!!!!!!!!!!!!!!!!!!!!!!!!!!! Program 2.1 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! !
! Please Note: !
! !
! (1) This computer program is written by Tao Pang in conjunction with !
! his book, "An Introduction to Computational Physics," published !
! by Cambridge University Press in 1997. !
! !
! (2) No warranties, express or implied, are made for this program. !
! !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
PROGRAM INTERPOLATION
!
! Main program for the Lagrange interpolation with the Aitken method.
! Copyright (c) Tao Pang 1997.
!
IMPLICIT NONE
INTEGER, PARAMETER :: N=5
REAL :: X,F,DF
REAL, DIMENSION (N) :: XI,FI
DATA XI/0.0,0.5,1.0,1.5,2.0/, &
FI/1.0,0.938470,0.765198,0.511828,0.223891/
!
X = 0.9
CALL AITKEN (N,XI,FI,X,F,DF)
WRITE (6,"(3F16.8)") X,F,DF
END PROGRAM INTERPOLATION
!
SUBROUTINE AITKEN (N,XI,FI,X,F,DF)
!
! Subroutine performing the Lagrange interpolation with the
! Aitken method. F: interpolated value. DF: error estimated.
! Copyright (c) Tao Pang 1997.
!
INTEGER, PARAMETER :: NMAX=21
INTEGER, INTENT (IN) :: N
INTEGER :: I,J
REAL, INTENT (IN) :: X
REAL, INTENT (OUT) :: F,DF
REAL :: X1,X2,F1,F2
REAL, INTENT (IN), DIMENSION (N):: XI,FI
REAL, DIMENSION (NMAX):: FT
!
IF (N.GT.NMAX) STOP 'Dimension of the data is too large.'
DO I = 1, N
FT(I) = FI(I)
END DO
!
DO I = 1, N-1
DO J = 1, N-I
X1 = XI(J)
X2 = XI(J+I)
F1 = FT(J)
F2 = FT(J+1)
FT(J) = (X-X1)/(X2-X1)*F2+(X-X2)/(X1-X2)*F1
END DO
END DO
F = FT(1)
DF = (ABS(F-F1)+ABS(F-F2))/2.0
END SUBROUTINE AITKEN