R角距离加权插值函数

Question

I would like use R for doing an Angular-Distance-Weighting Interpolation as described eg here (p. 3).

It is an interpolation which (1) weights the data points by distance relative to a correlation decay distance and (2) gives more weight to isolated data points.

My question is whether there is some package implementation of this in R or whether one would need to do it from scratch. My Google search did not get me anything obvious on this but I do not know R's interpolation packages so well. So if anybody has ever done this, please let me know.

Answer 1

There is no R package available..I wrote a simple function for Angular distance weighting (ADW) as implemented in Shepard 1968

[X,Y] are coordinates where you wish to estimate. [Xtrain,Ytrain] are the coordinates of data points. weights radial are the weights by distance.

compute_weight_by_theta = function(X,Y,xtrain,ytrain,weights.radial){
      N = length(xtrain)
      weight.directional = integer(N)
      for (i in 1:N){
        numerator = 0;
        denominator = 0;
        for (j in 1:N){
          xi = xtrain[i]; yi = ytrain[i]
          xj = xtrain[j]; yj = ytrain[j]
          if ((xi != xj) | (yi != yj)){
            Sj = weights.radial[j]
            Di = sqrt((X - xi)**2 + (Y - yi)**2)
            Dj = sqrt((X - xj)**2 + (Y - yj)**2)
            cos_theta = ((X-xi)*(X-xj) + (Y-yi)*(Y-yj)) / (Di*Dj)
            numerator = numerator + (1-cos_theta)*Sj
            denominator = denominator + Sj
          }
        }
        weight.directional[i] = numerator/denominator
      }
      return(weight.directional)
    }