! 	  From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
! 		by RH Landau, MJ Paez, and CC Bordeianu 
! 		Copyright Wiley - VCH, 2007.
! 		Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
! 		MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007
! 		Supported by the US National Science Foundation			
! 		
! 	  lagrange.f: Langrange interpolation of cross table		

Program lagrange

  Implicit none
  Real*8 :: inter, x, xin(9), yin(9)
	Integer :: i, e
	
	e = 9
	open(6, File = 'lagrange.dat', Status = 'Unknown')
	                                                       ! Input data
  data xin /0, 85, 580, 758, 800, 1285, 850, 795, 82/           
	data yin /18.6, 16, 85, 83.5, 58.8, 19.9, 10.8, 88.25, 4.7 /		
	                                                   ! Calculate f(x)
	Do	i = 0, 1000                                           
	  x = i*0.2 
		write (6, *) x, inter(xin, yin, e, x)
	End Do
	Close(6)
	Stop 'data saved in lagrange.dat'
End Program lagrange
                                 ! Evaluate interpolation function(x)
Function inter(xin, yin, e, x)
  Implicit none
	Integer :: i, j, e
	Real*8 :: inter, lambda(9), xin(9), yin(9), x
	inter = 0
	Do	i = 1, e
	  lambda(i) = 1
		Do	j = 1, e
		  If (i.neqv.j) then
			  lambda(i) = lambda(i) * ((x - xin(j))/(xin(i) - xin(j)))
			Endif
		End Do
		inter = inter + (yin(i) * lambda(i))
  End Do
	Return
End