```!   G05ZQF Example Program Text

!   Mark 26.1 Release. NAG Copyright 2016.

Module g05zqfe_mod

!     G05ZQF Example Program Module:
!            Parameters and User-defined Routines

!     .. Use Statements ..
Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Accessibility Statements ..
Private
Public                           :: cov2
!     .. Parameters ..
Integer, Parameter, Public       :: even = 1
Contains
Subroutine cov2(t1,t2,gamma,iuser,ruser)

!       .. Implicit None Statement ..
Implicit None
!       .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (Out) :: gamma
Real (Kind=nag_wp), Intent (In) :: t1, t2
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
Integer, Intent (Inout)        :: iuser(*)
!       .. Local Scalars ..
Real (Kind=nag_wp)             :: l1, l2, nu, rnorm, tl1, tl2
Integer                        :: norm
!       .. Intrinsic Procedures ..
Intrinsic                      :: abs, exp, sqrt
!       .. Executable Statements ..
!       Covariance parameters stored in ruser array.
norm = iuser(1)
l1 = ruser(1)
l2 = ruser(2)
nu = ruser(3)

tl1 = abs(t1)/l1
tl2 = abs(t2)/l2
If (norm==1) Then
rnorm = tl1 + tl2
Else If (norm==2) Then
rnorm = sqrt(tl1**2+tl2**2)
End If

gamma = exp(-(rnorm**nu))

Return

End Subroutine cov2
End Module g05zqfe_mod

Program g05zqfe

!     G05ZQF Example Main Program

!     .. Use Statements ..
Use g05zqfe_mod, Only: cov2, even
Use nag_library, Only: g05zqf, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: l1, l2, nu, rho, var, xmax, xmin,    &
ymax, ymin
Integer                          :: approx, icorr, icount, ifail, norm,  &
!     .. Local Arrays ..
Real (Kind=nag_wp)               :: eig(3), ruser(3)
Real (Kind=nag_wp), Allocatable  :: lam(:), xx(:), yy(:)
Integer                          :: iuser(1), m(2), maxm(2), ns(2)
!     .. Executable Statements ..
Write (nout,*) 'G05ZQF Example Program Results'
Write (nout,*)

!     Get problem specifications from data file

!     Put covariance parameters in communication arrays
iuser(1) = norm
ruser(1) = l1
ruser(2) = l2
ruser(3) = nu

Allocate (lam(maxm(1)*maxm(2)),xx(ns(1)),yy(ns(2)))

!     Get square roots of the eigenvalues of the embedding matrix
ifail = 0
yy,m,approx,rho,icount,eig,iuser,ruser,ifail)

!     Output results
Call display_results(approx,m,rho,eig,icount,lam)

Contains

!       .. Implicit None Statement ..
Implicit None
!       .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (Out) :: l1, l2, nu, var, xmax, xmin, ymax, &
ymin
Integer, Intent (Out)          :: icorr, norm, pad
!       .. Array Arguments ..
Integer, Intent (Out)          :: maxm(2), ns(2)
!       .. Executable Statements ..
!       Skip heading in data file

!       Read in norm, l1, l2 and nu for cov2 function
Read (nin,*) norm, l1, l2, nu

!       Read in variance of random field

!       Read in number of sample points in each direction

!       Read in maximum size of embedding matrix

!       Read in choice of scaling in case of approximation

Return

Subroutine display_results(approx,m,rho,eig,icount,lam)

!       .. Implicit None Statement ..
Implicit None
!       .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (In) :: rho
Integer, Intent (In)           :: approx, icount
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (In) :: eig(3)
Integer, Intent (In)           :: m(2)
Real (Kind=nag_wp), Intent (In) :: lam(m(1),m(2))
!       .. Local Scalars ..
Integer                        :: i
!       .. Executable Statements ..
!       Display size of embedding matrix
Write (nout,*)
Write (nout,99999) 'Size of embedding matrix = ', m(1)*m(2)

!       Display approximation information if approximation used
Write (nout,*)
If (approx==1) Then
Write (nout,*) 'Approximation required'
Write (nout,*)
Write (nout,99998) 'RHO = ', rho
Write (nout,99997) 'EIG = ', eig(1:3)
Write (nout,99999) 'ICOUNT = ', icount
Else
Write (nout,*) 'Approximation not required'
End If

!       Display square roots of the eigenvalues of the embedding matrix
Write (nout,*)
Write (nout,*) 'Square roots of eigenvalues of embedding matrix:'
Write (nout,*)
Do i = 1, m(1)
Write (nout,99996) lam(i,1:m(2))
End Do

Return

99999   Format (1X,A,I7)
99998   Format (1X,A,F10.5)
99997   Format (1X,A,3(F10.5,1X))
99996   Format (1X,8F8.4)

End Subroutine display_results

End Program g05zqfe
```