Evaluates the falling factorial basis of a given order, with respect to given design points, at arbitrary query points.
h_eval(k, xd, x, col_idx = NULL)Order for the falling factorial basis. Must be >= 0.
Design points. Must be sorted in increasing order, and have length
at least k+1.
Query points. Must be sorted in increasing order.
Vector of indices, a subset of 1:n where n = length(xd),
that indicates which columns of the constructed matrix should be returned.
The default is NULL, which is taken to mean 1:n.
Sparse matrix of dimension length(x) by length(col_idx).
The falling factorial basis functions of order \(k\), defined with
respect to design points \(x_1 < \ldots < x_n\), are denoted \(h^k_1,
\ldots, h^k_n\). For their precise definition and further references, see
the help file for h_mat(). The current function produces a matrix of
evaluations of the falling factorial basis at an arbitrary sequence of
query points. For each query point \(x\), this matrix has a corresponding
row with entries:
$$
h^k_j(x), \; j = 1, \ldots, n.
$$
h_mat() for constructing evaluations of the falling factorial
basis at the design points.