LagrangePolynomialApproximation.js

define([
        './defined'
    ], function(
        defined) {
    'use strict';

    /**
     * An {@link InterpolationAlgorithm} for performing Lagrange interpolation.
     *
     * @exports LagrangePolynomialApproximation
     */
    var LagrangePolynomialApproximation = {
        type : 'Lagrange'
    };

    /**
     * Given the desired degree, returns the number of data points required for interpolation.
     *
     * @param {Number} degree The desired degree of interpolation.
     * @returns {Number} The number of required data points needed for the desired degree of interpolation.
     */
    LagrangePolynomialApproximation.getRequiredDataPoints = function(degree) {
        return Math.max(degree + 1.0, 2);
    };

    /**
     * Interpolates values using Lagrange Polynomial Approximation.
     *
     * @param {Number} x The independent variable for which the dependent variables will be interpolated.
     * @param {Number[]} xTable The array of independent variables to use to interpolate.  The values
     * in this array must be in increasing order and the same value must not occur twice in the array.
     * @param {Number[]} yTable The array of dependent variables to use to interpolate.  For a set of three
     * dependent values (p,q,w) at time 1 and time 2 this should be as follows: {p1, q1, w1, p2, q2, w2}.
     * @param {Number} yStride The number of dependent variable values in yTable corresponding to
     * each independent variable value in xTable.
     * @param {Number[]} [result] An existing array into which to store the result.
     * @returns {Number[]} The array of interpolated values, or the result parameter if one was provided.
     */
    LagrangePolynomialApproximation.interpolateOrderZero = function(x, xTable, yTable, yStride, result) {
        if (!defined(result)) {
            result = new Array(yStride);
        }

        var i;
        var j;
        var length = xTable.length;

        for (i = 0; i < yStride; i++) {
            result[i] = 0;
        }

        for (i = 0; i < length; i++) {
            var coefficient = 1;

            for (j = 0; j < length; j++) {
                if (j !== i) {
                    var diffX = xTable[i] - xTable[j];
                    coefficient *= (x - xTable[j]) / diffX;
                }
            }

            for (j = 0; j < yStride; j++) {
                result[j] += coefficient * yTable[i * yStride + j];
            }
        }

        return result;
    };

    return LagrangePolynomialApproximation;
});