*)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
Allocate (ap((n*(n+1))/2),w(n),work(3*n))
Allocate (ap_in((n*(n+1))/2),dwda(n,n))
ifail = 0
Call x10aa_a1w_f(ad_handle,ifail)
Call nagad_a1w_ir_create
! Read the upper triangular part of the matrix A from data file
Read (nin,*)((ap_in(i+(j*(j-1))/2)%value,j=i,n),i=1,n)
Call nagad_a1w_ir_register_variable(ap_in)
ap = ap_in
! Solve the symmetric eigenvalue problem
! The NAG name equivalent of dspev_a1w is f08ga_a1w_f
Call f08ga_a1w_f(ad_handle,'No vectors',uplo,n,ap,w,dummy,1,work,info)
If (info==0) Then
! Print solution
Write (nout,*) 'Eigenvalues'
Write (nout,99999) w(1:n)%value
! 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(w(1)),abs(w(n)))
! Print the approximate error bound for the eigenvalues
Write (nout,*)
Write (nout,*) 'Error estimate for the eigenvalues'
Write (nout,99998) eerrbd%value
Else
Write (nout,99997) 'Failure in DSPEV_A1W. INFO =', info
Go To 100
End If
Do i = 1, n
Call nagad_a1w_ir_zero_adjoints
Call nagad_a1w_inc_derivative(w(i),1.0_nag_wp)
Call nagad_a1w_ir_interpret_adjoint_sparse(ifail)
Do j = 1, n
dwda(i,j) = nagad_a1w_get_derivative(ap_in(j*(j+1)/2))
End Do
End Do
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 nagad_a1w_ir_remove
Call x10ab_a1w_f(ad_handle,ifail)
99999 Format (3X,(8F8.4))
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4)
End Program f08ga_a1w_fe