Method interpolate

src/main/java/com/thealgorithms/maths/Neville.java:33–60

Evaluates the polynomial that passes through the given points at a specific x-coordinate. @param x The x-coordinates of the points. Must be the same length as y. @param y The y-coordinates of the points. Must be the same length as x. @param target The x-coordinate at which to evaluate the polynomia

(double[] x, double[] y, double target)

     * different, if the arrays are empty, or if x-coordinates are not unique.
     */
    public static double interpolate(double[] x, double[] y, double target) {
        if (x.length != y.length) {
            throw new IllegalArgumentException("x and y arrays must have the same length.");
        }
        if (x.length == 0) {
            throw new IllegalArgumentException("Input arrays cannot be empty.");
        }

        // Check for duplicate x-coordinates to prevent division by zero
        Set<Double> seenX = new HashSet<>();
        for (double val : x) {
            if (!seenX.add(val)) {
                throw new IllegalArgumentException("Input x-coordinates must be unique.");
            }
        }

        int n = x.length;
        double[] p = new double[n];
        System.arraycopy(y, 0, p, 0, n); // Initialize p with y values

        for (int k = 1; k < n; k++) {
            for (int i = 0; i < n - k; i++) {
                p[i] = ((target - x[i + k]) * p[i] + (x[i] - target) * p[i + 1]) / (x[i] - x[i + k]);
            }
        }

        return p[0];
    }
}