-
-
Save dburner/8550030 to your computer and use it in GitHub Desktop.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
/** | |
* At least two points are needed to interpolate something. | |
* @class Lagrange polynomial interpolation. | |
* The computed interpolation polynomial will be reffered to as L(x). | |
* @example | |
* var l = new Lagrange(0, 0, 1, 1); | |
* var index = l.addPoint(0.5, 0.8); | |
* console.log(l.valueOf(0.1)); | |
* | |
* l.changePoint(index, 0.5, 0.1); | |
* console.log(l.valueOf(0.1)); | |
*/ | |
var Lagrange = function(x1, y1, x2, y2) { | |
this.xs = [x1, x2]; | |
this.ys = [y1, y2]; | |
this.ws = []; | |
this._updateWeights(); | |
} | |
/** | |
* Adds a new point to the polynomial. L(x) = y | |
* @return {Number} The index of the added point. Used for changing the point. See changePoint. | |
*/ | |
Lagrange.prototype.addPoint = function(x, y) { | |
this.xs.push(x); | |
this.ys.push(y); | |
this._updateWeights(); | |
return this.xs.length-1; | |
} | |
/** | |
* Changes a previously added point. | |
*/ | |
Lagrange.prototype.changePoint = function(index, x, y) { | |
this.xs[index] = x; | |
this.ys[index] = y; | |
this._updateWeights(); | |
} | |
/** | |
* Recalculate barycentric weights. | |
*/ | |
Lagrange.prototype._updateWeights = function() { | |
var k = this.xs.length; | |
var w; | |
for (var j = 0; j < k; ++j) { | |
w = 1; | |
for (var i = 0; i < k; ++i) { | |
if (i != j) { | |
w *= this.xs[j] - this.xs[i]; | |
} | |
} | |
this.ws[j] = 1/w; | |
} | |
} | |
/** | |
* Calculate L(x) | |
*/ | |
Lagrange.prototype.valueOf = function(x) { | |
var a = 0; | |
var b = 0; | |
var c = 0; | |
for (var j = 0; j < this.xs.length; ++j) { | |
if (x != this.xs[j]) { | |
a = this.ws[j] / (x - this.xs[j]); | |
b += a * this.ys[j]; | |
c += a; | |
} else { | |
return this.ys[j]; | |
} | |
} | |
return b / c; | |
} |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Updated for modern JS, using class syntax and
evaluate
instead ofvalueOf
(which is a super special function name defined in the JS spec, only to be used to yield a primitive representation of the object itself), and without the add/change functions as creating aLagrange
instance once you have a new points list effectively costs nothing: