/** * Relative error. * * This is more difficult to calculate than it first appears [1,2]. The usual * formula for the relative error between an actual value A and an expected * value E is `|(A-E)/E|`, but: * * 1. If the expected value is 0, any other value has infinite relative error, * which is counter-intuitive: if the expected voltage is 0, getting 1/10th * of a volt doesn't feel like an infinitely large error. * * 2. This formula does not satisfy the mathematical definition of a metric [3]. * [4] solved this problem by defining the relative error as `|ln(|A/E|)|`, * but that formula only works if all values are positive: for example, it * reports the relative error of -10 and 10 as 0. * * Our implementation sticks with convention and returns: * * - 0 if the actual and expected values are both zero * - Infinity if the actual value is non-zero and the expected value is zero * - `|(A-E)/E|` in all other cases * * [1] https://math.stackexchange.com/questions/677852/how-to-calculate-relative-error-when-true-value-is-zero * [2] https://en.wikipedia.org/wiki/Relative_change_and_difference * [3] https://en.wikipedia.org/wiki/Metric_(mathematics)#Definition * [4] F.W.J. Olver: "A New Approach to Error Arithmetic." SIAM Journal on * Numerical Analysis, 15(2), 1978, 10.1137/0715024. * * @param {number} actual The actual value. * @param {number} expected The expected value. * @return {number} The relative error. */function relativeError(actual, expected) { if (actual === 0 && expected === 0) { return 0; } return Math.abs((actual - expected) / expected);}
export default relativeError;