How to use PolynomialSplineFunction from Apache Commons Math

Question

I do not understand number two:

The value of the polynomial spline function for an argument x is computed as follows:

1. The knot array is searched to find the segment to which x belongs. If x is less than the smallest knot point or greater than the largest one, an IllegalArgumentException is thrown.
2. Let j be the index of the largest knot point that is less than or equal to x. The value returned is polynomials[j](x - knot[j])

The polynomial array is always one value less than the knot array right? So the second section does not always work? Is there a better way to state number 2?

Link to documentation

Answer 1

That just says that if x belongs to the interval [knot[j], knot[j+1]], then the corresponding y value will be computed as polynomials[j](x - knot[j]). If your polynomials array's last index is n then the last knot interval will be [knot[n], knot[n+1]], meaning the last index of the knot array is n+1 (so 2 will always hold).