Investigate (and possibly relax) the condition that polynomial must be in [-1, 1]^M
Currently, the Minterpy polynomials especially its corresponding Grid
object can only be defined in [-1, 1]^M
. In particular, there is a hard check during the creation of a Grid
object that the points must indeed be in [-1, 1]^M
(see minterpy.core.verification.check_domain_fit()
that will raise an error if the generating points lie outside the domain.
The 2nd order Chebyshev points, for instance, are indeed defined in the interval [-1, 1]^M. But will this always be necessary? There may be other interpolating points that are defined in other interval. Functions to be interpolated may also be defined in some other intervals. Currently, users are responsible to carry out the transformation themselves.
There was a discussion about having the so-called "user-domain" to facilitate the linear transformation between the domains. In fact, the __init__()
method of a Minterpy polynomial class does include user_domain
(this name is not yet finalized). But this has never been further realized nor tested.
Investigate this condition, if possible to relax, then think of a better approach of handling different domains.