java - 如何使用 Apache Commons Math 中的 PolynomialSplineFunction

Question

我不明白第二点:

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])

多项式数组总是比结数组小一个值，对吗？那么第二部分并不总是有效？有没有更好的方法来说明第二点？

Link to documentation

Answer 1

这只是说，如果x属于区间[knot[j],knot[j+1]]，那么对应的y 值将计算为多项式[j](x - Node[j])。如果您的多项式数组的最后一个索引是n，那么最后一个knot间隔将为[knot[n], junction[n+1] ]]，这意味着 knot 数组的最后一个索引是 n+1(因此 2 始终有效)。