poly (Polynomials)

This module is used for evaluating the monomial basis functions which are commonly added to RBF interpolants

rbf.poly.mvmonos(x, degree, diff=None)

Multivariate monomial basis functions.

Parameters:

  • x ((..., D) float array) – Positions where the monomials will be evaluated.

  • degree (int or (M, D) int array) – If this is an int, it is the degree of polynomials spanned by the monomials. If this is an array, it is the power for each variable in each monomial.

  • diff ((D,) int array, optional) – Derivative order for each variable.

Returns:

(…, M) array – Alternant matrix where each monomial is evaluated at x.

Example

>>> pos = np.array([[1.0], [2.0], [3.0]])
>>> pows = np.array([[0], [1], [2]])
>>> mvmonos(pos, pows)
array([[ 1., 1., 1.],
       [ 1., 2., 4.],
       [ 1., 3., 9.]])

>>> pos = np.array([[1.0, 2.0], [2.0, 3.0], [3.0, 4.0]])
>>> pows = np.array([[0, 0], [1, 0], [0, 1]])
>>> mvmonos(pos, pows)
array([[ 1., 1., 2.],
       [ 1., 2., 3.],
       [ 1., 3., 4.]])