!   G05ZQF Example Program Text

!   Mark 27.3 Release. NAG Copyright 2021.

    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,  &
                                          pad
!     .. 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
      Call read_input_data(norm,l1,l2,nu,var,xmin,xmax,ymin,ymax,ns,maxm,      &
        icorr,pad)

!     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
      Call g05zqf(ns,xmin,xmax,ymin,ymax,maxm,var,cov2,even,pad,icorr,lam,xx,  &
        yy,m,approx,rho,icount,eig,iuser,ruser,ifail)

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

    Contains
      Subroutine read_input_data(norm,l1,l2,nu,var,xmin,xmax,ymin,ymax,ns,     &
        maxm,icorr,pad)

!       .. 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 (nin,*)

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

!       Read in variance of random field
        Read (nin,*) var

!       Read in domain endpoints
        Read (nin,*) xmin, xmax
        Read (nin,*) ymin, ymax

!       Read in number of sample points in each direction
        Read (nin,*) ns(1), ns(2)

!       Read in maximum size of embedding matrix
        Read (nin,*) maxm(1), maxm(2)

!       Read in choice of scaling in case of approximation
        Read (nin,*) icorr

!       Read in choice of padding
        Read (nin,*) pad

        Return

      End Subroutine read_input_data

      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