basis function matrix and coefficient vector

[121180875]

If I want to extract the basis function matrix and coefficient vector after completing interpolation, what steps should I take?

[stevengj]

By basis-function matrix I guess you mean the Chebyshev–Vandermonde matrix? We don't compute this matrix at all for interpolation (and instead use a much faster algorithm via FFTs). It is computed during regression, but is not saved. However, you can construct it by calling FastChebInterp.chebvandermonde (currently not documented, though).

Given a ChebPoly object c, the coefficients are c.coefs. Probably this should be documented too.

[dhjx1996]

Hi @stevengj, thank you for this great package! Following up on this issue, I have a 4D ChebPoly object, c, and I would like to get the power series coefficients, i.e. the coef argument for a 4-variable https://numpy.org/doc/2.1/reference/generated/numpy.polynomial.polynomial.Polynomial.html#numpy.polynomial.polynomial.Polynomial. I would appreciate some tips on how to do that (is the solution as simple as just flattening c.coefs?). Also, are c.coefs power series coefficients or Chebyshev series coefficients, i.e. for https://numpy.org/doc/stable/reference/generated/numpy.polynomial.chebyshev.Chebyshev.html#numpy.polynomial.chebyshev.Chebyshev)?

Thank you very much!

[stevengj]

The whole point of using Chebyshev polynomials is that you don't want to compute the monomial coefficients — that basis is very badly behaved at high degrees.

The Chebyshev polynomial coefficients are stored in c.coefs.

[dhjx1996]

Hi @stevengj, I understand that. I wanted to perform the conversion for comparison not computation. This answers my question though, thank you!