Polyharmonic Cubic Spline

[riziles]

I used math.js to create a multi-dimensional polyharmonic cubic spline interpolator and it worked great! My JavaScript experience is very limited, so there are probably better ways to do some of this:

import { matrix } from 'mathjs';
import * as math from 'mathjs';

function dist(x, y) {
  var x_mat = matrix(x);
  var y_mat = matrix(y);
  var diff = math.subtract(y_mat, x_mat);
  return Math.sqrt(math.multiply(diff, math.transpose(diff)));
}

let rbf = (Xdata, Ydata) => {
  let AB = [];
  for (var i in Xdata) {
    var row = [];
    for (var j in Xdata) {
      row.push(dist(Xdata[i], Xdata[j]) ** 3);
    }
    row.push(1.0);
    AB.push(row.concat(Xdata[i]));
  }
  // `.slice(0)` is used to make a copy of the arrays below
  // ... otherwise, fill will mutate the object calling
  var zeros = Xdata[0].slice(0).fill(0);
  var ones = Xdata.slice(0).fill(1);
  AB.push(ones.concat([0], zeros));
  var Xdata_t = math.transpose(matrix(Xdata))._data;
  for (i in Xdata_t) {
    AB.push(Xdata_t[i].concat([0], zeros));
  }
  var f_alt = Ydata.slice(0);
  var y_zeros = Ydata[0].slice(0).fill(0);
  for (i in Xdata[0].concat([0])) {
    f_alt.push(y_zeros);
  }
  var wv = math.multiply(math.inv(matrix(AB)), math.matrix(f_alt));
  var w = wv._data.slice(0, -3);
  var v = wv._data.slice(-3);
  let interp = (x) => {
    var total = 0;
    for (i in w) {
      total = math.add(total, math.multiply(w[i], dist(x, Xdata[i]) ** 3));
    }
    total = math.add(total, math.multiply(math.transpose(v), math.transpose([1].concat(x))));
    return total;
  };
  return interp;
};

export {rbf}

[josdejong]

😎 thanks for sharing @riziles

[riziles]

@josdejong, here it is used to make a pretty 3d surface plot: https://observablehq.com/d/845976115c3b0462