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interp

Purpose

General-purpose linear interpolation function

Synopsis

(1) function interp(VR:real,   XY: array(...) of real) :real

(2) function interp(VR:real,   X:  array(...) of real, Y: array(...) of real) :real

(3) function interp(VC:linctr, XY: array(...) of real) :gexp

(4) function interp(VC:linctr, XV: array(...) of xvitem) :gexp

(5) function interp(VG:gexp,   XY: array(...) of real) :gexp

(6) function interp(VG:gexp,   XV: array(...) of xvitem) :gexp

Arguments

VR	real value to be interpolated
VC	linear expression to be interpolated
VG	general expression to be interpolated
XY	real array of pairs of values with which to interpolate
X	real array of X-values with which to interpolate
Y	real array of Y-values with which to interpolate
XV	array of pairs of xvitems with which to interpolate

Return value

Forms (1) and (2) return the interpolated value. The remaining forms return the formula for interpolating the required value.

Example

Linear interpolation is typically used to estimate the value of a function at a point from known values at two adjacent points. As an example, suppose we want to estimate x², but are given values only at x=1(1), 2(4), 3(9), 4(16) and 5(25). Then, to estimate the square of (say) 2.5 we would take the value half way between x=2 and x=3 and obtain the result 6.5. The interp function performs the same operation. Its first argument is the value (constant or variable) that we are trying to interpolate. The other argument(s) contain the given values, either in a 2-dimensional real array of corresponding X and Y values (as in XY2 below), two 1-dimensional real arrays of X and corresponding Y values (as in X and Y below), or in a 1-dimensional array of values which contain successive pairs of values X and its corresponding Y (as in the remaining arrays below).

parameters
  n = 5
end-parameters
declarations
  XY2: array(1..n,1..2) of real
  XY: array(1..n*2) of real
  X, Y: array(1..n) of real
  XV: array(1..n*2) of xvitem
  V: mpvar
  R: real
end-declarations
  X := [1, 2, 3, 4, 5]
  Y := [1, 4, 9, 16, 25]
  XY:= [1,1, 2,4, 3,9, 4, 16, 5,25]
  forall (i in 1..n) do
    XY2(i,1) := X(i)
    XY2(i,2) := Y(i)
  end-do
  forall (i in 1..n*2) do
    XV(i) := XVitem(XY(i))
  end-do
  R := 2.5
  writeln("Estimate (XY) for ",R," is ",interp(R,XY))
  writeln("Estimate (XY2) for ",R," is ",interp(R,XY2))
  writeln("Estimate (X,Y) for ",R," is ",interp(R,X,Y))


  setparam("xslp_MaxXVArrayDimension",2)
  interp(V,XY2) <= 10
  setparam("xslp_MaxXVArrayDimension",1)
  interp(V+6,XY) <= 16
  interp(V^2,XV) <= 20

The first three uses of interp calculate an immediate value (all the arguments are constant). The last three uses all produce constraints (at least one of the arguments is not constant). The real arrays are effectively being used as XVs. Normally, only 1-dimensional arrays can be used. If a multi-dimensional array is to be used, then the parameter xslp_maxxvarraydimension must be set before the array is first referenced as an XV The parameter should be returned to its standard value (1) afterwards so that any inadvertent uses of multi-dimensional arrays are identified.

Further information

More complex uses of interp may require the use of the Func wrapper and custom-built XVs