polynomials.chebyshev#
This module provides computational routines relevant to polynomials in the Chebyshev basis.
- minterpy.utils.polynomials.chebyshev.evaluate_monomials(xx, exponents)[source]#
Evaluate the Chebyshev monomials at all query points.
- Parameters:
xx (
numpy.ndarray) – The array of query points of shape(k, m)at which the monomials are evaluated. The values must be in \([-1, 1]^m\).exponents (
numpy.ndarray) – The non-negative integer array of polynomial exponents (i.e., as multi-indices) of shape(N, m).
- Returns:
The value of each Chebyshev basis evaluated at each given point. The array is of shape
(k, N).- Return type:
- minterpy.utils.polynomials.chebyshev.evaluate_polynomials(xx, exponents, coefficients)[source]#
Evaluate polynomial(s) in the Chebyshev basis at all query points.
- Parameters:
xx (
numpy.ndarray) – The array of query points of shape(k, m)at which the monomials are evaluated. The values must be in \([-1, 1]^m\).exponents (
numpy.ndarray) – The non-negative integer array of polynomial exponents (i.e., as multi-indices) of shape(N, m).coefficients (
numpy.ndarray) – The array of coefficients of the polynomials of shape(N, Np). Multiple sets of coefficients (Np > 1) indicate multiple Chebyshev polynomials evaluated at the same time at the same query points.
- Return type:
Notes
The Chebyshev Polynomial has domain \([-1, 1]^m\).