import org.apache.commons.math3.analysis.polynomials.PolynomialFunctionNewtonForm; //导入依赖的package包/类
/**
 * Compute an interpolating function for the dataset.
 *
 * @param x Interpolating points array.
 * @param y Interpolating values array.
 * @return a function which interpolates the dataset.
 * @throws DimensionMismatchException if the array lengths are different.
 * @throws NumberIsTooSmallException if the number of points is less than 2.
 * @throws NonMonotonicSequenceException if {@code x} is not sorted in
 * strictly increasing order.
 */
public PolynomialFunctionNewtonForm interpolate(double x[], double y[])
    throws DimensionMismatchException,
           NumberIsTooSmallException,
           NonMonotonicSequenceException {
    /**
     * a[] and c[] are defined in the general formula of Newton form:
     * p(x) = a[0] + a[1](x-c[0]) + a[2](x-c[0])(x-c[1]) + ... +
     *        a[n](x-c[0])(x-c[1])...(x-c[n-1])
     */
    PolynomialFunctionLagrangeForm.verifyInterpolationArray(x, y, true);

    /**
     * When used for interpolation, the Newton form formula becomes
     * p(x) = f[x0] + f[x0,x1](x-x0) + f[x0,x1,x2](x-x0)(x-x1) + ... +
     *        f[x0,x1,...,x[n-1]](x-x0)(x-x1)...(x-x[n-2])
     * Therefore, a[k] = f[x0,x1,...,xk], c[k] = x[k].
     * <p>
     * Note x[], y[], a[] have the same length but c[]'s size is one less.</p>
     */
    final double[] c = new double[x.length-1];
    System.arraycopy(x, 0, c, 0, c.length);

    final double[] a = computeDividedDifference(x, y);
    return new PolynomialFunctionNewtonForm(a, c);
}