Program e02alfe

!     E02ALF Example Program Text

!     Mark 30.1 Release. NAG Copyright 2024.

!     .. Use Statements ..
      Use nag_library, Only: e02alf, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: dxx, ref, s, t, xx
      Integer                          :: i, ifail, j, m, n, neval
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:), x(:), y(:)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: exp, real
!     .. Executable Statements ..
      Write (nout,*) 'E02ALF Example Program Results'

!     Skip heading in data file
      Read (nin,*)

      Read (nin,*) n, m, neval
      Allocate (a(m+1),x(n),y(n))

      Read (nin,*)(x(i),y(i),i=1,n)

      ifail = 0
      Call e02alf(n,x,y,m,a,ref,ifail)

      Write (nout,*)
      Write (nout,*) '   Polynomial coefficients'
      Write (nout,99998)(a(i),i=1,m+1)
      Write (nout,*)
      Write (nout,99997) '   Reference deviation = ', ref
      Write (nout,*)
      Write (nout,*) '  x     Fit      exp(x)   Residual'

!     The neval evaluation points are equispaced on [0,1].
      dxx = 1.0_nag_wp/real(neval-1,kind=nag_wp)

      Do j = 1, neval
        xx = real(j-1,kind=nag_wp)*dxx

        s = a(m+1)

        Do i = m, 1, -1
          s = s*xx + a(i)
        End Do

        t = exp(xx)
        Write (nout,99999) xx, s, t, s - t
      End Do

99999 Format (1X,F5.2,2F9.4,E11.2)
99998 Format (6X,E12.4)
99997 Format (1X,A,E10.2)
    End Program e02alfe