F 9.8.2 Shepard Interpolation
SUBROUTINE SHPGLO(X,Y,FX,FY,F,W,R,N,DMUE,PHI)
C********************************************************************
C *
C Program name: SHPGLO *
C *
C********************************************************************
C *
C This subroutine computes one functional value at (X,Y) for given*
C nodes using the global Shepard method. *
C The exponent dmue must be specified externally. *
C DMUE should be chosen to lie betwen 2 and 6. *
C *
C********************************************************************
C *
C Input parameters: *
C ================= *
C X : X value for which we want to interpolate the Z value *
C Y : Y value for which we want to interpolate the Z value *
C FX, FY, F : vectors ..(0:N) with X and Y coordinates of nodes*
C (FX,FY) and corresponding functional value F. *
C N : Index of last node *
C DMUE : Exponent, 0 < DMUE < infinity, reasonable results can *
C be achieved for 2 < DMUE < 6. If on input DMUE <= 0, we *
C set DMUE = 2 internally. *
C *
C AUX VECTORS: *
C ============ *
C W, R : vectors ..(0:N) *
C *
C *
C Output parameters: *
C ================== *
C PHI : Interpolated Z value at (X,Y) *
C *
C********************************************************************
C *
C Required subroutines: none *
C *
C********************************************************************
C *
C Author : Bjoern Terwege *
C Date : 6.12.1995 *
C Source code : FORTRAN 77 *
C
C********************************************************************
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION R(0:N),W(0:N),FX(0:N),FY(0:N),F(0:N)
C
C Check that DMUE > 0, otherwise set DMUE = 2
C
IF(DMUE.LE.0.) DMUE=2
C
C Compute the R(I)
C
DO 20 I=0,N
R(I)=DSQRT(((X-FX(I))*(X-FX(I)))
F +((Y-FY(I))*(Y-FY(I))))
IF (R(I).EQ.0) THEN
PHI=F(I)
GOTO 333
ENDIF
20 CONTINUE
C
C Compute the sum in the denominator of W(I)
C
DO 30 J=0,N
SUM=0
DO 40 I=0,N
SUM=SUM+1/(R(I)**DMUE)
40 CONTINUE
C Berechnung der Gewichte W(I)
C
W(J)=1/(R(J)**DMUE)*1/SUM
30 CONTINUE
PHI=0
C
C Compute the approximate function value at (X,Y)
C
DO 50 J=0,N
PHI=PHI+W(J)*F(J)
50 CONTINUE
333 CONTINUE
RETURN
END