minterpy.gen_points#

Module with routines to create generating points for polynomial interpolants.

Generating points are the main ingredient of constructing a set of unisolvent nodes (i.e., interpolation nodes) on which a polynomial interpolant is uniquely determined.

In one dimension, a set of generating points is the same as the unisolvent nodes. In higher dimension, a set of unisolvent nodes are constructed based on the generating points in each dimension and the multi-index set of polynomial exponents.

minterpy.gen_points.gen_points_chebyshev(poly_degree, spatial_dimension)[source]#

Create generating points from Chebyshev points.

Parameters:

  • poly_degree (int)

  • spatial_dimension (int)

Return type:

ndarray

minterpy.gen_points.gen_points_from_values(generating_values, spatial_dimension)[source]#

Construct an array of generating points given values in one dimension.

Parameters:
Returns:

A two-dimensional array of floats whose columns are the generating points per spatial dimension. The shape of the array is (n + 1, m) where n is the maximum polynomial degree in one dimension and m is the spatial dimension.

Return type:

numpy.ndarray

minterpy.gen_points.chebychev_2nd_order(n)[source]#

Factory function of Chebychev points of the second kind.

Parameters:

n (int) – Degree of the point set, i.e. number of Chebychev points.

Returns:

Array of Chebychev points of the second kind.

Return type:

np.ndarray

minterpy.gen_points.gen_chebychev_2nd_order_leja_ordered(n)[source]#

Factory function of Leja ordered Chebychev points of the second kind.

Parameters:

n (int) – Degree of the point set, i.e. number of Chebychev points (plus one!).

Returns:

Array of Leja ordered Chebychev points of the second kind.

Return type:

np.ndarray