 
      SUBROUTINE LOEVL (XI,YI,NXG,XG,NYG,YG,NP,MP,AL,AB,NXO,XO,NYO
     1,YO,FO)
C
C     THIS SUBROUTINE EVALUATES THE INTERPOLANT FOR THE GRID VERSION OF
C     FRANKE'S METHOD.  THE FUNCTION IS EVALUATED AT THE GRID OF POINTS
C     INDICATED BY NXO, XO, NYO, YO, AND THESE VALUES ARE RETURNED
C     IN THE ARRAY FO, WHICH IS ASSUMED TO BE DIMENSIONED (NXO,NYO).
C
C     THE ARGUMENTS ARE AS FOLLOWS.
C
C        XI   - \
C        YI   - INPUT.  THE DATA POINTS (XI,YI,FI),I=1,...,NPI.
C        FI   - /
C        NXG  - INPUT.  THE NUMBER OF VERTICAL GRID LINES.
C        XG   - INPUT.  THE COORDINATES OF THE VERTICAL GRID LINES, IN
C                       INCREASING ORDER.
C        NYG  - INPUT.  THE NUMBER OF HORIZONTAL GRID LINES.
C        YG   - INPUT.  THE COORDINATES OF THE HORIZONTAL GRID LINES,
C                       IN INCREASING ORDER.
C        NP   - INPUT.  AN ARRAY WHICH GIVES THE INITIAL SUBSCRIPT IN
C                       THE ARRAY MP AT WHICH THE SUBSCRIPTS FOR THE
C                       LOCAL INTERPOLATION POINTS ARE STORED.
C        MP   - INPUT.  AN ARRAY WHICH GIVES THE SUBSCRIPTS FOR THE
C                       LOCAL INTERPOLATION POINTS.
C        AL   - INPUT.  THE COEFFICIENTS FOR THE LINEAR PART OF THE
C                       THIN PLATE SPLINE APPROXIMATIONS.
C        AB   - INPUT.  THE COEFFICIENTS FOR THE LOCAL THIN PLATE
C                       SPLINE APPROXIMATIONS.
C        NXO  - INPUT.  THE NUMBER OF XO VALUES AT WHICH THE INTERPO-
C                       LATION FUNCTION IS TO BE CALCULATED.
C        XO   - INPUT.  THE VALUES OF X AT WHICH THE INTERPOLATION
C                       FUNCTION IS TO BE CALCULATED.
C        NYO  - INPUT.  THE NUMBER OF YO VALUES AT WHICH THE INTERPO-
C                       LATION FUNCTION IS TO BE CALCULATED.
C        YO   - INPUT.  THE VALUES OF Y AT WHICH THE INTERPOLATION
C                       FUNCTION IS TO BE CALCULATED.
C        FO   - OUTPUT.  VALUES OF THE INTERPOLATION FUNCTION AT THE
C                       GRID POINTS INDICATED BY NXO, XO, NYO, YO.
C                       FO IS ASSUMED TO BE DIMENSIONED (NXO,NYO) IN THE
C                       CALLING PROGRAM.
C
 
 
