Interpolate a smooth, expensive function of a positive scalar

Evaluates f at Chebyshev-Lobatto nodes in log(x) over the range of x and interpolates barycentrically between them, which converges geometrically for a function analytic in log(x). The interpolant is checked against f halfway between the nodes; the nodes are doubled, reusing every evaluation, until the largest relative error there is below tolerance. When x has no more distinct values than the nodes would take, f is evaluated at those values directly instead.

Usage

interpolate_smooth_function(f, x, n_nodes = 33L, tolerance = 1e-09)

Arguments

f

Vectorised function of positive numbers.

x

Positive values at which f is wanted.

n_nodes

Number of nodes to start from.

tolerance

Largest relative error accepted at the check points.

Value

f at x, interpolated where that is cheaper than evaluating it.