orthopy
orthopy copied to clipboard
sigma-py
:triangular_ruler: Orthogonal polynomials in all shapes and sizes.
Singularity-free evaluation of collapsed-coordinate orthogonal polynomials, Robert C. Kirby, Texas Tech University https://cpb-us-w2.wpmucdn.com/sites.baylor.edu/dist/6/32/files/2015/01/dubrec-1dzeylu.pdf
Section 5.1 in > Orthogonal polynomials of several variables > Y. Xu, 2017, > https://arxiv.org/pdf/1701.02709.pdf. 
Section 5.4 in > Orthogonal polynomials of several variables > Y. Xu, 2017, > https://arxiv.org/pdf/1701.02709.pdf.
For higher-dimensional polynomials, the fitting data structure for each level would be a `numpy.array` of shape `(n, n, ...)`, but only the lower (or upper) triangle of `(n,n)` is used....
[The Clenshaw algorithm](https://en.wikipedia.org/wiki/Clenshaw_algorithm) allows the efficient computation of linear combination of recurrence-scheme polynomials. It'd be nice if this could be extended to all of the polynomials classes in orthopy. (Suggestion...
More details by Meurant (http://www.math.hkbu.edu.hk/ICM/LecturesAndSeminars/08OctMaterials/2/Slide2.pdf).