import defined from "./defined.js";
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/**
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* An {@link InterpolationAlgorithm} for performing Lagrange interpolation.
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*
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* @namespace LagrangePolynomialApproximation
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*/
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var LagrangePolynomialApproximation = {
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type: "Lagrange",
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};
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/**
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* Given the desired degree, returns the number of data points required for interpolation.
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*
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* @param {Number} degree The desired degree of interpolation.
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* @returns {Number} The number of required data points needed for the desired degree of interpolation.
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*/
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LagrangePolynomialApproximation.getRequiredDataPoints = function (degree) {
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return Math.max(degree + 1.0, 2);
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};
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/**
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* Interpolates values using Lagrange Polynomial Approximation.
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*
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* @param {Number} x The independent variable for which the dependent variables will be interpolated.
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* @param {Number[]} xTable The array of independent variables to use to interpolate. The values
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* in this array must be in increasing order and the same value must not occur twice in the array.
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* @param {Number[]} yTable The array of dependent variables to use to interpolate. For a set of three
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* dependent values (p,q,w) at time 1 and time 2 this should be as follows: {p1, q1, w1, p2, q2, w2}.
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* @param {Number} yStride The number of dependent variable values in yTable corresponding to
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* each independent variable value in xTable.
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* @param {Number[]} [result] An existing array into which to store the result.
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* @returns {Number[]} The array of interpolated values, or the result parameter if one was provided.
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*/
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LagrangePolynomialApproximation.interpolateOrderZero = function (
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x,
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xTable,
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yTable,
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yStride,
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result
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) {
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if (!defined(result)) {
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result = new Array(yStride);
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}
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var i;
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var j;
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var length = xTable.length;
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for (i = 0; i < yStride; i++) {
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result[i] = 0;
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}
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for (i = 0; i < length; i++) {
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var coefficient = 1;
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for (j = 0; j < length; j++) {
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if (j !== i) {
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var diffX = xTable[i] - xTable[j];
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coefficient *= (x - xTable[j]) / diffX;
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}
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}
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for (j = 0; j < yStride; j++) {
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result[j] += coefficient * yTable[i * yStride + j];
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}
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}
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return result;
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};
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export default LagrangePolynomialApproximation;
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