BasesAndSamples.jl
BasesAndSamples.jl
provides functions for generating some polynomial bases and point sets.
BasesAndSamples.basis_chebyshev
— MethodGenerate a basis of chebyshev polynomials up to degree d (inclusive)
BasesAndSamples.basis_gegenbauer
— MethodBasis for the Gegenbauer polynomials in dimension n up to degree d. This is the Gegenbauer polynomial with parameter lambda = n/2-1, or the Jacobi polynomial with alpha = beta = (n-3)/2. Normalized to evaluate to 1 at 1. Taken from arxiv/2001.00256, ancillary files, SemidefiniteProgramming.jl
BasesAndSamples.basis_jacobi
— FunctionGenerate the Jacobi polynomials with parameters alpha and beta up to degree d (inclusive)
BasesAndSamples.basis_laguerre
— MethodGenerate the Laguerre polynomials with parameter alpha up to degree d (inclusive)
BasesAndSamples.basis_monomial
— MethodGenerate the monomial basis in variables x... up to degree d (inclusive)
BasesAndSamples.sample_points_chebyshev
— FunctionGenerate the d+1 chebyshev points in [a,b]
BasesAndSamples.sample_points_chebyshev_mod
— FunctionGenerate the d+1 modified chebyshev points in [a,b]
BasesAndSamples.sample_points_padua
— MethodGenerate the Padua points for degree d
BasesAndSamples.sample_points_rescaled_laguerre
— MethodGenerate 'rescaled laguerre' points, as in SDPB
BasesAndSamples.sample_points_simplex
— MethodGenerate the sample points in the unit simplex with denominator d