Using lambdas'/functional programming features in Java 8, we can use some pretty concise and clear notation to approximate the derivative of a function at an x which is differentiable.
Derivatives::derive accepts a function, f(x), and returns its first derivative, f'(x), approximated using an arbitrarily low DX value, 0.0001.
Adapted from Joe Marshall's blogpost.
| import java.util.function.DoubleFunction; | |
| public class Derivatives { | |
| // approximate the limit | |
| private static final double DX = 0.0001; | |
| /** | |
| * @param f f(x), the function to derive | |
| * @return f'(x), the derivative of the f(x) | |
| */ | |
| private static DoubleFunction<Double> derive(DoubleFunction<Double> f) { | |
| return (x) -> (f.apply(x + DX) - f.apply(x)) / DX; | |
| } | |
| public static void main(String[] args) { | |
| { | |
| // f(x) = x^3 | |
| DoubleFunction<Double> cube = (x) -> x * x * x; | |
| // f'(x) = 3 * x^2 | |
| DoubleFunction<Double> cubeDeriv = derive(cube); | |
| // f'(2) = 3 * 2^2 = 12 | |
| assert Math.round(cubeDeriv.apply(2)) == 12.0; | |
| // f'(3) = 3 * 3^2 = 27 | |
| assert Math.round(cubeDeriv.apply(3)) == 27.0; | |
| // f'(4) = 3 * 4^2 = 48 | |
| assert Math.round(cubeDeriv.apply(4)) == 48.0; | |
| } | |
| { | |
| // f(x) = sin(x), f'(x) = cos(x) | |
| DoubleFunction<Double> sinDeriv = derive(Math::sin); | |
| // f'(2π) = cos(2π) = 1.0 | |
| assert Math.round(sinDeriv.apply(Math.PI * 2)) == 1.0; | |
| } | |
| } | |
| } |
